IRIT Ver. 11 User’s Manual A Solid modeling Program (C) Copyright 1989-2015 Gershon Elber EMail: [email protected] Join IRIT mailing list: [email protected] Mailing list: [email protected] Bug reports: [email protected] WWW Page: http://www.cs.technion.ac.il/~irit This manual is for IRIT Ver. 11. Contents 1 Introduction 1 2 Copyrights 1 3 Command Line Options and Set Up 3.1 IBM PC OS2 Speciﬁc Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 IBM PC Window 95/98/NT/2000/XP Speciﬁc Set Up . . . . . . . . . . . . . . . . . . 3.3 Unix Speciﬁc Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 4 5 4 First Usage 5 5 Line Editing 6 6 Data Types 6 7 Commands summary 7 8 Functions and Variables 9 9 Language description 10 11 12 Operator overloading 10.1 Overloading + . . . . . . . . . . . . . . . . 10.2 Overloading − . . . . . . . . . . . . . . . . 10.3 Overloading ∗ . . . . . . . . . . . . . . . . 10.4 Overloading / . . . . . . . . . . . . . . . . 10.5 Overloading ˆ . . . . . . . . . . . . . . . 10.6 Overloading Equal (Assignments) . . . . . 10.7 Comparison operators ==, ! =, <, >, <=, 10.8 Logical operators &&, , ! . . . . . . . . 10.9 Geometric Boolean Operations . . . . . . 10.10 Priority of operators . . . . . . . . . . . . 10.11 Grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 14 14 15 16 16 16 16 17 17 21 21 Function Description 11.1 NumericType returning functions 11.1.1 ABS . . . . . . . . . . . . 11.1.2 ACOS . . . . . . . . . . . 11.1.3 AREA . . . . . . . . . . . 11.1.4 ASIN . . . . . . . . . . . . 11.1.5 ATAN . . . . . . . . . . . 11.1.6 ATAN2 . . . . . . . . . . 11.1.7 COS . . . . . . . . . . . . 11.1.8 CLNTEXEC . . . . . . . 11.1.9 CPOLY . . . . . . . . . . 11.1.10 DSTPTLN . . . . . . . . 11.1.11 DSTPTPLN . . . . . . . . 11.1.12 DSTLNLN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 21 21 21 21 22 22 22 22 22 23 23 23 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.13 EXP . . . . . . . . . . . . . 11.1.14 FLOOR . . . . . . . . . . . 11.1.15 FMOD . . . . . . . . . . . . 11.1.16 LN . . . . . . . . . . . . . . 11.1.17 LOG . . . . . . . . . . . . . 11.1.18 MESHSIZE . . . . . . . . . 11.1.19 POWER . . . . . . . . . . . 11.1.20 RANDOM . . . . . . . . . . 11.1.21 SIN . . . . . . . . . . . . . 11.1.22 SIZEOF . . . . . . . . . . . 11.1.23 SQRT . . . . . . . . . . . . 11.1.24 TAN . . . . . . . . . . . . . 11.1.25 THISOBJ . . . . . . . . . . 11.1.26 VOLUME . . . . . . . . . . 11.2 GeometricType returning functions 11.2.1 ADAPISO . . . . . . . . . . 11.2.2 ALGSUM . . . . . . . . . . 11.2.3 ANALYFIT . . . . . . . . . 11.2.4 ANIMEVAL . . . . . . . . . 11.2.5 ANTIPODAL . . . . . . . . 11.2.6 AOFFSET . . . . . . . . . . 11.2.7 ARC . . . . . . . . . . . . . 11.2.8 ARC360 . . . . . . . . . . . 11.2.9 AREPARAM . . . . . . . . 11.2.10 BBOX . . . . . . . . . . . . 11.2.11 BELTCURVE . . . . . . . . 11.2.12 BFROM2IMG . . . . . . . . 11.2.13 BFROM3IMG . . . . . . . . 11.2.14 BLND2SRFS . . . . . . . . 11.2.15 BLHERMITE . . . . . . . . 11.2.16 BLSHERMITE . . . . . . . 11.2.17 BLOSSOM . . . . . . . . . 11.2.18 BOOLONE . . . . . . . . . 11.2.19 BOOLSUM . . . . . . . . . 11.2.20 BOUNDARY . . . . . . . . 11.2.21 BOX . . . . . . . . . . . . . 11.2.22 BSCTCONCN2 . . . . . . . 11.2.23 BSCTCONCON . . . . . . 11.2.24 BSCTCONCYL . . . . . . . 11.2.25 BSCTCONLN . . . . . . . 11.2.26 BSCTCONPL . . . . . . . . 11.2.27 BSCTCONPT . . . . . . . 11.2.28 BSCTCONSPR . . . . . . . 11.2.29 BSCTCYLCYL . . . . . . . 11.2.30 BSCTCYLPL . . . . . . . . 11.2.31 BSCTCYLPT . . . . . . . . 11.2.32 BSCTCYLSPR . . . . . . . 11.2.33 BSCTPLNLN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 23 23 23 24 24 24 24 24 24 25 25 25 25 25 25 26 27 28 28 28 29 30 30 31 31 31 33 33 33 34 35 36 36 38 38 38 39 39 39 40 40 41 41 41 42 42 43 11.2.34 11.2.35 11.2.36 11.2.37 11.2.38 11.2.39 11.2.40 11.2.41 11.2.42 11.2.43 11.2.44 11.2.45 11.2.46 11.2.47 11.2.48 11.2.49 11.2.50 11.2.51 11.2.52 11.2.53 11.2.54 11.2.55 11.2.56 11.2.57 11.2.58 11.2.59 11.2.60 11.2.61 11.2.62 11.2.63 11.2.64 11.2.65 11.2.66 11.2.67 11.2.68 11.2.69 11.2.70 11.2.71 11.2.72 11.2.73 11.2.74 11.2.75 11.2.76 11.2.77 11.2.78 11.2.79 11.2.80 11.2.81 BSCTPLNPT . . . BSCTSPRLN . . . BSCTSPRPL . . . BSCTSPRPT . . . BSCTSPRSPR . . BSCTTRSPT . . . BSCTTRSSPR . . BZR2BSP . . . . . BSP2BZR . . . . . C2CONTACT . . . C2RECTRGN . . . CALPHASECTOR CANGLEMAP . . CARCLEN . . . . CAREA . . . . . . CARRANGMNT . CARNGMNT2 . . CBEZIER . . . . . CBIARCS . . . . . CBISECTOR2D . CBISECTOR3D . CBSPLINE . . . . CCINTER . . . . . CCRVTR . . . . . CCRVTR . . . . . CCRVTREVAL . . CCUBICS . . . . . CDERIVE . . . . . CDIVIDE . . . . . CEDITPT . . . . . CENVOFF . . . . CEVAL . . . . . . CEXTREMES . . CFNCRVTR . . . CHELIX . . . . . . CIEXTREME . . . CINFLECT . . . . CINTEG . . . . . CINTERP . . . . . CIRCLE . . . . . . CIRCPOLY . . . . CLNTCRSR . . . CLNTREAD . . . CMESH . . . . . . CMOEBIUS . . . . CMORPH . . . . . CMULTIRES . . . CNORMAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 43 44 44 44 45 45 45 46 46 47 48 48 49 50 50 51 53 53 54 56 57 58 60 60 61 62 62 62 64 64 65 65 65 66 66 67 68 69 70 70 71 71 72 72 72 73 75 11.2.82 11.2.83 11.2.84 11.2.85 11.2.86 11.2.87 11.2.88 11.2.89 11.2.90 11.2.91 11.2.92 11.2.93 11.2.94 11.2.95 11.2.96 11.2.97 11.2.98 11.2.99 11.2.100 11.2.101 11.2.102 11.2.103 11.2.104 11.2.105 11.2.106 11.2.107 11.2.108 11.2.109 11.2.110 11.2.111 11.2.112 11.2.113 11.2.114 11.2.115 11.2.116 11.2.117 11.2.118 11.2.119 11.2.120 11.2.121 11.2.122 11.2.123 11.2.124 11.2.125 11.2.126 11.2.127 11.2.128 11.2.129 CNRMLCRV . CNVXHULL . COERCE . . . COMPOSE . . CON2 . . . . . CONE . . . . . CONICSEC . . CONTOUR . . CONVEX . . . COORD . . . . COVERISO . . COVERPT . . CPINCLUDE . CPOWER . . . CRAISE . . . . CRC2CRVTAN CREDUCE . . CREFINE . . . CREGION . . CREPARAM . CROSSEC . . . CRV2TANS . . CRVKERNEL CRVLNDST . . CRVPTDST . . CRVPTTAN . CSINE . . . . . CSPIRAL . . . CSURFACE . . CTANGENT . CTLPT . . . . CTRIMSRF . . CTRLCYCLE . CMESH . . . . CUBICCRVS . CVIEWMAP . CVISIBLE . . . CYLIN . . . . . CZEROS . . . DIST2FF . . . DUALITY . . . ELLIPSE3PT . EVOLUTE . . EXTRUDE . . FFCMPCRV . FFCOMPAT . FFCTLPTS . . FFEXTEND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 75 76 77 78 79 80 81 82 82 83 84 85 86 86 86 87 87 88 89 90 90 91 92 92 93 95 95 95 97 97 98 98 99 99 100 100 101 101 102 104 104 105 106 107 108 108 108 11.2.130 11.2.131 11.2.132 11.2.133 11.2.134 11.2.135 11.2.136 11.2.137 11.2.138 11.2.139 11.2.140 11.2.141 11.2.142 11.2.143 11.2.144 11.2.145 11.2.146 11.2.147 11.2.148 11.2.149 11.2.150 11.2.151 11.2.152 11.2.153 11.2.154 11.2.155 11.2.156 11.2.157 11.2.158 11.2.159 11.2.160 11.2.161 11.2.162 11.2.163 11.2.164 11.2.165 11.2.166 11.2.167 11.2.168 11.2.169 11.2.170 11.2.171 11.2.172 11.2.173 11.2.174 11.2.175 11.2.176 11.2.177 FFEXTREMA . FFEXTREME . FFGTYPE . . . FFKNTLNS . . . FFKNTVEC . . FFMATCH . . . FFMERGE . . . FFMESH . . . . FFMSIZE . . . . FFORDER . . . FFPOLES . . . . FFPTDIST . . . FFPTTYPE . . . FFSPLIT . . . . FFSPLTPOLES FITPMODEL . . FIXPLGEOM . . FIXPLNRML . . FMLNANAL . . GBOX . . . . . . GETATTR . . . GETLINE . . . . GETNAME . . . GGINTER . . . GPOINTLIST . GPOLYGON . . GPOLYLINE . . HAUSDORFF . HAUSDRPTS . . HERMITE . . . ILOFFSET . . . IMPLCTTRANS INSTANCE . . . IRITSTATE . . . ISGEOM . . . . ISOCLINE . . . KNOTCLEAN . KNOTREMOVE LINTERP . . . . LOFFSET . . . . MATDECOMP . MATDECOMP2 MATRECOMP . MAXEDGELEN MBEZIER . . . . MBISECTOR . . MBSPLINE . . . MDERIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 109 110 110 110 110 111 111 111 112 112 112 113 113 114 114 115 115 116 116 117 117 118 118 119 119 120 120 121 121 122 122 122 123 125 126 126 126 127 127 128 128 128 128 129 129 130 131 11.2.178 11.2.179 11.2.180 11.2.181 11.2.182 11.2.183 11.2.184 11.2.185 11.2.186 11.2.187 11.2.188 11.2.189 11.2.190 11.2.191 11.2.192 11.2.193 11.2.194 11.2.195 11.2.196 11.2.197 11.2.198 11.2.199 11.2.200 11.2.201 11.2.202 11.2.203 11.2.204 11.2.205 11.2.206 11.2.207 11.2.208 11.2.209 11.2.210 11.2.211 11.2.212 11.2.213 11.2.214 11.2.215 11.2.216 11.2.217 11.2.218 11.2.219 11.2.220 11.2.221 11.2.222 11.2.223 11.2.224 11.2.225 MDIVIDE . . . . MERGEPLLN . MERGEPOLY . MEVAL . . . . . MFROM2IMG . MFROM3IMG . MFROMMESH . MFROMMV . . MMERGE . . . . MOFFSET . . . MOMENT . . . . MPOWER . . . MRAISE . . . . MRCHCUBE . . MREFINE . . . MREGION . . . MREPARAM . . MREVERSE . . MSCIRC . . . . . MSCONE . . . . MSSPHERE . . MUNIVZERO . . MVCONTACT . MVEXPLICIT . MVINTER . . . NCCNTRPATH NCPCKTPATH MZERO . . . . . MPROMOTE . . NIL . . . . . . . OFFSET . . . . ORTHOTOMC . PATTRIB . . . . PCIRCLE . . . . PCRVTR . . . . PDECIMATE . . PDOMAIN . . . PINTERP . . . . PIMPRTNC . . . PLANE . . . . . PLANECLIP . . PLN3PTS . . . . PMORPH . . . . PNORMAL . . . POINT . . . . . POLARSIL . . . POLY . . . . . . POLYHOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 132 133 133 134 134 135 136 136 136 137 137 137 138 140 140 140 141 141 141 141 142 142 143 143 143 144 145 145 145 146 147 147 148 148 149 149 150 150 150 151 151 151 151 152 152 152 153 11.2.226 11.2.227 11.2.228 11.2.229 11.2.230 11.2.231 11.2.232 11.2.233 11.2.234 11.2.235 11.2.236 11.2.237 11.2.238 11.2.239 11.2.240 11.2.241 11.2.242 11.2.243 11.2.244 11.2.245 11.2.246 11.2.247 11.2.248 11.2.249 11.2.250 11.2.251 11.2.252 11.2.253 11.2.254 11.2.255 11.2.256 11.2.257 11.2.258 11.2.259 11.2.260 11.2.261 11.2.262 11.2.263 11.2.264 11.2.265 11.2.266 11.2.267 11.2.268 11.2.269 11.2.270 11.2.271 11.2.272 11.2.273 PPINCLUDE . PPINTER . . . PPROPFTCH PRINTER . . . PRISA . . . . . PSUBDIV . . . PT3BARY . . . PTHMSPR . . PTLNPLN . . PTPTLN . . . PTREGISTER PTS2PLLN . . PTS2PLYS . . PTSLNLN . . . QUADCRVS . QUADRIC . . RAYTRAPS . RFLCTLN . . RRINTER . . . RULEDFIT . . RULEDSRF . . RULEDTV . . SACCESS . . . SASPCTGRPH SASYMPEVAL SBEZIER . . . SBISECTOR . SBSPLINE . . SCRVTR . . . SCRVTREVAL SDDMMAP . . SDERIVE . . . SDIVCRV . . . SDIVIDE . . . SELFINTER . SETCOVER . SEDITPT . . . SEVAL . . . . SFLECNODAL SFOCAL . . . SFROMCRVS . SGAUSS . . . . SILHOUETTE SINTERP . . . SINTPCRVS . SKEL2DINT . SMEAN . . . . SMERGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 154 154 155 155 156 157 157 157 158 158 158 158 159 159 159 160 160 162 163 163 165 165 167 167 168 169 170 170 172 173 173 174 174 175 176 176 177 177 177 178 179 180 181 182 183 183 185 11.2.274 11.2.275 11.2.276 11.2.277 11.2.278 11.2.279 11.2.280 11.2.281 11.2.282 11.2.283 11.2.284 11.2.285 11.2.286 11.2.287 11.2.288 11.2.289 11.2.290 11.2.291 11.2.292 11.2.293 11.2.294 11.2.295 11.2.296 11.2.297 11.2.298 11.2.299 11.2.300 11.2.301 11.2.302 11.2.303 11.2.304 11.2.305 11.2.306 11.2.307 11.2.308 11.2.309 11.2.310 11.2.311 11.2.312 11.2.313 11.2.314 11.2.315 11.2.316 11.2.317 11.2.318 11.2.319 11.2.320 11.2.321 SMESH . . . . . SMOEBIUS . . . SMOOTHNRML SMOMENTS . . SMORPH . . . . SNORMAL . . . SNRMLSRF . . . SPARABOLC . . SPHERE . . . . SPLITLST . . . SPOWER . . . . SRADCRVTR . SRAISE . . . . . SRAYCLIP . . . SREFINE . . . . SREGION . . . . SREPARAM . . SREVERSE . . . SRF2TANS . . . SRF3TANS . . . SRFFFORM . . SRFLNDST . . . SRFKERNEL . . SRFPTDST . . . SRINTER . . . . SSINTER . . . . SSINTR2 . . . . STANGENT . . STRIMSRF . . . STRIVAR . . . . SURFPREV . . . SURFREV . . . SURFREVAXS . SURFREV2 . . . SURFREVAX2 . SVISIBLE . . . . SVOLUME . . . SWEEPSRF . . SWPSCLSRF . . SWUNGASUM . SYMBCPROD . SYMBDIFF . . . SYMBDPROD . SYMBIPROD . . SYMBPROD . . SYMBSUM . . . TBEZIER . . . . TBOOLONE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 186 186 186 187 187 188 188 189 189 189 190 190 191 191 191 192 193 193 194 195 196 196 197 197 198 198 198 199 199 200 200 201 201 202 202 203 204 205 207 207 208 209 209 210 210 211 212 11.2.322 TBOOLSUM . . . . . . 11.2.323 TBSPLINE . . . . . . . 11.2.324 TCRVTR . . . . . . . . 11.2.325 TDEFORM . . . . . . . 11.2.326 TDERIVE . . . . . . . . 11.2.327 TDIVIDE . . . . . . . . 11.2.328 TEDITPT . . . . . . . . 11.2.329 TEVAL . . . . . . . . . 11.2.330 TEXT2GEOM . . . . . 11.2.331 TEXTLAYSHP . . . . . 11.2.332 TEXTGEOM . . . . . . 11.2.333 TEXTWARP . . . . . . 11.2.334 TFROMSRFS . . . . . . 11.2.335 TINTERP . . . . . . . . 11.2.336 TMORPH . . . . . . . . 11.2.337 TNSCRCR . . . . . . . 11.2.338 TOFFSET . . . . . . . . 11.2.339 TORUS . . . . . . . . . 11.2.340 TPINCLUDE . . . . . . 11.2.341 TRAISE . . . . . . . . . 11.2.342 TREFINE . . . . . . . . 11.2.343 TREGION . . . . . . . 11.2.344 TREPARAM . . . . . . 11.2.345 TRIANGL . . . . . . . . 11.2.346 TRIMSRF . . . . . . . . 11.2.347 TRMSRFS . . . . . . . 11.2.348 TSBEZIER . . . . . . . 11.2.349 TSBSPLINE . . . . . . 11.2.350 TSDERIVE . . . . . . . 11.2.351 TSEVAL . . . . . . . . . 11.2.352 TSGREGORY . . . . . 11.2.353 TSNORMAL . . . . . . 11.2.354 TVIMPJACOB . . . . . 11.2.355 TVJACOBIAN . . . . . 11.2.356 TVLOAD . . . . . . . . 11.2.357 TVPREV . . . . . . . . 11.2.358 TVOLUME . . . . . . . 11.2.359 TVREV . . . . . . . . . 11.2.360 TVZRJACOB . . . . . . 11.2.361 UVPOLY . . . . . . . . 11.2.362 ZCOLLIDE . . . . . . . 11.2.363 ZTEXTRUDE . . . . . 11.3 Object transformation functions 11.3.1 HOMOMAT . . . . . . . 11.3.2 MAP3PT2EQL . . . . . 11.3.3 MATPOSDIR . . . . . . 11.3.4 PROJMAT . . . . . . . 11.3.5 RFLCTMAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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11.4.21 INCLUDE . . . . . 11.4.22 INSERTPOLY . . 11.4.23 INTERACT . . . . 11.4.24 IQUERY . . . . . . 11.4.25 LIST . . . . . . . . 11.4.26 LOAD . . . . . . . 11.4.27 LOGFILE . . . . . 11.4.28 MSLEEP . . . . . 11.4.29 NREF . . . . . . . 11.4.30 NRMLCONE . . . 11.4.31 NTH . . . . . . . . 11.4.32 PAUSE . . . . . . 11.4.33 PRINTF . . . . . . 11.4.34 PRINTFILE . . . 11.4.35 PROCEDURE . . 11.4.36 RESET . . . . . . 11.4.37 RMATTR . . . . . 11.4.38 SAVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 242 242 242 243 243 243 243 243 243 243 243 244 244 245 245 245 245 246 246 246 246 247 247 247 248 248 248 248 249 250 250 250 251 251 251 252 252 252 253 253 253 253 254 254 254 255 255 11.4.39 SETNAME . . . . . . . . . . 11.4.40 SNOC . . . . . . . . . . . . . 11.4.41 SYSTEM . . . . . . . . . . . 11.4.42 TIME . . . . . . . . . . . . . 11.4.43 VARLIST . . . . . . . . . . . 11.4.44 VECTOR . . . . . . . . . . . 11.4.45 VIEW . . . . . . . . . . . . . 11.4.46 VIEWOBJ . . . . . . . . . . 11.4.47 VIEWSET . . . . . . . . . . 11.4.48 WHILE . . . . . . . . . . . . 11.5 System variables . . . . . . . . . . . 11.5.1 AXES . . . . . . . . . . . . . 11.5.2 DRAWCTLPT . . . . . . . . 11.5.3 FLAT4PLY . . . . . . . . . . 11.5.4 MACHINE . . . . . . . . . . 11.5.5 POLY APPROX OPT . . . . 11.5.6 POLY APPROX UV . . . . . 11.5.7 POLY APPROX TOL . . . . 11.5.8 POLY APPROX TRI . . . . 11.5.9 POLY MERGE COPLANAR 11.5.10 PRSP MAT . . . . . . . . . . 11.5.11 RESOLUTION . . . . . . . . 11.5.12 VIEW MAT . . . . . . . . . . 11.6 System constants . . . . . . . . . . . 11.6.1 AMIGA . . . . . . . . . . . . 11.6.2 APOLLO . . . . . . . . . . . 11.6.3 BEZIER TYPE . . . . . . . . 11.6.4 BLACK . . . . . . . . . . . . 11.6.5 BLUE . . . . . . . . . . . . . 11.6.6 BSPLINE TYPE . . . . . . . 11.6.7 CLIENTS ALL . . . . . . . . 11.6.8 COL . . . . . . . . . . . . . . 11.6.9 CTLPT TYPE . . . . . . . . 11.6.10 CURVE TYPE . . . . . . . . 11.6.11 CYAN . . . . . . . . . . . . . 11.6.12 CYGWIN . . . . . . . . . . . 11.6.13 DEPTH . . . . . . . . . . . . 11.6.14 E1 . . . . . . . . . . . . . . . 11.6.15 E2 . . . . . . . . . . . . . . . 11.6.16 E3 . . . . . . . . . . . . . . . 11.6.17 E4 . . . . . . . . . . . . . . . 11.6.18 E5 . . . . . . . . . . . . . . . 11.6.19 E6 . . . . . . . . . . . . . . . 11.6.20 E7 . . . . . . . . . . . . . . . 11.6.21 E8 . . . . . . . . . . . . . . . 11.6.22 E9 . . . . . . . . . . . . . . . 11.6.23 FALSE . . . . . . . . . . . . . 11.6.24 GEOM CONST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 257 257 257 257 257 258 259 259 260 260 260 260 260 260 261 261 261 261 261 261 261 261 261 262 262 262 262 262 262 262 262 262 262 262 262 262 263 263 263 263 263 263 263 263 263 263 263 11.6.25 11.6.26 11.6.27 11.6.28 11.6.29 11.6.30 11.6.31 11.6.32 11.6.33 11.6.34 11.6.35 11.6.36 11.6.37 11.6.38 11.6.39 11.6.40 11.6.41 11.6.42 11.6.43 11.6.44 11.6.45 11.6.46 11.6.47 11.6.48 11.6.49 11.6.50 11.6.51 11.6.52 11.6.53 11.6.54 11.6.55 11.6.56 11.6.57 11.6.58 11.6.59 11.6.60 11.6.61 11.6.62 11.6.63 11.6.64 11.6.65 11.6.66 11.6.67 11.6.68 11.6.69 11.6.70 11.6.71 11.6.72 GEOM LINEAR . . . . GEOM CIRCULAR . . GEOM PLANAR . . . . GEOM SPHERICAL . . GEOM SRF OF REV . GEOM EXTRUSION . GEOM RULED SRF . . GEOM DEVELOP SRF GEOM SWEEP . . . . GREEN . . . . . . . . . GREGORY TYPE . . . HP . . . . . . . . . . . . IBMOS2 . . . . . . . . . KV DISC OPEN . . . . KV FLOAT . . . . . . . KV OPEN . . . . . . . . KV PERIODIC . . . . . LINUX . . . . . . . . . LIST TYPE . . . . . . . MACOSX . . . . . . . . MAGENTA . . . . . . . MATRIX TYPE . . . . MSDOS . . . . . . . . . MODEL TYPE . . . . . MULTIVAR TYPE . . . NUMERIC TYPE . . . OFF . . . . . . . . . . . ON . . . . . . . . . . . . P1 . . . . . . . . . . . . P2 . . . . . . . . . . . . P3 . . . . . . . . . . . . P4 . . . . . . . . . . . . P5 . . . . . . . . . . . . P6 . . . . . . . . . . . . P7 . . . . . . . . . . . . P8 . . . . . . . . . . . . P9 . . . . . . . . . . . . PARAM CENTRIP . . PARAM CHORD . . . . PARAM NIELFOL . . . PARAM UNIFORM . . PI . . . . . . . . . . . . PLANE TYPE . . . . . POINT TYPE . . . . . POLY TYPE . . . . . . POWER TYPE . . . . . RED . . . . . . . . . . . ROW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 263 264 264 264 264 264 264 264 264 264 264 264 264 264 265 265 265 265 265 265 265 265 265 265 265 265 265 266 266 266 266 266 266 266 266 266 266 266 266 266 267 267 267 267 267 267 267 11.6.73 11.6.74 11.6.75 11.6.76 11.6.77 11.6.78 11.6.79 11.6.80 11.6.81 11.6.82 11.6.83 11.6.84 11.6.85 11.6.86 11.6.87 SGI . . . . . . . . . . STRING TYPE . . . . SURFACE TYPE . . SUN . . . . . . . . . . TRIMSRF TYPE . . . TRISRF TYPE . . . . TRIVAR TYPE . . . TRUE . . . . . . . . . UNDEF TYPE . . . . UNIX . . . . . . . . . UNTRIMMED TYPE VECTOR TYPE . . . WINDOWS . . . . . . WHITE . . . . . . . . YELLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 267 267 267 267 267 268 268 268 268 268 268 268 268 268 12 Animation 268 12.1 How to create animation curves in IRIT . . . . . . . . . . . . . . . . . . . . . . . . . . 268 12.2 A more complete animation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 12.3 Another complete animation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 13 Display devices 13.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . 13.2 Conﬁguration Options . . . . . . . . . . . . . . . . . . . . . . . 13.3 Interactive mode setup . . . . . . . . . . . . . . . . . . . . . . . 13.4 Basic Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Animation Mode . . . . . . . . . . . . . . . . . . . . . . . . . . 13.6 Advanced (Programmable) Hardware Graphics Support . . . . 13.6.1 HDDM (Hardware Deformation Displacement Mapping) 13.6.2 HFFD (Hardware Free Form Deformation) . . . . . . . . 13.7 Speciﬁc Comments . . . . . . . . . . . . . . . . . . . . . . . . . 13.8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 15 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Utilities - General Usage 287 Poly3d-h - Hidden Line Removing Program 15.1 Introduction . . . . . . . . . . . . . . . . . . . 15.2 Command Line Options . . . . . . . . . . . . 15.3 Conﬁguration . . . . . . . . . . . . . . . . . . 15.4 Usage . . . . . . . . . . . . . . . . . . . . . . Illustrt - Simple line illustration 16.1 Introduction . . . . . . . . . . . 16.2 Command Line Options . . . . 16.3 Usage . . . . . . . . . . . . . . 273 275 277 279 282 282 282 283 284 285 286 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 287 288 289 289 ﬁlter 289 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 17 Aisoshad - Simple line illustration ﬁlter 292 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 17.2 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 17.3 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 18 IZebra - Simple zebra style, 18.1 Introduction . . . . . . . . 18.2 Command Line Options . 18.3 Usage . . . . . . . . . . . 19 LineShad - Simple line illustration ﬁlter 297 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 19.2 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 19.3 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 20 ihidden - Hidden Curve Removing Program 20.1 Introduction . . . . . . . . . . . . . . . . . . . 20.2 Command Line Options . . . . . . . . . . . . 20.3 Conﬁguration . . . . . . . . . . . . . . . . . . 20.4 Usage . . . . . . . . . . . . . . . . . . . . . . 21 parallel curve based rendering 295 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Irender - Simple Scan Line Renderer 21.1 Introduction . . . . . . . . . . . . . . 21.2 Command Line Options . . . . . . . 21.3 Conﬁguration . . . . . . . . . . . . . 21.4 Usage . . . . . . . . . . . . . . . . . 21.5 Advanced Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 300 301 302 302 . . . . . . . . . . . . . 302 . 302 . 303 . 305 . 305 . 305 22 3DS2Irit - AutoCad 3DS Data To IRIT ﬁle ﬁlter 311 22.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 22.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 23 Dat2Bin - Data To Binary Data ﬁle ﬁlter 312 23.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 23.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 24 Dat2Irit - Data To IRIT ﬁle ﬁlter 312 24.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 24.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 25 Dxf2Irit - DXF (Autocad) To IRIT ﬁlter 313 25.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 25.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 26 IGS2Irit - IGES Data To IRIT ﬁle ﬁlter 313 26.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 26.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 27 Iirit23js - IRIT To ThreeJS 27.1 Command Line Options . 27.2 Usage . . . . . . . . . . . 27.3 Advanced Usage . . . . . ﬁlter 314 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 28 Irit2Dxf - IRIT To DXF (Autocad) ﬁlter 316 28.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 28.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 29 Irit2Hgl - IRIT To HPGL ﬁlter 316 29.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 29.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 30 Irit2IGS - IRIT To IGES ﬁlter 318 30.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 30.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 31 Irit2Iv - IRIT To SGI’s Inventor ﬁlter 318 31.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 31.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 32 Irit2Nﬀ - IRIT To NFF ﬁlter 319 32.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 32.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 32.3 Advanced Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 33 Irit2Oﬀ - IRIT To OFF ﬁlter 321 33.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 33.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 34 Irit2Plg - IRIT To PLG (REND386) ﬁlter 322 34.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 34.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 35 Irit2pov - IRIT To POVRAY 35.1 Command Line Options . . 35.2 Usage . . . . . . . . . . . . 35.3 Advanced Usage . . . . . . 36 Irit2Ps - IRIT To PS ﬁlter 326 36.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 36.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 36.3 Advanced Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 37 Irit2Ray - IRIT To RAYSHADE ﬁlter 329 37.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 37.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 37.3 Advanced Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 raytracer ﬁlter 322 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 38 Irit2Scn - IRIT To SCENE (RTrace) 38.1 Command Line Options . . . . . . . 38.2 Usage . . . . . . . . . . . . . . . . . 38.3 Advanced Usage . . . . . . . . . . . 39 Irit2Stl - IRIT To STL ﬁlter 334 39.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 39.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 40 Irit2Wrl - IRIT To IGES ﬁlter 334 40.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 40.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 41 Irit2Wgl - IRIT To WGL ﬁlter 41.1 Command Line Options . . . . 41.2 Usage . . . . . . . . . . . . . . 41.3 Runtime Usage . . . . . . . . . 41.4 Browser Support . . . . . . . . 41.5 Usefull Links . . . . . . . . . . . . . . . . . . . . . . . . . ﬁlter 332 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 335 336 337 337 337 42 Irit2Xfg - IRIT To XFIG ﬁlter 337 42.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 42.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 43 Obj2irit - Wavefront OBJ format To IRIT data ﬁles 338 43.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 43.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 44 Oﬀ2irit - Geom View Oﬀ format To IRIT data ﬁles 339 44.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 44.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 45 Stl2Irit - Stl (stereo lithograph) data To IRIT ﬁle ﬁlter 339 45.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 45.2 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 46 Data File Format 340 47 Bugs and Limitations 349 IRIT Solid modeler 1 G. Elber 1 Introduction IRIT is a solid modeler developed for educational purposes. Although small, it is now powerful enough to create quite complex scenes. IRIT started as a polygonal solid modeler and was originally developed on an IBM PC under MSDOS. Version 2.0 was also ported to X11 and version 3.0 to SGI 4D systems. Version 3.0 also includes quite a few free form curves and surfaces tools. See the UPDATE.NEW ﬁle for more detailed update information. In Version 4.0, the display devices were enhanced, freeform curves and surfaces are more extensively supported, functions can be deﬁned, and numerous improvement and optimizations are added. 2 Copyrights BECAUSE IRIT AND ITS SUPPORTING TOOLS AS DOCUMENTED IN THIS DOCUMENT ARE LICENSED FREE OF CHARGE, I PROVIDE ABSOLUTELY NO WARRANTY, TO THE EXTENT PERMITTED BY APPLICABLE STATE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING, I GERSHON ELBER PROVIDE THE IRIT PROGRAM AND ITS SUPPORTING TOOLS ”AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THESE PROGRAMS IS WITH YOU. SHOULD THE IRIT PROGRAMS PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW WILL GERSHON ELBER, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY LOST PROFITS, LOST MONIES, OR OTHER SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR A FAILURE OF THE PROGRAMS TO OPERATE WITH PROGRAMS NOT DISTRIBUTED BY GERSHON ELBER) THE PROGRAMS, EVEN IF YOU HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. IRIT is a freeware solid modeler. It is not public domain since we hold copyrights on it. However, unless you are to sell or attempt to make money from any part of this code and/or any model you made with this solid modeler, you are free to make anything you want with it. In order to use IRIT commercially, you must license it ﬁrst - contact us is such a case. IRIT can be compiled and executed on numerous Unix/Linux systems as well as Windows 98/NT/2000/XP/Vista, Mac, OS2, and AmigaDOS. Also, under Windows, IRIT must be installed at a directory/path with no spaces. You are not obligated to me or to anyone else in any way by using IRIT. You are encouraged to share any model you made with it, but the models you made with it are yours, and you have no obligation to share them. You can use this program and/or any model created with it for non commercial and non proﬁt purposes only. An acknowledgement on the way the models were created would be nice but is not required. 3 Command Line Options and Set Up The IRIT program reads a ﬁle called irit.cfg each time it is executed. This ﬁle conﬁgures the system. It is a regular text ﬁle with comments, so you can edit it and properly modify it for your environment. G. Elber IRIT Solid modeler 2 This ﬁle is being searched for in the directory speciﬁed by the IRIT PATH environment variable. On Windows 64 bits compilation IRIT PATH64 will be searched ﬁrst, with a fall back to IRIT PATH. For example ’setenv IRIT PATH /u/gershon/irit/bin/’. If the variable is not set only the current directory is being searched for irit.cfg. In addition, if it exists, a ﬁle by the name of iritinit.irt will be automatically executed before any other ’.irt’ ﬁle. This ﬁle may contain any IRIT command. It is the proper place to put your predeﬁned functions and procedures, if you have any. This ﬁle will be searched much the same way irit.cfg is. The name of this initialization ﬁle may be changed by setting the StartFile entry in the conﬁguration ﬁle. This ﬁle is far more important starting at version 4.0, because of the new function and procedure deﬁnition that has been added, and which is used to emulate BEEP, VIEW, and INTERACT, for example. The solid modeler can be executed in text mode (see the .cfg and the -t ﬂag below) on virtually any system with a C compiler. Under all systems the following environment variables must be set and updated: path IRIT PATH IRIT PATH64 IRIT DISPLAY IRIT DISPLAY64 IRIT BIN IPC Add to path the directory where IRIT’s binaries are. Directory with conﬁg., help and IRIT’s binary ﬁles. On windows this access the 32 bit version of IRIT. Directory with conﬁg., help and IRIT’s 64 bits version (windows only) The graphics driver program/options. Must be in path. The graphics driver program/options for IRIT’s 64 bits version (windows only). Must be in path. If set, uses binary Inter Process Communication. For example, set path = ($path /u/gershon/irit/bin) setenv IRIT_PATH /u/gershon/irit/bin/ setenv IRIT_DISPLAY "xgldrvs -s-" setenv IRIT_BIN_IPC 1 to set /u/gershon/irit/bin as the binary directory and to use the sgi’s gl driver. If IRIT DISPLAY is not set, the server (i.e., the IRIT program) will prompt and wait for you to run a client (i.e., a display driver). if IRIT PATH is not set, none of the conﬁguration ﬁles, nor the help ﬁle will be found. If IRIT BIN IPC is not set, text based IPC is used, which is far slower. There is no real reason not to use IRIT BIN IPC, unless it does not work for you, for some reason. In addition, the following optional environment variables may be set. G. Elber IRIT Solid modeler IRIT MALLOC IRIT MALLOC ID IRIT NO SIGNALS IRIT SERVER HOST IRIT SERVER PORT IRIT TIME OUT IRIT INCLUDE LD LIBRARY PATH 3 If set, apply dynamic memory consistency testing. Programs will execute much slower in this mode. Sets the allocation unique ID when program will scream (abort) once this pointer is allocated, if IRIT MALLOC is set. If set, no signals are caught by IRIT. Internet Name of IRIT server (used by graphics driver). Used internally to the TCP socket number. Should not be set by users. Integer (seconds) for timing out when trying to execute a display device from IRIT. Default is 10 seconds. A semicolon separated list of directories, in which to look for the irt ﬁles to include. See INCLUDE command. If shared libraries are created, this variable must be updated to point to the shared libraries’ directory. For example, setenv setenv setenv setenv setenv IRIT_MALLOC 1 IRIT_MALLOC_ID 1234567890 IRIT_NO_SIGNALS 1 IRIT_SERVER_HOST irit.cs.technion.ac.il IRIT_INCLUDE "/d2/gershon/irit/irit/scripts;/tmp" IRIT MALLOC is useful for programmers, or when reporting a memory fatal error occurrence. This variable, when set as a non zero value, will activate the following (hexadecimal bit settings with any combination of the following): 0x01 0x02 0x04 0x08 0x10 0x20 A test for overwriting before the dynamic memory is allocated or immediately after it. Cheap in time. Savings of all allocated objects in a table for the detection of freeing unallocated objects and consistency of the entire dynamic memory. Time expensive. Zeros every freed object, once it is freed. On Windows environments - enables CrtCheckMemory checks every malloc/free, in debug compilation modes. On Windows environments - enables CrtCheckMemory checks every 16 mallocs/frees, in debug compilation modes. On Windows environments - keeps complete call stack info on every malloc, in debug compilation modes. IRIT NO SIGNALS is also useful for debugging when contorl-C is used within a debugger. The IRIT SERVER HOST/PORT controls the server/client (IRIT/Display device) communication. IRIT SERVER HOST and IRIT SERVER PORT are used in the unix and Window NT ports of IRIT. See the section on graphics drivers for more details. G. Elber IRIT Solid modeler 4 A session can be logged into a ﬁle as set via LogFile in the conﬁguration ﬁle. See also the LOGFILE command. The following command line options are available: IRIT [-t] [-s] [-g] [-q] [-i] [-z] {[-m ...]} [file.irt] -t -s -g -q -i -z -m ﬁle.irt 3.1 Puts IRIT into text mode. No graphics will be displayed and the display commands will be ignored. This is useful when one needs to execute an IRIT ﬁle to create data on a tty device... Run a Script and quit without prompting to stdin. IRIT under GUI mode. Should not be used by end users. Quiet mode with no regular output to stdout. IRIT under Interactive mode. Should not be used by end users. Prints usage message and current conﬁguration/version information. Optional option... If IRIT is compiled for debugging, allows setting three addition parameters of trap pointer, search pointer, and abort counter. A ﬁle to invoke directly instead of waiting to input from stdin. IBM PC OS2 Speciﬁc Set Up Under OS2 the IRIT DISPLAY environment variable must be set (if set) to os2drvs.exe without any option (-s- will be passed automatically). os2drvs.exe must be in a directory that is in the PATH environment variable. IRIT BIN IPC can be used to signal binary IPC which is faster. Here is a complete example: set IRIT_PATH=c:\irit\bin\ set IRIT_DISPLAY=os2drvs -sset IRIT_BIN_IPC=1 assuming the directory speciﬁed by IRIT PATH holds the executables of IRIT and is in PATH. If IRIT BIN IPC is not set, text based IPC is used which is far slower. There is no real reason not to use IRIT BIN IPC unless it does not work for you, for some reason. The OS2 executables are typically built using the EMX port of gnu C compiler. The distribution of the executables does not include the EMX run time library and any attempt to run IRIT will fail. You will get an error message such as ”File EMX does not exist”. You can get the run time from ftp to ftp-os2.nmsu.edu (aliased also as hobbes.NMSU.Edu) cd to os2/unix/emx09c (or a newer version number/level) get emxrt.zip and place its dlls in a place they would be found. 3.2 IBM PC Window 95/98/NT/2000/XP Speciﬁc Set Up The NT port uses sockets and is, in this respect, similar to the Unix port. The envirnoment variables IRIT DISPLAY, IRIT SERVER HOST, and IRIT BIN IPC should all be set in a similar way to the Unix speciﬁc setup. As a direct result, the server (IRIT) and the display device can run on diﬀerent hosts. For example, the server might be running on an NT system while the display device will be running on an SGI4D, exploiting the graphic’s hardware capabilities. Here is a complete example: G. Elber IRIT Solid modeler 5 set IRIT_PATH=c:\irit\bin\ set IRIT_DISPLAY=wntgdrvs -sset IRIT_BIN_IPC=1 Also, under Windows, IRIT must be installed in a directory/path with no spaces. 3.3 Unix Speciﬁc Set Up Under UNIX using X11 (x11drvs driver), add the following options to your .Xdefaults. Most are self explanatory. The Trans attributes control the transformation window, while the View attributes control the view window. SubWin attributes control the subwindows within the transformation window. #if COLOR irit*Trans*BackGround: irit*Trans*BorderColor: irit*Trans*BorderWidth: irit*Trans*TextColor: irit*Trans*SubWin*BackGround: irit*Trans*SubWin*BorderColor: irit*Trans*Geometry: irit*Trans*CursorColor: irit*View*BackGround: irit*View*BorderColor: irit*View*BorderWidth: irit*View*Geometry: irit*View*CursorColor: irit*MaxColors: #else irit*Trans*Geometry: irit*Trans*BackGround: irit*View*Geometry: irit*View*BackGround: irit*MaxColors: #endif 4 NavyBlue Red 3 Yellow DarkGreen Magenta =150x500+500+0 Green NavyBlue Red 3 =500x500+0+0 Red 15 =150x500+500+0 Black =500x500+0+0 Black 1 First Usage Commands to IRIT are entered using a textual interface, usually from the same window from which the program was executed. Some important commands to begin with are: 1. include(”ﬁle.irt”); - will execute the commands in ﬁle.irt. Note include can be recursive up to 10 levels. To execute the demo (demo.irt) simply type ’include(”demo.irt”);’. Another way to run the demo is by typing demo(); which is a predeﬁned procedure deﬁned in iritinit.irt. 2. help(””); - will print all available commands and how to get help on them. A ﬁle called irit.hlp will be searched as irit.cfg is being searched (see above), to provide the help. 3. exit(); - close everything and exit IRIT. G. Elber IRIT Solid modeler 6 Most operators are overloaded. This means that you can multiply two scalars (numbers), or two vectors, or even two matrices, with the same multiplication operator (∗). To get the on-line help on the operator ’∗’, type ’help(”∗”);’ The best way to learn this program (as any other program...) is by trying it. Print the manual and study each of the commands available. Study the demo programs (∗.irt) provided, as well. The ”best” mode in which to use IRIT is via the emacs editor. With this distribution an emacs mode for IRIT ﬁles (irt postﬁx) is provided (irit.el). Make your .emacs load this ﬁle automatically. Loading ﬁle.irt will switch emacs into an IRIT mode that supports the following keystrokes: Meta-E Meta-R Meta-S Meta-H Executes the current line Executes the current Region (Between Cursor and Mark) Executes a single line from input buﬀer Prints IRIT help on the current WORD the point is on using ’help(”WORD”);’ The ﬁrst time one of the above keystrokes is hit, emacs will fork an IRIT process so that IRIT’S stdin is controlled via the above commands. This emacs mode was tested under various Unix environments, under OS2 2.x/3.x, and under Windows 95/98/NT/2000/XP. 5 Line Editing The IRIT interpreter provides full line editing capabilities. The following are the available control options: ^a ^e ^f ^b ^d ^h (Backspace) ^i (Tab) ^k ^p ^n ^j (LineFeed) Beginning of line End of line Forward one character Backward one character Delete current character Delete backward one character Toggles overwrite/insert mode Kill to end of line Get previous history line Get next history line Done with this line Only lines entered from stdin will enter the history queue. The above control capabilities are fully conﬁgurable via the irit.cfg conﬁguration ﬁle. 6 Data Types These are the Data Types recognized by the solid modeler. They are also used to deﬁne the calling sequences of the diﬀerent functions below: IRIT Solid modeler ConstantType NumericType VectorType PointType CtlPtType PlaneType MatrixType PolygonType PolylineType CurveType SurfaceType TrimSrfType TriSrfType TrivarType MultivarType FreeformType GeometricType InstanceType GeometricTreeType StringType AnyType ListType G. Elber 7 Scalar real type that cannot be modiﬁed. Scalar real type. 3D real type vector. 3D real type point. Control point of a freeform curve or surface. 3D real type plane. 4 by 4 matrix (homogeneous transformation matrix). Object consists of polygons. Object consists of polylines. Object consists of curves. Object consists of surfaces. Object consists of trimmed surfaces. Object consists of triangular surfaces Object consists of trivariate functions. Object consists of multivariate functions. One of CurveType, SurfaceType, TrimSrfType, TrivarType, MultivarType, TriSrfType. One of Polygon/lineType, FreeformType. Object with a GeometryType and a Transformation. A list of GeometricTypes or GeometricTreeTypes. Sequence of chars within double quotes - ”A string”. Current implementation is limited to 80 chars. Any of the above. List of (any of the above type) objects. List size is dynamically increased, as needed. Although points and vectors are not the same, IRIT does not distinguish between them, most of the time. In this future this might change. 7 Commands summary These are all the commands and operators supported by the IRIT Solid Modeler: G. Elber IRIT Solid modeler + − ∗ / ^ = == != < > <= >= ABS ACOS ADAPISO ADWIDTH ALGSUM ANALYFIT ANIMEVAL ANTIPODAL AOFFSET ARC ARC360 AREA AREPARAM ASIN ATAN ATAN2 ATTRIB ATTRPROP ATTRVPROP AWIDTH BBOX BELTCURVE BFROM2IMG BFROM3IMG BLND2SRFS BLHERMITE BLSHERMITE BLOSSOM BOOLONE BOOLSUM BOUNDARY BOX BSCTCONCN2 BSCTCONCON BSCTCONCYL BSCTCONLN BSCTCONPL BSCTCONPT BSCTCONSPR BSCTCYLCYL BSCTCYLPL BSCTCYLPT BSCTCYLSPR BSCTPLNLN BSCTPLNPT BSCTSPRLN BSCTSPRPL BSCTSPRPT BSCTSPRSPR BSCTTRSPT BSCTTRSSPR BSP2BZR BZR2BSP C2CONTACT C2RECTRGN CALPHASECTOR CANGLEMAP CARCLEN CAREA CARRANGMNT CARNGMNT2 CBEZIER CBIARCS CBISECTOR2D CBISECTOR3D CBSPLINE CCINTER CCRVTR CCRVTR1PT CCRVTREVAL CCUBICS CDERIVE CDIVIDE CEDITPT CENVOFF CEVAL CEXTREMES CFNCRVTR CHDIR CHELIX CIEXTREME CINFLECT CINTERP CINTEG CIRCLE CIRCPOLY CLNTCLOSE CLNTCRSR CLNTEXEC CLNTREAD CLNTWRITE CMESH CMOEBIUS CMORPH CMULTIRES CNORMAL CNRMLCRV CNVXHULL COERCE COLOR COMMENT COMPOSE CON2 CONE CONICSEC CONTOUR CONVEX COORD COS COVERISO COVERPT CPATTR CPINCLUDE CPOLY CPOWER CRAISE CRC2CRVTAN CREDUCE CREFINE CREGION CREPARAM CROSSEC CRV2TANS CRVKERNEL CRVLNDST CRVPTDST CRVPTTAN CSINE CSPIRAL CSURFACE CTANGENT CTLPT CTRIMSRF CTRLCYCLE CUBICCRVS CVIEWMAP CVISIBLE CYLIN CZEROS DIST2FF DSTPTLN DSTPTPLN DSTLNLN DUALITY ELLIPSE3PT ERROR EVOLUTE EXEC EXIT EXP EXTRUDE FFCMPCRV FFCOMPAT FFCTLPTS FFEXTEND FFEXTREMA FFEXTREME FFGTYPE FFKNTLNS FFKNTVEC FFMATCH FFMERGE FFMESH FFMSIZE FFORDER FFPOLES FFPTDIST FFPTTYPE FFSPLTPOLES FFSPLIT FITPMODEL FIXPLGEOM FIXPLNRML FLOOR FMLNANAL FMOD FNFREE FOR FREE FUNCTION GBOX GETATTR GETLINE GETNAME GGINTER GPOINTLIST GPOLYGON GPOLYLINE HAUSDORFF HAUSDRPTS HELP HERMITE HOMOMAT IF ILOFFSET IMPLCTRANS INCLUDE INSERTPOLY INSTANCE INTERACT IQUERY IRITSTATE ISGEOM ISOCLINE 8 KNOTCLEAN KNOTREMOVE LINTERP LIST LN LOAD LOFFSET LOG LOGFILE MAP3PT2EQL MATDECOMP MATDECOMP2 MATRECOMP MATPOSDIR MAXEDGELEN MBEZIER MBISECTOR MBSPLINE MDERIVE MDIVIDE MERGEPLLN MERGEPOLY MESHSIZE MEVAL MFROM2IMG MFROM3IMG MFROMMESH MFROMMV MMERGE MOFFSET MOMENT MPOWER MPROMOTE MRAISE MRCHCUBE MREFINE MREGION MREPARAM MREVERSE MSCIRC MSLEEP MSCONE MSSPHERE MUNIVZERO MVCONTACT MVEXPLICIT MVINTER MZERO NCCNTRPATH NCPCKTPATH NIL G. Elber IRIT Solid modeler NREF NRMLCONE NTH OFFSET ORTHOTOMC PATTRIB PAUSE PCIRCLE PCRVTR PDECIMATE PDOMAIN PINTERP PIMPRTNC PLANE PLANECLIP PLN3PTS PMORPH PNORMAL POINT POLARSIL POLY POLYHOLES POWER PPINCLUDE PPINTER PPROPFTCH PRINTER PRINTF PRINTFILE PRISA PROCEDURE PROJMAT PSUBDIV PT3BARY PTHMSPR PTLNPLN PTPTLN PTREGISTER PTS2PLLN 8 PTS2PLYS PTSLNLN QUADCRVS QUADRIC RANDOM RAYTRAPS RFLCTLN RFLCTMAT RESET RMATTR ROTVEC ROTV2V ROTX ROTY ROTZ ROTZ2V ROTZ2V2 RRINTER RULEDFIT RULEDSRF RULEDTV SACCESS SASPCTGRPH SASYMPEVAL SAVE SBEZIER SBISECTOR SBSPLINE SCALE SCRVTR SCRVTREVAL SDDMMAP SDERIVE SDIVCRV SDIVIDE SEDITPT SELFINTER SETCOVER SETNAME SEVAL SFLECNODAL SFOCAL SFROMCRVS SGAUSS SILHOUETTE SIN SINTERP SINTPCRVS SIZEOF SKEL2DINT SMEAN SMERGE SMESH SMOEBIUS SMOMENTS SMOOTHNRML SMORPH SNOC SNORMAL SNRMLSRF SPARABOLC SPHERE SPLITLST SQRT SRADCRVTR SRAISE SRAYCLIP SREFINE SREGION SREPARAM SREVERSE SRF2TANS SRF3TANS SRFFFORM SRFLNDST SRFKERNEL SRFPTDST SRINTER 9 SSINTER SSINTR2 STANGENT STRIMSRF STRIVAR SURFPREV SURFREV SURFREVAXS SURFREV2 SURFREVAX2 SVISIBLE SVOLUME SWEEPSRF SWPSCLSRF SWUNGASUM SYMBCPROD SYMBDIFF SYMBDPROD SYMBIPROD SYMBPROD SYMBSUM SYSTEM TAN TBEZIER TBOOLONE TBOOLSUM TBSPLINE TCRVTR TDEFORM TDERIVE TDIVIDE TEDITPT TEVAL TEXTGEOM TEXT2GEOM TEXTLAYSHP TEXTWARP TFROMSRFS TIME TINTERP THISOBJ TMORPH TNSCRCR TOFFSET TORUS TPINCLUDE TRAISE TRANS TREFINE TREGION TREPARAM TRIANGL TRIMSRF TRMSRFS TSBEZIER TSBSPLINE TSDERIVE TSEVAL TSGREGORY TSNORMAL TVIMPJACOB TVJACOBIAN TVLOAD TVPREV TVOLUME TVREV TVZRJACOB UVPOLY VARLIST VECTOR VIEW VIEWOBJ VIEWSET VOLUME WHILE ZCOLLIDE ZTEXTRUDE Functions and Variables This section lists all the functions supported by the IRIT system according to their classes - mostly, the object type they return. Functions that return a NumericType: ABS ACOS AREA ASIN ATAN ATAN2 COS CLNTEXEC CPOLY DSTPTLN DSTPTPLN DSTLNLN EXP FLOOR FMOD LN LOG MESHSIZE POWER RANDOM SIN SIZEOF SQRT TAN THISOBJ VOLUME G. Elber IRIT Solid modeler 10 Functions that return a GeometricType: ADAPISO ALGSUM ANALYFIT ANIMEVAL ANTIPODAL AOFFSET ARC ARC360 AREPARAM BBOX BELTCURVE BFROM2IMG BFROM3IMG BLND2SRFS BLHERMITE BLSHERMITE BLOSSOM BOOLONE BOOLSUM BOUNDARY BOX BSCTCONCN2 BSCTCONCON BSCTCONCYL BSCTCONLN BSCTCONPL BSCTCONPT BSCTCONSPR BSCTCYLCYL BSCTCYLPL BSCTCYLPT BSCTCYLSPR BSCTPLNLN BSCTPLNPT BSCTSPRLN BSCTSPRPL BSCTSPRPT BSCTSPRSPR BSCTTRSPT BSCTTRSSPR BSP2BZR BZR2BSP C2CONTACT C2RECTRGN CALPHASECTOR CANGLEMAP CARCLEN CAREA CARRANGMNT CARNGMNT2 CBEZIER CBIARCS CBISECTOR2D CBISECTOR3D CBSPLINE CCINTER CCRVTR CCRVTR1PT CCRVTREVAL CCUBICS CDERIVE CDIVIDE CEDITPT CENVOFF CEVAL CEXTREMES CFNCRVTR CHELIX CIEXTREME CINFLECT CINTERP CIRCLE CIRCPOLY CLNTCRSR CLNTREAD CMESH CMOEBIUS CMORPH CMULTIRES CNORMAL CNRMLCRV CNVXHULL COERCE COMPOSE CON2 CONE CONICSEC CONTOUR CONVEX COORD COVERISO COVERPT CPINCLUDE CPOWER CRAISE CRC2CRVTAN CREDUCE CREFINE CREGION CREPARAM CROSSEC CRV2TANS CRVKERNEL CRVLNDST CRVPTDST CRVPTTAN CSINE CSPIRAL CSURFACE CTANGENT CTLPT CTRIMSRF CTRLCYCLE CUBICCRVS CVIEWMAP CVISIBLE CYLIN CZEROS DIST2FF DUALITY ELLIPSE3PT EVOLUTE EXTRUDE FFCMPCRV FFCOMPAT FFCTLPTS FFEXTEND FFEXTREMA FFEXTREME FFGTYPE FFKNTLNS FFKNTVEC FFMATCH FFMERGE FFMESH FFMSIZE FFORDER FFPOLES FFPTDIST FFPTTYPE FFKNTLNS FFSPLIT FITPMODEL FIXPLGEOM FIXPLNRML FMLNANAL GBOX GETATTR GETLINE GETNAME GGINTER GPOINTLIST GPOLYGON GPOLYLINE HAUSDORFF HAUSDRPTS HERMITE ILOFFSET IMPLCTRANS INSTANCE IRITSTATE ISGEOM ISOCLINE KNOTCLEAN KNOTREMOVE LINTERP LOFFSET MATDECOMP MATDECOMP2 MATRECOMP MAXEDGELEN MBEZIER MBISECTOR MBSPLINE MDERIVE MDIVIDE MERGEPLLN MERGEPOLY MEVAL MFROM2IMG MFROM3IMG MFROMMESH MFROMMV MMERGE MOFFSET MOMENT MPOWER MPROMOTE MRAISE MRCHCUBE MREFINE MREGION MREPARAM MREVERSE MSCIRC MSCONE MSSPHERE MUNIVZERO MVCONTACT MVEXPLICIT MVINTER MZERO NCCNTRPATH NCPCKTPATH NIL G. Elber IRIT Solid modeler OFFSET ORTHOTOMC PATTRIB PCIRCLE PCRVTR PDECIMATE PDOMAIN PINTERP PIMPRTNC PLANE PLANECLIP PLN3PTS PMORPH PNORMAL POINT POLARSIL POLY POLYHOLES PPINCLUDE PPINTER PPROPFTCH PRINTER PRISA PROCEDURE PSUBDIV PT3BARY PTHMSPR PTLNPLN PTPTLN PTREGISTER PTS2PLLN PTS2PLYS PTSLNLN QUADCRVS QUADRIC RAYTRAPS RFLCTLN RRINTER RULEDFIT RULEDSRF RULEDTV SACCESS SASPCTGRPH SASYMPEVAL SBEZIER SBISECTOR SBSPLINE SCRVTR SCRVTREVAL SDDMMAP SDERIVE SDIVCRV SDIVIDE SEDITPT SELFINTER SETCOVER SEVAL SFLECNODAL SFOCAL SFROMCRVS SINTPCRVS SGAUSS SILHOUETTE SINTERP SINTPCRVS SKEL2DINT SMEAN SMERGE SMESH SMOEBIUS SMOMENTS SMOOTHNRML SMORPH SNORMAL SNRMLSRF SPARABOLC SPHERE SPLITLST SRADCRVTR SRAISE SRAYCLIP SREFINE SREGION SREPARAM SREVERSE SRF2TANS SRF3TANS SRFFFORM SRFLNDST SRFKERNEL SRFPTDST SRINTER SSINTER SSINTR2 STANGENT STRIMSRF 11 STRIVAR SURFPREV SURFREV SURFREVAXS SURFREV2 SURFREVAX2 SVISIBLE SVOLUME SWEEPSRF SWPSCLSRF SWUNGASUM SYMBCPROD SYMBDIFF SYMBDPROD SYMBIPROD SYMBPROD SYMBSUM TBEZIER TBOOLONE TBOOLSUM TBSPLINE TCRVTR TDEFORM TDERIVE TDIVIDE TEDITPT TEVAL TEXTGEOM TEXT2GEOM TEXTLAYSHP TEXTWARP TFROMSRFS TINTERP TMORPH TNSCRCR TOFFSET TORUS TPINCLUDE TRAISE TREFINE TREGION TREPARAM TRIANGL TRIMSRF TRMSRFS TSBEZIER TSBSPLINE TSDERIVE TSEVAL TSGREGORY TSNORMAL TVIMPJACOB TVJACOBIAN TVLOAD TVPREV TVOLUME TVREV TVZRJACOB UVPOLY ZCOLLIDE ZTEXTRUDE Functions that create linear transformation matrices: HOMOMAT MAP3PT2EQL MATPOSDIR Miscellaneous functions: PROJMAT RFLCTMAT ROTVEC ROTV2V ROTX ROTY ROTZ ROTZ2V ROTZ2V2 SCALE TRANS G. Elber IRIT Solid modeler ADWIDTH ATTRIB ATTRPROP ATTRVPROP AWIDTH CHDIR CLNTCLOSE CLNTWRITE COLOR COMMENT CPATTR ERROR EXEC EXIT FNFREE FOR FREE FUNCTION HELP IF INCLUDE INSERTPOLY INTERACT IQUERY LIST LOAD LOGFILE MSLEEP NREF NRMLCONE 12 NTH PAUSE PRINTF PRINTFILE PROCEDURE RESET RMATTR SAVE SETNAME SNOC SYSTEM TIME VARLIST VECTOR VIEW VIEWOBJ VIEWSET WHILE Variables that are predeﬁned in the system: AXES DRAWCTLPT FLAT4PLY MACHINE POLY POLY POLY POLY APPROX APPROX APPROX APPROX OPT UV TOL TRI POLY MERGE COPLANAR PRSP MAT RESOLUTION VIEW MAT Constants that are predeﬁned in the system: AMIGA APOLLO BEZIER TYPE BLACK BLUE BSPLINE TYPE CLIENTS ALL COL CTLPT TYPE CURVE TYPE CYAN CYGWIN DEPTH E1 E2 E3 E4 E5 E6 E7 9 E8 E9 FALSE GREEN GREGORY TYPE HP IBMOS2 KV DISC OPEN KV FLOAT KV OPEN KV PERIODIC LINUX LIST TYPE MACOSX MAGENTA MATRIX TYPE MSDOS MODEL TYPE MULTIVAR TYPE NUMERIC TYPE OFF ON P1 P2 P3 P4 P5 P6 P7 P8 P9 PARAM CENTRIP PARAM CHORD PARAM NIELFOL PARAM UNIFORM PI PLANE TYPE POINT TYPE POLY TYPE POWER TYPE RED ROW SGI STRING TYPE SURFACE TYPE SUN TRIMSRF TYPE TRISRF TYPE TRIVAR TYPE TRUE UNDEF TYPE UNIX UNTRIMMED TYPE VECTOR TYPE WINDOWS WHITE YELLOW Language description The front end of the IRIT Solid Modeler is an inﬁx parser that mimics some C language behavior. The inﬁx operators that are supported are plus (+), minus (-), multiply (*), divide (/), and power (^), for numeric operators, with the same precedence as in C. IRIT Solid modeler G. Elber 13 However, unlike the C language, these operators are overloaded, 1 or diﬀerent action is taken, based upon the diﬀerent operands. This means that one can write ’1 + 2’, in which the plus sign denotes a numeric addition, or one can write ’PolyObj1 + PolyObj2’, in which case the plus sign denotes the Boolean operation of a union between two geometric objects. The exact way each operator is overloaded is deﬁned below. In this environment, reals, integers, and even Booleans, are all represented as real types. Data are automatically promoted as necessary. For example, the constants TRUE and FALSE are deﬁned as 1.0 and 0.0, respectively. Each expression is terminated by a semicolon. An expression can be as simple as ’a;’ which prints the value of variable a, or as complex as: for ( t = 1.1, 0.1, 1.9, cb1 = csurface( sb, COL, t ): color( cb1, green ): snoc( cb1, cb_all ) ); While an expression is terminated with a semicolon, a colon is used to terminate mini-expressions within an expression. Once a complete expression is read in (i.e., a semicolon is detected) and parsed correctly (i.e. no syntax errors are found), it is executed. Before each operator or a function is executed, parameter type matching tests are made to make sure the operator can be applied to these operand(s), or that the function gets the correct set of arguments. The parser is totally case insensitive, so Obj, obj, and OBJ will refer to the same object, while MergePoly, MERGEPOLY, and mergePoly will refer to the same function. Objects (Variables, if you prefer) need not be declared. Simply use them when you need them. Object names may be any alpha-numeric (and underscore) string of at most 30 characters. When assigned to an old object, the old object will be automatically deleted and if necessary, its type will be modiﬁed on the ﬂy. Example: V V V V = = = = sin( 45 * pi / 180.0 ); V * vector( 1, 2, 3 ); V * rotx( 90 ); V * V; will assign to V a NumericType equal to the sine of 45 degrees, the VectorType ( 1, 2, 3 ) scaled by the sine of 45, rotate that vector around the X axis by 90 degrees, and ﬁnally a NumericType which is the dot (inner) product of V with itself. The parser will read from stdin, unless a ﬁle is speciﬁed on the command line or an INCLUDE command is executed. In both cases, when the end of ﬁle is encountered, the parser will again wait for input from stdin. In order to execute a ﬁle and quit at the end of the ﬁle, put an EXIT command as the last command in the ﬁle. 1 In fact the C language does support overloaded operators to some extent: ’1 + 2’ and ’1.0 + 2.0’ implies invocation of two diﬀerent actions. G. Elber IRIT Solid modeler 10 14 Operator overloading The basic operators +, −, ∗, /, and ^ are overloaded. This section describes what action is taken by each of these operators depending on its arguments. 10.1 Overloading + The + operator is overloaded above the following domains: NumericType PointType VectorType MatrixType PolygonType PolygonType PolygonType CurveType CurveType CtlPtType ListType StringType StringType ModelType SurfaceType TrimSrfType + + + + + + + + + + + + + + + + NumericType PolygonType VectorType MatrixType PolygonType SurfaceType TrimSrfType CurveType CtlPtType CtlPtType ListType StringType RealType ModelType ModelType ModelType -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> NumericType PolygonType VectorType MatrixType PolygonType PolygonType PolygonType CurveType CurveType CurveType ListType StringType StringType ModelType ModelType ModelType (Point polyline profiling) (Vector addition) (Matrix addition) (Polygonal Boolean UNION operation) (Polygonal Boolean UNION operation) (Polygonal Boolean UNION operation) (Curve curve profiling) (Curve control point profiling) (Control points profiling) (Append lists operator) (String concat) (String concat, real as int string) (Freeform Boolean UNION operation) (Freeform Boolean UNION operation) (Freeform Boolean UNION operation) Note: Boolean UNION of two disjoint objects (no common volume) will result in the two objects being combined. It is the USER’s responsibility to make sure that the non intersecting objects are also disjoint - this system only tests for no intersection. Boolean UNION of two polyline objects will merge the list of polylines. 10.2 Overloading − The − operator is overloaded above the following domains: As a binary operator: NumericType VectorType MatrixType PolygonType PolygonType PolygonType ModelType SurfaceType TrimSrfType - NumericType VectorType MatrixType PolygonType SurfaceType TrimSrfType ModelType ModelType ModelType As a unary operator: -> -> -> -> -> -> -> -> -> NumericType VectorType MatrixType PolygonType PolygonType PolygonType ModelType ModelType ModelType (Vectoric difference) (Matrix difference) (Polygonal Boolean SUBTRACT op.) (Polygonal Boolean SUBTRACT op.) (Polygonal Boolean SUBTRACT op.) (Freeform Boolean SUBTRACT op.) (Freeform Boolean SUBTRACT op.) (Freeform Boolean SUBTRACT op.) G. Elber IRIT Solid modeler - NumericType PointType VectorType CtlPtType PlaneType StringType MatrixType PolygonType CurveType SurfaceType TrimSrfType ModelType -> -> -> -> -> -> -> -> -> -> -> -> NumericType PointType VectorType CtlPtType PlaneType StringType MatrixType PolygonType CurveType SurfaceType TrimSrfType ModelType 15 (Scale vector by -1) (Scale vector by -1) (Scale vector by -1) (Scale vector by -1) (Reverse the order of string’s characters) (Scale matrix by -1) (Boolean NEGATION operation) (Curve parameterization is reversed) (Surface parameterization is reversed) (Trim surface parameterization is reversed) (Model inside/outside flip) Note: Boolean SUBTRACT of two disjoint objects (no common volume) will result in an empty object. For both a curve and a surface parameterization, reverse operation (binary minus) causes the object normal to be ﬂipped as a side eﬀect. 10.3 Overloading ∗ The ∗ operator is overloaded above the following domains: NumericType VectorType VectorType VectorType VectorType PlaneType MatrixType MatrixType MatrixType MatrixType MatrixType MatrixType MatrixType PolygonType PolygonType PolygonType InstanceType ModelType SurfaceType TrimSrfType * * * * * * * * * * * * * * * * * * * * NumericType NumericType CurveType SurfaceType VectorType MatrixType NumericType PointType CtlPtType VectorType MatrixType GeometricType ListType PolygonType SurfaceType TrimSrfType MatrixType ModelType ModelType ModelType -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> -> NumericType VectorType CurveType SurfaceType NumericType PlaneType MatrixType PointType CtlPtType VectorType MatrixType GeometricType ListType PolygonType PolygonType PolygonType InstanceType ModelType ModelType ModelType (Vector scaling) (Inner product projection) (Inner product projection) (Inner product) (Plane transformation) (Matrix Scaling) (Point transformation) (Ctl Point transformation) (Vector transformation) (Matrix multiplication) (Object transformation) (Object hierarchy transform.) (Polygonal Boolean INTER. op.) (Polygonal Boolean INTER. op.) (Polygonal Boolean INTER. op.) (Transform of Instance’s matrix) (Freeform Boolean INTER. op.) (Freeform Boolean INTER. op.) (Freeform Boolean INTER. op.) Note: Boolean INTERSECTION of two disjoint objects (no common volume) will result in an empty object. Object hierarchy transform transforms any transformable object (GeometricType) found in the list recursively. Boolean INTERSECTION of two planar (XY plane) polyline objects will compute the intersection points of the two lists of polylines. Be aware that a plane multiplied by a matrix does not always do what you might expected. G. Elber IRIT Solid modeler 10.4 16 Overloading / The / operator is overloaded above the following domains: NumericType PointType PointType PolygonType PolygonType PolygonType ModelType SurfaceType TrimSrfType / / / / / / / / / NumericType PointType PolygonType PolygonType SurfaceType TrimSrfType ModelType ModelType ModelType -> -> -> -> -> -> -> -> -> NumericType PolyType PolygonType PolygonType PolygonType PolygonType ModelType ModelType ModelType (Polyline between two pts) (Point polyline profiling) (Polygonal Boolean CUT operation) (Polygonal Boolean CUT operation) (Polygonal Boolean CUT operation) (Freeform Boolean CUT operation) (Freeform Boolean CUT operation) (Freeform Boolean CUT operation) Note: Boolean CUT of two disjoint objects (no common volume) will result with an empty object. 10.5 Overloading ˆ The ^ operator is overloaded above the following domains: NumericType VectorType MatrixType PolygonType StringType StringType ^ ^ ^ ^ ^ ^ NumericType VectorType NumericType PolygonType StringType RealType -> -> -> -> -> -> NumericType VectorType MatrixType PolygonType StringType StringType (Cross product) (Matrix to the (int) power) (Boolean MERGE operation) (String concat) (String concat, real as real string) Note: Boolean MERGE simply merges the two sets of polygons without any intersection tests. Matrix powers must be positive integers or -1 or -2, in which case the matrix inverse (if it exists) or transpose is computed. 10.6 Overloading Equal (Assignments) Assignments are allowed as side eﬀects, in any place in an expression. If ”Expr” is an expression, then ”var = Expr” is the exact same expression with the side eﬀect of setting Var to that value. There is no guarantee of the order of evaluation, so using Vars that are set within the same expression is a bad practice. Use parentheses to force the order of evaluation, i.e., ”( var = Expr )”. 10.7 Comparison operators ==, ! =, <, >, <=, >= The conditional comparison operators can be applied to the following domains (o for a comparison operator): NumericType StringType PointType VectorType PlaneType CtlPtType MatrixType o o o o o o o NumericType StringType PointType VectorType PlaneType CtlPtType MatrixType -> -> -> -> -> -> -> NumericType NumericType NumericType NumericType NumericType NumericType NumericType G. Elber IRIT Solid modeler CurveType SurfaceType TrivarType TriSrfType MultivarType o o o o o CurveType SurfaceType TrivarType TriSrfType MultivarType -> -> -> -> -> 17 NumericType NumericType NumericType NumericType NumericType The returned NumericType is non-zero if the condition holds, or zero if not. The comparison operators other than == and ! = can be used on NumericTypes and StringType only. 10.8 Logical operators &&, , ! Complex logical expressions can be deﬁned using the logical and (&&), logical or (||) and logical not (!). These operators can be applied to NumericTypes that are considered Boolean results. That is, true for a non-zero value, and false otherwise. The returned NumericType is true if both operands are true for the and operator, at least one is true for the or operator, and the operand is false for the not operator. In all other cases, a false is returned. To make sure logical expressions are readable, the and and or operators are deﬁned to have the same priority. Use parentheses to disambiguate a logical expression and to make it more readable. 10.9 Geometric Boolean Operations The IRIT Solid Modeling System supports Boolean operations between polyhedra objects. Freeform objects will be automaticaly converted to a polygonal representation when used in Boolean operations. The +, ∗, and − are overloaded to denote Boolean union, intersection and subtraction when operating on geometric entities. − can also be used as an unary operator to reverse the object orientation inside out. IRIT supports Boolean operations on polyhedra models. A polyhedra based model is simply a collection of polygons. While a polyhedra is simply a set of polygons, this set must conform to certain conditions: • Every polygon has known adjacent polygons, for all its edges. • The model must be a 2-manifold. That is every edge is shared by exactly two polygons. • The model is expected to be closed. Actually only the resulting intersection curves must be closed and the objects participating in the Boleans might be open in unintersecting regions. • Every polygon has a normal that points into the model. That normal is inside/outside consistent with its adjacent polygons. In other words, for every polygon, one can locally determine the inside or the outside of the model. Moreover, every polygon has neighbors for all its edges, forming a closed object that consistently delineates inside from outside, globally. If your input geometry does not adhere to the above constrains, the Boolean operation is likely to fail. You can enable a special intersection-curves mode that only compute the intersection curves between the two input objects and does not form the output object. This special model is insensitive to many of the above constraints so you could use this model to examine the intersection curves and make sure there are indeed forming closed loops. You can enable this intersection-curves mode via ’iritstate(”intercrv”, true);’. See also IRITSTATE command. The Boolean operations are set operations conducted between two such models, M1 and M2 , that delineate inside from outside. Boolean Union, Boolean Intersection and Boolean Subtraction are the G. Elber IRIT Solid modeler 18 three common operations that resemble the exact semantic that is expected, when treating M1 and M2 as three-dimensional point sets. Certain attributes are propegated between input and output geometry, when processed through the Boolean operations module. If the vertices of the input geometry have normals, uv parametric coordinates (”uvvals” attribute), or rgb colors (”rgb” attribute), they will be propertly propagated and interpolated through the Booleans. Similarly, an integer ”ID” attribute that is placed on an input object will propagate into its polygons and all polygons in the output that are part of the input objects will be carrying this ”ID” attribute. The Boolean operations can be formulated into a binary tree structure also known as a Constructive Solid Geometry (CSG) tree. See, for example, Figure 1 for a sequence of Boolean operations on polyhedra model, deﬁning a Constructive Solid Geometry (CSG) tree. Example: resolution = 20; B = box(vector(-1, -1, -0.25), 2, 1.2, 0.5); C = con2(vector(0, 0, -1.5), vector(0, 0, 3), 0.7, 0.3); D E F G = = = = convex(B convex(C convex(B convex(B + * C); B); C); C); tr = rotx( -90 ) * roty( 40 ) * rotx( -30 ); All = list( D * tr * trans( vector( 0.6, 0.5, E * tr * trans( vector( 3.0, 0.0, F * tr * trans( vector( -2.0, 0.0, G * tr * trans( vector( 0.7, -1.0, * scale( vector( 0.25, 0.25, 0.25 ) ) * trans( vector( -0.1, -0.3, 0.0 ) ); view_mat = rotx( 0 ); view( list( view_mat, All ), on ); save( "booleans", list( view_mat, All ) ); 0.0 0.0 0.0 0.0 ) ) ) ) ), ), ), ) ) This is a complete example of how to compute the union, intersection and both diﬀerences of a box and a truncated cone. The result of this example can be seen in Figure 2 with its hidden lines removed. Special cases can be very diﬃcult to handle when considering Boolean operations. Consider an axes parallel bounding cube. Consider a second cube rotated α degrees from the ﬁrst cube. At large angles, the Boolean operations are fairly simple to compute. Nevertheless, as alpha approaches zero, the almost coplanar planes of the two intersecting cubes make it very diﬃcult to robustly and consistently compute their intersection. Figure 3 shows three such examples for α = 10, 1, 0.1 degrees, computed using IRIT. IRIT itself fails to return a valid result at α = 10−6 , complaining about theye inconsistency of its computation. Proper handling of coplanarity and almost tangent faces, in a robust manner, are one of the most challenging tasks in computing the Boolean operations. There are several ﬂags to control the Boolean operations. See IRITSTATE command for the ”InterCrv”, ”InterUV”, ”Coplanar”, and ”PolySort” states. G. Elber IRIT Solid modeler 19 S 3 = S 2 − C2 S 2 = S 1 − B2 C2 S 1 = B1 + C1 B2 B1 C1 Figure 1: A simple example of a polyhedra model, computed as a sequence of several Boolean operation, presented as a CSG tree. IRIT Solid modeler G. Elber 20 Figure 2: Geometric Boolean operations between a box and a truncated cone. Shown are union (left), intersection (bottom center), box minus the cone (top center), and cone minus the box (right). α = 10 degrees α = 1 degree α = 0.1 degrees Figure 3: Examples of robustness of Boolean Intersection operation. As the rotation anlge approaches zero, the coplanarity of the intersecting models puts very diﬃcult constraints on the robustness of the result. In this speciﬁc example, using IRIT, the operation fails at angles of 10e-6 and below. G. Elber IRIT Solid modeler 10.10 21 Priority of operators The following table lists the priority of the diﬀerent operators. Lowest priority Highest priority 10.11 Operator , : &&, || =, ==, ! =, <=, >=, <, > +, *, / ^ -, ! Name of operator comma colon logical and, logical or assignment, equal, not equal, less equal, greater equal, less, greater plus, minus multiply, divide power unary minus, logical not Grammar The grammar of the IRIT parser follows guidelines similar to those of the C language for simple expressions. However, complex statements diﬀer. See the IF, FOR, FUNCTION, and PROCEDURE below for the usage of these clauses. 11 Function Description The description below deﬁnes the parameters and returned values of the predeﬁned functions in the system, using the notation of functions in ANSI C. All the functions in the system, in alphabetic order, are listed are according to their classes. 11.1 11.1.1 NumericType returning functions ABS NumericType ABS( NumericType Operand ) returns the absolute value of the given Operand. 11.1.2 ACOS NumericType ACOS( NumericType Operand ) returns the arc cosine value (in radians) of the given Operand. 11.1.3 AREA NumericType AREA( PolygonType Object ) or NumericType AREA( CurveType Object ) returns the area of the given Object (in object units). IRIT Solid modeler 11.1.4 G. Elber 22 ASIN NumericType ASIN( NumericType Operand ) returns the arc sine value (in radians) of the given Operand. 11.1.5 ATAN NumericType ATAN( NumericType Operand ) returns the arc tangent value (in radians) of the given Operand. 11.1.6 ATAN2 NumericType ATAN2( NumericType Operand1, NumericType Operand2 ) returns the arc tangent value (in radians) of the given ratio: Operand1 / Operand2, over the whole circle. 11.1.7 COS NumericType COS( NumericType Operand ) returns the cosine value of the given Operand (in radians). 11.1.8 CLNTEXEC NumericType CLNTEXEC( StringType ClientName ) Initiate communication channels to a client named ClientName. ClientName is executed by this function as a sub process. Two communication channels are opened between the IRIT server and the new client, for read and write. See also CLNTCRSR, CLNTREAD, CLNTWRITE, and CLNTCLOSE. If ClientName is an empty string, the user is provided with the new communication port to be used and the server blocks for the user to manually execute the client after setting the proper IRIT SERVER HOST/PORT environment variables. Example: h1 = CLNTEXEC( "" ); h2 = CLNTEXEC( "nuldrvs -s-" ); executes two clients, one named nuldrvs while the other one is prompted for by the user. As a result of the second invokation of CLNTEXEC, the user will be prompted with a message similar to: Irit: Startup your program - I am waiting... setenv IRIT_SERVER_PORT 2182 and he/she will need to set the proper environment variable and execute their client manually. IRIT Solid modeler 11.1.9 G. Elber 23 CPOLY NumericType CPOLY( PolygonType Object ) returns the number of polygons in the given polygonal Object. 11.1.10 DSTPTLN NumericType DSTPTLN( PointType Pt, PointType LineOrig, VectorType LineRay ) returns the distance between a given point Pt and line LineOrig, LineRay. See also PTPTLN. 11.1.11 DSTPTPLN NumericType DSTPTPLN( PointType Pt, PlaneType Plane ) returns the distance between a given point Pt and plane Plane. 11.1.12 DSTLNLN NumericType DSTLNLN( PointType Line1Orig, VectorType Line1Ray, PointType Line2Orig, VectorType Line2Ray ) returns the distance between two lines deﬁned by point LineiOrig and ray LineiRay. See also PTSLNLN. 11.1.13 EXP NumericType EXP( NumericType Operand ) returns the natural exponential value of the given Operand. 11.1.14 FLOOR NumericType FLOOR( NumericType Operand ) returns the largest integer not greater than the Operand. 11.1.15 FMOD NumericType FMOD( NumericType Operand, NumericType Mod ) returns the ﬂoating point remainder of the division of the Operand by Mod. 11.1.16 LN NumericType LN( NumericType Operand ) returns the natural logarithm value of the given Operand. IRIT Solid modeler 11.1.17 G. Elber 24 LOG NumericType LOG( NumericType Operand ) returns the base 10 logarithm value of the given Operand. 11.1.18 MESHSIZE NumericType MESHSIZE( FreeformType Freeform, ConstantType Direction ) returns the size of the Freeform’s mesh in a Direction, which will be COL, ROW or DEPTH. For the case of a multivariate Freeform, the Direction is an integer value starting from 0. See also FFMSIZE. Examples: Len = MESHSIZE( Crv, COL ); RSize = MESHSIZE( Sphere, ROW ); CSize = MESHSIZE( Sphere, COL ); TVSize = MESHSIZE( TV, COL ) * MESHSIZE( TV, ROW ) * MESHSIZE( TV, DEPTH ); MVSize1 = MESHSIZE( MV, 1 ); 11.1.19 POWER NumericType POWER( NumericType Operand, NumericType Exp ) returns the Operand to the power of Exp. 11.1.20 RANDOM NumericType RANDOM( NumericType Min, NumericType Max ) returns a randomized value between Min and Max. See also ”RandomInit”, in the IRITSTATE function. 11.1.21 SIN NumericType SIN( NumericType Operand ) returns the sine value of the given Operand (in radians). 11.1.22 SIZEOF NumericType SIZEOF( PointTypr Pt | VectorType Vec | PlaneType Pln | CtlPtType CtlPt | ListType List | PolygonType Poly | CurveType Crv | StringType Str ) returns the size of a point, vector, plane, or control point (negative size if rational) or the length of a list if List, the number of polygons if Poly, the length of the control polygon if Crv, or the number of characters in string if Str. If, however, only one polygon is in Poly, it returns the number of vertices in that polygon. Example: G. Elber IRIT Solid modeler 25 len = SIZEOF( list( 1, 2, 3 ) ); numPolys = SIZEOF( axes ); numCtlpt = SIZEOF( circle( vector( 0, 0, 0 ), 1 ) ); will assign the value of 3 to the variable len, set numPolys to the number of polylines in the axes object, and set numCtlPt to 9, the number of control points in a circle. 11.1.23 SQRT NumericType SQRT( NumericType Operand ) returns the square root value of the given Operand. 11.1.24 TAN NumericType TAN( NumericType Operand ) returns the tangent value of the given Operand (in radians). 11.1.25 THISOBJ NumericType THISOBJ( StringType Object ) returns the object type of the given name of an Object. This can be one of the constants, UNDEF TYPE POLY TYPE NUMERIC TYPE POINT TYPE VECTOR TYPE PLANE TYPE MATRIX TYPE CURVE TYPE SURFACE TYPE STRING TYPE CTLPT TYPE LIST TYPE TRIVAR TYPE TRISRF TYPE TRIMSRF TYPE MODEL TYPE MULTIVAR TYPE This is also a way to ask if an object by a given name exists (if the returned type is UNDEF TYPE or not). 11.1.26 VOLUME NumericType VOLUME( PolygonType Object ) returns the volume of the given Object (in object units). It returns the volume of the polygonal object, not the volume of the object it might approximate. This routine decomposes all non-convex polygons to convex ones, as a side eﬀect (see CONVEX). 11.2 11.2.1 GeometricType returning functions ADAPISO CurveType ADAPISO( SurfaceType Srf, NumericType GenIsos, NumericType Dir, NumericType Eps, NumericType FullIso, NumericType SinglePath, ListType WeightPtSclWdt ) G. Elber IRIT Solid modeler 26 Constructs a coverage to Srf using isocurve (if GenIsos TRUE) in the Dir direction or coverage to Srf using quadrilaterals (if GenIsos FALSE). For isocuves, for any point p on surface Srf, there exists a point on one of the isocurves that is close to p within Eps. If FullIso, the extracted isocurves span the entire surface domain; otherwise they may span only a subset of the domain. If SinglePath, an approximation to a single path (Hamiltonian path) that visits all isocurves is constructed (not supported). If Srf has an integer ”AdapIsoMinSubdivLevel” attribute, it is used to set the minimal subdivision level used in the adaptive isocurve computations. If quadrilaterals are generated, one can force higher density of quads at some zone using the WeightPtSclWdt parameter that is a list of length three: (point of interest, weight of inﬂuence, scale factor). See also COVERPT, COVERISO. srf = sbezier( list( list( ctlpt( E3, -0.5, ctlpt( E3, 0.4, ctlpt( E3, -0.5, list( ctlpt( E3, 0.0, ctlpt( E3, 0.0, ctlpt( E3, 0.0, list( ctlpt( E3, 0.5, ctlpt( E3, -0.4, ctlpt( E3, 0.5, attrib( srf, "AdapIsoMinSubdivLevel", 2 ); aiso = ADAPISO( srf, TRUE, COL, 0.1, FALSE, -1.0, 0.0 ), 0.0, 0.1 ), 1.0, 0.0 ) ), -0.7, 0.1 ), 0.0, 0.0 ), 0.7, -0.2 ) ), -1.0, 0.1 ), 0.0, 0.0 ), 1.0, -0.2 ) ) ) ); FALSE, NIL() ); constructs an adaptive isocurve approximation with tolerance of 0.1 to surface srf in direction COL. Isocurves are allowed to span a subset of the surface domain. No single path is needed. The SinglePath option is currently not supported. 11.2.2 ALGSUM SurfaceType ALGSUM( CurveType Crv1, CurveType Crv2 ) Given two curves, compute a surface that is their algebraic sum: S(u, v) = C1 (u) + C2 (v) Example: c1 = circle( vector( 0.0, 0.0, 0.0 ), 0.7 ); c2 = ctlpt( E3, -0.2, -0.5, -1.5 ) + ctlpt( E3, 0.2, 0.5, 1.5 ); s1 = algsum( c1, c2 ); c2 = cbspline( 3, list( ctlpt( E3, 0.0, ctlpt( E3, 0.0, ctlpt( E3, 0.0, ctlpt( E3, 0.0, ctlpt( E3, 0.0, list( KV_OPEN ) ); s2 = algsum( c1, c2 ); 0.0, 0.0, 1.5, 0.0, 0.0, 0.0 0.7 1.0 1.3 2.0 ), ), ), ), ) ), (1) IRIT Solid modeler G. Elber 27 Figure 4: An algebraic sum of a circle and a line creating a cylinder (left) and a general sweep like surface (right), both using ALGSUM. creates two algebraic sum surfaces, one in the shape of a cylinder as a sum of a line and a circle, and one circular sweep like. See Figure 4. 11.2.3 ANALYFIT ListType ANALYFIT( ListType UVPts, ListType EucPts, NumericType FirstAtOrigin, NumericType Degree ) computes a surface ﬁt to the given paraametrized points data. The ﬁtted surface will be of bi-degree Degree, ﬁtting points EucPts at parameters UVPts. Needless to say EucPts and UVPts should be lists of points of similar length. If FirstAtOrigin is TRUE, all points are translated so the ﬁrst point in EucPts is at the origin. Only the ﬁrst coordinates of UVPts are used. Example: Fitting = nil(); Eps = 1e-2; PtPln = nil(): for (i = 1, 1, 100, snoc( point( random( -1, 1 ), random( -1, 1 ), random( -Eps, Eps ) ), PtPln ) ); IRIT Solid modeler G. Elber 28 BilinCoefs = ANALYFIT( PtPln, PtPln, 0, 1 ) ); ﬁts a bilinear to the given planar data with noise. See also the COERCE function from POWER TYPE to BEZIER TYPE, and FITPMODEL. 11.2.4 ANIMEVAL AnyType ANIMEVAL( NumericType Time, AnyType Object, NumericType EvalMats ) evaluates the animation curves in Object at time Time. The transformations for time Time are saved at the respective sub objects of Object as ”animation mat” matrices, if EvalMats is TRUE. If, however, EvalMats is FALSE, the evaluated/mapped geometry is returned directly. For example, mov_x = cbezier( list( ctlpt( E1, 0.0 ), ctlpt( E1, 1.0 ) ) ); attrib( axes, "animation", list( mov_x ) ); axes2 = ANIMEVAL( 0.5, axes, true ); and axes2 will have a matrix in attribute ”animation mat” of translation in x of 1/2. 11.2.5 ANTIPODAL ListType ANTIPODAL( CurveType Crv, NumericType SubdivTol, NumericType NumerTol ) or ListType ANTIPODAL( SurfaceType Srf, NumericType SubdivTol, NumericType NumerTol ) computes distinct antipodal pairs on curve Crv or on surface Srf. An antipodal pair deﬁnes two distinct locations on Crv or on Srf that a line through the two locations is orthogonal to the tangent space of the shape, at thouse locations. In other words, the normals to the freeform shape at those two locations are along the line connecting the locations. SubdivTol and NumerTol control the tolerance of the computation as in MZERO. Examples: A = ANTIPODAL( Srf, 1e-3, -1e-12 ); 11.2.6 AOFFSET CurveType AOFFSET( CurveType Crv, NumericType OffsetDistance, NumericType Epsilon, NumericType TrimLoops, NumericType BezInterp ) or CurveType AOFFSET( CurveType Crv, CurveType OffsetDistance, NumericType Epsilon, NumericType TrimLoops, NumericType BezInterp ) IRIT Solid modeler G. Elber 29 Figure 5: Adaptive oﬀset approximation (thick) of a B-spline curve (thin). On the left, the self intersections in the oﬀset computed in the right are eliminated. Both oﬀsets were computed using AOFFSET. (See also Figure 66.) computes an oﬀset of OﬀsetDistance with a globally bounded error (controlled by Epsilon). The smaller Epsilon is, the better the approximation to the oﬀset. The bounded error is achieved by adaptive reﬁnement of the Crv. If OﬀsetDistance is a (scalar) curve, the curve’s ﬁrst coordinate is used to prescribe a variable oﬀset amount along the curve. Both Crv and OﬀsetDistance must share the same parametric domain. If TrimLoops is TRUE or on, the regions of the object that self-intersect as a result of the oﬀset operation are trimmed away. If BezInterp is TRUE, each curve’s segment is interpolated instead of approximated. Example: OffCrv1 = AOFFSET( Crv, 0.5, 0.01, FALSE, FALSE ); OffCrv2 = AOFFSET( Crv, 0.5, 0.01, TRUE, FALSE ); computes an adaptive oﬀset to Crv with OﬀsetDistance of 0.5 and Epsilon of 0.01 and trims the self intersection loops in the second instance. See also OFFSET, TOFFSET, LOFFSET, and MOFFSET. See Figure 5. 11.2.7 ARC CurveType ARC( VectorType StartPos, VectorType Center, VectorType EndPos ) constructs an arc between the two end points StartPos and EndPos, centered at Center. THe arc will always be less than 180 degrees, so the shortest circular path from StartPos to EndPos is selected. The case where StartPos, Center, and EndPos are collinear is illegal, since it attempts to deﬁne a 180 degrees arc. The arc is constructed as a single rational quadratic Bezier curve. Example: Arc1 = ARC( vector( 1.0, 0.0, 0.0 ), vector( 1.0, 1.0, 0.0 ), vector( 0.0, 1.0, 0.0 ) ); constructs a 90 degrees arc, tangent to both the X and Y axes at coordinate 1. See Figure 6 (a). See also ARC360 IRIT Solid modeler G. Elber 30 Figure 6: A 90 degree arc constructed using the ARC constructor (left) and a 280 degrees arc (right) constructed using the ARC360 constructor. 11.2.8 ARC360 CurveType ARC360( VectorType Center, NumericType Radius, NumericType StartAngle, NumericType EndAngle ) constructs an arc between the two angles (degrees) StartAngle and EndAngle, centered at Center. The arc will always be less than 360 degrees. The arc is constructed as a rational quadratic B-spline curve. Example: Arc2 = ARC360( vector( 0.0, 0.0, 0.0 ), 1.0, 75, 355 ); constructs a 280 degrees arc. See Figure 6 (b). See also ARC. 11.2.9 AREPARAM AnyType AREPARAM( AnyType Obj, NumericType Min, NumericType Max ) Updates the time domain of the animation embedded in Obj to be from Min to Max. This function has an eﬀect only if Obj has animation(s) set for it. See the Animation section and ATTRIB to set animation attributes on objects. Example: ASrf = AREPARAM( Srf, 0, 2 ); Sets the animation time to be from zero to two time units. IRIT Solid modeler 11.2.10 G. Elber 31 BBOX ListType BBOX( GeometricTreeType Geom ) Given a (tree of) geometry, Geom computes its bounding box and return it as a list of six numbers: XMin/Max, YMin/Max, ZMin/Max, in this order. Example: B1 = BBOX( axes ); 11.2.11 BELTCURVE ListType BELTCURVE( PolyType Pulleys, NumericType Thickness, NumericType BoundingArcs, NumericType ReturnCrvs ) Computes a belt for a given set of Pulleys deﬁned as point list of the form (x, y, r) for each Pulley. Positive r designates a CW pulley whereas a negative r designates a CCW pulley. The thickness of the belt is deﬁned by Thickness. BoundingArcs is usually zero but if not, prescribes two bounding arcs for each linear segment of the belt. ReturnCrvs should be TRUE to simply return the two boundary curves of the belt or FALSE to return a list of arcs/lines of the belt. Example: B1 = BeltCurve( list( vector( 0, 0, 0.6 ), vector( 1, 3, -0.24 ), vector( 3, 3, -0.24 ), vector( 3, 1, 0.4 ), vector( 3, -1, 0.3 ), vector( 1, -1, 0.3 ), BeltThickness, CreateBoundingArcs, ReturnCrvs ), See Figure 7 for the result of this example. 11.2.12 BFROM2IMG ListType BFROM2IMG( StringType Img1, StringType Img2, NumericType DitherSize, NumericType MatchWidth, NumericType Positive, NumericType AugmentContrast, NumericType SpreadMethod, NumericType SphereRadius ) Constructs a 3D dithering cloud of blobs that looks like Img1 from one view direction and like Img2 from another view direction. DitherSize sets the 3D dithering size - 2, 3, or 4 for 2x2x2, 3x3x3 or 4x4x4. MatchWidth constraints the (bipartitte graph) matching between two rows in the two diﬀerent images and is measured in pixels. If Positive is true, the images are processed as is. If false, the images are negated ﬁrst. AugmentContrast allows control over contrast at the cost of more computation, or zero to disable. SpreadMethod is typically true to allow random spreading. SphereRadius sets the radius of the constructed blobs. See Figure 8 for the result of this example. Example: PTS = BFrom2Img( "BenGurion.ppm", "Herzl.ppm", 2, 21, true, 0, 2, 0.0 ); IRIT Solid modeler G. Elber 32 Figure 7: A belt deﬁned using the BELTCURVE function. Figure 8: A 3D dithering of two (three) images that creates a cloud of 3D points using the BFROM2IMG (BFROM3IMG) function. Herzl is seen from one view and Ben Gurion from another view. IRIT Solid modeler G. Elber 33 constructs a could of points that looks like Herzl from one view and Ben Gurion from another. See also BFROM3IMG, MFROM2IMG, and MFROM3IMG. 11.2.13 BFROM3IMG ListType BFROM3IMG( StringType Img1, StringType Img2, StringType Img3, NumericType DitherSize, NumericType MatchWidth, NumericType Positive, NumericType AugmentContrast, NumericType SpreadMethod, NumericType SphereRadius ) Constructs a 3D dithering cloud of blobs that looks like Img1 from one view direction, like Img2 from another view direction, and like Img3 from a third view direction. DitherSize sets the 3D dithering size - 2, 3, or 4 for 2x2x2, 3x3x3 or 4x4x4. MatchWidth constraints the (bipartitte graph) matching between two rows in the two diﬀerent images and is measured in pixels. If Positive is true, the images are processed as is. If false, the images are negated ﬁrst. AugmentContrast allows control over contrast at the cost of more computation, or zero to disable. SpreadMethod is typically true to allow random spreading. SphereRadius sets the radius of the constructed blobs. Example: PTS = BFrom2Img( "BenGurion.ppm", "Herzl.ppm", "Rabin.ppm", 2, 21, true, 0, 2, 0.0 ); constructs a could of points that looks like Herzl from one view, Ben Gurion from another, and Rabin from a third view. See also BFROM2IMG, MFROM2IMG, and MFROM3IMG. 11.2.14 BLND2SRFS SurfaceType BLND2SRFS( SurfaceType Srf1, SurfaceType Srf2, NumericType BlendDegree, NumericType TanScale ) constructs a new surface that blends Srf1 at UMin and Srf2 at UMax. BlendDegree can be 2 in which case the blending surface is C 0 continuous (to Srf1 and Srf2) or 4 to achieve C 1 continuity. Finally TanScale controls the strength of the tangential ﬁeld, if C 1 is sought. Example: BSrf = BLND2SRFS( Srf1, Srf2, 4, 1.0 ); See also HERMITE, BLHERMITE and BLSHERMITE 11.2.15 BLHERMITE SurfaceType BLHERMITE( CurveType Bndry1, CurveType Bndry2, CurveType Tan1, CurveType Tan2, CurveType Sctn, CurveType Nrml ) computes a Hermite blend surface that supports an arbitrary cross section. This constructs a surface between Bndry1 and Bndry2 so that the ﬁrst derivative continuity constraints, as prescribed by Tan1 at Bndry1 and Tan2 at Bndry2, are preserved. In addition, the interior between Bndry1 and Bndry2 will follow the shape of planar cross section curve Sctn and will be oriented along the vector ﬁeld prescribed by Nrml. Cross section Sctn is a planar curve that must start at (-1, 0) and G. Elber IRIT Solid modeler 34 end at (1, 0), and have zero speed at the ends (ﬁrst control point equals the second and is the same at the end). Example: c1 c2 d1 d2 = = = = ctlpt( ctlpt( ctlpt( ctlpt( e3, 0, 0, 0 ) + e3, 1, 0, 0 ) + e3, 1, 0, 1 ) e3, 1, 0, -0.1 ctlpt( e3, 0, 1, 0 ); ctlpt( e3, 1, 1, 0 ); + ctlpt( e3, 1, 0, 0.1 ); ) + ctlpt( e3, 1, 0, -1 ); s1 = hermite( c1, c2, d1, d2 ); color( s1, red ); cSec = cbspline( 3, list( ctlpt( e2, -1, ctlpt( e2, -1, ctlpt( e2, -0.14, ctlpt( e2, -0.65, ctlpt( e2, 0, ctlpt( e2, 0.65, ctlpt( e2, 0.14, ctlpt( e2, 1, ctlpt( e2, 1, list( kv_open ) ); n = ctlpt( e3, 0, 0, 1 ) + ctlpt( e3, 0, 0 ), 0 ), 0.26 ), 0.51 ), 0.76 ), 0.51 ), 0.26 ), 0 ), 0 ) ), 0, 1 ); s2 = BLHERMITE( c1, c2, d1, d2, cSec2, n ); color( s2, yellow ); constructs a regular Hermite surfaces s1 and a blending Hermite that follows the cross section cSec. See also HERMITE and BLSHERMITE. See Figure 9 (a). 11.2.16 BLSHERMITE SurfaceType BLSHERMITE( SurfaceType Srf, CurveType PCrv, CurveType Sctn, NumericType TanScale, AnyType Width, AnyType Height ) computes a Hermite blend surface on Srf along parametric curve of Srf, PCrv, the cross section Sctn, a tangent ﬁeld scale control TanScale, and the width and height control of Width and Height. Width and Height can be either a numeric value of expected width and height or a scalar ﬁeld curve prescribing the expected width and height along the constructed blend. The constructed surface, which is C1 continuous to Srf, is positioned along PCrv, a curve in the parametric domain of Srf. The cross section Sctn is a planar curve that must start at (-1, 0) and end at (1, 0), and have zero speed at the ends (ﬁrst control point equals the second and is the same at the end). TanScale controls how rapid the change in the tangent is, as we move away from the surface. Example: cSec = cbspline( 3, list( ctlpt( e2, -1, 0 ), G. Elber IRIT Solid modeler 35 Figure 9: Blending Hermite with a prescribed cross section (left) using BLHERMITE and blending Hermite with a prescribed cross section on a surface (right) using BLSHERMITE. ctlpt( e2, -1, ctlpt( e2, -0.5, ctlpt( e2, -0.7, ctlpt( e2, 0, ctlpt( e2, 0.7, ctlpt( e2, 0.5, ctlpt( e2, 1, ctlpt( e2, 1, list( kv_open ) ); 0 ), 0.2 ), 0.3 ), 0.5 ), 0.3 ), 0.2 ), 0 ), 0 ) ), s = -surfPRev( cregion( pcircle( vector( 0, 0, 0 ), 1 ), 0, 2 ) * rx( 90 ) ); s1 = BLSHERMITE( s, ctlpt( E2, 0, 1 ) + ctlpt( E2, 4, 1 ), cSec, 1, 0.2, 0.5 ); s2 = BLSHERMITE( s, ctlpt( E2, 0, 1.5 ) + ctlpt( E2, 4, 1.5 ), cSec, 0.1, 0.2, 0.5 ); s3 = BLSHERMITE( s, ctlpt( E2, 0, 0.3 ) + ctlpt( E2, 4, 0.3 ), cSec, 1.5, 0.2, 0.5 ); places three Hermite blend surfaces s1, s2, s3 using the cross section cSec on a unit sphere s. See also HERMITE and BLHERMITE. See Figure 9 (b). 11.2.17 BLOSSOM CtlPtType BLOSSOM( CurveType Crv, ListType BlossomVals ) G. Elber IRIT Solid modeler 36 or CtlPtType BLOSSOM( SurfaceType Srf, ListType BlossomVals ) computes the blossom of the given Crv or Srf and the given blossom values BlossomVals. For a Crv, BlossomVals is expected to hold a linear list of blossom values. For a Srf, BlossomVals is expected to hold two linear lists (for u and v) of blossom values. Example: c1 = cbezier( list( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( BLOSSOM( BLOSSOM( BLOSSOM( BLOSSOM( BLOSSOM( c1, c1, c1, c1, c1, list( list( list( list( list( 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, E2, E2, E2, E2, E2, 1.7, 0.7, 1.7, 1.5, 1.6, 0 1 1 1 1 ) ) ) ) ) ) ) ) ) ) 0.0 0.7 0.3 0.8 1.0 == == == == == ), ), ), ), ) ) ); coord( coord( coord( coord( coord( c1, c1, c1, c1, c1, 0 1 2 3 4 ) && ) && ) && ) && ); extracts the control points of an quadric Bezier curve via blossoming and compares this to the results obtained via a traditional extraction approach (via the COORD function). 11.2.18 BOOLONE SurfaceType BOOLONE( CurveType Crv ) Given a closed curve, the curve is subdivided into four segments equally spaced in the parametric space that are fed into BOOLSUM. This is useful if a surface should ”ﬁll” the area enclosed by a closed curve. Example: Srf = BOOLONE( circle( vector( 0.0, 0.0, 0.0 ), 1.0 ) ); creates a disk surface containing the area enclosed by the unit circle. See Figure 10. 11.2.19 BOOLSUM SurfaceType BOOLSUM( CurveType Crv1, CurveType Crv2, CurveType Crv3, CurveType Crv4 ) constructs a surface using the provided four curves as its four boundary curves. Curves do not have to have the same order or type, and will be promoted to their least common denominator. The end points of the four curves should match as follows: Crv1 Crv1 Crv2 Crv2 start point, end point, start point, end point, to to to to Crv3 Crv4 Crv3 Crv4 start point. start point. end point. end point. IRIT Solid modeler G. Elber 37 Figure 10: A Boolean sum of a circle creates a disk (left) using BOOLONE and a general Boolean sum of four curves (right) using BOOLSUM. where Crv1 and Crv2 are the two boundaries in one parametric direction, and Crv3 and Crv4 are the two boundaries in the other parametric direction. Example: Cbzr1 = cbezier( list( ctlpt( E3, 0.1, 0.1, 0.1 ), ctlpt( E3, 0.0, 0.5, 1.0 ), ctlpt( E3, 0.4, 1.0, 0.4 ) ) ); Cbzr2 = cbezier( list( ctlpt( E3, 1.0, 0.2, 0.2 ), ctlpt( E3, 1.0, 0.5, -1.0 ), ctlpt( E3, 1.0, 1.0, 0.3 ) ) ); Cbsp3 = cbspline( 4, list( ctlpt( E3, 0.1, 0.1, 0.1 ), ctlpt( E3, 0.25, 0.0, -1.0 ), ctlpt( E3, 0.5, 0.0, 2.0 ), ctlpt( E3, 0.75, 0.0, -1.0 ), ctlpt( E3, 1.0, 0.2, 0.2 ) ), list( KV_OPEN ) ); Cbsp4 = cbspline( 4, list( ctlpt( E3, 0.4, 1.0, 0.4 ), ctlpt( E3, 0.25, 1.0, 1.0 ), ctlpt( E3, 0.5, 1.0, -2.0 ), ctlpt( E3, 0.75, 1.0, 1.0 ), ctlpt( E3, 1.0, 1.0, 0.3 ) ), list( KV_OPEN ) ); Srf = BOOLSUM( Cbzr1, Cbzr2, Cbsp3, Cbsp4 ); IRIT Solid modeler 11.2.20 G. Elber 38 BOUNDARY AnyType BOUNDARY( AnyType Obj ) Given a geometric object Obj, let it be a surface, a trimed surface, or a polygonal model, returns the boundary of the shape. If Obj is a polygonal object originated with a surface and all vertices has ”uvvals” attributes, by placing ”SrfBoundary” attribute on Obj with the ”UMin VMin UMax VMax” surface domain, the surface boundary is will be properly detected, even if the surface is closed. Example: CBndry1 = BOUNDARY( Srf ); poly_approx_uv = 1; Pl = gpolygon( Srf, 1 ); attrib( Pl, "SrfBoundary", "0 0 1 2" ); # Domain of Srf [0, 1] x [0, 2] CBndry2 = BOUNDARY( Pl ); returns in CBndry1, the four boundary curves of tensor product surface Srf and in CBndry2, the edges on the tesselation of Srf, Pl, on the boundary of Srf, even if Srf is closed. 11.2.21 BOX PolygonType BOX( VectorType Point, NumericType Dx, NumericType Dy, NumericType Dz ) creates a BOX polygonal object, whose boundary is coplanar with the XY , XZ, and Y Z planes. The BOX is deﬁned by Point as base position, and Dx, Dy, Dz as BOX dimensions. Negative dimensions are allowed. Example: B = BOX( vector( 0, 0, 0 ), 1, 1, 1); creates a unit cube from 0 to 1 in all axes. 11.2.22 BSCTCONCN2 SurfaceType BSCTCONCN2( PointType ConeApx1, VectorType ConeDir1, NumericType ConeAngle1, PointType ConeApx2, VectorType ConeDir2, NumericType ConeAngle2 ) computes the bisector surface of two cones in general position. The cones’ apexes can be found in ConeApx1 and ConeApx2 with axes directions ConeDir1 and ConeDir2 and spanning angles of ConeAngle1 and ConeAngle2. Example: BisectSrf = BSCTCONCN2( Apx1, Dir1, Ang1, Apx2, Dir2, Ang2 ); See also BSCPCONCON, BSCTCONCYL, BSCTCYLCYL, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR, IRIT Solid modeler 11.2.23 G. Elber 39 BSCTCONCON SurfaceType | ListType BSCTCONCON( VectorType ConeDir1, NumericType ConeAngle1, VectorType ConeDir2, NumericType ConeAngle2, NumericType Size ) computes the bisector surface of two cones that share the same apex. The cones’ directions are ConeDir1 and ConeDir2 and the spanning angles of ConeAngle1 and ConeAngle2. ConeDir1 and ConeDir2 must be in the northern hemisphere; i.e. their Z coeﬃcient must be positive. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTCONCON( vector( 0, 0, 1 ), 50, vector( 0, 0, 1 ), 20, 1.0 ); computes the bisector of two concentric cones, which is also a cone. See also BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR 11.2.24 BSCTCONCYL SurfaceType BSCTCONCYL( PointType ConeApx1, VectorType ConeDir1, NumericType ConeAngle1, PointType CylPt2, VectorType CylDir2, NumericType CylRad2 ) computes the bisector surface of a cone and a cylinder in general position. The cones apex is in ConeApx1 with axes direction of ConeDir1 and spanning angles of ConeAngle1. The second cylinder starts at CylPt2, in direction CylDir2 and radius CylRad2. Example: BisectSrf = BSCTCONCYL( Apx1, Dir1, Ang1, Pt2, Dir2, Rad2 ); See also BSCPCONCON, BSCTCONCN2, BSCTCYLCYL, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR 11.2.25 BSCTCONLN SurfaceType | ListType BSCTCONLN( VectorType ConeDir, NumericType ConeAngle, VectorType LineDir, NumericType Size ) computes the bisector surface of a cone and a line through its apex. The cone’s direction is ConeDir and its spanning angle is ConeAngle. ConeDir and LineDir must be in the northern hemisphere; i.e. their Z coeﬃcient must be positive. Size controls the portion of the (inﬁnite) bisector actually represented. Example: IRIT Solid modeler G. Elber 40 BisectSrf = ( vector( 0, 0, 1 ), 45, vector( 0, 0.1, 1 ), 1 ); computes the bisector surface of a cone along the Z axis with spanning angle of 45 degrees, and a line through its apex in direction ( 0, 0.1, 1 ). See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR, 11.2.26 BSCTCONPL SurfaceType | ListType BSCTCONPL( PointType ConeApex, VectorType ConeDir, NumericType ConeAngle, NumericType Size ) computes the bisector surface of a general cone and the XY plane (Z = 0 plane). The cone’s apex is at ConeApex, the cone’s direction is ConeDir and its spanning angle is ConeAngle. Dir must be in the northern hemisphere; i.e. their Z coeﬃcient must be positive. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTCONPL( point( 0, 0, -0.3 ), vector( 1, 1, 1 ), 20, 1 ); computes the bisector surface of a cone with its apex at (0, 0, -0.3) along the axis (1, 1, 1) with spanning angle of 20 degrees, and the plane Z = 0. See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.27 BSCTCONPT SurfaceType | ListType BSCTCONPT( PointType ConeApex, VectorType ConeDir, NumericType ConeAngle, PointType Pt, NumericType Size ) computes the bisector surface of a cone in a general position and a point, Pt. The cone’s apex is at ConeApex, the cone’s direction is ConeDir and its spanning angle is ConeAngle. Size controls the portion of the (inﬁnite) bisector actually represented. Example: Bisect = BSCTCONPT( point( 0, 0, 0 ), vector( 0, 0, 1 ), 22, point( 0, 0.2, 0.7 ), 1 ); See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. IRIT Solid modeler 11.2.28 G. Elber 41 BSCTCONSPR SurfaceType | ListType BSCTCONSPR( PointType ConeApex, VectorType ConeDir, NumericType ConeAngle, PointType SptCntr, NumericType SprRadius, NumericType Size ) computes the bisector surface of a cone and a sphere. The cone’s apex is at ConeApex, the cone’s direction is ConeDir and its spanning angle is ConeAngle. The sphere is centered at SptCntr and has a radius of SprRadius. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTCONSPR( point( 0, 0, 0 ), vector( 0, 0, 1 ), 45, point( 0, 0, 1 ), 0.5, 2.0 ); computes the bisector between a cone along the Z axis with a 45 degree spanning angle and a sphere at (0, 0, 1) of radius 0.5. See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.29 BSCTCYLCYL SurfaceType BSCTCYLCYL( PointType CylPt1, VectorType CylDir1, NumericType CylRad1, PointType CylPt2, VectorType CylDir2, NumericType CylRad2 ) computes the bisector surface of two cylinders in a general position. The cylinders start at CylPt1 and CylPt2 and follow the directions CylDir1 and CylDir2. They have radii of CylRad1 and CylRad2. Example: BisectSrf = BSCTCYLCYL( Pt1, Dir1, Rad1, Pt2, Dir2, Rad2 ); See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.30 BSCTCYLPL SurfaceType | ListType BSCTCYLPL( PointType CylPos, VectorType CylDir, NumericType CylRadius, Size ) computes the bisector surface of a a cylinder and the XY plane (plane Z = 0). The cylinder is located at CylPos, in the direction of CylDir which also sets the length of the cylinder. The radius of the cylinder is CylRadius. Size controls the portion of the (inﬁnite) bisector actually represented. Example: IRIT Solid modeler G. Elber 42 Pt = point( 0.1, 0, 0.2 ); BisectSrf = BSCTCYLPL( point( 0, 0, 0.5 ), vector( 0, 0, 1 ), 0.2, 1 ); computed the bisector surface between a cylinder of radius 0.2 along the Z axis and the XY plane. See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.31 BSCTCYLPT SurfaceType | ListType BSCTCYLPT( PointType CylPos, VectorType CylDir, NumericType CylRadius, PointType Pt, NumericType Size ) computes the bisector surface of a a cylinder and a point, Pt. The cylinder is located at CylPos, in the direction of CylDir which also sets the length of the cylinder. The radius of the cylinder is CylRadius. Size controls the portion of the (inﬁnite) bisector actually represented. Example: Pt = point( 0.1, 0, 0.2 ); BisectSrf = BSCTCYLPT( point( 0, 0, 0.5 ), vector( 0, 0, 1 ), 0.2, Pt, 1 ); computes the bisector surface between a cylinder of radius 0.2 along the Z axis and a point at (0.1, 0, 0.2). See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR 11.2.32 BSCTCYLSPR SurfaceType | ListType BSCTCYLSPR( PointType CylPos, VectorType CylDir, NumericType CylRadius, PointType SprCntr, NumericType SprRadius, NumericType Size ) computes the bisector surface of a cylinder and a sphere. The cylinder is located at CylPos, in the direction of CylDir which also sets the length of the cylinder. The radius of the cylinder is CylRadius. The sphere is centered at SptCntr and has a radius of SprRadius. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTCYLSPR( point( 0, 0, 1.5 ), vector( 0, 0, 3 ), 0.2, point( 0, 0, 0 ), 0.7, 3 ); computed the bisector surface between a cylinder of radius 0.2 along the Z axis and a sphere at the origin with radius 0.7. See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. IRIT Solid modeler 11.2.33 G. Elber 43 BSCTPLNLN SurfaceType | ListType BSCTPLNLN( VectorType LineDir, NumericType Size ) computes the bisector surface of the XY plane (plane Z = 0) and a line in direction LineDir. The plane and the line are assumed to intersect at the origin. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTPLNLN( vector( 0, 0, 1 ), 1 ); computes the bisector of the XY plane and the Z axis (a cone). See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.34 BSCTPLNPT SurfaceType | ListType BSCTPLNPT( PointType Pt, NumericType Size ) computes the bisector surface of the XY plane (plane Z = 0) and a point Pt. This surface is a paraboloid of revolution. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTPLNPT( point( 0, 0, 1 ), 1 ); computes the bisector surface of the XY plane and the point (0, 0, 1). See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.35 BSCTSPRLN SurfaceType | ListType BSCTSPRLN( PointType SprCntr, NumericType SprRadius, NumericType Size ) computes the bisector surface of a sphere and the Z axis line. The sphere is centered at SptCntr and has a radius of SprRadius. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTSPRLN( vector( 2, 0, 0 ), 0.7, 1 ); See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. IRIT Solid modeler 11.2.36 G. Elber 44 BSCTSPRPL SurfaceType | ListType BSCTSPRPL( PointType SprCntr, NumericType SprRadius, NumericType Size ) computes the bisector surface of the XP plane (the plane Z = 0) and a sphere. This bisector surface is a paraboloid of revolution. The sphere is centered at SptCntr and has a radius of SprRadius. Size controls the portion of the (inﬁnite) bisector actually represented. Example: BisectSrf = BSCTSPRPL( point( 0, 0, 1.5 ), 0.7, 0.5 ); See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. See Figure 11. 11.2.37 BSCTSPRPT SurfaceType | ListType BSCTSPRPT( PointType SprCntr, NumericType SprRadius PointType Pt ) computes the bisector surface of a sphere and a point, Pt. The sphere is centered at SptCntr and has a radius of SprRadius. Example: Pt = point( 0, 0, 1 ); BisectSrf = BSCTSPRPT( point( 0, 0, 0 ), 0.7, Pt ); computes the bisector of a sphere of radius 0.7 centered at the origin, and the point (0, 0, 1). See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.38 BSCTSPRSPR SurfaceType | ListType BSCTSPRSPR( PointType Spr1Cntr, NumericType Spr1Radius PointType Spr2Cntr, NumericType Spr2Radius ) computes the bisector surface of two spheres. The spheres are centered at Spt1Cntr and Spt2Cntr and have a radii of Spr1Radius and Spr2Radius, respectively. Example: BisectSrf = ( point( 0, 0, 0 ), 0.7, point( 1, 0, 0 ), 0.2 ); compute the bisectors of a sphere at the origin with radius 0.7, and a sphere at (1, 0, 0) with a radius of 0.2. See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTTRSPT, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. IRIT Solid modeler 11.2.39 G. Elber 45 BSCTTRSPT SurfaceType | ListType BSCTTRSPT( PointType TrsPos, VectorType TrsDir, NumericType TrsMjrRad, NumericType TrsMnrRad, PointType Pt ) computes the bisector surface of a torus and a point, Pt. The torus is located at TrsPos, with its axis of symmetry TrsDir, a major radius of TrsMajorRad and a minor radius pf TrsMinorRad. Example: BisectSrf = BSCTTRSPT( point( 0.0, 0.0, 0.0 ), vector( 0.0, 0.0, 1.0 ), 0.7, 0.7, Pt ); See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSSPR, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. 11.2.40 BSCTTRSSPR SurfaceType | ListType BSCTTRSSPR( PointType TrsPos, VectorType TrsDir, NumericType TrsMjrRad, NumericType TrsMnrRad, PointType SprCntr, NumericType SprRadius ) computes the bisector surface of a torus and a sphere. The torus is located at TrsPos, with its axis of symmetry TrsDir, a major radius of TrsMajorRad and a minor radius pf TrsMinorRad. The sphere is centered at SptCntr and has a radius of SprRadius. Example: BisectSrf = BSCTTRSSPR( point( 0.0, 0.0, 0.0 ), vector( 0.0, 0.0, 1.0 ), 0.7, 0.7, point( 0.7, 0.0, 0.0 ), 0.7); See also BSCPCONCON, BSCTCONCN2, BSCTCONCYL, BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, CALPHASECTOR, CBISECTOR2D, CBISECTOR3D, SBISECTOR. See Figure 11. 11.2.41 BZR2BSP CurveType BZR2BSP( CurveType Crv ) or SurfaceType BZR2BSP( SurfaceType Srf ) creates a B-spline curve or a B-spline surface from the given Bezier curve or Bezier surface. The Bspline curve or surface is assigned an open end knot vector(s) with no interior knots, in the parametric domain of zero to one. Example: BspSrf = BZR2BSP( BzrSrf ); IRIT Solid modeler G. Elber 46 Figure 11: Bisectors of many CSG primitives such as points, lines, planes, spheres, cones, cylinders, and torii are rational. In (left), the rational bisector of a line and a sphere is shown while (right) shows the bisector of a sphere and a torus tangent to each other. See BSCTCONCON, BSCTCONLN, BSCTCONPL, BSCTCONPT, BSCTCONSPR, BSCTCYLPL, BSCTCYLPT, BSCTCYLSPR, BSCTPLNLN, BSCTPLNPT, BSCTSPRLN, BSCTSPRPL, BSCTSPRPT, BSCTSPRSPR, BSCTTRSPT, BSCTTRSSPR. 11.2.42 BSP2BZR CurveType | ListType BSP2BZR( CurveType Crv ) or SurfaceType | ListType BSP2BZR( SurfaceType Srf ) creates Bezier curve(s) or surface(s) from a given B-spline curve or a B-spline surface. The B-spline input is subdivided at all internal knots to create Bezier curves or surfaces. Therefore, if the input B-spline does have internal knots, a list of Bezier curves or surfaces is returned. Otherwise, a single Bezier curve or surface is returned. The returned Beziers will have BspDomainMin/Max attributes with the original Bspline domain of the Bezier. Example: BzrCirc = BSP2BZR( circle( vector( 0.0, 0.0, 0.0 ), 1.0 ) ); would subdivide the unit circle into four 90 degrees Bezier arcs returned in a list. 11.2.43 C2CONTACT CurveType C2CONTACT( CurveType C1, CurveType C2, NumericType StepSizeTol, NumericType SubdivTol, NumericType NumericTol ) computes precise 2-contact planar motion of one curve against the other, building the conﬁguration space of the possible motions. See also ”High-Precision Continuous Contact Motion for Planar IRIT Solid modeler G. Elber 47 Figure 12: The precise conﬁguration space (three axes for the three degrees of freedom - XY motion and rotation in the plane) is shown on the right for the two curves on the left. The speciﬁc conﬁguration on the left is designated as a point on the right. Computed by mapping the contacts formulation into algebraic constraints and solving them. Freeform Geometric Models”, Graphical Model, Vol 76, pp 580-592, 2014, by Yong-Joon Kim, Gershon Elber, and Myung-Soo Kim. Example: MotionPath = C2CONTACT( c1, c2, 1e-3, 1e-3, 1e-8 ); See Figure 12 for one example. See also MZERO and MUNIVZERO, MFROMMESH. 11.2.44 C2RECTRGN CurveType C2RECTRGN( ListType CrvsList, NumericType BndryAngleDeviate, NumericType OutputType, NumericType SizeRect, NumericType Smoothing ) divides the 2D region bounded by CrvsList into rectangular domains. BndryAngleDeviate sets the angle to split into a corner, at C 1 discontinuities inside the input curve(s). OutputType can be either 0, 1, or 2 for rectangles outout, freeform 4-sided regions, or full tensor product surface for each retion, respectively. SizeRect GERSHON Smoothing GERSHON Example: Srfs = C2RECTRGN( list( C1 ), 1, 2, 1.0, 0 ); See Figure 13 for one example. IRIT Solid modeler G. Elber 48 Figure 13: Divides the given curve into rectangle regions: into 4-sided polygons (left), 4-sided freeform regions (middle), and tensor product surfaces (right). 11.2.45 CALPHASECTOR SurfaceType CALPHASECTOR( ListType TwoCrvs, NumericType Alpha) or {CurveType | SurfaceType} CALPHASECTOR( ListType CrvPt, NumericType Alpha) computes the alpha sector for TwoCrvs of E3 type or between a curve and a point, CrvPt. Alpha varies between zero and one. An alpha-sector is created where for Alpha equals zero, the created surface will contain the ﬁrst curve, and whereas for Tolerance equals one, the created surface will contain the second curve. For CrvPt case, if the Crv is E2, the alpha sector is a curve and if it is E3, the alpha sector is a surface. See also CBISECTOR2D, CBISECTOR3D. Example: c1 = creparam( pcircle( vector( 0.0, 0.0, 0.0 ), 1 ), 0, 1 ); c2 = cbezier( list( ctlpt( E3, -1.0, 0.0, 1.0 ), ctlpt( E3, 1.0, 0.0, -1.0 ) ) ); c1 = coerce( c1, E3); AlphaSect = CALPHASECTOR( list( c1, c2 ), 0.2 ); interact( list( c1, c2, AlphaSect ) ); computes the alpha sector surface between the two curves c1 and c2 for alpha equals 0.2. 11.2.46 CANGLEMAP CurveType CANGLEMAP( CurveType Crv, NumericType SubdivTol, NumericType Angle, NumericType DiagSpan ) IRIT Solid modeler G. Elber 49 Figure 14: Angular maps computed for the given planar curve on the left, at 30, 60, and 90 degrees, using CANGLEMAP. Also show is the angular diagonal span in thin dark color. or SurfaceType CANGLEMAP( CurveType Crv, NumericType SubdivTol, NumericType Angle, NumericType DiagSpan ) computes the angular map of planar curve Crv. This bivariate map corresponds pairs of locations in Crv with tangents that are Angle degrees apart. If, for example, Angle is 90 degrees, locations with orthogonal tangents are identiﬁed. The zero set of this bivariate map provides the actual correspondence and this zero set is computed with SubdivTol accuracy. If SubdivTol is negative the function whose zero set is the angular map is returned instead. If DiagSpan is non zero, the angular diagonal span is sampled DiagSpan samples and is computed instead. The DiagSpan will provide for each parameter t the forward and backward step that could be taken before hitting an angular span of Angle degrees for the ﬁrst time. Example: AM = cAngleMap( Crv, 0.01, Angle, false ); ADS = cAngleMap( Crv, 0.01, Angle, 300 ); computes the Angular map of curve Crv ay angle Angle with subdivison tolerance 0.01 and then extract the angular diagonal span with the same parameters and 300 samples. Figure 14 provides some insight curve, with three angular maps of 30, 60 and 90 degrees. The angular diagonal span is also drawn in dark thin lines. See also CVIEWMAP, CVISIBLE, CARRANGMNT. 11.2.47 CARCLEN CurveType CARCLEN( CurveType Crv, NumericType Fineness, NumericType Order ) approximates an arc length curve out of the given curve Crv. The new approximated curve is sampled with tolerance that is governed by Fineness and will be of order Order. The returned curve is not guaranteed to share the exact same trace as the original curve Crv. G. Elber IRIT Solid modeler 50 Example: c2 = carclen( c, 1e-4, 3 ); approximates c as a quadratic arc length curve c2 by sampling the original curve with tolerance 1e-4. 11.2.48 CAREA CurveType CAREA( CurveType Crv ) computes the integral area curve, ACrv, of the given curve Crv, up to a sign. If Crv is a closed curve with domain t0 to t1, then the diﬀerence of ACrv(t1) - ACrv(t0) is the requested area. The integral area curve C(t) = (x(t), y(t)) is computed as the following integral: 1 2 t2 t1 −x (t)y(t) + x(t)y (t)dt Example: Crv = pcircle( vector( 0, 0, 0 ), 1 ); ACrv = CAREA( Crv ); Pi = abs( coord( ceval( ACrv, 4 ), 1 ) - coord( ceval( ACrv, 0 ), 1 ) ); is yet another way of approximating the value of Pi. See also SMOMENTS, SVOLUME and TVOLUME. 11.2.49 CARRANGMNT CurveType CARRANGMNT( CurveType Crvs, NumericType Eps, NumericType Operation, PointType CenterPt ) computations over the given arrangment of planar curves Crvs upto accuracy that is governed by Eps. Operation can be one of: • 1 - computes all the curve curve intersection locations in the arrangment and keep the results in ”InterPts” attributes on the returned curves. • 2 - computes all the curve curve intersection locations in the arrangment and split all curves at all those intersections. • 3 - computes Y-minimum lower envelop for this curves’ arrangement. • 4 - computes radial lower envelop around point Center Pt. CenterPt is ignored if Operation is not equal to 4. Example: LinearLowEnv = carrangmnt( Crvs, 1e-12, 3, 0 ); computes the Y-minimum envelop of curve Crvs. Figure 15 show one example of Y-minimum envelop of curves. See also CVIEWMAP, CVISIBLE, CANGLEMAP, CARNGMNT2. IRIT Solid modeler G. Elber 51 Figure 15: Y-minimum envelop for a set of curves, computed using CARRANGMNT. The lower envelop is shown in thick lines. 11.2.50 CARNGMNT2 CurveType CARNGMNT2( CurveType Crvs, NumericType Operation, ListType Params ) computations over the given arrangment of planar curves Crvs upto accuracy. Operation can be one of: • 1 - create a new arrangment. Params contains four items: (Tolerance for equality of end points, Planarity tolerance to consider arrangement planar, TRUE to project all curves to be on computed plane, Mask for input type to consider: 0x01 to handle polylines. 0x02 to handle curves. 0x04 to handle trimming curves in trimmed surfaces). • 2 - copy an arrangement. Params contains no items. • 3 - ﬁlter duplications in the input arrangement. Params contains two items: (Epsilon to consider the curves the same, TRUE to update end points to be the same). IRIT Solid modeler G. Elber 52 • 4 - ﬁlter duplications in the tangential input arrangement. Params contains one item: (Epsilon angle in degrees to consider two curves with the same tangent). • 5 - Splits curves at special points, Params contains two items: (Mask for splitting type to consider: 0x01 to split at inﬂection pts — 0x02 to split at max curvatures — 0x04 to split at C1 disconts, Tolerance of splitting computation). • 6 - Split piecewise curves at large angular deviation of adjacent edges. Params contains one item: (Angular deviation (in degrees) to split linear curves at). • 7 - Split curves at intersection locations. Params contains one item: (Intersection computation tolerance). • 8 - Splits curve near prescribed points. Params contains two items: (A list object of pts to examine and split if near them, Tolerance to consider a point near/on a curve). • 9 - Merge adjacent curves. Params contains one item: (Angular deviation (in degrees) to merge C1 discont. curves at). • 10 - Least square ﬁt linear curves. Params contains one item: (Fitting Parameter to ﬁt smooth quadratic C1 curves to linear curves. Higher order curves are not aﬀected. If Param positive, the ﬁtted curve size is set to InputCrvSize * FitC1Crv / 100 (i.e. Param serves as percetange of input size). If Param negative, the Fitted curve size is simply set to ABS(Param)) • 11 - Evaluate the curve arrangement. Params contains one item: (TRUE to ignore hanging curves that join other curves at only one of their end points). • 12 - Classify the curve arrangement. This returns nothing. Params contains one item. • 13 - Report the result. Params contains one item: (A mask of desired report: 0x01 to dump info on crvs — 0x02 to also dump the crvs — 0x04 to report end pts in arrangment if evaluated — 0x08 to report regions in arrangment if evaluated). • 14 - Dumps to stdout information on the arrangement. Params contains three item: (Style of expected output: 1 for individual crv segs in each region (loop etc.) or 2 for merged curves so every region is one curve or 3 for topology as an ordered list of curve segments and each region is a list of indices into the ﬁrst list. A negative -i index means index i but a reversed crv. 101, 102, 103: same as 1,2,3 but pt is evaluated at 1/13 of curve parameteric domain to identify orientation, Tolerance of topology reconstruction (in case 3 only), Zoﬀset in Z for the i’th region, by amount i*ZOﬀset). • 15 - Free a curve arrangement. Params contains no item. Example: ca1 = carngmnt2( crvs2, CA_CREATE, list( 1e-2, 1e-2, TRUE, 7 ) ); ca2 = carngmnt2( ca1, CA_BREAK_INTER, list( 1e-6 ) ); ca3 = carngmnt2( ca2, CA_EVAL_CA, list( TRUE ) ); dm = carngmnt2( ca3, CA_CLASSIFY, nil() ); CAFinal2 = carngmnt2( ca3, CA_OUTPUT, list( 2, 1e-2, 0.02 ) ); dm = carngmnt2( ca3, CA_REPORT, list( 1 ) ); dm = carngmnt2( ca3, CA_REPORT, list( 2 ) ); dm = carngmnt2( ca3, CA_REPORT, list( 4 ) ); dm = carngmnt2( ca3, CA_REPORT, list( 8 ) ); G. Elber IRIT Solid modeler 53 Creates a curves’ arrangment from crvs2 and classify into closed loops after breaking at all crv-crv intersections. See also CARRANGMNT. 11.2.51 CBEZIER CurveType CBEZIER( ListType CtlPtList ) creates a Bezier curve out of the provided control point list. CtlPtList is a list of control points, all of which must be of type (E1-E9 P1-P9), or regular PointType deﬁning the curve’s control polygon. The curve’s point type will be of a space which is the union of the spaces of all points. The created curve is polynomial (or rational), C(t) = k Pi Bi (t), (2) i=0 where Pi are the control points CtlPtList, and k is the degree of the curve, which is one less than the number of points. Example: s45 = sin(pi / 4); Arc90 = CBEZIER( list( ctlpt( P2, 1.0, 0.0, 1.0 ), ctlpt( P2, s45, s45, s45 ), ctlpt( P1, 1.0, 1.0 ) ) ); constructs an arc of 90 degrees as a rational quadratic Bezier curve. See also CBSPLINE, CPOWER and SBEZIER. 11.2.52 CBIARCS ListType CBIARCS( CurveType Crv, NumericType Tol, NumericType MaxAngle ) computes bi-arc ﬁtting to a given curve Crv, with a tolarence Tol in L-inﬁnity sense, and a maximum angular span of each arc of at most MaxAngle degrees. Returned is a list of arcs as rational Bezier curves with an arc ”center” point attribute to ease the reconstruction of the analytic representation of the geometry. Example: C1 = cbspline( 4, list( ctlpt( E3, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, ctlpt( E2, -0.287, -0.286, 0 ), 0.0272, -0.425 ), 0.265, -0.0839 ), 0.607, -0.165 ), 0.832, -0.205 ), 0.737, 0.042 ), 0.357, 0.103 ), 0.508, 0.298 ), 0.814, 0.649 ), 0.692, 0.775 ), 0.411, 0.391 ), IRIT Solid modeler G. Elber 54 Figure 16: Bi-arcs are ﬁtted to the given curve in the shape of a human hand, at two diﬀerent tolerances, using CBIARCS. ctlpt( E2, 0.301, 0.315 ), ctlpt( E2, 0.625, 0.945 ), ctlpt( E2, 0.49, 1.03 ), ctlpt( E2, 0.369, 0.829 ), ctlpt( E2, 0.185, 0.384 ), ctlpt( E2, 0.194, 0.518 ), ctlpt( E2, 0.243, 1.09 ), ctlpt( E2, 0.0653, 1.13 ), ctlpt( E2, 0.0644, 0.381 ), ctlpt( E2, 0.00925, 0.496 ), ctlpt( E2, -0.0113, 0.943 ), ctlpt( E2, -0.202, 0.954 ), ctlpt( E2, -0.147, 0.644 ), ctlpt( E2, -0.162, 0.208 ), ctlpt( E2, -0.337, -0.156 ) ), list( kv_periodic ) ); C1 = coerce( C1, kv_open ); Arcs = CBIARCS( Crv, 0.01, 90 ); computes bi-arcs ﬁtting to a given curve in the shape of a human hand, with arcs with at most 90 degrees and tolerance of 0.01. See Figure 16. See also QUADCRVS, CUBICCRVS. 11.2.53 CBISECTOR2D CurveType CBISECTOR2D( CurveType Crv, G. Elber IRIT Solid modeler NumericType NumericType NumericType NumericType NumericType 55 ZeroSet, BisectFunc, Tolerance, NumerImprove, SameNormal ) or CurveType CBISECTOR2D( ListType TwoCrvs, NumericType ZeroSet, NumericType BisectFunc, NumericType Tolerance, NumericType NumerImprove, NumericType SameNormal ) or SurfaceType CBISECTOR2D( ListType CrvPt, NumericType ZeroSet, NumericType UseNrmlTan, NumericType Tolerance, NumericType NumerImprove, NumericType SameNormal ) computes the self bisector curve(s) for Crv or the bisector(s) of TwoCrvs or the bisector of a curve and a point, CrvPt. If ZeroSet is TRUE, the zero-set surface is computed and is used mainly for displaying the zero-set. If it is FALSE, the bisector is returned. The zero-set is computing using the functions F1, F2 and F3 in the paper Gershon Elber and Myung Soo Kim, “Bisector Curves of Planar Rational Curves,” CAD, Vol 30, No 14, pp 1089-1096, December 1998 which is determined by the BisectFunc parameter. If BisectFunc = 1, then F1 is used and so on. Tolerance controls the accuracy of the computation, with 0.01 as a good starting value. If Tolerance is negative, NumerImprove can be either TRUE or FALSE, allowing or disabling a ﬁnal numerical improvement stage. SameNormal can also assume a TRUE or FALSE value, selecting only opposite facing normals, if TRUE. The bisector curve of a curve (E2) and a point CrvPt is computed analytically. Other parameters are ignored. See also CBISECTOR3D, CALPHASECTOR, SBISECTOR. Example: c1 = cbezier( list( ctlpt( E2, -0.5, -0.2 ctlpt( E2, 0.0, -0.2 ctlpt( E2, 0.6, 0.6 c2 = cbezier( list( ctlpt( E2, 0.3, -0.7 ctlpt( E2, -0.2, -0.7 ctlpt( E2, 0.7, 0.6 BisectCrvs = CBISECTOR2D( list( c1, c2 ), All = list( c1, c2, BisectCrvs ); interact( list( All, view_mat2d ) ); ), ), ) ) ); ), ), ) ) ); TRUE, 1, 0.01, true, false ); computes the bisector for planar curves as a set of bisector curves. See Figure 17. IRIT Solid modeler G. Elber 56 Figure 17: (left) Bisectors of two quadratic Bezier curves in the plane. (right) A bisector surface of a line and a circle in three space. See the CBISECTOR2D and CBISECTOR3D functions respectively. 11.2.54 CBISECTOR3D SurfaceType CBISECTOR3D( ListType TwoCrvs, NumericType BisectFunc) or SurfaceType CBISECTOR3D( ListType CrvPt, NumericType BisectFunc) computes the bisector surface TwoCrvs or the bisector surface of a curve and a point, CrvPt, in R3. The BisectFunc determines the function to be used for generating the bisector surface between the two E3 curves. If 1, a 3-space bisector surface is generated to the given curves or a curve and a point. If 4, a surface whose zero set prescribes the bisectors of the given curves is returned. For a bisector between a curve and a point, the BisectFunc parameter is ignored and a 3 space surface is always computed. See also CBISECTOR2D, CALPHASECTOR, SBISECTOR. Example: c1 = creparam( pcircle( vector( 0.0, 0.0, 0.0 ), 1 ), 0, 1 ); c2 = cbezier( list( ctlpt( E3, -1.0, 0.0, 1.0 ), ctlpt( E3, 1.0, 0.0, -1.0 ) ) ); c1 = coerce( c1, E3); BisectSrf = CBISECTOR3D( list( c1, c2 ), 1 ); interact( list( c1, c2, BisectSrf ) ); computes a bisector surface of a Z parallel line and a circle in the XY plane. See Figure 17. G. Elber IRIT Solid modeler 11.2.55 57 CBSPLINE CurveType CBSPLINE( NumericType Order, ListType CtlPtList, ListType KnotVector ) creates a B-spline curve out of the provided control point list, the knot vector, and the speciﬁed order. CtlPtList is a list of control points, all of which must be of type (E1-E9 P1-P9, or regular PointType deﬁning the curve’s control polygon. The curve’s point type will be of a space which is the union of the spaces of all points. The length of the KnotVector must be equal to the number of control points in CtlPtList plus the Order. If, however, the length of the knot vector is equal to #CtlPtList + Order + Order - 1, the curve is assumed to be periodic. The knot vector list may be speciﬁed as either list( KV OPEN ), list( KV FLOAT ) or list( KV PERIODIC ) in which a uniform open, uniform ﬂoating or uniform periodic knot vector with the appropriate length is automatically constructed. The created curve is the piecewise polynomial (or rational), C(t) = k Pi Bi,τ (t), (3) i=0 where Pi are the control points CtlPtList and k is the degree of the curve, which is one less than the Order or number of points. τ is the knot vector of the curve. Example: s45 = sin(pi / 4); HalfCirc = CBSPLINE( 3, list( ctlpt( P3, ctlpt( P3, ctlpt( P3, ctlpt( P3, ctlpt( P3, list( 0, 0, 0, 1, 1.0, 1.0, 0.0, s45, s45, s45, 1.0, 0.0, 1.0, s45, -s45, s45, 1.0, -1.0, 0.0, 1, 2, 2, 2 ) ); 0.0 0.0 0.0 0.0 0.0 ), ), ), ), ) ), constructs an arc of 180 degrees in the XZ plane as a rational quadratic B-spline curve. Example: c = CBSPLINE( 4, list( ctlpt( E2, 0.5, 0.5 ), ctlpt( E2, -0.5, 0.5 ), ctlpt( E2, -0.5, -0.5 ), ctlpt( E2, 0.5, -0.5 ) ), list( KV_PERIODIC ) ); color( c, red ); viewobj( c ); c1 = cregion( c, 3, 4 ); color( c1, green ); c2 = cregion( c, 4, 5 ); color( c2, yellow ); c3 = cregion( c, 5, 6 ); IRIT Solid modeler G. Elber 58 Figure 18: A cubic periodic curve created using KV PERIODIC end conditions. color( c3, cyan ); c4 = cregion( c, 6, 7 ); color( c3, magenta ); viewobj( list( c1, c2, c3, c4 ) ); creates a periodic curve and extracts its four polynomial domains as four open end B-spline curves. See Figure 18. See also CBEZIER, CPOWER and SBSPLINE. 11.2.56 CCINTER ListType CCINTER( CurveType Crv1, CurveType Crv2, NumericType Epsilon, NumericType SelfInter ) or SurfaceType CCINTER( CurveType Crv1, CurveType Crv2, NumericType Epsilon, NumericType SelfInter ) compute the intersection point(s) of Crv1 and Crv2 in the XY plane. Since this computation involves numeric operations, Epsilon controls the accuracy of the parametric values of the result. It returns a list of PointTypes, each containing the parameter of Crv1 in the X coordinate, and IRIT Solid modeler G. Elber 59 Figure 19: A intersection point of two freeform curve computed using CCINTER. the parameter of Crv2 in the Y coordinate. If, however, Epsilon is negative, a scalar ﬁeld surface representing the square of the distance function is returned instead. If SelfInter is TRUE, Crv1 and Crv2 can be the same curve, and self intersection points are searched for instead. Example: crv1 = cbspline( 3, list( ctlpt( E2, 0, 0 ), ctlpt( E2, 0, 0.5 ), ctlpt( E2, 0.5, 0.7 ), ctlpt( E2, 1, 1 ) ), list( KV_OPEN ) ); crv2 = cbspline( 3, list( ctlpt( E2, 1, 0 ), ctlpt( E2, 0.7, 0.25 ), ctlpt( E2, 0.3, 0.5 ), ctlpt( E2, 0, 1 ) ), list( KV_OPEN ) ); inter_pts = CCINTER( crv1, crv2, 0.0001, FALSE ); computes the parameter values of the intersection point of crv1 and crv2 to a tolerance of 0.0001. See Figure 19. G. Elber IRIT Solid modeler 11.2.57 60 CCRVTR ListType CCRVTR( CurveType Crv, NumericType Epsilon, NumericType Operation ) or CurveType CCRVTR( CurveType Crv, NumericType Epsilon, NumericType Operation ) computes the curvature ﬁeld’s magnitude square of Crv in the XY plane if Operation is 1, or its extreme points if Operation equals 2. This set includes not only points of maximum (convexity) and mimumum (concavity) curvature, but also points of zero curvature locations, such as inﬂection points. A list of parameter value(s) of the location(s) with extreme curvature along the Crv is returned in the latter case. Since this operation is partially numeric, Epsilon is used to set the needed accuracy. If, however, Operation is 3, the input curve is being split at the extreme curvature location and a list of curve segments is returned instead. This function computes the (square of the) curvature scalar ﬁeld for planar curves as, κ(t) = x (t)y (t) − x (t)y (t) 3 ((x (t))2 + (y (t))2 ) 2 , (4) and computes (the square of) kN for three-dimensional curves as the following vector ﬁeld, κ(t)N (t) = κ(t)B(t) × T (t) = (C × C ) × C C C × C = × . 3 C C C 4 (5) The extremum values are extracted from the computed curvature ﬁeld. This (square of the) curvature ﬁeld is a high order curve, even if the input geometry is of low order. This is especially true for rational curves, for which the quotient rule for diﬀerentiation is used and almost doubles the degree in every diﬀerentiation. See also CCRVTREVAL, CINFLECT, CNRMLCRV, CZEROS, CEXTREMES, and SCRVTR. Example: crv = cbezier( list( ctlpt( E2, -1.0, 0.5 ), ctlpt( E2, -0.5, -2.0 ), ctlpt( E2, 0.0, 1.0 ), ctlpt( E2, 1.0, 0.0 ) ) ) * rotz( 30 ); crvtr = CCRVTR( crv, 0.001, 2 ); pt_crvtr = nil(); pt = nil(); for ( i = 1, 1, sizeof( crvtr ), ( pt = ceval( crv, nth( crvtr, i ) ) ): snoc( pt, pt_crvtr ) ); interact( list( crv, pt_crvtr ) ); ﬁnds the extreme curvature points in Crv and displays them all with the curve. See Figure 20. 11.2.58 CCRVTR PolyType CCRVTR1PT( CurveType Crv, NumericType CtlPtIdx, NumericType Min, G. Elber IRIT Solid modeler 61 Figure 20: Extreme curvature locations on a freeform curve computed using CCRVTR. NumericType Max, NumericType SubdivTol, NumericType NumerTol, NumericType Operation ) or MultivarType CCRVTR1PT( CurveType Crv, NumericType CtlPtIdx, NumericType Min, NumericType Max, NumericType SubdivTol, NumericType NumerTol, NumericType Operation ) computes the topology changes in the curvature ﬁeld of curve Crv as control point index CtlPtIdx in the curve is moving. The motion of the control points is limited to be between Min and Max in X and Y. See MZERO for the meaning of the SubdivTol and NumerTol. The returned value depends on Operation: If Operation is 0, a multivariate of dim(Crv) + 1 that is representing the curvature topology ﬁeld is returned. If Operation is 1, the marching cubes of Operation == 0 is computed and returned as a polygonal surface. If Operation is 2 the silhouette of 1 is computed and returned and if Operation is 3 the result of 2 is evaluated back into Euclidean space. Example: MV = CCRVTR1PT( Crv, 4, Min, Max, 0.01, 1e-10, 1 ); 11.2.59 CCRVTREVAL NumericType CCRVTREVAL( CurveType Curve, NumericType t ) computes the curvature of curve Curve at parameter t. Example: k = CCRVTREVAL(Crv, 0.5 ); See also CCRVTR. IRIT Solid modeler G. Elber 62 Figure 21: A piecewise cubic ﬁt to a given general curve, at three diﬀerent tolerances, using CCUBICS. 11.2.60 CCUBICS CurveType CCUBICS( CurveType Crv, NumericType Tolerance ) returns a list of cubic curves approximating the given curve Crv to within Tolerance. Example: Crv = CCUBICS( Crv, 0.01 ); See Figure 21. See also CUBICCRVS, QUADCRVS, and CBIARCS. 11.2.61 CDERIVE CurveType CDERIVE( CurveType Curve ) returns a vector ﬁeld curve representing the diﬀerentiated curve, also known as the Hodograph curve. Example: Circ = circle( vector( 0.0, 0.0, 0.0 ), 1.0 ); Hodograph = CDERIVE( Circ ); See Figure 22. See also CINTEG, SDERIVE, TDERIVE, and MDERIVE 11.2.62 CDIVIDE ListType CDIVIDE( CurveType Curve, NumericType Param ) subdivides a curve into two sub-curves at the speciﬁed parameter value. Curve can be either a B-spline curve in which Param must be within the Curve’s parametric domain, or a Bezier curve in which Param can be arbitrary, extrapolating if not in the range of zero to one. It returns a list of the two sub-curves. The individual curves may be extracted from the list using the NTH command. Example: IRIT Solid modeler G. Elber 63 Figure 22: The Hodograph (thick) of a B-spline circle (thin) constructed as four 90 degrees rational Bezier arcs, computed using CDERIVE. Figure 23: A B-spline curve is subdivided into two distinct regions using CDIVIDE. IRIT Solid modeler G. Elber 64 CrvLst = CDIVIDE( Crv, 1.3 ); Crv1 = nth( CrvLst, 1 ); Crv2 = nth( CrvLst, 2 ); subdivides the curve Crv at the parameter value of 0.5. See Figure 23. See also SDIVIDE, TDIVIDE, and MDIVIDE 11.2.63 CEDITPT CurveType CEDITPT( CurveType Curve, CtlPtType CtlPt, NumericType Index ) provides a simple mechanism to manually modify a single control point number Index (base count is 0) in the Curve, by substituting CtlPt instead. CtlPt must have the same point type as the control points of the Curve. The original curve Curve is not modiﬁed. Example: CPt = ctlpt( E3, 1, 2, 3 ); NewCrv = CEDITPT( Curve, CPt, 1 ); constructs a NewCrv with the second control point of Curve being CPt. 11.2.64 CENVOFF SurfaceType CENVOFF( CurveType Curve, NumericType Height, NumericType Tolerance ) or ListType CENVOFF( CurveType Curve, NumericType Height, NumericType Tolerance ) computes the oﬀset envelope of a given planar curve Curve. The oﬀset envelope is the envelope of cones with apex on point on Curve in the Z direction. Height is the height of the cone which also equals the oﬀset distance or the width of the cones. Tolerance controls the accuracy of the oﬀset approximation. If the Curve is closed, two surfaces are created in the oﬀset envelope, one for the inside and another for the outside. If Curve is open, a single envelope oﬀset surface is computed, wrapping around both sides. Example: c1 = cbezier( list( ctlpt( E2, -0.8, 0.0 ), ctlpt( E2, -0.2, 1.0 ), ctlpt( E2, 0.2, 0.0 ), ctlpt( E2, 0.8, 0.6 ) ) ); s1 = CENVOFF( c1, 0.5, 0.01 ); computes an envelope oﬀset surface for a cubic Bezier curve c1 of Height of 0.5 and Tolerance of 0.01. See Figure 24. IRIT Solid modeler G. Elber 65 Figure 24: The envelope oﬀset of a freeform planar curve computed using CENVOFF. 11.2.65 CEVAL CtlPtType CEVAL( CurveType Curve, NumericType Param ) evaluates the provided Curve at the given Param value. Param should be in the curve’s parametric domain if the Curve is a B-spline curve, or between zero and one if the Curve is a Bezier curve. The returned control point has the same point type as the control points of the Curve. Example: CPt = CEVAL( Crv, 0.25 ); evaluates Crv at the parameter value of 0.25. See also SEVAL, MEVAL, TEVAL. 11.2.66 CEXTREMES ListType CEXTREMES( CurveType Crv, NumericType Epsilon, NumericType Axis ) computes the extreme set of the given Crv in the given axis (1 for X, 2 for Y, 3 for Z). Since this computation is numeric, an Epsilon is also required to specify the desired tolerance. It returns a list of all the parameter values (NumericType) in which the curve takes an extreme value. Example: extremes = CEXTREMES( Crv, 0.0001, 1 ); computes the extreme set of curve crv, in the X axis, with error tolerance of 0.0001. See also CZERO. See Figure 25. 11.2.67 CFNCRVTR CurveType CFNCRVTR( CurveType E2Crv, NumericType Samples, NumericType Order, NumericType ArcLen ) or CurveType CFNCRVTR( CurveType CrvtrE1Crv, NumericType Accuracy, NumericType Order, NumericType Periodic ) IRIT Solid modeler G. Elber 66 Figure 25: The X local extremums of a freeform curve are isolated using CEXTREMES. computes the curvature ﬁeld of planar curve E2Crv in the ﬁrst form, and reconstructs an E2 planar curve from the given curvature ﬁeld CrvtrE1Crv in the second form. In the ﬁrst form, Samples deﬁnes the numer of samples to use along the input curve while if ArcLen TRUE the samples are also made along the arc length of E2Crv. In the second form, a planar curve is reconstructed from the curvature ﬁeld of CrvtrE1Crv, with Accuracy to control the accuracy. If the reconstructed curve is suppose to be closed, set Periodic to TRUE. In both forms, Order sets the order of the return curve. Example: CrvtrField = CFNCRVTR( Crv, 1000, 2, TRUE ); 11.2.68 CHELIX CurveType CHELIX( NumericType NumLoops, NumericType Pitch, NumericType Radius, NumericType Samples, NumericType CtlPtsPerLoop ) constructs a polynomial approximation of a helical curve of NumLoops loops and speciﬁed Radius and Pitch. The curve is approximated as a least sqaures ﬁt of Samples samples and CtlPtsPerLoop control points per loop. Example: HelixcalCrv = chelix( 3, 0.333, 0.444, 100, 6 ); See Figure 26 for this helix 3 loops. See also CSPIRAL, CSIN 11.2.69 CIEXTREME ListType CIEXTREME( SurfaceType Srf, NumericType Dir, NumericType SubdivTol, NumericType NumerTol ) G. Elber IRIT Solid modeler 67 Figure 26: Approximates a helical curve using CHELIX. computes the X- or Y-extreme values of the implicit univariate deﬁned as the zero set of Srf. In addition, this function also detects hyperbolic tangent contact of Srf with the plane Z = 0. Dir speciﬁed the desired direction of the extremum to extract, one of COL or ROW. See MZERO for the meaning of the SubdivTol and NumerTol. Example: ViewMap = CIEXTREME( Srf, col, 0.01, 1e-9 ); See Figure 27. 11.2.70 CINFLECT ListType CINFLECT( CurveType Crv, NumericType Epsilon, NumericType Operation ) or CurveType CINFLECT( CurveType Crv, NumericType Epsilon, NumericType Operation ) computes and returns a scalar ﬁeld (the numerator of the curvature ﬁeld, the sign of the curvature ﬁeld if you like) whose zeros are the inﬂection points of Crv in the XY plane, if Operation is 1. G. Elber IRIT Solid modeler 68 Figure 27: An example of computing the X- and Y-extreme locations of this implicit curve deﬁned as the zero set of the surface. Also detected surface tangency contacts with the plane Z = 0. If Operation is 2, the inﬂection points are derived and returned as list of all the parameter values (NumericType) in which the curve has an inﬂection point. Since this computation is partially numeric, an Epsilon is also required to specify the desired tolerance. If, however, Operation is 3, the input curve Crv is being split at all the inﬂection points and the diﬀerent, inﬂection free, curve segements are returned in a list. The sign of curvature scalar ﬁeld is equal to, σ(t) = x (t)y (t) − x (t)y (t). (6) Example: inflect = CINFLECT( crv, 0.001, 2 ); pt_inflect = nil(); pt = nil(); for ( i = 1, 1, sizeof( inflect ), pt = ceval( crv, nth( inflect, i ) ): snoc( pt, pt_inflect ) ); interact( list( axes, crv, pt_inflect ) ); computes the set of inﬂection points of curve crv with error tolerance of 0.001. This set is then scanned in a loop and evaluated to the curve’s locations which are then displayed with the crv. See also CZEROS, CEXTREMES, and CCRVTR. See Figure 28. 11.2.71 CINTEG CurveType CINTEG( CurveType Crv ); returns a vector ﬁeld curve representing the integral curve. See also CDERIVE. IRIT Solid modeler G. Elber 69 Figure 28: The Inﬂection points of a freeform curve can be isolated using CINFLECT. 11.2.72 CINTERP CurveType CINTERP( ListType PtList, NumericType Order, NumericType Size, ConstantType Param, NumericType Periodic) or CurveType CINTERP( CurveType Crv, NumericType Order, NumericType Size, ConstantType Param, NumericType Periodic) or CurveType CINTERP( ListType PtList, NumericType Order, NumericType Size, ListType Params, NumericType Periodic) or CurveType CINTERP( CurveType Crv, NumericType Order, NumericType Size, ListType Params, NumericType Periodic) compute a B-spline curve that interpolates or approximates the list of points in PtList or a given curve Crv. The B-spline curve will have order Order and Size control points, and will be periodic if periodic is non zero. The knots will be spaced according to Param which can be one of PARAM UNIFORM, PARAM CHORD, PARAM CENTRIP, PARAM NEILFOL, or lists of parameter values and knots (see below). The PARAM UNIFORM prescribes a uniform knot sequence, PARAM CHORD speciﬁes knot spacing according to the chord length and PARAM CENTRIP according to the square root of the chord length. Finally, PARAM NEILFOL takes into consideration the angles between three consecutive points. A periodic curve will be coerced to have a PARAM UNIFORM knot sequence. If Params is a list object, it should contain two lists of numerical values. The ﬁrst list contains the parameter values at which to approximate or interpolate the data points. Hence, the length of this list must equal the length of the PtList data. The second list speciﬁes the knot vector of the construct B-spline curve. Use of Periodic end conditions can create cases with degenerated linear systems (determinant equal zero). Increase or decrease of the Order of the B-spline by one will resolve the problem. All points in PtList must be of type (E1-E9, P1-P9) control point, or regular PointType. If Size is equal to the number of points in PtList, the resulting curve will interpolate the data set. Otherwise, if Size is less than the number of points in PtList, the point data set will be least square approximated. At no time can Size be lower than Order. Size of zero forces interpolation by selecting Size to be the size of the data set. All interior knots will be distinct, preserving maximal IRIT Solid modeler G. Elber 70 Figure 29: A Helix, sampled at 100 locations, is least square ﬁtted using CINTERP by a quadratic B-spline curve and 21 control points. continuity. The resulting B-spline curve will have open end conditions. Example: pl = nil(); for ( x = 0, 1, 100, snoc(point(cos(x / 5), sin(x / 5), x / 50 - 1), pl) ); c = CINTERP( pl, 3, 21, PARAM_UNIFORM, false ); samples a helical curve at 100 points and least square ﬁt of a quadratic B-spline curve with 21 points to the data set. The curve will have a uniform knot spacing and is not periodic. See also SINTERP, TINTERP and LINTERP. See Figure 29. 11.2.73 CIRCLE CurveType CIRCLE( VectorType Center, NumericType Radius ) constructs a circle at the speciﬁed Center with the speciﬁed Radius. The returned circle is a B-spline curve of four piecewise Bezier 90 degree arcs. The construced circle is always parallel to the XY plane. Use the linear transformation routines to place the circle in the appropriate orientation and location. 11.2.74 CIRCPOLY PolygonType CIRCPOLY( VectorType Normal, VectorType Trans, NumericType Radius ) deﬁnes a circular polygon in a plane perpendicular to Normal that contains the Trans point. The constructed polygon is centered at Trans. RESOLUTION vertices will be deﬁned with Radius from distance from Trans. G. Elber IRIT Solid modeler 71 Alternative ways to construct a polygon are manual construction of the vertices using POLY, or the construction of a ﬂat ruled surface using RULEDSRF. 11.2.75 CLNTCRSR ListType CLNTCRSR( NumericType TimeOut ) reads the mouse coordinates as well as mouse events from displace devices, or times out after TimeOut miliseconds. A list object of two sub-objects, a points and a vector, named ” PickCrsr ” is returned. These point and vector deﬁne the three-dimensional line of the mouse in object space. Mouse events are typically processed by the display device. However, by the command ”CLNTPICKCRSR” (in iritinit.irt) which sends a ”PICKCRSR” request to the display devices, mouse events will be sent to the server. The server can be requested to keep mouse events for ”CLNTCRSR” to be read via the IritState command and the ”CursorKeep” attribute. Both the point and the vector will have a numeric attribute of ”EventType” that will have the following meaning: 1 2 5 Mouse motion event Mouse down event Mouse up event In case of a time out the returned list object will be empty and will have the name ” PickFail ”. Example: ClntPickCrsr( clients_all ); IritState( "CursorKeep", 1 ); Quit = 0; for ( i = 0, 1, 10, CLNTCRSR( 10000 ) ); ClntPickDone( clients_all ); IritState( "CursorKeep", 0 ); asks all clients to send mouse events to the server, asks the server to keep mouse events, and then reads 10 mouse events. 11.2.76 CLNTREAD AnyType CLNTREAD( NumericType Handler, NumericType Block ) reads one object from a client communication channel. Handler contains the index of the communication channel opened via CLNTEXEC. If no data is available in the communication channel, this function will block for at most Block milliseconds until data is found or timeout occurs. In the latter, a single StringType object is returned with the content of ”no data (timeout)”. If Handler equals -1, the regular display device (forked via, for example, VIEWOBJ command) is used. See also VIEWSET, CLNTWRITE, CLNTCLOSE, and CLNTEXEC. Example: G. Elber IRIT Solid modeler 72 h2 = clntexec( "xmtdrvs -s-" ); . . Model = CLNTREAD( h2 ); . . clntclose( h2,TRUE ); reads one object from client through communication channel h2 and saves it in variable model. 11.2.77 CMESH CurveType CMESH( SurfaceType Srf, ConstantType Direction, NumericType Index ) returns a single ROW or COLumn as speciﬁed by the Direction and Index (base count is 0) of the control mesh of surface Srf. The returned curve will have the same knot vector as Srf in the appropriate direction. See also CSURFACE. This curve is not necessarily in the surface Srf. It is equal to, C(t) = m Pij Bi (t), (7) i=0 and similar for the other parametric direction. Example: Crv = CMESH( Srf, COL, 0 ); extracts the ﬁrst column of surface Srf as a curve. MFROMMESH. 11.2.78 See also CSURFACE. See also SMESH, CMOEBIUS CurveType CMOEBIUS( CurveType Crv, NumericType Ratio ) rebalances the weights of a rational curve using the Moebius transformation. The shape of the curve remains identical while the speed is modiﬁed. Ratio controls the ratio between the last and the ﬁrst weights. If Ratio = 0, the ﬁrst and last weights are made equal. See also SMOEBIUS. 11.2.79 CMORPH CurveType CMORPH( CurveType Crv1, CurveType Crv2, NumericType Method, NumericType Blend ) or ListType CMORPH( CurveType Crv1, CurveType Crv2, NumericType Method, NumericType Blend ) IRIT Solid modeler G. Elber 73 create a new curve which is a metamorph of the two given curves. The two given curves must be compatible (see FFCOMPAT) before this blend is invoked. This is very useful if a sequence that ”morphs” one curve to another is to be created. Several metamorphosis methods are supported according to the value of Method, 0 1 2 3 4 5 Simple convex blend. Corner/Edge cutting scheme, scaled to same curve length. Corner/Edge cutting scheme, scaled to same bounding box. Same as 1 but with ﬁltering out of tangencies. Same as 2 but with ﬁltering out of tangencies. Multiresolution decomposition based metamorphosis. See CMULTRES. In Method 1, Blend is a number between zero (Crv1) and one (Crv2) deﬁning the similarity to Crv1 and Crv2, respectively. A single curve is returned. In Methods 2 to 5, Blend is a step size for the metamorphosis operation and a whole list describing the entire metamorphosis operation is returned. Examples: for ( i = 0, 1, 300, c = CMORPH( crv1a, crv1b, 0, i / 300.0 ): color( c, yellow ): viewobj( c ) ); crvs = CMORPH( crv1a, crv1b, 2, 0.003 ); snoc( crv1b, crvs ); for ( i = 1, 1, sizeof( crvs ), c = nth( crvs, i ): color( c, yellow ): viewobj( c ) ); Turtle2 = ffmatch( Wolf, Turtle, 20, 100, 2, false, 2 ); ffcompat( Wolf, Turtle2 ); for ( i = 0, 1, 25, c = CMORPH( Wolf, Turtle2, 0, i / 25 ): color( c, yellow ): viewobj( c ) ); creates three metamorphosis animation sequences, one that is based on a convex blend, and two that are based on corner/edge cutting schemes. See also PMORPH, SMORPH, TMORPH, and FFMATCH. See Figure 30. 11.2.80 CMULTIRES ListType CMULTIRES( CurveType Crv, NumericType Discont, NumericType LeastSquares ) IRIT Solid modeler G. Elber 74 Figure 30: A morphing sequence using convex blend (top left), edge cutting (top right), and using FFMATCH and convex blend (bottom). computes a multiresolution decomposition of curve Crv using least squares approximation, if LeastSquares is TRUE, or using B-Wavelets if LeastSquares is FALSE. The latter is optimal but slower. The resulting list of curves describes an hierarchy of curves in linear subspaces of the space in which Crv lay. If LeastSquares is TRUE, the curves could be summed algebraically to form Crv. Each of the curves in the hierarchy is a least squares approximation of Crv in the subspace in which it is deﬁned. If LeastSquares is FALSE, a list of orthogonal projections of the Crv onto the prescibed subspaces (by the knot sequences) is provided. Finally, Discont is a Boolean ﬂag that controls the way tangent discontinuities are preserved throughout the decomposition. If, however, Discont is -1, LeastSquares will indicate the index of the knot in Crv to compute its BWavelet function. Example: MRCrv = CMULTIRES( Animal, false, true ); sum = nth( MRCrv, 1 ); MRCrvs = list( sum * tx( 3.0 ) ); for ( ( i = 2 ), 1, sizeof( MRCrv ), sum = symbsum( sum, nth( MRCrv, i ) ): snoc( sum * tx( ( 3 - i ) * 1.5 ), MRCrvs ) ); All = MRCrvs * sc ( 0.25 ); view( All, on ); computes a multiresolution decomposition to curve CrossSec as MRCrv and displays all the decomposition levels by summing them all up. The use of none as on object name allows one to IRIT Solid modeler G. Elber 75 Figure 31: A multiresolution decomposition of a curve of an animal using least squares. The original curve is shown on the left. display an object in the display device without replacing the previous object in the display device, carrying the same name. This creates two metamorphosis animation sequences, one based on a convex blend and one based on a corner/edge cutting scheme. See Figure 31. 11.2.81 CNORMAL VectorType CNORMAL( CurveType Crv, NumericType TParam ) computes the normal vector to curve Crv at the parameter values TParam. The returned vector has a unit length. Example: Normal = CNORMAL( Crv, 0.5 ); computes the normal to Crv at the parameter value 0.5. See also CNRMLCRV, CTANGENT. 11.2.82 CNRMLCRV CurveType CNRMLCRV( CurveType Crv ) symbolically computes a vector ﬁeld curve representing the non-normalized normals of the given curve. That is, a normal vector ﬁeld, evaluated at t, provides a vector in the direction of the normal of the original curve at t. The normal curve once computed is in fact equal to kN where k is the curvature of Crv and N is its normal. Example: NrmlCrv = CNRMLCRV( Crv ); See also CCRVTR. 11.2.83 CNVXHULL PolygonType CNVXHULL( PolygonType Poly | PolylineType Poly, NumericType FineNess ); or CurveType CNVXHULL( CurveType Crv, NumericType FineNess ); IRIT Solid modeler G. Elber 76 Figure 32: A convex hull of a set of points and of a freeform B-spline curve. The left show a convex hull of a set of points. The right shows the convex hull (thick line) of a freeform curve. compute the convex hull of the given set of Poly or Curve with tolerance for curves only, which is governed by the polygon subdivision accuracy as set via FineNess. FineNess is ignored for polylines. For curves, the result might be partial if the curve is not closed or periodic. See also CRV2TANS and CRVPTTAN. Example: Pts1 = nil(); Pts2 = nil(); for ( i = 0, 1, 7, R = 0.2 + fmod( i, 2 ) / 2: Pt = ctlpt( E2, R * cos( i * 2 * pi / 8 ), R * sin( i * 2 * pi / 8 ) ): snoc( Pt, Pts1 ): snoc( coerce( Pt, point_type ), Pts2 ) ); Crv = coerce( cbspline( 4, Pts1, list( KV_PERIODIC ) ), KV_OPEN ); CHPts = CNVXHULL( poly( Pts2, 0 ), 0 ); CHCrv = CNVXHULL( Crv, 10 ); computes the convex hull of a given control polygon and freeform curve. See Figure 32. 11.2.84 COERCE AnyType COERCE( AnyType Object, ConstantType NewType ) provides a coercion mechanism between diﬀerent objects or object types. PointType, VectorType, PlaneType, and CtlPtType can be all coerced to each other by using the NewType of POINT TYPE, VECTOR TYPE, PLANE TYPE, or one of E1-E9, P1-P9 (CtlPtType). Similarly, CurveType, SurfaceType, TrimSrfType, TriSrfType, TrivarType, and MultivarType can all be coerced to hold diﬀerent CtlPtType control points, or even diﬀerent open end conditions from KV PERIODIC to KV FLOAT to KV OPEN. Freefroms can be coerced to a Power, Bezier or a B-spline type via the NewType of POWER TYPE, BEZIER TYPE or the BSPLINE TYPE. If a scalar (E1 or P1) curve is coerced to E2 or P2 curve or a scalar (E1 or P1), the surface is coerced to an E3 or P3 surface, and the Y IRIT Solid modeler G. Elber 77 (YZ) coordinate(s) is (are) updated to hold the parametric domain of the curve (surface). That is X = U (Y = V). Curves, Surfaces, and Trivariates can be coerced to/from Multivariates using the CURVE TYPE, SURFACE TYPE, TRIVAR TYPE and MULTIVAR TYPE. Trimmed B-spline surfaces can ve coerced to trimmed Bezier surfaces via a BEZIER TYPE coercion and to untrimmed tensor product pieces using UNTRIMMED TYPE. Example: CrvE2 = COERCE( Crv, E2 ); MultiVar == COERCE( COERCE( MultiVar, surface_type ), multivar_type ); BzrSrfs = COERCE( BspSrf, bezier_type ); coerces Crv to a new curve that will have an E2 CtlPtType control points. Coerction of a projective curve (P1-P9) to a Euclidean curve (E1-E9) does not preseve the shape of the curve. The second example coerces a bivariate MultiVar into a Srf and back and compares the result to the original multivariate MultiVar... The third example coerces a B-spline surface BspSrf to a Bezier form, returning one or more Bezier surfaces representing the same geometry as BspSrf. 11.2.85 COMPOSE CurveType COMPOSE( CurveType Crv1, CurveType Crv2 ) or CurveType COMPOSE( SurfaceType Srf, CurveType Crv ) or CurveType COMPOSE( SurfaceType Srf1, SurfaceType Srf2 ) or CurveType COMPOSE( TrivarType TV, SurfaceType Crv ) or CurveType COMPOSE( TrivarType TV, SurfaceType Srf ) symbolically compute the composition curve or surface. In the above ﬁrst form of Crv1(Crv2(t), Crv1 can be any curve while Crv2 is assumed to be a one-dimensional curve that is either E1 or P1 (higher dimensions are ignored). In the above second form of Srf(Crv(t)), the Srf can be any surface, while the Crv is assumed to be a two-dimensional curve, that is either E2 or P2 (higher dimensions are ignored). In the above third form of Srf1(srf2(u, v)), Srf2 can be any surface, while it is assumed to be a two-dimensional surface, that is either E2 or P2 (higher dimensions are ignored). Srf1 is a Bezier. In the above fourth form of TV(Crv(t)), the Crv can be any curve, while it is assumed to be a three-dimensional curve, that is either E3 or P3 (higher dimensions are ignored). TV is a Bezier. In the above ﬁfth form of TV(Srf(u, v)), the Srf can be any surface, while it is assumed to be a three-dimensional surface, that is either E3 or P3 (higher dimensions are ignored). TV is a Bezier. The second freeform must always be fully contained in the ﬁrst freeform’s parametric domain. Example: IRIT Solid modeler G. Elber 78 Figure 33: A circle in the parametric space of the freefrom surface is composed to create a closed loop curve on the surface using COMPOSE. srf = sbezier( list( list( ctlpt( E3, 0.0, ctlpt( E3, 0.0, ctlpt( E3, 0.0, list( ctlpt( E3, 0.5, ctlpt( E3, 0.5, ctlpt( E3, 0.5, list( ctlpt( E3, 1.0, ctlpt( E3, 1.0, ctlpt( E3, 1.0, crv = circle( vector( 0.5, 0.5, 0.0 ), 0.4 comp_crv = COMPOSE( srf, crv ); 0.0, 0.5, 1.0, 0.0, 0.5, 1.0, 0.0, 0.5, 1.0, ); 0.0 1.0 0.0 1.0 0.0 1.0 1.0 0.0 1.0 ), ), ) ), ), ), ) ), ), ), ) ) ) ); composes a circle Crv to be on the surface Srf. See Figure 33 and also Figure 105. See also TDEFORM. 11.2.86 CON2 PolygonType CON2( VectorType Center, VectorType Direction, NumericType Radius1, NumericType Radius2, NumericType Caps ) creates a truncated CONE geometric object, deﬁned by Center as the center of the main base of the CONE, with the Direction as both the CONE’s axis and the length of CONE, and the two radii Radius1/2 of the two bases of the CONE. If Caps equals zero, no caps are created. If Caps equal one (two), only the bottom (top) cap is created. If Caps equal three, both the top and the bottom caps are created. IRIT Solid modeler G. Elber 79 Figure 34: A cone (left) can be constructed using the CONE constructor and a truncated cone (right) using the constructor CONE2. Unlike the regular cone (CONE) constructor which inherits discontinuities in its generated normals at the apex, CON2 can be used to form a (truncated) cone with continuous normals. See RESOLUTION for the accuracy of the CON2 approximation as a polygonal model. See also CONE. See IRITSTATE’s ”PrimRatSrfs” and ”PrimRatSrfs” state variables. Example: Cone2 = CON2( vector( 0, 0, -1 ), vector( 0, 0, 4 ), 2, 1, 3 ); constructs a truncated cone with bases parallel to the XY plane at Z = −1 and Z = 3, and with radii of 2 and 1 respectively. Both caps are created. See Figure 34. 11.2.87 CONE PolygonType CONE( VectorType Center, VectorType Direction, NumericType Radius, NumericType Caps ) creates a CONE geometric object, deﬁned by Center as the center of the base of the CONE, Direction as the CONE’s axis and height, and Radius as the radius of the base of the CONE. If Caps equals zero, no cap is created. If Caps equal one, the bottom (top) cap is created. See RESOLUTION for accuracy of the CONE approximation as a polygonal model. Example: Cone1 = CONE( vector( 0, 0, 0 ), vector( 1, 1, 1 ), 1, 1 ); constructs a cone based in an XY parallel plane, centered at the origin with radius 1 and with tilted apex at ( 1, 1, 1 ). Only the bottom cap is created. See IRITSTATE’s ”PrimRatSrfs” and ”PrimRatSrfs” state variables. See also CON2. See Figure 34. G. Elber IRIT Solid modeler 11.2.88 80 CONICSEC CurveType CONICSEC( ListType ABCDEF, NumericType ZLevel, PointType StartPoint, PointType EndPoint ) or {PolygonType | SurfaceType } CONICSEC( ListType TwoCurves, NumericType ZLevel, NumericType Dist, NumericType EvalCurve ) In the ﬁrst form, this will construct a quadratic form that represents the planar conic section prescribed by the list of six coeﬃcients ABCDEF as: Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0, (8) The conic will be parallel to the XY plane at Z level of Zlevel. The section of the curve will be from StartPoint to EndPoint, or alternatively, unlimited by specifying ’oﬀ’ for StartPoint and EndPoint. The conic might be rational (for circles and ellipses, for example) or intergral (for parabolas). Alternatively, in the second form, if the ﬁrst list object parameter contains two planar curves in the XY plane, a piecewise linear curve at Z level of Zlevel is computed that presents the elliptic/hyperbolic distance Dist from the given two curves. The elliptic distance refers to the sum of distance (that equal Dist) to the two curves, while hyperbolic distance refers to the diﬀerence of distances. Finally, if EvalCurve = 0, the surface whose zero set is the desired curve, is returned instead. If EvalCurve = 1, distance curves are returned in the parametric space as correspondence between the two curves’ parameters. If EvalCurve = 2, the conic curves themselves are returned. Note only elliptic surfaces are compact and are reconstructed in whole. Example: Circ2 = CONICSEC( list( 1, 0, 1, 0, -0.5, -1 ), 0.0, point( 1.0, 0.0, 0.0 ) * ty( 0.25 ), point( -0.707, -0.707, 0.0 ) * ty( 0.25 ) ); Elp1 = CONICSEC( list( 1, 2, 4, 0.5, 2, -0.2 ), 0.0, off, off ); Prb1 = CONICSEC( list( 0.1, 0, 0, 0, 1, -1 ), 2, off, off ) * sc( 0.1 ); constructs a (portion of a) circle, an ellipse and a parabola as conic sections, and, c1 = cbspline( 3, list( ctlpt( E2, -1, -1 ), ctlpt( E2, 1, -1 ), ctlpt( E2, 1, 1 ), ctlpt( E2, -1, 1 ) ), list( KV_OPEN ) ); c2 = -c1 * sx( -1 ) * tx( 5 ); view( list( c1, c2 ), 1 ); G. Elber IRIT Solid modeler 81 resolution = 15; DistCrvE = list( CONICSEC( CONICSEC( CONICSEC( CONICSEC( CONICSEC( color( DistCrvE, green ); list( list( list( list( list( c1, c1, c1, c1, c1, c2 c2 c2 c2 c2 ), ), ), ), ), 1.0, 10, 2 ), 1.0, 9, 2 ), 1.0, 8, 2 ), 1.0, 7, 2 ), 1.0, 6, 2 ) ); computes the conic distance to the two curves c1 and c2 at distances of 6, 7, 8, 9, and 10. See also QUADRIC. 11.2.89 CONTOUR PolygonType CONTOUR( SurfaceType ContouredSrf, PlaneType ContourPlane, NumericType SubdivTol ) or PolygonType CONTOUR( SurfaceType ContouredSrf, PlaneType ContourPlane, NumericType SubdivTol, SurfaceType MappedSrf ) or PolygonType CONTOUR( SurfaceType ContouredSrf, PlaneType ContourPlane, NumericType SubdivTol, SurfaceType MappedSrf, ListType ValidatePt ) contours surface ContouredSrf by intersecting plane ContourPlane with ContouredSrf. If SubdivTol ¡ 1, the contours are derived using the multivariate solver and SubdivTol controls the subdivision accuracy. If SubdivTol ¿ 1 a polygonal approximating of ContouredSrf is ﬁrst derived and then polygon-polygon intersections are computed. If ContouredSrf is a scalar ﬁeld surface of type E1 or P1 and MappedSrf is provided, ContouredSrf is contoured above its parametric domain (U is X, V is Y) and the resulting parametric curve is composed with MappedSrf to yield the returned value. Further, if ValidatePt is prescribed, it should contain two elements, a vector, V, and an angle, A, in degrees. Only the contour points for which the normal of surface MappedSrf there has less than A degrees from V are returned. Example: resolution = 20; nglass = snrmlsrf( glass ) * vector( 1, 1, 1 ); sils = contour( nglass, plane( 1, 0, 0, 0 ), glass ); color( sils, cyan ); attrib( sils, "dwidth", 4 ); view( list( axes, glass, sils ), on ); IRIT Solid modeler G. Elber 82 Figure 35: Computes the silhouette of a freeform glass surface from viewing direction (1, 1, 1). On the left, the original view is seen. On the right, a diﬀerent, general, view is provided. computes the normal ﬁeld of the surface glass, projects it onto the viewing direction of (1, 1, 1) and contours the resulting scalar ﬁeld with the plane X = 0, to extract the silhouette curves from viewing direction (1, 1, 1). See Figure 35. 11.2.90 CONVEX PolygonType CONVEX( PolygonType Object ) or ListType CONVEX( ListType Object ) convert non-convex polygons in Object, into convex ones. New vertices are introduced into the polygonal data during this process. The Boolean operations require the input to have convex polygons only (although it may return non convex polygons...) and it automatically converts non-convex input polygons into convex ones, using this same routine. However, some external tools (such as irit2ray and poly3d-h) require convex polygons. This function must be used on the objects to guarantee that only convex polygons are saved into data ﬁles for these external tools. Example: CnvxObj = CONVEX( Obj ); save( "data", CnvxObj ); converts non-convex polygons into convex ones, so that the data ﬁle can be used by external tools requiring convex polygons. 11.2.91 COORD AnyType COORD( AnyType Object, NumericType Index ) G. Elber IRIT Solid modeler 83 extracts an element from a given Object, at index Index. From a PointType, VectorType, PlaneType, CtlPtType and MatrixType. A NumericType is returned with Index 0 for the X axis, 1 for the Y axis etc. Index 0 denotes the weight of CtlPtType. For a PolygonType that contains more than one polygon, the Indexth polygon is returned. For a PolygonType that contains a single Polygon, the Indexth vertex is returned. For a freeform object (curve, surface, etc.), the Indexth CtlPtType is returned. For a ListType, COORD behaves like NTH and returns the Indexth object in the list. For a StringType, the Indexth character is returned as its ASCII numeric code. Example: a = vector( 1, 2, 3 ); vector( COORD( a, 0 ), COORD( a, 1 ), COORD( a, 2 ) ); a = ctlpt( P2, 6, 7, 8, 9 ); ctlpt( P3, coord( a, 0 ), coord( a, 1 ), coord( a, 2 ), coord( a, 3 ) ); a = plane( 10, 11, 12, 13 ); plane( COORD( a, 0 ), COORD( a, 1 ), COORD( a, 2 ), COORD( a, 3 ) ); constructs a vector/ctlpt/plane and reconstructs it by extracting the constructed scalar components of the objects using COORD. See also COERCE. 11.2.92 COVERISO CurveType COVERISO( TrivarType TV, NumericType NewOfStrokes, NumericType StrokeType, PointType MinMaxPwrLen, NumericType StepSize, NumericType IsoVal, VectorType ViewDir ) computes a coverage for an iso surface of a trivariate function TV, using curves. NewOfStrokes strokes are distributed on the iso surface with a length that is set via MinMaxPwrLen. MinMaxPwrLen is a triplet of the form (Min, Max, Power) that determines the length of the strokes as, Avg = or, M ax + M in , 2 Dev = M ax − M in , 2 Length = Avg + Dev ∗ Random(0, 1)P wr . (9) (10) StepSize controls the steps size of the piecewise linear approximation formed and should typically be smaller than Min. StrokeType can be one of, 1 2 3 4 5 6 Draw Draw Draw Draw Draw Draw strokes strokes strokes strokes strokes strokes along along along along along along minimal principal curvature. maximal principal curvature. both principal curvatures. constant X planes. constant Y planes. constant Z planes. IRIT Solid modeler G. Elber 84 Figure 36: A uniform coverage of 500 curved strokes of an iso surface of a trivariate function, computed using COVERISO command. IsoVal controls the constant value of the iso surface level. See also ADAPISO, COVERPT, MRCHCUBE, TVLOAD. Finally, ViewDir is the direction of view, used for silhouette computation. Example: IsoVal = 0.12; Cover = CoverIso( ThreeCyls, 500, 1, vector( 3, 10, 1.0 ), 0.2, IsoVal ); draws 500 strokes on the iso surface of trivariate ThreeCyls at iso value IsoVal and step size of 0.2. Strokes are drawn in length of 3 to 10 along lines of curvatures of minimal curvature. See Figure 36 and also Figure 64. 11.2.93 COVERPT PolygonType COVERPT( PolygonType Model, NumericType NumOfPts, VectorType ViewDir ) computes a uniform point distribution on the given polygonal Model. Approximately NumOfPts points are uniformly distributed on the model’s surface, provided ViewDir is the zero vector. If ViewDir is a non zero vector, the distribution is made to be uniform from this given viewing direction. In all cases, NumOfPts is an upper bound of the the real number of distributed points, which will be in the same order. IRIT Solid modeler G. Elber 85 Figure 37: A uniform coverage of 1000 and 3000 points of a polygonal model in three space, computed using the COVERPT command. On the left, the distribution is directional, from the viewing direction, while on the right, shows a point distribution that is uniform in 3-space. Distant points are smaller, emulating point depth cueing. See also ADAPISO, COVERISO, FFPTDIST. Example: Pts1 = CoverPt( solid1, 1000, vector( 0, 0, 0 ) ); Pts2 = CoverPt( solid1, 3000, vector( 0, 0, -1 ) ); computes two uniform distributions of 1000 and 3000 points on Solid1. Pts1 is uniform in three space, while Pts2 is viewed uniform from the -Z direction. See Figure 37. 11.2.94 CPINCLUDE NumericType CPINCLUDE( CurveType Crv, PointType Pt, NumericType Tol ) tests if a point Pt is inside a 2D closed curve Crv. Returns TRUE if inside, FALSE otherwise. Tol governs the tolerance of the computations. Example: if ( CPINCLUDE( Crv, pt ) != 0, ... ); See also PPINCLUDE. G. Elber IRIT Solid modeler 11.2.95 86 CPOWER CurveType CPOWER( ListType CtlPtList ) creates a polynomial/rational curve out of the provided control point list. The created curve is employing the monomial power basis. CtlPtList is a list of control points, all of which must be of type (E1-E9 P1-P9), or regular PointType deﬁning the curve’s control polygon. The curve’s point type will be of a space which is the union of the spaces of all points. The created curve is the polynomial (or rational), C(t) = k Pi ti , (11) i=0 where Pi are the control points CtlPtList, and k is the degree of the curve, which is one less than the number of points. Example: c = CPOWER( list( ctlpt( E3, 0, 1, 0 ), ctlpt( E3, 1, 0, 0 ), ctlpt( E3, 0, 0, 1 ) ) ); c == coerce( coerce( c, bezier_type ), power_type ); constructs a quadratic power basis curve, coerces it to a Bezier form, coerces the Bezier form back to the power basis, and then compares the result for equality. See also CBEZIER, CBSPLINE and SPOWER. 11.2.96 CRAISE CurveType CRAISE( CurveType Curve, NumericType NewOrder ) Raise Curve to the NewOrder Order speciﬁed. Example: Crv = cbezier( list( ctlpt( E2, -0.7, ctlpt( E2, 0.0, ctlpt( E2, 0.7, Crv2 = CRAISE( Crv, 5 ); 0.3 ), 1.0 ), 0.0 ) ) ); raises the 90 degrees corner Bezier curve Crv to be a quadratic. See Figure 38. See also CREDUCE, TRAISE, SRAISE, and MRAISE. 11.2.97 CRC2CRVTAN ListType CRC2CRVTAN( CurveType Crv1, CurveType Crv2, NumericType Radius, NumericType Tol ) computes all circles that are bi-tangent to the given two curves Crv1 and Crv2. The circles will posses a radius of Radius. The accuracy of the computation is governed by the tolerance Tol. Returned is a list center point locations with ”Params” attributes of parameter values of the tangent locations at the two curves. Example: IRIT Solid modeler G. Elber 87 Figure 38: Raises a 90 degrees corner quadratic Bezier curve to a quintic using CRAISE. The control polygons are also shown. Cntrs = CRC2CRVTAN( c1, c2, R, 1e-3 ); computes all the circles of radius 0.1 that are bi-tangent to the two curves c1 and c2. Tolerance of computation is 1e-3. See Figure 39. See also SKEL2DINT, CRV2TANS, TNSCRCR. 11.2.98 CREDUCE CurveType CREDUCE( CurveType Curve, NumericType NewOrder ) reduces the Curve to the NewOrder Order speciﬁed. This function approximates the lower order curve in the inﬁnity norm sense, minimizing the maximal deviation between the original curve Curve and the low order curve NewOrder. NewOrder will identify with Curve only if Curve was degree raised before. Example: Crv = cbezier( list( ctlpt( E2, -0.7, 0.3 ), ctlpt( E2, 0.0, 1.0 ), ctlpt( E2, 0.7, 0.0 ) ) ); Crv2 = CREDUCE( craise( Crv, 5 ), 3 ); Crv == Crv2; Should restore the original quadratic order. I.e. Crv2 should identify with Crv and ”Crv == Crv2;” should return TRUE. See also CRAISE. 11.2.99 CREFINE CurveType CREFINE( CurveType Curve, NumericType Replace, ListType KnotList ) IRIT Solid modeler G. Elber 88 Figure 39: Computes all the bi-tangent circles to the given two curves via the CRC2CRVTAN function. provides the ability to Replace a knot vector of Curve, or reﬁne it. KnotList is a list of knots at which to reﬁne Curve. All knots should be contained in the parametric domain of the Curve. If the knot vector is replaced, the length of KnotList should be identical to the length of the original knot vector of the Curve. If Curve is a Bezier curve, it is automatically promoted to be a B-spline curve. Example: Crv2 = CREFINE( Crv, FALSE, list( 0.25, 0.5, 0.75 ) ); reﬁnes Crv and adds three new knots at 0.25, 0.5, and 0.75. See Figure 40. See also SREFINE, TREFINE, and MREFINE. 11.2.100 CREGION CurveType CREGION( CurveType Curve, NumericType MinParam, NumericType MaxParam ) extracts a region from the Curve between MinParam and MaxParam. Both MinParam and MaxParam should be contained in the parametric domain of the Curve, except for Bezier curves when MinParam and MaxParam can be arbitrary (extrapolating if not between zero and one). Example: SubCrv = CREGION( Crv, 0.3, 0.6 ); G. Elber IRIT Solid modeler 89 Figure 40: Reﬁnes a 90 degrees corner quadratic Bezier curve at three interior knots (the result is a B-spline curve) using CREFINE. The control polygons are also shown. extracts the region from the Crv from the parameter value 0.3 to the parameter value 0.6. See Figure 41. See also SREGION, TREGION, and MREGION. 11.2.101 CREPARAM CurveType CREPARAM( CurveType Curve, NumericType MinParam, NumericType MaxParam ) reparametrizes the Curve over a new domain from MinParam to MaxParam. This operation does not aﬀect the geometry of the curve and only aﬃne transforms its knot vector. A Bezier curve will automatically be promoted into a B-spline curve by this function. If MinParam equals MaxParam and both equates with one of the parameterization keywords of PARAM UNIFORM, PARAM CENTRIP, PARAM CHORD, or PARAM NIELFOL, then that parametrization is approximated for the curve, by changing the knot sequence. Note this last operation aﬀects the geometry of the curve. Example: arc1 = arc( vector( vector( vector( crv1 = arc( vector( vector( vector( arc( vector( vector( vector( 0.0, 0.0, 0.0 ), 0.5, 2.0, 0.0 ), 1.0, 0.0, 0.0 ) ); 1.0, 0.0, 0.75 ), 0.75, 0.0, 0.7 ), 0.5, 0.0, 0.85 ) ) + 0.5, 0.0, 0.75 ), 0.75, 0.0, 0.8 ), 1.0, 0.0, 0.65 ) ); IRIT Solid modeler G. Elber 90 Figure 41: Extracts a sub region from a curve using CREGION. arc1 = CREPARAM( arc1, 0, 10 ); crv1 = CREPARAM( crv1, 0, 10 ); sets the domain of the given two curves to be from zero to ten. The Bezier curve arc1 is promoted to a B-spline curve. See also SREPARAM, TREPARAM, and MREPARAM. 11.2.102 CROSSEC PolygonType CROSSEC( PolygonType Object ) This feature is NOT implemented. 11.2.103 CRV2TANS ListType CRV2TANS( CurveType Crv, NumericType FineNess ) or ListType CRV2TANS( ListType TwoCrvs, NumericType FineNess ) computes all the self bi-tangents of a Crv or all bi-tangents between TwoCrvs, in the XY plane. That is, all lines that are tangent to Crv at two diﬀerent locations. A list of points with X and Y coeﬃcients representing the two parametric locations on Crv or on TwoCrvs of the bi-tangent is returned. FineNess controls the numerical accuracy (sploution separation) of the computation. A value of 0.01 will provide a good start and the smaller this number is, the better the accuracy will be. See also CRVPTTAN and CNVXHULL. Example: IRIT Solid modeler G. Elber 91 Figure 42: Computes the bi-tangents of a freeform curve, using CRV2TANS. Tans = nil(); Crv2Tns = Crv2Tans( Crv, 0.01 ); for ( i = 1, 1, sizeof( Crv2Tns ), pt = nth( Crv2Tns, i ): snoc( ceval( Crv, coord( pt, 0 ) ) + ceval( Crv, coord( pt, 1 ) ), Tans ) ); ﬁnds the bi-tangents of Crv and converts them to a set of line segments. See Figure 42. See also CRC2CRVTAN, TNSCRCR 11.2.104 CRVKERNEL AnyType CRVKERNEL( CurveType Crv, NumericType Gamma, NumericType Euclid, AnyType Fineness, NumericType Mode ) computes the (gamma) kernel of a given planar curve Crv. If Gamma is zero, regular kernel is computed. Else, the gamma curves of Gamma degrees is being computed. If Euclid is TRUE then the result is returned in the Euclidean space, or if zero, in the parametric space. Mode can be 0 for a (gamma) kernel solution, 1 to extract silhouette sampling only out of the trivariate function, and 2 for the gamma kernel surface/trivariate functions themselves to be returned. Fineness controls the reﬁnement that is applied to the numeric solution. For Mode 0 it sets the number of knots to insert into the (x, y, t) trivariate function. In Mode 2, it lists two numeric values, the subdivision and IRIT Solid modeler G. Elber 92 numeric tolerances, of the silhouette extraction process (See MZERO for their meaning). In Mode 2, it controls the extent of the surfaces/trivariates. Example: Krnl = CrvKernel( Crv, 0, 0, list( 2, 3, 1 ), 0 ); computes the regular kernel of curve Crv with a reﬁnement of (2, 3, 1) in the three (x, y, t) axes of the computed trivariate function. 11.2.105 CRVLNDST NumericType CRVLNDST( CurveType Crv, PointType PtOnLine, VectorType LnDir, NumericType IsMinDist, NumericType Epsilon ) or ListType CRVLNDST( CurveType Crv, PointType PtOnLine, VectorType LnDir, NumericType IsMinDist, NumericType Epsilon ) compute the closest (if IsMinDist is TRUE, farthest if FALSE) point on the Curve to the line speciﬁed by PtOnLine and LnDir as a point on the line and a line direction. Since this operation is partially numeric, Epsilon is used to set the needed accuracy. It returns the parameter value of the location on Crv closest to the line. If, however, Epsilon is negative, -Epsilon is used instead, and all local extrema in the distance function are returned as a list (both minima and maxima). If the line and the curve intersect, the point of intersection is returned as the minimum. Example: Param = CRVLNDST( Crv, linePt, lineVec, TRUE, 0.001 ); ﬁnds the closest point on Crv to the line deﬁned by linePt and lineVec. See Figure 43. 11.2.106 CRVPTDST NumericType CRVPTDST( CurveType Crv, PointType Point, NumericType IsMinDist, NumericType Epsilon ) or ListType CRVPTDST( CurveType Crv, PointType Point, NumericType IsMinDist, NumericType Epsilon ) compute the closest (if IsMinDist is TRUE, farthest if FALSE) point on Crv to Point. Since this operation is partially numeric, Epsilon is used to set the needed accuracy. It returns the parameter value of the location on Crv closest to Point. If, however, Epsilon is negative, -Epsilon is used instead, and all local extrema in the distance function are returned as a list (both minima and maxima). Example: Param = CRVPTDST( Crv, Pt, FALSE, 0.0001 ); ﬁnds the farthest point on Crv from point Pt. See Figure 44. IRIT Solid modeler G. Elber 93 Figure 43: Computes the locations on the freeform curve with local extreme distance to the given line, using CRVLNDST. 11.2.107 CRVPTTAN ListType CRVPTTAN( CurveType Crv, PointType Pt, NumericType FineNess ) computes all the tangents to Crv that go through point Pt, all in the XY plane. A list of points with X and Y coeﬃcients representing the parametric locations on Crv of the bi-tangent is returned. FineNess controls the numerical accuracy of the computation. A value of 0.01 will provide a good start, and the smaller this number is, the better the accuracy will be. See also CRV2TANS and CNVXHULL. Example: Tans = nil(); Pt = point( 2, 0, 0 ); CrvPtTns = CrvPtTan( Crv, Pt, 0.01 ); for ( i = 1, 1, sizeof( CrvPtTns ), snoc( ceval( Crv, nth( CrvPtTns, i ) ) + coerce( Pt, e3 ), Tans ) ); ﬁnds the tangents of Crv through Pt and converts them to a set of line segments. See Figure 45. IRIT Solid modeler G. Elber 94 Figure 44: Computes the locations on the freeform curve with local extreme distance to the given point, using CRVPTDST. Figure 45: Computes the tangents of a freeform curve through a point, using CRVPTTAN. G. Elber IRIT Solid modeler 95 Figure 46: Approximates a sine wave curve using CSINE. 11.2.108 CSINE CurveType CSINE( NumericType NumCycles, NumericType Samples, NumericType CtlPtsPerVCycle ) constructs a polynomial approximation of a sine wave planar curve of NumCycles cycles. The curve is approximated as a least sqaures ﬁt of Samples samples and CtlPtsPerVCycle control points per loop. Example: SineW = csine( 3, 100, 16 ); See Figure 46 for this sine wave of 3 loops. See also CHELIX, CSPIRAL 11.2.109 CSPIRAL CurveType CSPIRAL( NumericType NumLoops, NumericType Pitch, NumericType Samples, NumericType CtlPtsPerLoop ) constructs a polynomial approximation of a spiral planar curve of NumLoops loops and speciﬁed Pitch. The curve is approximated as a least sqaures ﬁt of Samples samples and CtlPtsPerLoop control points per loop. Example: Spiral = cspiral( 5, 0.7, 500, 6 ); See Figure 47 for this spiral of 5 loops. See also CHELIX, CSIN 11.2.110 CSURFACE CurveType CSURFACE( SurfaceType Srf, ConstantType Direction, NumericType Param ) G. Elber IRIT Solid modeler 96 Figure 47: Approximates a spiral curve using CSPIRAL. or CurveType CSURFACE( TriSrfType Srf, ConstantType Direction, NumericType Param ) extract an isoparametric curve out of Srf in the speciﬁed Direction (ROW or COL (or DEPTH for triangular surface) at the speciﬁed parameter value Param. Param must be contained in the parametric domain of Srf in Direction direction. The returned curve is in the surface Srf. For a tensor product surface, it is equal to, C(t) = S(t, v0 ) = m n Pij Bi (t)Bj (v0 ) = i=0 j=0 m i=0 ⎛ ⎝ n j=0 ⎞ Pij Bj (u0 )⎠ Bi (t) = m Qi Bi (t), (12) i=0 where Qi = nj=0 Pij Bj (u0 ) are the coeﬃcients of the returned curve, and similar to the other parametric direction S(u0 , t). Param of CSURFACE is v0 in equation (12) For a triangular Bezier surface of degree n, it is equal to, C(v) = n! i j k u v w Pijk i!j!k! 0 i,j,k G. Elber IRIT Solid modeler = i,j = i = i 97 n! ui v j (1 − u0 − v)n−i−j Pijk i!j!(n − i − j)! 0 n! (n − i)! ui0 v j (1 − u0 − v)n−i−j Pijk i!(n − i)! j!(n − i − j)! j n! (n − i)! ui0 (1 − u0 )n−i i!(n − i)! j!(n − i − j)! j v 1 − u0 j (1 − v )n−i−j Pijk 1 − u0 as i + j + k = n, and u + v + w = 1.0. Hence, the resulting isoparametric curve is a weighted sum of n + 1 Bezier curves of varying degrees n − i formed by the diﬀerent rows/cols/depths of the triangular mesh. Param of CSURFACE is u0 in equation (13) Example: Crv = CSURFACE( Srf, COL, 0.45 ); extracts an isoparametric curve in the COLumn direction at the parameter value of 0.15 from surface Srf. See also CMESH, COMPOSE, FFKNTLNS, STRIVAR, and MFROMMV. See Figure 48. 11.2.111 CTANGENT VectorType CTANGENT( CurveType Curve, NumericType Param, NumericType Normalize ) computes the tangent vector to the Curve at the parameter value Param. The returned vector will have a unit length, if Normalize is TRUE. Example: Tang = CTANGENT( Crv, 0.5, true ); computes the unit tangent vector to Crv at the parameter value of 0.5. See also CNORMAL, CNRMLCRV. 11.2.112 CTLPT CPt = CTLPT( ConstantType PtType, NumericType Coord1, ... ) constructs a single control point to be used in the construction of curves and surfaces. Points can have from one to ﬁve dimensions, and may be either Euclidean or Projective (rational). Point type is set via the constants E1 to E9 and P1 to P9. The coordinates of the point are speciﬁed in order; weight is ﬁrst if rational. Examples: CPt1 = CTLPT( E3, 0.0, 0.0, 0.0 ); CPt2 = CTLPT( P2, 0.707, 0.707, 0.707 ); constructs an E3 point at the origin and a P2 rational point with a weight of 0.707. The Projective Pi points are speciﬁed as CTLPT(Pn, W, W X1, ... , W Xn). IRIT Solid modeler G. Elber 98 Figure 48: Extracts an isoparametric curve from the given surface, using CSURFACE. 11.2.113 CTRIMSRF ListType CTRIMSRF( TrimSrfType TSrf, NumericType Parametric ) extracts the trimming curves of a trimmed surface TSrf. If Parametric is not zero, then the trimming curves are extracted as parametric space curves of TSrf. Otherwise, the trimming curves are evaluated into Euclidean space as curves on the surface TSrf. Example: TrimCrvs = CTRIMSRF( TrimSrf, FALSE ); extracts the trimming curves of TrimSrf as Euclidean curves on TrimSrf. See Figure 49. 11.2.114 CTRLCYCLE ListType CTRLCYCLE( CurveType Crv, NumericType CycleLength, NumericType SubdivTol, NumericType NumericTol ) Computes a control cycle of the given CycleLength around the given control Crv. Solution is computed by mapping the problem to an algebraic set of constraints. See MZERO for the meaning of SubdivTol and NumericTol. IRIT Solid modeler G. Elber 99 Figure 49: Extracts the trimming curves in Euclidean space (middle) and parametric space (right) of a trimmed surface (left), using CTRIMSRF. Figure 50: Cycles of length three (in black) to a linear control curve (left) and a cubic control curve (right), computed using CTRLCYCLE. Example: CyclePts = CTRLCYCLE( CtrlCrv, 3, 0.001, 1e-8 ); computes a cycle of length 3 to curve CtrlCrv. See Figure 50. 11.2.115 CMESH 11.2.116 CUBICCRVS ListType CUBICCRVS( CurveType Crv, NumericType Tolerance, NumericType MaxLen ) IRIT Solid modeler G. Elber 100 approximates given curve Crv using piecewise cubic curves upto the prescribed tolerance Tolerance. If MaxLen is positive it is used to limit the arc length of the cubic curves’ segments. Example: PCubicCrvs = CUBICCRVS( Crv, 0.01, 0.5 ); creates a piecewise cubic approximation to curve Crv upto tolerance 0.01 and maximal arc length of cubic segments of 0.5. See also QUADCRVS, CBIARCS, and CCUBICS. 11.2.117 CVIEWMAP PolygonType CVIEWMAP( CurveType Crv, CurveType ViewCrv, NumericType SubdivTol, NumericType NumerTol, NumericType TrimInvisible ) computes algebraic constraints that reﬂects the visible domain of planar curve Crv as seen from direction prescribed by planar vector curve ViewCrv. ViewCrv is typically a unit circle curve, parametrizing all possible (360 degrees) planar views. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. If TrimInvisible is FALSE, the return set prescribes the 2D silhouette locations on Crv from the speciﬁc view direction. If TrimInvisible is TRUE, attempt ismade to remove the invisile portions. Result is returned as 3D polylines, in (t, v, r) space where t and r parametrize Crv and v parametrizes ViewCrv. This, since a silhouette point Crv(t) could hide a independent curve location Crv(r). Example: ViewMap = CVIEWMAP( Crv, pcircle( vector( 0, 0, 0 ), 1 ), 0.1, 1e-6, 0 ); See also CANGLEMAP, CVISIBLE, CARRANGMNT. 11.2.118 CVISIBLE PolygonType CVIVISIBLE( CurveType Crv, PointType Pt, NumericType Eps ) or PolygonType CVIVISIBLE( CurveType Crv, VectorType Dir, NumericType Eps ) computes the visible regions of planar curve Crv as seen from either view point Pt or from view direction Dir. Eps controls the accuracy of the computation. Dir must have its Z components zero, whereas Pt’s Z coeﬃcient must be one. Example: Crvs = CVISIBLE( c, Pt, 1e-5 ); See Figure 51 for an example. See also CANGLEMAP, CVIEWMAP, CARRANGMNT, SETCOVER. IRIT Solid modeler G. Elber 101 Figure 51: The visibility of the given curve on the left is sampled along its 360 degrees to create a visibility atlas of the curve on the right, using CVISIBLE. Then SETCOVER is used to ﬁnd the minimal set that can see the entire curve, esselntially solving the so-called art-gallery problem. 11.2.119 CYLIN PolygonType CYLIN( VectorType Center, VectorType Direction, NumericType Radius, NumericType Caps ) creates a CYLINder geometric object, deﬁned by Center as the center of the base of the CYLINder, Direction as the CYLINder’s axis and height, and Radius as the radius of the base of the CYLINder. If Caps equals zero, no caps are created. If Caps equal one (two), only the bottom (top) cap is created. If Caps equal three, both the top and the bottom caps are created. See RESOLUTION for the accuracy of the CYLINder approximation as a polygonal model. See IRITSTATE’s ”PrimRatSrfs” and ”PrimRatSrfs” state variables. Example: Cylinder1 = CYLIN( vector( 0, 0, 0 ), vector( 1, 0, 0 ), 10, 3 ); constructs a cylinder with two caps of radius 10 along the X axis from the origin to X = 1. See Figure 52. 11.2.120 CZEROS ListType CZEROS( CurveType Crv, NumericType Epsilon, NumericType Axis ) computes the zero set of the given Crv in the given axis (1 for X, 2 for Y, 3 for Z). Since this computation is numeric, an Epsilon is also required to specify the desired tolerance. It returns a list of all the parameter values (NumericType) the curve is zero. Example: IRIT Solid modeler G. Elber 102 Figure 52: A cylinder primitive can be constructed using the CYLIN constructor. xzeros = CZEROS( cb, 0.001, 1 ); pt_xzeros = nil(); pt = nil(); for ( i = 1, 1, sizeof( xzeros ), pt = ceval( cb, nth( xzeros, i ) ): snoc( pt, pt_xzeros ) ); interact( list( axes, cb, pt_xzeros ), 0 ); computes the X zero set of curve cb with error tolerance of 0.001. This set is then scanned in a loop and evaluated to the curve’s locations, which are then displayed. See also CINFLECT. See Figure 53. 11.2.121 DIST2FF SurfaceType DIST2FF( CurveType Crv1, CurveType Crv2, NumericType DistType ) or MultivarType DIST2FF( CurveType Crv1, SurfaceType Srf2, NumericType DistType ) or MultivarType DIST2FF( SurfaceType Srf1, SurfaceType Srf2, NumericType DistType ) computes the distance function between the two given freeform shapes. The returned variety is bi-variate, tri-variate, or a four-variate, depending on the dimensionality of the input, in order. Based on DistType, the following distance functions could be used: IRIT Solid modeler G. Elber 103 Figure 53: Computes the zero set of a given freeform curve, in the given axis, using CZEROS. DistType Value 0 1 2 3 Description Computes the distance vector function, (V1 - V2). Computes the distance square function, (V1 - V2)^2. Projection of the distance vector onto the normal ﬁeld of the ﬁrst varietly, ¡ V1 - V2, N1 ¿. Projection of the distance vector onto the normal ﬁeld of the second varietly, ¡ V1 - V2, N2 ¿. In cases 2 and 3, the normal ﬁeld is not a unit ﬁeld. Example: Crv1 = cbezier( list( ctlpt( E1, .2 ), ctlpt( E2, 0.5, 4 ), ctlpt( E2, 1.3, 0.05 ) ) ) * sy( 0.2 ); Crv2 = cbezier( list( ctlpt( E1, -.2 ), ctlpt( E2, 0.25, 1.9 ), ctlpt( E2, 1.3, 0.05 ) ) ) * ty( 0.3 ) * sx( 1.5 ); bb = bbox( dist2ff( Crv1, Crv2, 1 ) ); computes a bound on the minimal and maximal distance square between the given two curves, by computing a bounding box on this scalar distance square ﬁeld. G. Elber IRIT Solid modeler 104 Figure 54: Two examples of a dual curve (left) and a dual surface (right) computed using the DUALITY function. The duals are shown in thin black color. 11.2.122 DUALITY CurveType DUALITY( CurveType Curve ) or SurfaceType DUALITY( SurfaceType Srf ) computes the dual curve/surface to the given curve/surface. The dual shape is a mapping of every point to a line (plane) in R2 (R3). Example: Ellipsoid = sphereSrf( 1.1 ) * sx( 2 ) * sy( 1.2 ); DualEllip = DUALITY( Ellipsoid ); See Figure 54. 11.2.123 ELLIPSE3PT ListType ELLIPSE3PT( PointType Pt1, PointType Pt2, PointType Pt3, NumericType Offset ) computes the 6 coeﬃcients A-F of, Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0, (13) deﬁning the ellipse of minimal area that bounds these 3 points Pti. computation is conducted in the XY plane, with Z ignored. If Oﬀset is not zero, the ellipse is oﬀset approximated by Oﬀset amount. Example: G. Elber IRIT Solid modeler Pt1 = point( random( -0.5, 0.5 ), Pt2 = point( random( -0.5, 0.5 ), Pt3 = point( random( -0.5, 0.5 ), 105 random( -0.5, 0.5 ), random( -0.5, 0.5 ), random( -0.5, 0.5 ), 0 ); 0 ); 0 ); EllImp = ELLIPSE3PT( Pt1, Pt2, Pt3, 0 ); Ell = ConicSec( EllImp, 0, off, off ); color( Ell, yellow ); adwidth( Ell, 2 ); creates three random points in the XY plane and compute the implicit minimal area ellipse for these three points. the Ellipse is realized geometrically using the ConicSec function. See also CONICSEC, IMPLCTTRANS, QUADRIC, MAP3PT2EQL. 11.2.124 EVOLUTE CurveType EVOLUTE( CurveType Curve ) or SurfaceType EVOLUTE( SurfaceType Srf ) compute the evolute of a curve or a surface. For curves, the evolute is deﬁned as, E(t) = C(t) + N (t) , κ(t) where N (t) is the unit normal of C(t) and k(t) is its curvature. E(t) is computed symbolically as the symbolic sum of C(t) and N (t) κ(t) = = = (14) N (t) κ(t) where the latter is, κ(t)N (t) k2 (t) C (t)6 (C (t) × C (t)) × C (t) C (t)4 (C (t) × C (t))2 ((C (t) × C (t)) × C (t)) C (t)2 (C (t) × C (t))2 (15) For surfaces, this function computes the mean evolute which is equal to, E(u, v) = S(u, v) + n(u, v) , 2H(u, v) (16) where n(u, v) is the unit normal of S(u, v) and H(u, v) is the mean curvature. E(u, v) is computed symbolically. The result of this symbolic computation is exact (upto machine precision), unlike similar operations such as OFFSET or AOFFSET, that are only approximated. Example: crv = cbspline( 3, list( ctlpt( E3, -1.0, 0.1, 0.2 ), IRIT Solid modeler G. Elber 106 Figure 55: The evolute (thick) of a freeform curve (thin) can be computed using EVOLUTE. ctlpt( E3, -0.1, ctlpt( E3, 0.1, ctlpt( E3, 1.0, ctlpt( E3, 0.1, list( KV_OPEN ) ); cev = EVOLUTE( Crv ); 1.0, 0.1, 0.1, 1.0, 0.1 1.0 0.1 0.2 ), ), ), ) ), See Figure 55. See also SMEAN. 11.2.125 EXTRUDE PolygonType EXTRUDE( PolygonType Object, VectorType Dir, NumericType Caps ) or SurfaceType EXTRUDE( CurveType Object, VectorType Dir, NumericType Caps ) or TrivarType EXTRUDE( SurfaceType Object, VectorType Dir, NumericType Caps ) or TrivarType EXTRUDE( ListType Object, VectorType Dir, NumericType Caps ) create an extrusion of the given Object. If the Object is a PolygonObject, its ﬁrst polygon is used as the base for the extrusion in Dir direction. If the Object is a CurveType, an extrusion surface is constructed. If the Object is a SurfaceType, an extrusion trivariate is constructed. If the Object is a ListType, a list of extruded objects is created for the objects found in Object. If Caps equals zero, no caps are created. If Caps equal one (two), only the bottom (top) cap is created. If Caps equal three, both the top and the bottom caps are created. Note that caps are created for a closed Object only, so the Object must be either a polygon or a closed curve for caps to be generated. Direction Dir cannot be coplanar with the polygon plane. The curve may be nonplanar. IRIT Solid modeler G. Elber 107 Figure 56: An extrusion of a freeform curve using EXTRUDE to create a freeform surface. Example: Cross = cbspline( 3, list( ctlpt( E2, -0.018, 0.001 ), ctlpt( E2, 0.018, 0.001 ), ctlpt( E2, 0.019, 0.002 ), ctlpt( E2, 0.018, 0.004 ), ctlpt( E2, -0.018, 0.004 ), ctlpt( E2, -0.019, 0.001 ) ), list( KV_OPEN ) ); Cross = Cross + -Cross * scale( vector( 1, -1, 1 ) ); Napkin = EXTRUDE( Cross * scale( vector( 1.6, 1.6, 1.6 ) ), vector( 0.02, 0.03, 0.2 ), 0 ); constructs a closed cross section Cross by duplicating one half of it in reverse and merging the two sub-curves. Cross is then used as the cross section for the extrusion operation. See Figure 56. See also ZTEXTRUDE. 11.2.126 FFCMPCRV FFCMPCRV( CurveType Crv1, CurveType Crv2, NumericType Tolerance ) compares the given two curves, Crv1 and Crv2 for an identical trace. Curves could have identical trace while with diﬀerent degrees (via degree raising of one of them), diﬀeret knot sequences (by applying reﬁnements to either curves or both), or even diﬀerent speed (via composition). This function reduces both curves to a canonical representation by reverse engineering unnecessary degree raising, reﬁnements, or composition and then compare the two curves upto the given tolerance Tolerance. Returned is a list of 5 numeric values. The ﬁrst number equals 1 if the curves are the same, 2 if the are the same but domain is not exactly the same, or 3 f the curves are diﬀerent. The other four numbers in the list are the domains of the two given curves that overlap as (Start1, End1, Start2, End2). IRIT Solid modeler G. Elber 108 Example: Similarity = FFCMPCRV( Crv1, Crv2, 1e-6 ); 11.2.127 FFCOMPAT FFCOMPAT( CurveType Crv1, CurveType Crv2 ) or FFCOMPAT( SurfaceType Srf1, SurfaceType Srf2 ) make the given two curves or surfaces compatible by making them share the same point type, the same curve type, the same degree, and the same continuity. The same point type is gained by promoting a lower dimension into a higher one, and non-rational to rational points. Bezier curves are promoted to B-spline curves if necessary, for curve type compatibility. Degree compatibility is achieved by raising the degree of the lower order curve. Continuity is achieved by reﬁning both curves to the space with the same (unioned) knot vector. This function returns nothing and compatibility is made in place. Example: FFCOMPAT( Srf1, Srf2 ); See also CMORPH and SMORPH. 11.2.128 FFCTLPTS ListType FFCTLPTS( FreeformType Freeform ); returns all the control points of the given Freeform in a single list. See Also FFPTTYPE, FFGTYPE, FFKNTVEC, FFMSIZE, FFORDER. Example: Ctls = FFCTLPTS( Srf1 ); 11.2.129 FFEXTEND CurveType FFEXTEND( CurveType Crv, ListType Ends, ListType ExtendEps, Numeric RemoveExtraKnots ) or SurfaceType FFEXTEND( SurfaceType Srf, ListType Ends, ListType ExtendEps, Numeric RemoveExtraKnots ) If a Crv, extends the given Crv in either one of its two ends as is speciﬁed by the list Ends of two Booleans parameters, an amount equals to ExtendEps. If a Srf, extends the given Srf in either one of its four sides as is speciﬁed by the list Ends of four Booleans parameters, an amount equals to ExtendEps. If RemoveExtraKnots is true redundant knots are removed. The extension IRIT Solid modeler G. Elber 109 is computed so that the new entity will preserve the original domain and hence will be identical for the original domain, to the input. Example: C1ext = FFEXTEND( c1, list( true, true ), list( 0.1 ), true ); extends curve c1 at both its ends by 0.1. 11.2.130 FFEXTREMA ListType FFEXTREMA( CurveType Crv, NumericType Euclidean ) or ListType FFEXTREMA( SurfaceType Srf, NumericType Euclidean ) or ListType FFEXTREMA( trivarType TV, NumericType Euclidean ) computes and returns the parameter locations of local extrema values of given scalar freeform (a curve, surface, or trivariate). Returned is a list of parameter locations where the extreme is taking place (interior location, boundary location or possibly C 1 discontinuity location. However, if Euclidean is true, the results are mapped to Euclidean space. Example: Extrema = FFEXTREMA( Srf, false ); computes a list of all parameter locations where Srf assumes local extrema. See also FFEXTREME 11.2.131 FFEXTREME CtlPtType FFEXTREME( CurveType Crv, NumericType Minimum ) or CtlPtType FFEXTREME( SurfaceType Srf, NumericType Minimum ) or CtlPtType FFEXTREME( trivarType TV, NumericType Minimum ) compute a bound on the extreme values a curves Crv or surface Srf or trivariate TV can assume. Returned control point provides a bound on the minimum (maximum) values that can be assumed if Minimum is TRUE (FALSE). Example: Bound = FFEXTREME( Srf, false ); computes a bound on the maximal values Srf can assume. See also FFEXTREMA G. Elber IRIT Solid modeler 11.2.132 110 FFGTYPE NumericType FFGTYPE( FreeformType Freeform ) returns the geometric type (BEZIER TYPE, BSPLINE TYPE etc.) of the given freeform. See Also FFGTYPE, FFCTLPTS, FFKNTVEC, FFMSIZE, FFORDER, PDOMAIN. 11.2.133 FFKNTLNS CurveType FFKNTLNS( SurfaceType Srf, NumericType Pllns ) or PolyType FFKNTLNS( SurfaceType Srf, NumericType Pllns ) returns all isoparametric curves that are at an interior knot of the surface Srf. If, however, Pllns is true, the result is converted to a piecewise linear approximation (i.e. polylines). Example: KntCrvs = FFKNTLNS( Srf, false ); See also GPOLYLINE, CSURFACE and CMESH. 11.2.134 FFKNTVEC ListType FFKNTVEC( FreeformType Freeform ) returns all the knot vector(s) of the given Freeform in a list of knot vector(s). See Also FFPTTYPE, FFGTYPE, FFCTLPTS, FFMSIZE, FFORDER. Example: KVs = FFKNTVEC( Srf1 ); 11.2.135 FFMATCH FFMATCH( CurveType Crv1, CurveType Crv2, NumericType Reduce, NumericType Samples, NumericType ReparamOrder, NumericType Rotate, NumericType NormType, NumericType MaxError ) computes a reparametrization to Crv2 so it ﬁts Crv1, the best under some prescribed norm, NormType. Currently the following norms are valid for NormType Value 1 2 3 4 5 Description Suitable for ruled and blended curves, for modeling. See RULEDSRF. Suitable for metamorphosis of curves. See CMORPH. Distance norm in ”walking the dog” notion. Bisector (skeleton) matching norm for two curves. Another variant for ruled and blended curves, for modeling. See RULEDSRF. IRIT Solid modeler G. Elber 111 Whenever negative norms can result (for example, in cases were self intersection cannot be prevented in ruled surface constructions), one can allow negativity with no extra penalty by applying negative NormType. Use of positive-only norms would yield no output at all if no matching with positive weights can be established, whereas allowing negative norm values would result in a globally optimal result, but with possible self intersectiions. The reparametrization is computed by sampling a ﬁxed set of size Samples oﬀ both curves, and ﬁtting a B-spline curve of length Reduce as the reparametrization curve. Hence, Reduce must be less than or equal to Samples. The reparametrization curve will have order of ReparamOrder. If Rotate is TRUE or ON, then attempt is made to rotate the reparametrization of the curves. Rotation can be used on closed curves only. if MaxError is TRUE the maximal error is minimized. Otherwise, the error’s sum over the entire domain is minimized. See RULEDSRF and CMORPH for examples. 11.2.136 FFMERGE CurveType FFMERGE( ListType E1Curves, NumericType PointType ) or SurfaceType FFMERGE( ListType E1Surfaces, NumericType PointType ) or MultivarType FFMERGE( ListType E1Multivars, NumericType PointType ) merge the scalar curves/surfaces/multivariates in the list of curves E1Curves or list of surfaces E1Surfaces or list of multivariates E1Multivars to one vector curve/surface/multivariate of point type PointType. Example: Srf = FFMERGE( list( SrfW, SrfX, SrfY ), P2 ); merges three scalar surfaces into a single surface with point type P2. See also FFSPLIT. 11.2.137 FFMESH ListType FFMESH( FreeformType Freeform ) returns the control mesh/polygon of the given Freeform in a list. See Also FFCTLPTS, FFKNTVEC, FFORDER, FFPTTYPE, FFMSIZE. Example: SrfMesh = FFMESH( Srf ); 11.2.138 FFMSIZE ListType FFMSIZE( FreeformType Freeform ) returns the size of the control mesh/polygon of the given freeform in a list. See Also MESHSIZE, FFMESH, FFPTTYPE, FFGTYPE, FFCTLPTS, FFKNTVEC, FFORDER, PDOMAIN. Example: MSizes = FFMSIZE( Srf1 ); G. Elber IRIT Solid modeler 11.2.139 112 FFORDER ListType FFORDER( FreeformType Freeform ) returns all the orders of the given Freeform in a single list. See Also FFPTTYPE, FFGTYPE, FFCTLPTS, FFKNTVEC, FFMSIZE, PDOMAIN. Example: Orders = FFORDER( Srf1 ); 11.2.140 FFPOLES NumericType FFPOLES( FreeformType Freeform ); returns TRUE if the given Freeform has poles, FALSE otherwise. Poles are zeros in the weights of rational functions. Example: HasPoles = FFPOLES( Srf1 ); See also FFSPLTPOLES 11.2.141 FFPTDIST ListType FFPTDIST( CurveType Crv, NumericType Param, NumericType NumOfPts ) or ListType FFPTDIST( SurfaceType Srf, NumericType Param, NumericType NumOfPts ) compute a uniform point distribution for Crv or Srf. If Param is FALSE, the distribution is selected to be uniform in the Euclidean space; otherwise if TRUE, the distribution is made uniform in the parametric space. NumOfPts sets the number of points in the distribution. The returned list of points prescribes parameter values in the freeforms. For Crv, the returned list is a list of reals, in the parameter space of Crv. For Srf, the returned list is a list of points, whose X and Y coeﬃcients hold the U and V parameters of Srf. See also COVERPT. Example: c1 = cbezier( list( ctlpt( ctlpt( ctlpt( ctlpt( color( c1, magenta ); E2, -1.0, 0.0 ), E2, -1.0, 0.1 ), E2, -0.9, -0.1 ), E2, 0.9, 0.0 ) ) ); pts = FFPTDIST( c1, true, 300 ); e2pts = nil(); for ( i = 1, 10, sizeof( pts ), pt = ceval( c1, coord( nth( pts, i ), 0 ) ): snoc( pt, e2pts ) ); IRIT Solid modeler G. Elber 113 Figure 57: (top) A distribution of 30 points uniformly in Euclidean space. (bottom) A distribution of 30 points uniformly in parameteric space. Both examples were computed using FFPTDIST. interact( list( e2pts, c1 ) ); pts = FFPTDIST( c1, false, 300 ); e2pts = nil(); for ( i = 1, 10, sizeof( pts ), pt = ceval( c1, coord( nth( pts, i ), 0 ) ): snoc( pt, e2pts ) ); interact( list( e2pts, c1 ) ); computes the distribution of 100 points in curve c1 which has highly nonuniform speed characteristics. Two distributions are computed, one to be uniform in the parametric space and one to be uniform in the Euclidean space. See Figure 57. 11.2.142 FFPTTYPE NumericType FFPTTYPE( FreeformType Freeform ) returns the point type (E2, P4 etc.) of the given freeform. See Also FFGTYPE, FFCTLPTS, FFKNTVEC, FFMSIZE, FFORDER, PDOMAIN. 11.2.143 FFSPLIT ListType FFSPLIT( CurveType Crv ) or ListType FFSPLIT( SurfaceType Srf ) or ListType FFSPLIT( MultivarType MV ) split the given curve Crv or surface Srf or multivariate MV into its scalar components that are returned as a list of scalar curves/surfaces/multivariates. Example: E1Srfs = FFSPLIT( circle( vector( 0, 0, 0 ), 1 ) ); splits the circle which is a curve in P3 into four scalar curves (W, X, Y, Z) that are returned in a single list. See also FFMERGE, FFPTTYPE. G. Elber IRIT Solid modeler 11.2.144 114 FFSPLTPOLES ListType FFSPLTPOLES( CurveType Crv, NumericType SubdivTol, NumericType NumericTol, NumericType Offset ) or ListType FFSPLTPOLES( SurfaceType Srf, NumericType SubdivTol, NumericType NumericTol, NumericType Offset ) Splits the given rational Crv or Srf at its poles (locations were the denominator vanish). In the case of surfaces, the result is a list of trimmed surfaces as the poles are not necessarily isoparameteric. If Oﬀset is not zero, the neighborhood of the pole is clipped as well upto a distance oﬀset in the parametric domain from the pole. Example: Crvs = FFSPLTPOLES( crv, 0.01, 1e-10, 0.001 ); See also FFPOLES 11.2.145 FITPMODEL ListType FITPMODEL( PolygonType PlObj, NumericType FitType, NumericType Tol, NumericType NumIters ) ﬁts a primitive object to the given polygonal model, PlObj. The numeric ﬁtting process is controled via a bound on the number of iterations NumIters and the resulting tolerance of the ﬁt that is required, Tol. Returned is a list of numeric values with the error of the ﬁt as the ﬁrst value. The rest of the list numeric values are the coeﬃcients of the algebraic ﬁtted form (see table below). FitType can be one of: 0 1 2 3 4 A Planar face. Returned list holds (A, B, C, D), the four coeﬃcients of the plane equation. A Sphere. Returned list holds (Xcntr, Ycntr, Zcntr, Radius) of the ﬁtted sphere. A Cylinder. Returned list holds (Xcntr, Ycntr, Zcntr, Xdir, Ydir, Zdir, Radius) of the ﬁtted cylinder. A Circle. Returned list holds (Xcntr, Ycntr, Radius) of the ﬁtted circle. A Cone. Returned list holds (Xcntr, Ycntr, Zcntr, Xdir, Ydir, Zdir, Radius) of the ﬁtted cone. Example: resolution = 20; x1 = triangl( sphere( vector( 1, 2, 3 ), 4 ), 1 ); SprParams = FitPModel( x1, 1, 0.01, 100 ); Computes a ﬁtted sphere to a polygonal approximation of a sphere. See also ANALYFIT. G. Elber IRIT Solid modeler 11.2.146 115 FIXPLGEOM PolygonType FIXPLGEOM( PolygonType PlObj, NumericType Oper, NumericType Eps ) or ListType FIXPLGEOM( ListType Obj, NumericType Oper, NumericType Eps ) cleans polygonal geometry. based on Oper, the following will be conducted: 0 1 Remove identical duplicated polygons. Remove zero length edges. The clean up of an object will be applied individually to each part found in the object list Obj. Example: Obj2 = FIXPLGEOM( Obj, 0 ); Obj3 = FIXPLGEOM( Obj2, 1 ); Obj4 = FIXPLNRML( Obj3, 2 ); cleans duplicated polygons, zero length edges, and then reorient the result. See also FIXPLNRML. 11.2.147 FIXPLNRML PolygonType FIXPLNRML( PolygonType PlObj, NumericType TrustInfo ) or ListType FIXPLNRML( ListType Obj, NumericType TrustInfo ) corrects inconsistencies in polygonal geometry, between normals of polygons and normals at the vertices based on TrustInfo. If TrustInfo is 0 1 2 3 Trust the normals at the vertices. Trust the normals of the polygons. Reorient all the polygon’s normals and vertices normals to follow the orientation of ﬁrst polygon. Same as 2 but splits disjoints part in the input to diﬀerent objects. The computation on an object will be applied individually to each part found in the object list Obj. Option 2 of TrustInfo will correct cases where adjacent polygons are not oriented the same, based on detection of adjacencies. Example: Obj2 = FIXPLNRML( Obj, 2 ); See also FIXPLGEOM and SMOOTHNRML. IRIT Solid modeler G. Elber 116 Figure 58: A ruled surface ﬁtting along two diﬀerent parametric directions of the input surface, computed using FMLNANAL. In blue, the boundaries of the strips are shown while in red, the tangency curves are presented, between the original surface and the ﬁtted ruled surface. 11.2.148 FMLNANAL CurveType FMLNANAL( SurfaceType Srf, NumericType Tolerance, NumericType Euclidean, NumericType CrvSizeReduction, NumericType SubdivTol, NumericType NumericTol ) computes a piecewise ruled surface approximation to given surface Srf, where the ﬁt always starts from VMin parametric direction. The strips ﬁts Srf to within Tolerance. If Euclidean is true, the result is evaluated into Euclidean space, otherwise it is returned in the parametric domain of Srf. CrvSizeReduction is used as a curve ﬁtting size limit for the intermediate rail curves of the fruled ﬁtting. See MZERO for the meaning of SubdivTol and NumericTol. Example: Strips = FMLNANAL( Srf2, 0.01, true, 40, 0.01, 1e-10 ); See Figure 58. See also PRISA. 11.2.149 GBOX PolygonType GBOX( VectorType Point, VectorType Dx, VectorType Dy, VectorType Dz ) creates a parallelepiped - generalized BOX polygonal object, deﬁned by Point as its base position, and Dx, Dy, Dz as 3 3D vectors to deﬁne the 6 faces of this generalized BOX. The regular BOX object is a special case of GBOX where Dx = vector(Dx, 0, 0), Dy = vector(0, Dy, 0), and Dz = vector(0, 0, Dz). Dx, Dy, Dz must all be independent in order to create an object with positive volume. Example: GB = GBOX( vector( 0.0, -0.35, 0.63 ), vector( 0.5, 0.0, 0.5 ), vector( -0.5, 0.0, 0.5 ), vector( 0.0, 0.7, 0.0 ) ); See Figure 59. IRIT Solid modeler G. Elber 117 Figure 59: A warped box in a general position can be constructed using the GBOX constructor. 11.2.150 GETATTR AnyType GETATTR( AnyType Obj, StringType Name ) provides a mechanism to fetch an attribute named Name from object Obj. Example: attrib( axes, "test", 15 ); a = GETATTR( axes, "test" ); will set the value of a to be 15. 11.2.151 GETLINE AnyType GETLINE( NumericType RequestedType ) provides a method to get input from the keyboard within functions and or subroutines. RequestedType can be a NUMERIC TYPE, POINT TYPE, VECTOR TYPE, or PLANE TYPE in which the entered line will be parsed into one, three, or four numeric values (operated by either spaces or commas) and the proper object will be created and returned. In any other case, including failure to parse the numeric input, a STRING TYPE object will be constructed from the entered line. Example: G. Elber IRIT Solid modeler 118 Pt = GETLINE( point_type ); to read one point (three numeric values) from stdin. 11.2.152 GETNAME StringType GETNAME( ListType ListObj, NumericType Index ) gets the name of a sub object of index Index in list object ListObj. Index of the ﬁrst element is one. Example: A = list( XX, Second, C ); GETNAME( A, 1 ); returns the name of the second element, ”Second”. See also SETNAME. 11.2.153 GGINTER ListType GGINTER( CurveType Srf1Axis, CurveType Srf1Rad, CurveType Srf2Aixs, CurveType Srf2Rad, NumericType SubdivTol, NumericType ZeroSetFunc ) computes the intersection curves of the given two ring surfaces, deﬁned as spine surfaces with axis SrﬁAxis, i = 1, 2 and circular cross section along the normal plane of the axis curve with radii SrﬁRad. The ring ring intersection (RRI) problem is tranformed into a zero set ﬁnding on another function. If ZeroSetFunc is true, the function whose zero set provides the RRIsolution is returned. Otherwise, if ZeroSetFunc is false, the RRI solution itself is returned. The zero set is computed via numerical zero set ﬁnding methods and Tolerance controls the ﬁneness of the approximated solution. See Figure 60. Example: s1 = cylinSrf( 4, 1 ) * tz( -2 c1 = cbezier( list( ctlpt( E3, ctlpt( E3, r1 = cbezier( list( ctlpt( E1, ); 0.0, 0.0, -1.0 ), 0.0, 0.0, 1.0 ) ) ); 1.0 ) ) ); s2 = cylinSrf( 4, 1 ) * tz( -2 c2 = cbezier( list( ctlpt( E3, ctlpt( E3, r2 = cbezier( list( ctlpt( E1, ) * rx( 90 ) * tx( 0.5 ); 0.5, -1.0, 0.0 ), 0.5, 1.0, 0.0 ) ) ); 1.0 ) ) ); ZeroSetSrf = coerce( GGINTER( c1, r1, c2, r2, 0.1, true ), e3 ) * rotx( -90 ) * roty( -90 ); resolution = 100; ZeroSet = contour( ZeroSetSrf, plane( 0, 0, 1, 0 ) ); interact( list( ZeroSetSrf * sz( 0.1 ), ZeroSet, axes ) ); c = nth( GGINTER( c1, r1, c2, r2, 0.03, false ), 1 ); interact( list( s1, s2, c ) ); IRIT Solid modeler G. Elber 119 Figure 60: Computation of the intersection curve between two ring surfaces via the GGINTER command. On the left, the zero set function is displayed while on the right, the computed intersection between two ocylinders is shown. constructs two cylinders as s1 and s2, deﬁnes the same two cylinders as a ring surface with axes spines of c1 and c2 and a constant radius, one in r1 and r2, and computes the zero set of the intersection and the intersection curve itself. See also RRINTER, SSINTER and SSINTR2. 11.2.154 GPOINTLIST PolylineType GPOINTLIST( GeometryTreeType Object, NumericType Optimal, NumericType Merge ) converts all Curves(s), (Trimmed) Surface(s), and Trivariate(s) Object into pointlists using the RESOLUTION variable. The larger the RESOLUTION is, the ﬁner the resulting approximation will be. Returns a single pointlist object if Merge is TRUE. If Optimal is false, the points are sampled at equally spaced intervals in the parametric space. If Optimal true, a better, more expensive computationally algorithm is used to derive optimal sampling locations so as to minimize the maximal distance between the curve and piecewise linear approximation (L inﬁnity norm). Example: Pts = GPOINTLIST( list( Srf1, Srf2, Srf3, list( Crv1, Crv2, Crv3 ) ), true, true ); See also GPOLYGON, GPOLYLINE. 11.2.155 GPOLYGON PolygonType GPOLYGON( GeometryTreeType Object, NumericType Normals ) IRIT Solid modeler G. Elber 120 approximates all Surface(s)/Trimmed surface(s)/Trivariate(s) in Object with polygons using the POLY APPROX OPT, POLY APPROX TRI, POLY MERGE COPLANAR, RESOLUTION and FLAT4PLY variables. If POLY APPROX OPT is FALSE, RESOLUTION vaguely prescribes the number of uniform (in parametric space) samples to sample the surface in each direction. If POLY APPROX OPT is TRUE, POLY APPROX TOL prescribes the maximal deviation of the polygonal approximation from the original surface, in object space coordinates. IF POLY APPROX TRI is TRUE, only triangles are generated on the output set. POLY MERGE COPLANAR controls the way coplanar adjacent polygons are merged into one (or not.) FLAT4PLY is a Boolean ﬂag controlling the conversion of an (almost) ﬂat patch into four (TRUE) or two (FALSE) polygons. Normals are computed to polygon vertices using surface normals, so Gouraud or Phong shading can be exploited. It returns a single polygonal object. If Normals is set, surface normals will be evaluated at the vertices. Otherwise ﬂat shading and constant normals across polygons are assumed. Example: Polys = GPOLYGON( list( Srf1, Srf2, Srf3 ), off ); converts to polygons the three surfaces Srf1, Srf2, and Srf3 with no normals. See also GPOINTLIST, GPOLYLINE, POLY APPROX OPT, POLY APPROX TOL, POLY APPROX TRI, POLY APPROX UV, POLY MERGE COPLANAR, RESOLUTION and FLAT4PLY. 11.2.156 GPOLYLINE PolylineType GPOLYLINE( GeometryTreeType Object, NumericType Optimal ) converts all Curves(s), (Trimmed) Surface(s), and Trivariate(s) Object into polylines using the RESOLUTION variable. The larger the RESOLUTION is, the ﬁner the resulting approximation will be. It returns a single polyline object. If Optimal is false, the points are sampled at equally spaced intervals in the parametric space. If Optimal true, a better, more expensive computationally algorithm is used to derive optimal sampling locations so as to minimize the maximal distance between the curve and piecewise linear approximation (L inﬁnity norm). Example: Polys = GPOLYLINE( list( Srf1, Srf2, Srf3, list( Crv1, Crv2, Crv3 ) ), on ); converts to polylines the three surfaces Srf1, Srf2, and Srf3 and the three curves Crv1, Crv2, and Crv3. See also GPOINTLIST, GPOLYGON, RESOLUTION and FLAT4PLY. 11.2.157 HAUSDORFF ListType HAUSDORFF( PointType Obj1, CurveType Obj2, NumericType Eps, NumericType OneSided ) or ListType HAUSDORFF( CurveType Obj1, CurveType Obj2, NumericType Eps, NumericType OneSided ) IRIT Solid modeler G. Elber 121 computes the Hausdorﬀ distance between Obj1 and Obj2, with Eps as the tolerance of the computation. Note obj1 or Obj2 can be either a point, a curve, and to a certain extent a surface. If OneSided is TRUE, the one sided Hausdorﬀ distance from Obj1 to Obj2 is computed. Returned is a list of two items, the ﬁrst prescribes the parameter location of the Hausdorﬀ distance event on the Obj1 and the second prescribes the parameter location of the Hausdorﬀ distance event on Obj2. Example: HDRes = hausdorff( O1, O2, Eps, false ); 11.2.158 HAUSDRPTS NumericType HAUSDRPTS( SurfaceType Srf1, SurfaceType Srf2, NumericType NumPts, NumericType HausdorffDir ) ConstantType Direction, NumericType Index ) computes an Hausdorﬀ distance estimate between the given two surfaces by sampling NumPts points on both and computing distances between the points. HausdorﬀDir sets the distance direction computation: 1 for Hausdorﬀ distance from Srf1 to Srf2, 2 for Hausdorﬀ distance from Srf2 to Srf3, and 3 for a symmetric estimate. Example: HD = HAUSDRPTS( Srf1, Srf2, 100, 3 ); 11.2.159 HERMITE SurfaceType HERMITE( CurveType Bndry1, CurveType Bndry2, CurveType Tan1, CurveType Tan2 ) or CurveType HERMITE( PointType Bndry1, PointType Bndry2, VectorType Tan1, VectorType Tan2 ) construct a cubic ﬁt between Bndry1 and Bndry2 so that ﬁrst derivative continuity constraints, as prescribed by Tan1 at Bndry1 and Tan2 at Bndry2, are preserved. It returns either a curve or a surface, according to type of input parameters. Example: h00 = HERMITE( point( 0, 0, 0 ), point( 1, 1, 0 ), vector( 1, 0, 0 ), vector( 1, 0, 0 ) ); constructs a curve in the shape of the ﬁrst basis function of the cubic Hermite basis functions. See also BLHERMITE, BLSHERMITE and BLND2SRFS. G. Elber IRIT Solid modeler 11.2.160 122 ILOFFSET NumericType ILOFFSET( CurveType Crv, CurveType OffsetCrv ) examines if the oﬀset curve OﬀsetCrv has local self-intersections with respect to the original input curve Crv. Returns TRUE if local self intersections detected, FALSE otherwise. Example: SelfInterTst = iloffset( cpawn, cpawnOffset ); 11.2.161 IMPLCTTRANS ListType IMPLCTTRANS( 1, ListType ImplicitConicSec, MatrixType Mat ) or ListType IMPLCTTRANS( 2, ListType ImplicitQuadric, MatrixType Mat ) transforms a given conic section as the 6 coeﬃcients A-F of: Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0, (17) in which case 6 coeﬃcients are expected in ImplicitQuadric or transforms a given quadric section given as the 10 coeﬃcients A-J, Ax2 + By 2 + Cz 2 + Dxy + Exz + F yz + Gx + Hy + Iz + J = 0, (18) using the given transformation matrix Mat. Example: ImplicitMappedEllipse = IMPLCTRANS( 1, ImplicitEllipse, Mat ); See also CONICSEC, QUADRIC, ELLIPSE3PT, MAP3PT2EQL. 11.2.162 INSTANCE InstanceType INSTANCE( StringType GeomName, MatrixType Mat ); creates an instance of the geometry prescribed by GeomName to be related to a diﬀerent position as speciﬁed by matrix Mat. The use of instances is advantageous where the same geometry is to be displayed/processed in several diﬀerent locations in space. A modiﬁcation of the original geometry Geom will aﬀect all instances that reference it. The reference is by the original object’s name. The original object can be a single object or a whole hierarchy of objects. Example: Tea1 = INSTANCE( "Teapot", tx( 10 ) ); Tea2 = INSTANCE( "Teapot", tx( 20 ) ); Tea3 = INSTANCE( "Teapot", tx( 30 ) ); viewobj( list( Teapot, Tea1, Tea2, Tea3 ) ); will display four teapots 10 units apart along X. G. Elber IRIT Solid modeler 11.2.163 123 IRITSTATE AnyType IRITSTATE( StringType State, AnyType Data ) sets a state variable in the IRIT Solid Modeller and returns the old value, if applicative. Current supported state variables are: State Name Data Type Comments BoolPerturb NumericType BoolFreeform VectorType CmpObjEps BspProdMethod NumericType NumericType CnvxPl2Vrtcs NumericType Coplanar NumericType CursorKeep NumericType DebugMalloc StringType DebugFunc NumericType Dependency NumericType DoGraphics NumericType DumpLevel NumericType Controls epsilon-pertubation in Booleans. Zero value to disable. Sets the tolerances used by the freeform Boolean operations among models as triplet (Subdivision Tol, Numeric Tol, Trace Tol). Sets the epsilon to use to compare two objects. 1 for B-spline sym. products via interpolation, 2 for blossoming B-spline based product, and 0 for B-spline sym. products via Bezier decomposition. TRUE to try and split non convex polygons toward vertices, which is usually more eﬃcient. If TRUE, Coplanar polygons are handled by the Boolean operations. If TRUE, keep mouse events reported by the display devices for CLNTCRSR to read. If ”Reset”, memory allocation is cleared/reset. No ”Free unallocated pointer” test after ”Reset”. If ”Print”, all allocated blocks are printed. Otherwise, used as ”address, n”: ptr address to search for with abort() called after n mallocs. > 0 user func. debug information. > 2 print params on entry, ret. val. on exit. > 4 global var. list operations. 0 for no object dependency propagations, 1 for automatic dependency propagation, in evaluation. TRUE to enable any graphics display thru the display devices. FALSE to disable it. Bitmask to control the way variables/expressions are dumped. Only object names/types if all 0. Scalars and vectors are dumped if 0x01. Curves and Surfaces are dumped if 0x02. Polygons/lines are dumped if DumpLvl 0x04. List objects are traversed recursively if 0x10. List objects are dumped verbatim if 0x20. Dependency information is dumped if 0x40. G. Elber IRIT Solid modeler EchoSource FastPolys NumericType NumericType FlatLoad NumericType FloatFrmt GMEpsilon StringType NumericType HierarchyVisible NumericType InterCrv NumericType InterUV NumericType LoadFont StringType MVBivarOutPllns NumericType MvDmnExt NumericType MvDmnReduce NumericType MvGradPrecond NumericType MvHPlnTst NumericType MvNConeTst NumericType MVSbdvTolAction NumericType MvSnglrPts NumericType PolySort NumericType If TRUE, IRIT scripts are echoed to stdout. If 0x01, surface polygons are computed fast and are only approximated. If 0x02, surface normals are computed fast and are only approximated. If 0x01 — 0x02, both are fast and approximated. If TRUE, the hierarchy of loaded objects is ﬂattened into a linear list. Speciﬁes a new printf ﬂoating point format. Controls the epsilon of the basic geometry processing computation (point on plane etc.) If TRUE, insert all sub objects into Irit’s DB, when an object is inserted to the DB. See also IritState’s PropagateNames. If TRUE, Boolean operations creates only intersection curves. If FALSE, full Boolean operation results. If TRUE, Boolean operations creates only UV intersection curves (if InterCrv is set). Speciﬁes a new IRIT font ﬁle to use in TEXTGEOM commands. Sets the way univariate solution are returned by the multivariate solver (see MZERO and MUNIVZERO). Positive to extend domains of multivariates by this relative-to-SubdivTol value to ensure catching zeros on the boundaries. Zero to disable. TRUE to use domain reduction in multivariate zero set ﬁnding, FALSE to disable. TRUE to apply gradient preconditioning in the multivariate zero set ﬁnding, FALSE to disable. TRUE to use hyperplane tests in multivariate zero set ﬁnding, FALSE to disable. TRUE to use normal cone tests in multivariate zero set ﬁnding, FALSE to ignore such tests. Controls the behaviour of the multivariate solver (See MZERO and MUNIVZERO) when reaching the subdivision tolerance. TRUE to also dump out singular solutions, FALSE to ignore singularities. Axis of Polygon Intersection sweep in Boolean operations: 0 for X axis, 1 for Y axis, 2 for Z axis. 124 G. Elber IRIT Solid modeler PrimRatSrfs NumericType PrimType NumericType PropagateNames NumericType RandomInit NumericType TCrvs2Lin NumericType TrimCrvs NumericType UVBoolean NumericType 125 TRUE for rational exact primitive surfaces, FALSE for approximated polynomial (integral) surfaces. See also PrimType. 0 for primitive construction as polygonal objects, 1 for freeform surfaces, 2 for freeform model objects, 3 for freeform volumetric trivariates. See also PrimRatSrfs. If true, sub objects are assigned unique names derived from their parent name. See also IritState’s HierarchyVisible. Initialize the seed random number generator in IRIT. See also the RANDOM function. if TRUE, trimmed surfaces, when subdivided, also forces all trimming curves to be linear as a side eﬀect. if FALSE, higher order trimmed curves are left as is. Number of samples the higher order trimmed curves are sampled, in piecewise linear approximation. If zero, computed symbolically as composition. If TRUE, Boolean between surfaces returns UV instead of Euclidean curves. Example: IRITSTATE( "DebugFunc", 3 ); IRITSTATE( "FloatFrmt", "%8.5lg" ); To print parameters of user deﬁned functions on entry, and return value on exit. Also selects a ﬂoating point printf format of ” 11.2.164 ISGEOM ListType ISGEOM( AnyType Obj, NumericType GeomType, NumericType Eps ) veriﬁes if the given freeform geometry in Obj is a line, circle, plane, sphere, surface of revolution, extrusion, ruled surface, or a sweep surface, upto some tolerance Eps. GeomType prescribes the type to check for as one of the GEOM LINE/CIRCLE etc. constants. The return value is a list of two objects. The ﬁrst is a numeric value with the success/failure of the result. A zero is returned in a failure case whereas non zero value hints on the direction relevant. As an example a ruled surface along U will return 1 and a ruled surface along V will return a 2. The second object is a list with the construction entities of Obj, if any. For example, for a detected sphere, the center and radius will be returned. Example: b = nth( ISGEOM( Crv, GEOM_LINE ), 1 ) || nth( ISGEOM( Crv, GEOM_CIRCLE ), 1 ); checks if Crv is either line or a circle, ignoring the construction entities. IRIT Solid modeler 11.2.165 G. Elber 126 ISOCLINE SurfaceType ISOCLINE( SurfaceType Srf, VectorType ViewDir, NumericType Theta, NumericType SubdivTol, NumericType Euc, NumericType Mode ) computes the isocline edges of the given Srf from the prescribed viewing direction ViewDir. Isocline curves are curves on the surface at which location the surface normal forms a ﬁxed angle, Theta, in degrees, with the prescribed viewing direction, ViewDir. The selection of 90 degrees for Theta results in the extraction of silhouette edges. The end result is a piecewise linear approximation of the exact isocline edges, and its accuracy is controlled via the RESOLUTION variable. If Mode is zero, the isoclines are simply computed and returned. If Mode is either -1 or +1, the surface regions with normals with angles of less than or great than Theta are returned as trimmed surfaces. If Mode is either -2, the surface regions with normals with angles of less than than Theta are returned along with ruled surface that are stitched along the removed region. This -2 mode is useful in mold design. SubdivTol controls the accuracy of the computation. If Euc is TRUE, the isocline edges are returned on the surface, in Euclidean space. Otherwise, the isocline edges are returned in the parametric space of Srf. Example: Resolution = 10; Isocs = ISOCLINE( glass, vector( 1, -2, 1 ), 80, 0.01, true, 0 ); computes the isocline edges forming 80 degrees between the surface normal and the given viewing direction (1, -2, 1) for surface glass, and returns the isocline edges in the Euclidean space. See also SILHOUETTE. 11.2.166 KNOTCLEAN CurveType KNOTCLEAN( CurveType Crv ) cleans unnecessary knots from the given curve Crv. The returned curve is identical to the given curve, but in, possibly, a sub space with less knots. Note this function can undo reﬁnement operations. c1 = pcircle( vector( 0, 0, 0 ), 1 ); c1r1 = crefine( c1, FALSE, list( 0.1, 0.3, 0.7, 1.5, 1.7, 1.7, 1.7, 1.7, 2.3, 2.3, 2.7, 3.5, 3.5, 3.5 ) ); c1r2 = KNOTCLEAN( c1r1 ); c1 == c1r2; reﬁnes a polynomial circle approximation and then restores the original curve via the KNOTCLEAN operation. The last line validates this cleaning. See also KNOTREMOVE. 11.2.167 KNOTREMOVE CurveType KNOTREMOVE( CurveType Crv, NumericType Tolerance ) removes knots from curve Crv so as to keep the global error less than the Tolerance. c1r = KNOTREMOVE( c1, 0.01 ); curve c1r is the curve with the minimum number of knots possible such that the global error (distance between c1 and c1r) is less than 0.01. See also KNOTCLEAN. IRIT Solid modeler 11.2.168 G. Elber 127 LINTERP ListType LINTERP( ListType PtList) computes a least squares ﬁt of a line to a list of points, PtList. A list of three elements, a point on the ﬁtted line, a unit vector in the direction of the line and the average distance between a point and the ﬁtted line, is returned. Example: R = 10; Rx = Random( -1, 1 ); Ry = Random( -1, 1 ); Rz = Random( -1, 1 ); Pts = nil(); Len = 1.0; NumPts = 100; for ( i = 1, 1, NumPts, Pt = ctlpt( E3, ( Random( -R, R ) ( Random( -R, R ) ( Random( -R, R ) snoc( Pt, Pts ) ); Pts = Pts * trans( vector( random( -10, random( -10, random( -10, LnFit LnPos LnDir LnErr = = = = + Rx * i * 2 ) / NumPts, + Ry * i * -5 ) / NumPts, + Rz * i * Pi ) / NumPts ): -10 ), -10 ), -10 ) ) ); LINTERP( Pts ); nth( LnFit, 1 ); nth( LnFit, 2 ); nth( LnFit, 3 ); randomly samples 100 points to be approximately along a line and computes a least squares ﬁt of a line to this data. LnPos, LnDir, and LnErr contain a point on the ﬁtted line, the unit direction of the ﬁtted line and the average distance between a point and the line, respectively. See also CINTERP and SINTERP. 11.2.169 LOFFSET CurveType LOFFSET( CurveType Crv, NumericType OffsetDistance, NumericType NumOfSamples, NumericType NumOfDOF, NumericType Order ) approximates an oﬀset of OﬀsetDistance by sampling NumOfSamples samples along the oﬀset curve and least square ﬁtting them using a B-spline curve of order Order and NumOfDOF control points. Example: OffCrv1 = LOFFSET( Crv, -0.4, 100, 10, 4 ); See also OFFSET, TOFFSET, AOFFSET, and MOFFSET. IRIT Solid modeler 11.2.170 G. Elber 128 MATDECOMP ListType MATDECOMP( MatrixType Mat ); decomposes a given homogeneous transformation into its scaling and translation vectors, and a pure (orthogonal) rotation matrix. Example: MATDECOMP( rx( 45 ) * sy( 3 ) * sx( 2 ) * tx( 5 ) * ty( 7 ) ); would result in the ”(2, 3, 1)” scaling vector, ”(5, 7, 0)” translation vector and a rotation around X matrix of 45 degrees, all in one returned list object. See also MATDECOMP2 and MATRECOMP 11.2.171 MATDECOMP2 ListType MATDECOMP2( MatrixType Mat ); decomposes a given homogeneous transformation into its three Euler rotation angles, RotX, RotY, RotZ, unifrom scale factor, and three translation factors, and returns a list of these seven numeric coeﬃcients. Example: MATDECOMP2( rx( 90 ) * sc( 3 ) * tx( 5 ) * ty( 7 ) ); would result in the numeric list of ”(Pi/2, 0, 0, 3, 5, 7, 0)”. See also MATDECOMP and MATRECOMP 11.2.172 MATRECOMP MatrixType MATRECOMP( ListType MatCoeffs ); Recomposes the seven numeric coeﬀcients of (RotX, RotY, RotZ, Scale, TransX, TransY, TransZ) to an homogeneous matrix. Example: MATRECOMP( list( Pi/2, 0, 0, 3, 5, 7, 0 ) ); would result in an homogeneous matrix that rotates by 90 degrees in x, scales by a factor of 3 and translates by 5 and 7 in x and y, respectively. See also MATDECOMP and MATDECOMP2. 11.2.173 MAXEDGELEN PolyType MAXEDGELEN( PolyType Pl, NumericType MaxLen ); splits all triangles in polygonal object Pl to triangles with edges no greater than MaxLen in length. Example: PlNew = MAXEDGELEN( Pl, 0.5 ); See also TRIANGL G. Elber IRIT Solid modeler 11.2.174 129 MBEZIER MultivarType MBEZIER( ListType Orders, ListType CtlPts ) creates a Bezier polynomial/rational multivariate out of the provided control mesh. Orders is a list of orders whose size deﬁne the number of dimensions that the multivariate has. CtlPts is a linear list of control points. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the multivariate’s control mesh. The multivariate’s point type will be of a space which is the union of the spaces of all points. Example: MV = MBEZIER( list( 4 ), list( ctlpt( ctlpt( ctlpt( ctlpt( E3, -1, 0.5, 2 ), E1, 3 ), E3, 0, -1.5, 0 ), E2, -1, 3.5 ) ) ); constructs a univariate cubic multivariate object. See also MPOWER and MBSPLINE 11.2.175 MBISECTOR ListType MBISECTOR( MultivarType MV1, MultivarType MV2, NumericType RetType, NumericType SubdivTol, NumericType NumerTol ) computes the bisector surface in R3 of two surfaces or a curve and a surface, posed as multivariate functions. The returned results depend upon the value of RetType. If RetType = 1, the algebraic constraints are returned as a list of multivariates. If RetType = 2, a list of points in R3 on the bisector sheet(s) is returned. If RetType = 3, a list of points in (u, v, x, y, z) space, as E5 points, is returned, where (u, v) are the respective parameter locations of the (must be) surface MV1. These E5 points can then directly be employed by SINTERP through which to ﬁt a surface. Finally, if RetType = 4, marching cubes is applied to extract a piecewise linear approximation of the solution, in Euclidean space. This bisector problem is posed as a set of two multivariate algebraic constraints with three variables. The simultaneous solution of these constraints is computed using the MZERO function. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. Example: s1 = sbezier( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( color( s1, red ); s2 = sbezier( list( list( ctlpt( ctlpt( ctlpt( list( ctlpt( E3, E3, E3, E3, 0, 2, 0, 2, 0, 0, 2, 2, 0 0 0 0 ), ) ), ), ) ) ) ) * tx( -1 ) * ty( -1 ); E3, E3, E3, E3, 0, 1, 2, 0, 0, 0, 0, 1, 2 1 2 1 ), ), ) ), ), G. Elber IRIT Solid modeler ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( color( s2, magenta ); E3, E3, E3, E3, E3, 1, 2, 0, 1, 2, 1, 1, 2, 2, 2, 0 1 2 1 2 130 ), ) ), ), ), ) ) ) )* tx( -1 ) * ty( -1 ); ms1 = coerce( s1, multivar_type ); ms2 = coerce( s2, multivar_type ); mb1 = MBISECTOR( ms1, ms2, 3, 0.3, -0.001 ); b1 = sinterp( mb1, 3, 3, 4, 4, PARAM_UNIFORM ); mb2 = MBISECTOR( ms1, ms2, 2, 0.3, -0.001 ); interact( list( s1, s2, mb2, b1 ) ); c = cbezier( list( ctlpt( E3, ctlpt( E3, color( c, red ); 0, 0, 0, 0, 0 ), 2 ) ) ); mc = coerce( c, multivar_type ); mb1 = MBISECTOR( mc, ms1, 3, 0.2, -0.001 ); b1 = sinterp( mb1, 3, 3, 8, 8, PARAM_UNIFORM ); mb2 = MBISECTOR( mc, ms1, 2, 0.2, -0.001 ); interact( list( c, s1, mb2, b1 ) ); computes two examples of a bisector between a plane and a biquadratic surface and between a plane and a line. The cloud of points is computed twice, once interpolated by a surface, and also displayed as is. See Figure 61. 11.2.176 MBSPLINE MultivarType MBSPLINE( ListType Lengths, ListType Orders, ListType CtlPts, ListType KVLst ) creates a Bspline polynomial/rational multivariate out of the provided control mesh of lengths Lengths and orders Orders in each axis. The sizes of Lengths and Orders deﬁne the number of dimensions that the multivariate has. CtlPts is a linear list of control points. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the multivariate’s control mesh. The multivariate’s point type will be of a space which is the union of the spaces of all points. KVLst is a list of knot sequences of the new Bspline multivariate. Example: MV = MBSPLINE( list( 3, 3 ), list( 3, 3 ), list( ctlpt( E1, 0 ), IRIT Solid modeler G. Elber 131 Figure 61: A bisector between two surfaces (left) and a plane and a line (right) computed using MBISECTOR. ctlpt( E2, 0.25, 1 ), ctlpt( E3, 0.5, 0.25, 2 ), ctlpt( E3, 0.5, -1, 3 ), ctlpt( E3, 0.75, 0.25, 4 ), ctlpt( E3, 1, -0.5, 5 ), ctlpt( E3, 1, 0, 6 ), ctlpt( E3, 1.25, 1, 7 ), ctlpt( E3, 1.3, 0.25, 8 ) ), list( list( kv_open ), list( kv_open ) ) ); constructs a bivariate quadratic multivariate object. See also MPOWER and MBEZIER. 11.2.177 MDERIVE MultivarType MDERIVE( MultivarType MV, NumericType Dir ) returns a vector ﬁeld multivariate representing the diﬀerentiated multivariate MV, in the given direction. Evaluation of the returned multivariate at a given parameter value will return a vector tangent to TV in Dir at that parameter value. DMV = MDERIVE( MV, 2 ); computes the partial derivative of the multivariate MV with respect to its second variable. See also CDERIVE, SDERIVE, and TDERIVE. G. Elber IRIT Solid modeler 11.2.178 132 MDIVIDE MultivarType MDIVIDE( MultivarType MV, ConstantType Direction, NumericType Param ) subdivides a multivariate into two at the speciﬁed parameter value Param in the speciﬁed Direction. MV can be either a B-spline multivariate in which Param must be contained in the parametric domain of the multivariate, or a Bezier multivariate in which Param can be arbitrary, extrapolating if not in the range of zero to one. It returns a list of the two sub-multivariates. The individual multivariates may be extracted from the list using the NTH command. Example: MvDiv = MDIVIDE( Mv2, 3, 0.3 ); Mv2a = nth( MvDiv, 1 ) * tx( -2.2 ); Mv2b = nth( MvDiv, 2 ) * tx( 2.0 ); subdivides Mv2 at the parameter value of 0.3 in the direction 3 and then extracts the two subdivided multivariate. See also CDIVIDE, SDIVIDE, and TDIVIDE. 11.2.179 MERGEPLLN PolygonType MERGEPLLN( PolygonType PolyList, NumericType Eps ) or PolygonType MERGEPLLN( ListType PolyList, NumericType Eps ) merges a set of polylines/polyline objects in PolyList to larger polyline object. All elements in the PolyList in the second form must be of PolygonType type. This function merges two polylines if their end point is the same upto Eps. Example: Vrtx1 Vrtx2 Vrtx3 Vrtx4 Polys = = = = = vector( -3, -2, -1 ); vector( 3, -2, -1 ); vector( 3, 2, -1 ); vector( -3, 2, -1 ); list( poly( list( Vrtx1, poly( list( Vrtx3, poly( list( Vrtx3, poly( list( Vrtx1, Vrtx2 Vrtx2 Vrtx4 Vrtx4 ), ), ), ), true true true true ), ), ), ) ); Polys = MERGEPLLN( Polys, 1e-6 ); will merge the four 2-vertices polylines into one polyline prescribing a square. Note polylines might be reversed in the merging process. See also MERGEPOLY. IRIT Solid modeler G. Elber 133 Figure 62: Individual polygons can be merged into a complete model using MERGEPOLY. 11.2.180 MERGEPOLY PolygonType MERGEPOLY( ListType PolyList ) merges a set of polygonal objects in the PolyList list to a single polygonal object. All elements in the ObjectList must be of PolygonType type. This function performs the same operation as the overloaded ^ operator would, but may be more convenient to use under some circumstances. Example: Vrtx1 Vrtx2 Vrtx3 Vrtx4 Poly1 = = = = = vector( -3, -2, -1 ); vector( 3, -2, -1 ); vector( 3, 2, -1 ); vector( -3, 2, -1 ); poly( list( Vrtx1, Vrtx2, Vrtx3, Vrtx4 ), false ); Vrtx1 Vrtx2 Vrtx3 Vrtx4 Poly2 = = = = = vector( -3, 2, 1 ); vector( 3, 2, 1 ); vector( 3, -2, 1 ); vector( -3, -2, 1 ); poly( list( Vrtx1, Vrtx2, Vrtx3, Vrtx4 ), false ); Vrtx1 Vrtx2 Vrtx3 Vrtx4 Poly3 = = = = = vector( -3, -2, 1 ); vector( 3, -2, 1 ); vector( 3, -2, -1 ); vector( -3, -2, -1 ); poly( list( Vrtx1, Vrtx2, Vrtx3, Vrtx4 ), false ); PolyObj = MERGEPOLY( list( Poly1, Poly2, Poly3 ) ); See Figure 62. See also INSERTPOLY, SPLITLST. 11.2.181 MEVAL CtlPtType MEVAL( MultivarType MV, ListType Params ) IRIT Solid modeler G. Elber 134 evaluates the provided multivariate MV at the given Params values. Params is a list of NumericTypes of length equal to the dimension of the multivariate that must be contained in the multivariate parametric domain, if MV is a B-spline multivariate, or all between zero and one if MV is a Bezier multivariate. The returned control point has the same type as the control points of MV. Example: CPt = MEVAL( MV1, list( 0.1, 0.25, 0.22, 0.7 ) ); evaluates the four-variate MV1 at the parameter values of (0.1, 0.25, 0.22, 0.7). See also CEVAL, SEVAL, TEVAL. 11.2.182 MFROM2IMG CurveType MFROM2IMG( StringType Img1, StringType Img2, NumericType DoTexture, GeometricType Blob, NumericType BlobSpread, NumericType BlobColor, NumericType Resolution, NumericType Negative, NumericType Intensity, NumericType MinIntensity, NumericType MergePolys ) Constructs a 3D model of numerous tiny blobs that looks like Img1 from one view direction, like Img2 from another view direction. DoTexture TRUE adds UV paramterization to the geometry so it can be used with textures. If Blob cis a geometric object, it is used as the (tiny) blob element. Otherwise a cross blob is employed. Blob must be normalized in size to [0, 1]3 unit cube. If blob coloring methods are used, it must be a list of three diﬀerent geometries to be used for the three diﬀerent axes. BlobSpread sets the blobs spreading methods to be used. 0 for random placement and 1 to 7 for seven diﬀerent placements along 3D diagonal planes. Set BlobColor to 0 for no color, 1 for gray levels, and 2 for colored blobs. Resolution sets the number of blobs to position in each axes of the three dimensional cube of blobs. If Negative TRUE, dark blobs are positioned over light background. If FALSE, light blobs over dark background is used. Intensity controls the gray scaling factor. MinIntensity prescribes the minimal level. if zero, blobs might be scaled to zero in one diemsion which will make it diﬃcult to manufacture this model. Set MinIntensity to TRUE to merge all polygons in the diﬀerent blobs into one object. Example: resolution = 6; Blob = sphere( vector( 0, 0, 0 ), 0.35 ); M1 = MFrom2Img( "BenGurion.ppm", "Herzel.ppm", FALSE, Blob, 0, 0, 25, FALSE, 1.0, 0.01, TRUE ) See Figure 63. See also MFROM3IMG, BFROM2IMG and BFROM3IMG. 11.2.183 MFROM3IMG CurveType MFROM3IMG( StringType Img1, StringType Img2, StringType Img3, NumericType DoTexture, GeometricType Blob, NumericType BlobSpread, NumericType BlobColor, NumericType Resolution, NumericType Negative, NumericType Intensity, NumericType MinIntensity, NumericType MergePolys ) IRIT Solid modeler G. Elber 135 Figure 63: A 3D model consisting of many small spherical blobs mimics one image from one view and a diﬀerent image from an orthogonal view. Model constructed using the MFROM2IMG command. Left image shows Ben Gurion, right image shows Herzl and the middle image is a general view of the 3D model. Constructs a 3D model of numerous tiny blobs that looks like Img1 from one view direction, like Img2 from another view direction, and like Img3 from a third view direction. DoTexture TRUE adds UV paramterization to the geometry so it can be used with textures. If Blob cis a geometric object, it is used as the (tiny) blob element. Otherwise a cross blob is employed. Blob must be normalized in size to [0, 1]3 unit cube. If blob coloring methods are used, it must be a list of three diﬀerent geometries to be used for the three diﬀerent axes. BlobSpread sets the blobs spreading methods to be used. 0 for random placement and 1 to 7 for seven diﬀerent placements along 3D diagonal planes. Set BlobColor to 0 for no color, 1 for gray levels, and 2 for colored blobs. Resolution sets the number of blobs to position in each axes of the three dimensional cube of blobs. If Negative TRUE, dark blobs are positioned over light background. If FALSE, light blobs over dark background is used. Intensity controls the gray scaling factor. MinIntensity prescribes the minimal level. if zero, blobs might be scaled to zero in one diemsion which will make it diﬃcult to manufacture this model. Set MinIntensity to TRUE to merge all polygons in the diﬀerent blobs into one object. Example: M2 = MFrom3Img( "BenGurion.ppm", "Herzel.ppm", "Rabin.ppm", FALSE, FALSE, 1, 1, 40, FALSE, 1.0, 0.01, 1 ); See also MFROM2IMG, BFROM2IMG and BFROM3IMG. 11.2.184 MFROMMESH MultivarType MFROMMESH( MultivarType MV, MumericType Dir, NumericType Index ) extracts a multivariate out of a multivariate, MV, as the Index’s plane of the control mesh of MV in direction Dir. Example: cmesh( s, row, 2 ) == coerce( MFROMMESH( coerce( s, multivar_type ), 1, 2 ), curve_type ); IRIT Solid modeler G. Elber 136 coerces surface s to a multivariate, extracts a one-dimensional-less multivariate (a curve) from the second direction (ﬁrst direction is direction zero), at index 2 and compares the result for equality to the curve extracted using cmesh from s. 11.2.185 MFROMMV MultivarType MFROMMV( MultivarType MV, NumericType Dir, NumericType Param ) extracts a multivariate of one lower dimension from multivariate MV by extracting an iso-variate of MV in direction Dir at parameter value Param. Example: MVFirst = MFROMMV( MV, 0, FirstParam ); extracts a multivariate for one less dimension than MV as the constant ﬁrst parameter of MV at parameter value FirstParam. See also STRIVAR, CSURFACE. 11.2.186 MMERGE MultivarType MMERGE( MultivarType MV1, MultivarType MV2, NumericType Dir, NumericType Discont ) merges MV1 and MV2 together into one multivariate along the direction Dir. The ﬁrst direction starts from zero. If Discont, the merge is assumed to be along a discontoinuous edge. Example: MVFirst = MMERGE( M1, M2, 2, false ); merges M1 and M2 along the third direction. See also SMERGE, 11.2.187 MOFFSET CurveType MOFFSET( CurveType Crv, NumericType OffsetDistance, NumericType AngularError ) computes an oﬀset of OﬀsetDistance with a globally bounded error (controlled by AngularError). The smaller the AngularError is, the better the approximation to the oﬀset. The bounded error is achieved by adaptive reﬁnement of the Crv. The oﬀset is computed via matching of the tangent ﬁelds of the given curve Crv and an arc spanning the same angular domain. Further, AngularError measures the angular deviation allowed between the two tangent ﬁelds. Example: OffCrv1 = MOFFSET( Crv, -0.4, 10 ); OffCrv2 = MOFFSET( Crv, -0.4, 5 ); computes an oﬀset approximation to Crv with OﬀsetDistance of -0.4 and AngularError of 10 and 5 degrees, respectively. See also OFFSET, TOFFSET, AOFFSET, LOFFSET, and FFMATCH. G. Elber IRIT Solid modeler 11.2.188 137 MOMENT PointType MOMENT( CurveType Crv, 0 ); or VectorType MOMENT( CurveType Crv, 1 ); approximate the zero and ﬁrst moments of curve Crv. Example: a = circle( vector( 0, 0, 0 ), 1 ); a = cregion( a, 0, 1 ); p = moment( a, 0 ); v = moment( a, 1 ); view(list(a, p, v), on); a = cregion( a, 0, 1 ) * rz( 45 ); p = moment( a, 0 ); v = moment( a, 1 ); view(list(a, p, v), on); computes and displays the zero and ﬁrst moments of a quarter of a circle in two orientations. See also SMOMENTS, SVOLUME and TVOLUME. 11.2.189 MPOWER MultivarType MPOWER( ListType Orders, ListType CtlPts ) creates a polynomial/rational multivariate out of the provided control mesh. Orders is a list of orders whose size deﬁne the number of dimensions that the multivariate has. The created multivariate employs the monomial power basis. CtlPts is a linear list of control points. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the multivariate’s control mesh. The multivariate’s point type will be of a space which is the union of the spaces of all points. Example: MV = MPOWER( list( 4 ), list( ctlpt( ctlpt( ctlpt( ctlpt( E3, -1, 0.5, 2 ), E3, 3, -1.5, 0 ), E3, 0, -1.5, 0 ), E3, -1, 3.5, 0 ) ) ); constructs a univariate cubic multivariate object. See also MBEZIER and MBSPLINE. 11.2.190 MRAISE MultivarType MRAISE( MultivarType TV, ConstantType Direction, NumericType NewOrder ) G. Elber IRIT Solid modeler 138 raises Srf to the speciﬁed NewOrder in the speciﬁed Direction. Example: MV2 = MRAISE( MRAISE( MV2, 0, 4 ), 1, 4 ); raises multivariate MV1 to a cubic in the ﬁrst and second directions. See also TRAISE, SRAISE, and CRAISE. 11.2.191 MRCHCUBE PolygonType MRCHCUBE( ListType VolumeSpec, PointType CubeDim, NumericType SkipFactor, NumericType IsoVal ) applies (a variation of) the marching cubes algorithm (see W. E. Lorensen and H. E. Cline. ”Marching Cubes: A High Resolution 3D Surface Construction Algorithm.” Computer Graphics (SIGGRAPH ’87 Proceedings), Vol. 21, No. 4, pp 163-169, July 1987.) to the given volumetric data set or trivariate. VolumeSpec can be a list of four or ﬁve objects as follows: 1 4 5 a list of image ﬁle names as list( list( ImageName1, ..., ImageNameN) ) a 4-tuple of the form (TrivarType TV, NumericType Axis, NumericType SamplingFactor, NumericType TVNormal) a 5-tuple of the form (StringType FileName, NumericType DataType, NumericType Width, NumericType Height, NumericType Depth ) In the ﬁrst case, the list of images are considered slices in the volume. All images are read in and stacked together to form the volume. The RGB colors are converted into a gray scale values. In the second case, the trivariate TV is iso surface contoured at level IsoVal along the prescribed Axis (Note a trivariate need not be a scalar function, whereas Marching Cubes assumes a scalar function). The sampling rate of the trivariate is governed by SamplingFactor with SamplingFactor equal 1.0 sets sampling rate that equates with the dimensions of the trivaariate (control mesh volume size). If TVNormals is not zero, much more accurate normals are derived using the trivariate function though it is also slower. Otherwise, ﬁrst order diﬀerencing on the cubes is employed for normal estimation. In the third case, the volume ﬁle prescribed by FileName is loaded and iso surface contoured. The ﬁle is assumed to hold Width * Height * Depth (Width ﬁrst, Depth order last) scalar numeric values of type DataType: 1 2 3 4 5 6 Regular ﬂoat or int ASCII (separated by white spaces) Two bytes short integer. Four bytes long integer. One byte (char) integer. Four bytes ﬂoat. Eight bytes double. IRIT Solid modeler G. Elber 139 Figure 64: The result of applying Marching Cubes to a trivariate scalar function using the MRCHCUBE command. Beware of the little vs big Endian problem! We assume here that you have read the volume in the same machine type in which this ﬁle was written. CubeDim allows the user to prescribe the real cell size (not necessarily cubical). SkipFactor allows the skipping of data in large data sets. SkipFactor = 1 skips nothing. SkipFactor = 2, skips every other scalar value, reducing in half all dimensions, etc. Last but not least, IsoVal sets the iso surface level. See also COVERISO, TVLOAD, and TMORPH. Example: IsoSrf = MRCHCUBE( list( ThreeCyls, 1, 1, TRUE ), point( 1, 1, 1 ), 1, 0.12 ); iso surface contours the X axis of trivariate ThreeCyls and uses the trivariate to get better normals’ estimations. Cell size is unit cube like, no dat is skipped and the iso surface level is 0.12. See Figure 64 and also Figure 36. IRIT Solid modeler 11.2.192 G. Elber 140 MREFINE MultivarType MREFINE( MultivarType TV, ConstantType Direction, NumericType Replace, ListType KnotList ) provides the ability to Replace a knot vector of MV or reﬁne it in the speciﬁed direction Direction. KnotList is a list of knots at which to reﬁne MV. All knots should be contained in the parametric domain of MV in Direction. If the knot vector is replaced, the length of KnotList should be identical to the length of the original knot vector of MV in Direction. If MV is a Bezier multivariate, it is automatically promoted to be a B-spline multivariate. Example: MV = MREFINE( MREFINE( MREFINE( MV, 0, FALSE, list( 0.333, 0.667 ) ), 1, FALSE, list( 0.333, 0.667 ) ), 2, FALSE, list( 0.333, 0.667 ) ); reﬁnes MV in the ﬁrst three directions by adding two more knots at 0.333 and 0.667. See also CREFINE, SREFINE, and TREFINE. 11.2.193 MREGION MultivarType MREGION( MultivarType MV, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) extracts a region of MV between MinParam and MaxParam in the speciﬁed Direction. Both MinParam and MaxParam should be contained in the parametric domain of MV in Direction. Example: MV1r1 = MREGION( MV1, 3, 0.1, 0.2 ); MV1r2 = MREGION( MV1, 3, 0.4, 0.6 ); MV1r3 = MREGION( MV1, 3, 0.99, 1.0 ); extracts three regions of MV1 along the 4th (directions are counted from zero) direction. See also CREGION, SREGION, and TREGION. 11.2.194 MREPARAM MultivarType MREPARAM( MultivarType MV, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) reparametrizes MV over a new domain from MinParam to MaxParam, in the prescribed Direction. This operation does not aﬀect the geometry of the multivariate and only aﬃne transforms its knot vectors. A Bezier multivariate will automatically be promoted into a B-spline surface by this function. Example: MV = MREPARAM( MREPARAM( MV, 0, 0.1, 1.9 ), 1, 0.1, 0.9 ); ensures that the multivariate MV is deﬁned over [0.1, 0.9] in the ﬁrst two directions. See also CREPARAM, SREPARAM, and TREPARAM. IRIT Solid modeler 11.2.195 G. Elber 141 MREVERSE MultivarType MREVERSE( MultivarType MV, NumericType Dir1, NumericType Dir2 ) reverses MV by ﬂipping the given two parametric directions, Dir1 and Dir2, (starting to count directions from zero). If, however, Dir2 is negative, the multivariate is reversed by ﬂipping the direction of MV in Dir1. Example: RevMV = MREVERSE( MV, 2, 4 ); reverses MV by ﬂipping the third and ﬁfth directions of MV. See also SREVERSE. 11.2.196 MSCIRC CurveType MSCIRC( PolyType Poly, ListType Tols ) or CurveType MSCIRC( ListType Geom, ListType Tols ) computes a minimum spanning circle to polyline(s) (ﬁrst form), or to a list of curves (second form). Tols is a list of two numeric values, SubdivTol and NumerTol, that are used only if the minimum spannng circle of a set of curves is required. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. The returned circle will have ’center’ and ’radius’ attributes with the circles parameters. If a cone is returned, ’angle’ and ’center’ of the cone will be returned. Example: Msc = MSCIRC( Crvs, list( 0.01, 1e-10 ) ): See Figure 65. 11.2.197 MSCONE ListType MSCONE( ListType Vecs ) computes the minimum spanning cone of a set of input vectors, Vecs. Returned is a list of the cone’s parameters as well as a geometry representation of the cone. Example: MSC = MSCONE( Vecs ); See also MSCIRC and MSSPHERE 11.2.198 MSSPHERE SurfaceType MSSPHERE( ListType Pts ) computes a minimum spanning sphere to a list of 3D points. Returned is a geometric representation of the cone with ”radius” and ”center” attributes of the parameters of the sphere. Example: MSS = MSSPHERE( Pts ); IRIT Solid modeler G. Elber 142 Figure 65: The minimum spanning circle of a set of planar curves is computed with the aid of MSCIRC. Two examples are shown. 11.2.199 MUNIVZERO ListType MUNIVZERO( ListType MVs, NumericType StepSize, NumericType SubdivTol, NumericType NumerTol ) computes the simultaneous zeros of several scalar multivariate functions, in MVs. The system is assumed to be underdetermined, having n constraints in n + 1 degrees of freedom (parameters). StepSize speciﬁes the marching step size. SubdivTol speciﬁes the subdivision tolerance in the parametric domain of the multivariates, whereas NumerTol prescribes the tolerance of the numerical improvement stage. A numerical improvement stage is applied if |NumerTol| < SubdivTol. If NumerTol is negative, and a numeric improvement stage is indeed applied, all points that fail to improve to the requested accuracy are purged away. A list of piecewise linear solution curves, each designating one univariate in the parameter space of the multivariates, is returned. Example: UnivZeroMVs = MUNIVZERO( list( MV1, MV2, MV3 ), 0.01, -1e-6 ); . See also SSINTR2, CONTOUR and MZERO. 11.2.200 MVCONTACT MultivarType MVCONTACT( SurfaceType S1, SurfaceType S2, ListType MotionCrvs, NumericType SubdivTol, NumericType NumerTol, NumericType UseExprTrees ) IRIT Solid modeler G. Elber 143 computes the contact locations, if any, when S1 is stationary and S2 is moving along the MotionCrvs animation curves. Currently only ”MOV XYZ” and ”SCL” animation curves are supported. SubdivTol and NumerTol control the tolerance of the computation as in MZERO. If UseExpreTrees, expression trees are used in the computation which is typically faster. Example: Cntct = MVCONTACT( s1, s2, list( mov_xyz ), 0.02, -1e-14, true ); 11.2.201 MVEXPLICIT MultivarType MVEXPLICIT( NumericType Dim, StringType Expression ) constructs a multivariate power basis from the given polynomial Expression. The Expression can be any inﬁx notational expression using +-/*^ with no parenthesis. The parameters are the 26 letters A-Z. The dimension of the multivariate is set by Dim and should be in line with the variables used. A stands for the ﬁrst dimension, B for the second, etc., so if Dim equal 3, only A, B, and C could appear in Expression. Having a higher letter with a lower dimension constitutes an error. Example: M1 = coerce( mvexplicit( 2, "A^2 + B^2 - 1" ), bezier_type ); M2 = coerce( mvexplicit( 2, "4 * A^2 + B^2 / 4 - 1" ), bezier_type ); constructs two scalar saddle Bezier bivariate surfaces, represented as multivariates. 11.2.202 MVINTER MultivarType MVINTER( ListType Geometry, NumericType SubdivTol, NumericType NumerTol, NumericType UseExprTrees ) computes the intersection of two planar curves (Geometry is a list of two planar curves) or three surfaces (Geometry is a list of three surfaces). SubdivTol and NumerTol control the tolerance of the computation as in MZERO. If UseExpreTrees, expression trees are used in the computation which is typically faster. Example: Sln1 = MVINTER( list( c1, c2 ), 0.001, 1e-8, true ); 11.2.203 NCCNTRPATH ListType NCCNTRPATH( PolyType Obj, NumericType Offset, NumericType ZBaseLevel, NumericType TPathSpace, NumericType Units ) or ListType NCCNTRPATH( SurfaceType Obj, NumericType Offset, NumericType ZBaseLevel, NumericType TPathSpace, NumericType Units ) builds Numerically controlled (NC) tool path to mill (machine) the given Obj geometry. The Oﬀset prescribes the necessary oﬀset, due to the tool’s ball end radius. ZBaseLevel sets a base level the toolpath will not go below. and Units sets the used units with 0 for inches and 1 for mm. The IRIT Solid modeler G. Elber 144 toolpath is built as parallel contours of the (oﬀset of the) input Obj, contours that are TPathSpace spacing apart. The following attributes are optional and supported by NCCNTRPATH: NCCntrBBox NCCntrClip NCCntrMaxDepthStep NCCntrSlowOnPlunge A string attribute with six numeric values as ”XMin XMax YMin YMax ZMin ZMax”. Bounds the working space of the contouring. A closed polyline object to clip the ﬁnal toolpath to be conﬁned to its interior. Speciﬁes how deep can tool plunge in compared to the last depth, in the last contour. Adds additional paths to conﬁrm to this, if needed. If set and plung this much, generates toolpath with ”RelFeedrate” attributes to slowdown. Example: Tea = load( "teapot" ); NCPath = NCCntrPath( Tea, 1/4, 0.0, 1/8, 0 ); attrib( NCPath, "NCRetractZLevel", 3.5 ); attrib( NCPath, "NCMaxXYBridgeGap", 0.25 ); save( "NCPath.nc", NCPath ); NC data can be saved using the SAVE command in G-code if the saved ﬁle type is ”.nc”. See SAVE for more, including the meaning of the diﬀerent attributes in the above example. See also NCPCKTPATH. 11.2.204 NCPCKTPATH ListType NCPCKTPATH( PolyType Obj, NumericType ToolRadius, NumericType RoughOffset, NumericType TPathSpace, NumericType TPathJoin, NumericType Units, NumericType TrimSelfInters ) computes tool path to 2D pocket machining from +Z direction the given Obj geometry (a closed curve or a closed polygon). ToolRadius sets the oﬀset to use in the pocket whereas RoughOﬀset sets the oﬀset to use during roughing (RoughOﬀset better be larger than ToolRadius). TPathSpace sets the space between adjacent pockets slices in the zigzag motion and TPathJoin prescribes the maximum distance to connect adjacent slices (if larger a full retracting will be performed). Units sets the used units with 0 for inches and 1 for mm and if TrimSelfInters is TRUE also attempts to eliminate self intersections due to the applied oﬀsets. Example: TPath = NCPcktPath( Crv, 0.05, 0.06, 0.02, 0.05, 0, true ); attrib( TPath, "NCRetractZLevel", 1.0 ); attrib( TPath, "NCMaxXYBridgeGap", 0.05 ); save( "TPath.nc", TPath ); NC data can be saved using the SAVE command in G-code if the saved ﬁle type is ”.nc”. See SAVE for more, including the meaning of the diﬀerent attributes in the above example. See also NCCNTRPATH. IRIT Solid modeler 11.2.205 G. Elber 145 MZERO ListType MZERO( ListType MVs, NumericType SubdivTol, NumericType NumerTol ) computes the simultaneous zeros of several scalar multivariate functions, in MVs. SubdivTol speciﬁes the subdivision tolerance in the parametric domain of the multivariates, whereas NumerTol prescribes the tolerance of the numerical improvement stage. A numerical improvement stage is applied if |NumerTol| < SubdivTol. If NumerTol is negative, and a numeric improvement stage is indeed applied, all points that fail to improve to the requested accuracy are purged away. A list of control points, each designating one location in the parameter space of the multivariates, is returned. The number of multivariates cannot exceed the dimension of the multivariates. That is, if the MVs are trivariates, then, at most, three of them may be provided. If less are provided, then the dimension of the solution space is larger than zero and a ﬁnite cloud of points sampled from that solution space will be returned. Example: ZeroMVs = MZERO( list( MV1, MV2, MV3 ), 0.01, -1e-6 ); . See also CONTOUR and MUNIVZERO. 11.2.206 MPROMOTE PromMV = MPROMOTE( MultivarType MV, ListType AddDir ); or PromMV = MPROMOTE( MultivarType MV, ListType NewDimStartAxis ); promote the multivariate MV to a higher dimension. In the ﬁrst form (a list of one numeric value), the multivariate will be promoted to have one more dimension (i.e. a bivariate would become a trivariate). The new added axis will be AddDir. The second form (a list of two numeric values) allows the original multivariate to be placed at axes from StartAxis and have a new dimensional NewDim. Example: ms = coerce( srf, multivar_type ); coerce( mfrommv( MPROMOTE( ms, list( 0 ) ), 0, 0.5 ), surface_type ) == srf; coerces a surface to a multivariate, promotes it to a trivariate-multivariate, extracts an iso-surface bivariate-multivariate along the new introduced axis from the trivariate-multivariate and compares it to the original surface. It should be equal! 11.2.207 NIL ListType NIL() creates an empty list so data can be accumulated in it. See CINFLECT or CZEROS for examples. See also LIST and SNOC. IRIT Solid modeler 11.2.208 G. Elber 146 OFFSET PolygonType OFFSET( PolygonType Poly, NumericType OffsetDistance, NumericType Smoothing, NumericType MiterEdge ) or CurveType OFFSET( CurveType Crv, NumericType OffsetDistance, NumericType Tolerance, NumericType BezInterp ) or CurveType OFFSET( CurveType Crv, CurveType OffsetDistance, NumericType Tolerance, NumericType BezInterp ) or SurfaceType OFFSET( SurfaceType Srf, NumericType OffsetDistance, NumericType Tolerance, NumericType BezInterp ) or TrimSrfType OFFSET( TrimSrfType TrimSrf, NumericType OffsetDistance, NumericType Tolerance, NumericType BezInterp ) oﬀset Poly, Crv, Srf or a TrimSrf, by translating all the vertices or control points in the direction of the normal of the poly/curve or of the (trimmed) surface by an OﬀsetDistance amount. For a Poly object, the input can be a single polygon or a single polyline, in which case the oﬀset is computed in the XY plane, or can be a polygonal model in which case the oﬀset is computed in R3 . In the former case, the result is an oﬀset of the original polygon/line in the XY plane and is exact. In the latter case, the normals at the vertices of the polygonal model are employed (and are locally estimated if non detected), and all vertices are moved in the vertices normals, scaled by this oﬀset distance. For oﬀset in R3 , if Smoothing is TRUE, normals at the vertices are always recomputed and smoothed out. Also for an oﬀset in R3 , if MiterEdge is positive, attempts to properly compenstate for miter edges’ based oﬀset is made, upto a scaling factor set by the value of MiterEdge. Otherwise, each control point has a node parameter value associated with it, which is used to compute the normal. The returned curve or surface only approximates the real oﬀset. If the resulting approximation does not satisfy the accuracy required by Tolerance, Crv or Srf or TrimSrf is subdivided and an oﬀset approximation ﬁt is computed for the two halves. For curves, one can request a Bezier interpolation scheme in the oﬀset approximation by setting BezInterp. BezInterp is not yet supported for (trimmed) surfaces. Negative OﬀsetDistance denotes oﬀset in the reversed direction of the normal. If the curve is a 3D curve (E3 or P3) the oﬀset is computed using the nornal of the frenet frame of the curve. Make sure you use a 2D curve (E2 or P2) for a proper oﬀset in the plane. If OﬀsetDistance is a (scalar) curve, the curve’s ﬁrst coordinate is used to prescribe a variable oﬀset amount along the curve for which we compute the variable oﬀset. Both Crv and OﬀsetDistance must share the same parametric domain. Example: OffCrv = OFFSET( Crv, -0.4, 0.1, off ); IRIT Solid modeler G. Elber 147 Figure 66: Oﬀset approximation (thick) of a B-spline curve (thin). (See also Figure 5.) oﬀsets Crv by the amount of −0.4 in the reversed normal direction, Tolerance of 0.1 and no Bezier interpolation. See also TOFFSET, AOFFSET, LOFFSET and MOFFSET. See Figure 66. 11.2.209 ORTHOTOMC CurveType ORTHOTOMC( CurveType Crv, PointType Pt, NumericType K ) or, SurfaceType ORTHOTOMC( SurfaceType Srf, PointType Pt, NumericType K ) compute the K-orthotomic of freeform curves and surfaces. See Fundamentals of Computer Aided Geometric Design, by J. Hoschek and D. Lasser. A K-orthotomic equal, P t + K (F − P t), N N, (19) where F is the curve or surface and N is its unit normal ﬁeld. Example: pt = point( 0, 0.35, 0 ); crv = cbezier( list( ctlpt( E2, -0.8, -0.6 ), ctlpt( E2, -0.3, -0.2 ), ctlpt( E2, 0.0, 0.0 ), ctlpt( E2, 0.8, -0.6 ) ) ); Orth = ORTHOTOMC( crv, pt, 2 ); interact( list( Orth, crv, pt ) * tx( 0.5 ) ) ); computes the orthotomic of a cubic Bezier curve that has an inﬂection point. Note that inﬂection points are reduced to cusps in the orthotomic result. See Figure 67. 11.2.210 PATTRIB AnyType PATTRIB( PolyType Poly, NumericType Index, StringType Name, AnyType Value ) IRIT Solid modeler G. Elber 148 Figure 67: An orthotomic (thick) of a cubic Bezier curve. The inﬂection point in the cubic Bezier is reduced to a cusp in the orthotomic. Computed using the ORTHOTOMC command. provides a mechanism to set/get an attribute to a vertex of a polygon. Unlike the regular ATTRIB/RMATTR functions, PATTRIB allows access to the Index vertex in polygon Poly, access that is otherwise impossible. Index starts at zero for the ﬁrst vertex. The attribute will have a name Name and a value Value. If Value is NIL(), no attributes are set and the named attribute, if any, is returned. This PATTRIB function only allows numeric values or strings as Value. For example, PATTRIB( Tri, 0, "rgb", "255,0,0"); PATTRIB( Tri, 1, "rgb", "0,255,0"); PATTRIB( Tri, 2, "rgb", "0,0,255"); sets the RGB values of the three vertices of triangle Tri. See also PNORMAL, ATTRIB, ATTRPROP, GETATTR, RMATTR, CPATTR. 11.2.211 PCIRCLE CurveType PCIRCLE( VectorType Center, NumericType Radius ) is the same as CIRCLE but approximates the circle as a polynomial curve. See also CIRCLE. 11.2.212 PCRVTR PolyType PCRVTR( PolyType Pl, NumericType NumOfRings, NumericType CubicFit ) G. Elber IRIT Solid modeler 149 estimates curvature properties of given polygonal model Pl, assuming Pl originated from a continuous freeform surfaces. NumOfRings sets the number of rings around a vertex that will be used to estimate the curvature properties of the vertex. If (CubicFit is TRUE, a cubic ﬁt is computed to the local vertex neighborhood, or a quadratic ﬁt, if FALSE. The return polygonal object is identical to Pl, but with the following attributes set at each vertex: ”K1Curv” ”K2Curv” ”KCurv” ”HCurv” ”D1” ”D2” First principal curvature value Second principal curvature value The Gaussian Curvature The Mean Curvature The ﬁrst principal direction The second principal direction See also PPROPFTCH. 11.2.213 PDECIMATE PolygonType PDECIMATE( PolygonType Obj, NumericType DecimType, NumericType Threshold ) Given a polygonal model, Obj, decimate and merge polygons, eﬀectively reducing the size of the data subject to a maximal deviation distance as controlled via Threshold and DecimType. DecimType can be either TRUE when Threshold has a continuous zero to one control over the output size or FALSE when Threshold prescribes the exact number of polygons desired. Example: gcross = cbspline( 3, list( ctlpt( E3, 0.3, ctlpt( E3, 0.1, ctlpt( E3, 0.1, ctlpt( E3, 0.5, ctlpt( E3, 0.6, list( KV_OPEN ) ); resolution = 30; glass = surfprev( gcross ); 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 0.1 0.4 0.5 0.8 ), ), ), ), ) ), pglass = gpolygon( glass, false ); dglass = PDECIMATE( pglass, false, 0.5 ); creates a surface of a glass, approximates it with polygons and then decimates the latter. See Figure 68 for the original and decimated polygonal glass. 11.2.214 PDOMAIN ListType PDOMAIN( FreeformType Freeform ) returns the parametric domain of the given Freeform. See also MESHSIZE, FFCTLPTS, FFKNTVEC, FFMESH, FFMSIZE, FFPTTYPE, FFORDER. Example: circ_domain = PDOMAIN( circle( vector( 0.0, 0.0, 0.0 ), 1.0 ) ); IRIT Solid modeler G. Elber 150 Figure 68: A polygonal object (left) can be decimated and reduced (right) to within a given tolerance by using PDECIMATE. 11.2.215 PINTERP PlaneType PINTERP( ListType PtsList ) least squares ﬁts a plane to a given set of points PtsList. Example: Pln = PINTERP( Pts ); 11.2.216 PIMPRTNC PolyType PIMPRTNC( PolyType Pl, NumericType GenImprtncPolylines ) computes the importance of a local neighborhood in a triangular polygonal mesh bf Pl, based on the dihedral angles of the edges in that neighborhood. If GenImprtncPolylines FALSE, every vertex in the returned mesh will have a ”SilImp” (See the connection of this importance to silhouettes?) attribute with its importance. Otherwise, if GenImprtncPolylines TRUE, polylines that stylistically convey the importance of the diﬀerent regions in this mesh are returned. Example: Pl = triangl( box( vector( 0, 0, 0 ), 1, 2, 3 ), 1 ); PlImp = PIMPRTNC( Pl, 0 ); 11.2.217 PLANE PointType PLANE( NumericType A, NumericType B, NumericType C, NumericType D ) creates a plane type object, using the four provided NumericType coeﬃcients. See also VECTOR, POINT. IRIT Solid modeler 11.2.218 G. Elber 151 PLANECLIP ListType PLANECLIP( PolyType Poly, PlaneType Pln ) clips a polygonal model Poly against a plane Pln. Three polygonal objects are returned in a list: polygons on the positive side of the plane, polygons that intersect the plane, and polygons on the negative side of the plane, in this order. If one of these lists is empty, a numeric zero is substituted. Example: Pls = PLANECLIP( Pl, plane( 1, 1, 0, 0 ) ); clips polygonal object Pl against the plane X+Y=0. 11.2.219 PLN3PTS PlaneType PLN3PTS( PointType Pt1, PointType Pt2, PointType Pt3 ) computes a plane out of three points. Example: Pl1 = PLN3PTS( point( 0, 0, 0 ), point( 0, 1, 0 ), point( 1, 0, 0 ) ); 11.2.220 PMORPH PlaneType PMORPH( PolyType Pl1, PolyType Pl2, NumericType Blend ) creates a new polygonal object which is a metamorph of the two given polygonal objects that share the same topology. That is, Pl1 and Pl2 must share the same number of polygons and the i’th polygon in Pl1 must be equal in its number of vertices to the i’th polygon of Pl2. This is very useful if a sequence that ”morphs” one polygonal model to another is to be created. Example: Pl1 = con2( vector( 0.0, -0.5, -0.5 ), vector( 0.0, 0.0, 1.0 ), 0.4, 0.1, 3 ); Pl2 = con2( vector( 0.0, 0.5, 0.0 ), vector( 0.0, 0.0, 1.0 ), 0.1, 0.4, 3 ); Pl = PMORPH( Pl1, Pl2, 0.5 ); creates a cylinder out of two truncated cones, using PMORPH. See also CMORPH and SMORPH. 11.2.221 PNORMAL PointType PNORMAL( PolyType Poly, NumericType Index, VectorType Normal ) provides a mechanism to set/get the normal of vertex number Index in a polygon Poly. Index starts at zero for the ﬁrst vertex. Normal replaces the current normal that is also returned. If Normal is not a VectorType, no new normal is set but the current normal is still returned, allowing normals to be queried. For example, PNORMAL( Tri, 0, vector( 1, 0, 0 ) ); PNORMAL( Tri, 1, vector( 0, 1, 0 ) ); sets the normals of the ﬁrst two vertices in triangle Tri to be the X and Y axes, respectively. See also PATTRIB. IRIT Solid modeler G. Elber 152 Figure 69: Polar silhouette computed for this glass shaped surface using the POLARSIL 11.2.222 POINT PointType POINT( NumericType X, NumericType Y, NumericType Z ) Creates a point type object, using the three provided NumericType scalars. See also VECTOR, PLANE. 11.2.223 POLARSIL PolygonType POLARSIL( SurfaceType Srf, VectorType ViewDir, NumericType SubdivTol, NumericType EuclideanSpace ) Computes the polar silhouettes of surface Srf from view direction ViewDir. Equal to ¡ S(u, v) x N(u, v), VDir ¿ = 0. If EuclideanSpace TRUE, the polar silhouettes are returned in Euclidean space, over Srf. Otherwise, the polar silhouettes are returned in the parametric domain of Srf. SubdivTol controls the accuracy of the computation of the polar silhouettes. Example: pSil = polarsil( glass, vector( 1, 0, 0 ), 0.01, true ); See Figure 69 for this example. 11.2.224 POLY PolygonType POLY( ListType VrtxList, NumericType IsPolyline ) creates a single polygon/polyline (and therefore open) object, deﬁned by the vertices in VrtxList (see LIST). All elements in VrtxList must be one of PointType, VectorType, CtlPtType, or PolygonType types. If IsPolyline, a polyline is created; otherwise, a polygon. Example: V1 V2 = vector( 0.0, 0.0, 0.0 ); = vector( 0.3, 0.0, 0.0 ); G. Elber IRIT Solid modeler Figure 70: Polygons or polylines can be manually constructed using the POLY constructor. V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 I = = vector( 0.3, 0.0, = vector( 0.2, 0.0, = vector( 0.2, 0.0, = vector( 0.3, 0.0, = vector( 0.3, 0.0, = vector( 0.0, 0.0, = vector( 0.0, 0.0, = vector( 0.1, 0.0, = vector( 0.1, 0.0, = vector( 0.0, 0.0, POLY( list( V1, V2, FALSE ); 0.1 0.1 0.5 0.5 0.6 0.6 0.5 0.5 0.1 0.1 V3, ); ); ); ); ); ); ); ); ); ); V4, V5, V6, V7, V8, V9, V10, V11, V12 ), constructs an object with a single polygon in the shape of the letter I. See Figure 70. 11.2.225 POLYHOLES PolygonType POLYHOLES( PolygonType OuterPoly, PolygonType Island ) or PolygonType POLYHOLES( PolygonType OuterPoly, ListType Islands ) 153 G. Elber IRIT Solid modeler 154 merges the given Island(s) into the main polygon OuterPoly, creating a polygon with holes. The outer polygon OuterPoly is assumed to be oriented in the opposite direction to that of the Island(s). 11.2.226 PPINCLUDE NumericType PPINCLUDE( PolyType Pl, PointType Pt ) tests if a point Pt is inside a 3D closed polyhedra Pl in 3-space or if a point Pt is inside a 2D closed polygon Pl in 2-space, if Pl contains only one (planar) polygon. Returns TRUE if inside, FALSE otherwise. Example: if ( PPINCLUDE( Pl, pt ), ... ); See also CPINCLUDE. 11.2.227 PPINTER ListType PPINTER( PolyType Pl1, PolyType Pl2 ) computes the intersection of two individual polygons in R3, Pl1 and Pl2. Similar results can also be obtained via Boolean operations. Example: Pl1 = poly( list( point( -1, -1, 0 point( -1, 1, 0 point( 1, 1, 0 point( 1, -1, 0 Pl2 = Pl1 * rx( 70 ) * tx( 0.5 ); ), ), ), ) ), false ); Inter1 = PPINTER( Pl1, Pl2 ); iritstate( "intercrv", true ); Inter2 = Pl1 * Pl2; computes the intersection edge of two polygons in two diﬀerent ways. Note, however, that while PPINTER considers only the ﬁrst polygon in a polygonal object, the Boolean operations considers them all. 11.2.228 PPROPFTCH PolyType PPROPFTCH( PolyType Pl, NumericType PropType, ListType PropParam ) computes piecwise linear curves over polygonal mesh Pl. The extracted curves could be one of, Property Attribute Value Isophotes Gaussian Crvtr Mean Crvtr PropType 0 1 2 3 PropParam list( AttrName, AttrValue ) list( ViewDir, InclinationAngle ) list( NumRingCrvtrAprx, CrvtrVal ) list( NumRingCrvtrAprx, CrvtrVal ) G. Elber IRIT Solid modeler 155 The NumRingCrvtrAprx speciﬁes how many rings around a vertex should be considered when the curvature of the vertex is estimated. Typically 1. Example: Pl1 = PPropFtch( Srf, 1, list( normalize( vector( 1, 1, 1 ) ), 90 ) ); Pl2 = PPropFtch( Srf, 1, list( normalize( vector( 1, -1, 1 ) ), 90 ) ); Pl3 = PPropFtch( Srf, 1, list( normalize( vector( 1, 0, 1 ) ), 90 ) ); extracts silhouettes from surface Srf (note an InclinationAngle of 90 degrees extract silhouettes), from three diﬀerent viewing direction. See also PCRVTR, SILHOUETTE, ISOCLINE, PPROPFTCH and SASPCTGRPH. 11.2.229 PRINTER ListType PRINTER( PolyType Pl, NumericType RayPt, NumericType RayDir ) computes the number of XY planar intersection of ray (RayPt, RayDir) with a single polygon Pl. Returned is the number of interesections found. 11.2.230 PRISA ListType PRISA( SurfaceType Srfs, NumericType SamplesPerCurve, NumericType Epsilon, ConstantType Dir, VectorType Space, NumericType CrossSecs ) or ListType PRISA( TrimSrfType TrimSrfs, NumericType SamplesPerCurve, NumericType Epsilon, ConstantType Dir, VectorType Space, NumericType CrossSecs ) compute a layout (prisa) of the given surface(s) Srfs or TrimSrfs, and return a list of (trimmed) surface objects representing the layout. The surface is approximated to within Epsilon in direction Dir into a set of ruled surfaces, and then developable surfaces that are laid out ﬂat onto the XY plane. If Epsilon is negative, the piecewise ruled surface approximation in 3-space is returned. SamplesPerCurve controls the piecewise linear approximation of the boundary of the ruled/developable surfaces. Space is a vector whose X component controls the space between the diﬀerent surfaces’ layout, and whose Y component controls the space between diﬀerent layout pieces. If CrossSecs is not zero, the 3D cross sections, approximated as planar, of each laid out region are also provided. Example: cross = cbspline( 3, list( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, E3, 0.7, 0.7, 0.1, 0.1, 0.6, 0.8, 0.8, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0. ), 0.06 ), 0.1 ), 0.6 ), 0.6 ), 0.8 ), 1.4 ), IRIT Solid modeler G. Elber 156 Figure 71: The layout (prisa in hebrew...) of a freeform surface can be approximated using the PRISA function. ctlpt( E3, 0.6, 0.0, 1.6 ) ), list( KV_OPEN ) ); wglass = surfrev( cross ); wgl_ruled = PRISA( wglass, 6, -0.1, COL, vector( 0, 0.25, 0.0 ), false ); wgl_prisa = PRISA( wglass, 6, 0.1, COL, vector( 0, 0.25, 0.0 ), true ); computes a layout of a wine glass in wgl prisa and a three-dimensional ruled surface approximation of wglass in wgl ruled. See Figure 71. See also FMLNANAL. 11.2.231 PSUBDIV CurveType PSUBDIV( PolyType Plgns, NumericType SubdivisionScheme, NumericType Numiterations, NumericType SmoothNormals, NumericType TrianglesOnly, NumericType AdditionalParam ) applies one of several subdivision schemes to the given polygonal object Plgns. The SubdivisionScheme can be one of: Catmull Clark if 0, Loop if 1, Butterﬂy if 2. The number of subdivision iterations applied is set by Numiterations. If SmoothNormals is TRUE, a normal approximation scheme is applied to the result, for the vertices of the model, by averaging adjacent faces normals at each vertex. If TrianglesOnly, the output is examined and non triangles are dividied into triangles. Finally, if the Butterﬂy scheme is applied, AdditionalParam is used as the tension. CatmulRomPl = PSUBDIV( Plgns, 0, 1, 1, 1, 0 ); See Figure 72. G. Elber IRIT Solid modeler 157 Figure 72: Applied a subdivision scheme for polygonal models using the PSUBDIV command. From left to right: Original half-a-pawn model, Catmull Clark, Loop, and Butterﬂy, after one iteration. 11.2.232 PT3BARY VectorType PT3BARY( PointType Pt1, PointType Pt2, PointType Pt3, PointType InteriorPt ) computes the barycentric coordinates of InterPt with respect to the triangle deﬁned by Pt1, Pt2, Pt3. A vector of three coeﬃcents, which are the weights of the three points of the triangle, are returned. InteriorPt is assumed to be in the triangle. Example: Coeffs = PT3BARY( point( point( point( point( 11.2.233 0, 0, 1, 0, 0, 1, 0.25, 0 ), 0 ), 0 ), 0.25, 0.0 ) ); PTHMSPR ListType PTHMSPR( NumericType Size ) computes a fairly uniform distribution of points on a hemisphere. Size hints at the distance between adjacent placed points. Example: Pts = PTHMSPR( 0.1 ); 11.2.234 PTLNPLN VectorType PTLNPLN( PointType LineOrig, VectorType LineRay, PlaneType Plane ) computes the point of intersection of given line LineOrig, LineRay with plane Plane. Example: InterPt = PtLnPln( point( 1, 0, 1 ), vector( 1, 1, 1 ), Plane( 0, 0, 1, 0 ) ); IRIT Solid modeler 11.2.235 G. Elber 158 PTPTLN VectorType PTPTLN( PointType Point, PointType LineOrig, VectorType LineRay ) computes the point on line LineOrig, LineRay that is closest to point Point. See also DSTPTLN. Example: ClosestPt = PTPTLN( point( 0, 0, 0 ), point( 1, 1, 0 ), vector( 1, 1, 1 ) ); 11.2.236 PTREGISTER MatrixType PTREGISTER( ListType PtSet1, ListType PtSet2, NumericType StepSize, NumericType Tolerance ) registers one points set, PtSet1, with another, PtSet2. The two points sets are assumed to be rigid motion of one another. StepSize controls the step size of the numerical process and must be a positive real less than 1.0. The larger StepSize is, the faster the convergance with less stability. Finally, Tolerance prescribes the necessary accuraacy in L-inﬁnity sense. This function will converge for small rotational deviations only. Pt1 = nil(); for (i = 0, 1, 15, Pt = point( random( -.7, .7 ), random( -.7, .7 ), random( -.7, .7 ) ): snoc( Pt * tx( 0 ), Pt1 ) ); Pt2 = Pt1 * rx( 13 ) * ry( 5 ) * rz( 11 ) * tx( 0.1 ) * ty( 0.03 ) * tz( -0.05 ); Tr = PTREGISTER( Pt1, Pt2, 1, 1e-6 ); 11.2.237 PTS2PLLN ListType PTS2PLLN( ListType Points, NumericType MaxMatchDist ) matches the given cloud of points in a list of polylines. MaxMatchDist is used as the maximal distance between two adjacent points to connect. Example: Pts = nil(); for ( i = 0, 1, 100, t = random( 0, 2 * Pi ): snoc( point( cos( t ), sin( t ), 0 ), Pts ) ); Pll = PTS2PLLN( Pts, 0.1 ); connects 100 random points on the unit circle into a polyline approximating an (almost) complete circle. 11.2.238 PTS2PLYS PolylineType PTS2PLYS( ListType Points, NumericType MergeTol ) merges a list of points Points to polylines. Merges the points until two adjacent points are at most MergeTol apart. Points is a list of with PointType or CtlPtType. In the later case the control point can be of arbitrary dimension. IRIT Solid modeler 11.2.239 G. Elber 159 PTSLNLN ListType PTSLNLN( PointType Line1Orig, VectorType Line1Ray, PointType Line2Orig, VectorType Line2Ray ) computes the closest two points on the two lines deﬁned by point LineiOrig and ray LineiRay. See also DSTLNLN. A list object with the two points is returned. Example: ClosestPts = PtsLnLn( point( 1, 0, 0 ), vector( 0, 1, 0 ), point( 0, 1, 0 ), vector( 1, 0, 0 ) ); 11.2.240 QUADCRVS ListType QUADCRVS( CurveType Crv, NumericType Tolerance, NumericType MaxLen ) approximates given curve Crv using piecewise quadratic curves upto the prescribed tolerance Tolerance. If MaxLen is positive it is used to limit the arc length of the cubic curves segments. Example: PQaudCrv = QUADCRVS( Crv, 0.01, 0.5 ); creates a piecewise quadratic approximation to curve Crv upto tolerance 0.01 and maximal arc length of cubic segments of 0.5. See also CUBICCRVS, CBIARCS. 11.2.241 QUADRIC ListType QUADRIC( ListType ABCDEFGHIJ ) ) or ListType QUADRIC( ListType ABCDEFZ ) ) in the ﬁrst form, constructs a quadric parametric surface whose coeﬃcients are the ten coeﬃcients in the list ABCDEFGHIJ: Ax2 + By 2 + Cz 2 + Dxy + Exz + F yz + Gx + Hy + Iz + J = 0. (20) In the second form, promotes the given conic curve whose coeﬃcients are the ﬁrst six coeﬃcients in the list ABCDEFZ: (21) Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0. into a quadric surface with height in z of Z amount, the seven’th list element. Example: Sph = QUADRIC( list( 1, 1 , 1 , 0, 0, Hyp1s = QUADRIC( list( 1, 1, -1, 0, 0, Hyp2s = QUADRIC( list( 1, -1, -1, 0, 0, Ellipse = list( 1, 0, 2, 0, 0, -1 ): Ellipsoid = QUADRIC( Ellipse + list( 0.1 ) 0, 0, 0, ); 0, 0, 0, 0, 0, 0, 0, -1 ) ); 0, -1 ) ); 0, -1 ) ); IRIT Solid modeler G. Elber 160 constructs four quadric surfaces, a sphere, a portion of a hyperboloid of one sheet, a portion of a hyperboloid of two sheets, and promotes an ellipse to an ellipsoid of Z height of 0.1. Note only elliptic surfaces are compact and are reconstructed in whole. Because the parametrization of the quadric is predetermined, one might need to use SREGION and SMOEBIUS to extract subregions and/or reparametrize the surface. See also CONICSEC, IMPLCTTRANS, ELLIPSE3PT. 11.2.242 RAYTRAPS ListType RAYTRAPS( ListType Crvs, NumericType Orient NumericType SubdivTol, NumericType NumerTol, NumericType UserExprTree ) or ListType RAYTRAPS( ListType Srfs, NumericType Orient NumericType SubdivTol, NumericType NumerTol, NumericType UserExprTree ) computes locations on the given planar curves or 3-space surfaces that would bounce rays from one object to the next, in an inﬁnite cycle. Such traps are denoted ray traps. Ray-traps are computed for the given list of Crvs or Srfs, in the given order. The ray-trap problem is posed as a set of n multivariate algebraic constraints with n variables, given n objects prescribed in Crvs or Srfs. The simultaneous solution of these constraints is computed using the MZERO function. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. If Orient, attempt is made to orient the curves/surfaces which is likely to speed up the process. If UserExprTree, expression trees constraints are used instead of tensor products. Again, typically faster and much less memory use. Example: Crv1 = pcircle( vector( -0.75, -0.75, 0 ), 0.5 ); Crv2 = Crv1 * sc( 1.5 ) * tx( 2 ); Crv3 = Crv1 * sc( 0.5 ) * tx( 0.2 ) * ty( 0.6 ); Tris = RayTraps( list( Crv1, Crv2, Crv3 ), 0.1, -1e-6 ); computes the ray-traps between three circles. See Figure 73. 11.2.243 RFLCTLN ListType RFLCTLN( SurfaceType Srf, VectorType ViewDir, ListType LinesSprs, NumericType Euclidean ) computes reﬂection lines/ovals to the given surface Srf as seen from view direction ViewDir. The resulting piecewise linear curves are in Euclidean space if Euclidean is TRUE and in Srf parameter space, otherwise. The reﬂection/ovals themselves are deﬁned via LinesSprs. For reﬂection lines, LinesSprs consists of list( LineDir, list( LinePos1, LinePos2, ... , LinePosN ) ); IRIT Solid modeler G. Elber Figure 73: Computes all ray-traps between three circles, using RAYTRAPS. deﬁning n parallel lines with direction LineDir through point LinePos1 to LinePosN. For reﬂection ovals, LinesSprs consists of list( SprCntr, list( Rad1, Rad2, ... , RadN ) ); deﬁning n co-spherical spheres, all located at SprCntr with radii of Rad1 to RadN. Example: resolution = 20; RefLns = RflctLn( Srf, vector( 0, 1, 2 ), list( vector( 0, 0, 1 ), list( point( -3.0, 2, 0 ), point( -1.5, 2, 0 ), point( 0.0, 2, 0 ), point( 1.5, 2, 0 ), point( 3.0, 2, 0 ) ) ), true ); RefOvals = RflctLn( Srf, vector( 1, 1, 0 ), list( point( 0, 2, 0 ), list( 5, 25, 45, 65, 85 ) ), 161 G. Elber IRIT Solid modeler 162 Figure 74: Computation of the intersection curve between two ruled surfaces via the RRINTER command. On the left, the four intersection curves are shown, while (right) shows the computed function whose zero set provides the request RRI solution. true ); computes the reﬂection lines of surface Srf from viewing direction ( 0, 1, 2 ) having ﬁve reﬂected lines and computes ﬁve reﬂection ovals from viewing direction ( 1, 1, 0 ). See also ReﬂectLns attributes in the display devices. 11.2.244 RRINTER ListType RRINTER( CurveType Srf1Crv1, CurveType Srf1Crv2, CurveType Srf2Crv1, CurveType Srf2Crv2, NumericType SubdivTol, NumericType ZeroSetFunc ) computes the intersection curves of the given two ruled surfaces, deﬁned as Srf iCrv1 ∗ v + Srf iCrv2 ∗ (1 − v), i = 1, 2, v ∈ [0, 1]. (22) The ruled ruled intersection (RRI) problem is tranformed into a zero set ﬁnding on another function. If ZeroSetFunc is true, the function whose zero set provides the RRIsolution is returned. Otherwise, if ZeroSetFunc is false, the RRI solution itself is returned. The zero set is computed via numerical zero set ﬁnding methods and Tolerance controls the ﬁneness of the approximated solution. If Tolerance is negative, the absolute value is employed as Tolerance but the intersection curves are computed as if the two ruled surfaces are inﬁnite (i.e. v is unbounded). See Figure 74. Example: c1 = cbezier( list( ctlpt( E3, -1.0, -1.0, -1.0 ), ctlpt( E3, -0.5, 8.0, -1.0 ), ctlpt( E3, 0.0, -15.0, -1.0 ), ctlpt( E3, 0.5, 8.0, -1.0 ), ctlpt( E3, 1.0, -1.0, -1.0 ) ) ); c2 = c1 * sc( 0.7 ) * tz( 1.7 ); G. Elber IRIT Solid modeler 163 r1 = ruledSrf( c1, c2 ); c1 = pcircle( vector( 0, 0, 0 ), 0.3 ) * tz( 2 ); c2 = c1 * sc( 0.5 ) * tz( -3 ); r2 = ruledSrf( c1, c2 ) * ry( 90 ); c = RRINTER( cMesh( r1, cMesh( r1, cMesh( r2, cMesh( r2, 0.1, false row, row, row, row, ); 0 1 0 1 ), ), ), ), interact( list( r1, r2, nth( c, 1 ) ) ); See also SSINTER, SSINTR2 and GGINTER. 11.2.245 RULEDFIT SurfaceType RULEDFIT( SurfaceType Srf, NumericType Dir, NumericType DomainExtension, NumericType SamplingRate ) ﬁts a ruled surface to the given general surface Srf along the speciﬁed Dir direction. Normally DomainExtension is zero by can be used to extend the domain so the ruling can start/end outside Srf’s domain. Finally SamplingRate sets the number of samples to use along the ﬁtting Dir. Example: rSrf = ruledfit( Srf, col, 0.0, 40 ); ﬁts a ruled surface to Srf along the col direction with no extension and 40 samples. See Figure 75. See also RULEDSRF. 11.2.246 RULEDSRF SurfaceType RULEDSRF( CurveType Crv1, CurveType Crv2 ) or PolygonType RULEDSRF( PolygonType Poly1, PolygonType Poly2 ) construct a ruled surface between the two curves Crv1 and Crv2 or two polylines Poly1 and Poly2. The curves do not have to have the same order or type, and will be promoted to their least common denominator. The polys must have the same number of points and both must be either polygons or polylines. Example: c1 = cbspline( 3, list( ctlpt(E3, 1.7, 0.0 , 0 ctlpt(E3, 0.7, 0.7 , 0 ), ), G. Elber IRIT Solid modeler Figure 75: A ruled surface ﬁtting to a general hyperbolic surface using RULEDFIT. ctlpt(E3, 1.7, ctlpt(E3, 1.5, ctlpt(E3, 1.6, list( KV_OPEN ) ); c2 = cbspline( 3, list( ctlpt(E3, 0.7, ctlpt(E3,-0.7, ctlpt(E3, 0.7, ctlpt(E3,-0.7, ctlpt(E3, 0.7, list( KV_OPEN ) ); 0.3 , 0 0.8 , 0 1.0 , 0 ), ), ) ), 0.0 0.2 0.5 0.7 1.0 ), ), ), ), ) ) , , , , , , 0 0 0 0 0 srf1 = RULEDSRF( c1, c2 ); interact( list( c1, c2, srf1 ), on ); c2a = ffmatch( c1, c2, 50, 100, 2, false, 1 ); srf2 = RULEDSRF( c1, c2a ); interact( list( c1, c2, srf2 ), on ); 164 IRIT Solid modeler G. Elber 165 Figure 76: A naive construction of a ruled surface (left) using RULEDSRF results in self intersection. FFMATCH is employed (right) to automatically resolve this self intersection. constructs a planar ruled surface between two curves, c1 and c2. The naive construction causes self intersection, but by employing FFMATCH the self intersection can be resolved. See Figure 76. See also FFMATCH and RULEDFIT. 11.2.247 RULEDTV TrivarType RULEDTV( SurfaceType Srf1, SurfaceType Srf2 ) constructs a ruled trivariate between the two surfaces Srf1 and Srf2. The surfaces do not have to have the same order or type, and will be promoted to their least common denominator. Example: s1 = boolone( pcircle( vector( 0, 0, 0 ), 1 ) ); s2 = boolone( pcircle( vector( 0, 0, 1 ), 0.5 ) ); tv = RULEDTV( s1, s2 ); constructs a truncated cone-volume as a ruled trivariate between two surfaces, s1 and s2. See Figure 77. See also EXTRUDE, TFROMSRFS. 11.2.248 SACCESS ListType SACCESS( SurfaceType AccessSrf, AnyType OrientFieldSrf, SurfaceType CheckSrf, NumericType SubdivTol, NumericType NumericTol ) computes the domain on the AccessSrf surface that is accessible from the orientation that is optionally prescribed by OrientFieldSrf, without gouging into the CheckSrf surface. If OrientFieldSrf is not a surface, the normal ﬁeld of AccessSrf is employed. AccessSrf and OrientFieldSrf must share a (u, v) domain, whereas CheckSrf can present a diﬀerent (s, t) domain. The accuracy of the computation is governed by a two stage solution, a subdivision stage with tolerance SubdivTol followed by a numerical improvement stage with NumericTol accuracy. The second, numeric, stage is invoked only if NumericTol ¡ SubdivTol. IRIT Solid modeler G. Elber 166 Figure 77: A ruled volume as a trivariate between two disc surfaces, created via the RULEDTV function. The returned results are a set of points on the boundary of the accessible region. The points are in E4 space as (u, v, s, t) 4-tuples. Example: c = cregion( pcircle( vector( 0, 0, 0 ), 1 ), 1, 3 ) * ry( 90 ); pSphere = surfPRev( c ) * sc( 0.3 ) * tz( 1 ); Pln = ruledSrf( ctlpt( E3, -1, -1, 0 ) + ctlpt( E3, -1, ctlpt( E3, 1, -1, 0 ) + ctlpt( E3, 1, 1, 0 ), 1, 0 ) ); Pts = SACCESS( Pln, 0, pSphere, 0.1, 1e-5 ); sPts = nil(); sPtsErr = nil(); for ( i = 1, 1, sizeof( Pts ), Pt = nth( Pts, i ): Err = getAttr( Pt, "Error"): if ( Err > 1e-5, snoc( seval( Pln, coord( Pt, 1 ), coord( Pt, 2 ) ), sPtsErr ), snoc( seval( Pln, coord( Pt, 1 ), coord( Pt, 2 ) ), sPts ) ) ); color( sPts, green ); color( sPtsErr, red ); IRIT Solid modeler G. Elber 167 Figure 78: The limit of the accessible area of the plane along the normal direction, without gouging into the sphere is computed and presented using the SACCESS function. interact( list( pSphere, Pln, sPts, sPtsErr ) ); computes the access domain of plane Pln along the normal, Z, direction while preventing gouging into the check surface pSphere. See Figure 78. See MZERO for the meaning of SubdivTol and NumerTol. 11.2.249 SASPCTGRPH PolyType SASPCTGRPH( SurfaceType Srf ) approximates the aspect graph of surface Srf by computing the principal directions with zero curvature at the parabolic points of Srf. The aspect graph is deﬁned over the unit sphere and identiﬁes all direction from which the silhouette curves of Srf change topology. Example: AG = SAspctGrph( Srf ); See also SILHOUETTE. 11.2.250 SASYMPEVAL ListType SASYMPEVAL( SurfaceType Srf, NumericType U, NumericType V, NumericType Euclidean ) evalutes the asymptotic direction of surface Srf at parametric location (U, V), if any. If Euclidean is not zero, the directions are returned in Euclidean space, otherwise, in parametric space. Returned is a list of upto two vectors. Example: AsympDir = SAsympEval( Srf, u, v, true ); See also SCRVTR. G. Elber IRIT Solid modeler 168 Figure 79: A Bezier surface (left) of degree 3 by 5 and a B-spline surface (right) of degree 3 by 3 (bi-quadratic). Both share the same control mesh. 11.2.251 SBEZIER SurfaceType SBEZIER( ListType CtlMesh ) creates a Bezier surface using the provided control mesh. CtlMesh is a list of rows, each of which is a list of control points. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the surface’s control mesh. The surface’s point type will be of a space which is the union of the spaces of all points. The created surface is the piecewise polynomial (or rational) surface, S(u, v) = m n Pij Bi (u)Bj (v) (23) i=0 j=0 where Pij are the control points CtlMesh, and m and n are the degrees of the surface, which are one less than the number of points in the appropriate direction. Example: Srf = SBEZIER( list ( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, See Figure 79. See also CBEZIER, SBSPLINE and SPOWER. 0.0, 1.0, 2.0, 0.0, 1.0, 2.0, 0.0, 1.0, 2.0, 0.0, 1.0, 2.0, 0.0, 1.0, 2.0, 1.0 0.0 1.0 0.0 2.0 0.0 2.0 0.0 2.0 0.0 2.0 0.0 1.0 0.0 1.0 ), ), ) ), ), ), ) ), ), ), ) ), ), ), ) ), ), ), ) ) ) ); IRIT Solid modeler G. Elber 169 Figure 80: (a) Bisector surface of a plane and a point computed using the SBISECTOR command. 11.2.252 SBISECTOR SurfaceType SBISECTOR( SurfaceType Srf, PointType Pt ) computes the bisector surface of a given surface to a point. See also CBISECTOR2D, CBISECTOR3D. Example: s = ruledSrf( ctlpt( E3, -1.0, -1.0, 0.0 ) + ctlpt( E3, ctlpt( E3, -1.0, 1.0, 0.0 ) + ctlpt( E3, pt = point( 0.0, 0.0, 1.0 ); bisect = SBISECTOR( s, pt ); interact( list( s, pt, bisect ) ); computes the bisector surface of a plane and a point. See Figure 80. 1.0, -1.0, 0.0 ), 1.0, 1.0, 0.0 ) ); G. Elber IRIT Solid modeler 11.2.253 170 SBSPLINE SurfaceType SBSPLINE( NumericType UOrder, NumericType VOrder, ListType CtlMesh, ListType KnotVectors ) creates a B-spline surface from the provided UOrder and VOrder orders, the control mesh CtlMesh, and the two knot vectors KnotVectors. CtlMesh is a list of rows, each of which is a list of control points. All control points must be of point type (E1-E9, P1-P9), or regular PointType deﬁning the surface’s control mesh. The surface’s point type will be of a space which is the union of the spaces of all points. KnotVectors is a list of two knot vectors. Each knot vector is a list of NumericType knots of length #CtlPtList plus the Order. If, however, the length of the knot vector is equal to #CtlPtList + Order + Order - 1, the curve is assumed to be periodic. The knot vector may also be a list of a single constant KV OPEN or KV FLOAT or KV PERIODIC, in which a uniform knot vector with the appropriate length and with an open, ﬂoating or periodic end condition will be constructed automatically. The created surface is the piecewise polynomial (or rational) surface, S(u, v) = m n i=0 j=0 Pij Bi,χ (u)Bj,ξ (v) (24) where Pij are the control points CtlMesh, and m and n are the degrees of the surface, which are one less than UOrder and VOrder. χ and ξ are the two knot vectors of the surface. Example: Mesh = list ( list( ctlpt( E3, 0.0, 0.0, 1.0 ), ctlpt( E3, 0.0, 1.0, 0.0 ), ctlpt( E3, 0.0, 2.0, 1.0 ) ), list( ctlpt( E3, 1.0, 0.0, 0.0 ), ctlpt( E3, 1.0, 1.0, 2.0 ), ctlpt( E3, 1.0, 2.0, 0.0 ) ), list( ctlpt( E3, 2.0, 0.0, 2.0 ), ctlpt( E3, 2.0, 1.0, 0.0 ), ctlpt( E3, 2.0, 2.0, 2.0 ) ), list( ctlpt( E3, 3.0, 0.0, 0.0 ), ctlpt( E3, 3.0, 1.0, 2.0 ), ctlpt( E3, 3.0, 2.0, 0.0 ) ), list( ctlpt( E3, 4.0, 0.0, 1.0 ), ctlpt( E3, 4.0, 1.0, 0.0 ), ctlpt( E3, 4.0, 2.0, 1.0 ) ) ); Srf = SBSPLINE( 3, 3, Mesh, list( list( KV_OPEN ), list( 3, 3, 3, 4, 5, 6, 6, 6 ) ) ); constructs a bi-quadratic B-spline surface with its ﬁrst knot vector having a uniform knot spacing with open end conditions. See Figure 79. See also CBSPLINE, SBEZIER and SPOWER. 11.2.254 SCRVTR SurfaceType SCRVTR( SurfaceType Srf, ConstType PtType, ConstType Dir ) G. Elber IRIT Solid modeler 171 symbolically computes the extreme curvature bound on Srf. If Dir is either ROW or COL, then the normal curvature square of Srf in Dir is computed symbolically and returned. Otherwise, an upper bound on the sum of the squares of the two principle curvatures is symbolically computed and returned. The returned value is a surface that can be evaluated to the curvature bound, given a UV location. The returned surface value is a scalar ﬁeld of point type P1 (scalar rational). However, if PtType is one of E1, P1, E3, or P3, the returned surface is coerced to this given type. If the types are one of E3, or P3, then the Y and Z axes are set to be equivalent to the U and V parametric domains. This function computes the square of the normal curvature scalar ﬁeld for surfaces as (in the U parametric direction, same for V), 2 n, ∂∂uS2 (25) κun (u, v) = ∂S ∂S ∂u , ∂u and computes ξ(u, v) = k1 (u, v)2 + k2 (u, v)2 as the scalar ﬁeld of ξ(u, v) = (g11 l22 + l11 g22 − 2g12 l12 )2 − 2 |G| |L| , |G|2 n2 (26) where gij and lij are the coeﬃcients of the ﬁrst and second fundamental forms G and L. See also CCRVTR, SCRVTREVAL, SASYMPEVAL. Example: cross = cbspline( 3, list( ctlpt( E2, 0.0, 0.0 ), ctlpt( E2, 0.8, 0.0 ), ctlpt( E2, 0.8, 0.2 ), ctlpt( E2, 0.07, 1.4 ), ctlpt( E2, -0.07, 1.4 ), ctlpt( E2, -0.8, 0.2 ), ctlpt( E2, -0.8, 0.0 ), ctlpt( E2, 0.0, 0.0 ) ), list( KV_OPEN ) ); cross = coerce( cross, e3 ); s = sFromCrvs( list( cross, cross * trans( vector( 0.5, 0, 1 ) ), cross * trans( vector( 0, 0, 2 ) ) ), 3, KV_OPEN ); view( list( s, axes ), on ); UCrvtrZXY = scrvtr( s, E3, row ); VCrvtrZXY = scrvtr( s, E3, col ); UCrvtrXYZ = UCrvtrZXY * rotx( -90 ) * roty( -90 ) * scale( vector( 1, 1, 0.001 ) ); VCrvtrXYZ = VCrvtrZXY * rotx( -90 ) * roty( -90 ) * scale( vector( 1, 1, 10 ) ); color( UCrvtrXYZ, red ); color( VCrvtrXYZ, magenta ); view( list( UCrvtrXYZ, VCrvtrXYZ ), off ); CrvtrZXY = scrvtr( s, E3, off ); IRIT Solid modeler G. Elber 172 Figure 81: From left to right: original surface, normal curvature in the U direction, normal curvature in the V direction, sum of the square of principle curvatures (diﬀerent scales). All computed using SCRVTR. CrvtrXYZ = CrvtrZXY * rotx( -90 ) * roty( -90 ) * scale( vector( 1, 1, 0.001 ) ); color( CrvtrXYZ, green ); view( CrvtrXYZ, off ); computes the square of the normal curvature in the U and V directions, ﬂips its scalar value from X to Z using rotations and scales the ﬁelds to reasonable values, and then displays them. It also displays a total bound on the normal curvature. Due to the large degree of the resulting ﬁelds, be aware that rational surfaces will compute into large degree curvature bound ﬁelds. See also IRITSTATE ”InterpProd” option for faster symbolic computation. See Figure 81. 11.2.255 SCRVTREVAL ListType SCRVTREVAL( SurfaceType Srf, NumericType U, NumericType V, NumericType Euclidean ) computes the principle curvatures and directions of surface Srf at parametric location (U, V). A list of four elements (k1, V1, k2, V2), with k1/V1 being the ﬁrst principle curvature/direction and k2/V2 being the second, is returned. If Euclidean is TRUE then the principle curvatures are returned in Euclidean space. Consecutive calls with the same surface Srf to SCRVTREVAL will yield more eﬃcient evaluations as derivative data is cached. Example: Crvtr = SCRVTREVAL( Srf, 0.5, 0.5, True ); K = nth( Crvtr, 1 ) * nth( Crvtr, 3 ); computes the Total (Gaussian) curvatures, K = k1 * k2, of Srf at (0.5, 0.5). See also SCRVTR. G. Elber IRIT Solid modeler + 173 = Figure 82: Polygonal geometry (left) could be tiled over arbitrary surface, torus in this case (middle), to yield a bumpy shape (right) using the SDDMMAP function. 11.2.256 SDDMMAP PolyType SDDMMAP( SurfaceType BaseSrf, PolyType Bump, NumericType UDup, NumericTye VDup, NumericTye LclUVs ) Tiles a composition of Bump over surface BaseSrf UDup by VDup times, creating a detailed bump geometry. Bump can be any polygonal geometry whatsoever with XY coordinates that are contained in the unit square [0, 1] x [0, 1], while Z serves as the elevation above the surface. The composed geometry could inherit the UV texture ccordinates from the UV coordinates found in Bump if LclUVs is TRUE or inherit BaseSrf UV coordinates if LclUVs is FALSE. Example: BaseTorus = torusSrf( 1, 0.2 ); BumpTorus = SDDMMAP( BaseTorus, BumpPolyObj, 6, 8, on ); constructs a bumpy BumpTorus with a bump tiled 6 x 8 times over the surface. See Figure 82. See also TEXTWARP, TDEFORM. 11.2.257 SDERIVE SurfaceType SDERIVE( SurfaceType Srf, NumericType Dir ) returns a vector ﬁeld surface representing the diﬀerentiated surface in the given direction (ROW or COL). Evaluation of the returned surface at a given parameter value will return a vector tangent to Srf in Dir at that parameter value. DuSrf = SDERIVE( DvSrf = SDERIVE( Normal = coerce( coerce( Srf, ROW ); Srf, COL ); seval( DuSrf, 0.5, 0.5 ), VECTOR_TYPE ) ^ seval( DvSrf, 0.5, 0.5 ), VECTOR_TYPE ); computes the two partial derivatives of the surface Srf and computes its normal as their cross product, at the parametric location (0.5, 0.5). See also CDERIVE, TDERIVE, and MDERIVE. IRIT Solid modeler G. Elber 174 Figure 83: A surface can be subdivided along a general curve that splits its domain into two distinct regions using SDIVCRV. Left shows the input and the right shows the result (after shifting a bit the two surface regions). 11.2.258 SDIVCRV CurveType SDIVCRV( SurfaceType Srf, CurveType Crv) subdivides surface Srf into two along curve Crv, assuming that: Crv is a simple curve in the UV parametrci domain of Srf and that Crv divides the domain of Srf into two regions by starting and ending on two opposite boundaries of Srf. Either Crv starts and ends in Umin.UMax or VMin/VMax of Srf. Example: Srfs = SDIVCRV( Srf, Crv ); See Figure 83. See also SDIVIDE. 11.2.259 SDIVIDE SurfaceType SDIVIDE( SurfaceType Srf, ConstantType Direction, NumericType Param ) or TrimSrfType SDIVIDE( TrimSrfType Srf, ConstantType Direction, NumericType Param ) subdivide a (possibly trimmed) surface into two at the speciﬁed parameter value Param in the speciﬁed Direction (ROW or COL). Srf can be either a B-spline surface in which Param must be IRIT Solid modeler G. Elber 175 Figure 84: A surface can be subdivided into two distinct regions using SDIVIDE. contained in the parametric domain of the surface, or a Bezier surface in which Param can be arbitrary, extrapolating if not in the range of zero to one. It returns a list of upto two sub-surfaces. The individual surfaces may be extracted from the list using the NTH command. If Srf is a trimmed surface, it may be the case that one of the two subdivided surfaces is completely trimmed out, and hence only one surface will be returned. Example: SrfLst = SDIVIDE( Srf, ROW, 0.5 ); Srf1 = nth( SrfLst, 1 ); Srf2 = nth( SrfLst, 2 ); subdivides Srf at the parameter value of 0.5 in the ROW direction. See Figure 84. See also CDIVIDE, SDIVCRV, TDIVIDE, and MDIVIDE 11.2.260 SELFINTER ListType SELFINTER( CurveType Crv, NumericType SubdivTol, NumericType NumerTol, NumericType MinNrmlDeviation, NumericType Euclidean ) or ListType SELFINTER( SurfaceType Srf, NumericType SubdivTol, NumericType NumerTol, NumericType MinNrmlDeviation, G. Elber IRIT Solid modeler 176 NumericType Euclidean ) computes the self intersection locations/curves of a given curve or surface. Returned is a list of points/piecewise linear curves. The returned locations, if in the parameteric space (see below), are pairs of parameter values along the curve in case of a curve and a 4-tuple holding the pair of surface location, in case of surfaces. See MZERO for the meaning of SubdivTol and NumerTol. If MinNrmlDeviation is positive it speciﬁes the minimal deviation angle required for the two normal at the self intersection (of the two diﬀerent interesecting locations), in degrees. If negative, a diﬀerent approach algother is used that eliminates the redundant diagonal factor in the self intersection constraint. If Euclidean, the returned data is in Euclidean space. Otherwise, the returned data is in parameteric space. Example: si1 = selfinter( crv, 0.001, 1e-10, 15.0, true ); si2 = selfinter( crv, 0.001, 1e-10, -1.0, true ); 11.2.261 SETCOVER ListType SETCOVER( ListType RangesSet, NumericType OverlapTolerance ) computes the minimal subset of the given set RangesSet, that covers the entire domain spanned by RangesSet. A range is a list object with two numeric values, the start and end of this speciﬁc range. Each element in RangesSet can be either a range, or a list of ranges. OverlapTolerance speciﬁes the tolerance to use in overlapping ranges. Returned is a list of indices (ﬁrst element zero) that prescribe the minimal coverage. Note that the former case of a single range per element is solved in an almost linear time whereas the later case of multiple ranges per element is exponential. Hence, do not attempt to ﬁnd minimal coverage of more than a few elements in the later case. Example: Ranges = list( list( 0.0, list( 0.1, list( 0.3, list( 0.1, Indcs = SETCOVER( Ranges, 0.4 ), 0.4 ), 1.0 ), 0.9 ) ); 1e-7 ); and SETCOVER should return ”list( 0, 2 )”, the two indices of the ranges that cover this domain of [0, 1]. See also CVISIBLE. 11.2.262 SEDITPT SurfaceType SEDITPT( SurfaceType Srf, CtlPtType CPt, NumericType UIndex, NumericType VIndex ) provides a simple mechanism to manually modify a single control point number UIndex and VIndex (base count is 0) in the control mesh of Srf by substituting CtlPt instead. CtlPt must have the same point type as the control points of Srf. The original surface Srf is not modiﬁed. Example: CPt = ctlpt( E3, 1, 2, 3 ); NewSrf = SEDITPT( Srf, CPt, 0, 0 ); constructs a NewSrf with the ﬁrst control point of Srf being CPt. IRIT Solid modeler 11.2.263 G. Elber 177 SEVAL CtlPtType SEVAL( SurfaceType Srf, NumericType UParam, NumericType VParam ) or CtlPtType SEVAL( TrimSrfType Srf, NumericType UParam, NumericType VParam ) evaluates the provided (possibly trimmed) surface Srf at the given UParam and VParam parameters. Both UParam and VParam should be contained in the surface parametric domain if Srf is a B-spline surface, or between zero and one if Srf is a Bezier surface. The returned control point has the same type as the control points of Srf. Example: CPt = SEVAL( Srf, 0.25, 0.22 ); evaluates Srf at the parameter values of (0.25, 0.22). See also CEVAL, MEVAL, TEVAL. 11.2.264 SFLECNODAL PolyType SFLECNODAL( SurfaceType Srf, NumericType SubdivTol, NumericType NumericTol, NumericType ContactOrder ) computes the ﬂecnodal curves over a given freeform geometry, Srf, if ContactOrder is 4.. The ﬂecnodal curves are curves of contact of order three with a line in an asymptotic direction. SubdivTol and NumericTol controls the subdivision and numeric tolerances of the approximation. Typically the subdivision tolerance is fairly coarse. This function can also be used to compute ﬂecnodal points of contact, if ContactOrder is set to 4. Example: flecs = SFlecnodal( srf, 0.05, -1e-6, 3 ); See also MZERO for the meaning of SubdivTol and NumerTol. 11.2.265 SFOCAL SurfaceType SFOCAL( SurfaceType Srf, NumericType Dir ) evaluates the focal surface ﬁeld of surface Srf using the normal curvature in the isoparametric direction as given by Dir (either ROW or COL). Note this function is not using the principal curvatures as is generaly the case for focal surfaces. Example: gcross = cbspline( 3, list( ctlpt( E3, 0.3, ctlpt( E3, 0.1, ctlpt( E3, 0.1, ctlpt( E3, 0.5, ctlpt( E3, 0.6, list( KV_OPEN ) ); 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 0.1 0.4 0.5 0.8 ), ), ), ), ) ), IRIT Solid modeler G. Elber 178 Figure 85: A focal surface (right) of a glass surface (left) can be computed using SFOCAL. glass = surfprev( gcross ); color( glass, red ); gfocal = SFOCAL(glass, col); evaluates the focal surface using the COL isoparametric direction’s normal curvature of the glass surface. See Figure 85. 11.2.266 SFROMCRVS SurfaceType SFROMCRVS( ListType CrvList, NumericType OtherOrder, NumericType OtherEndCond ) constructs a surface by substituting the curves in CrvList as rows in a control mesh of a surface. The curves in CrvList are made compatible by promoting Bezier curves to B-splines if necessary, and raising the degrees and reﬁning as required before substituting the control polygons of the curves as rows in the mesh. The other direction order is set by OtherOrder, which cannot be larger than the number of curves. If B-spline (OtherOrder is smaller than number of curves) end conditions are set via OtherEndCond and can be one of KV OPEN, KV FLOAT or KV PERIODIC. The surface interpolates the ﬁrst and last curves only, if a Bezier or open end conditions are selected; otherwise, no curve is interpolated. See also SINTERP, SINTPCRVS. Example: Crv1 = cbspline( 3, list( ctlpt( E3, 0.0, 0.0, 0.0 ), ctlpt( E3, 1.0, 0.0, 0.0 ), IRIT Solid modeler G. Elber 179 Figure 86: A surface can be constructed from a list of curves substituted as rows into its mesh using SFROMCRVS. The surface does not necessarily interpolate the curves. ctlpt( E3, 1.0, 1.0, 0.0 ) ), list( KV_OPEN ) ); Crv2 = Crv1 * trans( vector( 0.0, 0.0, 1.0 ) ); Crv3 = Crv2 * trans( vector( 0.0, 1.0, 0.0 ) ); Srf = SFROMCRVS( list( Crv1, Crv2, Crv3 ), 3, KV_OPEN ); See Figure 86. 11.2.267 SGAUSS SurfaceType SGAUSS( SurfaceType Srf, NumericType NumerOnly ) evaluates the Gaussian curvature (K) ﬁeld of surface Srf. If NumerOnly is TRUE, only the numerator of the Gaussian curvature is derived. Otherwise, if NumerOnly is FALSE, the full exact Gaussian ﬁeld is derived. NumerOnly TRUE may be used in cases where the zero set of K is needed (parabolic lines). Example: Srf1 = hermite( cbezier( list( ctlpt( E3, 0.0, 0.0, 0.0 ), G. Elber IRIT Solid modeler 180 Figure 87: The Gaussian curvature ﬁeld (right) of the quadratic by cubic surface (left) is computed using SGAUSS. The Gaussian curvature ﬁeld is scaled down to %1 to ﬁt into the ﬁgure. Compare with ﬁgure 91. ctlpt( ctlpt( cbezier( list( ctlpt( ctlpt( ctlpt( cbezier( list( ctlpt( ctlpt( ctlpt( cbezier( list( ctlpt( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, 0.5, 1.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2, 0.0, 1.0, 0.8, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 ), ) ) ), ), ) ) ), ), ) ) ), ), ) ) ), ), ), ) ); SGauss = SGAUSS( Srf1, false ); evaluates the Gaussian curvaure of Srf1. See Figure 87. See also EVOLUTE and SMEAN. 11.2.268 SILHOUETTE PolyType SILHOUETTE( SurfaceType Srf, VectorType ViewDir, NumericType SubdivTol, NumericType Euc ) or PolyType SILHOUETTE( PolyType Pl, VectorType ViewDir, NumericType SubdivTol, NumericType Euc ) IRIT Solid modeler G. Elber 181 Compute the silhouette edges of the given Srf or Pl from the prescribed viewing direction ViewDir. The end result is a piecewise linear approximation of the exact silhouette, and its accuracy is controlled via the SubdivTol, in the case of a freeform surface Srf. If Euc is TRUE, the silhouette curves are returned on the surface, in Euclidean space. Otherwise, the silhouette curves are returned in the parametric space of Srf. Both Euc and the RESOLUTION variables have no aﬀect in the case of a polygonal model Pl. Example: Resolution = 10; Sils = SILHOUETTE( glass, vector( 1, -2, 1 ), 0.01, true ); computes the silhouette curves of surface glass as viewed from viewing direction (1, -2, 1), and returns the silhouette curves in Euclidean space. See also ISOCLINE, PPROPFTCH and SASPCTGRPH. 11.2.269 SINTERP SurfaceType SINTERP( ListType PtList, NumericType UOrder, NumericType VOrder, NumericType USize, NumericType VSize, ConstantType Param) computes a B-spline polynomial surface that interpolates or approximates the rectangular grid or scattered set of points in PtList. The B-spline surface will have orders UOrder and VOrder and mesh of size USize by VSize control points. If the data is on a grid, the knots will be spaced according to Param which can be one of PARAM UNIFORM, PARAM CHORD, PARAM CENTRIP, or PARAM NEILFOL. Currently, only PARAM UNIFORM is supported. For a scattered point set, the Param parameter is ignored. PtList is a list of points for grid data in which all lists carry the same amount of points, thereby deﬁning a rectangular grid. For scattered data, PtList is a linear list of points. All points in PtList must be of type (E1-E9, P1-P9) control point, or regular PointType. If USize and VSize are equal to the number of points in the grid data set of PtList, the resulting surface will interpolate the data set. Otherwise, if USize or VSize is less than the number of points in the grid of PtList, the point data set will be least square approximated. At no time can USize or VSize be larger that the number of points in PtList or lower than UOrder and VOrder, respectively. If USize or VSize are zero, the grid size is used, forcing an interpolation of the data set. If PtList contains a linear list of points, these points are treated as scattered. Each scattered point is assumed to be holding the parameteric location at which to interpolate its ﬁrst two coeﬃcients. The other coeﬃcients are the interpolation values. In other words, to interpolate scattered data of type E3, E5 control points in a linear list must be provided in (u, v, x, y, z) format. Scattered data is interpolated over a unit square (0 to 1) parameteric domain in both u and v. All interior knots will be distinctly preserving maximal continuity. The resulting B-spline surface will have open end conditions. See also SINTPCRVS, SFROMCRVS. Example: pl = nil(); pll = nil(); for ( x = -5, 1, 5, pl = nil(): for ( y = -5, 1, 5, IRIT Solid modeler G. Elber 182 Figure 88: A surface least square ﬁtting a data set with insuﬃcient degrees of freedom (left) and actually interpolating the data set (right), all using SINTERP. snoc( point( x, y, sin( x * Pi / 2 ) * cos( y * Pi / 2 ) ), pl ) ): snoc( pl, pll ) ); s1 = SINTERP( pll, 3, 3, 8, 8, PARAM_UNIFORM ); s2 = SINTERP( pll, 3, 3, 11, 11, PARAM_UNIFORM ); samples an explicit surface sin(x) * cos(y) at a grid of 11 by 11 points, least square ﬁt with a grid of size of 8 by 8 surface s1, and interpolates surface s2 using this data set. See also CINTERP and LINTERP. See Figure 88. 11.2.270 SINTPCRVS SurfaceType SINTPCRVS( ListType CrvList, NumericType OtherOrder, NumericType OtherEndCond, NumericType OtherParam ) constructs a surface by ﬁtting it to the curves in CrvList. The curves in CrvList are made compatible by promoting Bezier curves to B-splines if necessary, and raising the degrees and reﬁning as required before ﬁtting a surface through them all. The other direction order is set by OtherOrder, which cannot be larger than the number of curves. If B-spline (OtherOrder is smaller than number of curves) end conditions are set via OtherEndCond and can be one of KV OPEN, KV FLOAT or KV PERIODIC. Finally OtherParam sets the parametrization in the other direction and can be one of PARAM CENTRIP, PARAM CENTRIP, PARAM CHORD, or PARAM NIELFOL. See also SINTERP, SFROMCRVS. Example: Crv1 = cbspline( 3, list( ctlpt( E3, 0.0, ctlpt( E3, 1.0, ctlpt( E3, 1.0, list( KV_OPEN ) ); Crv2 = Crv1 * trans( vector( 0.0, 0.0, 0.0, 0.0 ), 0.0, 0.0 ), 1.0, 0.0 ) ), 1.0 ) ); IRIT Solid modeler G. Elber 183 Figure 89: A surface can be ﬁtted to a list of curves using SINTPCRVS. Crv3 = Crv2 * trans( vector( 0.0, 1.0, 0.0 ) ); Srf = SINTPCRVS( list( Crv1, Crv2, Crv3 ), 3, KV_OPEN ); See Figure 89. 11.2.271 SKEL2DINT ListType SKEL2DINT( CurveType Crv1 | PointType Pt1 | CtlPtType Pt1, CurveType Crv2 | PointType Pt2 | CtlPtType Pt1, CurveType Crv3 | PointType Pt3 | CtlPtType Pt1, NumericType OutExtent, NumericType Epsilon, NumericType FineNess, ListType MZeroTols ) computes locations in the plane of points that are equadistant from the three given entities. Entities can be points or control points or curves, all in the XY plane. The equadistant points are computed as the mutual intersection of the bisectors of the entities. Inﬁnite bisectors (such as the bisector of two points) are extended up to OutExtent. Epsilon controls the tolerances while FineNess controls the subdivision ﬁneness in the bisector intersection computations. MZeroTols controls the subdivision/numeric tolerances of the MV solver, as a list of the two numeric tolerances. Exanple: Crv1 = pcircle( vector( -0.5, 0.7, 0.0 ), 0.3 ); Crv2 = pcircle( vector( -0.4, -0.6, 0.0 ), 0.5 ); Crv3 = pcircle( vector( 0.3, 0.2, 0.0 ), 0.4 ); EquaPt = SKEL2DINT( Crv1, Crv2, Crv3, 100, 0.1, 150, list( 1e-3, -1e-9 ) ): computes the eight points that are equadistant to three circles. See Figure 90. See also CRC2CRVTAN. 11.2.272 SMEAN SurfaceType SMEAN( SurfaceType Srf, NumericType NumerOnly ) evaluates the mean curvature ﬁeld of surface Srf as follows: if NumerOnly is true, it computes the numerator of only the Mean curvature. Otherwise, if NumerOnly is false, the square of the exact Mean curvature ﬁeld is derived. NumerOnly TRUE may be used in cases where the zero set of H is needed (k1 == -k2 points). Example: G. Elber IRIT Solid modeler 184 Figure 90: Computes the eight points that are equadistant to three circles, using SKEL2DINT. Srf1 = hermite( cbezier( list( ctlpt( ctlpt( ctlpt( cbezier( list( ctlpt( ctlpt( ctlpt( cbezier( list( ctlpt( ctlpt( ctlpt( cbezier( list( ctlpt( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, 0.0, 0.5, 1.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2, 0.0, 1.0, 0.8, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 ), ), ) ) ), ), ) ) ), ), ) ) ), ), ) ) ), ), ), ) ); SMean = SMEAN( Srf1, false ); evaluates the square of the mean curvature of Srf1. See Figure 91. See also EVOLUTE and SGAUSS. G. Elber IRIT Solid modeler 185 Figure 91: The square of the mean curvature ﬁeld (right) of the quadratic by cubic surface (left) is computed using SMEAN. The square of the mean curvature ﬁeld is scaled down to %1 to ﬁt into the ﬁgure. Compare with ﬁgure 87. 11.2.273 SMERGE SurfaceType SMERGE( SurfaceType Srf1, SurfaceType Srf2, NumericType Dir, NumericType SameEdge ) merges two surfaces along the requested direction (ROW or COL). If SameEdge is non-zero (ON or TRUE), then the common edge is assumed to be identical and copied only once. Otherwise (OFF or FALSE), a ruled surface is constructed between the two surfaces along the (not) common edge. Example: MergedSrf = SMERGE( Srf1, Srf2, ROW, TRUE ); See also MMERGE. 11.2.274 SMESH SurfaceType SMESH( TrivarType TV, MumericType Dir, NumericType Index ) extracts a surface out of a trivariate, TV, as the Index’s plane of the control mesh of TV in direction Dir. Dir can be one of COL, ROW, DEPTH. Example: tv = tbezier( list( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( s0 = SMESH( tv, col, 0 ); s1 = SMESH( tv, col, 1 ); E3, E3, E3, E3, E3, E3, E3, E3, 0.1, 0.2, 0.3, 0.4, 2.4, 2.2, 2.3, 2.1, 0.0, 0.1, 2.2, 2.3, 0.8, 0.7, 2.6, 2.5, 0.8 ), 2.4 ) ), 0.2 ), 2.0 ) ) ), 0.1 ), 2.3 ) ), 0.5 ), 2.7) ) ) ) ); IRIT Solid modeler G. Elber 186 extracts the two (ﬁrst and last) planes in direction col out of trivariate tv. See also STRIVAR, CMESH, MFROMMESH. 11.2.275 SMOEBIUS CurveType SMOEBIUS( CurveType Crv, NumericType Ratio, NumericType Dir ) rebalances the weights of a rational surface using the Moebius transformation. The shape of the surface remains identical, while the speed is modiﬁed in the direction Dir. Ratio controls the ratio between the last and ﬁrst weights of the ﬁrst row/column. If Ratio = 0, the ﬁrst and last weights are made equal. See also CMOEBIUS. 11.2.276 SMOOTHNRML ListType SMOOTHNRML( ListType Obj, NumericType MaxAngle ) or PolygonType SMOOTHNRML( PolygonType Obj, NumericType MaxAngle ) Given a (list of) polygonal object(s), Obj, compute normals to the vertices by averaging the normals of the polygons that share the vertices. Only vertices where the deviation between the polygons’ normals and the averaged normal is less than MaxAngle are updated. If MaxAngle is negative, all vertices normals are cleared and all polygon normals reevaluated. This is useful for polygonal data sets that have no vertex normals. Example: A = box( vector( -1, -1, -1 ), 2, 2, 2 ); B = SMOOTHNRML( A, 90 ); computes average normals to a curve resulting in the smoothly shaded display of a cube. See also FIXPLNRML. 11.2.277 SMOMENTS SurfaceType SMOMENTS( SurfaceType Srf, NumericType Moment, NumericType Axis1, NumericType Axis2, NumericType Eval ) or NumericType SMOMENTS( SurfaceType Srf, NumericType Moment, NumericType Axis1, NumericType Axis2, NumericType Eval ) compute the integral moment surface, MSrf, of the given surface Srf, up to a sign. The computed moment can be either a ﬁrst order moment when Moment = 1, or a second order moment when Moment = 2. If Srf is a closed surface with domain (u0, v0) to (u1, v1), then the diﬀerence of MSrf(u1, v1) - MSrf(u0, v0) is the requested moment. Otherwise, the computation is for the volume IRIT Solid modeler G. Elber 187 Figure 92: A morphing sequence between a bottle and a glass. Snapshots computed using SMORPH. occupied between the surface Srf and the XY plane. If Eval is TRUE, the actual numerical value of the moment is returned. The moment integral surface is returned if Eval is FALSE. Axis1 and Axis2 prescribe the two axes to compute the moments for a second order moment computation. For a ﬁrst order moment computation only Axis1 is considered. Example: Spr = surfPRev( cregion( pcircle( vector( 0, 0, 0 ), 1 ), 1, 3 ) * ry( 90 ) ); SMOMENTS( Spr, 2, 1, 1, 2, 1 ); computes the second order XX moment of a polynomial approximation of a unit sphere, using method one. See also TVOLUME, SVOLUME, MOMENT and CAREA. 11.2.278 SMORPH SurfaceType SMORPH( SurfaceType Srf1, SurfaceType Srf2, NumericType Blend ) creates a new surface which is a convex blend of the two given surfaces. The two given surfaces must be compatible (see FFCOMPAT) before this blend is invoked. This is very useful if a sequence that ”morphs” one surface to another is to be created. Example: for ( i = 0.0, 1.0, 11.0, Msrf = SMORPH( Srf1, Srf2, i / 11.0 ): color( Msrf, white ): attrib( Msrf, "rgb", "255,255,255" ): attrib( Msrf, "reflect", "0.7" ): save( "morp1-" + i, Msrf ) ); creates a sequence of 12 surfaces, morphed from Srf1 to Srf2 and saves them in the ﬁles ”morph0.itd” to ”morph-11.itd”. See also PMORPH, CMORPH and TMORPH. See Figure 92. 11.2.279 SNORMAL VectorType SNORMAL( SurfaceType Srf, NumericType UParam, NumericType VParam ) or IRIT Solid modeler G. Elber 188 Figure 93: A vector ﬁeld normal (right) computed for a unit sphere (left) using SNRMLSRF. The normal ﬁeld degenerates at the north and south poles because the surface is not regular there. VectorType SNORMAL( TrimSrfType Srf, NumericType UParam, NumericType VParam ) compute the normal vector to (possibly trimmed) surface Srf at the parameter values UParam and VParam. The returned vector has a unit length. Example: Normal = SNORMAL( Srf, 0.5, 0.5 ); computes the normal to Srf at the parameter values (0.5, 0.5). See also SNRMLSRF. 11.2.280 SNRMLSRF SurfaceType SNRMLSRF( SurfaceType Srf ) symbolically computes a vector ﬁeld surface representing the non-normalized normals of the given surface. That is, the normal surface, evaluated at (u, v), provides a vector in the direction of the normal of the original surface at (u, v). The normal surface is computed as the symbolic cross product of the two surfaces representing the partial derivatives of the original surface. Example: NrmlSrf = SNRMLSRF( Srf ); See Figure 93. 11.2.281 SPARABOLC ListType SPARABOLC( SurfaceType Srf, NumericType SubdivTol, NumericType NumericTol, NumericType Euclidean, DecompSrfs ) IRIT Solid modeler G. Elber 189 computes the parabolic edges of a freeform surface, Srf, as the zero set of the Gaussian curvature. A scalar ﬁeld with the sign of the Gauss curvature is computed and its zero is derived. SubdivTol and NumericTol controls the subdivision and numeric tolerances of the approximation. Typically the subdivision tolerance is fairly coarse. If Euclidean is false, the list of (piecewise linear) parabolic curves is returned in the parametric space of Srf. Otherwise, if Euclidean is true, the parabolic curves are mapped onto Srf. if DecompSrfs is set, the surface is divided into several trimed surfaces along the parabolic lines, creating regions that are solely convex, concave, and saddle-like. Example: pl = nil(); pll = nil(); for ( x = -3, 1, 3, pl = nil(): for ( y = -3, 1, 3, snoc( point( x, y, sin( x * Pi / 2 ) * cos( y * Pi / 2 ) ), pl ) ): snoc( pl, pll ) ); EggBase = sinterp( pll, 4, 4, 0, 0, PARAM_UNIFORM ); Resolution = 15; Parab = SPARABOLC( EggBase, 0.005, 1e-6, true, false ); constructs a surface in the shape of an egg carton’s base and then derives its parabolic edges in Euclidean space. See also MZERO for the meaning of SubdivTol and NumerTol. 11.2.282 SPHERE PolygonType SPHERE( VectorType Center, NumericType Radius ) creates a SPHERE geometric object, deﬁned by Center as the center of the SPHERE, and with Radius as the radius of the SPHERE. See RESOLUTION for accuracy of SPHERE approximation as a polygonal model. See IRITSTATE’s ”PrimRatSrfs” and ”PrimRatSrfs” state variables. 11.2.283 SPLITLST ListType SPLITLST( AnyType LinkedListObj ) splits an objected of several linked list data elements such as polygons, curves, or suraces, into a list object that contains an object for each of the individual objects. Example: ObjLst = SPLITLST( axes ); splits the axes object into a list object of several objects each holding a single polyline. 11.2.284 SPOWER SurfaceType SPOWER( ListType CtlMesh ) G. Elber IRIT Solid modeler 190 creates a polynomial/rational surface out of the provided control mesh. The created surface employs the monomial power basis. CtlMesh is a list of rows, each of which is a list of control points. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the surface’s control mesh. The surface’s point type will be of a space which is the union of the spaces of all points. The created surface is the polynomial (or rational), C(u, v) = n m Pij ui v i (27) i=0 j=0 where Pij are the control points CtlMesh. and m and n are the degrees of the surface, which are one less than the number of points in the appropriate direction. Example: s = SPOWER( list( list( ctlpt( E3, 1, 0, 1 ), ctlpt( E3, 0, 1, 1 ) ), list( ctlpt( E3, 0, 0, 1 ), ctlpt( E3, 0, 0, 1 ) ) ) ); s == coerce( coerce( s, bezier_type ), power_type ); constructs a bilinear power basis surface, coerces it to a Bezier form, coerces the Bezier form back to a power basis, and then compares the result for equality. See also CBEZIER, SBSPLINE and SPOWER. 11.2.285 SRADCRVTR SurfaceType SRADCRVTR( SurfaceType Srf, VectorType ViewDir, NumericType SubdivTol, NumericType SubdivTol, NUmericType MergeTol ) computes the radial curvature of surface Srf, as viewed from view direction ViewDir. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. MergeTol speciﬁes the tolerance to use to merge points into polygons, 11.2.286 SRAISE SurfaceType SRAISE( SurfaceType Srf, ConstantType Direction, NumericType NewOrder ) raises Srf to the speciﬁed NewOrder in the speciﬁed Direction. Example: Srf = ruledSrf( cbezier( list( ctlpt( E3, -0.5, -0.5, 0.0 ), ctlpt( E3, 0.5, -0.5, 0.0 ) ) ), cbezier( list( ctlpt( E3, -0.5, 0.5, 0.0 ), ctlpt( E3, 0.5, 0.5, 0.0 ) ) ) ); Srf = SRAISE( SRAISE( Srf, ROW, 3 ), COL, 3 ); constructs a bilinear ﬂat-ruled surface and raises both its directions to be a bi-quadratic surface. See also TRAISE, MRAISE, and CRAISE. IRIT Solid modeler 11.2.287 G. Elber 191 SRAYCLIP ListType SRAYCLIP( PointType Pt, VectorType Dir, SurfaceType Srf ) computes the intersection of ray (Pt, Dir) with Bezier surface Srf, using the Bezier clipping scheme. The returned list is of the form ”list( NumInters, UV0, EucPt0, ..., UVn, EucPtn )”. Example: InterPts = SRayClip( point( 0, 0, 0 ), vector( 0, 0, 1 ), Srf ); computes the intersection of surface Srf with the positive Z axis. 11.2.288 SREFINE SurfaceType SREFINE( SurfaceType Srf, ConstantType Direction, NumericType Replace, ListType KnotList ) provides the ability to Replace a knot vector of Srf or reﬁne it in the speciﬁed direction Direction (ROW or COL). KnotList is a list of knots at which to reﬁne Srf. All knots should be contained in the parametric domain of Srf in Direction. If the knot vector is replaced, the length of KnotList should be identical to the length of the original knot vector of Srf in Direction. If Srf is a Bezier surface, it is automatically promoted to be a B-spline surface. Example: Srf = SREFINE( SREFINE( Srf, ROW, FALSE, list( 0.333, 0.667 ) ), COL, FALSE, list( 0.333, 0.667 ) ); reﬁnes Srf in both directions by adding two more knots at 0.333 and 0.667. See also CREFINE, TREFINE, and MREFINE. 11.2.289 SREGION SurfaceType SREGION( SurfaceType Srf, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) or TrimSrfType SREGION( TrimSrfType Srf, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) extract a region of Srf between MinParam and MaxParam in the speciﬁed Direction. Both MinParam and MaxParam should be contained in the parametric domain of Srf in Direction, except for Bezier surfaces when MinParam and MaxParam can be arbitrary (extrapolating if not between zero and one). Example: Srf = ruledSrf( cbezier( list( ctlpt( E3, -0.5, -0.5, 0.5 ), ctlpt( E3, 0.0, 0.5, 0.0 ), ctlpt( E3, 0.5, -0.5, 0.0 ) ) ), cbezier( list( ctlpt( E3, -0.5, 0.5, 0.0 ), ctlpt( E3, 0.0, 0.0, 0.0 ), ctlpt( E3, 0.5, 0.5, 0.5 ) ) ) ); SubSrf = SREGION( Srf, ROW, 0.3, 0.6 ); G. Elber IRIT Solid modeler 192 Figure 94: A region can be extracted from a freeform surface using SREGION. extracts the region of Srf from the parameter value 0.3 to the parameter value 0.6 along the ROW direction. The COLumn direction is extracted as a whole. See Figure 94. See also CREGION, TREGION, and MREGION. 11.2.290 SREPARAM SurfaceType SREPARAM( SurfaceType Srf, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) or TrimSrfType SREPARAM( TrimSrfType Srf, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) reparametrize Srf over a new domain from MinParam to MaxParam, in the prescribed Direction. This operation does not aﬀect the geometry of the (trimmed) surface and only aﬃne transforms its knot vectors. A Bezier (trimmed) surface will automatically be promoted into a B-spline surface by this function. If MinParam equals MaxParam and both equates with one of the parameterization keywords of PARAM CENTRIP, PARAM CENTRIP, PARAM CHORD, or PARAM NIELFOL, then that parametrization is approximated for the surface, by changing the knot sequence. Note this last operation aﬀects the geometry of the surface. Example: srf = sbspline( 2, 4, list( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( E3, E2, E3, E2, E3, E2, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0 ), 1.0 ), 2.0, 1.0 ) ), 0.0 ), 1.0, 2.0 ), 2.0 ) ), G. Elber IRIT Solid modeler list( ctlpt( E3, 2.0, ctlpt( E2, 2.0, ctlpt( E3, 2.0, list( ctlpt( E2, 3.0, ctlpt( E3, 3.0, ctlpt( E2, 3.0, list( ctlpt( E3, 4.0, ctlpt( E2, 4.0, ctlpt( E3, 4.0, list( list( KV_OPEN ), list( KV_OPEN ) ) ); 0.0, 2.0 1.0 ), 2.0, 2.0 0.0 ), 1.0, 2.0 2.0 ) ), 0.0, 1.0 1.0 ), 2.0, 1.0 193 ), ) ), ), ), ) ) ), srf = sreparam( sreparam( srf, ROW, 0, 1 ), COL, 0, 1 ); ensures that the (trimmed) B-spline surface is deﬁned over the unit size parametric domain. See also CREPARAM, TREPARAM, and MREPARAM. 11.2.291 SREVERSE SurfaceType SREVERSE( SurfaceType Srf ) or TrimSrfType SREVERSE( TrimSrfType Srf ) reverse Srf by ﬂipping the U and V parametric directions. Note that the unary minus (i.e -Srf) also reverses the surface by reversing the U parametric direction. If the surface is a trimmed surface, the trimming curves are ﬂipped accordingly to yield the same shape. RevSrf = SREVERSE( Srf ); See also MREVERSE. 11.2.292 SRF2TANS ListType SRF2TANS( SurfaceType Srf1, SurfaceType Srf2, NumericType SubdivTol, NumericType NumericTol ) computes the developable sheet(s) bi-tangent to given two surfaces Srf1 and Srf2. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. Returns are lists, one per developable sheet, of piecewise linear curves in E4, having two pairs of parameter values of the bi-tangent points in the two input surfaces, in their parametric domain. Example: c1 = cbspline( 3, list( ctlpt( ctlpt( ctlpt( ctlpt( E2, -1, -1 ), E2, 1, -1 ), E2, 1, 1 ), E2, -1, 1 ) ), IRIT Solid modeler G. Elber 194 Figure 95: Extracts self bi-tangent developable out of the given surface using SRF2TANS. c1 = c2 = s1 = s2 = list( kv_periodic ) ); coerce( c1, kv_open ); cbspline( 3, list( ctlpt( E3, 0.8, -0.2, -0.3 ctlpt( E3, 0.5, 0.0, -0.2 ctlpt( E2, -0.45, -0.21 ), ctlpt( E2, -0.45, 0.32 ), ctlpt( E3, 0.5, -0.0, 0.2 ctlpt( E3, 0.8, 0.28, 0.3 list( kv_open ) ); sregion( sweepSrf( c1 * sc( 0.1 ), c2, off ), sregion( sweepSrf( c1 * sc( 0.1 ), c2, off ), ), ), ), ) ), col, 0, 0.5 ); col, 0.5, 1.0 ); BiTans = SRF2TANS( s1, s2, 0.1, 1e-6 ); computes the self bi-tangencies of a given bottle-like surface. See Figure 95. See also SRF3TANS. 11.2.293 SRF3TANS ListType SRF3TANS( ListType Srfs, NumericType Orientation, NumericType SubdivTol, NumericType NumericTol ) computes the plane(s) tri-tangent to given three surfaces Srfs. Srfs can be either a list of three surfaces or a list of one surface in which self bi-tangencies are being sought. If Orientation is 0 all tri-tangent planes are returned. Otherwise, if Orientation equal +1 or -1, tri-tangent sheets(s)with G. Elber IRIT Solid modeler 195 same or diﬀerent tangency orienation are returned, respectively. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. Returns are lists, one per developable sheet, of sample points in E6, having three pairs of parameter values of the tri-tangent points in the three surfaces, in their parametric domain. Example: c2 = cbspline( 3, list( ctlpt( E3, 0.8, -0.2, -0.3 ), ctlpt( E3, 0.5, 0.0, -0.2 ), ctlpt( E2, -0.45, -0.21 ), ctlpt( E2, -0.45, 0.32 ), ctlpt( E3, 0.5, -0.0, 0.2 ), ctlpt( E3, 0.8, 0.28, 0.3 ) ), list( kv_open ) ); s1 = sFromCrvs( list( c2 * sc( 0.001 ), c2, c2 * tz( 1.0 ), c2 * sc( 0.001 ) * tz( 1.0 ) ), 3, kv_open ) * sc( 0.1 ); s2 = s1 * ry( 14 ) * tx( 0.6 ) * tz( 0.02 ); s3 = s1 * rx( 12 ) * ty( 0.6 ) * tx( 0.3 ) * tz( 0.01 ); TriTans = SRF3TANS( list( s1, s2, s3 ) Edges = nil(); for ( i = 1, 1, sizeof( TriTans ), Pt = nth( TriTans, i ): snoc( seval( s1, coord( Pt, 1 ), seval( s2, coord( Pt, 3 ), snoc( seval( s1, coord( Pt, 1 ), seval( s3, coord( Pt, 5 ), snoc( seval( s2, coord( Pt, 3 ), seval( s3, coord( Pt, 5 ), * sz( 1 ), 1, 0.5, -1e-6 ); coord( coord( coord( coord( coord( coord( Pt, Pt, Pt, Pt, Pt, Pt, 2 4 2 6 4 6 ) ) ) ) ) ) ) + ), Edges ): ) + ), Edges ): ) + ), Edges ) ); computes the two outer oriented tri-tangencies to three approximate ellipsoids. Extract and draw the two tri-tangent triangles. See Figure 96. See also SRF2TANS. 11.2.294 SRFFFORM ListType SRFFFORM( SurfaceType Srf, NumericType Form ) derives the four coeﬃcients of the 1st, 2nd or 3rd surface fundamental forms. Form can be one of 1, 2, or 3 only, designating the requested form. Since this 2x2 matrix is symmetric, only three coeﬃcients are returned as a list of three scalar surfaces as (A11, A12 == A21, A22). Example: FFF = SRFFFORM( Srf, 1 ); SFF = SRFFFORM( Srf, 2 ); TFF = SRFFFORM( Srf, 3 ); computes the three fundamental forms of Srf. IRIT Solid modeler G. Elber 196 Figure 96: Extracts tri-tangent planes out of the given three approximate ellipsoids using SRF3TANS. 11.2.295 SRFLNDST PointType SRFLNDST( SurfaceType Srf, PointType LnPt, VectorType LnDir, NumericType IsMinDist, NumericType SubdivTol, NumericType NumerTol ) compute the minimal (IsMinDist TRUE) or maximal (IsMinDist FALSE) distance betweeb surface Srf and the line deﬁned by LnPt, a point on the line, and LnDir, the direction of the line. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. Example: Dst = SRFLNDST( Srf, LnPoint, vector( 1, 1, 1 ), TRUE, 0.1, 1e-6 ); computes the minimal distance between Srf and line LnPoint/Vector( 1, 1, 1 ). See also SRFPTDST, CRVLNDST. PolyType SRFKERNEL( SurfaceType Srf, NumericType Fineness, NumericType SkipRate ) 11.2.296 SRFKERNEL PolyType SRFKERNEL( SurfaceType Srf, NumericType Fineness, NumericType SkipRate ) approximates the kernel of (closed and continuous) surface Srf by deriving the parabolic points of Srf and intersecting half planes tangent to Srf and placed at a sampled set of parabolic locations. The ﬁneness of the parabolic curves’ approximation is governed by Fineness and the sampling rate is controled by SkipRate. Example: Krnl = SRFKERNEL( Srf, 40, 15 ); estimates the kernel of Srf with Fineness of 40 and SkipRate of 15. IRIT Solid modeler 11.2.297 G. Elber 197 SRFPTDST PointType SRFPTDST( SurfaceType Srf, PointType Pt NumericType IsMinDist, NumericType SubdivTol, NumericType NumerTol ) compute the minimal (IsMinDist TRUE) or maximal (IsMinDist FALSE) distance between surface Srf and point Pt. See MZERO for the meaning of the SubdivTol and NumerTol tolerances. Example: Dst = SRFPTDST( Srf, Pt1, FALSE, 0.1, 1e-6 ); computes the maximal distance between Srf and point Pt1. See also SRFLNDST, CRVPTDST. 11.2.298 SRINTER PointType SRINTER( SurfaceType Srf, PointType RayOrigin, VectorType RayDirection, NumericType Tolerance ) computes the ﬁrst intersection, if any, of the prescribed ray originating from RayOrigin in direction RayDirection with surface Srf. It returns the intersection point in the parametric space of Srf with the U and V coordinates as the X and Y coeﬃcients of the returned value. The intersection is computed between the ray and a polygonal approximation of the surface Srf as set via the RESOLUTION variable. If RayDirection is the zero vector, the closest position on Srf to RayOrigin is returned instead. Tolerance sets the accuracy of the computation. This function is tailored toward many invokations of ray-surface test against the same surface. Hence, it caches local data for faster processing. To signal the function that the processing of the current surface is complete, use a Tolerance of zero. Example: RayOrigin = point( 2, 0.1, 0.3 ); RayDir = vector( -4, 0, 0 ); RayLine = coerce( RayOrigin, E3 ) + coerce( RayOrigin + RayDir, E3 ); color( RayLine, magenta ); attrib( RayLine, "dwidth", 2 ); resolution = 80; InterPt = SRINTER( glass, RayOrigin, RayDir, 0.001 ); InterPtE3 = seval( glass, coord( InterPt, 0 ), coord( InterPt, 1 ) ); color( InterPtE3, cyan ); attrib( InterPtE3, "dwidth", 3 ); view( list( InterPtE3, RayLine, glass, axes ), 1 ); InterPt = SRINTER( glass, RayOrigin, RayDir, 0.0 ); This is a complete example of constructing a ray and intersecting it against a surface of a glass at two diﬀerent resolutions, resulting in two diﬀerent accuracies. See also RESOLUTION. IRIT Solid modeler 11.2.299 G. Elber 198 SSINTER ListType SSINTER( SurfaceType Srf1, SurfaceType Srf2, NumericType Euclidean, NumericType Epsilon, NumericType Alignment ) computes the intersection curve of two surfaces, Srf1 and Srf2, up to Epsilon accuracy. The returned data is in Euclidean space if Euclidean is true; otherwise it is in the parametric space. A list of two lists (for the two surfaces) of n curves each, where n is the number of intersection curves, is returned. If Alignment is true, the surfaces are rotated to that one bbox of one surface whose axes are aligned, increasing the probability of detecting disjoint cases. Example: s1 = sphereSrf( 0.35 ) * trans( vector( 0.0, 0.1, 0.2 ) ); s2 = coneSrf( 1, 0.5 ); Inter = nth( SSINTER( s1, s2, true, 0.1, false ), 1 ); computes the Euclidean intersection curves of a cone and a sphere, in general positions. The Euclidean curves on the ﬁrst surface are extracted while purging the Euclidean curves on the second surface. See also RRINTER, SSINTR2 and GGINTER. 11.2.300 SSINTR2 ListType SSINTR2( SurfaceType Srf1, SurfaceType Srf2, NumericType Step, NumericType SubdivTol, NumericType NumerTol, NumericType Euclidean ) computes the intersection curve of two surfaces, Srf1 and Srf2, up to SubdivTol/NumerTol accuracy. The returned data is in Euclidean space if Euclidean is true; otherwise it is in the parametric space. Step controls the forward step size while tracing the intersection curves. A list of pairs of (piecewise linear) intersection curves is returned, one for each connected component. If Euclidean is true a Euclidean curve is also evaluated and returned. Example: s1 = sphereSrf( 0.35 ) * trans( vector( 0.0, 0.1, 0.2 ) ); s2 = coneSrf( 1, 0.5 ); Inter = nth( SSINTR2( s1, s2, 0.01, 0.01, 1e-8, false ), 1 ); computes the intersection curves of a cone and a sphere in parameter spaces. See also MUNIVZERO, RRINTER, SSINTER and GGINTER. 11.2.301 STANGENT VectorType STANGENT( SurfaceType Srf, ConstantType Direction, NumericType UParam, NumericType VParam, NumericType Normalize ) or IRIT Solid modeler G. Elber 199 VectorType STANGENT( TrimSrfType Srf, ConstantType Direction, NumericType UParam, NumericType VParam, NumericType Normalize ) compute the tangent vector to the (possibly trimmed) surface Srf at the parameter values UParam and VParam in Direction. The returned vector has a unit length. If Normalize TRUE, the returned vector is normalized as well. Example: Tang = STANGENT( Srf, ROW, 0.5, 0.6, TRUE ); computes the unit tangent to Srf in the ROW direction at the parameter values (0.5, 0.6). 11.2.302 STRIMSRF SurfaceType STRIMSRF( TrimSrfType TSrf ) extracts the surface of a trimmed surface TSrf. Example: Srf = STRIMSRF( TrimSrf ); extracts the surface of TrimSrf. 11.2.303 STRIVAR SurfaceType STRIVAR( TrivarType TV, ConstantType Direction, NumericType Param ) ) extracts an iso surface from a trivariate function TV in the speciﬁed Direction (ROW or COL or DEPTH) at the speciﬁed parameter value Param. Param must be contained in the parametric domain of TV in Direction direction. The returned surface is in the trivariate TV. Example: TV1 = tbezier( list( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( Srf = STRIVAR( TV1, col, 0.4 ); E3, E3, E3, E3, E3, E3, E3, E3, 0.1, 0.2, 0.3, 0.4, 2.4, 2.2, 2.3, 2.1, 0.0, 0.1, 2.2, 2.3, 0.8, 0.7, 2.6, 2.5, 0.8 ), 2.4 ) ), 0.2 ), 2.0 ) ) ), 0.1 ), 2.3 ) ), 0.5 ), 2.7) ) ) ) ); extracts an iso surface of TV1, in the col direction at parameter value 0.4. See Figure 97. See also SMESH, CSURFACE, MFROMMV. G. Elber IRIT Solid modeler 200 Figure 97: Extracts an iso bilinear surface from a trilinear function, using STRIVAR. 11.2.304 SURFPREV SurfaceType SURFPREV( CurveType Object ) This is the same as SURFREV but approximates the surface of revolution as a polynomial surface. The object must be a polynomial curve. The behaviour of this function can be modiﬁed if ”Rational” attribute is provided with a non zero value to construct a precise surface of revolution instead of a polynomial approximation. Further if ”StartAngle” and ”EndAngle” are found with valid angular prescription (in degrees), only that angular slice out of the surface of revolution is constructed. See SURFREV. 11.2.305 SURFREV PolygonType SURFREV( PolygonType Object ) or SurfaceType SURFREV( CurveType Object ) create a surface of revolution by rotating the ﬁrst polygon/curve of the given Object, around the Z axis. Use the linear transformation functions to position a surface of revolution in a diﬀerent orientation. Example: VTailAntn = SURFREV( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, 0.001, 0.01, 0.01, 0.03, 0.03, 0.001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0 1.0 0.8 0.7 0.3 0.0 ) ) ) ) ) ) + + + + + ); constructs a piecewise linear B-spline curve in the XZ plane and uses it to construct a surface of revolution by rotating it around the Z axis. See also SURFPREV, SURFREVAXS, SURFREV2, SURFREVAX2, and TVREV. See Figure 98. IRIT Solid modeler G. Elber 201 Figure 98: A surface of revolution, VTailAntn in surfrev documentation, can be constructed using SURFREV or SURFPREV. 11.2.306 SURFREVAXS PolygonType SURFREVAXS( PolygonType Object, VectorType Axis ) or SurfaceType SURFREVAXS( CurveType Object, VectorType Axis ) create a surface of revolution by rotating the ﬁrst polygon/curve of the given Object, around the Axis axis. Use the linear transformation functions to position a surface of revolution in a diﬀerent location. Example: Glass = SURFREVAXS( GCross, vector( 1, 0, 1 ) ); constructs a surface of revolution by rotating GCross around the axis of (1, 0, 1). See also SURFPREV, SURFREV, SURFREV2, SURFREVAX2. 11.2.307 SURFREV2 PolygonType SURFREV2( PolygonType Object, NumericType StartAngle, NumericType EndAngle ) or SurfaceType SURFREV2( CurveType Object, NumericType StartAngle, NumericType EndAngle ) IRIT Solid modeler G. Elber 202 create a surface of revolution by rotating the ﬁrst polygon/curve of the given Object, around the Z axis. The rotation does not form a complete circle and is from the StartAngle to the EndAngle only, in degrees, starting from the X axis toward the Y axis, in the XY plane. Use the linear transformation functions to position a surface of revolution in a diﬀerent orientation. Example: Glass = SURFREV2( GCross, 45, 180 ); constructs a surface of revolution by rotating it around the Z axis from 45 to 180 degrees. See also SURFPREV, SURFREVAXS, SURFREV, SURFREVAX2. 11.2.308 SURFREVAX2 PolygonType SURFREVAX2( PolygonType Object, NumericType StartAngle, NumericType EndAngle, VectorType Axis ) or SurfaceType SURFREVAX2( CurveType Object, NumericType StartAngle, NumericType EndAngle, VectorType Axis ) create a surface of revolution by rotating the ﬁrst polygon/curve of the given Object, around the Axis axis. The rotation does not form a complete circle and is from the StartAngle to the EndAngle only, in degrees, starting from the X axis toward the Y axis, in the XY plane. Use the linear transformation functions to position a surface of revolution in a diﬀerent location. Example: T4 = SURFREVAX2( PolyCross, 90, 360, vector( 1, 0, 1 ) ); constructs a polygonal surface of revolution by rotating PolygonType PolyCross around the axis (1, 0, 1), from 45 to 180 degrees. See also SURFPREV, SURFREVAXS, SURFREV2, SURFREV. 11.2.309 SVISIBLE ListType SVISIBLE( SurfaceType Srf, NumericType Resolution, NumericType ConeSize ) computes a decomposition of a freeform surface Srf into regions, each visible with a cone visibility of ConeSize degrees from one direction. In other words, all points in one region have angular deviation of their surface normal of less than ConeSize degrees from the set viewing direction. Resolution controls the accuracy of the computation; the higher this value is, more exact the result. 20 is a good starting value. Each returned region is a trimmed surface that has a ”ViewDir” attribute that contains the viewing direction of this region. Example: IRIT Solid modeler G. Elber 203 Figure 99: A decomposition of a freeform surface into cone visible regions of 30 degrees. The direction of visibility is also presented. Computed using the SVISIBLE command. c1 = cbezier( list( ctlpt( E3, 1.0, 0.0, 0.5 ctlpt( E3, 1.1, 0.0, 0.0 ctlpt( E3, 1.0, 0.0, -0.5 Simp = sregion( surfPRev( c1 ), col, 0.0, 1.0 Decomp = SVISIBLE( Simp, 20, 30 * pi / 180 ); ), ), ) ) ); ) * rz( 45 ) * rx( 90 ); SimDecomp = nil(); Mod = 5; for ( i = 1, 1, sizeof( Decomp ), o = nth( Decomp, i ): v = getattr( o, "ViewDir" ): l = ( ctlpt( E3, 0, 0, 0 ) + coerce( v, e3 ) ) * sc( 1.5 ): j = floor( ( i - 1 ) / Mod ): snoc( list( o, Simp, l, axes ) * view_mat * tx( ( i - 1 - j * Mod ) * 2 - 4 ) * ty( -j * 2 ), SimDecomp ) ); view( SimDecomp, on ); decomposes a given surface Simp into regions of 30 degrees at most, goes over the decomposed regions and orders them ﬁve in a row. See Figure 99. 11.2.310 SVOLUME SurfaceType SVOLUME( SurfaceType Srf, NumericType Method, NumericType Eval ) or NumericType SVOLUME( SurfaceType Srf, NumericType Method, NumericType Eval ) G. Elber IRIT Solid modeler 204 computes the integral volume surface, VSrf, of the given surface Srf, up to a sign. If Srf is a closed surface with domain (u0, v0) to (u1, v1), then the diﬀerence of VSrf(u1, v1) - VSrf(u0, v0) is the requested volume. Otherwise, the computation is for the volume occupied between the surface Srf and the XY plane if Method equals one, and the volume occupied between the surface Srf and the origin if Method equals two. If Eval is TRUE, the actual numerical value of the volume is returned. The volume integral surface is returned if Eval is FALSE. Example: Spr = surfPRev( cregion( * ry( 90 SVOLUME( Spr, 1, 1 ) * 3 SVOLUME( Spr, 2, 1 ) * 3 pcircle( vector( 0, 0, 0 ), 1 ), 1, 3 ) ) ); / 4; / 4; are yet another two ways of approximating the value of Pi. See also TVOLUME, SMOMENTS and CAREA. 11.2.311 SWEEPSRF SurfaceType SWEEPSRF( CurveType CrossSection | ListType CrossSectionList, CurveType Axis, CurveType FrameCrv | VectorType FrameVec | ConstType OFF ) constructs a generalized cylinder surface. This function sweeps a speciﬁed cross section CrossSection along the provided Axis. If a list of curves CrossSectionList is speciﬁed instead, the cross sections are blended along the Axis of the curve so that the ﬁrst/last cross section in the list ﬁts the ﬁrst/last location on the Axis. By default, when frame speciﬁcation is OFF, the orientation of the cross section is computed using the Axis curve tangent and normal. However, unlike the Frenet frame, attempt is made to minimize the normal change, as can happen along inﬂection points in Axis. If a VectorType FrameVec is provided as a frame orientation setting, it is used to ﬁx the binormal direction to this value. In other words, the orientation frame has a ﬁxed binormal. If a CurveType FrameCrv is speciﬁed as a frame orientation setting, this vector ﬁeld curve is evaluated at each placement of the cross section to yield the needed binormal. The resulting sweep is only an approximation of the real sweep. The resulting sweep surface will not be exact, in general. Reﬁnement of the axis curve at the proper location, where accuracy is important, should improve the accuracy of the output. The parametric domains of FrameCrv do not have to match the parametric domain of Axis, and its parametric domain is automatically made compatible by this function. Example: Cross = arc( vector( vector( vector( arc( vector( vector( vector( arc( vector( vector( vector( 0.2, 0.2, 0.0, 0.0, 0.1, 0.1, 0.8, 0.8, 1.0, 0.0, 0.2, 0.2, 0.4, 0.4, 0.5, 0.5, 0.3, 0.3, 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ), ), ) ) + ), ), ) ) + ), ), ) ) + IRIT Solid modeler G. Elber 205 Figure 100: Three examples of the use of SWEEPSRF (Srf1, Srf2, Srf3 from left to right in sweepsrf documentation). Axis = Axis Srf1 Srf2 Srf3 = = = = arc( vector( 1.0, 0.1, 0.0 ), vector( 0.9, 0.1, 0.0 ), vector( 0.9, 0.0, 0.0 ) ) + ctlpt( E2, 0.2, 0.0 ); arc( vector( -1.0, 0.0, 0.0 ), vector( 0.0, 0.0, 0.1 ), vector( 1.0, 0.0, 0.0 ) ); crefine( Axis, FALSE, list( 0.25, 0.5, 0.75 ) ); SWEEPSRF( Cross, Axis, OFF ); SWEEPSRF( Cross, Axis, vector( 0.0, 1.0, 1.0 ) ); SWEEPSRF( Cross, Axis, cbezier( list( ctlpt( E3, 1.0, 0.0, 0.0 ), ctlpt( E3, 0.0, 1.0, 0.0 ), ctlpt( E3, -1.0, 0.0, 0.0 ) ) ) ); constructs a rounded rectangle cross section and sweeps it along an arc, while orienting it several ways. The axis curve Axis is manually reﬁned to better approximate the requested shape. See also SWPSCLSRF for sweep with scale. See Figure 100. 11.2.312 SWPSCLSRF SurfaceType SWPSCLSRF( CurveType CrossSection | ListType CrossSectionList, CurveType Axis, NumericType Scale | CurveType ScaleCrv, CurveType FrameCrv | VectorType FrameVec | ConstType OFF, NumericType ScaleRefine ) constructs a generalized cylinder surface. This function sweeps a speciﬁed cross section CrossSection along the provided Axis. If a list of curves CrossSectionList is speciﬁed instead, the cross sections are blended along the Axis of the curve so that the ﬁrst/last cross section in the list ﬁts the ﬁrst/last location on the Axis. The cross section may be scaled by a constant value Scale, or scaled along the Axis parametric direction via a scaling curve ScaleCrv. By default, when frame speciﬁcation is OFF, the orientation of the cross section is computed using the Axis curve tangent and normal. However, unlike the Frenet frame, attempt is made to minimize the normal change, as can happen along inﬂection points in Axis. If a VectorType FrameVec is provided as a frame orientation setting, it is used to ﬁx the binormal direction to this value. In other words, the orientation frame has a ﬁxed binormal. If a CurveType FrameCrv is speciﬁed as a frame orientation setting, IRIT Solid modeler G. Elber 206 this vector ﬁeld curve is evaluated at each placement of the cross section to yield the needed binormal. ScaleReﬁne is an integer value to deﬁne possible reﬁnement of the Axis to reﬂect the information in ScalingCrv. A value of zero will force no reﬁnement while a value of n > 0 will insert n times the number of control points in ScaleCrv into Axis, better emulating the scaling requested. The resulting sweep is only an approximation of the real sweep. The scaling and axis placement will not be exact, in general. Manual reﬁnement (in addition to ScaleReﬁne) of the axis curve at the proper location, where accuracy is important, should improve the accuracy of the output. The parametric domains of ScaleCrv and FrameCrv do not have to match the parametric domain of Axis, and their domains are made compatible by this function. Example: Cross = arc( vector( -0.11, -0.1, 0.0 ), vector( -0.1, -0.1, 0.0 ), vector( -0.1, -0.11, 0.0 ) ) + arc( vector( 0.1, -0.11, 0.0 ), vector( 0.1, -0.1, 0.0 ), vector( 0.11, -0.1, 0.0 ) ) + arc( vector( 0.11, 0.1, 0.0 ), vector( 0.1, 0.1, 0.0 ), vector( 0.1, 0.11, 0.0 ) ) + arc( vector( -0.1, 0.11, 0.0 ), vector( -0.1, 0.1, 0.0 ), vector( -0.11, 0.1, 0.0 ) ) + ctlpt( E2, -0.11, -0.1 ); scaleCrv = cbspline( 3, list( ctlpt( E2, 0.05, 1.0 ctlpt( E2, 0.1, 0.0 ctlpt( E2, 0.2, 2.0 ctlpt( E2, 0.3, 0.0 ctlpt( E2, 0.4, 2.0 ctlpt( E2, 0.5, 0.0 ctlpt( E2, 0.6, 2.0 ctlpt( E2, 0.7, 0.0 ctlpt( E2, 0.8, 2.0 ctlpt( E2, 0.85, 1.0 list( KV_OPEN ) ); Axis = circle( vector( 0, 0, 0 ), 1 ); Frame = circle( vector( 0, 0, 0 ), 1 ) * rotx( 90 ) * trans( vector( 1.5, 0.0, ), ), ), ), ), ), ), ), ), ) ), 0.0 ) ); Srf1 = SWPSCLSRF( Cross, Axis, scaleCrv, off, 0 ); Srf2 = SWPSCLSRF( Cross, Axis, scaleCrv, off, 2 ); Srf3 = SWPSCLSRF( Cross, Axis, 1.0, Frame, 0 ); constructs a rounded rectangle cross section and sweeps it along a circle, while scaling and orienting in several ways. The axis curve Axis is automatically reﬁned in Srf2 to better approximate the requested scaling. See also SWEEPSRF for sweep with no scale. See Figure 101. G. Elber IRIT Solid modeler 207 Figure 101: Three examples of the use of SWPSCLSRF (Srf1, Srf2, Srf3 from left to right in SWPSCLSRF documentation). 11.2.313 SWUNGASUM SurfaceType SWUNGASUM( CurveType Crv1, CurveType Crv2 ) Given two curves, compute a swung surface that equals: S(r, t) = (x1 (r)x2 (t), x1 (r)y2 (t), y1 (r)) (28) Example: circ = circle( vector( 0.0, 0.0, 0.0 ), 1.5 ) * ry( 90 ); arc1 = arc( vector( 0.0, 1.0, 0.0 ), vector( 0.0, 0.0, 0.0 ), vector( 1.0, 0.0, 0.0 ) ); as1 = SWUNGASUM( circ * ry( -90 ), arc1 ); arc1 = cregion( circle( vector( 0.0, 0.0, 0.0 c2 = coerce( cbspline( 3, list( ctlpt( E2, 1.0, ctlpt( E2, 0.2, ctlpt( E2, 0.0, ctlpt( E2, -0.2, ctlpt( E2, -1.0, ctlpt( E2, -0.2, ctlpt( E2, 0.0, ctlpt( E2, 0.2, list( KV_PERIODIC ) ), KV_OPEN ); as2 = SWUNGASUM( arc1, c2 ); ), 1.5 ), 0, 2 ) * rz( 90 ); 0.0 0.2 1.0 0.2 0.0 -0.2 -1.0 -0.2 ), ), ), ), ), ), ), ) ), creates two algebraic sum surfaces, one in the shape of a cylinder as a sum of a line and a circle, and one circular sweep. See Figure 102. 11.2.314 SYMBCPROD CurveType SYMBCPROD( CurveType Crv1, CurveType Crv2 ) IRIT Solid modeler G. Elber 208 Figure 102: An algebraic swung sum of a circle and a line creating a portion of a sphere (left) and a general swung surface between a circle and a periodic curve (right), both using SWUNGASUM. or SurfaceType SYMBCPROD( SurfaceType Srf1, SurfaceType Srf2 ) or MultivarType SYMBCPROD( MultivarType MV1, MultivarType MV2 ) compute the symbolic cross product of the two given curves/surfaces/multivariates as a curve, surface or multivariate. Example: NrmlSrf = SYMBCPROD( sderive( Srf, ROW ), sderive( Srf, COL ) ) computes a normal surface as the cross product of the two surface partial derivatives (see SNRMLSRF). See also SYMBIPROD, SYMBDPROD, SYMBPROD, SYMBSUM, SYMBDIFF. 11.2.315 SYMBDIFF CurveType SYMBDIFF( CurveType Crv1, CurveType Crv2 ) or SurfaceType SYMBDIFF( SurfaceType Srf1, SurfaceType Srf2 ) or MultivarType SYMBDIFF( MultivarType MV1, MultivarType MV2 ) IRIT Solid modeler G. Elber 209 compute the symbolic diﬀerence of the two given curves/surfaces/multivariates as a curve, surface or multivariate. The diﬀerence is computed coordinate-wise. Example: DiffCrv = SYMBDIFF( Crv1, Crv2 ) DistSqrCrv = symbdprod( DiffCrv, DiffCrv ) See also SYMBCPROD, SYMBDPROD, SYMBIPROD, SYMBPROD, SYMBSUM. 11.2.316 SYMBDPROD CurveType SYMBDPROD( CurveType Crv1, CurveType Crv2 ) or CurveType SYMBDPROD( CurveType Crv1, VectorType Vec2 ) or SurfaceType SYMBDPROD( SurfaceType Srf1, SurfaceType Srf2 ) or SurfaceType SYMBDPROD( SurfaceType Srf1, VectorType Vec2 ) or MultivarType SYMBDPROD( MultivarType MV1, MultivarType MV2 ) or MultivarType SYMBDPROD( MultivarType MV1, VectorType Vec2 ) compute the symbolic dot (inner) product of the two given curves/surfaces/multivariates as a scalar curve/surface/multivariate. As an alternative, one parameter can also be a regular vector. Example: DiffCrv = symbdiff( Crv1, Crv2 ) DistSqrCrv = SYMBDPROD( DiffCrv, DiffCrv ) computes a scalar curve that at parameter t is equal to the distance square between Crv1 at t and Crv2. See also SYMBCPROD, SYMBIPROD, SYMBPROD, SYMBSUM, SYMBDIFF. 11.2.317 SYMBIPROD NumericType SYMBIPROD( CurveType Crv, NumericType Order1, NumericType Order2 ) or NumericType SYMBIPROD( NumericType Dummy, NumericType Idx1, NumericType Idx2 ) G. Elber IRIT Solid modeler 210 compute the inner product of two B-spline basis functions. The ﬁrst form deﬁnes the function space to be the same as the function space of Crv of order Order1 (ﬁrst basis function) by Order2. The second basis function in the inner product is deﬁned as, Bi,o1 (t)Bj,o2 (t)dt. (29) The second form prescribes the indices of the two basis functions, i and j. The ﬁrst form returns zero in case of an error. The second form returns the result of the inner product. Example: SYMBIPROD( Crv = pcircle( vector( 0, 0, 0 ), 1 ), 4, 4 ); for ( i = 0, 1, nth( ffmsize( Crv ), 1 ) - 1, for ( j = 0, 1, nth( ffmsize( Crv ), 1 ) - 2, printf( "%3.3f ", list( SYMBIPROD( 0, i, j ) ) ) ): printf( "\\n", nil() ) ); prints all possible inner products of the B-spline function space of pcircle, of cubics vs. cubics. See also SYMBCPROD, SYMBDPROD, SYMBPROD, SYMBSUM, SYMBDIFF. 11.2.318 SYMBPROD CurveType SYMBPROD( CurveType Crv1, CurveType Crv2 ) or SurfaceType SYMBPROD( SurfaceType Srf1, SurfaceType Srf2 ) or MultivarType SYMBPROD( MultivarType MV1, MultivarType MV2 ) compute the symbolic product of the two given curves/surfaces/multivariates as a curve, surface or multivariate. The product is computed coordinate-wise. Example: ProdSrf = SYMBPROD( Srf1, Srf2 ) See also SYMBCPROD, SYMBDPROD, SYMBIPROD, SYMBSUM, SYMBDIFF. 11.2.319 SYMBSUM CurveType SYMBSUM( CurveType Crv1, CurveType Crv2 ) or SurfaceType SYMBSUM( SurfaceType Srf1, SurfaceType Srf2 ) or MultivarType SYMBSUM( MultivarType MV1, MultivarType MV2 ) G. Elber IRIT Solid modeler 211 compute the symbolic sum of the two given curves/surfaces/multivariates as a curve, surface or multivariate. The sum is computed coordinate-wise. Example: SumCrv = SYMBSUM( Crv1, Crv2 ) See also SYMBCPROD, SYMBDPROD, SYMBIPROD, SYMBPROD, SYMBDIFF. 11.2.320 TBEZIER TrivarType TBEZIER( ListType CtlMesh ) creates a Bezier trivariate using the provided control mesh. CtlMesh is a list of planes, each of which is a list of rows, each of which is a list of control points. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the trivariate’s control mesh. The surface point type will be of a space which is the union of the spaces of all points. The created trivariate is the piecewise polynomial (or rational) function, T (u, v, w) = m n l i=0 j=0 k=0 Pijk Bi (u)Bj (v)Bk (w) (30) where Pijk are the control points CtlMesh, and l, m and n are the degrees of the trivariate, which are one less than the number of points in the appropriate direction. Example: TV = TBEZIER( list( list( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( list( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( list( ctlpt( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 1.2, 1.4, 1.6, 1.8, 0.1, 0.5, 0.1, 1.3, 1.7, 1.3, 2.4, 2.6, 2.8, 0.1, 0.2, 0.3, 1.2, 1.4, 1.6, 2.3, 2.5, 2.7, 0.0 1.1 2.2 0.5 1.7 2.9 0.5 1.4 2.3 0.5 1.7 2.9 0.0 1.2 2.4 0.9 1.7 2.5 ), ), ) ), ), ), ) ), ), ), ) ) ), ), ), ) ), ), ), ) ), ), ), ) ) ) ) ); creates a trivariate Bezier which is linear in the ﬁrst direction, and quadratic in the second and third. See Figure 103. IRIT Solid modeler G. Elber 212 Figure 103: A trivariate Bezier of degree 2 by 3 by 3 (left) and a trilinear B-spline (right). Both share the same control mesh. 11.2.321 TBOOLONE TrivarType TBOOLONE( SurfaceType Srf ) Given a surface closed in one direction (like a sweep of a closed curve), the surface is subdivided into four segments in the parametric space that are then fed into TBOOLSUM. This is useful if a volume bounded by Srf should be ”ﬁlled” abd parameterized. Example: Srf = TBOOLSUM( CylinderSrf ); creates a cylinder volume, parameterizing the entire volume of CylinderSrf. See Figure 104. See also TBOOLSUM, BOOLONE. 11.2.322 TBOOLSUM TrivarType TBOOLSUM( SurfaceType Srf1, SurfaceType Srf2, SurfaceType Srf3, SurfaceType Srf4, SurfaceType Srf5, SurfaceType Srf6 ) constructs a volume using the provided six surfaces as its six boundary surfaces. Surfaces do not have to have the same order or type, and will be promoted to their least common denominator. The end boundary curves of the six surfaces should match. Surfaces Srf1, Srf2, Srf3, and Srf4 should share one parameteric direction and should form a topological cylinder where Srf5 and Srf6 serve as two bottom and top caps for. Srf5 and Srf6 are optional and if not provided, surface Boolean sum is use to construct them from surfaces Srf1, Srf2, Srf3, and Srf4. Example: tv = TBOOLSUM( sregion( s, col, 0, 1 ), sregion( s, col, 1, 2 ), IRIT Solid modeler G. Elber 213 Figure 104: A volumetric Boolean sum of a cylinder (left) using TBOOLONE and a general volumetric Boolean sum of six surfaces (right) using TBOOLSUM. sregion( s, col, 2, 3 ), sregion( s, col, 3, 4 ), 0, 0 ); constructs a volume for the interior of surface s as will TBOOLONE when operated on s. See also TBOOLONE, BOOLSUM. 11.2.323 TBSPLINE TrivarType TBSPLINE( NumericType UOrder, NumericType VOrder, NumericType WOrder, ListType CtlMesh, ListType KnotVectors ) creates a B-spline trivariate with the provided UOrder, VOrder and WOrder orders, the control mesh CtlMesh, and the three knot vectors in KnotVectors. CtlMesh is a list of planes, each of which is a list of rows, each of which is a list of control points. All control points must be of point type (E1-E9, P1-P9), or regular PointType deﬁning the trivariate’s control mesh. Trivariate point type will be of a space which is the union of the spaces of all points. KnotVectors is a list of three knot vectors. Each knot vector is a list of NumericType knots of length #CtlPtList plus the Order. If, however, the length of the knot vector is equal to #CtlPtList + Order + Order - 1, the curve is assumed to be periodic. The knot vector may also be a list of a single constant, KV OPEN, KV FLOAT or G. Elber IRIT Solid modeler 214 KV PERIODIC, in which a uniform knot vector with the appropriate length and with open, ﬂoating or periodic end conditions will be constructed automatically. The created surface is the piecewise polynomial (or rational) surface, T (u, v, w) = n l m i=0 j=0 k=0 Pijk Bi,χ (u)Bj,ξ (v)Bk,φ (w) (31) where Pijk are the control points CtlMesh, and l, m and n are the degrees of the surface, which are one less than UOrder, VOrder and WOrder and χ, ξ and φ are the three knot vectors of the trivariate. Example: TV = TBSPLINE( 2, 2, 2, list( list( list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( list( KV_OPEN ), list( KV_OPEN ), list( KV_OPEN ) ) ); 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 1.2, 1.4, 1.6, 1.8, 0.1, 0.5, 0.1, 1.3, 1.7, 1.3, 2.4, 2.6, 2.8, 0.1, 0.2, 0.3, 1.2, 1.4, 1.6, 2.3, 2.5, 2.7, 0.0 1.1 2.2 0.5 1.7 2.9 0.5 1.4 2.3 0.5 1.7 2.9 0.0 1.2 2.4 0.9 1.7 2.5 ), ), ) ), ), ), ) ), ), ), ) ) ), ), ), ) ), ), ), ) ), ), ), ) ) ) ), constructs a trilinear B-spline trivariate with open end conditions. See Figure 103. TCRVTR 11.2.324 TCRVTR AnyType TCRVTR( TrivarType TV, PointType Pos, NumericType ComputeWhat ) computes diﬀerential curvature properties of an isosurface of the given trivariate TV at the given (parameteric) location Pos. Following the value of ComputeWhat, the result equals, G. Elber IRIT Solid modeler -1 0 1 2 3 215 Initialization (a must prelude) Conclusion (a must postlude) Returns a vector hold of the gradient Returns a list of three vectors equal to the Hessian of this location Returns a list of two scalar values (Principle curvatures) and two vectors (Principal directions). Every evaluation must start with an invocation of ComputeWhat equal to -1 and terminate with ComputeWhat 0. In both cases, 1 is returned in case of success. Example: TCRVTR( Grad1 = Grad2 = Grad3 = Grad4 = TCRVTR( 11.2.325 TV, point( 0, 0, 0 TCRVTR( TV, point( TCRVTR( TV, point( TCRVTR( TV, point( TCRVTR( TV, point( TV, point( 0, 0, 0 ), 0, 0, 0, 1, ), -1 ); # Prelude 0, 0 ), 1 ); 0, 1 ), 1 ); 1, 0 ), 1 ); 0, 0 ), 1 ); 0 ); #Postlude TDEFORM AnyType TDEFORM( GeometryType Tile, SurfaceType DeformingSrf, NumericType UTiles, NumericType VTiles, NumericType WTiles, NumericType FitTile, NumericType Precise ) or AnyType TDEFORM( GeometryType Tile, TrivarType DeformingTV, NumericType UTiles, NumericType VTiles, NumericType WTiles, NumericType FitTile, NumericType Precise ) Tiles Tile UTiles x VTiles (x WTiles) times inside the surface domain of DeformingSrf or the volumetric domain of DeformingTV by compose Tile with DeformingSrf or DeformingTV. Result is precisely deformed, using composition, if DeformingSrf, where the Tile can be almost any geometric type (a curve, a (trimmed) surface, etc.). If Tile is a surface, DeformingSrf must be a Bezier surface. Result is approximated if DeformingTV and Precise is FALSE, by mapping only (control) points through the trivariate. In this case, if Precise is TRUE and Tile is either a curve or a (trimmed) surface, the computation will indeed be precise using composition. The Tile is supposed to span [0, 1]2 or [0, 1]3 and if FitTile is TRUE, the Tile is ﬁrst scaled into that domain. Example: Geom = TDEFORM( Tubes, TV, 2, 2, 4, FALSE, FALSE ); See Figure 105. See also SDDMMAP, TEXTWARP, G. Elber IRIT Solid modeler 216 Figure 105: Geometry can be composed into trivariate volumetric splines using the TDEFORM command. Here, three orthogonal tubes (middle) are composed into a trivariate (left) 2x2x4 times, yeilding the approximated result on the right. 11.2.326 TDERIVE TrivarType TDERIVE( TrivarType TV, NumericType Dir ) returns a vector ﬁeld trivariate representing the diﬀerentiated trivariate in the given direction (ROW, COL, or DEPTH). Evaluation of the returned trivariate at a given parameter value will return a vector representing the partial derivative of TV in Dir at that parameter value. TV = tbezier( list( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( E1, E1, E1, E1, E1, E1, E1, E1, 0.1 0.2 0.3 0.4 2.4 2.2 2.3 2.1 ), ) ), ), ) ) ), ), ) ), ), ) ) ) ) ); DuTV = TDERIVE( TV, ROW ); DvTV = TDERIVE( TV, COL ); DwTV = TDERIVE( TV, DEPTH ); computes the gradiate of a scalar trivariate ﬁeld, by computing its partials with respect to u, v, and w. See also CDERIVE, SDERIVE, and MDERIVE. 11.2.327 TDIVIDE TrivarType TDIVIDE( TrivarType TV, ConstantType Direction, NumericType Param ) subdivides a trivariate into two at the speciﬁed parameter value Param in the speciﬁed Direction (ROW, COL, or DEPTH). TV can be either a B-spline trivariate in which Param must be contained IRIT Solid modeler G. Elber 217 Figure 106: A trivariate can be subdivided into two distinct regions using TDIVIDE. in the parametric domain of the trivariate, or a Bezier trivariate in which Param must be in the range of zero to one. It returns a list of the two sub-trivariates. The individual trivariates may be extracted from the list using the NTH command. Example: TvDiv = TDIVIDE( Tv2, depth, 0.3 ); Tv2a = nth( TvDiv, 1 ) * tx( -2.2 ); Tv2b = nth( TvDiv, 2 ) * tx( 2.0 ); subdivides Tv2 at the parameter value of 0.3 in the DEPTH direction, See Figure 106. See also CDIVIDE, SDIVIDE, and MDIVIDE 11.2.328 TEDITPT TrivarType TEDITPT( TrivarType TV, CtlPtType CPt, NumericType UIndex, NumericType VIndex ) NumericType WIndex ) provides a simple mechanism to manually modify a single control point number UIndex, VIndex and WIndex (base count is 0) in the control mesh of Srf by substituting CtlPt instead. CtlPt must have the same point type as the control points of Srf. Original surface Srf is not modiﬁed. Example: CPt = ctlpt( E3, 1, 2, 3 ); NewTV = TEDITPT( TV, CPt, 0, 0, 0 ); constructs a NewTV with the ﬁrst control point of TV being CPt. 11.2.329 TEVAL CtlPtType TEVAL( TrivarType TV, NumericType UParam, NumericType VParam, NumericType WParam ) IRIT Solid modeler G. Elber 218 Figure 107: Outline fonts can be used to synthesize text geometry, using the TEXT2GEOM command. evaluates the provided trivariate TV at the given UParam, VParam and WParam values. UParam, VParam, WParam must be contained in the surface parametric domain if TV is a Bspline trivariate, or between zero and one if TV is a Bezier trivariate. The returned control point has the same type as the control points of TV. Example: CPt = TEVAL( TV1, 0.25, 0.22, 0.7 ); evaluates TV at the parameter values of (0.25, 0.22, 0.7). See also CEVAL, SEVAL, MEVAL. 11.2.330 TEXT2GEOM CurveType TEXT2GEOM( StringType Text, StringType Font, NumericType FontStyle, NumericType SpaceWidth, NumericType EdgeType3D, NumericType Setup3D, NumericType Tolerance, NumericType OutputType ) synthesizes geometry that represents Text in one long line. The font that is used to synthesized the text is an outline font Font, whereas under windows Font simple lists the font name (i.e. ”Times New Roman”) and under other system Font speciﬁes the full path of an outline ttf font ﬁle. FontStyle selects regular font if 0, italics if 1, bold if 2, and italic bold if 3. Might be ignored if speciﬁc font does not support the speciﬁc style. SpaceWidth controls the space between diﬀerent characters. EdgeType3D sets for 3D text syntehsis, the edge style than can be one of regular if 1, chamferred if 2 or rounded if 3. Ignored for 2D text. If 3D text generated is chamferred, Setup3D sets a 2D vector that controls the chamfering oﬀset amount. If solid text is to be generated, Tolerance controls the accuracy of the polygonal approximations. OutputType selects the type of output geometry to create: 0 for Bezier curves, 1 for Bspline curves, 2 for 2D solid text, 3 for solid 3D polygonal text, 4 for 2D trimmed surfaces text, 5 for 3D trimmed surfaces text. Example: Text = TEXT2GEOM( "This is a test example of some 3D text", "Times New Roman", 0, 0, 2, list( 0.01, 0.1 ), 0.001, 1 ); See Figure 107 for the result of this example. See also TEXTLAYSHP, TEXTGEOM, and TEXTWARP. 11.2.331 TEXTLAYSHP CurveType TEXTLAYSHP( StringType Text, StringType Font, NumericType FontStyle, NumericType Size, NumericType Space, NumericType Tolerance NumericType EdgeType3D, NumericType Setup3D, G. Elber IRIT Solid modeler 219 NumericType AlignmentType, NumericType OutputType, PolyType BoundingRegion ) or CurveType TEXTLAYSHP( StringType Text, StringType Font, NumericType FontStyle, NumericType Size, VectorType Space, NumericType Tolerance NumericType EdgeType3D, NumericType Setup3D, NumericType AlignmentType, NumericType OutputType, CurveType BoundingRegion ) synthesizes geometry that represents Text inside BoundingRegion. The font that is used to synthesized the text is an outline font Font, whereas under windows Font simple lists the font name (i.e. ”Times New Roman”) and under other system Font speciﬁes the full path of an outline ttf font ﬁle. FontStyle selects regular font if 0, italics if 1, bold if 2, and italic bold if 3. Might be ignored if speciﬁc font does not support the speciﬁc style. Size simply scales the text. Space is a vector of size three: (WordWidth, SpaceWidth, LineHeight), controling the space between diﬀerent words, characters, and lines, respectively. If solid text is to be generated, Tolerance controls the accuracy of the polygonal approximations. EdgeType3D sets for 3D text syntehsis, the edge style than can be one of regular if 1, chamferred if 2 or rounded if 3. Ignored for 2D text. If 3D text generated is chamferred, Setup3D sets a 2D vector that controls the chamfering oﬀset amount. AlignmentType selects the type of text alignments: 0 for left, 1 for center, 2 for right, and 3 for wide (full width) alignments. OutputType selects the type of output geometry to create: 0 for Bezier curves, 1 for Bspline curves, 2 for 2D solid text, 3 for solid 3D polygonal text, 4 for 2D trimmed surfaces text, 5 for 3D trimmed surfaces text Example: Heart = cbspline( 4, list( ctlpt( E2, 0, 0.6 ), ctlpt( E2, 0.2, 1 ), ctlpt( E2, 1, 1 ), ctlpt( E1, 1.2 ), ctlpt( E2, 0.8, -0.6 ), ctlpt( E2, 0, -1 ), ctlpt( E2, 0, -1 ), ctlpt( E2, -0.8, -0.6 ), ctlpt( E1, -1.2 ), ctlpt( E2, -1, 1 ), ctlpt( E2, -0.2, 1 ), ctlpt( E2, 0, 0.6 ) ), list( kv_open ) ) * sc( 10 ); Str = "This is a test example of some 3D text. "; text = TextLayShp( Str + Str + Str + Str + Str + Str + Str + Str, "Courier New", 2, 0.67, list( 35, 10, 34 ), 0.001, 0, G. Elber IRIT Solid modeler 220 Figure 108: Outline fonts can be used to synthesize text geometry and conﬁne it to arbitrary 2D shaped boundary, using the TEXTLAYSHP command. list( 0.01, 0.5 ), 3, 1, Heart ); See Figure 108 for the result of this example. See also TEXT2GEOM, TEXTGEOM, and TEXTWARP. 11.2.332 TEXTGEOM AnyType TEXTGEOM( StringType Str, VectorType Spacing, NumericType Scaling ) creates a displayable geometry that represents the text in Str, with Spacing space between individual characters. Each character is scaled by Scaling where scaling of one generates a close to unit size character. Example: a = TEXTGEOM("Text", vector( 0.12, 0, 0 ), 0.1 ); b = TEXTGEOM("IRIT", vector( 0, -0.12, 0 ), 0.1 ); creates a horizontal Text and a vertical top to bottom IRIT, both as geometrical objects. See TEXTWARP, TEXTLAYSHP, TEXT2GEOM and IRITSTATE’s ”LoadFont” state variable. IRIT Solid modeler G. Elber 221 Figure 109: Font and text warping using the TEXTWARP function. 11.2.333 TEXTWARP AnyType TEXTWARP( Surface Srf, StringType Text, NumericType HSpace, NumericType VBase, NumericType VTop, NumericType Ligature ) warps the given text, Text, using surface Srf as warping function with HSpace setting the horizontal spacing between characters, VBase and VTop controls the vertical spacing of the characters in Srf, and Ligature, if not zero, sets the amount to contract the distance between two adjacent characters. Example: c = cbezier( list( ctlpt( e2, -1.5, -0.5 ), ctlpt( e2, -2, 0 ), ctlpt( e2, -1, 1 ), ctlpt( e2, 0, -2 ), ctlpt( e2, 1, 0 ) ) ); s = sreparam( ruledSrf( c, offset( c, -0.4, 0.02, off ) ), col, 0, 6 ); Txt = TEXTWARP( s, "Text Warping Toolkit", 0.08, 0.25, 0.75, 0 ); See also TEXTGEOM, TEXTLAYSHP, TEXT2GEOM and IRITSTATE’s ”LoadFont” state variable. 11.2.334 TFROMSRFS TrivarType TFROMSRFS( ListType SrfList, NumericType OtherOrder, NumericType OtherEndCond ) constructs a trivariate by substituting the surfaces in SrfList as planes in a control mesh of a trivariate. Surfaces in SrfList are made compatible by promoting Bezier surfaces to B-splines if necessary, and raising degree and reﬁning as required before substituting the control meshes of the surfaces as planes in the mesh of the trivariate. The other, third, direction order is controlled by OtherOrder and OtherEndCond. OtherOrder cannot be larger than the number of surfaces, and OtherEndCond prescribes the desired end conditions as one of KV OPEN, KV FLOAT or KV PERIODIC. IRIT Solid modeler G. Elber 222 Figure 110: A trivariate (thin lines) is constructed via ﬁve planar surfaces (thick lines) using the TFROMSRFS constructor... The trivariate interpolates the ﬁrst and last surfaces only. Example: s1 = sbezier( list( list( ctlpt( E3, -0.5, -0.5, ctlpt( E3, -0.5, 0.5, list( ctlpt( E3, 0.5, -0.5, ctlpt( E3, 0.5, 0.5, Srfs = list( s1 * sc( 2.0 ), s1 * sx( 1.4 ) * ry( 45 ) * tz( 1.0 s1 * ry( 90 ) * trans( vector( 1.0, s1 * sx( 1.4 ) * ry( 135 ) * trans( s1 * sc( 2.0 ) * ry( 180 ) * trans( color( Srfs, red ); 0 0 0 0 ), ) ), ), ) ) ) ) * sc( 0.3 ); ), 0.0, 1.1 ) ), vector( 2.0, 0.0, 1.0 ) ), vector( 2.0, 0.0, 0.0 ) ) ); ts = TFROMSRFS( Srfs, 3, kv_open ); color( ts, green ); view( list( Srfs, ts ), on ); constructs a trivariate from ﬁve planar surfaces and displays both the trivariate and the ﬁve planar surfaces, in diﬀerent colors. See Figure 110. See also EXTRUDE, RULEDTV, SFROMCRVS. 11.2.335 TINTERP TrivarType TINTERP( TrivarType TV, NumericType ULength, NumericType VLength, NumericType WLength, NumericType UOrder, NumericType VOrder, NumericType WOrder ); or IRIT Solid modeler G. Elber 223 TrivarType TINTERP( ListType PtList, NumericType ULength, NumericType VLength, NumericType WLength, NumericType UOrder, NumericType VOrder, NumericType WOrder ); Given a trivariate data structure or a list of points in R3, the above computes a ﬁtted trivariate in the prescribed function space (i.e. U/V/WLength and U/V/WOrder) that interpolates/least squares approximates the given trivariate, TV, at the node parameter values. PtList is a list of points in Rn, n ¿ 3. The ﬁrst three coordinates of each points in PtList prescribes the (u, v, w) parametric value and the rest, the interpolation values. To construct a mapping from R3 to R3, the points of PtList should be in R6. To construct a scalar trivariate function, R4 points are expected. The (u, v, w) points are assumed to be containted in a unit curve paramteric space - zero to one in all three dimensions. If U/V/WOrder are zero and the ﬁrst parameter is a trivariate, the respective order is taken for TV. If U/V/WLength are zero and the ﬁrst parameter is a trivariate, the respective length is taken for TV. Example: tv = tbspline( 3, 3, 2, list( list( list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( ctlpt( E3, ctlpt( E3, ctlpt( E3, list( list( KV_OPEN ), list( KV_OPEN ), list( KV_OPEN ) ) ); 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 1.2, 1.4, 1.6, 1.8, 2.8, 2.6, 2.4, 2.2, 2.9, 2.7, 2.5, 2.3, 2.1, 0.1, 0.5, 0.1, 1.3, 1.7, 1.3, 2.4, 2.6, 2.8, 0.1, 0.2, 0.3, 1.2, 1.4, 1.6, 2.3, 2.5, 2.7, 0.1, 0.7, 0.2, 1.1, 1.2, 1.3, 2.9, 2.8, 2.7, 0.0 1.1 2.2 0.5 1.7 2.9 0.5 1.4 2.3 0.5 1.7 2.9 0.0 1.2 2.4 0.9 1.7 2.5 0.4 1.3 2.2 0.4 1.5 2.6 0.7 1.7 2.7 ), ), ) ), ), ), ) ), ), ), ) ) ), ), ), ) ), ), ), ) ), ), ), ) ) ), ), ), ) ), ), ), ) ), ), ), ) ) ) ), IRIT Solid modeler G. Elber 224 tvi = TINTERP( tv, 0, 0, 0, 0, 0, 0 ); creates a quadratic by quaratic by linear trivariate tvi that interpolates the control points of tv at the node parameter values. 11.2.336 TMORPH TrivarType TMORPH( TrivarType TV1, SurfaceType TV2, NumericType Blend ) creates a new trivariate which is a convex blend of the two given trivariates. The two given trivariates must be compatible (see FFCOMPAT) before this blend is invoked. This isv ery useful if a sequence that ”morphs” one trivariate to another is to be created and in combination with MRCHCUBE. Example: Size = 0.05; for ( i = 0, step, 1.0, Tv = TMORPH( Tv1, Tv2, i ): view( mrchcube( list( Tv, 1, off ), point( Size, Size, Size ), 1, IsoVal ), on ) ); creates a sequence of 1/step trivariates, morphed from Tv1 to Tv2 and displays an extracted iso surface at level IsoVal. See also MRCHCUBE, PMORPH, CMORPH and SMORPH. 11.2.337 TNSCRCR ListType TNSCRCR( PointType Cntr1, NumericType Rad1, PointType Cntr2, NumericType Rad2, NumericType OuterTans ) computes the two outer, if OuterTans TRUE, or the two inner if OuterTans FALSE, bi-tangents between the prescribed two circles. Note the bi-tangents might no exist of one circle is containt in the other. Example: T1 = TnsCrCr( point( -2, 0.3, 0 ), 0.7, point( 1, 0, 0 ), 1, 0 ); T2 = TnsCrCr( point( -2, 0.3, 0 ), 0.7, point( 1, 0, 0 ), 1, 1 ); See also CRC2CRVTAN. 11.2.338 TOFFSET ListType TOFFSET( CurveType Crv, CurveType OffCrv, ListType Params ) or ListType TOFFSET( SurfaceType Srf, SurfaceType OffSrf, ListType Params ) Trims local and global self intersections in curve OﬀCrv (surface OﬀSrf) that is an oﬀset approximation to curve Crv (surface Srf) with parameters Params as follows: For curves, Params contains the 4 paramers (Method, SubdivTol, TrimAmount, NumerTol) stating with the Method of trimming which can be 1 of distance map trmming or 2 for self intersection via uv-elimination. 2nd paramter IRIT Solid modeler G. Elber 225 is the tolerance of the subdivision search, 3rd is the trimming amount which should be a tad below the oﬀset distance and the last parameter is a numerical tolerance to improve trimmed locations. For surfaces Params hold 5 parameters (TrimAmount, Validate, Euclidean, SubdivTol, NumerTol). The TrimAmount is again a tad below the oﬀset distance, Validate is a boolean to activate the ﬁlering of self intersecting regions, Eculidean sets the output form to be in Euclidean or parametric space and ﬁnally SubdivTol and NumerTol is used by the multivariate solver. Example: c0 = cbspline( 3, list( ctlpt( E2, -1, 3 ), ctlpt( E2, -0.3, 0 ), ctlpt( E2, 0.3, 0 ), ctlpt( E2, 1, 3 ) ), list( kv_open ) ); for ( i = -5, 1, 5, if ( i != 0, ofst = 0.15 * i: co = offset( c0, ofst, 0.0001, off ): none = TOFFSET( c0, co, list( 1, 15, abs( ofst * 0.999 ), 0.001 ) ): color( none, i + 6 ): viewobj( none ) ) ); approximates several oﬀset curves at oﬀset amounts of 0.15 * i to curve c0 and trim the self intersections detected in them. See Figure 111. 11.2.339 TORUS PolygonType TORUS( VectorType Center, VectorType Normal, NumericType MRadius, NumericType mRadius ) creates a TORUS geometric object, deﬁned by Center as the center of the TORUS, Normal as the normal to the main plane of the TORUS, MRadius and mRadius as the major and minor radii of the TORUS. See RESOLUTION for the accuracy of the TORUS approximation as a polygonal model. See IRITSTATE’s ”PrimRatSrfs” and ”PrimRatSrfs” state variables. Example: T = TORUS( vector( 0.0, 0.0, 0.0), vector( 0.0, 0.0, 1.0), 0.5, 0.2 ); constructs a torus with its major plane as the XY plane, major radius of 0.5, and minor radius of 0.2. See Figure 112. 11.2.340 TPINCLUDE CurveType TPINCLUDE( TrivarType TV, PointType Pt, NumericType Sampling ) examines if Pt is inside the triavariate TV. The function is optimizied for many point including in a trivairate tests. If Sampling is positive, a data structure is prepared with the given Sampling rate, for coming queries. If sampling is negative, the structure is freed and if sampling is zero, the actualy inclusion test is conducted. Example: IRIT Solid modeler G. Elber Figure 111: Properly trimmed oﬀsets could be created using the TOFFSET function. 226 IRIT Solid modeler G. Elber 227 Figure 112: A torus primitive can be constructed using a TORUS constructor... TPInclude( tv2, point( 0, 0, 0 ), 20 ); # Prep. aux data. for ( i = 0, 1, 1000, if ( TPInclude( tv2, nth( Pts, i ), 0 ), # actual query. printf( "Point is inside\n", nil() ), printf( "Point is outside\n", nil() ) ); TPInclude( tv2, point( 0, 0, 0 ), -1 ); # Free aux data. 11.2.341 TRAISE TrivarType TRAISE( TrivarType TV, ConstantType Direction, NumericType NewOrder ) raises TV to the speciﬁed NewOrder in the speciﬁed Direction. Example: tv1r = TRAISE( traise( traise( tv1, row, 4 ), col, 4 ), depth, 4 ); ensures that the trivariate is a tricubic. See also MRAISE, SRAISE, and CRAISE. 11.2.342 TREFINE TrivarType TREFINE( TrivarType TV, ConstantType Direction, NumericType Replace, ListType KnotList ) provides the ability to Replace a knot vector of TV or reﬁne it in the speciﬁed direction Direction (ROW, COL, or DEPTH). KnotList is a list of knots at which to reﬁne TV. All knots should be contained in the parametric domain of TV in Direction. If the knot vector is replaced, the length of IRIT Solid modeler G. Elber 228 KnotList should be identical to the length of the original knot vector of TV in the Direction. If TV is a Bezier trivariate, it is automatically promoted to be a B-spline trivariate. Example: TV = TREFINE( TREFINE( TREFINE( TV, ROW, FALSE, list( 0.333, 0.667 ) ), COL, FALSE, list( 0.333, 0.667 ) ), DEPTH, FALSE, list( 0.333, 0.667 ) ); reﬁnes TV in all directions by adding two more knots at 0.333 and 0.667. See also CREFINE, SREFINE, and MREFINE. 11.2.343 TREGION TrivarType TREGION( TrivarType TV, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) extracts a region of TV between MinParam and MaxParam in the speciﬁed Direction. Both MinParam and MaxParam should be contained in the parametric domain of TV in the Direction. Example: Tv1 = tbezier( list( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( list( list( ctlpt( ctlpt( list( ctlpt( ctlpt( E3, E3, E3, E3, E3, E3, E3, E3, 0.1, 0.2, 0.3, 0.4, 2.4, 2.2, 2.3, 2.1, 0.0, 0.1, 2.2, 2.3, 0.8, 0.7, 2.6, 2.5, 0.8 ), 2.4 ) ), 0.2 ), 2.0 ) ) ), 0.1 ), 2.3 ) ), 0.5 ), 2.7) ) ) ) ); Tv1r1 = TREGION( Tv1, row, 0.1, 0.2 ); Tv1r2 = TREGION( Tv1, row, 0.4, 0.6 ); Tv1r3 = TREGION( Tv1, row, 0.99, 1.0 ); extracts three regions of Tv1 along the ROW direction. See Figure 113. See also CREGION, SREGION, and MREGION. 11.2.344 TREPARAM TrivarType TREPARAM( TrivarType TV, ConstantType Direction, NumericType MinParam, NumericType MaxParam ) reparametrizes TV over a new domain from MinParam to MaxParam, in the prescribed Direction. This operation does not aﬀect the geometry of the trivariate and only aﬃne transforms its knot vectors. A Bezier trivariate will automatically be promoted into a B-spline surface by this function. Example: Tv = TREPARAM( TREPARAM( TREPARAM( tv, row, 0, 1 ), col, 0, 1 ), depth, 0, 1 ); ensures that the trivariate is deﬁned over the unit size parametric cube. See also CREPARAM, SREPARAM, and MREPARAM. IRIT Solid modeler G. Elber 229 Figure 113: A region can be extracted from a freeform trivariate using TREGION. 11.2.345 TRIANGL PolygonType TRIANGL( PolygonType Model, NumericType Regular ) converts Model into a new model with exactly the same shape that holds only triangles. If the Regular is not zero, the object is regularized as well. Example: final2 = triangl( final, false ); See also MAXEDGELEN 11.2.346 TRIMSRF TrimSrfType TRIMSRF( SurfaceType Srf, CurveType TrimCrv, NumericType HasUpperLevel ) or TrimSrfType TRIMSRF( SurfaceType Srf, ListType TrimCrvs, NumericType HasUpperLevel ) create a trimmed surface from the provided surface Srf and the trimming curve TrimCrv or curves TrimCrvs. If HasUpperLevel is FALSE, an additional trimming curve is automatically added that contains the entire parametric domain of Srf. No validity test is performed on the trimming curves which are assumed to be two-dimensional curves contained in the parametric domain of Srf. Example: spts = list( list( ctlpt( E3, 0.1, 0.0, 1.0 ), ctlpt( E3, 0.3, 1.0, 0.0 ), IRIT Solid modeler G. Elber 230 ctlpt( E3, 0.0, 2.0, 1.0 ) ), list( ctlpt( E3, 1.1, 0.0, 0.0 ), ctlpt( E3, 1.3, 1.5, 2.0 ), ctlpt( E3, 1.0, 2.1, 0.0 ) ), list( ctlpt( E3, 2.1, 0.0, 2.0 ), ctlpt( E3, 2.3, 1.0, 0.0 ), ctlpt( E3, 2.0, 2.0, 2.0 ) ), list( ctlpt( E3, 3.1, 0.0, 0.0 ), ctlpt( E3, 3.3, 1.5, 2.0 ), ctlpt( E3, 3.0, 2.1, 0.0 ) ), list( ctlpt( E3, 4.1, 0.0, 1.0 ), ctlpt( E3, 4.3, 1.0, 0.0 ), ctlpt( E3, 4.0, 2.0, 1.0 ) ) ); sb = sbspline( 3, 3, spts, list( list( KV_OPEN ), list( KV_OPEN ) ) ); TCrv1 = cbspline( 2, list( ctlpt( E2, 0.3, 0.3 ), ctlpt( E2, 0.7, 0.3 ), ctlpt( E2, 0.7, 0.7 ), ctlpt( E2, 0.3, 0.7 ), ctlpt( E2, 0.3, 0.3 ) ), list( KV_OPEN ) ); TCrv2 = circle( vector( 0.5, 0.5, 0.0 ), 0.25 ); TCrv3 = cbspline( 3, list( ctlpt( E2, 0.3, 0.3 ), ctlpt( E2, 0.7, 0.3 ), ctlpt( E2, 0.7, 0.7 ), ctlpt( E2, 0.3, 0.7 ) ), list( KV_PERIODIC ) ); TSrf1 = TRIMSRF( sb, TCrv1, false ); TSrf2 = TRIMSRF( sb, TCrv1, true ); TSrf3 = TRIMSRF( sb, list( TCrv1, TcRv2 * ty( 1 ), TCrv3 * ty( 2 ) ), false ); constructs three trimmed surfaces. Tsrf1 contains the outer boundary and excludes what is inside TCrv1, TSrf2 contains only the domain inside TCrv1. TCrv3 has three holes corresponding to the three trimming curves. See also TRMSRFS. See Figure 114. 11.2.347 TRMSRFS TrimSrfType TRMSRFS( SurfaceType Srf, CurveType Cntrs ) or TrimSrfType TRMSRFS( SurfaceType Srf, PolyType Cntrs ) or IRIT Solid modeler G. Elber 231 Figure 114: Three trimmed surfaces created from the same B-spline surface. The original surface is outline by thin lines and the trimmed surfaces are outlined by thick lines. TrimSrfType TRMSRFS( SurfaceType Srf, ListType Cntrs ) create a set of trimmed surfaces from the provided surface Srf and the set of contours Cntrs in Srf’s parametric domain. The contours in Cntrs can be polylines, curves, or a list of such entities. The contours in Cntrs must be either closed or start and end on the boundary of the parametric domain of Srf. Further, these contours must be (self) intersection free. Finally, all trimming input is ﬁrst converted to a piecewise linear representation. The returned result is a (list of) trimmed surfaces, each deﬁning one sub-region that results from Cntrs’s trimming. Example: tsrfs = TRMSRFS( srf, list( poly( list( point( 0.0, 0.2, 0.0 ), point( 1.0, 0.5, 0.0 ) ), true ), cbezier( list( ctlpt( E2, 0.0, 2.5 ), ctlpt( E2, 0.5, 2.5 ), ctlpt( E2, 0.5, 3.0 ) ) ) ) ); interact( list( nth( tsrfs, 1 ) * tz( -0.2 ), nth( tsrfs, 2 ) * tz( 0.0 ), nth( tsrfs, 3 ) * tz( 0.2 ) ) ); constructs trimmed surfaces using two contours. One contour is a polyline with two points, and the other is a quadratic Bezier curve. See also TRIMSRF. See Figure 115. 11.2.348 TSBEZIER SurfaceType TSBEZIER( NumericType Order, ListType CtlMesh ) G. Elber IRIT Solid modeler 232 Figure 115: Three trimmed surfaces created from the same B-spline surface using the TRMSRFS and two prescribed contour in the surface’s parametric domain. creates a triangular Bezier surface of order Order using the provided control mesh. CtlMesh is a list of control points of size (Order + 1) * Order / 2. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the surface’s control polygon. The surface point type will be of a space which is the union of the spaces of all points. The created surface is the piecewise polynomial (or rational) surface, S(u, v) = m n! i j k u v w Pijk i!j!k! i,j,k=0 (32) where Pijk are the control points CtlMesh, and i + j + k = m and m are the degree of the surface, which are one less than Order. Example: b = TSBEZIER( 3, list( ctlpt( E3, 0.0, ctlpt( E3, 0.3, ctlpt( E3, 0.7, 0.0, 0.0, 0.0, 0.4 ), 0.3 ), 0.8 ), ctlpt( E3, 0.2, ctlpt( E3, 0.4, 0.4, 0.5, 1.0 ), 1.0 ), ctlpt( E3, 0.5, 1.0, 0.7 ) ) ); See Figure 116. See also TSGREGORY and TSBSPLINE. 11.2.349 TSBSPLINE TriSrfType TSBSPLINE( NumericType Order, NumericType Length, ListType CtlMesh, ListType KnotVector ) IRIT Solid modeler G. Elber 233 Figure 116: A triangular Bezier surface of degree 2 or order 3. creates a B-spline surface from the provided Order and Length, the control mesh CtlMesh, and the knot vector KnotVector. CtlMesh is a list of control points of size (Length + 1) * Length / 2. All control points must be of point type (E1-E9, P1-P9), or regular PointType deﬁning the surface’s control mesh. The surface point type will be of a space which is the union of the spaces of all points. KnotVector is a list of NumericType knots of length Length plus the Order. The knot vector may also be a list of a single constant KV OPEN or KV FLOAT, in which a uniform knot vector with the appropriate length and with an open or ﬂoating end condition will be constructed automatically. Not fully supported at this time. See also TSBEZIER and TSGREGORY. 11.2.350 TSDERIVE TriSrfType TSDERIVE( TriSrfType Srf, NumericType Dir ) returns a vector ﬁeld surface representing the diﬀerentiated triangular surface in the given direction (ROW, COL, or DEPTH). Evaluation of the returned surface at a given parameter value will return a vector tangent to Srf in Dir at that parameter value. DuSrf = TSDERIVE( Srf, ROW ); DvSrf = TSDERIVE( Srf, COL ); Normal = coerce( tseval( DuSrf, 0.5, 0.25, 0.25 ), VECTOR_TYPE ) ^ coerce( tseval( DvSrf, 0.5, 0.25, 0.25 ), VECTOR_TYPE ); computes two partial derivatives of the surface Srf and computes its normal as their cross product, at the parametric location (0.5, 0.25, 0.25). See also TSNORMAL G. Elber IRIT Solid modeler 11.2.351 234 TSEVAL CtlPtType TSEVAL( TriSrfType Srf, NumericType UParam, NumericType VParam, NumericType WParam ) evaluates the provided triangular surface Srf at the given UParam, VParam, WParam parameters. UParam, VParam, and WParam must all be non negative and must sum to one for a Bezier triangular surface or to the maximum domain, if a B-spline surface. Example: CPt = TSEVAL( Srf, u, v, 1.0 - u - v ); evaluates Srf at the parameter values prescribed by u and v. 11.2.352 TSGREGORY SurfaceType TSGREGORY( NumericType Order, ListType CtlMesh ) cCreates a triangular Gregory surface of order Order using the provided control mesh. CtlMesh is a list of control points of size (Order + 1) * Order / 2 + 3. All control points must be of type (E1-E9, P1-P9), or regular PointType deﬁning the surface’s control polygon. The surface point type will be of a space which is the union of the spaces of all points. The created surface is the polynomial (or rational) surface, S(u, v) = m n! i j k u v w Pijk i!j!k! i,j,k=0 (33) where Pijk are the control points CtlMesh, and i + j + k = m and m are the degree of the surface, which are one less than Order, where Pijk for i = j = 1, or i = k = 1, or j = k = 1 are the three Gregory, double points. Example: Srf = tsgregory( list( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( 5, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, E3, 2, -1, 0 ), 2.3, -1, 0.25 ), 2.6, -1, 0.25 ), 2.8, -1, 0.13 ), 3, -1, 0 ), 2.25, -0.7, 0.25 ), 2.5, -0.7, -0.25 ), 2.6, -0.7, -0.15 ), 2.75, -0.7, 0.25 ), 2.4, -0.4, 0.25 ), 2.5, -0.4, 0 ), 2.6, -0.4, -0.25 ), 2.45, -0.2, 0.12 ), 2.55, -0.2, -0.12 ), 2.5, 0, 0 ), 2.5, -0.7, -0.25 ), 2.6, -0.7, -0.15 ), 2.5, -0.4, 0 ) ) ); Not fully supported at this time. See also TSBEZIER and TSBSPLINE. G. Elber IRIT Solid modeler 11.2.353 235 TSNORMAL VectorType TSNORMAL( TriSrfType Srf, NumericType UParam, NumericType VParam, NumericType WParam) computes the normal vector to a triangular surface Srf at the parameter values UParam, VParam, WParam. The returned vector has a unit length. UParam, VParam, and WParam must all be non negative and must sum to one for a Bezier triangular surface or to the maximum domain, if a B-spline surface. Example: Normal = TSNORMAL( Srf, 0.5, 0.5, 0.0 ); computes the normal to Srf at the parameter values (0.5, 0.5, 0.0). 11.2.354 TVIMPJACOB TrivarType TVIMPJACOB( TrivarType TV, NumericType StepSize, NumericType NumIter ) numerically improves, if possible, the parametrization of TV so that the diﬀerence between the minimal and maximal determinant of the Jacobian of TV is reduced. It is equal to, C(t) = m Pij Bi (t), (34) i=0 and similar for the other parametric direction. Example: TV = TVIMPJACOB( TV, 0.001, 10 ); See also TVJACOBIAN and TVZRJACOB. 11.2.355 TVJACOBIAN TrivarType TVJACOBIAN( TrivarType TV ) computes a scalar trivariate ﬁeld from the given scalar trivariate TV that equals the determinant of teh jacobian of TV. Example: exList = ffextrema( TVJACOBIAN( tv ), false ): computes extreme Jaciban values in the parametrization of tv. See also TVIMPJACOB and TVZRJACOB. G. Elber IRIT Solid modeler 11.2.356 236 TVLOAD TrivarType TVLOAD( StringType FileName, NumericType DataType, VectorType VolSize, VectorType Orders ) loads a volumetric data set from ﬁle FileName in as a trivariate of orders Orders. DataType can be one of: 1 2 3 4 5 6 Regular ASCII (separated by white spaces). Two bytes short integer. Four bytes long integer. One byte (char) integer. Four bytes ﬂoat. Eight bytes double. Beware of the little vs big Endian problem! We assume here you have read the volume in the same machine type in which this ﬁle was written. VolSize provides the dimensions of the volume, with width ﬁrst and depth last. Uniform open end condition knot vectors are constructed to all three axes. Example: Tv = TVLOAD( "3dhead", 1, vector( 32, 32, 13 ), vector( 3, 3, 3 ) ); loads the data set ”3dhead” of size (32, 32, 13) as a triquadratic function. THe sata set is assumed to contain ASCII numeric values. See also MRCHCUBE. 11.2.357 TVPREV TrivarType TVPREV( SurfaceType Srf ) or TrivarType TVPREV( ListType SrfList ) computes trivariate of revolution for the given polynomial surface(s) by rotating the input along the Z axis. Result is a polynomial approximation for the real circular shape. Example: Tv = TVRev( Disk ); Create a a trivariate torus, TV by rotating the input Disk surface along the Z axis. The behaviour of this function can be modiﬁed if ”Rational” attribute is provided with a non zero value to construct a precise rational trivariate of revolution and a polynomial approximation otherwise. Further if ”StartAngle” and ”EndAngle” are found with valid angular prescription (in degrees), only that angular slice out of the trivariate of revolution is constructed. See also SURFPREV, TVREV. G. Elber IRIT Solid modeler 11.2.358 237 TVOLUME NumericType TVOLUME( TrivarType TV, NumericType VolType ) Computes the volume enclosed by trivariate, TV. If VolType is TRUE, volume is integrates over the six faces’ surfaces with respect to the XY plane. If VolType is FALSE, the integration of the six face surfaces is with respect to the origin, Example: V = TVolume( TV1 ); See also SVOLUME, SMOMENTS and CAREA. 11.2.359 TVREV TrivarType TVREV( SurfaceType Srf ) or TrivarType TVREV( ListType SrfList ) computes trivariate of revolution for the given surface(s) by rotating the input along the Z axis. Example: Tv = TVRev( Disk ); Createa a trivariate torus, TV by rotating the input Disk surface along the Z axis. See also SURFREV, TVPREV. See Figure 117. 11.2.360 TVZRJACOB PolyType TVZRJACOB( TrivarType TV, NumericType Euclidean, NumericType SkipRate, NumericType Fineness ) computes the zero set of the Jacobian of the given trivariate, TV. This zero set is the implicit boundary of the trivariate and, for example, equals the envelop of the sweep of a bivariate surface in space (see example below). The zero set is returned as a polygonal data set approximation with Fineness tolerance. If Euclidean, the resulting polygons are in Euclidean space. Otherwise, the polygons are returned in the trivariate’s parametric domain. Finally, SkipRate provides a mechanism to skip to every SkipRate row, column and plane while a SkipRate skips nothing. Let T (u, v, w) = (xT (u, v, w), yT (u, v, w), zT (u, v, w)). Then, the zero of the Jacobian equals, 0= Example: ∂xT ∂u ∂yT ∂u ∂zT ∂u ∂xT ∂v ∂yT ∂v ∂zT ∂v ∂xT ∂w ∂yT ∂w ∂zT ∂w = xT , yT × zT . (35) IRIT Solid modeler G. Elber 238 Figure 117: A trivariate of revolution in the shape of a torus is creating by rotating a disk surface. Figure 118: The envelope of the motion of the wine glass surface in space can be derived with the aid of the TvZrJacob function. Tv = tfromsrfs( list( Srf, Srf * tx( 3 ) * ty( 3 ), Srf * tx( 6 ) ), 3 ); Tv1ZeroJacobian = TVZRJACOB( Tv, 1, 1, 0 ); A trivariate TV is constructed as a sweep of surface Srf along a quadratic Bezier curve with (0, 0), (3, 3), (6, 0) as control points, and then the zero set of the Jacobian is derived to yield the envelope of this motion of Srf. See Figure 118. See also TVJACOBIAN and TVIMPJACOB. IRIT Solid modeler 11.2.361 G. Elber 239 UVPOLY PolyType UVPOLY( PolyType Obj, ListType Scales, ListType Translates ); Sets UV coordinates to polygonal object Obj. The UV coordinates are set using the XY Euclidean coordinates if Scales is a list that holds two scaling factors (XScale, YScale), or the UV coordinates are set via the two largest span in XYZ for each polygon, if Scales is a list of three scaling factors (XScale, YScale, ZScale). Translates oﬀers a way to shift the UV coordinates in the texture 2D domain, Translates of (0, 0) does nothing. Needless to say, the ?Scale factors scales the Euclidean coordinates before being sets as UV texture coordinates. Example: UVCube = UVPOLY( Cube, list( 1, 1, 1 ), list( 0, 0 ) ); sets UV coordinates to the six faces of the cube, each face with UV values between zero and one. 11.2.362 ZCOLLIDE NumericType ZCOLLIDE( GeometricTreeType Obj1, GeometricTreeType Obj2, NumericType Fineness, NumericType NumOfIters ); Given two objects, Obj1 and Obj2, where Obj1 is assumed to be above (in the Z direction) Obj2, this function computes the amount that Obj1 could be moved down, the -Z direction, until it collides with Obj2. The collision detection is considered using a polygonal approximation that has a Fineness resolution (see RESOLUTION variable). The computation cost is linear in NumOfIters with quadratic accuracy convergence. Values of ten for both Fineness and NumOfIters are reasonable selections. While Obj1 is considered in its exact form, in Obj2, only the bbox of the shape is considered. Example: view( chair, 1 ); for ( x = 0, 1, 5, b = box( vector( x / 10, 0, 2 ), 0.1, 0.1, 0.1 ): view( b * tz( ZCOLLIDE( chair, b, 10, 10 ) ), 0 ) ); places and draws six diﬀerent cubes on top of the object called chair. 11.2.363 ZTEXTRUDE SurfaceType ZTEXTRUDE( CurveType CrossSection, NumericType Rational, NumericType ZPitch ) or TrivarType ZTEXTRUDE( SurfaceType CrossSection, NumericType Rational, NumericType ZPitch ) IRIT Solid modeler G. Elber 240 Figure 119: A twisting extrusion can be constructed via the ZTEXTRUDE command. Here a start shaped planar surface ( in blue) is extruded and twisted to created the shown trivariate (in red). constructs an extrusion of CrossSection in the +Z direction while twisting (rotation the CrossSection along the Z axis). ZPitch sets the Z extrusion amount (for 360 rotation) as we advances in the +Z direction. If Rational is TRUE the result is a precise rational freeform. If FALSE, a polynomial approximation is constructed instead. Example: TV = ZTEXTRUDE( Srf, TRUE, 1 ); See Figure 119 for an example. See also EXTRUDE. 11.3 Object transformation functions All the routines in this section construct a 4 by 4 homogeneous transformation matrix representing the required transform. These matrices may be concatenated to achieve more complex transforms using the matrix multiplication operator ∗. For example, the expression m = trans( vector( -1, 0, 0 ) ) * rotx( 45 ) * trans( vector( 1, 0, 0 ) ); constructs a transform to rotate an object around the X = 1 line, 45 degrees. A matrix representing the inverse transformation can be computed as: InvM = m ^ -1 See also overloading of the - operator. G. Elber IRIT Solid modeler 11.3.1 241 HOMOMAT MatrixType HOMOMAT( ListType MatData ) creates an arbitrary homogeneous transformation matrix by manually providing its 16 coeﬃcients. Example: step = 10; for ( a = 1, 1, 720 / step, view_mat = save_mat * HOMOMAT( list( list( 1, list( 0, list( 0, list( 0, view( list( view_mat, axes ), on ) ); 0, 1, 0, 0, 0, 0, 1, 0, 0 ), 0 ), -a * step / 500 ), 1 ) ) ): looping and viewing through a sequence of perspective transforms, created using the HOMOMAT constructor. See also RFLCTMAT and PROJMAP. 11.3.2 MAP3PT2EQL MatrixType MAP3PT2EQL( PointType Pt1, PointType Pt2, PointType Pt3 ) computes the transofrmation matrix in the XY plane that takes the given three planar points into an equilateral triangle around the origin. Example: Mat = MAP3PT2EQL( Pt1, Pt2, Pt3 ); See also ELLIPSE3PT, CONICSEC. 11.3.3 MATPOSDIR MatrixType MATPOSDIR( PointType Pos, VectorType Dir, VectorType UpDir ) creates a viewing transformation matrix of a viewer at Pos, looking at direction Dir and upper view of UpDir. Example: step = 10; for ( a = 1, 1, 720 / step, view_mat = MATPOSDIR( point( 0.5, 0.1, 0.5 ), vector( 0.0, 1.0, 0.0 ), vector( cos( a * step * Pi / 360 ), 0, sin( a * step * Pi / 360 ) ) ): view( list( view_mat, axes ), on ) ); looping and viewing through a sequence of transforms, created using the MATPOSDIR constructor. IRIT Solid modeler 11.3.4 G. Elber 242 PROJMAT MatrixType PROJMAT( PlaneType ProjPlane, VectorType EyePos, NumericType EyeInf ) constructs a projection matrix to project the universe onto the given projection plane ProjPlane, with the eye position at EyePos (divided by EyeInf). Note that if EyeInf is zero, the eye is at inﬁnity. Example: PMat = PROJMAT( plane( 0, 0, 1, -0.1 ), vector( 1, 1, 1 ), 0 ); contstructs a projection matrix PMat onto the Z = -0.1 plane with a view direction of ( 1, 1, 1 ). See also RFLCTMAP, HOMOMAT. 11.3.5 RFLCTMAT MatrixType RFLCTMAT( PlaneType RflctPlane ) constructs a reﬂection matrix to reﬂect the universe along the given reﬂection plane RﬂctPlane. Example: PMat = RFLCTMAT( plane( 0, 0, 1, 0 ) ); constructs a reﬂection matrix PMat around the Z = 0 plane. See also PROJMAP, HOMOMAT. 11.3.6 ROTV2V MatrixType ROTV2V( VectorType Vec1, VectorType Vec2 ) creates a rotation that takes vector Vec1 to vector Vec2. See also ROTVEC, ROTZ2V, ROTZ2V2. 11.3.7 ROTVEC MatrixType ROTVEC( VectorType Vec, NumericType Angle ) creates a rotation around the vector Vec matrix with Angle degrees. See also ROTV2V, ROTZ2V, ROTZ2V2. 11.3.8 ROTX MatrixType ROTX( NumericType Angle ) creates a rotation around the X transformation matrix with Angle degrees. 11.3.9 ROTY MatrixType ROTY( NumericType Angle ) creates a rotation around the Y transformation matrix with Angle degrees. IRIT Solid modeler 11.3.10 G. Elber 243 ROTZ MatrixType ROTZ( NumericType Angle ) creates a rotation around the Z transformation matrix with Angle degrees. 11.3.11 ROTZ2V MatrixType ROTZ2V( VectorType Dir ) creates a rotation matrix that takes Z axis into Dir. Length of Dir is ignored. See also ROTV2V, ROTVEC, ROTZ2V2. 11.3.12 ROTZ2V2 MatrixType ROTZ2V2( VectorType Dir, VectorType Dir2 ) creates a rotation matrix that takes the Z axis into Dir, while the X axis is aligned with Dir2. The lengths of Dir and Dir2 are ignored. See also ROTV2V, ROTVEC, ROTZ2V, ROTVEC. 11.3.13 SCALE MatrixType SCALE( VectorType ScaleFactors ) creates a scaling by the ScaleFactors transformation matrix. 11.3.14 TRANS MatrixType TRANS( VectorType TransFactors ) creates a translation by the TransFactors transformation matrix. 11.4 11.4.1 General purpose functions ADWIDTH ADWIDTH( GeometricType Object, NumericType DWidth ) sets the width of the object. This display width is used in pixels in display devices for width of line drawing, if supported by the display device. See also ATTRIB, COLOR, and AWIDTH. This function is equivalent to using, ATTRIB( Object, ”dwidth”, DWidth ); 11.4.2 ATTRIB ATTRIB( AnyType Object, StringType Name, AnyType Value ) provides a mechanism to add an attribute of any type to an Object, with name Name and value Value. This ATTRIB function is tuned and optimized toward numeric values or strings as Value although any other object type can be saved as attribute. These attributes may be used to pass information to other programs about this object, and are saved with the objects in data ﬁles. Attributes placed on a list object or even a whole hierarchy of IRIT Solid modeler G. Elber 244 objects will be propagated into all items in the list or hierarchy. There are a few exception to this propagation. The ”animation” attribute is not propagated and is kept in the internal nodes, forming a hierachy of animation commands for all the objects contained in the list/hierarchy. The ”invisible” attribute is saved at all levels of the hierarchy, used to denote a complete sub tree that is invisible (yet can serve as a source at which instances can point). For example, ATTRIB(Glass, "rgb", "255,0,0"); ATTRIB(Glass, "refract", "1.4"); . . . RmAttr(Glass, "rgb"); # Removes "rgb" attribute. sets the RGB color and refraction index of the Glass object and later removes the RGB attribute. Attribute names are case insensitive. Spaces are allowed in the Value string, as well as the double quote itself, although the latter must be escaped: ATTRIB(Glass, "text", "Say \"this is me\""); See also RMATTR for removal of attributes, CPATTR for copying them, GETATTR to get an attribute, ATTRPROP for setting attributes on all subtrees of parts, as well as AWIDTH, ADWIDTH, COLOR and PATTRIB. 11.4.3 ATTRPROP ATTRPROP( AnyType Object, StringType Name, AnyType Value ) Same as ATTRIB but propagates the attributes to all sub-parts of the object. See also ATTRVPROP. Example: Glass1 = list( Base, Handle, Wine ); Glass2 = list( Base, Handle, Wine ); attrib( Glass1, "ptexture", "marble1.gif" ); ATTRPROP( Glass2, "ptexture", "marble1.gif" ); In Glass1, only Glass1 will be set with ”texture” while in Glass2, the ”texture” attribute will propagate to the sub-parts of Glass2, namely to the Base, Handle, Wine. 11.4.4 ATTRVPROP ATTRVPROP( AnyType Object, StringType Name ) Propagates an Object attribute named Name to the vertices in Object. Typically for RGB color values. Example: Obj2 = ATTRVPROP( Obj, "RGB" ); IRIT Solid modeler 11.4.5 G. Elber 245 AWIDTH AWIDTH( GeometricType Object, NumericType Width ) sets the width of the object to one of those speciﬁed below. This width is used in real object side dimensions in tools such as scan converters and rendering tools for rendering lines and curves, as well as postscript. See also ATTRIB, COLOR, and ADWIDTH. This function is equivalent to using, ATTRIB( Object, ”width”, Width ); 11.4.6 CHDIR CHDIR( StringType NewDir ) sets the current working directory to be NewDir. 11.4.7 CLNTCLOSE CLNTCLOSE( NumericType Handler, NumericType Kill ) closes a communication channel to a client. Handler contains the index of the communication channel opened via CLNTEXEC. If Kill, the client is sent an exit request for it to die. Otherwise, the communication is closed and the client runs standing alone. See also VIEWOBJ, VIEWSET, CLNTREAD, CLNTWRITE, and CLNTEXEC. Example: h2 = clntexec( "nuldrvs -s-" ); . . . CLNTCLOSE( h2,TRUE ); closes the connection to the nuldrvs client, opened via CLNTEXEC. 11.4.8 CLNTWRITE CLNTWRITE( NumericType Handler, AnyType Object ) writes one object Object to a communication channel of a client. Handler contains the index of the communication channel opened via CLNTEXEC. If the Handler equals -1, the regular display device (forked via, for example, VIEWOBJ command) is used. If Handler equals CLIENTS ALL, a broadcast of Object to all clients is performed. See also VIEWOBJ, VIEWSET, CLNTREAD, CLNTCLOSE, and CLNTEXEC. Example: h2 = clntexec( "nuldrvs -s-" ); . . IRIT Solid modeler G. Elber 246 CLNTWRITE( h2, Model ); . . clntclose( h2,TRUE ); writes the object named Model to client through communication channel h2. 11.4.9 COLOR COLOR( GeometricType Object, NumericType Color ) sets the color of the object to one of those speciﬁed below. Note that an object has a default color (see irit.cfg ﬁle) according to its origin - loaded with the LOAD command, PRIMITIVE, or a BOOLEAN operation result. The system internally supports colors (although you may have a B&W system) and the colors recognized are: BLACK, BLUE, GREEN, CYAN, RED, MAGENTA, YELLOW, and WHITE. See the ATTRIB command for more ﬁne control of colors using the RGB attribute. See also AWIDTH and AWIDTH. This function is equivalent to using, ATTRIB( Object, ”color”, Color ); 11.4.10 COMMENT COMMENT Two types of comments are allowed: 1. One-line comment: starts anywhere in a line at the ’#’ character, up to the end of the line. 2. Block comment: starts at the COMMENT keyword followed by a unique character (anything but white space), up to the second occurrence of that character. This is a fast way to comment out large blocks. Example: COMMENT $ This is a comment $ 11.4.11 CPATTR CPATTR( AnyType DestObj, AnyType SrcObj ) copies all attribute from object SrcObj into object DestObj. All attributes, if any, in DestObj are purged. Needless to say, both objects must exist at the time of attribute copy. See also ATTRIB, ATTRPROP, GETATTR, RMATTR. 11.4.12 ERROR ERROR( StringType Message); breaks the execution and returns to the IRIT main loop, after printing a Message to the screen. This may be useful in user deﬁned functions to break execution in cases of fatal errors. IRIT Solid modeler 11.4.13 G. Elber 247 EXEC EXEC( StringType Command ); executes a string Command in the IRIT interepreter, indirectly. Example: Univariate2Bezier = function( Polynom, Deg ): x: f: return = nil(): f = 1: for ( x = 0, 0.05 / Deg, 1, EXEC( "f = " + Polynom ): snoc( ctlpt( E1, f ), return ) ): return = coerce( cinterp( return, Deg + 1, Deg + 1, PARAM_UNIFORM, FALSE ), bezier_type ); deﬁnes a function that converts univariate expressions into explicit, E1, Bezier curves. For example ”Univariate2Bezier( ”3 * x ^ 2 - 2 * x + 5”, 3 );” would return a cubic Bezier curve representing ”3 * x ^ 2 - 2 * x + 5”. 11.4.14 EXIT EXIT() exits from the solid modeler. NO warning is given! 11.4.15 FOR FOR( NumericType Start, NumericType Increment, NumericType End, AnyType Body ) executes the Body (see below), while the FOR loop conditions hold. Start, Increment, End are evaluated ﬁrst, and the loop is executed while <= End if Increment > 0, or while >= End if Increment < 0. If Start is of the form ”Variable = Expression”, then that variable is updated on each iteration, and can be used within the body. The body may consist of any number of regular commands, separated by COLONs, including nesting FOR loops to an arbitrary level. Example: step = 10; rotstepx = rotx(step); FOR ( a = 1, 1, 360 / step, view_mat = rotstepx * view_mat: view( list( view_mat, axes ), ON ) ); displays axes with a view direction that is rotated 10 degrees at a time around the X axis. IRIT Solid modeler 11.4.16 G. Elber 248 HELP HELP( StringType Subject ) provides help on the speciﬁed Subject. Example: HELP(""); will list all IRIT help subjects. 11.4.17 FNFREE FNFREE( StringType UserFuncName ) frees a user deﬁned function named UserFuncName. See also FREE. 11.4.18 FREE FREE( GeometricType Object ) Because of the usually huge size of geometric objects, this procedure may be used to free them. Reassigning a value (even of diﬀerent type) to a variable automatically releases the old variable’s allocated space as well. See also FNFREE. 11.4.19 FUNCTION FuncName = FUNCTION(Prm1, Prm2, ... , PrmN):LclVal1:LclVar2: ... :LclVarM: FuncBody; deﬁnes a function named FuncName with N parameters and M local variables (N, M >= 0). Here is a (simple) example of a function with no local variables and a single parameter that computes the square of a number: sqr = FUNCTION(x): return = x * x; Functions can be deﬁned with optional parameters and optional local variables. A function’s body may contain an arbitrary set of expressions including for/while loops, (user) function calls, or even recursive function calls, all separated by colons. The returned value of the function is the value of an automatically deﬁned local variable named return. The return variable is a regular local variable within the scope of the function and can be used as any other variable. If a variable’s name is found in neither the local variable list nor the parameter list, it is searched for in the global variable list (outside the scope of the function). Binding of names of variables is static as in the C programming language. Because binding of variables is performed in execution time, there is a somewhat less restrictive type checking of parameters of functions that are invoked within a user’s deﬁned function. A function can invoke itself, i.e., it can be recursive. However, since a function should be deﬁned when it is called, a dummy function should be deﬁned before the recursive one is deﬁned: IRIT Solid modeler G. Elber 249 factorial = function(x):return = x; # Dummy function. factorial = function(x): if (x <= 1, return = 1, return = x * factorial(x - 1)); Overloading is valid inside a function as it is outside. For example, for add = FUNCTION(x, y): return = x + y; the following function calls are all valid: add(1, 2); add(vector(1,2,3), point(1,2,3)); add(box(vector(-3, -2, -1), 6, 4, 2), box(vector(-4, -3, -2), 2, 2, 4)); Finally, here is a more interesting example that computes an approximation of the length of a curve, using the sqr function deﬁned above: distptpt = FUNCTION(pt1, pt2): return = sqrt(sqr(coord(pt1, 1) - coord(pt2, 1)) + sqr(coord(pt1, 2) - coord(pt2, 2)) + sqr(coord(pt1, 3) - coord(pt2, 3))); crvlength = FUNCTION(crv, n):pd:t:t1:t2:dt:pt1:pt2:i: return = 0.0: pd = pdomain(crv): t1 = nth(pd, 1): t2 = nth(pd, 2): dt = (t2 - t1) / n: pt1 = coerce(ceval(crv, t1), e3): for (i = 1, 1, n, pt2 = coerce(ceval(crv, t1 + dt * i), e3): return = return + distptpt(pt1, pt2): pt1 = pt2); Try, for example: crvlength(circle(vector(0.0, 0.0, 0.0), 1.0), 30) / 2; crvlength(circle(vector(0.0, 0.0, 0.0), 1.0), 100) / 2; crvlength(circle(vector(0.0, 0.0, 0.0), 1.0), 300) / 2; See PROCEDURE and IRITSTATE’s ”DebugFunc” for more. 11.4.20 IF IF( NumericType Cond, AnyType TrueBody { , AnyType FalseBody } ) executes TrueBody (a group of regular commands, separated by COLONs - see FOR loop) if the Cond holds, i.e., it is a numeric value other than zero, or optionally, if it exists, executes FalseBody. If the Cond does not hold, i.e., it evaluates to a numeric value equal to zero. Examples: G. Elber IRIT Solid modeler 250 IF ( machine == IBMOS2, resolution = 5, resolution = 10 ); IF ( a > b, max = a, max = b ); sets the resolution to 10, unless running on an IBMOS2 system, in which case the RESOLUTION variable will be set to 5 in the ﬁrst statement, and set to max to the maximum of a and b in the second statement. 11.4.21 INCLUDE INCLUDE( StringType FileName ) executes the script ﬁle FileName. Nesting of an include ﬁle is allowed up to 10 levels deep. If an error occurs, all open ﬁles in all nested ﬁles are closed and data are waited for at the top level (standard input). Files are searched for inclusion in the current directory. If not found, and the inclusion is from a diﬀerent ﬁle at some directory, that directory is searched as well. Finally, if all the above fails, the directories speciﬁed via the IRIT INCLUDE environment variable are also searched. A script ﬁle can contain any command the solid modeler supports. Example: INCLUDE( "/tmp/general.irt" ); includes the ﬁle ”/tmp/general.irt”. Any inclusion inside general.irt will search for the included ﬁle in the current directory, then in /tmp, and then in the directories speciﬁed via IRIT INCLUDE. 11.4.22 INSERTPOLY INSERTPOLY( PolyType Poly, PolyType Polys ) inserts, in place, Poly as a new polygon of object Polys. After the completion of this function Poly is unmodiﬁed but Polys has a new polygon in it. Example: X = poly( list( point( point( point( point( Y = X * tz( 1 ); INSERTPOLY( Y, X ); 0, 0, 1, 1, 0, 1, 1, 0, 0 0 0 0 ), ), ), ) ), false ); At the end of the execution of this sequence of command, X contains two polygons, one at Z = 0 and one at Z = 1. See also MERGEPOLY, SPLITLST. 11.4.23 INTERACT INTERACT( GeometryTreeType Object ) This is a user-deﬁned function (see iritinit.irt) that does the following, in order outlined: 1. Clear the display device. 2. Display the given Object. G. Elber IRIT Solid modeler 251 3. Pause for a keystroke. This user-deﬁned function in version 4.0 of IRIT is an emulation of the INTERACT function that used to exist in previous versions. Example: INTERACT( list( view_mat, Axes, Obj ) ); displays and interacts with the object Obj and the predeﬁned object Axes. VIEW MAT will be used to set the starting transformation. See VIEW and VIEWOBJ for more. 11.4.24 IQUERY IQUERY( NumericType QueryType ) A low level query tool for checking the current state of the IRIT internal tables. According to the values of QueryType the following is printed to stdout: QueryType 1 2 11.4.25 Printed content All the known functions/user deﬁned functions/constants and parameters/returned values (if any). All the knwon keywords LIST ListType LIST( AnyType Elem1, AnyType Elem2, ... ) constructs an object as a list of several other objects. Only a reference is made to the Elements, so modifying Elem1 after being included in the list will aﬀect Elem1 in that list next time list is used! Each inclusion of an object in a list increases its internal used reference. The object is freed iﬀ theused reference is zero. As a result, attempt to delete a variable (using FREE) which is referenced in a list removes the variable, but the object itself is freed only when the list is freed. 11.4.26 LOAD AnyType LOAD( StringType FileName ) loads an object from the given FileName. The object may be any object deﬁned in the system, including lists, in which the structure is recovered and reconstructed as well (internal objects are inserted into the global system object list if they have names). If no ﬁle type is provided, ”.itd” is assumed. This command can also be used to load binary ﬁles. ASCII regular data ﬁles usually take longer to load than binary ﬁles due to the required parsing. Binary data ﬁles can be loaded directly, like ASCII ﬁles in IRIT, but can only be inspected through IRIT tools such as dat2irit. A binary data ﬁle must have a ”.ibd” (IRIT Binary Data) type in its name. Compressed ﬁles can be loaded if the given ﬁle name has a postﬁx of ”.Z” or .”.gz”. The gnu utility ”gzip” will be invoked via a pipe for that purpose. See also IRITSTATE’s option ”FlatLoad” for optioanl ﬂattening of the object hierarechy during a load. IRIT Solid modeler 11.4.27 G. Elber 252 LOGFILE LOGFILE( NumericType Set ) or LOGFILE( StringType FileName ) If Set is non zero (see TRUE/FALSE and ON/OFF), then everything printed in the input window will go to the log ﬁle speciﬁed in the irit.cfg conﬁguration ﬁle. This ﬁle will be created the ﬁrst time logﬁle is turned ON. If a string FileName is provided, it will be used as a log ﬁle name from now on. It also closes the current log ﬁle. A ”LOGFILE( on );” must be issued after a log ﬁle name change. Example: LOGFILE( "Data1" ); LOGFILE( on ); printf( "Resolution = %lf\\n", list( resolution ) ); LOGFILE( off ); to print the current resolution level into ﬁle Data1. 11.4.28 MSLEEP MSLEEP( NumericType MilliSeconds ) causes the solid modeller to sleep for the prescribed time in milliseconds. Example: for ( i = 1, 1, sizeof( crvs ), c = nth( crvs, i ): color( c, yellow ): msleep(20): viewobj( c ) ); displays an animation sequence and sleeps for 20 milliseconds between iterations. 11.4.29 NREF AnyType NREF( ListType ListObject, NumericType Index ) returns a reference to the Index (base count 1) element of the list ListObject. The reference points to the original object and hence can be used to modify (add attributes for example) to objects in lists. Assignment of this reference to a new object would result in a copy of the object. In contrast, a FREE of a reference to an object would have an undeﬁned result. Example: Lst = list( a, b, c ); attrib( NREF( Lst, 2 ), "NewAttr", on ); adds a new attribute to the second element of Lst. See also NTH. G. Elber IRIT Solid modeler 11.4.30 253 NRMLCONE ListType NRMLCONE( SurfaceType Srf ) computes a cone that bounds all normals of surface Srf. A list of two objects, the axis vector of the cone and the opening radius, in radians, is returned. Example: NCone = NRMLCONE( Srf ); Cn = Cone( vector( 0, 0, 0 ), normalize( nth( NCone, 1 ) ), nth( NCone, 2 ), 0 ) * tz( 1.0 ) * sc( 0.75 ); computes a normals’ cone for surface Srf and builds a real cone following these limits. 11.4.31 NTH AnyType NTH( ListType ListObject, NumericType Index ) returns the Index (base count 1) element of the list ListObject. Example: Lst = list( a, list( b, c ), d ); Lst2 = NTH( Lst, 2 ); and now Lst2 is equal to ’list( b, c )’. See also NREF. 11.4.32 PAUSE PAUSE( NumericType Flush ) waits for a keystroke. This is nice to have if a temporary stop in a middle of an included ﬁle (see INCLUDE) is required. If Flush is TRUE, then the input is ﬁrst ﬂushed to guarantee that the actual stop will occur. 11.4.33 PRINTF PRINTF( StringType CtrlStr, ListType Data ) This results in a formatted printing routine, following the concepts of the C programming language’s printf routine. CtrlStr is a string object for which the following special ’%’ commands are supported: %d, %i, %u %o, %x, %X %e, %f, %g, %E, %F %s %pe, %pf, %pg %ve, %vf, %vg %Pe, %Pf, %Pg, %De, %Df, %Dg, Prints the numeric object as an integer or unsigned integer. Prints the numeric object as an octal or hexadecimal integer. Prints the numeric object in several formats of ﬂoating point numbers. Prints the string object as a string. Prints the three coordinates of the point object. Prints the three coordinates of the vector object. Prints the four coordinates of the plane object. Prints the given object in IRIT’s data ﬁle format. IRIT Solid modeler G. Elber 254 All the ’%’ commands can include any modiﬁer that is valid in the C programming language PRINTF routine, including l (long), preﬁx character(s), size, etc. The point, vector, plane, and object commands can also be modiﬁed in a similar way, to set the format of the numeric data printed. Also supported are the newline and tab using the backslash escape character: PRINTF("\\tThis is the char \"\\%\"\\n", nil()); Backslashes should be escaped themselves as can be seen in the above example. Here are few more examples: PRINTF("this is a string \"%s\" and this is an integer %8d.\\n", list("STRING", 1987)); PRINTF("this is a vector [%8.5lvf]\\n", list(vector(1,2,3))); IritState("DumpLevel", 9); PRINTF("this is a object %8.6lDf...\\n", list(axes)); PRINTF("this is a object %10.8lDg...\\n", list(axes)); This implementation of PRINTF is somewhat diﬀerent than the C programming language’s version, because the backslash always escapes the next character during the processing stage of IRIT’s parser. That is, the string ’\\tThis is the char \"\\%\"\\n’ is actually parsed by the IRIT’s parser into ’\tThis is the char "\%"\n’ because this is the way the IRIT parser processes strings. The latter string is the one that PRINTF actually sees. See also PRINTFILE for ways to redirect PRINTF to a ﬁle.. 11.4.34 PRINTFILE PRINTFILE( StringType FileName ); Sets the ﬁle PRINTF prints to to FileName. Any newer call to PRINTFILE will close the current ﬁle used so far. If FileName is an empty string, PRINTF will print to stdout. 11.4.35 PROCEDURE ProcName = PROCEDURE(Prm1, Prm2, ... , PrmN):LclVal1:LclVar2: ... :LclVarM: ProcBody; A procedure is a function that does not return a value, and therefore the returned variable (see FUNCTION) should not be used. A procedure is identical to a function in every other way. See FUNCTION for more. 11.4.36 RESET RESET() clears all variables and initializes the environment to the starting state. User deﬁned functions, however, are kept intact. IRIT Solid modeler 11.4.37 G. Elber 255 RMATTR RMATTR( AnyType Object, StringType Name ) removes attribute named Name from object Object. This function will have no aﬀect on the Object if the Object has no attribute named Name. See also ATTRIB, ATTRPROP, GETATTR, CPATTR. 11.4.38 SAVE SAVE( StringType FileName, AnyType Object ) saves the provided Object in the speciﬁed ﬁle name FileName. No extension type is needed (ignored if speciﬁed), and ”.itd” is supplied by default. The Object can be any object type, including list, in which the structure is saved recursively. See also LOAD. If a display device is actively running at the time SAVE is invoked, its transformation matrix will be saved with the same name but with extension type of ”.imd” instead of ”.itd”. This command can also be used to save binary ﬁles. ASCII regular data ﬁles usually take longer to load than binary ﬁles due to the required parsing. Binary data ﬁles can be loaded directly like ASCII ﬁles in IRIT, but must be inspected through IRIT tools such as dat2irit. A binary data ﬁle must have a ”.ibd” (IRIT Binary Data) type in its name. This command can also save geometry in one of the following formats: IGES ﬁle, If the ﬁle type is either ”igs” or ”iges”. STL ﬁle, if the ﬁle type is ”stl”. If Object has the int attribute ”RegularTriang” as TRUE, the geometry will be regularized ﬁrst (no T junctions). If Object has the int attribute ”MultiObjSplit”, the data will be saved in one large STL object in one ﬁle if 0, one STL object per IRIT object in one ﬁle if 1, or in one ﬁle per IRIT obejct if 2. OBJ ﬁle. if the ﬁle type is ”obj”. VRML ﬁle. if the ﬁle type is ”wrl”. CNC Gcode tool path ﬁle, if the ﬁle type is either ”nc” or ”gcode”. For this format, only univariate data sets (polylines and curves) will be processed and saved as 3-axis G code commands. The following attributes are supported in this mode, if found in Object: G. Elber IRIT Solid modeler ”NCCommentChar” ”NCDownPlungeFast” ”NCFeedRate” ”NCBridgeRelFeedRate” ”NCMaxXYBridgeGap” ”NCMaxZBridgeGap” ”NCRetractZLevel” ”NCReverseZ” ”NCUpRetractFast” 256 Holds a string of one character to deﬁne the comment character. If exists a header comment is dumped as well. distance, above the plunging destination to move down in fast g0 motion. Inﬁnity to disable and plunge in g1 all the way, or zero to plunge fast in g0 all way. Feedrate to use. Default is 10 mm per second. Relative feedrate to use (relative to NCFeedRate) when bridging from one polyline/curve to the next. The maximal gap in the XY plane to bridge between adjacent polylines/curves without retraction. By default, this value is one mm (0.04inch). The maximal gap in Z to bridge between adjacent polylines/curves without retraction. By default, this value is two mm (0.08inch). Set as the Z retraction level above the (bounding box) of the model. By default, the retration level will be one inch 925mm) above the bounding box of the model. If set to a non negative value, the Z coordinates are assumed reversed. That is the +Z is down. By default +Z is assumed up. If TRUE, up retracting will be in fast g0 motion. Otherwise, if FALSE, g1 will be used. On some platforms, ﬁles will be saved compressed if the given ﬁle name has a postﬁx of ”.Z” or ”.gz”. The gnu ”gzip” utility will be invoked via a pipe for that purpose. Example: SAVE( "oObj1.ibd.Z", Obj1 ); Saves Obj1 in the ﬁle Obj1.ibd.Z as compressed binary ﬁle. 11.4.39 SETNAME SETNAME( ListType ListObj, NumericType Index, StringType NewName ) sets the name of a sub object of index Index in list object ListObj to a new name NewName. The index of the ﬁrst element is zero. Example: A = list( 1, 2, 3 ); SETNAME( A, 0, "First" ); sets the name of the ﬁrst element in object A to ”First”. While it is not a good idea to modify names of objects in the top level global space, one can use this function to do exactly that. To rename the object ”Axes” to ”XYZ”, do: SETNAME( list( Axes ), 0, "XYZ" ); See also GETNAME. IRIT Solid modeler 11.4.40 G. Elber 257 SNOC SNOC( AnyType Object, ListType ListObject ) This is similar to the lisp cons operator but puts the new Object in the end of the list ListObject instead of at the beginning. Example: Lst = list( axes ); SNOC( Srf, Lst ); and now Lst is equal to the list ’list( axes, Srf )’. 11.4.41 SYSTEM SYSTEM( StringType Command ) executes a system command Command. For example, SYSTEM( "ls -l" ); 11.4.42 TIME TIME( NumericType Reset ) returns the time in seconds from the last time TIME was called with Reset TRUE. This time is CPU time if such support is available from the system (times function), and otherwise, is real time (time function). The time is automatically reset at the beginning of the execution of this program. Example: Dummy = TIME( TRUE ); . . . TIME( FALSE ); prints the time in seconds between the above two time function calls. 11.4.43 VARLIST VARLIST() lists all the currently deﬁned objects in the system. 11.4.44 VECTOR VectorType VECTOR( NumericType X, NumericType Y, NumericType Z ) sreates a vector type object, using the three provided NumericType scalars. See also PLANE, POINT. G. Elber IRIT Solid modeler 11.4.45 258 VIEW VIEW( GeometricTreeType Object, NumericType ClearWindow ) displays the (geometric) object(s) as given in Object. If ClearWindow is non zero (see TRUE/FALSE and ON/OFF), the window is ﬁrst cleared (before drawing the objects). Example: VIEW( Axes, FALSE ); displays the predeﬁned object Axes in the viewing window on top of what is drawn already. In version 4.0, this function is emulated (see iritinit.irt) using the VIEWOBJ function. In order to use the current viewing matrix, VIEW MAT should be provided as an additional parameter. For example, VIEW( list( view_mat, Obj ), TRUE ); However, since VIEW is a user deﬁned function, the following will not use VIEW MAT as one would expect: VIEW( view_mat, TRUE ); because VIEW MAT will be renamed inside the VIEW user deﬁned function to a local (to the user deﬁned function) variable. In iritinit.irt one can ﬁnd several other useful VIEW related functions: VIEWCLEAR VIEWREMOVE VIEWDISC VIEWEXIT VIEWSAVE BEEP VIEWSTATE Clears all data displayed on the display device. Removes the object speciﬁed by name from display. Disconnects from display device (which is still running) while allowing IRIT to connect to a new device. Forces the display device to exit. Requests the display device to save transformation matrix. An emulation of the BEEP command of versions prior to 4.0. Allows change to the state of the display device. For the above VIEW related functions, only VIEWREMOVE, VIEWSAVE, and VIEWSTATE require parameters, which are the ﬁle name and view state, respectively. The view state can be one of several commands. See the display device section for more. Examples: VIEWCLEAR(); VIEW( axes, off ); VIEWSTATE( "LngrVecs" ); VIEWSTATE( "DrawStyle" ); VIEWSAVE( "matrix1" ); VIEWREMOVE( "axes" ); VIEWDISC(); IRIT Solid modeler 11.4.46 G. Elber 259 VIEWOBJ VIEWOBJ( GeometricTreeType Object ) displays the (geometric) object(s) as given in Object. Object may be any GeometricType or a list of other GeometricTypes nested to an arbitrary level. Unlike IRIT versions prior to 4.0, VIEW MAT is not explicitly used as the transformation matrix. In order to display with a VIEW MAT view, VIEW MAT should be listed as an argument (in that exact name) to VIEWOBJ. The same is true for the perspective matrix PRSP MAT. Example: VIEWOBJ( list( view_mat, Axes ) ); displays the predeﬁned object Axes in the viewing window using the viewing matrix VIEW MAT. 11.4.47 VIEWSET VIEWSET( NumericType DispHandle ) sets the current display device to be DispHandle. DispHandle is returned by the CLNTEXEC command. The use of the reserved constant of CLIENTS ALL would broadcast the viewing commands to all objects. Example: h1 = clntexec( DispDeviceName ); h2 = clntexec( DispDeviceName ); clntwrite( h1, sphere( vector( 0, 0, 0 ), 1 ) ); clntwrite( h2, axes ); pause(); VIEWSET( h1 ); viewclear(); viewobj( list( sphere( vector( 0, 0, 0 ), 1 ), axes ) ); VIEWSET( h2 ); viewclear(); viewobj( list( sphere( vector( 0, 0, 0 ), 1 ), axes ) ); pause(); VIEWSET( CLIENTS_ALL ); viewobj( axes ); pause(); viewexit(); IRIT Solid modeler G. Elber 260 opens two display devices, and displays a unit sphere to the ﬁrst, and the axes object, to the second. After a pause, displays both objects on both display devices, then pauses and exits from both. See also VIEWOBJ, CLNTEXEC, CLNTCLOSE, CLNTREAD, CLNTWRITE. 11.4.48 WHILE WHILE( NumericType Cond, AnyType Body ) executes the Body (see below), while the WHILE loop condition Cond is evaluated into a non zero value. Cond is evaluated before each iteration. The body may consist of any number of regular commands, separated by COLONs, including nesting loops to an arbitrary level. Example: deg = 0; rotstepx = rotx( 10 ); WHILE ( deg < 360, deg = deg + 10: view_mat = rotstepx * view_mat: view( list( view_mat, axes ), ON ) ); displays axes with a view direction that is rotated 10 degrees at a time around the X axis. 11.5 System variables System variables are predeﬁned objects in the system. Any time IRIT is executed, these variable are automatically deﬁned and set to values which are sometimes machine dependent. These are regular objects in any other sense, including the ability to be deleted or overwritten. One can modify, delete, or introduce other objects using the iritinit.irt ﬁle. 11.5.1 AXES Predeﬁned polyline object (PolylineType) that describes the XY Z axes. 11.5.2 DRAWCTLPT Predeﬁned Boolean variable (NumericType) that controls whether curves’ control polygons and surfaces’ control meshes are drawn (TRUE) or not (FALSE). Default is FALSE. 11.5.3 FLAT4PLY Predeﬁned Boolean object (NumericType) that controls the way almost ﬂat surface patches are converted to polygons: four polygons (TRUE) or only two polygons (FALSE). Default value is FALSE. 11.5.4 MACHINE Predeﬁned numeric object (NumericType) holding the machine type as one of the following constants: MSDOS, SGI, HP, APOLLO, SUN, UNIX, IBMOS2, WINDOWS, AMIGA, CYGWIN, MACOSX, and LINUX. IRIT Solid modeler G. Elber 261 POLY APPROX OPT 11.5.5 A variable controlling the algorithm to tesselate surfaces into polygons. If FALSE, that is, uniform, in parametric space, sampling is used. If TRUE, maximal deviation between the polygonal approximation and the surface is used, with distance as prescribed by POLY APPROX TOL. 11.5.6 POLY APPROX UV A Boolean predeﬁned variable. If TRUE, UV values of surface polygonal approximation are placed on the attribute lists of vertices. POLY APPROX TOL 11.5.7 A numeric predeﬁned tesselation control on the distance between the surface and its polygonal approximation in POLY APPROX OPT settings. POLY APPROX TRI 11.5.8 A numeric predeﬁned tesselation control. If TRUE, only triangles are generated in surface tesselations. POLY MERGE COPLANAR 11.5.9 A numeric predeﬁned surface tesselation control. If TRUE, coplanar adjacent polygons are merged into one. 11.5.10 PRSP MAT Predeﬁned matrix object (MatrixType) to hold the perspective matrix used/set by VIEW and/or INTERACT commands. See also VIEW MAT. 11.5.11 RESOLUTION Predeﬁned numeric object (NumericType) that sets the accuracy of the polygonal primitive geometric objects and the approximation of curves and surfaces. It holds the number of divisions into which a circle is divided (with minimum value of 4). If, for example, RESOLUTION is set to 6, then a generated CONE will eﬀectively be a six-sided pyramid. It also controls the ﬁneness of freeform curves and surfaces when they are approximated as piecewise linear polylines, and the ﬁneness of freeform surfaces when they are approximated as polygons. 11.5.12 VIEW MAT Predeﬁned matrix object (MatrixType) to hold the viewing matrix used/set by VIEW and/or INTERACT commands. See also PRSP MAT. 11.6 System constants The following constants are used by the various functions of the system to signal certain conditions. Internally, they are represented numerically, although, in general, their exact value is unimportant and may be changed in future versions. In the rare circumstance that you need to know their values, simply type the constant as an expression. Example: IRIT Solid modeler G. Elber MAGENTA; 11.6.1 AMIGA A constant designating an AMIGA system, in the MACHINE variable. 11.6.2 APOLLO A constant designating an APOLLO system, in the MACHINE variable. 11.6.3 BEZIER TYPE A constant deﬁning a Bezier freeform geometry. 11.6.4 BLACK A constant deﬁning a BLACK color. 11.6.5 BLUE A constant deﬁning a BLUE color. 11.6.6 BSPLINE TYPE A constant deﬁning a B-spline freeform geometry. 11.6.7 CLIENTS ALL A constant deﬁning a request to address (broadcast to) all clients. 11.6.8 COL A constant deﬁning the COLumn or U direction of a surface or a trivariate mesh. 11.6.9 CTLPT TYPE A constant deﬁning an object of type control point. 11.6.10 CURVE TYPE A constant deﬁning an object of type curve. 11.6.11 CYAN A constant deﬁning a CYAN color. 11.6.12 CYGWIN A constant designating an IBM system running under Cygwin, in the MACHINE variable. 11.6.13 DEPTH A constant deﬁning the DEPTH direction of a trivariate mesh. See TBEZIER, TBSPLINE. 262 IRIT Solid modeler 11.6.14 G. Elber E1 A constant deﬁning an E1 (X only coordinate) control point type. 11.6.15 E2 A constant deﬁning an E2 (X and Y coordinates) control point type. 11.6.16 E3 A constant deﬁning an E3 (X, Y and Z coordinates) control point type. 11.6.17 E4 A constant deﬁning an E4 control point type. 11.6.18 E5 A constant deﬁning an E5 control point type. 11.6.19 E6 A constant deﬁning an E6 control point type. 11.6.20 E7 A constant deﬁning an E7 control point type. 11.6.21 E8 A constant deﬁning an E8 control point type. 11.6.22 E9 A constant deﬁning an E9 control point type. 11.6.23 FALSE A zero constant. May be used as a Boolean operand. 11.6.24 GEOM CONST Designates a constant shape. 11.6.25 GEOM LINEAR Designates a shape of a (piecewise) linear curve. 11.6.26 GEOM CIRCULAR Designates a shape of a circle/arc. 263 IRIT Solid modeler 11.6.27 G. Elber 264 GEOM PLANAR Designates a planar shape. 11.6.28 GEOM SPHERICAL Designates a spherical shape. 11.6.29 GEOM SRF OF REV Designates a shape that is (a portion of) a surface of revolution.. 11.6.30 GEOM EXTRUSION Designates a shape that is an extrusion surface. 11.6.31 GEOM RULED SRF Designates a shape that is a ruled surface. 11.6.32 GEOM DEVELOP SRF Designates a shape that is a ruled surface. 11.6.33 GEOM SWEEP Designates a shape that is a sweep surface. 11.6.34 GREEN A constant deﬁning a GREEN color. 11.6.35 GREGORY TYPE A constant deﬁning a Gregory freeform geometry. 11.6.36 HP A constant designating an HP system, in the MACHINE variable. 11.6.37 IBMOS2 A constant designating an IBM system running under OS2, in the MACHINE variable. 11.6.38 KV DISC OPEN A constant deﬁning an open end condition with a discontinuous uniformly spaced knot vector. That is, all interior knots are of multiplicity order -1 and are equally spaced. 11.6.39 KV FLOAT A constant deﬁning a ﬂoating end condition uniformly spaced knot vector. IRIT Solid modeler 11.6.40 G. Elber KV OPEN A constant deﬁning an open end condition uniformly spaced knot vector. 11.6.41 KV PERIODIC A constant deﬁning a periodic end condition with a uniformly spaced knot vector. 11.6.42 LINUX A constant designating an IBM system running under Linux, in the MACHINE variable. 11.6.43 LIST TYPE A constant deﬁning an object of type list. 11.6.44 MACOSX A constant designating an IBM system running under Mac OSX, in the MACHINE variable. 11.6.45 MAGENTA A constant deﬁning a MAGENTA color. 11.6.46 MATRIX TYPE A constant deﬁning an object of type matrix. 11.6.47 MSDOS A constant designating an MSDOS system, in the MACHINE variable. 11.6.48 MODEL TYPE A constant deﬁning an object of type model. 11.6.49 MULTIVAR TYPE A constant deﬁning an object of type multivariate function. 11.6.50 NUMERIC TYPE A constant deﬁning an object of type numeric. 11.6.51 OFF Synonym for FALSE. 11.6.52 ON Synonym for TRUE. 265 IRIT Solid modeler 11.6.53 G. Elber 266 P1 A constant deﬁning a P1 (W and WX coordinates, in that order) rational control point type. 11.6.54 P2 A constant deﬁning a P2 (W, WX, and WY coordinates, in that order) rational control point type. 11.6.55 P3 A constant deﬁning a P3 (W, WX, WY, and WZ coordinates, in that order) rational control point type. 11.6.56 P4 A constant deﬁning a P4 rational control point type. 11.6.57 P5 A constant deﬁning a P5 rational control point type. 11.6.58 P6 A constant deﬁning a P6 rational control point type. 11.6.59 P7 A constant deﬁning a P7 rational control point type. 11.6.60 P8 A constant deﬁning a P8 rational control point type. 11.6.61 P9 A constant deﬁning a P9 rational control point type. 11.6.62 PARAM CENTRIP A constant deﬁning a centripetal length parametrization. 11.6.63 PARAM CHORD A constant deﬁning a chord length parametrization. 11.6.64 PARAM NIELFOL A constant deﬁning a Neilson-Foley parametrization. 11.6.65 PARAM UNIFORM A constant deﬁning an uniform parametrization. IRIT Solid modeler 11.6.66 G. Elber PI The constant of 3.141592... 11.6.67 PLANE TYPE A constant deﬁning an object of type plane. 11.6.68 POINT TYPE A constant deﬁning an object of type point. 11.6.69 POLY TYPE A constant deﬁning an object of type poly. 11.6.70 POWER TYPE A constant deﬁning a power basis freeform geometry. 11.6.71 RED A constant deﬁning a RED color. 11.6.72 ROW A constant deﬁning the ROW or V direction of a surface or a trivariate mesh. 11.6.73 SGI A constant designating an SGI system, in the MACHINE variable. 11.6.74 STRING TYPE A constant deﬁning an object of type string. 11.6.75 SURFACE TYPE A constant deﬁning an object of type surface. 11.6.76 SUN A constant designating a SUN system, in the MACHINE variable. 11.6.77 TRIMSRF TYPE A constant deﬁning an object of type trimmed surface. 11.6.78 TRISRF TYPE A constant deﬁning an object of type triangular surface. 267 IRIT Solid modeler 11.6.79 G. Elber 268 TRIVAR TYPE A constant deﬁning an object of type trivariate function. 11.6.80 TRUE A non zero constant. May be used as a Boolean operand. 11.6.81 UNDEF TYPE A constant deﬁning an object of no type (yet). 11.6.82 UNIX A constant designating a generic UNIX system, in the MACHINE variable. 11.6.83 UNTRIMMED TYPE A constant deﬁning an untrimmed freeform geometry. 11.6.84 VECTOR TYPE A constant deﬁning an object of type vector. 11.6.85 WINDOWS A constant designating an IBM system running under Windows, in the MACHINE variable. 11.6.86 WHITE A constant deﬁning a WHITE color. 11.6.87 YELLOW A constant deﬁning a YELLOW color. 12 Animation The animation tool adds the capability of animating objects using forward kinematics, exploiting animation curves. Each object has diﬀerent attributes, that prescribe its motion, scale, and visibility as a function of time. Every attribute has a name, which designates its role. For instance, an attribute animation curve named MOV X describes a translation motion along the X axis. 12.1 How to create animation curves in IRIT Let OBJ be an object in IRIT which we want to animate. Animation curves are either scalar (E1/P1) curves or three-dimensional (E3/P3) curves with one of the following name preﬁxes: IRIT Solid modeler MOV X, MOV Y, MOV Z MOV XYZ ROT X, ROT Y, ROT Z SCL X, SCL Y, SCL Z SCL VISIBLE G. Elber 269 Translation along one axis Arbitrary translation along all three axes Rotating around a single axis (degrees) Scale along a single axis Global scale Visibility The visibility curve is a scalar curve that enables the display of the object if the visibility curve is positive at time t and disables the display (hides) the object if the visibility curve is negative at time t. A positive visibility value between zero and one also hints at the opacity of the object, if supported; one means fully opaque. The animation curves are all attached as an attribute named ”animation” to the object OBJ. Example: mov_x = cbezier( list( ctlpt( E1, 0.0 ), ctlpt( E1, 1.0 ) ) ); scl = cbezier( list( ctlpt( E1, 1.0 ), ctlpt( E1, 0.1 ) ) ); rot_y = cbezier( list( ctlpt( E1, 0.0 ), ctlpt( E1, 0.0 ) ); ctlpt( E1, 360.0 ) ) ); attrib(OBJ, "animation", list( mov_x, scl, rot_y ) ); The above will animate OBJ between time zero and one (Bezier curves are always between zero and one), by moving it a unit size in the X direction, scaling it to angular speed from zero to 360 degrees. OBJ can now be saved into a ﬁle or displayed via one of the regular viewing commands in IRIT (i.e. VIEWOBJ). Animation is not always between zero and one. To that end, one can apply the CREPARAM function to modify the parametric domain of the animation curve. The convention is that if the time is below the starting value of the parametric domain, the starting value of the curve is used. Similarly, if the time is beyond the end of the parameter domain of the animation curve, the end value of the animation curve is used. Example: CREPARAM( mov_x, 3.0, 5.0 ); to set the time of the motion in the x axis to be from t = 3 to t = 5. For t < 3, use mov x(3), and for t > 5, use mov x(5). The animation curves are regular objects in the IRIT system. Hence, only one object named mov x or scl can exist at one time. If you create a new object named mov x, the old one is overwritten! To preserve old animation curves you can detach the old ones by executing ’free(mov x)’ which will remove the object named mov x from IRIT’s object list but not from its previously used locations within other list objects, if any. A diﬀerent way to do this is to call the animation curves mov x1, mov x2 etc. as only the preﬁx of the name is veriﬁed. For example: mov_x = cbezier( list( ctlpt( E1, 0.0 ), ctlpt( E1, 1.0 ) ) ); attrib(obj1, "animation", list( mov_x ) ); G. Elber IRIT Solid modeler 270 free(mov_x); mov_x1 = cbezier( list( ctlpt( E1, 2.0 ), ctlpt( E1, 3.0 ) ) ); mov_x2 = cbezier( list( ctlpt( E1, 2.0 ), ctlpt( E1, 3.0 ) ) ); attrib(obj2, "animation", list( mov_x1, mov_x2 ) ); free(mov_x); Notice the way we have two animation curves translating obj2 in x. This is somewhat artiﬁcial but makes more sense if other transformations appear in between. One can evaluate an object with animation curves at a certain time, only to ﬁnd the proper expected transformation matrix at that time on the object as an ”animation mat” attribute. The following example deﬁnes a user deﬁned TransformAnim function that creates a transformed object out of object that was evaluated with ANIMEVAL. Then, a simple loop (slowly) animates the scene... TransformAnim = function( Obj ): return = 0; TransformAnim = function( Obj ): m: i: if ( thisobj( "Obj" ) == list_type, return = nil(): for ( i = 1, 1, sizeof( Obj ), snoc( TransformAnim( nth( Obj, i ) ), return ) ), return = Obj * tx( 0 ) ): m = getattr( Obj, "animation_mat" ): if ( thisobj( "m" ) == matrix_type, return = return * m ); for ( t = 0, 0.1, 1, ANIMEVAL( t, Object ): view( TransformAnim( Object ), 1 ) ); Animation of movies are supported to a certain extent. A movie animation is prescribed using a ”pmovie” (parametric texture movie) attribute. The format of the ”pmovie” attribute is as follows "MovieName {, S X Y {Z}} {, F} {, R} {, T=tmin,tmax}" where ”S X, Y, Z,” prescribes image scaling much like regular ”ptexture” attributes (how many times the image will span the object?) with the default being for the movie to span the entire object and ’F’ requests the ﬂipping of the X and Y axes of the movie, again much like in the ”ptexture’ attribute. Further, ”T=tmin,tmax” sets the time range to execute the animation at, beginning to end and ’R’, if set, request that the movie will be repeated modulus this (tmin,tmax) domain. 12.2 a b c d = = = = A more complete animation example box( vector( 0, box( vector( 0, box( vector( 0, sphere( vector( 0, 0, 0, 0, 0 ), 1, 1, 0 ), 1, 1, 0 ), 1, 1, 0, 0), 0.7 1 ); 1 ); 1 ); ); G. Elber IRIT Solid modeler pt0 pt1 pt2 pt6 pt360 pt10 pt11 pt12 pt13 = = = = = = = = = ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( ctlpt( visible mov_x mov_y mov_z rot_x = = = = = rot_y rot_z scl = = = scl_x scl_y scl_z mov_xyz = = = = e1, e1, e1, e1, e1, 0.0 ); 1.0 ); 2.0 ); 6.0 ); 360.0 ); e1, -4.0 ); e1, 1.0 ); e1, 4.0 ); e1, -1.0 ); creparam( cbezier( list( pt10, pt11 ) ), 0.0, 5.0 ); creparam( cbezier( list( pt0, pt6, pt2 ) ), 0.0, 1.2 ); mov_x; mov_x; creparam( cbspline( 2, list( pt0, pt360, pt0 ), list( KV_OPEN ) ), 1.2, 2.5 ); rot_x; rot_x; creparam( cbezier( list( pt1, pt2, pt1, pt2, pt1 ) ), 2.5, 4.0 ); scl; scl; scl; creparam( circle( vector( 0, 0, 0 ), 2.0 ), 4.0, 5.0 ); attrib( d, "animation", list( mov_xyz, visible ) ); free( visible ); visible = creparam( cbezier( list( pt12, pt13 ) ), 0.0, 5.0 ); attrib( a, "animation", list( rot_x, mov_x, scl, scl_x, visible ) ); attrib( b, "animation", list( rot_y, mov_y, scl, scl_y, visible ) ); attrib( c, "animation", list( rot_z, mov_z, scl, scl_z, visible ) ); color( color( color( color( a, b, c, d, red ); green ); blue ); cyan ); demo = list( a, b, c, d ); interact( demo ); viewanim( 0, 5, 0.01 ); 271 IRIT Solid modeler G. Elber 272 In this example, we create four objects, three cubes and one sphere. Animation curves to translate the three cubes along the three axes for time period of t = 0 to t = 1.2 are created. Rotation curves to rotate the three cubes along the three axes are then created for time period t = 1.2 to t = 2.5. Finally, for time period t = 2.5 to t = 4.0. the cubes are (not only) unifomly scaled. For time period t = 4 to t = 5, the cubes become invisible and the sphere, which becomes visible, is rotated along a circle of radius 2. 12.3 Another complete animation example This example demonstrates the ability to put ”animation” attributes on internal nodes of a hierarchy, thereb, aﬀecting the entire set of objects in the hierachy. Herein, we present an robotic arm with three edges and two joints. BoxLength = 2; BoxWidth = 2; BoxHeight = 10; LowerBox = box( vector( -BoxLength / 2, -BoxWidth / 2, 0 ), BoxLength, BoxWidth, BoxHeight); MiddleBox = box( vector( -BoxLength / 2, -BoxWidth / 2, 0 ), BoxLength, BoxWidth, BoxHeight); UpperBox = box( vector( -BoxLength / 2, -BoxWidth / 2, 0 ), BoxLength, BoxWidth, BoxHeight); Cn1 = cone( vector( 0, 0, 0 ), vector( 0, BoxHeight / 3, 0 ), 1 ); color( color( color( color( LowerBox, magenta ); MiddleBox, yellow ); UpperBox, cyan ); Cn1, green ); rot_x1 = creparam( cbspline( 3, list( ctlpt( E1, 0 ), ctlpt( E1, -200 ), ctlpt( E1, 200 ), ctlpt( E1, 0 ) ), list( KV_OPEN ) ), 0, 3 ); rot_x2 = creparam( cbspline( 4, list( ctlpt( E1, 0 ), ctlpt( E1, 400 ), ctlpt( E1, -400 ), ctlpt( E1, 0 ) ), list( KV_OPEN ) ), 0, 3 ); rot_y = creparam( cbspline( 2, list( ctlpt( E1, 0 ), ctlpt( E1, 100 ), ctlpt( E1, -100 ), G. Elber IRIT Solid modeler 273 ctlpt( E1, 0 ) ), list( KV_OPEN ) ), 0, 3 ); rot_z = creparam( cbspline( 2, list( ctlpt( E1, 0 ), ctlpt( E1, 1440 ) ), list( KV_OPEN ) ), 0, 3 ); Translate = trans( vector( 0, 0, BoxHeight ) ); attrib( Cn1, "animation", list( rot_z, Translate ) ); Upr = list( Cn1, UpperBox ); attrib( Upr, "animation", list( rot_y, Translate ) ); Mid = list( Upr, MiddleBox ); attrib( Mid, "animation", list( rot_x2, Translate ) ); rbt_hand = list( Mid, LowerBox ); attrib( rbt_hand, "animation", list( rot_x1 ) ); view( rbt_hand, 1 ); In this example, we create four objects, three cubes and one cone, simulating a robotic hand with three edges an a gripper (the cone). The animation is deﬁned hierarchically, making it very easy to model the robot. 13 Display devices The following display device drivers are available, Device Name Invocation Environment xgldrvs xogldrvs xgladap xgldrvs -sxogldrvs -sxgladap -s- x11drvs xmtdrvs xglmdrvs wntdrvs wntgdrvs wntgaiso os2drvs amidrvs nuldrvs x11drvs -sxmtdrvs -sxglmdrvs -swntdrvs -swntgdrvs -swntgaiso -sos2drvs -samidrvs -snuldrvs -s- [-d] [-D] SGI 4D GL regular driver. SGI 4D Open GL/Motif driver. SGI 4D GL adaptive isocurve experimental driver. X11 driver. X11 Motif driver. SGI 4D GL and X11/Motif driver. IBM PC Windows NT driver. IBM PC Windows NT Open GL driver. IBM PC OGL Adap. Iso. driver. IBM PC OS2 2.x/3.x driver. AmigaDOS 2.04+ driver. A device to print the object stream to stdout. IRIT Solid modeler G. Elber 274 All display devices are clients communicating with the (IRIT) server using IPC (inter process communication). On Unix and Windows NT, sockets are used. A Windows NT client can talk to a server (IRIT) on a Unix host if hooked to the same network. On OS2 pipes are used, and both the client and server must run on the same machine. On AmigaDOS exec messages are used, and both the client and server must run on the same machine. While all display devices support object(s) transformations via a transformation control window, many of the display devices allow one to click and drag on the viewing window to rotate (Left Button) and to translate (Right Button). This mode exploits the mouse’s two degrees of freedom to provide intuitive dual axis rotation and translation. Most display devices supports two levels of ﬁneness. A rough display is used when in the middle of a transformation operation (i.e. the mouse button is down/dragged), while a ﬁne object display is employed when the display is idle (mouse button is up). See also option ’-E’. The (IRIT) server will automatically start a client display device if the IRIT DISPLAY environment variable is set to the name and options of the display device to run. For example: setenv IRIT_DISPLAY xgldrvs -sThe display device must be in a directory that is in the environment variable path. Most display devices require the ’-s-’ ﬂags to run in a non-standalone mode, or a client-server mode. Most drivers can also be used to display data in a standalone mode (i.e., no server). For example: xgldrvs -s solid1.itd irit.imd Eﬀectively, all the display devices are also data display programs. Therefore, some functionality is not always as expected. For example, the Quit button will always force the display device to quit, even if popped up from IRIT, but will not cause IRIT to quit as might logically expected. In fact, the next time IRIT will try to communicate with the display device, it will ﬁnd the broken connection and will start up a new display device. Most display devices recognize attributes found on objects. The following attributes are usually recognized (depending on the device capability): • Color: Selects the drawn color of the object to be one of the 8/16 predeﬁned colors in the IRIT system: white, red, green, blue, yellow, cyan, magenta, black. • DWidth: Sets the width in pixels of the drawn object, when drawn as a wireframe. • Light source: Mark a points object as a light source. Such a marked object is not rendered but rather used to set a light source position. A light source object also honors ”index” attribute that sets the light source number (between 0 and 9), and ”type” which can be either ”point infty” for a light source direction (light source at inﬁnity) or ”point pos” for a point light source. See also ”advanced usage” in the irender program. • ReﬂectLns: Allows the display of reﬂection lines oﬀ a freeform surface. The ”ReﬂectLns” attribute is a list object of two subobjects, a vector and a list of points. The vector is the reﬂection lines’ direction (all reﬂection lines are parallel) and the list of points is a list of points on the diﬀerent reﬂection lines. For example, attrib( S, "RflctLines", list( vector( 0, 0, 1 ), list( point( -1.6, 2, 0 ), G. Elber IRIT Solid modeler 275 point( -0.8, 2, 0 ), point( 0.0, 2, 0 ), point( 0.8, 2, 0 ), point( 1.6, 2, 0 ) ) ) ); deﬁnes ﬁve reﬂection lines to be reﬂected oﬀ surface S, all in the direction of (0, 0, 1) and on the plane Y = 2. See also RFLCTLN command. • RGB: Overwrites (if supported) the COLOR attribute (if given) and sets the color of the object to the exact prescribed RGB set. • StrScale, StrPos, StrSpace: Allows control over string drawing, controlling the scale of the string, its position, and the spacing between characters in the string. All display devices recognize all the command line ﬂags and all the conﬁguration options in a conﬁguration ﬁle, as described below. The display devices will attempt to honor the requests, to the best of their ability. For example, only gl and OpenGL devices can render shaded models, and so only they will honor all DrawStyle conﬁguration options. 13.1 Command Line Options ???drvs [-s] [-u] [-n] [-N] [-i] [-c] [-C] [-m] [-a] [-g "x1,x2,y1,y2"] [-G "x1,x2,y1,y2"] [-I #IsoLines] [-F PlgnOpti PlgnFineNess] [-R] [-f PllnOpti PllnFineNess] [-E RelLowRes] [-p] [-l LineWidth] [-r] [-A Shader] [-B] [-2] [-d] [-D] [-L NormalLen] [-4] [-k SketchType Sil Shd Imp] [-K] [-b "R,B,G (background)"] [-S "x,y,z,w{,a,d,s} (LgtSrcPosADS)"] [-1] [-e PickDist] [-O PickObjType] [-Z ZMin ZMax] [-M] [-W WireSetup] [-P] [-o] [-x ExecAnimCmd] [-X Min,Max,Dt,R{,flags}] [-w InitWidget] [-T] [-z] DFiles • -s: Runs the driver in a standalone mode. Otherwise, the driver will attempt to communicate with the IRIT server. • -u: Forces a unit matrix. That is, input data are not transformed at all. • -n: Draws normals of vertices. • -N: Draws normals of polygons. • -i: Draws internal edges (created by IRIT) - default is not to display them; this option will also force their display. • -c: Sets depth cueing on. Drawings that are closer to the viewer will be drawn in more intense color. • -C: Caches the piecewise linear geometry so curves and surface can be redisplayed faster. Purging it will free memory, on the other hand. • -m: Provides some more information on the parsed data ﬁle(s). • -a: Activate antialiased lines and shaded display. IRIT Solid modeler G. Elber 276 • -g x1,x2,y1,y2: Prescribes the position and location of the transformation window by prescribing the domain of the window in screen space pixels. • -G x1,x2,y1,y2: Prescribes the position and location of the viewing window by prescribing the domain of the window in screen space pixels. • -I #IsoLines: Speciﬁes the number of isolines per surface, per direction. A speciﬁcation of zero isolines is possible only on the command line and it denotes the obvious. • -F PolyOpti FineNess: Controls the method used to approximate surfaces into polygons. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -R: Use optimized polygonal strips instead of lists of polygons, if possible. This feasibility depends on the support of the underlying hardware/graphics libraries. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed dveiation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -E RelLowRes: Sets the relative ﬁneness of curves and surface while the input device is active, such as in a drag operation. • -p: Sets the width of drawn points. • -l LineWidth: Sets the linewidth, in pixels. Default is one pixel wide. • -r: Activate solid Rendering mode. Draws object as shaded solid. • -A Shader: Shader can be one of 0 (None), 1 (Background), 2 (Flat), 3 (Gouraud), or 4 (Phong). • -B: Back face culling of polygons. • -2: Double buﬀering. Prevents screen ﬂicker at the possible cost of fewer colors. • -d: Debug objects. Prints to stderr all objects read from the communication port with the server IRIT. • -D: Debug input. Prints to stderr all characters read from communcation port with the server IRIT. Lowest level of communication. • -L NormalLen: Sets the length of the drawn normals in thousandths of a unit. • -4: Forces four polygons per almost ﬂat region in the surface to polygon conversion. Otherwise two polygons only. • -k SketchType Sil Shd Imp: Sets the strokes type (one of 1 (isoparametric curves), 2 (lines of curvature), 3 (silhoutees)), and the silhouette and shader powers (between zero and one) and strokes improtance factor, in interactive line art strokes (See -W). • -K: Captures the image underneath the display device and use that as a bacKground image. • -b BackGround: Sets the background color as three RGB integers in the range of 0 to 255. IRIT Solid modeler G. Elber 277 • -S x,y,z,w{,a,d,s} (LgtSrcPosADS): Sets the lighting by setting the light source position as well as the optional Ambient, Diﬀuse, and Specular intensities. • -1: One or two sides for light sources. • -e PickDist: Sets the distance to the near and far Z clipping planes. • -O PickObjType: A binary mask that controls which object can be picked: bit 0 - not used, bit 1 - poly, bit 2 - numeric, bit 3 - point, bit 4 - vector, bit 5 - Plane, bit 6 - matrix, bit 7 curve, bit 8 - surface, bit 9 - string, bit 10 - list object, bit 11 - ctl pt, bit 12 - trimmed srf, bit 13 - trivariate, bit 14 - instance, bit 15 - triangular srf, bit 16 - model, bit 17 - multivariate. • -Z ZMin ZMax: Sets the near and far Z clipping planes. • -M: Draw control mesh/polygon of curves and surfaces, as well. • -W WireSetup: Controls the line drawing of the freeforms where WireSetup is a mask that controls: bit 0: Draw curves and surfaces using a set of isocurves (see -I and -f), bit 1: Draw boundary curves of surfaces, bit 2: Draw silhouette curves of surfaces, bit 3: Draw surfaces in sketch style line art (see -k). bit 4: Draw surfaces’ reﬂection lines (surface also must have a ”ReﬂectLns” attribute - see attributes above). • -P: Draws curves and surfaces using a set of polygons (see -F). • -o: Reverses the Orientation by ﬂipping all normals (see -n, -N). • -x ExecAnimCmd: Command to execute as a subprocess every iteration of display of an animation sequence. This command can, for example, save the display into an image ﬁle, saving the animation sequence. One parameter, which is an running index starting from one, is passed. • -X Min,Max,Dt,R{,ﬂags}: Executes an animation sequence between Min time to Max time in steps of Dt. R repetitions of the animations are executed. Flags could be any combination of: ’s’: Flag to specify the saving of the animation as individual data ﬁles, one per frame, for high quality rendering. ’t’: Two way animation - bounce back and forth. ’b’: Reset the animation back to its starting position. ’x’: Flag to force the display device to exit upon completion of the animation. • -w InitWidget: Sets the widgets that are displayed initially (as an or’ed mask): 1 - Environment widget, 2 - Animation widget, 4 - Curves widget, 8 - surfaces widget, 16 - Shading widget, 32 Pick objects widget, 64 - Object transforms widget. • -T: Enable continuous moTion. Objects continue to move indeﬁnitely following the last transformation applied. • -z: Prints version number and current defaults. 13.2 Conﬁguration Options The conﬁguration ﬁle is read before the command line options are processed. Therefore, all options in this section can be overridden by the appropriate command line option, if any. • TransPrefPos: Preferred location (Xmin, YMin, Xmax, Ymax) of the transformation window. IRIT Solid modeler G. Elber 278 • ViewPrefPos: Preferred location (Xmin, YMin, Xmax, Ymax) of the viewing window. • BackGround: Background color. Same as ’-b’. • Internal: Draws internal edges. Same as ’-i’. • LightSrcPos: Sets the location of the (ﬁrst) light source as a rational four coeﬃcient location. W of zero sets the light source at inﬁnity. • ExecAnimCmd: Executes a command at each step of the animation. Same as ’-x’. • ExecAnimation: Executes an animation sequence on startup. Same as ’-X’. • DrawVNormal: Draws normals of vertices. Same as ’-n’. • DrawPNormal: Draws normals of polygons. Same as ’-n’. • MoreVerbose: Provides some more information on the parsed data ﬁle(s). Same as ’-m’. • UnitMatrix: Forces a unit matrix. That is, input data are not transformed at all. Same as ’-u’. • DrawStyle: Requests a shaded surface rendering, or isocurve/polyline surface rendering, or point rendering. • BFaceCull: Requests the removal of back facing polygons, for better visibility. • DoubleBuﬀer: Requests drawing using a double buﬀer, if any. • DebugObjects: Debugs objects. Prints to stderr all objects read from the communication port with the server IRIT. Same as ’-d’. • DebugEchoInput: Debugs input. Prints to stderr all characters read from the communication port with the server IRIT. Lowest level of communication. • DepthCue: Sets depth cueing on. Drawings that are closer to the viewer will be drawn in more intense color. Same as ’-c’. • CacheGeom: Normally piecewise linear approximation of freefroms is cached. By setting this option to FALSE, no such auxiliary data is saved, reducing the memory overhead. Same as ’-C’. • FourPerFlat: Forces four polygons per almost ﬂat region in the surface to polygon conversion. Otherwise two polygons only. Same as ’-4’. • AntiAlias: Requests the drawing of antialiased lines. • DrawSurfaceMesh: Draws control mesh/polygon of curves and surfaces, as well. Same as ’-M’. • DrawSurfacePoly: Draws curves and surfaces (surfaces are drawn using a set of isocurves, see -I, or polygons, see -f). Same as ’-P’. • StandAlone: Runs the driver in a standalone mode. Otherwise, the driver will attempt to communicate with the IRIT server. Same as ’-s’. • PolyStrips: Renders using polygonal strips, if possible. Same as ’-R’. IRIT Solid modeler G. Elber 279 • ContMotion: Renders using continuous motions. Objects continue to move indeﬁnitely, following the last transformation applied. Same as ’-T’. • NumOfIsolines: Speciﬁes number of isolines per surface, per direction. Same as ’-I’. • PllnFineNess: Speciﬁes the samples per (iso)curve or tolerance of approximation. See ’-f’. • LineWidth: Sets the linewidth, in pixels. Default is one pixel wide. Same as ’-l’ • AdapIsoDir: Selects the direction of the adaptive isoline rendering. • PolygonOpti: Controls the method used to subdivide a surface into polygons that approximate it. See ’-F’. • PolylineOpti: Controls the method used to subdivide a curve into polylines that approximate it. See ’-f’. • ShadingModel: One of 1 (Flat), 2 (Gouraud), or 3 (Phong). Same as ’-A’. • TransMode: Selects between object space transformations and screen space transformation. • ViewMode: Selects between perspective and orthographic views. • NormalLength: Sets the length of the drawn normals in thousandths of a unit. Same as ’-L’. • ZClipMin: Sets the minimal clipping plane in Z. Same as ’-Z’. • ZClipMax: Sets the maximal clipping plane in Z. Same as ’-Z’. • PlgnFineNess: Controls the ﬁneness of the surface to polygon subdivision. See ’-F’. 13.3 Interactive mode setup Commands that aﬀect the status of the display device can also be sent via the communication port with the IRIT server. The following commands are recognized as string objects with object name of ”COMMAND ”: IRIT Solid modeler ANIMATE TMin TMax Dt BEEP CLEAR CLONEOBJ OBJNAME DCLEAR DISCONNECT EDITCRV CRVNAME EDITOBJ OBJNAME EDITSRF SRFNAME EXIT GETOBJ NAME HIGHLIGHT1 NAME HIGHLIGHT2 NAME IMGSAVE NAME MSAVE NAME PICKCRSR PICKDONE PICKNAME PICKOBJ REMOVE NAME STATE COMMAND UNHIGHLIGHT G. Elber Animates current scene from TMin to TMax in Dt steps. Makes some sound. Clears the display area. All objects are deleted. Clone the object OBJNAME. Delays clear. Same as CLEAR but delayed until next object is sent from the server. Useful for animation. Closes connection with the server, but does not quit. Requests immediate editing mode of crv CRVNAME. Requests immediate editing mode of obj OBJNAME. Requests immediate editing mode of srf SRFNAME. Closes connection with the server and quits. Requests the object named NAME that is returned in the output channel to the server. Color the object named NAME with highlight1 color. Color the object named NAME with highlight2 color. Save the current display in an image ﬁle named NAME. Save the current matrix in a ﬁle named NAME. Requests to interactively sample mouse/cursor events for mouse-up, mouse-down, and mouse-move-while-down. Stop interactive pick reports to server. Stops all PICKCRSR, PICKNAME and PICKOBJ modes. Requests to interactively pick an object by name that is returned in the output channel to the server. Requests to interactively pick an object that is returned in the output channel to the server. Requests the removal of object named NAME from display. Changes the state of the display device. See below. Unhighlight all highlighted objects. The following commands are valid for the STATE COMMAND above, 280 IRIT Solid modeler MouseSense: ScrnObjct: PerspOrtho: DepthCue: CacheGeom: DrawStyle: ShadingMdl: BFaceCull: DblBuﬀer: AntiAlias: DrawIntrnl: DrawVNrml: DrawPNrml: DrawPlgns: DSrfMesh: DSrfWire: DSrfBndry: DSrfSilh: DSrfPoly: DSrfSktch: 4PerFlat: NumIsos: PolyAprx: PllnAprx: LenVecs: WidthLines: WidthPts: Front: Side: Top: Isometry: 4Views: Clear: ResAdapIso: ResRldSrf: RuledSrfApx: AdapIsoDir: LowResRatio: ClipAtPoles: G. Elber 281 Mouse sensitivity control. Controls screen/object transformation mode. Controls perspective/orthographic trans. mode. Controls depth cueing drawing. Cache the created piecewise linear geometry. Controls isocurve/shaded solid/points rendering. Controls shading model for solid solid drawing. Cull backfacing polygons. Controls single/double buﬀer mode. Controls antialiased lines. Controls drawing of internal lines. Controls drawing of normals of vertices. Controls drawing of normals of polygons. Controls drawing of polygonal objects as polygons. Controls drawing of control meshes/polygons. Controls drawing of curves/surfaces as wireframes. Controls drawing of boundary curves of surfaces. Controls drawing of silhouette curves of surfaces. Controls drawing of curves/surfaces as polygons. Controls drawing of surfaces as sketches. Controls 2/4 polygons per ﬂat surface regions. Controls the number of isocurves in a surface. Controls the surface tesselation ﬁneness. Controls the curves to polylines ﬁneness. Controls the length of displayed normal vectors. Controls the width of the drawn lines. Controls the width of the cross of drawn points. Selects a front view. Selects a side view. Selects a top view. Selects an isometric view. Selects a four views mode. Clears the viewing area. Controls the resolution of a number of adaptive isocurves. Controls the resolution of ruled srfs in adaptive isocurves. Controls the ruled surface approx. in adaptive isocurves. Controls the row/col direction of adaptive isocurves. Controls the low/high resolution ratios. Controls the optional clipping of polygons/lines at poles. Obviously not all state options are valid for all drivers. The IRIT server deﬁnes in iritinit.irt several user-deﬁned functions that exercise some of the above state commands, such as VIEWSTATE and VIEWSAVE. VIEWSTATE accepts a second parameter which can be -1 to toggle the value, 0 to reset the value or 1 to set it. If the state value is real, 1 doubles its value and 0 halfs it. In addition to state modiﬁcation via communication with the IRIT server, modes can be interactively modiﬁed on most of the display devices using a pop-up menu that is activated using the right button in the transformation window. This pop-up menu is somewhat diﬀerent in diﬀerent drivers, but its entries closely follow the entries of the above state command table. IRIT Solid modeler G. Elber 282 All driver support three special matrices. The VIEW MAT can set the current viewing direction and PRSP MAT can set the current perspective view. Finally, CONT MAT can set the current continuous motion (see also ’-T’ option). Animation of movies are supported to a certain extent. A movie animation is prescribed using a ”pmovie” (parametric texture movie) attribute. The format of the ”pmovie” attribute is as follows 13.4 Basic Attributes The display devices support basic graphics capabilities like color via the ”color” attribute that selects between 15 basic diﬀerent colors and the”rgb” attribute that allows full ”red, green. blue” speciﬁcation. If both ”rgb” and ”color” are found in the same object, the ”rgb” attribute will govern. Some display devices also support transparency via the ”transp” attributes that expects a translucency value between zero and one. Some display devices also support parameteric texture via the ”ptexture attribute” that can look like (see also irender for a more elaborated ”ptexture” options that are not supported by the ????drvs devices. "ImageName {, S X Y {Z}} {, F} {, N}" where ”S X, Y, Z,” prescribes image scaling (how many times the image will span the object?) with the default being for the movie to span the entire object, ’F’ requests the ﬂipping of the X and Y axes of the image, and ’N’ optionally forces a reload the image as a New image, even if an image by this exact same name was already loaded and is cached. 13.5 Animation Mode All the display drivers are now able to animate objects with animation curve attributes on them. For more on the way animation curves can be created, see the Animation Section of this manual. (Section 12). Once a scene with animation curve attributes is being loaded into a display device, one can enter ”animation” mode using the ”Animation” button available in all display devices. The user is then prompted (either graphically or in a textual based interface) for the starting time, termination time and step size of the animation. The parameter space of the animation curve serves as the time domain. The default starting and terminating times are set as the minimal and maximal parametric domain values of all animation curves. An object at time t below the minimal parametric value will be placed at the starting value of the animation curve. Similarly, an object at time t above the maximal parametric value will be placed at the termination value of the animation curve. The user can also set a bouncing back and forth mode, the number of repetitions, and if desired, request the saving of all the diﬀerent scenes in the animation as separate ﬁles so a high quality animation can be created. A string object can be viewed as the text of selected PS font (See -N). The string position is set via a ”StrPos” vector attribute (default to the origin), and ”StrScale” real attribute to control the string height in world unit (default to 0.1). Text will always be in a plane parallel to the XY plane. 13.6 Advanced (Programmable) Hardware Graphics Support Programmable hardware allows us to change the standard pipeline of the GPU. This features enables users to create dedicated GPU programs (called shaders) to implement advanced rendering algorithms. Under Windows, IRITS OpenGL display device is able to use programmable hardware features. In order to use these advanced hardware rendering features, the GPU must support the proper shader IRIT Solid modeler G. Elber 283 model. The display device will ignore advanced hardware features attributes if the local GPU does not support the proper shaders requirements. The following advanced hardware features are supported by IRIT: 13.6.1 HDDM (Hardware Deformation Displacement Mapping) Deformation displacement mapping is a technique that allows us to tile the geometry of a given object without the limitations of strict displacement mapping. Requirements: Shader model 3.0 and above Shader ﬁle: ddm vshd.cg Shader Language: CG Shaders compilation: run time. Supported geometries: All surfaces and polygonal models with UV values In order to use DDM texture in an object, a ”DTexture” attribute string must be deﬁned for the object ([.] are optional): ”TileFileName, T TilesU TilesV, [S SamplingU SamplingV], [H Shader], [Z Scale], [OB/OA], [RU/CU/CRU], [RV/CV/CRV], [M], [NO/NT], [A AnimationSamples]” where • TileFileName: The DDM Tile. • T TilesU TilesV: Number of tiles to place. • S SamplingU SamplingV: Number of samples to take on the original object (default S=T). • H Shader: Shader ﬁlename (default: ddm vshd.cg). • Z Scale: Z Scale factor on tiles Z axes (default = 1). • OB/OA: Draw the original object before the tiles (OB) or draw the original object after the tiles (OA). This matters when using tiles with transparency (Default: dont draw original object). • RU/CU/CRU, RV/CV/CRV: How the tiles should be handled when overlapping the objects UV domain: RU, RV: Repeat end conditions. CU, CV: Clamp end conditions. CRU, CRV: Clamp to tile size - simulates repeat with clamping (handles the stretch side eﬀect in the background of objects with only 1 side when using simple repeat. (Default: RU, RV) • M: Use multitiles (see below). • NO/NT: Normal calculation methods oﬀset (NO), or tangent plane mapping (NT) (Default: NO). • Animation Samples: The number of samples from a continuous animation sequence that is deﬁned on an object (default: 1). Examples: [DTexture "horn.itd, H ddm_vshd.cg, T 4 16, S 32 64, CRU, CV, Z 0.7, NT"] [DTexture "stone-t1.itd, H ddm_vshd.cg, T 6 1, S 64 64, CU, RV, Z -0.1, M, NO"] DDM supports usage of more than one tile per object. When using multitiles, tiles are placed randomly on the object. To use multitiles, an ’M ﬂag should placed in the dtexture attribute. Furthermore, an additional ”DTextureFiles” attributes must be deﬁned for the object with the following string: ”Tileﬁle1, tileﬁle2, tileﬁle3...”. The maximum number of supported tiles is 10. Example: G. Elber IRIT Solid modeler 284 [DTextureFiles "stone-t4.itd stone-t3.itd stone-t2.itd stone-t6.itd"] The tile geometry also supports some attributes such as animation. The following animations are supported: • MORPH: Morphing between two compatible tiles (same number of vertices) according to the curve. The morphing is between the DDM tiles (”DTexture” attribute) and the ﬁrst tile in the ”DTextureFiles” attribute (hence, using morph requires multitiles). • SCL Z: Z scale of the tile (in tile space) according to the animation curve (see also animation in IRIT and the display device). • MOV U/MOV V: Change the UV placement of the tile in the parametric space of the base, textured, surface, according to the animation curve. • RECT TILE, or HEX TILE or TRIG TILE or TRIG TILE REV: DDM supports four types of tiles: Rectangle: Hexagon: Triangle: Reversed Triangle: Creates square tiling. Creates honeycomb tiling. Tiles the surfaces using triangles. Tiles the surfaces using reversed triangles. In order to deﬁne the type of tiling, one of the above attributes should be added to the tile object: 13.6.2 HFFD (Hardware Free Form Deformation) FFD is a technique which deforms objects by deforming the space in which the object is embedded. Requirements: Shader model 3.0 and above Shader ﬁle: ddm vshd.cg Shader Language: CG Shaders compilation: run time. Supported geometries: All surfaces and polygonal models with UV values In order to use FFD in an object, an ”FFD texture” attribute must be added to the object with the following string: ”ObjectFile, ShaderType, DrawTV, ScaleX, ScaleY, ScaleZ, AnimationSamples, OﬀsetX, OﬀsetY, OﬀsetZ, NormalCalcMethod” where • Objectﬁle: The ﬁle of the object to use with TV. • ShaderType: 0 - Single Phase Shader (Limited shader), 1 - Double Phase Shader • DrawTV: 0 - Dont draw the trivariate object. 1 - Draw the trivariate object. • ScaleX, ScaleY, ScaleZ: The scale of the object in xyz. • AnimationSamples: Number of times to sample object when object has animation, along the animation. • OﬀsetX, OﬀsetY, OﬀsetZ: The oﬀset of the object in xyz axes. • NormalCalcMethod: 0 - No shading (use original normal values), 1 - Normal oﬀset calculation, 2 - Tangent plane mapping Examples: [FFD_texture "porschesc.itd, 1, 0, 1.8, 0.15, 1.8, 0, 0, 0, 0, 2"] IRIT Solid modeler 13.7 G. Elber 285 Speciﬁc Comments • The x11drvs supports the following X Defaults (searched at /.Xdefaults): #ifndef COLOR irit*MaxColors: irit*Trans*BackGround: irit*Trans*BorderColor: irit*Trans*TextColor: irit*Trans*SubWin*BackGround: irit*Trans*SubWin*BorderColor: irit*Trans*CursorColor: irit*View*BackGround: irit*View*BorderColor: irit*View*CursorColor: #else irit*MaxColors: irit*Trans*BackGround: irit*Trans*BorderColor: irit*Trans*TextColor: irit*Trans*SubWin*BackGround: irit*Trans*SubWin*BorderColor: irit*Trans*CursorColor: irit*View*BackGround: irit*View*BorderColor: irit*View*CursorColor: #endif irit*Trans*BorderWidth: irit*Trans*Geometry: irit*View*BorderWidth: irit*View*Geometry: 1 Black White White Black White White Black White White 15 NavyBlue Red Yellow DarkGreen Magenta Green NavyBlue Red Red 3 =150x500+510+0 3 =500x500+0+0 • The Motif-based display drivers contain three types of gadgets which can be operated in the following manner. Scales: can be dragged or clicked outside for single (mouse’s middle button) or continuous (mouse’s left button) action. Pushbuttons: activated by clicking the mouse’s left button. The control panel: allows rotation, translation of the objects in three axes, determining of the perspective ratio, viewing an object from top, side, front or isometrically, determining scale factor and clipping settings, and operating the matrix stack. The environment window toggles between screen or object transformation, depth cue on or oﬀ, orthographic or perspective projection, wireframe or solid display, single or double buﬀering, showing or hiding normals, including or excluding the surface’s mesh and curve’s control polygon, surface drawing using isolines or polygons, and four or two polygons per ﬂat patch. Some display devices allow for the inclusion or exclusion of internal edges, and enable or disable of antialiased lines. Scales in the X11/Motif based devices set normals length, lines width, control sensitivity, the number of islolines and samples, etc. • The locations of windows as set via [-g] and [-G] and/or via the conﬁguration ﬁle overwrite in x11drvs the Geometry X11 defaults. To use the Geometry X11 default, use ’-G ” ”’ and ’-g ” ”’ or set the string to empty size in the conﬁguration ﬁle. G. Elber IRIT Solid modeler 286 • In os2drvs, only -G is used to specify the dimensions of the parent window that holds both the viewing and the transformation window. • In os2drvs, the following key strokes are available as shortcuts: Key ^x ^s ^f ^d ^t ^i ^p ^n ^v ^g ^b ^c ^m 13.8 Function Quit Save Front View Side View Top View Isometric VIew Perspetive/Orthographic View Internal Edges View Vertices’ Normals View Polygons’ Normals Backface Culling Depth Cue View Control Mesh/Poly Examples xglmdrvs -z prints all the options and their current values. xglmdrvs -B -i -l 3 solid1.itd displays the model of solid1.itd using backface culling (’-B’), with internal edges (’-i’), and line width of 3. xglmdrvs -r -A flat wiggle.itd displays the model of wiggle.itd shaded (’-r’) using ﬂat shading (’-A’). xglmdrvs -I 40 -u -b 255 255 255 wiggle.itd displays the model of wiggle.itd using isolines’ density of 40 (’-I’), using unit matrix to begin with (’-u’), and a white background (’-b’). xglmdrvs -X 0,2,0.1,sx -r anim.itd executes the animation in anim.itd, from time 0 to time 2 in steps of 0.1. The animation is saved in one frame per ﬁle (ﬂag ’s’ in ’-X’) and the display device exists once the animation has terminated (ﬂag ’x’ in ’-X’)). The animation will be shaded (’-r’). IRIT Solid modeler 14 G. Elber 287 Utilities - General Usage The IRIT Solid Modeler is accompanied by quite a few utilities. They can be subdivided into two major groups. The ﬁrst includes auxiliary tools such as illustrt and poly3d-h. The second includes ﬁlters such as irit2ray and irit2ps. All these tools operate on input ﬁles, and most of the time produce data ﬁles. In all utilities that read ﬁles, the dash (’-’) can be used to read stdin. Example: poly3d-h solid1.itd | irit2ps - > solid1.ps All the utilities have command line options. If an option is set by a ’-x’, then ’-x-’ resets the option. The command line options overwrite the settings in conﬁg ﬁles, and the reset option is useful for cases where the option is set by default, in the conﬁguration ﬁle. All utilities can read a sequence of data ﬁles. However, the last transformation matrices found (VIEW MAT and PRSP MAT) are actually used. Example: poly3d-h solid1.itd | x11drvs solid1.itd - solid1.imd x11drvs will display the original solid1.itd ﬁle with its hidden version, as computed by poly3d-h, all with the solid1.imd, ignoring all other matrices in the data stream. Compressed ﬁles with a postﬁx ”.Z” or ”.gz” will be automatically uncompressed on read and write. The following is legal: poly3d-h solid1.itd.Z | x11drvs solid1.itd.Z - solid1.imd where solid1.itd.Z was saved from within IRIT using the command save( "solid1.itd.Z", solid1 ); or similarly. The gnu utility ”gzip” is used for the purpose of (un)compressing the data via pipes. See also SAVE and LOAD. 15 15.1 Poly3d-h - Hidden Line Removing Program Introduction poly3d-h is a program to remove hidden lines from a given polygonal model. Freeform objects are preprocessed into polygons with controlled ﬁneness. See Figure 120 for some output examples which use this tool. The program performs 4 passes over the input: 1. Preprocesses and maps all polygons in a scene, and sorts them. 2. Generates edges out of the polygonal model and sorts them (preprocessing for the scan line algorithm) into buckets. 3. Intersects edges, and splits edges with non-homogeneous visibility (the scan line algorithm). 4. Applies a visibility test on each edge. This program can handle CONVEX polygons only. From IRIT one can ensure that a model consists of convex polygons only, using the CONVEX command: IRIT Solid modeler G. Elber 288 Figure 120: Some examples of the use of the hidden line removal tool, poly3d-h, to remove hidden lines. CnvxObj = convex( Obj ); just before saving it into a ﬁle. Surfaces are always decomposed into triangles. poly3d-h output is in the form of polylines. It is a regular IRIT data ﬁle that can be viewed using any of the display devices, for example. 15.2 Command Line Options poly3d-h [-b] [-m] [-i] [-e #Edges] [-H] [-4] [-W Width] [-F PolyOpti FineNess] [-q] [-o OutName] [-t AnimTime] [-c] [-z] DFiles > OutFile • -b: BackFacing - if an object is closed (such as most models created by IRIT), backfacing polygons can be deleted, thereby speeding up the process by at least a factor of two. • -m: More - provides some more information on the parsed data ﬁle(s). • -i: Internal edges (created by IRIT) - default is not to display them, and this option will force their display, as well. • -e n: Number of edges to use from each given polygon (default all). Handy as ’-e 1 -4’ for freeform data. • -H: Dumps both visible lines and hidden lines as separated objects. Hidden lines will be dumped using a diﬀerent (dimmer) color and (a narrower) line width. • -4: Forces four polygons per almost ﬂat region in the surface to polygon conversion. Otherwise two polygons only. • -W Width: Selects a default width for visible lines in inches. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. IRIT Solid modeler G. Elber 289 • -q: Quiet mode. No printing aside from fatal errors. Disables -m. • -o OutName: Name of output ﬁle. Default is stdout. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. • -c: Clips data to screen (default). If disabled (’-c-’), data outside the view screen ([-1, 1] in x and y) are also processed. Some of the options may be turned on in poly3d-h.cfg. They can then be turned oﬀ in the command line as ’-?-’. 15.3 Conﬁguration The program can be conﬁgured using a conﬁguration ﬁle named poly3d-h.cfg. This is a plain ASCII ﬁle you can edit directly and set the parameters according to the comments there. ’poly3d-h -z’ will display the current conﬁguration as read from the conﬁguration ﬁle. The conﬁguration ﬁle is searched in the directory speciﬁed by the IRIT PATH environment variable. For example, ’setenv IRIT PATH /u/gershon/irit/bin/’. If the IRIT PATH variable is not set, the current directory is searched. 15.4 Usage As this program is not interactive, usage is quite simple, and the only control available is the command line options. The images in Figure 120 were created using the following commands: poly3d-h -W 0.01 -H -q molecule.itd view1.itd | irit2ps - > molecule.ps poly3d-h -W 0.02 -q solid2h.itd view2.itd | irit2ps - > solid2h.ps poly3d-h -W 0.02 -H -q dodechdr.itd view3.itd | irit2ps -d -0.59 0.59 - > dodechdr.ps If a certain surface should be polygonized into a ﬁner/coarser set of polygons than the rest of the scene, one can set a ”resolution” attribute which speciﬁes the relative FineNess resolution of this speciﬁc surface. Further, ”u resolution” and ”v resolution” might be similarly used to set relative resolution for the u or v direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. See also IHidden. 16 16.1 Illustrt - Simple line illustration ﬁlter Introduction illustrt is a ﬁlter that processes IRIT data ﬁles and dumps out modiﬁed IRIT data ﬁles. illustrt can be used to make simple, nice illustrations of data. The features of illustrt include depth sorting, hidden line clipping at intersection points, and vertex enhancements. illustrt is designed to closely interact with irit2ps, although it is not neceessary to use irit2ps on illustrt output. See Figure 121 for some output examples which use this tool. IRIT Solid modeler G. Elber 290 Figure 121: Some examples of the use of the illustration tool, illustrt. 16.2 Command Line Options illustrt [-I #UIso[:#VIso[:#WIso]]] [-f PolyOpti SampTol] [-s] [-M] [-P] [-p] [-O] [-l MaxLnLen] [-a] [-t TrimInter] [-o OutName] [-Z InterSameZ] [-m] [-T AnimTime] [-z] DFiles • -I #UIso[:#VIso[:#WIso]]: Speciﬁes the number of isolines per surface/trivariate, per direction. If #VIso is not speciﬁed, #UIso is used for #VIso as well and so no. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -s: sorts the data in Z depth order that emulates hidden line removal once the data are drawn. • -M: Dumps the control mesh/polygon as well. • -P: Dumps the curve/surface as isocurves. • -p: Dumps vertices of polygons/lines as points. • -O: Handles polygonal objects as possibly open. This will generate two identical edges for an edge shared by two adjacent polygons. This can be useful for open or isolated polygons. • -l MaxLnLen: Breaks long lines into shorter ones with maximal length of MaxLnLen. This option is necessary to achieve good depth depending on line width in the ’-d’ option of irit2ps. IRIT Solid modeler G. Elber 291 • -a: Takes into account the angle between the two (poly)lines that intersect when computing how much to trim. See also -t. • -t TrimInter: Each time two (poly)line segments intersect in the projection plane, the (poly)line that is farther away from the viewer is clipped by the TrimInter amount from both sides. See also -a. • -o OutName: Name of output ﬁle. Default is stdout. • -Z InterSameZ: The maximal Z depth diﬀerence of intersection curves to be be considered invalid. • -m: More talkative mode. Prints processing information. • -T AnimTime: If the data contain animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. 16.3 Usage illustrt is a simple line illustration tool. It processes geometry such as polylines and surfaces and dumps geometry with attributes that will make nice line illustrations. illustrt is geared mainly toward its use with irit2ps to create postscript illustrations. Here is a simple example: illustrt -s -l 0.1 solid1.itd | irit2ps -W 0.05 -d 0.2 0.6 -u - > solid.ps makes sure all segments piped into irit2ps are shorter than 0.1 and sorts them in order to make sure hidden surface removal is correctly applied. Irit2ps is invoked with depth cueing activated, and a default width of 0.05. illustrt dumps out regular IRIT data ﬁles, so output can be handled like any other data set. illustrt does the following processing to the input data set: • Converts surfaces to isocurves (’-I’ ﬂag) and isocurves and curves to polylines (’-S’ ﬂag), and converts polygons to polylines. Polygonal objects are considered closed and even though each edge is shared by two polygons, only a single one is generated. • Finds the intersection location in the projection plane of all segments in the input data set and trims away the far segment at both sides of the intersection point by an amount controlled by the ’-t’ and ’-a’ ﬂags. • Breaks polylines and long lines into short segments, as speciﬁed via the ’-l’ ﬂag, so that width depth cueing can be applied more accurately (see irit2ps’s ’-d’ ﬂag) as well as the Z sorting. • Generates vertices of polygons in the input data set as points in output data controlled via the ’-p’ ﬂag. set. • Applies a Z sort to the output data, if ’-s’, so drawing in order of the data will produce a properly hidden surface removal drawing. Here is a more complex example. Make sure tubular is properly set via ”attrib(solid1, ”tubular”, 0.7);” and invoke: IRIT Solid modeler G. Elber 292 illustrt -s -p -l 0.1 -t 0.05 solid1.itd | irit2ps -W 0.05 -d 0.2 0.6 -p h 0.05 -u - > solid.ps makes sure all segments piped into irit2ps are shorter than 0.1, generates points for the vertices, sorts the data in order to make sure hidden surface removal is correctly applied, and trims the far edge by 0.05 at an intersection point. Irit2ps is invoked with depth cueing activated and a default width of 0.05, points are drawn as hollowed circles of default size 0.05, and lines are drawn tubular. Objects in the input stream that have an integer attribute by the name of ”IllustrtNoProcess” are passed to the output unmodiﬁed. If this attribute value is ¡= 0, the object is sent to the output stream immediately (in the beginning of the output stream. If this attribute value is ¿ 0, the object is sent to the output stream at the end (in the end of the output stream. Objects in the input stream that have a real attribute by the name of ”IllustrtShadeBG” are copied and rendered also in the background with a gray color as set by this attribute (between zero and one). If a regular color/rgb attribute is found on the object, this value will scale that as well. Objects in the input stream that have an attribute by the name of ”SpeedWave” will have a linear segment added that emulates fast motion with the following attributes, "Randomness,DirX,DirY,DirZ,Len,Dist,LenRandom,DistRandom, width". Objects in the input stream that have an attribute by the name of ”HeatWave” will have a spiral curves added that emulate a heat wave in the +Z axis with the following attributes, "Randomness,Len,Dist,LenRandom,DistRandom, width". Examples: attrib(Axis, "IllustrtNoProcess", 1); attrib(Srf, "IllustrtShadeBG", 0.7); attrib(Obj, "SpeedWave", "0.0005,1,0,0,5,3,3,2,0.05"); attrib(Obj, "HeatWave", "0.015,0.1,0.03,0.06,0.03,0.002"); 17 Aisoshad - Simple line illustration ﬁlter 17.1 Introduction Aisoshad is a ﬁlter that processes IRIT data ﬁles of freeform shapes and dumps out modiﬁed IRIT data ﬁles in the form of short univariate strokes. Aisoshad can be used to make simple yet nice line art illustrations of geometry that is based solely on isoparametric curves. Aisoshad employs a simple shader to determine the density of the isoparametric strokes as well as the thickness etc. Output of aisoshad can be piped into the irit2ps postscript postprocessor. See Figure 122 for output examples of using this tool. 17.2 Command Line Options aisoshad [-o OutName] [-m] [-i] [-F PolyOpti FineNess] [-f PolyOpti SampTol] [-r RndrMdl] [-c CosPwr] [-s SdrPwr] [-l Lx Ly Lz] [-R Random] [-d AdapDir] [-t SrfZTrans] [-M MinSubdiv] [-D AdapDist] [-w AdapIsoWidth] [-S WidthScale] [-W] [-u] [-Z ZbufSize] [-b] [-z] DFiles • -o OutName: Name of output ﬁle. Default is stdout. IRIT Solid modeler G. Elber 293 Figure 122: Examples of the use of the aisoshad illustration tool to line art illustrative drawing using isoparametric curves. In (left), silhouettes are emphasized, while in (right) a light source above and to the right is placed using a cosine shader. • -m: More talkative mode. Prints processing information. • -i: Solve symbolic products using interpolations. Faster but the generated output is not as compact as possible. • -I #IsoLines: Speciﬁes number of isolines per surface, per direction. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. Default is 0 and 20.0 (no optimal sampling with ﬁneness of 20.0 (real number)). • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -r: Selects the rendering model of the shader as follows: 1. Cosine shader, diﬀuse only, light source regular. 2. Cosine shader, diﬀuse only, light source as two lights from opposite directions. 3. Cosine shader, has specular term, light source regular. 4. Cosine shader, has specular term, light source as two lights. IRIT Solid modeler G. Elber 294 5. Shader emphasizing the silhouette areas of the model. 6. Shader estimating distance decay from a point light source. • -c CosPower: Controls the cosine shader’s power. • -s SdrPower: Controls the shader’s relative inﬂuence. • -l Lx Ly Lz: Sets the light source position/direction. • -R Random: Controls the levels of randomness that the isoparametric curves perturb. Low levels of randomness would leave visible artifacts while too high levels would disturb the shading. Should be greater than one or negative one to disable. • -d AdapDir: Sets the isoparametric directions of the strokes. Either 0, 1, or 2 for U direction, V direction or both U and V directions, respectively. • -t SrfZTrans: The amount to translate the created line strokes in Z, in order to prevent Z ﬁghting with the rendered object itself. • -M MinSubdiv: Sets the minimal number of subdivision to enforce during the isoparametric strokes’ construction. This ﬂag should be used rarely and typically MinSubdiv should be low and close to one. • -D AdapDist: Sets the distance between adjacent isocurves. The smaller AdapDist is, the denser the coverage of the strokes will be. • -w AdapIsoWidth: Sets the default width attribute of the generated strokes. • -S WidthScale: Controls the relative variance of the width of the strokes in variable width strokes. • -W: If set, enables variable width strokes. • -u: If set, maps the strokes to screen space. Otherwise, strokes are mapped back to object space. • -Z ZbufSize: Sets the size of the (square) Z buﬀer to set. • -b: If set, generates a binary IRIT data ﬁle that holds the strokes. Otherwise, IRIT text ﬁle will be created. • -z: Print version number and current defaults. 17.3 Usage Aisoshad is a simple line art illustration tool that generates strokes that follow the isoparametric curves. It processes freeform geometry such as surfaces and dumps geometry with attributes that makes nice line illustrations. Aisoshad is geared mainly toward its use with irit2ps to create postscript illustrations. Here is a simple example: aisoshad -Z -500 -F 0 50 -s 10 -c 1 -D 0.3 -r 5 wglass.itd view.imd | irit2ps -W 0.05 -d 0.2 0.6 -u - > wglass1.ps IRIT Solid modeler G. Elber 295 that creates line art illustrations of a wine glass wglass.itd with hidden strokes removed via a Z-buﬀer of size 500 that will be displayed on screen, polygonal ﬁneness of 50 for the surface of the glass, shader power of 10 and cosine power of 1, isoparametric curves maximal distance of 0.3, and shader number 5 that emphasizes silhouettes. The output of the shader is piped to a irit2ps ﬁlter to postscript that sets the width of the strokes to be a function of depth. Figure 122 (a) shows the result of this example. Here is another example: aisoshad -Z 700 -R 4 -F 0 50 -l 1 1 1 -D 0.02 -r 2 wglass.itd view.imd irit2ps -W 0.005 -d 0.2 0.6 -u - > wglass2.ps that creates line art illustrations of a wine glass wglass.itd with hidden strokes removal via a Z-buﬀer of size 700 that is allocated oﬀ-line in core memory, polygonal ﬁneness of 50 for the surface of the glass, a light source at (1, 1, 1), isoparametric curves maximal distance of 0.02, and a cosine shader number 2. The output of the shader is piped to a irit2ps ﬁlter to postscript that sets the width of the strokes to be a function of depth. Figure 122 (b) shows the result of this example. Transparent objects, or objects with the ”transp” attribute, would generate strokes as regular surfaces but would not participate in the hidden strokes removal. An ”AdapIsoDir” attribute that is found on some surface object would override the global isoparametric direction’s setup of strokes as is set via the ’d’ option. See also the illustrt, izebra, lineshad, and irit2ps tools. 18 IZebra - Simple zebra style, parallel curve based rendering 18.1 Introduction Izebra is a ﬁlter that processes IRIT data ﬁles into a 2D striped, zebra style illustration that gives the user an illusionary depth cue. The output is also an IRIT data ﬁle in the form of freeform curves. Izebra can be used to make simple yet nice art illustrations of geometry that is based on a speciﬁc style inspired by the artist Victor Vasarely. Izebra employs a Z buﬀer to determine the density and warping of the stripes. Output of izebra can be piped into the irit2ps postscript postprocessor. See Figure 123 for output examples which use this tool. 18.2 Command Line Options IZebra [-o OutName] [-m] [-O ImgOper] [-F PolyOpti FineNess] [-u] [-I NumIters] [-Z ZbufSize] [-B CbcBspSize] [-D DataSrf] [-A StripeAngle] [-b] [-s Stripes] [-S ZScale] [-d ZInitDepth] [-z] DFiles • -o OutName: Name of output ﬁle. Default is stdout. • -m: More talkative mode. Prints processing information. • -O ImgOper: By default, the Z buﬀer is employed directly. However, once the Z buﬀer is fully evaluated and before beginning the stripes processing, one can apply a ﬁlter to the Z map of the Z buﬀer. The ﬁlter can be a ﬁrst order Roberts derivative if ”-O 1”, a second order Laplacian if ”-O 2”, or an inverted depth if ”-O 3”. IRIT Solid modeler G. Elber 296 Figure 123: Examples of the use of the izebra illustration tool toward line art illustrative drawings. On the left, the Utah teapot is rendered, while on the right, a chess piece, a pawn, is portrayed. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. Default is 0 and 20.0 (no optimal sampling with ﬁneness of 20.0 (real number)). • -u: Forces a unit matrix. That is, input data are not transformed at all. • -I NumIters: Puts a bound on the number of iterations in the numerical processing stage. • -Z ZbufSize: ZbufSize sets the size of the (square) Z buﬀer to set. • -B CbcBspSize: Sets the mesh size of the constructed uniform cubic B-spline grid, if no data surface is speciﬁed by ’-D’. • -D DataSrf: If speciﬁed, provides the name of the uniform cubic B-spline to load and warp. Overrides the ’-B’ option. • -A StripeAngle: Sets the angle of the stripes with respect to the horizontal line, in degrees. • -b: If set, generates a binary IRIT data ﬁle that holds the stripes. Otherwise, an IRIT text ﬁle will be created. • -s Stripes: If set, prescribes the number of strips to extract as iso parametric curves of the warped B-spline surface. Otherwise, the warped B-spline surface itself is dumped out. • -S ZScale: A relative factor to control the eﬀect of the depth on the warping amount. This should be around one. • -d ZInitDepth: By default, the Z buﬀer is initialized to a depth of zero which amounts to no warping of the B-spline surface. Here is a proper way to prescribe a diﬀerent background depth (which will cause warping in the surface). IRIT Solid modeler G. Elber 297 • -z: Print version number and current defaults. 18.3 Usage Izebra is a simple stripes art illustration tool that generates stripes that follow a warped B-spline surface as its isoparametric curves. It processes the given geometry, such as surfaces, into a Z map of a Z buﬀer and warps a B-spline surface that is placed over it, with a warping amount that is a function of the locally detected depth. IZebra dumps out stripes geometry that makes nice illusionary illustrations. IZebra is geared mainly toward its use with irit2ps to create postscript illustrations. Here is a simple example: izebra -m -Z 500 -B 150 -I 10 -F 0 100 -A 140 -S 0.35 pawn.itd | irit2ps -f 0 300 -u -B -0.45 -0.75 0.65 0.75 -W 0.004 -I 0:250 - > pawn.ps creates striped illustrations of a pawn chess piece, with the aid of a Z-buﬀer of size 500 by 500, a uniform cubic B-spline surface with mesh size of 150 by 150, polygonal ﬁneness of 100 for the surface of the pawn, rotation of stripes of 140 degrees and Z scale factor of 0.35. Ten iterations will be conducted during the numerical processing of the data. The output of izebra is piped by the irit2ps ﬁlter to postscript that extracts 250 isoparametric curves out of the dumped warped surface and sets the width of the strokes to be 0.004. Figure 123 (a) shows the result of this example. Here is another example: izebra -m -Z 500 -B 200 -I 10 -F 0 100 -A -90 -S 0.4 teapot.itd | irit2ps -f 0 200 -u -B -0.55 -0.35 0.55 0.35 -W 0.007 -I 0:150 - > teapot.ps creates striped illustrations of the Utah Teapot, with the aid of a Z-buﬀer of size 500 by 500, a uniform cubic B-spline surface with mesh size of 200 by 200, polygonal ﬁneness of 100 for the surface of the teapot, rotation of stripes of -90 degrees and Z scale factor of 0.4. Ten iterations will be conducted during the numerical processing of the data. The output of izebra is piped by the irit2ps ﬁlter to postscript that extracts 150 isoparametric curves out of the dumped warped surface and sets the width of the strokes to be 0.007. Figure 123 (b) shows the result of this example. See also the illustrt, aisoshad, lineshad, and irit2ps tools. 19 19.1 LineShad - Simple line illustration ﬁlter Introduction Lineshad is a ﬁlter that processes IRIT data ﬁles of freeform shapes and dumps out modiﬁed IRIT data ﬁles in the form of short univariate strokes. Lineshad can be used to make simple yet nice line art illustrations of geometry that is based on arbitrarily stroked curves on the surfaces. Lineshad employs a simple shader to determine the density of the isoparametric strokes as well as the thickness etc. Output of lineshad can be piped into the irit2ps postscript postprocessor. See Figure 124 for output examples using this tool. 19.2 Command Line Options lineshad [-o OutName] [-m] [-F PolyOpti FineNess] [-R RelStepSize] [-f PolyOpti SampTol] [-r RndrMdl] [-c CosPwr] [-s SdrPwr] [-i Intensity] [-l Lx Ly Lz] [-v Vx Vy Vz] [-w Width] IRIT Solid modeler G. Elber 298 Figure 124: Examples of the use of the lineshad illustration tool to line art illustrative drawing using isoparametric curves. On the left, silhouettes are emphasized, while on the right, a light source above and to the right is placed using a cosine shader. [-d Density] [-t SrfZTrans] [-S WidthScale] [-T Texture] [-Z ZbufSize] [-b] [-z] DFiles • -o OutName: Name of output ﬁle. Default is stdout. • -m: More talkative mode. Prints processing information. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. Default is 0 and 20.0 (no optimal sampling with ﬁneness of 20.0 (real number)). • -R RelStepSize: Relative control (default to 1.0) on the step size taken during the numerical marching on the surfaces in the diﬀerent strokes’ patterns. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -r: Selects the rendering model of the shader as follows: 1. Dumps only the uniform point distribution. 2. Cosine shader, diﬀuse only, light source regular. IRIT Solid modeler G. Elber 299 3. Cosine shader, diﬀuse only, light source as two lights from opposite directions. 4. Cosine shader, has specular term, light source regular. 5. Cosine shader, has specular term, light source as two lights. 6. Shader emphasizing the silhouette areas of the model. 7. Shader estimating distance decay from a point light source. • -c CosPower: Controls the cosine shader’s power. • -s SdrPower: Controls the shader’s relative inﬂuence. -i Intensity: Controls the global density of the constructed line art. The larger Intensity is, the denser the drawing becomes. • -l Lx Ly Lz: Sets the light source position/direction. • -v Vx Vy Vz: Sets the viewing direction; typically, the Z axis. • -w Width: Sets the width of the generated strokes. • -d Density: Relative control (default to 1.0) of the density of the uniform point distribution from which the strokes are developed. • -t SrfZTrans: Amount of created line strokes in Z to translate, in order to prevent Z from ﬁghting with the rendered object itself. • -S WidthScale: Controls the relative variance of the width of the strokes in variable width strokes. • -T Textures: Selects the pattern of the strokes. Texture can be one of: 1. ”isoparam[,0,1,2w]”: Isoparametric curves will be created in a similar way to the aisoshad tool. Following the ”isoparam” string, one can optionally specify the isoparametric direction as 0, 1 or 2 for U, V, or both, and a second ’w’ character for optional variable width. This option extracts exact isoparametric curves from the given surface. 2. ”wood[,Dx,Dy,Dz]”: A strokes’ style following layers of wood will be used. Optionally, a direction normal to the layers can be speciﬁed, with a default being the Z axis. 3. ”vood[,Ry,Rz]”: A variation on the wood texture, this time with a layered orientation set via two rotation angles around Y and Z. 4. ”isomarch[,0,1,2]”: Similar to ”isparam” but numerically march on the surface in the isoparametric direction. Again, 0, 1, or 2 stands for U, V, or both isoparametric directions. 5. ”silhouette[,t,n,tn]”: Extract strokes emphasizing the silhoeutte areas from the given viewing direction. Strokes can be extracted in the direction of the surface normal near the silhouette area if option ”,n” is given, tangent along the surface if ”,t”, or both if ”,tn”. 6. ”iTexture”: Employ a raster image as a texture image on the surface with the gradient of the image serving as the strokes direction. The name of the image itself (must be in urt rle format) is expected in a ”iTexture” attribute on the speciﬁc object. 7. ”curvature[,0,1,2]”: Develop strokes along lines of curvatures. Strokes are developed along the minimal curvature if ”,0”, the maximal curvature if ”,1”, and both if ”,2”. 8. ”CurveStroke”: An XY curve object is expected as a ”CurveStroke” attribute on the same object and serves as a speciﬁcation of motion in the parametric space of the surface for each given point. IRIT Solid modeler G. Elber 300 • -Z ZbufSize: ZbufSize sets the size of the (square) Z buﬀer to set. • -b: If set, generates a binary IRIT data ﬁle that holds the strokes. Otherwise, an IRIT text ﬁle will be created. • -z: Print version number and current defaults. 19.3 Usage lineshad is a simple line art illustration tool that generates strokes that follow the isoparametric curves. It processes freeform geometry such as surfaces, and dumps geometry with attributes that makes nice line illustrations. lineshad is geared mainly toward its use with irit2ps to create postscript illustrations. Here is a simple example: lineshad -Z -500 -F 0 50 -T "isoparam" -d 0.5 -c 10 -r 2 wglass.itd view.imd | irit2ps -W 0.002 -u - > wglass3.ps creates line art illustrations of a wine glass wglass.itd with hidden strokes removal via a Z-buﬀer of size 500 that will be displayed on screen, polygonal ﬁneness of 50 for the surface of the glass, shader that employs isoparametric curves, relative density of distribution of 0.5, and cosine power of 10 of the cosine shader number 2. Figure 124 (a) shows the result of this example. Here is another example: lineshad -Z -500 -F 0 50 -T "wood,1,1,1" -d 6 -c 10 -r 2 wglass.itd view.imd | irit2ps -W 0.002 -u - > wglass4.ps creates line art illustrations of a wine glass wglass.itd with hidden strokes removal via a Z-buﬀer of size 500 that is allocated oﬀ-line in core memory, polygonal ﬁneness of 50 for the surface of the glass, a light source at (1, 1, 1) for the wood strokes’ style, relative point distribution of 6, and a cosine power of 10 for the cosine shader number 2. Figure 124 (b) shows the result of this example. Transparent objects, or objects with the ”transp” attribute, will generate strokes as regular surfaces but will not participate in the hidden strokes removal. A string ”itexture” attribute is expected if ”itexture” strokes’ style is used. A curve object as the ”CurveStroke” attribute is expected if ”CurveStroke” is employed. One can override the strokes’ style as it is set via the ’-T’ command line option by setting an ”lTexture” string attribute with the prefered strokes’ style of this object. One can modify the relative density of some speciﬁc object by placing a real number attribute named ”PtsDensity” on the object. See also the illustrt, izebra, aisoshad, and irit2ps tools. 20 20.1 ihidden - Hidden Curve Removing Program Introduction ihidden is a program to remove hidden curves from a given surface model. Only freeform objects are processed in ihidden. See Figure 125 for some output examples which use this tool. The program performs 3 passes over the input: 1. Preprocesses and extracts the diﬀerent curves in a scene, boundary curves, silhouette curves, isoparametric curves and discontinuity curves. 2. Solves for all the intersections of the diﬀerent curves in the parametric space, and at that point splits the curves into curve segments. IRIT Solid modeler G. Elber 301 Figure 125: Some examples of the use of hidden curve removal tool, ihidden, to remove hidden curves. 3. Applies a visibility test to each segment of curve. This program can handle non self interesecting surfaces only. Further, surfaces that intersect other surfaces and are not properly trimmed into a model are likely to result in the wrong answer as well. The output of ihidden is in the form of curves. It is a regular IRIT data ﬁle that can be viewed using any of the display devices, for example. 20.2 Command Line Options ihidden [-q] [-H] [-M] [-I #UIso[:#VIso[:#WIso]]] [-d] [-s Stage] [-b] [-o OutName] [-t Tolerance] [-Z ZBufSz] [-T AnimTime] [-z] DFiles • -q: Quiet - provides no information on the progress if TRUE. • -H: Dumps both visible lines and hidden curves as separated objects. Hidden curves will be dumped using a narrower line width. • -M: Force conversion of (active) curves to be monotone. • -I #UIso[:#VIso[:#WIso]]: Speciﬁes the number of isolines per surface/trivariate, per direction. If #VIso is not speciﬁed, #UIso is used for #VIso as well and so on. • -d: Add to also display C1 discontinuity curves. • -s: Speciﬁes the step at which to stop this process, where step 3, as described above, will complete the entire hidden curve removal process and is the default. • -b: If set, generates a binary IRIT data ﬁle that holds the strokes. Otherwise, an IRIT text ﬁle will be created. IRIT Solid modeler G. Elber 302 • -o OutName: Name of output ﬁle. Default is stdout. • -t Tolerance: Tolerance of computation. • -Z ZBufSz: Size of the Z buﬀer in the visibility testing process. • -T AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. Some of the options may be turned on in ihidden.cfg. They can then be turned oﬀ in the command line as ’-?-’. 20.3 Conﬁguration The program can be conﬁgured using a conﬁguration ﬁle named ihidden.cfg. This is a plain ASCII ﬁle you can edit directly and set the parameters according to the comments there. ’ihidden -z’ will display the current conﬁguration as read from the conﬁguration ﬁle. The conﬁguration ﬁle is searched in the directory speciﬁed by the IRIT PATH environment variable. For example, ’setenv IRIT PATH /u/gershon/irit/bin/’. If the IRIT PATH variable is not set, the current directory is searched. 20.4 Usage As this program is not interactive, usage is quite simple, and the only control available is using the command line options. The images in Figure 125 were created using the following commands: ihidden ih_glass.itd | irit2ps -d -W 0.02 - > ih_glass.ps ihidden -H ih_wiggl.itd | irit2ps -d -W 0.02 - > ih_wiggl.ps If a certain surface should contain more or less isoparametric curves, a relative change could be applied to some speciﬁc object via the ”num of isolines” attribute. If a ”transp” attribute is found on some object, it will generate all the curves but will not aﬀect the visibility (i.e. be fully transparent). See also Poly3d-h. 21 21.1 Irender - Simple Scan Line Renderer Introduction irender is a program to render IRIT scenes into images. It is a software based Z buﬀer that is able to create images in few formats. Several of its features includes parametric and volumetric texture mapping, shadow computations, transparency and antialiasing. Freeform objects are preprocessed into polygons with controlled ﬁneness. See Figure 126 for some output examples of using this tool. IRIT Solid modeler G. Elber 303 Figure 126: Some examples of the use of irender scan convertion tool to render images of IRIT scenes. Highlights can be seen in the molecule image while the glass is rendered transparent. 21.2 Command Line Options irender [-v] [-s XSize YSize] [-Z Znear Zfar] [-a Ambient] [-b R G B] [-B] [-F PolyOpti FineNess] [-f PolyOpti SampPerCrv] [-M Flat/Gouraud/Phong/None] [-p PtRad] [-P WMin [WMax]] [-S] [-T] [-t AnimTime] [-N ClrQuant SilWidth [SilR SilG SilB]] [-A FilterName] [-d] [-l] [-V] [-n] [-i rle/ppm{3,6}/png] [-o OutName] [-z] files • -v: Verbose mode. Prints informative messages as it progresses. • -s XSize YSize: Sets the size of the output image, in pixels. Default to 512x512. • -Z Znear Zfar: Sets the near and far cliping planes with default of no clipping. • -a Ambient: Sets the ambient lighting fraction. Between zero (no ambient lighting) and one. Default to 0.2. • -b R G B: Sets the background color. Each of thre R,G,B colors is an integer value between zero and 255. Default to black. • -B: Apply back face culling. Somewhat faster, but only correct for closed objects. Default is no back face culling. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. Default is 0 and 20.0 (no optimal sampling with ﬁneness of 20.0 (real number)). IRIT Solid modeler G. Elber 304 • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -M Flat/Gouraud/Phong/None: Selects the shader to be used. Default to Phong if has normals of vertices, Flat if no normals are found. The None options exactly paints the objects with the given color, applying no shader. • -p PtRad]: Width of rendered points (as spheres). • -P WMin [WMax]: Width of rendered polyline, in world units. If only WMin is speciﬁed, all polylines are set to have WMin width. Otherwise, if WMax is prescribed as well, polylines’ width is set to be proportional to their depth with WMax is the width of closest polyline and WMin the farest polyline. Polylines and curves will be ignored without the setting of this option. • -S: Enable shadow computation. No shadows will be rendered without -S. The is no shadow support for this release of irender. • -T: Enable transparency computation. No transparent object will be processed without -T. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -N ClrQuant SilWidth [SilR SilG SilB]: Requests cartooN style NPR rendering. Two eﬀects could be activated using this option: the colors could be quantized into ClrQuant levels or, alternatively a value of zero for ClrQuant denotes no quantization. Also, open boundaries and silhouettes could be rendered if SilWidth ¿ 0.0 at SilWidth polyline width and optional color SilR SilG SilB. • -A FilterName: Selects an antialiasing ﬁlter. FilterName can be one of ’none’, ’box’, ’triangle’, ’quadratic’, ’cubic’, ’catrom’, ’mitchell’, ’gaussian’, ’sinc, and ’bessel’. Default is ’none’. • -d: Output will be in the form of Z depth instead of a color image. Output will be 32 bits depth instead of RGBA. • -V: Output will be in form of visibility map: a map in model’s UV coordinates that represents the visibility of the model from the speciﬁed rendering direction. • -n: Reverses the normals of vertices and planes, globally. • -i rle/ppm{3,6}/png: Selects output image type. Currently the Utah Raster Toolkit’s (URT) rle format is being supported as well as the PPM and PNG formats. PPM can be either P6 or P3 style. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -z: Prints version number and current defaults. Some of the options may be turned on in irender.cfg. They can be then turned oﬀ in the command line as ’-?-’. IRIT Solid modeler 21.3 G. Elber 305 Conﬁguration The program can be conﬁgured using a conﬁguration ﬁle named irender.cfg. This is a plain ASCII ﬁle you can edit directly and set the parameters according to the comments there. ’irender -z’ will display the current conﬁguration as read from the conﬁguration ﬁle. The conﬁguration ﬁle is searched in the directory speciﬁed by the IRIT PATH environment variable. For example, ’setenv IRIT PATH /u/gershon/irit/bin/’. If the IRIT PATH variable is not set, the current directory is searched. 21.4 Usage As this program is not interactive, usage is quite simple, and the only control available is using the command line options. The images in Figure 126 were created using the following commands: irender -s 350 350 -b 255 255 255 -S -A sinc -i rle lightsrc.itd molecule.itd view_mat.itd > molecule.rle irender -s 700 700 -F 0 64 -M Flat -b 255 255 255 -T -A sinc -i rle glass.itd view_mat.itd > glass.rle 21.5 Advanced Usage One can specify several attributes that aﬀect the way the scene is rendered. The attributes can be generated within IRIT. See also the ATTRIB IRIT command. Surface color is controlled on two levels. If the object has an RGB attribute, it is used. Otherwise, a color as set via the IRIT COLOR command. If a vertex of a poly object has an RGB attribute it will overwrite the object’s RGB color for that vertex. If a certain surface should be ﬁner/coarser than the rest of the scene, one can set a ”resolution” attribute which speciﬁes the relative FineNess resolution of this speciﬁc surface. Further, ”u resolution” and ”v resolution” might be similarly used to set relative resolution for the u or v direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. Points are rendered as small spheres with size (radius) that is controlled by the ”width” attribute found on the object or the radius that is speciﬁed by the ’-p’ option as default size. Objects are rendered with no shading if ”NoShading” attribute is found on them. Example: attrib( Ball, "rgb", "255,0,0" ); color( Sphere, white ); The cosine exponent of the phong shader can be set for a speciﬁc object via the SRF COSINE attribute, with 128 as default value. An object can aﬀect its diﬀuse and specular components via the DIFFUSE and SPECULAR real attributes, with 0.4 as default value. Example: attrib( Ball, "srf_cosine", 16 ); attrib( Ball, "diffuse", 0.7 ); attrib( Ball, "specular", 1.0 ); G. Elber IRIT Solid modeler 306 An object can be drawn transparent instead of opaque, if it has a ”transp” attribute. A transparent value of one denotes a completely transparent object, while a value of zero means a completely opaque object. Transparent objects will be rendered as such if and only if the ’-T’ command line option is set. Example: attrib( final, "transp", 0.5 ); An object can have its silhouettes (and boundary curves) rendered if a real ”SilWidth” attribute with width larger than zero is speciﬁed. ”SilColor” will then set the color of the rendered outline curves. See also ’-N’ which sets this option globally. Several types of texture mapping are supported. Parametric texture may be attached to a parametric surface where the prescribed image is mapped onto the rectangular parametric domain of the surface. The parametric texture may be applied with the following options: ’D’ x y z ’O’ x y z ’S’ Su Sv {Sw} ’A’ a ’T’ TextureType Vector that will be rotated to Z along with the texture coordinates. Applies to ’T’ 1, 2 or 3. Default to the Z axis. a point to which that texture Origin will be translated. Applies to ’T’ 1, 2 or 3. Default to origin. Scales the coordinates in u and v. Scale factors of 1.0 would cover the entire surface once. Default to scale factors of 1.0. If Sw is speciﬁed for a polygonal object, each polygonal is locally scaled based on its maximal projection on one of the main, XY XZ or YZ, planes. If (Su = Sv = 0) for freeforms, the texture coords are undergoing no scale at all (assuming image domain of zero to one in all axes). Angle of rotation in degrees of texture map with respect to main axis. Applies to ’T’ 1, 2 or 3. Default to no rotations. with 0 denotes regular parametric texture, 1 denotes spherical coordinates, 2 denotes spherical bijective coordinates, 3 denotes cylinderical coordinates, 4 denotes planar coordinates. Regular parametric texture employs the inherited surface parametrization of the freeform surface and can only be used on parametric surfaces. Spherical, cylinderical, and planar coordinate transformations are useable for all types of geometry from polygons to freeform surfaces and is fairly straightforward with the origin as set by ’O’ being the center of the mapping while the direction set by ’D’ controls the north pole of the sphere, the axis of the cylinder, and the normal of the plane. Finally, the angle set by ’A’ rotates the texture around this ’D’ prescribed axis. The spherical bijective mapping is more complex. An object identical to the textured object should be found as an ”PTextureBijectObj” that contains the identical topology of the original object. The original object must be genus zero non convex, while the attribute object must be a genus zero convex G. Elber IRIT Solid modeler 307 object with the origin as set via ’O’, inside this convex object. It is likely that both the original object and its attribute object will be a polygonal object. Both objects must contain triangles only. A bijective mapping is then conducted from every point on the original non convex object to the convex attribute object and from there through spherical mapping to the texture map. Example: attrib( attrib( attrib( attrib( Srf1, Srf2, Srf3Triangs, Srf3Triangs, "ptexture", "checker.ppm, S 1 1, A 45" ); "ptexture", "checker.ppm, S 1 3, T 1, O 1 1 1, D 0 0 1" ); "ptexture", "checker.ppm, S 1 2, T 1, O 1 1 1, D 0 0 1" ); "PTextureBijectObj", Srf3ConvexTriangles ); Srf1 is a parametrically textured map using spherical mapping, Srf2 is a parametrically textured map using cylinderical mapping and Srf3Triangs is a parametrically textured map using spherical bijective mapping and Srf3ConvexTriangles is the convex topologically equivalent object. The program will automatically detect the image type according to the ﬁle’s type. Note that regular parametric texture may be applied to parametric surfaces only, whereas the spherical, cylinderical and planar parametric textures may be used on all types of geometry. Depending upon the way irender is compiled, texture images could be in ppm format (always), or gif, png, and rle. If the image has an alpha channel (fully supported in png and rle and binary supported in gif images via its transparent color) it is honored if transparency (-T) is activated. A second type of texture mapping can be applied to all geometric objects. Herein, a procedural texture mapping is employed. The currently supported textures are camouf checker chocolate contour curvature marble ncontour orange wood punky Camouﬂage style Checker style Chocolate chips style Parallel plane contouring Gaussian/Mean etc. curvature Marble style Constant normal angle to major axis Bump mapping orange style Wood style Colorful punky style A second parameter that must be provided for procedural textures is the scaling factor of the texture, which can be either one parameter of uniform scaling or a vector of three coeﬃcients for scaling in x, y, and z. For contour style, the scale denotes the spacing of the contouring planes in X, Y and Z. For ncontour style, the scale also denotes the spacing of the adjacent constant normal contours. Related attributes are ”texture color” and ”texture width” that support the color and the width of the textured strokes. Example: attrib( Obj1, "texture", "marble, 2" ); attrib( Obj2, "texture", "wood, 1 0.5 2.5" ); which sets Obj1 to have a marble procedural texture with a uniform scaling factor of 2 and a wood texture for Obj2 with scaling factors of (1, 0.5, 2.5) in x, y, and z. In addition, the appearance of each procedural texture can be controlled by optional parameters which are diﬀerent for each texture. Each texture parameter is recognized by a letter; to enter a G. Elber IRIT Solid modeler 308 parameter, add to the attribute string the paramter letter followed by the value or values. Each parameter should be separated by a comma. Example: attrib( Obj1, "texture", "wood, 2, b 0.3, o 5 5 5" ); sets Obj1 to have a wood procedural texture with a scaling factor of 2, a Brightness level of 0.3, and the Origin point at (5,5,5). The optional parameters are: checker: ’z’ x y z ’o’ x y z ’b’ x ’CP’ f ’C1’ r g b ’C2’ r g b ’C3’ r g b a vector to which the Z axis will be rotated. a point to which the Origin will be translated. the brightness of the checker color scaling, should be between 0 and 1. To force a 2D checker plane orthogonal to the vector that is speciﬁed via the ’z’ option. A second optional color for the checkerboard. A third optional color for the checkerboard, used in the second layer of the checker volume. A fourth optional color for the checkerboard, used in the second layer of the checker volume. chocolate: ’W’ w ’d’ x the ’width’ of chocolate piece (zero to half). the ’depth’ of the bumps on the bump-mapping. contour: ’W’ w ’C’ r g b the ’width’ of contour. the color of the contour in RGB betweeo zero and one (”C 1 1 1” fully is white). curvature: The curvature texture has no optional parameter, but the ﬁrst scale parameter has a special meaning. A scale of 0 >0 <0 Paints convex regions in red, concave in green, and saddle-like in yellow. Paints the Gaussian curvature in convex regions in red to magenta, in concave regions in yellow to green, and in saddle-like in cyan to blue. Paints the Mean curvature in positive mean curvature regions in yellow to green and in negative Mean curvature in red to magenta. G. Elber IRIT Solid modeler 309 If this ﬁrst scale parameter is non zero, its absolute value is used to modify the blending speeds between the diﬀerent colors. marble: ’z’ x y z ’o’ x y z ’t’ f s ’f’ x a vector to which the Z axis will be rotated. a point to which the Origin will be translated. the scale of the turbulence noise, and the factor to multiply that noise. the ’frequency’ of the marble layers. ncontour: ’W’ w ’C’ r g b the ’width’ of contour. the color of the contour in RGB betweeo zero and one (”C 1 1 1” fully is white). orange: ’d’ x the ’depth’ of the bumps on the bump-mapping. wood: ’z’ x y z ’o’ x y z ’b’ x ’c’ f s ’w’ n f ’f’ x ’r’ f s a vector to which Z axis will be rotated. a point to which the Origin will be translated. the brightness of the wood color scaling, should be between 0 and 1. the scale of the noise in the wood center axis and the factor by which to multiply that noise. the number of angles to sample noise when creating distortion in the circle shape of the wood cylinders, and the factor by which to multiply that noise. the ’frequency’ of the wood cylinders. the scale of the wood-ﬁbers noise, and the factor by which to multiply that noise. punky: ’b’ x the brightness/saturation of the punky color. More Examples: attrib( Obj1, "texture", "marble, 2, t 3.0 12.0, f 7.0" ); attrib( Obj2, "texture", "contour, 1 0.5 2.5, W 0.004, C 1 1 0" ); sets Obj1 to have a marble procedural texture with a uniform scaling factor of 2, and new turbulance and frequency factors. This also sets a contouring texture for Obj2 with scaling factors of (1, 0.5, 2.5) in x, y, and z, in yellow color and width 0.004. G. Elber IRIT Solid modeler 310 In addition, a scalar surface spanning the same parameteric domain as an original surface may be used as a texture mapping function. Herein, the scalar function texture is evaluated at each UV parameter value and is mapped through a color scale to yield the output color. This type of texture is useful for stress maps or analysis maps on top of freeform surfaces. Several related attributes are supported: ”stexture scale” which prescribes the color scale image (only its ﬁrst column is employed), and ”stexture bound” that sets the domain that will be clipped to the min max values. Funally, ”stexture func” can hold the functions ”sqrt” or ”abs” to be applied to the evaluated surface value. Example: attrib( attrib( attrib( attrib( Srf, Srf, Srf, Srf, "stexture", scrvtr( Srf, P1, off ) ); "stexture_scale", "color_scale.ppm" ); "stexture_func", "sqrt" ); "stexture_bound", "0.0 100.0" ); where scrvtr computes a scalar ﬁeld to Srf that represents the sum of the squares of the principle curvatures. The evaluated scalar texture surface’s value is piped through a sqrt function. The ﬁrst column of the image of color scale.ppm is used to set the coloring scale for curvature bounds values between 0.0 and 100.0. Both ”stexture scale” and ”stexture bound” are optional. The default color scale maps the min/max values from blue to red through green. The default scalar surface texture bound is computed as the extreme values of the ”stexture” surface. While the program has a default for lighting which is two light sources at opposite directions at (1, 1, 1) and (-1, -1, -1), one can overwrite this default. A POINT TYPE object with LIGHT SOURCE attribute denotes a light source. If irender detects one or more light sources in the input stream, the default light sources are not created. Two types of light sources may be prescribed, a parallel at inﬁnity or a point at a ﬁnite distance light source, distinguished by a TYPE attribute of either POINT POS or POINT INFTY. A point light source can be colored; an RGB attribute will set its (diﬀuse) color. Specular color defaults to white but can be set via the ”SpecRGB” attribute. Ambient color defaults to black but can be set via the ”AmbtRGB” attribute. A point light source will cast shadows, if and only if, it has a SHADOW attribute (one needs to apply the ’-S’ command line option as well for rendering shadows). Finally, one can construct two mirrored light sources at opposite directions if the TWOLIGHT attribute is added to the light source object. Example: Light1 = point( attrib( Light1, attrib( Light1, attrib( Light1, attrib( Light1, 0, 0, 10 ); "light_source", on ); "shadow", on ); "rgb", "255,0,0" ); "type", "point_pos" ); Light2 = point( attrib( Light2, attrib( Light2, attrib( Light2, 1, 1, 1 ); "light_source", on ); "twolight", on ); "type", "point_infty" ); constructs two lights sources with Light1 with red color positioned at (0, 0, 10) and casting shadows, while Light2 will create two mirrored white parallel lights sources in the direction of (1, 1, 1) and (-1, -1, -1), as its irender’s default. Visibility Maps IRIT Solid modeler G. Elber 311 if the -V option is selected, the output will be a visibility map. Visibility maps are created in the model’s UV (texture) space and are composed of 4 colors: • White: if pixel isn’t mapped. I.e. the model UV’s map does not cover this pixel • Green: if the pixel is a (UV location of a Eculidean) visible location. • Red: if pixel is (UV location of a Eculidean) invisible location. • Yellow: if large errors are detected while calculating pixel’s visibility. This indeterministic result is due to almost vertical polygns, typically. Tips for geting higher quality visibility map: 1. Use the -s option for larger output resolution. 2. Use the -F option for ﬁner polygonal sampling of surfaces. Controlling the output can also be done by object attributes, as follow: Use the ’tan angle’ property to change the yellow area of output. A rendered triangle will be colored in yellow if it’s surface is close to being vertical, or tangent to the view, z, axis. Change the ’tan angle’ property to get maximal value of normalized scalar product of triangle normal and z axis. Below that value the triangle will be colored yellow. Default value: 0.1. Example: attrib( Obj1, "tan\_angle", 0.1 ); Use ’critic ar’ to change the unmapped area of output. Poor aspect ratio of triangles leads to major errors. Aspect ratio is deﬁned as the ratio of largest edge by the smallest edge of triangle. Any triangle with aspect ratio larger than ’critic ar’ will not be mapped. Default value: 20. attrib( Obj2, "critic_ar", 20 ); 22 3DS2Irit - AutoCad 3DS Data To IRIT ﬁle ﬁlter Converts ’.3ds’ data ﬁles to ’.itd’ IRIT data ﬁles. 22.1 Command Line Options 3ds2Irit [-m] [-c ClrScale] [-o OutName] [-b] [-z] 3DSFile • -m: More information ﬂag. • -c ClrScale: Scaling the color values (intensity control). • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -b: If set, generates a binary IRIT data ﬁle that holds the strokes. Otherwise, an IRIT text ﬁle will be created. • -z: Print version number and current defaults. 22.2 Usage 3ds2irit converts Autocad’s 3DS data ﬁles into IRIT data ﬁles. The current version provides only partial support, mainly due to lack of documentation examples on the dxf format and the convoluted way freeform surfaces are saved. Example: 3ds2irit file.3ds > file.itd IRIT Solid modeler 23 G. Elber 312 Dat2Bin - Data To Binary Data ﬁle ﬁlter 23.1 Command Line Options dat2bin [-t] [-z] {[-c QuantVal]} DFiles • -t: Dumps data to stdout as text instead of binary. -z: Print version number and current defaults. -c: Optional option that is available only if compressed binary ﬁles are supported. Dumps data to stdout as compressed binary ﬁle with a quanitization level of QuantVal. 23.2 Usage The user may sometimes wish to convert .itd data ﬁles into a binary form, for example, for fast loading of ﬁles with large geometry. Binary ﬁles can be somewhat larger and are unreadable in editors but are much faster to load. A binary ﬁle must have a ’.ibd’ ﬁle type. Example: dat2bin b58polys.itd > b58polys.ibd dat2bin -t b58polys.ibd | more The above converts a text ﬁle b58polys.itd into a binary ﬁle b58polys.ibd and shows the content of the binary ﬁle by converting it back to text. At this time data through pipes must be in text. That is, the following is illegal: dat2bin b58polys.itd | xglmdrvs It should be remembered that the binary format is not documented and it might change in the future. Moreover, it is machine dependent and can very well may be unreadable between diﬀerent platforms. 24 Dat2Irit - Data To IRIT ﬁle ﬁlter Converts ’.itd’ and ’.ibd’ data ﬁles to ’.irt’ IRIT scripts. Optionally, if compressed binary ﬁles are supported, also handle ’.icd’ compressed data ﬁles. 24.1 Command Line Options dat2irit [-z] DFiles • -z: Print version number and current defaults. 24.2 Usage Users may sometimes wish to convert .itd data ﬁles into a form that can be fed back to IRIT - a ’.irt’ ﬁle. This ﬁlter does exactly that. Example: dat2irit b58.itd > b58-new.irt IRIT Solid modeler 25 G. Elber 313 Dxf2Irit - DXF (Autocad) To IRIT ﬁlter Converts Autocad’s, DXF data ﬁles into IRIT data ﬁles. 25.1 Command Line Options dxf2irit [-m] [-f] [-o OutName] [-z] DXFFile • -m: Provides some more information on the data ﬁle(s) parsed. • -f: Coerces ﬂoating end conditions to constructed freeform surfaces. Default is open end conditions. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -z: Prints version number and current defaults. 25.2 Usage dxf2irit converts Autocad’s DXF data ﬁles into IRIT data ﬁles. The current version provides only partial support for the conversion of freeform surfaces, mainly due to lack of documentation examples on the dxf format and the convoluted way freeform surfaces are saved. Example: dxf2irit file.dxf > file.itd 26 IGS2Irit - IGES Data To IRIT ﬁle ﬁlter Converts ’.igs’ data ﬁles to ’.itd’ IRIT data ﬁles. 26.1 Command Line Options IGS2Irit [-m] [-M] [-c] [-a] [-s] [-o OutName] [-b] [-z] IGSFile • -m: More information ﬂag. • -M: Even more information ﬂag - dumps all parsed entities. • -c: Clips trimmed surfaces to the minimal domain as prescribed by the trimming curves. • -a: Dumps all. Without this ﬂag setting, only top level objects, that are referenced by no other object, will be dumped out. • -s: Dumps surfaces only. When set only (trimmed) surfaces are dumped. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -b: If set, generates a binary IRIT data ﬁle that holds the data. Otherwise, an IRIT text ﬁle will be created. • -z: Print version number and current defaults. IRIT Solid modeler 26.2 G. Elber 314 Usage igs2irit converts IGES data ﬁles into IRIT data ﬁles. Example: igs2irit file.igs > file.itd 27 Iirit23js - IRIT To ThreeJS ﬁlter 27.1 Command Line Options irit23JS [-l] [-4] [-p] [-F PolyOpti FineNess] -i InName -o OutName [-T] [-t AnimTime] [-z] • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -p: for perspective camera, or orthographic camera otherwise. • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. Default FineNess is 20. • -o OutName: Specify the ﬁle path to the output ﬁle. • -i InName: Specify the ﬁle path to the input ﬁle. • -T: Talkative mode. Prints processing information. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. 27.2 Usage Irit23js extracts the relevant data from Irit object ﬁles and converts the object’s polygon data to a format that can be loaded into THREE.js via JSON ﬁle (see http://json.org/). The result is an HTML ﬁle that can be used to view the Irit model in various web browsers (Internet Explorer, Google Chrome, Firefox, Safari, etc), with help from THREE.js, and using WebGL rendering. Four ﬁles are created in all: three with a ’.js’ (JavaScript) extension and one with an ’.html’ extension. Two of the JavaScript ﬁles are required in order for the viewer to function properly. The ﬁrst is ’irit23js.js’, which is a version of the THREE.js library, and the second is ’iritOC.js’, which is a THREE.js (Orbit Controls) library that allows the user to pan, orbit, and zoom within the viewer. These two ﬁles can be obtained by downloading the package from the ’download’ link on the three.js website (see http://threejs.org/). The last JavaScript ﬁle is the actual geometry output ﬁle that is written in JSON (JavaScript Object Notation) format, and contains the polygon data for each object. Polygon data exists in this JSON ﬁle as vertices, materials, textures, normals, colors, UVs, and faces IRIT Solid modeler G. Elber 315 (refer to https://github.com/mrdoob/three.js/wiki/JSON-Model-format-3 for an explanation of this formatting). The HTML ﬁle allows the user to directly view the model in the browser, as well as manipulate it with the mouse and arrow keys if so desired. In order to view the model in a web browser, the ﬁles must be uploaded to a website, and all four of them should be placed in the same web directory. This is the intended use, but if a user would like to view the model from his/her ﬁle system, the HTML ﬁle must be opened with Firefox or run locally through any web browser (IE, Firefox, Chrome, Safari, etc). This restriction is a consequence of the same-origin policy. A user attempting this second option should take a look at the methods listed on this page: https://github.com/mrdoob/three.js/wiki/How-to-run-things-locally. If a model contained a texture in Irit, its image name within irit23js has been modiﬁed to end with a ’.jpg’ extension, if it wasn’t already an image of that type. If the user wishes to see a texture displayed on the model, the texture image must be placed in the same directory as the above four output ﬁles, and its name must match the one speciﬁed in the JavaScript ﬁle written in JSON (look for the ’materials’ property and the ’mapDiﬀuse’ attribute). Example: irit23js -l -F 0 5 -i C:/irit/data/b58.itd -o C:/irit/b58.js creates b58.js, b58Viewer.html, irit3js.js, and iritOC.js. The model is created with low resolution (FineNess of 5). At such low resolution, it may very well happen that triangles will have normals ”over the edge” since a single polygon may approximate a highly curved surface. This problem will not arise if high ﬁneness is used: irit23js -l -F 0 30 -i C:/irit/data/b58.itd -o C:/irit/b58.js creates ir b58.js, ir b58Viewer.html, irit3js.js, and iritOC.js. The model is created with high resolution (FineNess of 30), so it will have smooth curves and surfaces. 27.3 Advanced Usage One can specify surface qualities for individual surfaces of a model. Several such attributes are supported by irit23js and can be set within IRIT. See also the ATTRIB IRIT command. Example: attrib( srf1, "resolution", 2 ); will force srf1 to have twice the default resolution, as set via the ’-F’ ﬂag. Almost ﬂat patches are converted to polygons. The rectangle can be converted into two polygons (by subdividing along one of its diagonals) or into four by introducing a new point at the patch center. This behavior is controlled by the ’-4’ ﬂag, but can be overwritten for individual surfaces by setting ”twoperﬂat” or ”fourperﬂat”. irit23js speciﬁc properties are controlled via the following attributes: ”transp” and ”ptexture”. The value of these attributes must be strings as it is copied verbatim. Example: attrib( legs, "transp", "0.3" ); attrib( legs, "ptexture", "wood.jpg,2" ); attrib( table, "ptexture", "marble.jpg" ); An optional scale can be prescribed to textures. In the above example wooden legs’ (that are also transparent...) texture is selected with a texture scaling factor of 2. Surface color is controlled on two levels. If the object has an RGB attribute, it is used. Otherwise a color as set via the IRIT COLOR command is used, if set. Example: IRIT Solid modeler G. Elber 316 attrib( tankBody, "rgb", "244,164,96" ); 28 Irit2Dxf - IRIT To DXF (Autocad) ﬁlter Converts IRIT data ﬁles into Autocad’s, DXF data ﬁles. 28.1 Command Line Options irit2dxf [-s Scale] [-t Tx Ty Tz] [-i] [-f] [-F PolyOpti FineNess] [-4] [-o OutName] [-T] [-a AnimTime] [-z] DFiles • -s Scale: Global scaling factor of the converted geometry. • -t Tx Ty Tz: a Vector of size three of translation factors along the X, Y, and Z axes. • -i: Shows internal edges as well. • -f: Dumps freeforms as converted polygonal geometry. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -4: Forces four polygons per almost ﬂat region in the surface to polygon conversion. Otherwise two polygons only. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -T: Talkative mode. Prints processing information. • -a AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. 28.2 Usage irit2dxf converts IRIT data ﬁles into Autocad’s DXF data ﬁles. The current version provides only partial support for the direct conversion of freeform surfaces, mainly due to lack of documentation examples on the dxf format and the convoluted way freeform surfaces are saved. Nonetheless, freeform surfaces can be converted into polygons using the ’-f’ ﬂag. Example: irit2dxf -z -t 1 2 3 -F 0 20 -4 -o file.dxf file.itd 29 Irit2Hgl - IRIT To HPGL ﬁlter Converts IRIT geometry into the HL Graphics Language used by HP’s plotters. IRIT Solid modeler 29.1 G. Elber 317 Command Line Options irit2hgl [-t XTrans YTrans] [-I #UIso[:#VIso[:#WIso]]] [-f PolyOpti SampTol] [-F PolyOpti FineNess] [-M] [-G] [-T] [-a AnimTime] [-i] [-o OutName] [-z] DFiles • -t XTrans YTrans: X and Y translation. of the image. Default is (0, 0). • -I #UIso[:#VIso[:#WIso]]: Speciﬁes the number of isolines per surface/trivariate, per direction. If #VIso is not speciﬁed, #UIso is used for #VIso as well and so no. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. This enforces the dump of freefrom geometry as polygons. • -M: Dumps the control mesh/polygon as well. • -G: Dumps the freeform geometry. • -T: Talkative mode. Prints processing information. • -a AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -i: Internal edges (created by IRIT) - default is not to display them, and this option will force their display. • -o OutName: Name of output ﬁle. By default the name of the ﬁrst data ﬁle from DFiles list is used. See below on the output ﬁles. • -z: Prints version number and current defaults. 29.2 Usage Irit2Hgl converts freeform surfaces and polygons into polylines in a format that can be used by HPGL. Example: irit2Hgl -M -f 0 16 saddle.itd > saddle.hgl However, one can overwrite the viewing matrix by appending a new matrix in the end of the command line, created by the display devices: x11drvs b58.itd irit2Hgl -M -f 0 16 b58.itd irit.imd > saddle.hgl where irit.imd is the viewing matrix created by x11drvs. IRIT Solid modeler 30 G. Elber 318 Irit2IGS - IRIT To IGES ﬁlter Converts IRIT data ﬁles into IGES/IGS data ﬁles. 30.1 Command Line Options Irit2igs [-m] [-o OutName] [-t AnimTime] [-u] [-z] IritFile • -m: More information ﬂag. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -t AnimTime: If has animation data, time of dump. • -u: Forces a unit transformation matrix. • -z: Prints version number and current defaults. 30.2 Usage Irit2IGS converts IRIT data ﬁles into IGES data ﬁles. Example: Irit2IGS -u -o file.igs file.itd 31 Irit2Iv - IRIT To SGI’s Inventor ﬁlter IV is the format used by the Inventor modeling/rendering package from SGI. 31.1 Command Line Options irit2iv [-l] [-4] [-P] [-F PolyOpti FineNess] [-f PolyOpti SampTol] [-T] [-t AnimTime] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -P: Polygonize freeform shapes. Default is to leave freeform curves and surfaces as is. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). IRIT Solid modeler G. Elber 319 • -T: Talkative mode. Prints processing information. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. 31.2 Usage Irit2Iv converts freeform surfaces and polygons into polygons and saved in iv Inventor’s ASCII ﬁle format. Example: irit2iv solid1.itd > solid1.iv Surfaces are converted to polygons with ﬁneness control: irit2iv -F 0 16 - view.imd < saddle.itd > saddle.iv Note the use of ’-’ for stdin. 32 Irit2Nﬀ - IRIT To NFF ﬁlter 32.1 Command Line Options irit2nff [-l] [-4] [-c] [-F PolyOpti FineNess] [-o OutName] [-T] [-t AnimTime] [-g] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -c: Output ﬁles should be ﬁltered by cpp. When set, the usually huge geometry ﬁle is separated from the main nﬀ ﬁle that contains the surface properties and view parameters. By default all data, including the geometry, are saved into a single ﬁle with type extension ’.nﬀ’. Use of ’-c’ will pull out all the geometry into a ﬁle with the same name but a ’.geom’ extension, which will be included using the ’#include’ command. The ’.nﬀ’ ﬁle should, in that case, be preprocessed using cpp before being piped into the nﬀ renderer. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -o OutName: Name of output ﬁle. By default the name of the ﬁrst data ﬁle from the DFiles list is used. See below on the output ﬁles. • -T: Talkative mode. Prints processing information. IRIT Solid modeler G. Elber 320 • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -g: Generates the geometry ﬁle only. See below. • -z: Prints version number and current defaults. 32.2 Usage Irit2Nﬀ converts freeform surfaces into polygons in a format that can be used by an NFF renderer. Usually, one ﬁle is created with the ’.nﬀ’ type extension. Since the number of polygons can be extremely large, a ’-c’ option is provided, which separates the geometry from the surface properties and view speciﬁcation, but requires preprocessing by cpp. The geometry is isolated in a ﬁle with the extension ’.geom’ and included (via ’#include’) in the main ’.nﬀ’ ﬁle. The latter holds the surface properties for all the geometry as well as the viewing speciﬁcation. This allows for the changing of the shading or viewing properties while editing small (’.nﬀ’) ﬁles. If ’-g’ is speciﬁed, only the ’.geom’ ﬁle is created, preserving the current ’.nﬀ’ ﬁle. The ’-g’ ﬂag can be speciﬁed only with ’-c’. In practice, it may be useful to create a low resolution approximation of the model, change viewing/shading parameters in the ’.nﬀ’ ﬁle until a good view and/or surface quality is found, and then run Irit2Nﬀ once more to create a high resolution approximation of the geometry using ’-g’. Example: irit2nff -c -l -F 0 8 b58.itd creates b58.nﬀ and b58.geom with low resolution (FineNess of 5). Once done with parameter setting, a ﬁne approximation of the model can be created with: irit2nff -c -l -g -F 0 64 b58.itd which will only recreate b58.geom (because of the -g option). One can overwrite the viewing matrix by appending a new matrix in the end of the command line, created by a display device: xgldrvs b58.itd irit2nff -l -F 0 32 b58.itd irit.imd where irit.imd is the viewing matrix created by xgldrvs. 32.3 Advanced Usage One can specify surface qualities for individual surfaces of a model. Several such attributes are supported by Irit2Nﬀ and can be set within IRIT. See also the ATTRIB IRIT command. If a certain surface should be ﬁner/coarser than the rest of the scene, one can set a ”resolution” attribute which speciﬁes the relative FineNess resolution of this speciﬁc surface. Further, ”u resolution” and ”v resolution” might be similarly used to set relative resolution for the u or v direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. Example: attrib( srf1, "resolution", 2 ); IRIT Solid modeler G. Elber 321 will force srf1 to have twice the default resolution, as set via the ’-f’ ﬂag. Almost ﬂat patches are converted to polygons. The rectangle can be converted into two polygons (by subdividing along one of its diagonals) or into four by introducing a new point at the center of the patch. This behavior is controlled by the ’-4’ ﬂag, but can be overwritten for individual surfaces by setting a ”twoperﬂat” or a ”fourperﬂat” attribute. NFF speciﬁc properties are controlled via the following attributes: ”kd”, ”ks”, ”shine”, ”trans”, ”index”. Refer to the NFF manual for detail. Example: attrib( srf1, "kd", 0.3 ); attrib( srf1, "shine", 30 ); Surface color is controlled on two levels. If the object has an RGB attribute, it is used. Otherwise, a color, as set via the IRIT COLOR command, is used if set. Example: attrib( tankBody, "rgb", "244,164,96" ); 33 Irit2Oﬀ - IRIT To OFF ﬁlter Converts IRIT data ﬁles into OFF data ﬁles. 33.1 Command Line Options Irit2Off [-l] [-4] [-n] [-F PolyOpti FineNess] [-E VrtxEps] [-o OutName] [-m] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -n: Vertex Normals - Dumps the normals of the vertices with the coordinates. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -E VrtxEps: Epsilon to consider two vertices same. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -m: More information ﬂag. • -z: Prints version number and current defaults. IRIT Solid modeler 33.2 G. Elber 322 Usage Irit2Oﬀ converts IRIT data ﬁles into Geom View OFF data ﬁles. Example: Irit2Off -m -o file.off file.itd 34 Irit2Plg - IRIT To PLG (REND386) ﬁlter PLG is the format used by the rend386 real time renderer for the IBM PC. 34.1 Command Line Options irit2plg [-l] [-4] [-F PolyOpti FineNess] [-T] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -T: Talkative mode. Prints processing information. • -z: Prints version number and current defaults. 34.2 Usage Irit2Plg converts freeform surfaces and polygons into polygons in a format that can be used by the REND386 renderer. Example: irit2plg solid1.itd > solid1.plg Surfaces are converted to polygons with ﬁneness control: irit2plg -F 0 16 - view.imd < saddle.itd > saddle.plg Note the use of ’-’ for stdin. 35 35.1 Irit2pov - IRIT To POVRAY raytracer ﬁlter Command Line Options irit2pov [-l] [-4] [-C] [-F PolyOpti FineNess] [-f PolyOpti SampTol] [-o OutName] [-g] [-p Zmin Zmax] [-P] [-M] [-T] [-t AnimTime] [-I #UIso[:#VIso[:#WIso]]] [-s ObjSeq#] [-i Includes] [-z] DFiles IRIT Solid modeler G. Elber 323 • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -C: Constructs bicubic Bezier patches whenever possible as POVRAY supports this type of surface. Polynomial Bezier surfaces of orders up to and including bicubic (order 4, degree 3) are degree raised to bicubic. Piecewise polynomials B-spline surfaces are split into Bezier patches. Higher order surfaces and rational surfaces are always converted into polygons. • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4, -C, and -l. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -o OutName: Name of output ﬁle. By default the name of the ﬁrst data ﬁle from the DFiles list is used. See below on the output ﬁles. • -g: Generates the geometry ﬁle only. See below. • -p Zmin Zmax: Sets the ratios between the depth cue and the width of the dumped polylines. See also -P. Closer lines will be drawn wider. • -P: Forces dumping polygons as polylines with thickness controlled by -p. • -M: If -P (see -P and -p), then convert the control mesh/polygon to polylines which are represented as a sequence of truncated cones. • -T: Talkative mode. Prints processing information. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -I #UIso[:#VIso[:#WIso]]: Speciﬁes the number of isolines per surface/trivariate, per direction. If #VIso or #WIso is not speciﬁed, #UIso is used for #VIso etc. • -s ObjSeq#: Sets object sequence number if there is no object name. Default 1. • -i Includes: Expands the comma’s separated list of POVRAY include ﬁle names into POVRAY include commands at the beginning of the created POVRAY output ﬁle. • -z: Prints version number and current defaults. IRIT Solid modeler 35.2 G. Elber 324 Usage Irit2pov converts freeform surfaces into polygons in a format that can be used by the POVRAY ray tracing program. Two ﬁles are created, one with a ’.geom’ extension and one with a ’.pov’ extension. Since the number of polygons can be extremely large, the geometry is isolated in the ’.geom’ ﬁle and is included (via ’#include’) in the main ’.pov’ ﬁle. The latter holds the surface properties for all the geometry as well as viewing and POVRAY speciﬁc commands. This allows for the changing of the shading or the viewing properties while editing small (’.pov’) ﬁles. If ’-g’ is speciﬁed, only the ’.geom’ ﬁle is created, preserving the current, possibly manually modiﬁed, ’.pov’ ﬁle. In practice, it may be useful to create a low resolution approximation of the model, change the viewing/shading parameters in the ’.pov’ ﬁle until a good view and/or surface quality is found, and then run Irit2pov once more to create a high resolution approximation of the geometry using ’-g’. Example: irit2pov -l -F 0 5 b58.itd creates b58.pov and b58.geom with low resolution (FineNess of 5). At such low resolution it may very well happen that triangles will have normals ”over the edge” since a single polygon may approximate a highly curved surface. One can ray trace this scene using a command similar to: POVRAY -Q0 +Ib58 Once done with a parameter setting for POVRAY, a ﬁne approximation of the model can be created with: irit2pov -l -g -F 0 64 b58.itd which will only recreate b58.geom (because of the -g option). Interesting eﬀects can be created using the depth cue support and polyline conversion of irit2pov. For example, irit2pov -P -p -0.0 0.5 solid1.itd will dump solid1 as a set of polylines (represented as truncated cones in POVRAY) with varying thickness according to the z depth. Another example is irit2pov -P -p -0.1 1.0 saddle.itd which dumps the isolines extracted from the saddle surface with varying thickness. Each time a data ﬁle is saved in IRIT, it can be saved with the viewing matrix of the last INTERACT by saving the VIEW MAT object as well. I.e.: save( "b58", b58 ); However, one can overwrite the viewing matrix by appending a new matrix in the end of the command line, created by the display devices: xglmdrvs b58.itd irit2pov -l -F 0 16 b58.itd irit.imd // Also creates irit.imd where irit.imd is the viewing matrix created by xglmdrvs. The output name, by default, is the last input ﬁle name, so you might want to provide an explicit name with the -o ﬂag. IRIT Solid modeler 35.3 G. Elber 325 Advanced Usage One can specify surface qualities for individual surfaces of a model. Several such attributes are supported by Irit2pov and can be set within IRIT. See also the ATTRIB IRIT command. If a certain surface should be ﬁner/coarser than the rest of the scene, one can set a ”resolution” attribute which speciﬁes the relative FineNess resolution of this speciﬁc surface. Further, ”u resolution” and ”v resolution” might be similarly used to set relative resolution for the u or v direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. Example: attrib( srf1, "resolution", 2 ); will force srf1 to have twice the default resolution as set via the ’-f’ ﬂag. Almost ﬂat patches are converted to polygons. The rectangle can be converted into two polygons (by subdividing along one of its diagonals) or into four by introducing a new point at the patch center. This behavior is controlled by the ’-4’ ﬂag, but can be overwritten for individual surfaces by setting ”twoperﬂat” or ”fourperﬂat”. POVRAY also supports bicubic Bezier patches and the ’-C’ option of irit2pov supports that. In such a case, the resolution that is requested from POVRAY to polygonize these patches approximately follows the resolution as selected via the ’-F’ ﬂag of irit2pov. Nevertheless, one can override the requested resolution via the ”steps”, ”u steps”, and ”v steps” attributes to irit2pov data ﬁles that are transferred directly to POVRAY’s bicubic Bezier patches. The ”steps” attributes sets both ”u steps” and ”v steps”. While the program has a default for lighting which is a point light source at (1, 2, 10), one can overwrite this default. A POINT TYPE object with LIGHT SOURCE attribute in the data stream denotes a light source. If irit2pov detects one or more light sources in the input stream, the default light sources are not created. A point light source can be colored, when an RGB attribute will set its color. Example: l1 - point( 5, 5, 5 ); attrib( l1, "rgb", "255, 0, 0" ); creates a red light source at (5, 5, 5). POVRAY speciﬁc properties are controlled via the following attributes: ”ambient”, ”diﬀuse”, ”brilliance”, ”phong”, ”phong size”, ”specular”, ”roughness”, ”metallic”, ”reﬂection”, ”crand”, ”conserve energy”, ”irid”, ”ior”, ”caustics”, ”dispersion”, ”dispersion samples”, ”fade distance”, ”fade power”, ”fade color”. One can prescribe a whole property block of POV attributes via the ”texture”, ”pigment”, ”ﬁnish”, ”halo”, and ”normal”. The values of this attributes must be strings as they are copied verbatim. Refer to POVRAY’s manual for their exact meaning. Example: attrib( attrib( attrib( attrib( legs, "ambient", 0.1 ); pot, "matallic", "" ); table, "ior", 1.4 ); bird, "finish", "ambient 0 diffuse 1 specular 1" ); Surface color is controlled on two levels. If the object has an RGB attribute, it is used. Otherwise a color as set via the IRIT COLOR command is used, if set. Example: IRIT Solid modeler G. Elber 326 attrib( tankBody, "rgb", "244,164,96" ); Transparency is controlled via the ”transp” attribute, with values between zero and one. Example: attrib( Glass, "transp", 0.9 ); 36 Irit2Ps - IRIT To PS ﬁlter 36.1 Command Line Options irit2ps [-l] [-4] [-s Size] [-I #UIso[:#VIso[:#WIso]]] [-F PolyOpti FineNess] [-f PolyOpti SampTol] [-M] [-G] [-P] [-W LineWidth] [-w WidenLen WidenWidth] [-b R G B] [-B X1 Y1 X2 Y2] [-c] [-C] [-T] [-t AnimTime] [-N FontName] [-i] [-o OutName] [-d [Zmin Zmax]] [-D [Zmin Zmax]] [-p PtType PtSize] [-u] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -s Size: Controls the size of the postscript output in inches. Default is to ﬁll the entire screen. • -I #UIso[:#VIso[:#WIso]]: Speciﬁes the number of isolines per surface/trivariate, per direction. If #VIso or #WIso is not speciﬁed, #UIso is used for #VIso etc. • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -M: Dumps the control mesh/polygon as well. • -G: Dumps the curve/surface (as freeform geometry). Default. See -I, -C, -f for control on polyline approximation. • -P: Dumps the curve/surface (as polygons). See -F, -l, -4 for control on polygonal approximation. • -W #LineWidth: Sets the line drawing width in inches. Default is as thin as possible. This option will overwrite only those objects that do not have a ”width” attribute. See also -d. If LineWidth is negative, its absolute value is used to scale the current width of the object if it has one, or the default width otherwise. • -w WidenLen WidenWidth: Widens the end points of polylines if they should be made wider, and if so, to what width. IRIT Solid modeler G. Elber 327 • -b R G B: Sets a colored background. RGB are three integers prescribing the Red, Green, and Blue coeﬃcients. If there is no -c (i.e. a gray level drawing), this color is converted to a gray level using RGB to T.V. Y(IQ) channel conversion. • -B X1 Y1 X2 Y2: Clips the drawing area outsize the bounding box from (X1, Y1) to (X2, Y2). • -c: Creates a color postscript ﬁle. • -C: Curve mode. Dumps freeform curves and surfaces as cubic Bezier curves. Higher order curves and surfaces and/or rationals are approximated by cubic Bezier curves. This option generates data ﬁles that are roughly a third of piecewise linear postscript ﬁles (by disabling this feature, -C-), but it takes a longer time to compute. • -T: Talkative mode. Prints processing information. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -N FontName: Sets the font to use when dumping text out of string objects. • -i: Internal edges (created by IRIT) - the default is not to display them, and this option will force displaying them as well. • -o OutName: Name of output ﬁle. Default is stdout. • -d [Zmin Zmax]: Sets the ratios between the depth cue and the width of the dumped data. See also -W, -p. Closer lines/points will be drawn wider/larger. Zmin and Zmax are optional. The object’s bounding box is otherwise computed and used. • -D [Zmin Zmax]: Same as -d, but depth cue the color or gray scale instead of width. You might need to consider the sorting option of the illustrt tool (-s of illustrt) for proper drawings. Only one of -d and -D can be used. • -p PtType PtSize: Speciﬁes the way points are drawn. PtType can be one of H, F, C for Hollow circle, Full Circle, or Cross. PtSize speciﬁes the size of the point to be drawn, in inches. Vectors will also be drawn as points, but with an additional thin line to the origin. See also -d. • -u: Forces a unit matrix transformation, i.e. no transformation. • -z: Prints version number and current defaults. 36.2 Usage Irit2Ps converts freeform surfaces and polygons into a postscript ﬁle. Example: irit2ps solid1.itd > solid1.ps Surfaces are converted to polygons with ﬁneness control: irit2ps -f 0 32 -c -W 0.01 saddle.itd > saddle.ps creates a postscript ﬁle for the saddle model, in color, and with lines 0.01 inch thick. IRIT Solid modeler 36.3 G. Elber 328 Advanced Usage One can specify several attributes that aﬀect the way the postscript ﬁle is generated. The attributes can be generated within IRIT. See also the ATTRIB IRIT command. If a certain object should be thinner or thicker than the rest of the scene, one can set a ”width” attribute which speciﬁes the line width in inches of this speciﬁc object. Example: attrib( srf1, "width", 0.02 ); will force srf1 to have this width, instead of the default as set via the ’-W’ ﬂag. If a (closed) object, a polygon, for example, needs to be ﬁlled, a ”ﬁll” attribute should be set. Example: attrib( poly, "fill", true ); will ﬁll poly. If an object, a polygon, for example, needs to be painted/ﬁlled in a gray level instead of black, a ”gray” attribute should be set, with a value equal to the gray level desired. Example: attrib( poly, "gray", 0.5 ); will draw/ﬁll poly with %50 gray. Dotted or dashed line eﬀects can be created using a ”dash” attribute which is a direct postScript dash string. A simple form of this string is ”[a b]” in which a is the drawing portion (black) in inches, followed by b inches of white space. See the postScript manual for more about the format of this string. Here is an example for a dotted-dash line. attrib( poly, "dash", "[0.006 0.0015 0.001 0.0015] 0" ); Surface color is controlled (for color postscript only - see -c) on two levels. If the object has an RGB attribute, it is used. Otherwise, a color as set via the IRIT COLOR command is used. Example: attrib( Ball, "rgb", "255,0,0" ); An object can be drawn as ”tubes” instead of full lines. The ratio between the inner and the outer radii of the tube is provided as the TUBULAR attribute: attrib( final, "tubular", 0.7 ); The depth cueing option of irit2ps could be disabled for individual objects by placing an integer attribute ”DepthCue” with the FALSE value: attrib( final, "DepthCue", FALSE ); IRIT Solid modeler G. Elber 329 The ”resolution” attribute controls the relative ﬁneness of polygonal approximation of surfaces, and ”u resolution” and ”v resolution” similarly control this relative ﬁneness along one parametric direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. A string object can be dumped as text of a selected PS font (See -N). The string position is set via a ”StrPos” vector attribute (default to the origin), and ”StrScale” real attribute to control the string height in world unit (default to 0.1). Text will always be dumped horizontally. Example: Text = "Some text"; attrib( Text, "StrPos", vector( 1, 2, 3 ) ); attrib( Text, "StrScale", 0.1 ); Will print the Text ”Some text” at location (1, 2, 3). The text height be be 0.1. 37 Irit2Ray - IRIT To RAYSHADE ﬁlter 37.1 Command Line Options irit2ray [-l] [-4] [-G GridSize] [-F PolyOpti FineNess] [-f PolyOpti SampTol] [-o OutName] [-g] [-p Zmin Zmax] [-P] [-M] [-T] [-t AnimTime] [-I #UIso[:#VIso[:#WIso]]] [-s ObjSeq#] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -G GridSize: Usually objects are grouped as lists of polygons. This ﬂag will coerce the usage of the RAYSHADE grid structure, with GridSize being used as the grid size along the object bounding box’s largest dimension. • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -o OutName: Name of output ﬁle. By default, the name of the ﬁrst data ﬁle from the DFiles list is used. See below on the output ﬁles. • -g: Generates the geometry ﬁle only. See below. • -p Zmin Zmax: Sets the ratios between the depth cue and the width of the dumped polylines. See also -P. Closer lines will be drawn wider. IRIT Solid modeler G. Elber 330 • -P: Forces dumping polygons as polylines with thickness controlled by -p. • -M: If -P (see -P and -p), will then convert the control mesh/polygon to polylines which are represented as a sequence of truncated cones. • -T: Talkative mode. Prints processing information. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -I #UIso[:#VIso[:#WIso]]: Speciﬁes the number of isolines per surface/trivariate, per direction. If #VIso or #WIso is not speciﬁed, #UIso is used for #VIso etc. • -s ObjSeq#: Sets object sequence number if no object name. Default 1. • -z: Prints version number and current defaults. 37.2 Usage Irit2Ray converts freeform surfaces into polygons in a format that can be used by the RAYSHADE ray tracing program. Two ﬁles are created, one with a ’.geom’ extension and one with a ’.ray’ extension. Since the number of polygons can be extremely large, the geometry is isolated in the ’.geom’ ﬁle and is included (via ’#include’) in the main ’.ray’ ﬁle. The latter holds the surface properties for all the geometry as well as viewing and RAYSHADE speciﬁc commands. This allows for the changing of the shading or viewing properties while editing small (’.ray’) ﬁles. If ’-g’ is speciﬁed, only the ’.geom’ ﬁle is created, preserving the current ’.ray’ ﬁle. In practice, it may be useful to create a low resolution approximation of the model, change the viewing/shading parameters in the ’.ray’ ﬁle until a good view and/or surface quality is found, and then run Irit2Ray once more to create a high resolution approximation of the geometry using ’-g’. Example: irit2ray -l -F 0 5 b58.itd creates b58.ray and b58.geom with low resolution (FineNess of 5). At such low resolution it may very well happen that triangles will have normals ”over the edge” since a single polygon may approximate a highly curved surface. That will cause RAYSHADE to issue an ”Inconsistent triangle normals” warning. This problem will not arise if high ﬁneness is used. One can ray trace this scene using a command similar to: RAYSHADE -p -W 256 256 b58.ray > b58.rle Once done with the parameter setting for RAYSHADE, a ﬁne approximation of the model can be created with: irit2ray -l -g -F 0 64 b58.itd which will only recreate b58.geom (because of the -g option). Interesting eﬀects can be created using the depth cue support and polyline conversion of irit2ray. For example, irit2ray -G 5 -P -p -0.0 0.5 solid1.itd G. Elber IRIT Solid modeler 331 will dump solid1 as a set of polylines (represented as truncated cones in RAYSHADE) with varying thickness according to the z depth. Another example is irit2ray -G 5 -P -p -0.1 1.0 saddle.itd which dumps the isolines extracted from the saddle surface with varying thickness. Each time a data ﬁle is saved in IRIT, it can be saved with the viewing matrix of the last INTERACT by saving the VIEW MAT object as well. I.e.: save( "b58", b58 ); However, one can overwrite the viewing matrix by appending a new matrix in the end of the command line, created by the display devices: os2drvs b58.itd irit2ray -l -F 0 16 b58.itd irit.imd // Also creates irit.imd where irit.imd is the viewing matrix created by os2drvs. The output name, by default, is the last input ﬁle name, so you might want to provide an explicit name with the -o ﬂag. 37.3 Advanced Usage One can specify surface qualities for individual surfaces of a model. Several such attributes are supported by Irit2Ray and can be set within IRIT. See also the ATTRIB IRIT command. If a certain surface should be ﬁner/coarser than the rest of the scene, one can set a ”resolution” attribute which speciﬁes the relative FineNess resolution of this speciﬁc surface. Further, ”u resolution” and ”v resolution” might be similarly used to set relative resolution for the u or v direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. Example: attrib( srf1, "resolution", 2 ); will force srf1 to have twice the default resolution, as set via the ’-f’ ﬂag. Almost ﬂat patches are converted to polygons. The rectangle can be converted into two polygons (by subdividing along one of its diagonals) or into four by introducing a new point at the patch center. This behavior is controlled by the ’-4’ ﬂag, but can be overwritten for individual surfaces bu setting ”twoperﬂat” or ”fourperﬂat”. RAYSHADE speciﬁc properties are controlled via the following attributes: ”specpow”, ”reﬂect”, ”transp”, ”body”, ”index”, and ”texture”. The value of these attributes must be strings as it is copied verbatim. Refer to RAYSHADE’s manual for their meaning. Example: attrib( attrib( attrib( attrib( legs, "transp", "0.3" ); legs, "texture", "wood,2" ); table, "texture", "marble" ); table, "reflect", "0.5" ); IRIT Solid modeler G. Elber 332 An optional scale can be prescribed to textures. In the above example wooden legs’ (that are also transparent...) texture is selected with a texture scaling factor of 2. Surface color is controlled on two levels. If the object has an RGB attribute, it is used. Otherwise a color as set via the IRIT COLOR command is used, if set. Example: attrib( tankBody, "rgb", "244,164,96" ); 38 Irit2Scn - IRIT To SCENE (RTrace) ﬁlter SCENE is the format used by the RTrace ray tracer. This ﬁlter was donated by Antonio Costa ([email protected]), the author of RTrace. 38.1 Command Line Options irit2scn [-l] [-4] [-F PolyOpti FineNess] [-o OutName] [-g] [-T] [-t AnimTime] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated as a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -o OutName: Name of output ﬁle. By default the name of the ﬁrst data ﬁle from DFiles list is used. See below on the output ﬁles. • -g: Generates the geometry ﬁle only. See below. • -T: Talkative mode. Prints processing information. • -t AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -z: Prints version number and current defaults. 38.2 Usage Irit2Scn converts freeform surfaces and polygons into polygons in a format that can be used by RTrace. Two ﬁles are created, one with a ’.geom’ extension and one with a ’.scn’ extension. Since the number of polygons can be extremely large, the geometry is isolated in the ’.geom’ ﬁle and is included (via ’#include’) in the main ’.scn’ ﬁle. The latter holds the surface properties for all the geometry as well as viewing and RTrace speciﬁc commands. This allows for the changing of the shading or viewing properties while editing small (’.scn’) ﬁles. If ’-g’ is speciﬁed, only the ’.geom’ ﬁle is created, preserving the current ’.scn’ ﬁle. IRIT Solid modeler G. Elber 333 In practice, it may be useful to create a low resolution approximation of the model, adjust the viewing/shading parameters in the ’.scn’ ﬁle until a good view and/or surface quality is found, and then run Irit2Scn once more to create a high resolution approximation of the geometry using ’-g’. Example: irit2scn -l -F 0 8 b58.itd creates b58.scn and b58.geom with low resolution (FineNess of 5). One can ray trace this scene after converting the scn ﬁle to a sﬀ ﬁle, using scn2sﬀ provided with the RTrace package. Once done with the parameter setting of RTrace, a ﬁne approximation of the model can be created with: irit2scn -l -g -F 0 64 b58.itd which will only recreate b58.geom (because of the -g option). One can overwrite the viewing matrix by appending a new matrix at the end of the command line, created by the display devices: wntdrvs b58.itd irit2scn -l -F 0 8 b58.itd irit.imd where irit.imd is the viewing matrix created by wntdrvs. The output name, by default, is the last input ﬁle name, so you might want to provide an explicit name with the -o ﬂag. 38.3 Advanced Usage One can specify surface qualities for individual surfaces of a model. Several such attributes are supported by Irit2Scn and can be set within IRIT. See also the ATTRIB IRIT command. If a certain surface should be ﬁner/coarser than the rest of the scene, one can set a ”resolution” attribute which speciﬁes the relative FineNess resolution of this speciﬁc surface. Further, ”u resolution” and ”v resolution” might be similarly used to set relative resolution for the u or v direction only. The ”crv resolution” attribute controls the relative ﬁneness of curves as polylines. The ”num of isolines” attribute controls the relative number of isoparametric curves. Example: attrib( srf1, "resolution", 2 ); will force srf1 to have twice the default resolution, as set via the ’-f’ ﬂag. Almost ﬂat patches are converted to polygons. The patch can be converted into two polygons (by subdividing along one of its diagonals) or into four by introducing a new point at the patch center. This behavior is controlled by the ’-4’ ﬂag, but can be overwritten for individual surfaces by setting ”twoperﬂat” or ”fourperﬂat”. RTrace speciﬁc properties are controlled via the following attributes: ”SCNrefraction”, ”SCNtexture”, ”SCNsurface. Refer to the RTrace manual for their meaning. Example: attrib( srf1, "SCNrefraction", 0.3 ); Surface color is controlled on two levels. If the object has an RGB attribute, it is used. Otherwise a color as set via IRIT COLOR command is used, if set. Example: attrib( tankBody, "rgb", "244,164,96" ); IRIT Solid modeler 39 G. Elber 334 Irit2Stl - IRIT To STL ﬁlter 39.1 Command Line Options irit2stl [-l] [-4] [-r] [-F PolyOpti FineNess] [-E VrtxEps] [-s] [-S] [-o OutName] [-m] [-u] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -r: Regularize and triangulate the input data if not regularized and with triangles only to begin with. • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -E VrtxEps: Tolerance of two adjacent verices to be considered the same. Vertices that are considered the same are collapsed to an identical location. • -s: Dumps each object as a separated ”solid” - ”endsolid” brackets. • -S: Dumps each object as a separated ”solid” - ”endsolid” brackets in a separated stl ﬁle, with ﬁle name appended with numeric index. • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -m: More information ﬂag. • -u: Forces a unit matrix. That is, input data are not transformed at all. • -z: Prints version number and current defaults. 39.2 Usage Irit2Stl converts freeform surfaces and polygons into the STL (Stereolithography) ﬁle format. The STL data should be a closed solid in general but no such validity check is conducted by irit2stl. Example: irit2stl -u solid2.itd > solid2.stl 40 Irit2Wrl - IRIT To IGES ﬁlter Converts IRIT data ﬁles into IGS data ﬁles. IRIT Solid modeler 40.1 G. Elber 335 Command Line Options irit2wrl [-l] [-4] [-u] [-F PolyOpti FineNess] [-f PolyOpti SampTol] [-o OutName] [-T] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. • -u: Forces a unit matrix. That is, input data are not transformed at all. • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -T: More talkative/information ﬂag. • -z: Prints version number and current defaults. 40.2 Usage Irit2Wrl converts IRIT data ﬁles into Geom View OFF data ﬁles. Example: Irit2Wrl -m -o file.off file.itd 41 Irit2Wgl - IRIT To WGL ﬁlter 41.1 Command Line Options irit2wgl [-l] [-4] [-F PolyOpti FineNess] [-C] [-w CanvasWidth] [-h CanvasHeight] [-b R G B] [-W] [-D] [-P] [-M] [-d DrawMode] [-T] [-v ViewAngle] [-p ProjectionMode] [-a R G B] [-o OutName] [-z] DFiles • -l: Linear - forces linear (degree two) surfaces to be approximated by a single polygon along their linear direction. Although most of the time linear direction can be represented exactly using a single polygon, even a bilinear surface can have a freeform shape (saddle-like) that is not representable using a single polygon. Note that although this option will better emulate the surface shape, it will create unnecessary polygons in cases where one is enough. • -4: Four - Generates four polygons per ﬂat patch. Default is 2. IRIT Solid modeler G. Elber 336 • -F PolyOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. • -C: HideCtrlBar - Hides the scene control bar. • -w CanvasWidth: Width of the html canvas in pixels. • -h CanvasWidth: Height of the html canvas in pixels. • -b R G B: Sets the background color. Each of thre R,G,B colors is an integer value between zero and 255. Default is black. • -W: ShowWorldAxes - Shows axes relative to the world. • -D: DisableDepthTest - Disables the depth test. • -P: EnablePicking - Enables picking. • -M: ShowModelAxes - Shows axes relative to the model. • -d DrawMode: The draw mode of the model. 1, 2 and 4 for wireframe, solid and texture, respectively (default is wireframe). • -T: ModelTrans - Transformation will be relative to model coordinates. By default (or -T-), transformation is relative to world coordinates. • -v ViewAngle: The view angle of the camera. 0 for the original view angle and 1, 2, 3, 4, 5 and 6 for front, back, right, left, top and bottom view angles, respectively (default is original view angle). • -p ProjectionMode: The projection mode of the scene. 0 for orthographic projection (the default) and 1 for perspective projection. • -a R G B: Sets the global ambient light intensity. Each of thre R,G,B colors is a double value between 0 and 1. Default is 0.2 for each component. • -o OutName: Name of output ﬁle. Default is stdout. • -z: Prints version number and current defaults. 41.2 Usage Irit2Wgl converts IRIT data ﬁles into WebGL based HTML data ﬁles. Example: irit2wgl teapot.itd > teapot.html If an output ﬁle name is supplied, the output will consist of three ﬁles all having the same ﬁle name, but a diﬀerent extension - html ﬁle, javascript ﬁle and css ﬁle. For example, the following command will output the ﬁles teapot.html, teapot.js and teapot.css: irit2wgl -o teapot teapot.itd If an output ﬁle name is not supplied, the entire output data is dumped into the standard output. In order to load that data into the web, it should be redirected into an html ﬁle. IRIT Solid modeler 41.3 G. Elber 337 Runtime Usage Right click the mouse in order to translate the model, Left click the mouse in order to rotate the mode and press the middle button in order to scale the model. If picking is enabled, right click the mouse in order to pick an object. Please notice that when picking is enabled, the right mouse button is used both for picking objects and for translating the model. 41.4 Browser Support Make sure that your graphics drivers are up to date. When running under Windows, make sure you have the Microsoft DirectX runtime installed. Explorer: WebGL is not supported in with Internet Explorer. Firefox: WebGL is supported in version 4 or higher. However, it is recommended to upgrade to the latest version available. In case of security errors, set the following Firefox security ﬂag to false: about:conﬁg -¿ set security.ﬁleuri.strict origin policy as false Chrome: WebGL is available in the stable release of Chrome. If you catch the error ”Uncaught Error: SECURITY ERR: DOM Exception 18”, run Chrome with ”–allow-ﬁle-access-from-ﬁles”. For debugging WebGL with Chrome, WebGL Inspector is highly recommended: http://benvanik.github.com/WebGLInspector/ Opera: WebGL is supported in Opera 12 alpha. Safari: WebGL is supported on Mac OS X 10.6 in the WebKit nightly builds. After downloading and installing the browser, open the Terminal and type the following: defaults write com.apple.Safari WebKitWebGLEnabled -bool YES This command only needs to be run once. All future invocations of the browser will run with WebGL enabled. 41.5 Usefull Links To check if your browser supports WebGL, visit the following page: http://get.webgl.org/ WebGL speciﬁcation can be found at: https://www.khronos.org/registry/webgl/specs/1.0/ WebGL tutorial (Lesson 0 provides good troubleshootong tips): http://learningwebgl.com/blog/ WebGL Techniques and Performance presentation: http://www.youtube.com/watch?v=rfQ8rKGTVlg 42 Irit2Xfg - IRIT To XFIG ﬁlter 42.1 Command Line Options irit2xfg [-s Size] [-t XTrans YTrans] [-I #UIso[:#VIso[:#WIso]]] [-f PolyOpti SampTol] [-F PolyOpti FineNess] [-M] [-G] [-T] [-a AnimTime] [-i] [-o OutName] [-z] DFiles • -s Size: Size in inches of the page. Default is 7 inches. • -t XTrans YTrans: X and Y translation. of the image. Default is (0, 0). • -I #UIso[:#VIso]: Speciﬁes the number of isolines per surface, per direction. If #VIso is not speciﬁed, #UIso is used for #VIso as well. • -f PolyOpti SampTol: Controls the method used to approximate curves into polylines. If PolyOpti == 0, equally spaced intervals are used. For PolyOpti == 1, SampTol (real number) IRIT Solid modeler G. Elber 338 speciﬁes the maximal allowed deviation tolerance of the piecewise linear approximation from the original curve. Default is 0 64 (uniform sampling with 64 samples). • -F PolygonOpti FineNess: Optimality of polygonal approximation of surfaces. See the variable POLY APPROX OPT for the meaning of FineNess. See also -4. This enforces the dump of freefrom geometry as polygons. • -M: Dumps the control mesh/polygon as well. • -G: Dumps the freeform geometry. • -T: Talkative mode. Prints processing information. • -a AnimTime: If the data contains animation curves, evaluate and process the scene at time AnimTime. • -i: Internal edges (created by IRIT) - default is not to display them, and this option will force their display. • -o OutName: Name of output ﬁle. By default, the name of the ﬁrst data ﬁle from DFiles list is used. See output ﬁles below. • -z: Prints version number and current defaults. 42.2 Usage Irit2Xfg converts freeform surfaces and polygons into polylines in a format that can be used by XFIG. Example: irit2Xfg -T -f 0 16 saddle.itd > saddle.xfg However, one can overwrite the viewing matrix by appending a new matrix at the end of the command line, created by the display devices: x11drvs b58.itd irit2Xfg -T -f 0 16 b58.itd irit.imd > saddle.xfg where irit.imd is the viewing matrix created by x11drvs. 43 Obj2irit - Wavefront OBJ format To IRIT data ﬁles converts Waverfront’s OBJ data ﬁles into IRIT data ﬁles. 43.1 Command Line Options obj2irit [-m] [-r] [-o OutName] [-z] OBJFile • -m: Provides some more information on the data ﬁle(s) parsed. • -r: Reverses all polygons’ orientation in generated data. • -o OutName: Name of output ﬁle. By default, the output goes to stdout. • -z: Prints version number and current defaults. IRIT Solid modeler 43.2 G. Elber 339 Usage obj2irit converts Wavefront’s OBJ data ﬁles into IRIT data ﬁles. The current version provides only partial support for the direct conversion of freeform surfaces, mainly due to luck of examples of freeform surfaces in obj format. Example: obj2irit -o file.itd file.obj 44 Oﬀ2irit - Geom View Oﬀ format To IRIT data ﬁles Converts Geom View’s Oﬀ data ﬁles into IRIT data ﬁles. 44.1 Command Line Options Off2irit [-o OutName] [-z] OffFile • -o OutName: Name of output ﬁle. By default the output goes to stdout. • -z: Prints version number and current defaults. 44.2 Usage Oﬀ2irit converts Geom View’s Oﬀ data ﬁles into IRIT data ﬁles. Example: Off2irit - < file.off > file.itd 45 Stl2Irit - Stl (stereo lithograph) data To IRIT ﬁle ﬁlter Converts ’.stl’ stereolithography data ﬁles to ’.irt’ IRIT scripts. Both binary and text STL ﬁles are supported. 45.1 Command Line Options stl2irit [-b] [-w] [-n] [-o OutName] [-z] STLFile • • -b: The stl ﬁle is a binary stl. -w: Perform an endian swap on all read data. Little vs. Big Endian is supported for binary STL ﬁles only. -n: Flip orientation of all polygons by ﬂipping their normals. -o OutName: Name of output ﬁle. By default, the output goes to stdout. -z: Print version number and current defaults. 45.2 Usage stl2irit converts stereo-lithography STL data ﬁles into IRIT data ﬁles. Example: stl2irit -o file.itd file.stl G. Elber IRIT Solid modeler 46 340 Data File Format This section describes the data ﬁle format used to exchange data between IRIT and its accompanying tools. [OBJECT {ATTRS} OBJNAME [NUMBER n] | [POINT x y z] | [VECTOR x y z] | [CTLPT POINT_TYPE {w} x y {z}] | [STRING "a string"] | [MATRIX m00 m10 m20 m30 ... ... ... ... m03 m13 m23 m33] ;A polyline should be drawn from first point to last. Nothing is drawn ;from last to first (in a closed polyline, last point is equal to first). | [POLYLINE {ATTRS} #PTS ;#PTS = number of points. [{ATTRS} x y z] [{ATTRS} x y z] . . . [{ATTRS} x y z] ] ;Defines a closed planar region. Last point is NOT equal to first, ;and a line from last point to first should be drawn when the boundary ;of the polygon is drawn. | [POLYGON {ATTRS} #PTS [{ATTRS} x y z] [{ATTRS} x y z] . . . [{ATTRS} x y z] ] ;Defines a "cloud" of points. | [POINTLIST {ATTRS} #PTS [{ATTRS} x y z] [{ATTRS} x y z] IRIT Solid modeler G. Elber . . . [{ATTRS} x y z] ] ;Defines a polygon triangle strip. At least 3 vertices are expected. ;Last point is NOT equal to first, and a line from last point to first ;should be drawn when the boundary of the polygon is drawn. | [POLYSTRIP {ATTRS} #PTS [{ATTRS} x y z] [{ATTRS} x y z] . . . [{ATTRS} x y z] ] ;Defines an instance - a geometric reference (by name, SRF13 below) ;and a transformation matrix to apply to this geoemtry | [INSTANCE SRF13 m00 ... m03 m10 ... m13 m20 ... m23 m30 ... m33] ;Defines a Bezier curve with #PTS control points. If the curve is ;rational, the rational component is introduced first. | [CURVE BEZIER {ATTRS} #PTS POINT_TYPE [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a Bezier surface with #UPTS * #VPTS control points. If the ;surface is rational, the rational component is introduced first. ;Points are printed row after row (#UPTS per row), #VPTS rows. | [SURFACE BEZIER {ATTRS} #UPTS #VPTS POINT_TYPE [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] 341 IRIT Solid modeler G. Elber ;Defines a Bezier triangular surface with (#PTS + 1) * #PTS / 2 control ;points, of order ORDER. If the surface is rational, the rational ;component is introduced first. Note #PTS holds number of points along ;an edge and is exactly equal to ORDER. Points are printed sequentially. | [TRISRF BEZIER {ATTRS} #PTS POINT_TYPE [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a Bezier trivariate with #UPTS * #VPTS * #WPTS control ;points. If the trivariate is rational, the rational component is ;introduced first. Points are printed row after row (#UPTS per row), ;#VPTS rows, #WPTS layers (depth). | [TRIVAR BEZIER {ATTRS} #UPTS #VPTS #WPTS POINT_TYPE [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a Bezier multivariate of #Dim dimensions (#Dim = 1 for a ;curve, #Dim = 2 for a surface, #Dim = 3 for a trivariate, etc.) ;with (Dim1#PTS * ... * Dim1#PTS) control points. If the multivariate ;is rational, the rational component is introduced first. | [MULTIVAR BEZIER {ATTRS} #Dim Dim1#PTS ... DimN#PTS POINT_TYPE [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a B-spline curve of order ORDER with #PTS control points. If the ;curve is rational, the rational component is introduced first. ;Note that the length of knot vector is equal to #PTS + ORDER. ;If the curve is periodic, KVP prefix the knot vector that has length of ;’Length + Order + Order - 1’. | [CURVE BSPLINE {ATTRS} #PTS ORDER POINT_TYPE [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;Knot vector [{ATTRS} {w} x y z ...] 342 IRIT Solid modeler G. Elber [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a B-spline surface with #UPTS * #VPTS control points, of order ;UORDER by VORDER. If the surface is rational, the rational component ;is introduced first. ;Points are printed row after row (#UPTS per row), #VPTS rows. ;If the surface is periodic in some direction, KVP prefix the knot vector ;that has length of ’Length + Order + Order - 1’. | [SURFACE BSPLINE {ATTRS} #UPTS #VPTS UORDER VORDER POINT_TYPE [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;U Knot vector [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;V Knot vector [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a B-spline triangular surface with (#PTS + 1) * #PTS / 2 control ;points, of order ORDER. If the surface is rational, the rational ;component is introduced first. ;Points are printed sequentially. | [TRISRF BSPLINE {ATTRS} #PTS ORDER POINT_TYPE [KV {ATTRS} kv0 kv1 kv2 ...] ;Knot vector [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a B-spline trivariate with #UPTS * #VPTS * #WPTS control ;points. If the trivariate is rational, the rational component is ;introduced first. Points are printed row after row (#UPTS per row), ;#VPTS rows, #WPTS layers (depth). ;If trivariate is periodic in some direction, KVP prefix the knot vector ;that has length of ’Length + Order + Order - 1’. | [TRIVAR BSPLINE {ATTRS} #UPTS #VPTS #WPTS UORDER VORDER WORDER POINT_TYPE [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;U Knot vector [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;V Knot vector [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;W Knot vector 343 IRIT Solid modeler G. Elber [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a B-spline multivariate of #Dim dimensions (#Dim = 1 for a ;curve, #Dim = 2 for a surface, #Dim = 3 for a trivariate, etc.) ;with (Dim1#PTS * ... * Dim1#PTS) control points. If the multivariate ;is rational, the rational component is introduced first. | [MULTIVAR BSPLINE {ATTRS} #Dim Dim1#PTS ... DimN#PTS POINT_TYPE [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;Dim1 Knot vector . . . [KV{P} {ATTRS} kv0 kv1 kv2 ...] ;DimN Knot vector [{ATTRS} {w} x y z ...] [{ATTRS} {w} x y z ...] . . . [{ATTRS} {w} x y z ...] ] ;Defines a trimmed surface. Encapsulates a surface (can be either a ;B-spline or a Bezier surface) and prescribes its trimming curves. ;There can be an arbitrary number of trimming curves (either Bezier ; or B-spline). Each trimming curve contains an arbitrary number of ;trimming curve segments, while each trimming curve segment contains ;a parameteric representation optionally followed by a Euclidean ;representation of the trimming curve segment. | [TRIMSRF [SURFACE ... ] [TRIMCRV [TRIMCRVSEG [CURVE ... ] ] . . . [TRIMCRVSEG [CURVE ... ] ] 344 IRIT Solid modeler G. Elber ] . . . [TRIMCRV [TRIMCRVSEG [CURVE ... ] ] . . . [TRIMCRVSEG [CURVE ... ] ] ] ] ;Defines a model. A model contains a set of (trimmed) surfaces along ;with a set of trimming curves that are shared by (at most) two ;surfaces each. ;The trimming curves must form closed loops in each surface. | [MODEL #TrimSrfs #TrimSegs ;A surface in the model holds a regular surface and a set of ;closed loops that defines the trimming loops of the surface. [MDLTSRF #Loops ;Number of trimming loops [SURFACE ... ] ;Each trimming loop is a list of trimming curve segments. ;If the index is negative, it denotes the traversal of the ;curve in reverse order. [MDLLOOP trim seg’s indices] ;Negative index - reversed . . . [MDLLOOP trim seg’s indices] ;Negative index - reversed ] . . . [MDLTSRF #Loops ;Number of trimming loops [SURFACE ... ] [MDLLOOP trim seg’s indices] ;Negative index - reversed . . . 345 IRIT Solid modeler [MDLLOOP trim seg’s indices] G. Elber 346 ;Negative index - reversed ] ;The trimming curve segments can hold a parameteric curve of the ;in first surface, a parametric curve in the second surface, and a ;a Euclidean representation, in this order. A 3 bits mask ’CurveMask’ ;says what is available, as one bit per curve type. ;’#1stSrf’ and ’#2ndSrf’ specify the two surfaces that share ;this boundary trimming curve, with 0 denoting no surface. [MDLTSEG CurveMask #1stSrf #2ndSrf ;CurveMask = 5 [CURVE ... ] [CURVE ... ] ] . . . [MDLTSEG CurveMask #1stSrf #2ndSrf ;CurveMask = 7 [CURVE ... ] [CURVE ... ] [CURVE ... ] ] ] ] POINT_TYPE -> E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 ATTRS -> [ATTRNAME ATTRVALUE] | [ATTRNAME] | [ATTRNAME ATTRVALUE] ATTRS Some notes: * This deﬁnition for the text ﬁle is designed to minimize the reading time and space. All information can be read without backward or forward referencing. * An OBJECT must never hold diﬀerent geometry types or other entities. I.e. CURVEs, SURFACEs, and POLYGONs must all be in diﬀerent OBJECTs. * Attributes should be ignored if not needed. The attribute list may have any length and is always terminated by a token that is NOT ’[’. This simpliﬁes and disambiguates the parsing. * Comments may appear between ’[OBJECT ...]’ blocks, or immediately after OBJECT OBJNAME, and only there. A comment body can be anything not containing the ’[’ or the ’]’ tokens (signals start/end of block). Some of the comments in the above deﬁnition are illegal and appear there only for the sake of IRIT Solid modeler G. Elber 347 clarity. * It is preferable that geometric attributes such as NORMALs be saved on the geometric structure level (POLYGON, CURVE or vertices) while graphical and other attribures such as COLORs will be saved on the OBJECT level. * Objects may be contained in other objects to an arbitrary level. Here is an example that exercises most of the data format: This is a legal comment in a data file. [OBJECT DEMO [OBJECT REAL_NUM And this is also a legal comment. [NUMBER 4] ] [OBJECT A_POINT [POINT 1 2 3] ] [OBJECT A_VECTOR [VECTOR 1 2 3] ] [OBJECT CTL_POINT [CTLPT E3 1 2 3] ] [OBJECT STR_OBJ [STRING "string"] ] [OBJECT UNIT_MAT [MATRIX 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ] [OBJECT [COLOR 4] POLY1OBJ [POLYGON [PLANE 1 0 0 0.5] 4 [-0.5 0.5 0.5] [-0.5 -0.5 0.5] [-0.5 -0.5 -0.5] [-0.5 0.5 -0.5] ] [POLYGON [PLANE 0 -1 0 0.5] 4 [0.5 0.5 0.5] IRIT Solid modeler G. Elber [-0.5 0.5 0.5] [-0.5 0.5 -0.5] [0.5 0.5 -0.5] ] ] [OBJECT [COLOR 63] ACURVE [CURVE BSPLINE 16 4 E2 [KV 0 0 0 0 1 1 1 2 3 4 5 6 7 8 9 10 11 11 11 11] [0.874 0] [0.899333 0.0253333] [0.924667 0.0506667] [0.95 0.076] [0.95 0.76] [0.304 1.52] [0.304 1.9] [0.494 2.09] [0.722 2.242] [0.722 2.318] [0.38 2.508] [0.418 2.698] [0.57 2.812] [0.57 3.42] [0.19 3.572] [0 3.572] ] ] [OBJECT [COLOR 2] SOMESRF [SURFACE BEZIER 3 3 E3 [0 0 0] [0.05 0.2 0.1] [0.1 0.05 0.2] [0.1 -0.2 0] [0.15 0.05 0.1] [0.2 -0.1 0.2] [0.2 0 0] [0.25 0.2 0.1] [0.3 0.05 0.2] ] ] ] 348 IRIT Solid modeler 47 G. Elber 349 Bugs and Limitations As with any program of more than one line, this is far from perfect. Some limitations, as well as simpliﬁcations, are laid out below. * If the intersection curve of two objects falls exactly on polygon boundaries, for all polygons, the system will scream that the two objects do not intersect at all. Try to move one by EPSILON into the other. I probably should ﬁx this one - it is supposed to be relatively easy. * Avoid degenerate intersections that result in a point or a line. They will probably cause wrong propagation of the inner and outer parts of one object relative to another. Always extend your object beyond the other object. * If two objects have no intersection in their boundary, IRIT assumes they are disjoint: a union simply combines them, and the other Boolean operators return a NULL object. One should ﬁnd a FAST way (3D Jordan theorem) to ﬁnd the relation between the two (A in B, B in A, A disjoint B) and according to that, make a decision. * Since the Boolean sum implementation constructs ruled surfaces with uniform speed, it might return a somewhat incorrect answer, given non-uniform input curves. * The parser is out of hand and diﬃcult to maintain. There are several memory leaks there that one should ﬁx. * Rayshade complains a lot about degenerate polygons on irit2ray output. To alleviate the problem, change the ’equal’ macro in common.h in libcommon of rayshade from EPSILON (1e-5) to 1e-7 or even lower. * On the motif-based drivers (xmtdrvs etc.) clicking the mouse left and right of the scale’s button produces stepped transformations. This step size is constant, and is not proportional to the distance between the mouse’s position and the position of the button. The reason for the ﬂaw is incorrect callback information returned from the scale in repetitive mode. * Binary data ﬁles are not documented, nor will they be. They might change in the future and are in fact machine dependent. Hence, one platform might fail to read another’s binary data ﬁle.

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