# PSTricks - University of Washington math department

PSTricks
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User’s Guide1
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PostScript macros for Generic TeX
Timothy Van Zandt
25 July 2003
Version 97
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Department of Economics and Political Science
Boulevard de Constance
77305 Fontainebleau Cedex
France
1
Documentation repackaged in 2003 by Denis Girou <Denis.Girou@idris.fr>
Contents
Welcome to PSTricks
1
Part I
3
The Essentials
1 Arguments and delimiters
3
2 Color
4
3 Setting graphics parameters
4
4 Dimensions, coordinates and angles
5
5 Basic graphics parameters
7
Part II
Basic graphics objects
6 Lines and polygons
9
9
7 Arcs, circles and ellipses
11
8 Curves
13
9 Dots
15
10 Grids
16
11 Plots
18
Part III
More graphics parameters
23
12 Coordinate systems
23
13 Line styles
23
14 Fill styles
25
27
16 Custom styles
29
Part IV
Custom graphics
31
17 The basics
31
18 Parameters
31
19 Graphics objects
32
20 Safe tricks
35
1
21 Pretty safe tricks
37
22 For hackers only
38
Part V
Picture Tools
40
23 Pictures
40
24 Placing and rotating whatever
41
25 Repetition
44
26 Axes
46
Part VI
Text Tricks
50
27 Framed boxes
50
28 Clipping
53
29 Rotation and scaling boxes
56
Part VII
Nodes and Node Connections
58
30 Nodes
59
31 Node connections
61
32 Node connections labels: I
70
33 Node connection labels: II
74
34 Attaching labels to nodes
75
35 Mathematical diagrams and graphs
76
36 Complex examples
80
Part VIII
Trees
84
37 Overview
84
38 Tree Nodes
85
39 Tree orientation
88
40 The distance between successors
89
41 Spacing between the root and successors
91
42 Edges
92
43 Edge and node labels
94
2
44 Framing
98
45 Details
98
46 The scope of parameter changes
101
47 Complex examples
103
Part IX
Filling and Tiling
111
48 Overview
111
49 Usage
112
50 Examples
116
50.1
Kind of tiles . . . . . . . . . . . . . . . . . . . . . . 116
50.2
External graphic files . . . . . . . . . . . . . . . . . 122
50.3
Tiling of characters . . . . . . . . . . . . . . . . . . 123
50.4
“Dynamic” tiling . . . . . . . . . . . . . . . . . . . 124
Part X
Three Dimensional Graphics
129
51 Overview
129
52 Usage
129
53 More details
140
Part XI
Other features
145
54 Special coordinates
145
55 Coils and zigzags
148
56 Overlays
150
151
58 Typesetting text along a path
152
59 Stroking and filling character paths
155
60 Importing EPS files
157
61 Exporting EPS files
159
Part XII
Writing high-level macros
163
62 Overview
163
3
63 Usage
164
63.1
Integer parameters . . . . . . . . . . . . . . . . . . . 165
63.2
Real parameters . . . . . . . . . . . . . . . . . . . . 166
63.3
String parameters . . . . . . . . . . . . . . . . . . . 168
63.4
Boolean parameters . . . . . . . . . . . . . . . . . . 169
63.5
Coordinate arguments . . . . . . . . . . . . . . . . . 170
63.6
Generic template for a package . . . . . . . . . . . . 184
64 Examples
186
64.1
Basic example : cogged wheels . . . . . . . . . . . . 186
64.2
Advanced example: test tube . . . . . . . . . . . . . 188
64.3
Advanced example: Gantt charts . . . . . . . . . . . 208
64.4
Advanced example: overlapped colored surfaces1 . . 214
64.5
Advanced example: three dimensional lighten effect . 225
4 Driver file
230
5 ‘pst-li3d’ LATEX wrapper
230
6 ‘pst-li3d’ code
231
6.1
Preambule . . . . . . . . . . . . . . . . . . . . . . . 231
6.2
Definition of the parameters . . . . . . . . . . . . . . 232
6.3
Main macros . . . . . . . . . . . . . . . . . . . . . . 234
6.4
Auxiliary macro . . . . . . . . . . . . . . . . . . . . 236
6.5
Closing . . . . . . . . . . . . . . . . . . . . . . . . 237
Part XIII
Obsolete commands
238
247
8 Color commands
247
9 Put commands
248
10 Coordinates commands
Help
A PDF output files
250
251
251
A.1
Compilers with internal support of PSTricks . . . . . 252
A.2
PostScript to PDF converters . . . . . . . . . . . . . 252
A.3
PdfTEX workarounds . . . . . . . . . . . . . . . . . 252
4
B Animated graphics
255
B.1
Pure PSTricks graphics . . . . . . . . . . . . . . . . 255
B.2
Non pure PSTricks graphics . . . . . . . . . . . . . 259
C Generation of code by external programs
261
D Loops
265
E Recursion
269
F Computations
272
G Storing and retrieving data in arrays
277
H Random
281
I Coordinates
287
I.1 Relative coordinates . . . . . . . . . . . . . . . . . . 287
J Nodes
292
J.1 Getting the coordinates of a node . . . . . . . . . . . 292
J.2 Positions relative to nodes . . . . . . . . . . . . . . . 293
K Boxes
294
297
L.1 How to inactivate the PSTricks macros . . . . . . . . 297
L.2 Monochrome version of all or some graphics . . . . . 297
L.3 How to improve the rendering of halftones? . . . . . 298
L.4 Including PostScript code . . . . . . . . . . . . . . . 298
L.5 ConTEXt color macros support . . . . . . . . . . . . 300
L.6 Scope of parameters changes . . . . . . . . . . . . . 302
L.7 Defining parameters using macros . . . . . . . . . . 302
L.8 Line type connections . . . . . . . . . . . . . . . . . 304
L.9 Boxes of same sizes for trees and diagrams . . . . . . 306
L.10 Reference points . . . . . . . . . . . . . . . . . . . . 308
L.11 Dashed and dotted hatched styles . . . . . . . . . . . 309
L.12 Axes with labels using commas as separators . . . . 310
L.13 Alphabetic labels on axes . . . . . . . . . . . . . . . 311
L.14 Two different axes . . . . . . . . . . . . . . . . . . . 312
L.15 Polar Plots . . . . . . . . . . . . . . . . . . . . . . . 314
5
L.16 Non filled arrows . . . . . . . . . . . . . . . . . . . 318
L.17 Lines under a curve . . . . . . . . . . . . . . . . . . 319
L.18 Dashed lines . . . . . . . . . . . . . . . . . . . . . . 321
M Troubleshooting
326
6
Welcome to PSTricks
PSTricks is a collection of PostScript-based TEX macros that is compatible
with most TEX macro packages, including P LAIN TEX, LATEX and ConTEXt,
PSTricks gives you color, graphics, rotation, trees and overlays. PSTricks
puts the icing (PostScript) on your cake (TEX)!
comes with the PSTricks package. Even if PSTricks has already been installed for you, give read-me.pst a look over.
This User’s Guide verges on being a reference manual, meaning that it is
not designed to be read linearly. Here is a recommended strategy: Finish reading this brief overview of the features in PSTricks. Then thumb
(Essentials) and read it carefully. Refer to the remaining sections as the
need arises.
When you cannot figure out how to do something or when trouble arises,
check out the appendices (Help). You just might be lucky enough to find
a solution. There is also a LATEX file samples.pst of samples that is distributed with PSTricks. Look to this file for further inspiration.
This documentation is written with LATEX. Some examples use LATEX specific constructs and some don’t. However, there is nothing LATEX specific
about any of the macros, nor is there anything that does not work with
LATEX. This package has been tested with P LAIN TEX, LATEX and ConTEXt
and should work with other TEX macro packages as well.
pstricks
The main macro file is pstricks.tex/pstricks.sty. Each of the PSTricks
macro files comes with a .tex extension and a .sty extension; these are
equivalent, but the .sty extension means that you can include the file name
as a LATEX package.
There are numerous supplementary macro files. A file, like the one above
and the left, is used in this User’s Guide to remind you that you must input
a file before using the macros it contains.
For most PSTricks macros, even if you misuse them, you will not get
PostScript errors in the output. However, it is recommended that you resolve any TEX errors before attempting to print your document. A few
PSTricks macros pass on PostScript errors without warning. Use these with
care, especially if you are using a networked printer, because PostScript errors can cause a printer to bomb. Such macros are pointed out in strong
terms, using a warning like this one:
Welcome to PSTricks
1
PS
Warning: Use macros that do not check for PostScript errors
with care. PostScript errors can cause a printer to bomb!
Keep in mind the following typographical conventions in this User’s Guide.
• All literal input characters, i.e., those that should appear verbatim
in your input file, appear in upright Helvetica and Helvetica-Bold
fonts.
• Meta arguments, for which you are supposed to substitute a value
(e.g., angle) appear in slanted Helvetica-Oblique and HelveticaBoldOblique fonts.
• The main entry for a macro or parameter that states its syntax appears in a large bold font, except for the optional arguments, which
are in medium weight. This is how you can recognize the optional
arguments.
• References to PSTricks commands and parameters within paragraphs
are set in Helvetica-Bold.
Welcome to PSTricks
2
I
1
The Essentials
Arguments and delimiters
Here is some nitty-gritty about arguments and delimiters that is really important to know.
The PSTricks macros use the following delimiters:
Curly braces
Brackets (only for optional arguments)
Parentheses and commas for coordinates
= and , for parameters
{arg}
[arg]
(x,y )
par1=val1, …
Spaces and commas are also used as delimiters within arguments, but in
this case the argument is expanded before looking for the delimiters.
Always use a period rather than a comma to denote the decimal point, so
that PSTricks doesn’t mistake the comma for a delimiter.
The easiest mistake to make with the PSTricks macros is to mess up the
arguments, or other unilluminating errors such as the following:
! Use of \get@coor doesn’t match its definition.
! Paragraph ended before \pst@addcoor was complete.
! Forbidden control sequence found while scanning use of \check@arrow.
! File ended while scanning use of \lput.
Delimiters are generally the first thing to check when you get errors with a
PSTricks macro.
Since PSTricks macros can have many arguments, it is useful to know that
you can leave a space or new line between any arguments, except between
arguments enclosed in curly braces. If you need to insert a new line between
arguments enclosed in curly braces, put a comment character % at the end
of the line.
As a general rule, the first non-space character after a PSTricks macro
should not be a [ or (. Otherwise, PSTricks might think that the [ or ( is
actually part of the macro. You can always get around this by inserting a
pair {} of braces somewhere between the macro and the [ or (.
The Essentials
3
2
Color
The grayscales
black, darkgray, gray, lightgray, and white,
and the colors
red, green, blue, cyan, magenta, and yellow
are predefined in PSTricks.
This means that these names can be used with the graphics objects that are
described in later sections.
1
2
3
4
1
2
3
4
3
\psset{fillstyle=solid}%
\pscircle[fillcolor=yellow]{1.5}
\definecolor{LightOrange} {cmyk}{0,0.2,0.4,0}%
\pscircle[fillcolor=LightOrange](3.2,0){1.5}
\psset{unit=3}%
\multido{\nHue=0.01+0.01}{100}{%
\definecolor{MyColor}{hsb}{\nHue,1,1}%
\pscircle[linewidth=0.01,linecolor=MyColor]{\nHue}}
Setting graphics parameters
PSTricks uses a key-value system of graphics parameters to customize the
macros that generate graphics (e.g., lines and circles), or graphics combined with text (e.g., framed boxes). You can change the default values of
parameters with the command \psset, as in
1
2
\psset{fillcolor=yellow}
\psset{linecolor=blue,framearc=.3,dash=3pt 6pt}
The general syntax is:
The Essentials: Color
4
\psset{par1=value1,par2=value2,… }
As illustrated in the examples above, spaces are used as delimiters for some
of the values. Additional spaces are allowed only following the comma that
separates par =value pairs (which is thus a good place to start a new line
if there are many parameter changes). E.g., the first example is acceptable,
but the second is not:
1
2
\psset{fillcolor=yellow, linecolor=blue}
\psset{fillcolor= yellow,linecolor =blue }
The parameters are described throughout this User’s Guide, as they are
needed.
Nearly every macro that makes use of graphics parameters allows you to
include changes as an optional first argument, enclosed in square brackets.
For example,
1
\psline[linecolor=green,linestyle=dotted](8,7)
draws a dotted, green line. It is roughly equivalent to
1
{\psset{linecolor=green,linestyle=dotted}\psline(8,7)}
For many parameters, PSTricks processes the value and stores it in a peculiar form, ready for PostScript consumption. For others, PSTricks stores
the value in a form that you would expect. In the latter case, this User’s
Guide will mention the name of the command where the value is stored.
This is so that you can use the value to set other parameters. E.g.,
1
\psset{linecolor=\psfillcolor,doublesep=.5\pslinewidth}
However, even for these parameters, PSTricks may do some processing and
error-checking, and you should always set them using \psset or as optional
parameter changes, rather than redefining the command where the value is
stored.
4
Dimensions, coordinates and angles
Whenever an argument of a PSTricks macro is a dimension, the unit is
optional. The default unit is set by the
unit=dim
Default: 1cm
parameter. For example, with the default value of 1cm, the following are
equivalent:
The Essentials: Dimensions, coordinates and angles
5
1
2
\psset{linewidth=.5cm}
\psset{linewidth=.5}
By never explicitly giving units, you can scale graphics by changing the
value of unit.
You can use the default coordinate when setting non-PSTricks dimensions
as well, using the commands
\pssetlength{cmd}{dim}
where cmd is a dimension register (in LATEX parlance, a “length”), and dim
is a length with optional unit. These are analogous to LATEX’s \setlength
Coordinate pairs have the form (x,y ). The origin of the coordinate system
is at TEX’s currentpoint. The command \SpecialCoor lets you use polar
coordinates, in the form (<r>;<a>), where r is the radius (a dimension) and
a is the angle (see below). You can still use Cartesian coordinates. For a
complete description of \SpecialCoor, see Section 54.
The unit parameter actually sets the following three parameters:
xunit=dim
yunit=dim
runit=dim
Default: 1cm
Default: 1cm
Default: 1cm
These are the default units for x-coordinates, y-coordinates, and all other
coordinates, respectively. By setting these independently, you can scale the
x and y dimensions in Cartesian coordinate unevenly. After changing yunit
to 1pt, the two \psline’s below are equivalent:
1
2
3
\psset{yunit=1pt}
\psline(0cm,20pt)(5cm,80pt)
\psline(0,20)(5,80)
The values of the runit, xunit and yunit parameters are stored in the dimension registers \psunit (also \psrunit), \psxunit and \psyunit.
Angles, in polar coordinates and other arguments, should be a number giving the angle in degrees, by default. You can also change the units used for
angles with the command
\degrees[num]
num should be the number of units in a circle. For example, you might use
1
\degrees[100]
The Essentials: Dimensions, coordinates and angles
6
to make a pie chart when you know the shares in percentages. \degrees
without the argument is the same as
1
\degrees[360]
The command
is short for
\degrees[6.28319]
\SpecialCoor lets you specify angles in other ways as well.
5
Basic graphics parameters
The width and color of lines is set by the parameters:
linewidth=dim
linecolor=color
Default: .8pt
Default: black
The linewidth is stored in the dimension register \pslinewidth, and the
linecolor is stored in the command \pslinecolor.
The regions delimited by open and closed curves can be filled, as determined by the parameters:
fillstyle=style
fillcolor=color
When fillstyle=none, the regions are not filled. When fillstyle=solid,
the regions are filled with fillcolor. Other fillstyle’s are described in Section 14.
The graphics objects all have a starred version (e.g., \psframe*) which
draws a solid object whose color is linecolor. For example,
1
\psellipse*(1,.5)(1,.5)
Open curves can have arrows, according to the
arrows=arrows
The Essentials: Basic graphics parameters
7
parameter. If arrows=-, you get no arrows. If arrows=<->, you get arrows
on both ends of the curve. You can also set arrows=-> and arrows=<-,
if you just want an arrow on the end or beginning of the curve, respectively. With the open curves, you can also specify the arrows as an optional
argument enclosed in {} brackets. This should come after the optional parameters argument. E.g.,
1
\psline[linewidth=2pt]{<-}(2,1)
Other arrow styles are described in Section 15
If you set the
showpoints=true/false
Default: false
parameter to true, then most of the graphics objects will put dots at the
appropriate coordinates or control points of the object.2 Section 9 describes
how to change the dot style.
2
The parameter value is stored in the conditional \ifshowpoints.
The Essentials: Basic graphics parameters
8
II
6
Basic graphics objects
Lines and polygons
The objects in this section also use the following parameters:
Default: 0pt
linearc=dim
The radius of arcs drawn at the corners of lines by the \psline and
\pspolygon graphics objects. dim should be positive.
Default: 0
framearc=num
In the \psframe and the related box framing macros, the radius of
rounded corners is set, by default, to one-half num times the width
or height of the frame, whichever is less. num should be between 0
and 1.
cornersize=relative/absolute
Default: relative
If cornersize is relative, then the framearc parameter determines
the radius of the rounded corners for \psframe, as described above
(and hence the radius depends on the size of the frame). If cornersize is absolute, then the linearc parameter determines the radius of
the rounded corners for \psframe (and hence the radius is of constant
size).
Now here are the lines and polygons:
\psline*[par]{arrows}(x0,y0 )(x1,y1)… (xn,yn)
This draws a line through the list of coordinates. For example:
2
1
1
\psline[linewidth=2pt,linearc=.25]{->}(4,2)(0,1)(2,0)
0
0
1
2
3
4
\qline(coor0)(coor1)
This is a streamlined version of \psline that does not pay attention to
the arrows parameter, and that can only draw a single line segment.
Note that both coordinates are obligatory, and there is no optional
Basic graphics objects
9
argument for setting parameters (use \psset if you need to change
the linewidth, or whatever). For example:
1
1
\qline(0,0)(2,1)
0
0
1
2
\pspolygon*[par](x0,y0 )(x1,y1)(x2,y2)… (xn,yn)
This is similar to \psline, but it draws a closed path. For example:
2
1
1
2
\pspolygon[linewidth=1.5pt](0,2)(1,2)
\pspolygon*[linearc=.2,linecolor=darkgray](1,0)(1,2)(4,0)(4,2)
0
0
1
2
3
4
\psframe*[par](x0,y0 )(x1,y1)
\psframe draws a rectangle with opposing corners (x0,y0) and (x1,y1).
For example:
2
1
1
2
3
\psframe[linewidth=2pt,framearc=.3,fillstyle=solid,
fillcolor=lightgray](4,2)
\psframe*[linecolor=white](1,.5)(2,1.5)
0
0
1
2
3
4
\psdiamond*[par](x0,y0)(x1,y1)
\psdiamond draws a diamond centered at (x0,y0), and with the half
width and height equal to x1 and y1, respectively.
2
1
1
2
\psdiamond[framearc=.3,fillstyle=solid,
fillcolor=lightgray](2,1)(1.5,1)
0
0
1
2
3
4
The diamond is rotated about the center by
gangle=angle
Default: 0
\pstriangle*[par](x0,y0)(x1,y1)
\pstriangle draws an isosceles triangle with the base centered at
(x0,y0), and with width (base) and height equal to x1 and y1, re-
spectively.
2
1
1
\pstriangle*[gangle=10](2,.5)(4,1)
0
0
1
2
3
4
Basic graphics objects: Lines and polygons
10
7
Arcs, circles and ellipses
This draws a circle whose center is at (x0,y0) and that has radius
2
1
1
\pscircle[linewidth=2pt](.5,.5){1.5}
0
-1
-1
0
1
2
This is a streamlined version of \pscircle*. Note that the two arguments are obligatory and there is no parameters arguments. To
change the color of the disks, you have to use \psset:
1
2
\psset{linecolor=gray}
\qdisk(2,3){4pt}
This draws a wedge whose center is at (x0,y0), that has radius radius, and that extends counterclockwise from angle1 to angle2 . The
angles must be specified in degrees. For example:
2
1
1
\pswedge[linecolor=gray,linewidth=2pt,fillstyle=solid]{2}{0}{70}
0
0
1
2
\psellipse*[par](x0,y0 )(x1,y1)
(x0,y0) is the center of the ellipse, and x1 and y1 are the horizontal
and vertical radii, respectively. For example:
1
0
1
\psellipse[fillcolor=lightgray](.5,0)(1.5,1)
-1
-1
0
1
2
This draws an arc from angleA to angleB , going counter clockwise,
for a circle of radius radius and centered at (x,y ). You must include
either the arrows argument or the (x,y ) argument. For example:
Basic graphics objects: Arcs, circles and ellipses
11
2
1
1
\psarc*[showpoints=true](1.5,1.5){1.5}{215}{0}
0
0
1
2
3
See how showpoints=true draws a dashed line from the center to
the arc; this is useful when composing pictures.
\psarc also uses the parameters:
arcsepA=dim
Default: 0pt
angleA is adjusted so that the arc would just touch a line of
width dim that extended from the center of the arc in the direction of angleA.
arcsepB=dim
This is like arcsepA, but angleB is adjusted.
arcsep=dim
This just sets both arcsepA and arcsepB.
Default: 0pt
Default: 0
These parameters make it easy to draw two intersecting lines and
then use \psarc with arrows to indicate the angle between them. For
example:
3
2
1
2
1
3
\SpecialCoor
\psline[linewidth=2pt](4;50)(0,0)(4;10)
\psarc[arcsepB=2pt]{->}{3}{10}{50}
0
0
1
2
3
4
This is like \psarc, but the arc is drawn clockwise. You can achieve
the same effect using \psarc by switching angleA and angleB and
the arrows.3
\psellipticarc*[par]{arrows}(x0,y0 )(x1,y1){angleA}{angleB}
This draws an elliptic from angleA to angleB , going counter clockwise, with (x0,y0) the center of the ellipse and x1 and y1 the horizontal and vertical radii, respectively. For example:
1
0
1
\psellipticarc[showpoints=true,arrowscale=2]{->}(.5,0)(1.5,1){215}{0}
-1
-1
0
1
2
3
However, with \pscustom graphics object, described in Part IV, \psarcn is not
redundant.
Basic graphics objects: Arcs, circles and ellipses
12
See how showpoints=true draws a dashed line from the center to
the arc; this is useful when composing pictures.
Like \psarc, \psellipticarc use the arcsep/arcsepA/arcsepB parameters.
Unlike \psarc, \psellipticarcuse the dimen parameter.
\psellipticarcn*[par]{arrows}(x0,y0 )(x1,y1){angleA}{angleB}
This is like \psellipticarc, but the arc is drawn clockwise. You can
achieve the same effect using \psellipticarc by switching angleA
and angleB and the arrows.4
8
Curves
\psbezier*[par]{arrows}(x0,y0 )(x1,y1)(x2,y2)(x3,y3)
\psbezier draws a bezier curve with the four control points. The
curve starts at the first coordinate, tangent to the line connecting to
the second coordinate. It ends at the last coordinate, tangent to the
line connecting to the third coordinate. The second and third coordinates, in addition to determining the tangency of the curve at the
endpoints, also “pull” the curve towards themselves. For example:
b
1
\psbezier[linewidth=2pt,showpoints=true]{->}(0,0)(1,4)(2,1)(4,3.5)
b
b
showpoints=true puts dots in all the control points, and connects
curve.
\parabola*[par]{arrows}(x0,y0)(x1,y1)
Starting at (x0,y0), \parabola draws the parabola that passes through
(x0,y0) and whose maximum or minimum is (x1,y1). For example:
4
However, with \pscustom graphics object, described in Part IV, \psellipticarcn is
not redundant.
Basic graphics objects: Curves
13
3
2
1
2
1
3
\parabola*(1,1)(2,3)
\psset{xunit=.01}
\parabola{<->}(400,3)(200,0)
0
0
1
2
3
4
The next three graphics objects interpolate an open or closed curve through
the given points. The curve at each interior point is perpendicular to the
line bisecting the angle ABC, where B is the interior point, and A and C are
the neighboring points. Scaling the coordinates does not cause the curve to
scale proportionately.
The curvature is controlled by the following parameter:
curvature=num1 num2 num3
Default: 1 .1 0
You have to just play around with this parameter to get what you
want. Individual values outside the range -1 to 1 are either ignored
or are for entertainment only. Below is an explanation of what each
number does. A, B and C refer to three consecutive points.
Lower values of num1 make the curve tighter.
Lower values of num2 tighten the curve where the angle ABC is
greater than 45 degrees, and loosen the curve elsewhere.
num3 determines the slope at each point. If num3 =0, then the curve
is perpendicular at B to the bisection of ABC. If num3 =-1, then
the curve at B is parallel to the line AC. With this value (and only
this value), scaling the coordinates causes the curve to scale proportionately. However, positive values can look better with irregularly
spaced coordinates. Values less than -1 or greater than 2 are converted to -1 and 2, respectively.
Here are the three curve interpolation macros:
\pscurve*[par]{arrows}(x1,y1)… (xn,yn)
This interpolates an open curve through the points. For example:
2
b
b
1
1
2
b
\pscurve[showpoints=true]{<->}(0,1.3)(0.7,1.8)
(3.3,0.5)(4,1.6)(0.4,0.4)
0
0
1
2
3
4
Note the use of showpoints=true to see the points. This is helpful
when constructing a curve.
Basic graphics objects: Curves
14
\psecurve*[par]{arrows}(x1,y1)… (xn,yn)]
This is like \pscurve, but the curve is not extended to the first and
last points. This gets around the problem of trying to determine how
the curve should join the first and last points. The e has something to
do with “endpoints”. For example:
4
b
3
2
1
b
2
1
\psecurve[showpoints=true](.125,8)(.25,4)(.5,2)
(1,1)(2,.5)(4,.25)(8,.125)
b
b
b
0
0
1
2
3
4
\psccurve*[par]{arrows}(x1,y1)… (xn,yn)
This interpolates a closed curve through the points. c stands for
“closed”. For example:
1
b
b
1
0
0
b
1
2
9
3
b
2
\psccurve[showpoints=true]
(.5,0)(3.5,1)(3.5,0)(.5,1)
4
Dots
The graphics objects
\psdot*[par ](x1,y1)
\psdots*[par ](x1,y1)(x2,y2 )… (xn,yn)
put a dot at each coordinate.
What a “dot” is depends on the value of the
dotstyle=style
Default: *
parameter. This also determines the dots you get when showpoints=true.
The dot styles are also pretty intuitive:
Basic graphics objects: Dots
15
Style
Example
Style
b
b
b
b
b
bc
bc
bc
bc
bc
bC
bC
bC
bC
bC
x
×
×
×
×
×
+
+ + + + +
Bdiamond
B+
+ + + + +
diamond*
asterisk
* * * * *
triangle
*
o
Bo
square
Bsquare
square*
diamond
Basterisk
*
*
*
*
*
Btriangle
oplus
⊕
⊕
⊕
⊕
⊕
triangle*
otimes
⊗
⊗
⊗
⊗
⊗
pentagon
|
|
|
|
|
|
Bpentagon
B|
|
|
|
|
|
pentagon*
Example
rs
rs
rs
rs
rs
rS
rS
rS
rS
rS
r
r
r
r
r
d
l
d
l
d
l
d
l
d
l
D
l
D
l
D
l
D
l
D
l
l
l
l
l
l
t
u
t
u
t
u
t
u
t
u
T
u
T
u
T
u
T
u
T
u
u
u
u
u
u
p
q
p
q
p
q
p
q
p
q
P
q
P
q
P
q
P
q
P
q
q
q
q
q
q
Except for diamond, the center of dot styles with a hollow center is colored
fillcolor.
Here are the parameters for changing the size and orientation of the dots:
dotsize=dim ‘num’
Default: 2pt 2
The diameter of a circle or disc is dim plus num times linewidth
(if the optional num is included). The size of the other dots styles
is similar (except for the size of the | dot style, which is set by the
tbarsize parameter described on page 29).
dotscale=num1 ‘num2’
Default: 1
The dots are scaled horizontally by num1 and vertically by num2 .
If you only include num1, the arrows are scaled by num1 in both
directions.
dotangle=angle
Default: 0
After setting the size and scaling the dots, the dots are rotated by
angle.
10
Grids
PSTricks has a powerful macro for making grids and graph paper:
\psgrid(x0,y0 )(x1,y1)(x2,y2 )
\psgrid draws a grid with opposing corners (x1,y1) and (x2,y2). The intervals are numbered, with the numbers positioned at x0 and y0 . The coor-
dinates are always interpreted as Cartesian coordinates. For example:
Basic graphics objects: Grids
16
2
1
1
0
-1
0
1
2
\psgrid(0,0)(-1,-1)(3,2)
3
-1
(Note that the coordinates and label positioning work the same as with
\psaxes.)
The main grid divisions occur on multiples of xunit and yunit. Subdivisions are allowed as well. Generally, the coordinates would be given as
integers, without units.
If the (x0,y0) coordinate is omitted, (x1,y1) is used. The default for (x1,y1)
is (0,0). If you don’t give any coordinates at all, then the coordinates of the
current \pspicture environment are used or a 10x10 grid is drawn. Thus,
you can include a \psgrid command without coordinates in a \pspicture
environment to get a grid that will help you position objects in the picture.
The main grid divisions are numbered, with the numbers drawn next to
the vertical line at x0 (away from x2 ) and next to the horizontal line at x1
(away from y2 ). (x1,y1) can be any corner of the grid, as long as (x2,y2) is
the opposing corner, you can position the labels on any side you want. For
example, compare
1
1
\psgrid(0,0)(4,1)
1
\psgrid(4,1)(0,0)
0
0
1
2
3
4
and
0
1
2
3
4
1
0
The following parameters apply only to \psgrid:
gridwidth=dim
Default: .8pt
The width of grid lines.
gridcolor=color
Default: black
The color of grid lines.
griddots=num
Default: 0
If num is positive, the grid lines are dotted, with num dots per division.
Basic graphics objects: Grids
17
gridlabels=dim
Default: 10pt
The size of the numbers used to mark the grid.
gridlabelcolor=color
Default: black
The color of the grid numbers.
subgriddiv=int
Default: 5
The number of grid subdivisions.
subgridwidth=dim
Default: .4pt
The width of subgrid lines.
subgridcolor=color
Default: gray
The color of subgrid lines.
subgriddots=num
Default: 0
Like griddots, but for subdivisions.
Here is a familiar looking grid which illustrates some of the parameters:
1
0
1
\psgrid[subgriddiv=1,griddots=10,gridlabels=7pt](-1,-1)(3,1)
-1
-1
0
1
2
3
Note that the values of xunit and yunit are important parameters for \psgrid, because they determine the spacing of the divisions. E.g., if the value
of these is 1pt, and then you type
1
\psgrid(0,0)(10in,10in)
you will get a grid with 723 main divisions and 3615 subdivisions! (Actually, \psgrid allows at most 500 divisions or subdivisions, to limit the
damage done by this kind of mistake.) Probably you want to set unit to
.5in or 1in, as in
1
11
pst-plot
\psgrid[unit=.5in](0,0)(20,20)
Plots
The plotting commands described in this part are defined in pst-plot.tex /
pst-plot.sty, which you must load first (for various simple and more elaborated examples, you can refer to the two articles published by Herbert Voß
Basic graphics objects: Plots
18
and Laura E. Jackson in Die TeXnische Komödie in 2002 [33] and [81] (in
German)).5
The \psdots, \psline, \pspolygon, \pscurve, \psecurve and \psccurve
graphics objects let you plot data in a variety of ways. However, first you
have to generate the data and enter it as coordinate pairs (x,y ). The plotting macros in this section give you other ways to get and use the data.
(Section 26 tells you how to generate axes.)
To parameter
plotstyle=style
Default: line
determines what kind of plot you get. Valid styles are dots, line, polygon,
curve, ecurve, ccurve. E.g., if the plotstyle is polygon, then the macro
becomes a variant of the \pspolygon object.
You can use arrows with the plot styles that are open curves, but there is no
optional argument for specifying the arrows. You have to use the arrows
Warning: No PostScript error checking is provided for
the data arguments. Read Appendix L.4 before including
PostScript code in the arguments.
PS
There are system-dependent limits on the amount of data TEX
and PostScript can handle. You are much less likely to exceed
the PostScript limits when you use the line, polygon or dots
plot style, with showpoints=false, linearc=0pt, and no arrows.
Note that the lists of data generated or used by the plot commands cannot
contain units. The values of \psxunit and \psyunit are used as the unit.
\fileplot*[par]{file}
\fileplot is the simplest of the plotting functions to use. You just
need a file that contains a list of coordinates (without units), such as
generated by Mathematica or other mathematical packages. The data
can be delimited by curly braces { }, parentheses ( ), commas, and/or
white space. Bracketing all the data with square brackets [ ] will
significantly speed up the rate at which the data is read, but there are
system-dependent limits on how much data TEX can read like this in
one chunk. (The [ must go at the beginning of a line.) The file should
not contain anything else (not even \endinput), except for comments
marked with %.
5
For plotting commands in three dimensions, see the ‘pst-3dplot’ contribution package [54] from Herbert Voß.
Basic graphics objects: Plots
19
\fileplot only recognizes the line, polygon and dots plot styles, and it
ignores the arrows, linearc and showpoints parameters. The \listplot command, described below, can also plot data from file, without
these restrictions and with faster TEX processing. However, you are
less likely to exceed PostScript’s memory or operand stack limits
with \fileplot.
If you find that it takes TEX a long time to process your \fileplot
command, you may want to use the \PSTtoEPS command described
on page 160. This will also reduce TEX’s memory requirements.
\dataplot*[par]{commands}
\dataplot is also for plotting lists of data generated by other pro-
grams, but you first have to retrieve the data with one of the following
commands:
\savedata{command}[data]
data or the data in file should conform to the rules described above
for the data in \fileplot (with \savedata, the data must be delimited
by [ ], and with \readdata, bracketing the data with [ ] speeds things
up). You can concatenate and reuse lists, as in
1
2
3
4
\dataplot{\foo\bar}
\dataplot[origin={0,1}]{\bar}
The \readdata and \dataplot combination is faster than \fileplot if
you reuse the data. \fileplot uses less of TEX’s memory than \readdata and \dataplot if you are also use \PSTtoEPS.
Here is a plot of Integral(sin(x)). The data was generated by Mathematica, with
1
Table[{x,N[SinIntegral[x]]},{x,0,20}]
and then copied to this document.
1
t
u
t
u
t
u
t
u
2
t
u
t
uu
t
tu
u
tu
tu
tu
ut
t
t t
u
tu
t
tu
tu
uu
tu
3
4
5
6
7
8
t
u
9
10
\psset{xunit=.2cm,yunit=1.5cm}
\savedata{\mydata}[
{{0, 0}, {1., 0.946083}, {2., 1.60541}, {3., 1.84865}, {4., 1.7582},
{5., 1.54993}, {6., 1.42469}, {7., 1.4546}, {8., 1.57419},
{9., 1.66504}, {10., 1.65835}, {11., 1.57831}, {12., 1.50497},
{13., 1.49936}, {14., 1.55621}, {15., 1.61819}, {16., 1.6313},
{17., 1.59014}, {18., 1.53661}, {19., 1.51863}, {20., 1.54824}}]
\dataplot[plotstyle=curve,showpoints=true,
dotstyle=triangle]{\mydata}
\psline{<->}(0,2)(0,0)(20,0)
Basic graphics objects: Plots
20
\listplot*[par]{list}
\listplot is yet another way of plotting lists of data. This time, list
should be a list of data (coordinate pairs), delimited only by white
space. list is first expanded by TEX and then by PostScript. This
means that list might be a PostScript program that leaves on the
stack a list of data, but you can also include data that has been retrieved with \readdata and \dataplot. However, when using the line,
polygon or dots plotstyles with showpoints=false, linearc=0pt
and no arrows, \dataplot is much less likely than \listplot to exceed PostScript’s memory or stack limits. In the preceding example,
these restrictions were not satisfied, and so the example is equivalent
to when \listplot is used:
1
2
3
4
...
\listplot[plotstyle=curve,showpoints=true,
dotstyle=triangle]{\mydata}
...
\psplot*[par]{xmin }{xmax }{function}
\psplot can be used to plot a function f (x), if you know a little
PostScript. function should be the PostScript code for calculating
f (x). Note that you must use x as the dependent variable. PostScript
is not designed for scientific computation, but \psplot is good for
graphing simple functions right from within TEX. E.g.,
1
\psplot[plotpoints=200]{0}{720}{x sin}
plots sin(x) from 0 to 720 degrees, by calculating sin(x) roughly
every 3.6 degrees and then connecting the points with \psline. Here
are plots of sin(x) cos((x/2)2 ) and sin2 (x):
1
2
3
4
5
6
\psset{xunit=1.2pt}
\psplot[linecolor=gray,linewidth=1.5pt,plotstyle=curve]%
{0}{90}{x sin dup mul}
\psplot[plotpoints=100]{0}{90}{x sin x 2 div 2 exp cos mul}
\psline{<->}(0,-1)(0,1)
\psline{->}(100,0)
\parametricplot*[par]{tmin }{tmax }{function}
This is for a parametric plot of (x(t), y(t)). function is the PostScript
code for calculating the pair x(t) y(t).
For example,
Basic graphics objects: Plots
21
3
b
b
b
b
b
2
1
1
b
b
2
b
b b
b
0
0
1
2
b
\parametricplot[plotstyle=dots,plotpoints=13]%
{-6}{6}{1.2 t exp 1.2 t neg exp}
b
3
plots 13 points from the hyperbola xy = 1, starting with (1.2−6 , 1.26 )
and ending with (1.26 , 1.2−6 ).
Here is a parametric plot of (sin(t), sin(2t)):
1
2
3
4
5
\psset{xunit=1.7cm}
\parametricplot[linewidth=1.2pt,plotstyle=ccurve]%
{0}{360}{t sin t 2 mul sin}
\psline{<->}(0,-1.2)(0,1.2)
\psline{<->}(-1.2,0)(1.2,0)
The number of points that the \psplot and \parametricplot commands
calculate is set by the
plotpoints=int
Default: 50
parameter. Using curve or its variants instead of line and increasing the
value of plotpoints are two ways to get a smoother curve. Both ways increase the imaging time. Which is better depends on the complexity of the
computation. (Note that all PostScript lines are ultimately rendered as a
series (perhaps short) line segments.) Mathematica generally uses lineto to
connect the points in its plots. The default minimum number of plot points
for Mathematica is 25, but unlike \psplot and \parametricplot, Mathematica increases the sampling frequency on sections of the curve with greater
fluctuation.
Basic graphics objects: Plots
22
III
More graphics parameters
The graphics parameters described in this part are common to all or most
of the graphics objects.
12
Coordinate systems
The following manipulations of the coordinate system apply only to pure
graphics objects.
A simple way to move the origin of the coordinate system to (x,y ) is with
the
origin={coor}
Default: 0pt,0pt
This is the one time that coordinates must be enclosed in curly brackets {}
rather than parentheses ().
A simple way to switch swap the axes is with the
Default: false
swapaxes=true
parameter. E.g., you might change your mind on the orientation of a plot
after generating the data.
13
Line styles
The following graphics parameters (in addition to linewidth and linecolor)
determine how the lines are drawn, whether they be open or closed curves.
Default: solid
linestyle=style
Valid styles are none, solid, dashed and dotted.
dash=dim1 dim2
Default: 5pt 3pt
The black-white dash pattern for the dashed line style. For
example:
1
\psellipse[linestyle=dashed,dash=3pt 2pt](2,1)(2,1)
More graphics parameters
23
Default: 3pt
dotsep=dim
The distance between dots in the dotted line style. For example
1
\psline[linestyle=dotted,dotsep=2pt]{|-»}(4,1)
border=dim
Default: 0pt
A positive value draws a border of width dim and color
bordercolor on each side of the curve. This is useful for giving the
impression that one line passes on top of another. The value is saved
in the dimension register \psborder.
bordercolor=color
Default: white
See border above.
For example:
1
2
3
4
5
6
\psline(0,0)(1.8,3)
\psline[border=2pt]{*->}(0,3)(1.8,0)
\psframe*[linecolor=gray](2,0)(4,3)
\psline[linecolor=white,linewidth=1.5pt]{<->}(2.2,0)(3.8,3)
\psellipse[linecolor=white,linewidth=1.5pt,
bordercolor=gray,border=2pt](3,1.5)(.7,1.4)
doubleline=true/false
Default: false
When true, a double line is drawn, separated by a space that is
doublesep wide and of color doublecolor. This doesn’t work as
expected with the dashed linestyle, and some arrows look funny as
well.
doublesep=dim
Default: 1.25\pslinewidth
See doubleline, above.
doublecolor=color
Default: white
See doubleline, above.
Here is an example of double lines:
1
2
\psline[doubleline=true,linearc=.5,
doublesep=1.5pt]{->}(0,0)(3,1)(4,0)
Default: false
When true, a shadow is drawn, at a distance shadowsize from the
original curve, in the direction shadowangle, and of color
More graphics parameters: Line styles
24
Default: 3pt
Default: -45
Default: darkgray
Here is an example of the shadow feature, which should look
familiar:
1
2
3
xunit=1.1](-1,-.55)(-1,.5)(-.8,.5)(-.8,.65)
(-.2,.65)(-.2,.5)(1,.5)(1,-.55)
Here is another graphics parameter that is related to lines but that applies
only to the closed graphics objects \psframe, \pscircle, \psellipse and
\pswedge:
dimen=outer/inner/middle
Default: outer
It determines whether the dimensions refer to the inside, outside or middle
of the boundary. The difference is noticeable when the linewidth is large:
3
2
1
2
3
1
4
\psset{linewidth=.25cm}
\psframe[dimen=inner](0,0)(2,1)
\psframe[dimen=middle](0,2)(2,3)
\psframe[dimen=outer](3,0)(4,3)
0
0
1
2
3
4
With \pswedge, this only affects the radius; the origin always lies in the
middle the boundary. The right setting of this parameter depends on how
you want to align other objects.
14
Fill styles
The next group of graphics parameters determine how closed regions are
filled. Even open curves can be filled; this does not affect how the curve is
painted.
fillstyle=style
Default: none
Valid styles are
More graphics parameters: Fill styles
25
none, solid, vlines, vlines*, hlines, hlines*, crosshatch,
crosshatch* and boxfill.
vlines, hlines and crosshatch draw a pattern of lines, according to
the four parameters list below that are prefixed with hatch. The *
versions also fill the background, as in the solid style.
The boxfill style, which require to load the ‘pst-fill’ package, allow to
fill (tile) the area with an arbitrary pattern defined using the
\psboxfill macro (see the Part IX).
fillcolor=color
Default: white
The background color in the solid, vlines*, hlines* and crosshatch*
styles.
Default: .8pt
hatchwidth=dim
Width of lines.
Default: 4pt
hatchsep=dim
Width of space between the lines.
hatchcolor=color
Default: black
Color of lines. Saved in \pshatchcolor.
hatchangle=rot
Default: 45
Rotation of the lines, in degrees. For example, if hatchangle is set
to 45, the vlines style draws lines that run NW-SE, and the hlines
style draws lines that run SW-NE, and the crosshatch style draws
both.
Here is an example of the vlines and related fill styles:6
1
2
3
4
5
\pspolygon[fillstyle=vlines](0,0)(0,3)(4,0)
\pspolygon[fillstyle=hlines](0,0)(4,3)(4,0)
\pspolygon[fillstyle=crosshatch*,fillcolor=black,
hatchcolor=white,hatchwidth=1.2pt,hatchsep=1.8pt,
hatchangle=0](0,3)(2,1.5)(4,3)
Default:
This allow to use two different styles for the same area. This is specially useful when the boxfill style is used.
6
PSTricks adjusts the lines relative to the resolution so that they all have the same width
and the same intervening space. Otherwise, the checkered pattern in this example would
be noticeably uneven, even on 300 dpi devices. This adjustment is resolution dependent,
and may involve adjustments to the hatchangle when this is not initially a multiple of 45
degrees.
More graphics parameters: Fill styles
26
Each of the pure graphics objects (except those beginning with q) has a
starred version that produces a solid object of color linecolor. (It automatically sets linewidth to zero, fillcolor to linecolor, fillstyle to solid, and
linestyle to none.)
15
Lines and other open curves can be terminated with various arrowheads,
t-bars or circles. The
Default: -
arrows=style
parameter determines what you get. It can have the following values, which
are pretty intuitive:7
Value
<->
>-<
«-»
»-«
|-|
|*-|*
|<->|
|<*->|*
[-]
(-)
o-o
*-*
oo-oo
**-**
c-c
cc-cc
C-C
Example Name
None
T-bars, flush to endpoints.
T-bars, centered on endpoints.
Square brackets.
Rounded brackets.
Circles, centered on endpoints.
Disks, centered on endpoints.
Circles, flush to endpoints.
Disks, flush to endpoints.
Extended, rounded ends.
Flush round ends.
Extended, square ends.
You can also mix and match. E.g., ->, *-) and [-> are all valid values of the
arrows parameter.
Well, perhaps the c, cc and C arrows are not so obvious. c and C correspond
to setting PostScript’s linecap to 1 and 2, respectively. cc is like c, but
7
This is TEX’s version of WYSIWYG.
More graphics parameters: Arrowheads and such
27
adjusted so that the line flush to the endpoint. These arrows styles are
noticeable when the linewidth is thick:
1
2
3
4
-
\psline[linewidth=.5cm](0,0)(0,2)
\psline[linewidth=.5cm]{c-c}(1,0)(1,2)
\psline[linewidth=.5cm]{cc-cc}(2,0)(2,2)
\psline[linewidth=.5cm]{C-C}(3,0)(3,2)
c-c cc-cc C-C
Almost all the open curves let you include the arrows parameters as an
optional argument, enclosed in curly braces and before any other arguments
(except the optional parameters argument). E.g., instead of
1
\psline[arrows=<-,linestyle=dotted](3,4)
you can write
1
\psline[linestyle=dotted]{<-}(3,4)
The exceptions are a few streamlined macros that do not support the use of
arrows (these all begin with q).
The size of these line terminators is controlled by the following parameters. In the description of the parameters, the width always refers to the
dimension perpendicular to the line, and length refers to a dimension in the
direction of the line.
Default: 1.5pt 2
arrowsize=dim ‘num’
The width of arrowheads is dim plus num times linewidth (if the
optional ‘num’ is inclued). See the diagram below.
Default: 1.4
arrowlength=num
Length of arrowheads, as a fraction of the width, as shown below.
Default: .4
arrowinset=num
Size of inset for arrowheads, as a fraction of the length, as shown
below.
arrowsize
length
inset
width
length
inset
=
=
=
=
width
More graphics parameters: Arrowheads and such
dim num
num × linewidth + dim
arrowlength × width
arrowinset × length
28
tbarsize=dim ‘num’
Default: 2pt 5
The width of a t-bar, square bracket or rounded bracket is dim plus
num times linewidth (if the optional ‘num’ is included). linewidth,
plus dim.
bracketlength=num
Default: .15
The height of a square bracket is num times its width.
rbracketlength=num
Default: .15
The height of a round bracket is num times its width.
arrowscale=arrowscale=num1 num2
Default: 1
Imagine that arrows and such point down. This scales the width of
the arrows by num1 and the length (height) by num2 . If you only include one number, the arrows are scaled the same in both directions.
Changing arrowscale can give you special effects not possible by
changing the parameters described above. E.g., you can change the
width of lines used to draw brackets.
The size of dots is controlled by the dotsize parameter.
16
Custom styles
You can define customized versions of any macro that has parameter changes
as an optional first argument using the \newpsobject command:
\newpsobject{name}{object}{par1=value1,… }
as in
1
2
3
\newpsobject{myline}{psline}{linecolor=green,linestyle=dotted}
\newpsobject{mygrid}{psgrid}{subgriddiv=1,griddots=10,
gridlabels=7pt}
The first argument is the name of the new command you want to define.
The second argument is the name of the graphics object. Note that both of
these arguments are given without the backslash. The third argument is the
special parameter values that you want to set.
With the above examples, the commands \myline and \mygrid work just
like the graphics object \psline it is based on, and you can even reset the
parameters that you set when defining \myline, as in:
1
\myline[linecolor=gray,dotsep=2pt](5,6)
Another way to define custom graphics parameter configurations is with the
More graphics parameters: Custom styles
29
\newpsstyle{name}{par1=value1,… }
command. You can then set the style graphics parameter to name, rather
than setting the parameters given in the second argument of \newpsstyle.
For example,
1
2
\newpsstyle{mystyle}{linecolor=green,linestyle=dotted}
\psline[style=mystyle](5,6)
More graphics parameters: Custom styles
30
IV
17
Custom graphics
The basics
PSTricks contains a large palette of graphics objects, but sometimes you
need something special. For example, you might want to shade the region
between two curves. The
\pscustom*[par ]{commands}
command lets you “roll you own” graphics object.
Let’s review how PostScript handles graphics. A path is a line, in the mathematical sense rather than the visual sense. A path can have several disconnected segments, and it can be open or closed. PostScript has various operators for making paths. The end of the path is called the current point, but
if there is no path then there is no current point. To turn the path into something visual, PostScript can fill the region enclosed by the path (that is what
fillstyle and such are about), and stroke the path (that is what linestyle and
At the beginning of \pscustom, there is no path. There are various commands that you can use in \pscustom for drawing paths. Some of these
(the open curves) can also draw arrows. \pscustom fills and strokes the
path at the end, and for special effects, you can fill and stroke the path along
the way using \fill and \stroke (see below).
Driver notes: \pscustom uses \pstverb and \pstunit. There are system-dependent
limits on how long the argument of \special can be. You may run into this limit
using \pscustom because all the PostScript code accumulated by \pscustom is
the argument of a single \special command.
18
Parameters
You need to keep the separation between drawing, stroking and filling paths
in mind when setting graphics parameters. The linewidth and linecolor
parameters affect the drawing of arrows, but since the path commands do
not stroke or fill the paths, these parameters, and the linestyle, fillstyle and
related parameters, do not have any other effect (except that in some cases
Custom graphics
31
linewidth is used in some calculations when drawing the path). \pscustom and \fill make use of fillstyle and related parameters, and \pscustom
and \stroke make use of plinestyle and related parameters.
For example, if you include
1
\psline[linewidth=2pt,linecolor=blue,fillstyle=vlines]{<-}(3,3)(4,0)
in \pscustom, then the changes to linewidth and linecolor will affect the
size and color of the arrow but not of the line when it is stroked, and the
change to fillstyle will have no effect at all.
The shadow, border, doubleline and showpoints parameters are disabled in \pscustom, and the origin and swapaxes parameters only affect
\pscustom itself, but there are commands (described below) that let you
achieve these special effects.
The dashed and dotted line styles need to know something about the path
in order to adjust the dash or dot pattern appropriately. You can give this
information by setting the
linetype=int
Default: 0
parameter. If the path contains more than one disconnected segment, there
is no appropriate way to adjust the dash or dot pattern, and you might as
well leave the default value of linetype. Here are the values for simple
paths:
Value
0
-1
-2
-3
1
n>1
19
Type of path
Open curve without arrows.
Open curve with an arrow at the beginning.
Open curve with an arrow at the end.
Open curve with an arrow at both ends.
Closed curve with no particular symmetry.
Closed curve with n symmetric segments.
Graphics objects
You can use most of the graphics objects in \pscustom. These draw paths
and making arrows, but do not fill and stroke the paths.
There are three types of graphics objects:
Special Special graphics objects include \psgrid, \psdots, \qline and \qdisk.
You cannot use special graphics objects in \pscustom.
Custom graphics: Graphics objects
32
Closed You are allowed to use closed graphics objects in \pscustom, but
their effect is unpredictable.8 Usually you would use the open curves
plus \closepath (see below) to draw closed curves.
Open The open graphics objects are the most useful commands for drawing paths with \pscustom. By piecing together several open curves,
you can draw arbitrary paths. The rest of this section pertains to the
open graphics objects.
By default, the open curves draw a straight line between the current point,
if it exists, and the beginning of the curve, except when the curve begins
with an arrow. For example
3
2
1
2
1
3
\pscustom{%
\psarc(0,0){1.5}{5}{85}
\psarcn{->}(0,0){3}{85}{5}}
0
0
1
2
3
Also, the following curves make use of the current point, if it exists, as a
first coordinate:
\psline and \pscurve.
The plot commands, with the line or curve plotstyle.
\psbezier if you only include three coordinates.
For example:
3
2
1
2
1
3
\pscustom[linewidth=1.5pt]{%
\psplot[plotstyle=curve]{.67}{4}{2 x div}
\psline(4,3)}
0
0
1
2
3
4
We’ll see later how to make that one more interesting. Here is another
example
8
The closed objects never use the current point as an coordinate, but typically they will
close any existing paths, and they might draw a line between the currentpoint and the closed
curved.
Custom graphics: Graphics objects
33
3
2
1
2
1
3
\pscustom{%
\psline[linearc=.2]{|-}(0,2)(0,0)(2,2)
\psbezier{->}(2,2)(3,3)(1,0)(4,3)}
0
0
1
2
3
4
However, you can control how the open curves treat the current point with
the
liftpen=0/1/2
Default: 0
parameter.
If liftpen=0, you get the default behavior described above. For example
3
2
1
2
1
3
\pscustom[linewidth=2pt,fillstyle=solid,fillcolor=gray]{%
\pscurve(0,2)(1,2.5)(2,1.5)(4,3)
\pscurve(4,1)(3,0.5)(2,1)(1,0)(0,.5)}
0
0
1
2
3
4
If liftpen=1, the curves do not use the current point as the first coordinate
(except \psbezier, but you can avoid this by explicitly including the first
coordinate as an argument). For example:
3
2
1
2
1
3
\pscustom[linewidth=2pt,fillstyle=solid,fillcolor=gray]{%
\pscurve(0,2)(1,2.5)(2,1.5)(4,3)
\pscurve[liftpen=1](4,1)(3,0.5)(2,1)(1,0)(0,.5)}
0
0
1
2
3
4
If liftpen=2, the curves do not use the current point as the first coordinate,
and they do not draw a line between the current point and the beginning of
the curve. For example
3
2
1
2
1
3
\pscustom[linewidth=2pt,fillstyle=solid,fillcolor=gray]{%
\pscurve(0,2)(1,2.5)(2,1.5)(4,3)
\pscurve[liftpen=2](4,1)(3,0.5)(2,1)(1,0)(0,.5)}
0
0
1
2
3
4
Later we will use the second example to fill the region between the two
curves, and then draw the curves.
Custom graphics: Graphics objects
34
20
Safe tricks
The commands described under this heading, which can only be used in
\pscustom, do not run a risk of PostScript errors (assuming your document
compiles without TEX errors).
\newpath
Clear the path and the current point.
\moveto(coor)
This moves the current point to (x,y ).
\closepath
This closes the path, joining the beginning and end of each piece
(there may be more than one piece if you use \moveto).9
\stroke[par ]
This strokes the path (non-destructively). \pscustom automatically
strokes the path, but you might want to stroke it twice, e.g., to add a
border. Here is an example that makes a double line and adds a border
(this example is kept so simple that it doesn’t need \pscustom at all):
3
1
2
2
3
1
4
5
\psline(0,3)(4,0)
\pscustom[linecolor=white,linewidth=1.5pt]{%
\psline(0,0)(4,3)
\stroke[linewidth=5\pslinewidth]
\stroke[linewidth=3\pslinewidth,linecolor=black]}
0
0
1
2
3
4
\fill[par ]
This fills the region (non-destructively). \pscustom automatically
fills the region as well.
\gsave
This saves the current graphics state (i.e., the path, color, line width,
coordinate system, etc.) \grestore restores the graphics state. \gsave
and \grestore must be used in pairs, properly nested with respect to
TEX groups. You can have have nested \gsave-\grestore pairs.
9
Note that the path is automatically closed when the region is filled. Use \closepath if
you also want to close the boundary.
Custom graphics: Safe tricks
35
\grestore
See above.
Here is an example that fixes an earlier example, using \gsave and
\grestore:
1
2
3
4
5
6
7
\psline{<->}(0,3)(0,0)(4,0)
\pscustom[linewidth=1.5pt]{
\psplot[plotstyle=curve]{.67}{4}{2 x div}
\gsave
\psline(4,3)
\fill[fillstyle=solid,fillcolor=gray]
\grestore}
Observe how the line added by \psline(4,3) is never stroked, because
it is nested in \gsave and \grestore.
Here is another example:
3
1
2
2
3
4
1
5
6
7
0
0
1
2
3
\pscustom[linewidth=1.5pt]{
\pscurve(0,2)(1,2.5)(2,1.5)(4,3)
\gsave
\pscurve[liftpen=1](4,1)(3,0.5)(2,1)(1,0)(0,.5)
\fill[fillstyle=solid,fillcolor=gray]
\grestore}
\pscurve[linewidth=1.5pt](4,1)(3,0.5)(2,1)(1,0)(0,.5)
4
Note how I had to repeat the second \pscurve (I could have repeated
it within \pscustom, with liftpen=2), because I wanted to draw a
line between the two curves to enclose the region but I didn’t want
this line to be stroked.
The next set of commands modify the coordinate system.
\translate(coor)
Translate coordinate system by (x,y ). This shifts everything that
comes later by (x,y ), but doesn’t affect what has already been drawn.
\scale{num1 num2}
Scale the coordinate system in both directions by num1, or horizontally by num1 and vertically by num2 .
\rotate{angle}
Rotate the coordinate system by angle.
\swapaxes
Switch the x and y coordinates. This is equivalent to
Custom graphics: Safe tricks
36
1
2
\rotate{-90}
\scale{-1 1 scale}
\msave
Save the current coordinate system. You can then restore it with
\mrestore. You can have nested \msave-\mrestore pairs. \msave
and \mrestore do not have to be properly nested with respect to TEX
groups or \gsave and \grestore. However, remember that \gsave
and \grestorealso affect the coordinate system. \msave-\mrestore
lets you change the coordinate system while drawing part of a path,
and then restore the old coordinate system without destroying the
path. \gsave-\grestore, on the other hand, affect the path and all
other componments of the graphics state.
\mrestore
See above.
And now here are a few shadow tricks:
Strokes a replica of the current path, using the various shadow parameters.
Makes a shadow of the region enclosed by the current path as if it
were opaque regions.
\movepath(coor)
Moves the path by (x,y ). Use \gsave-\grestore if you don’t want to
lose the original path.
21
Pretty safe tricks
The next group of commands are safe, as long as there is a current point!
\lineto(coor)
This is a quick version of \psline(<coor>).
\rlineto(coor)
This is like \lineto, but (x,y ) is interpreted relative to the current
point.
\curveto(x1,y1)(x2,y2)(x3,y3)
This is a quick version of \psbezier(x1,y1)(x2,y2)(x3,y3).
Custom graphics: Pretty safe tricks
37
\rcurveto(x1,y1)(x2,y2)(x3,y3)
This is like \curveto, but (x1,y1), (x2,y2) and (x3,y3) are interpreted relative to the current point.
22
For hackers only
PS
For PostScript hackers, there are a few more commands. Be sure to read
Appendix L.4 before using these. Needless to say:
Warning: Misuse of the commands in this section can cause
PostScript errors.
The PostScript environment in effect with \pscustom has one unit equal
to one TEX pt.
\code{code}
Insert the raw PostScript code.
\dim{dim}
Convert the PSTricks dimension to the number of pt’s, and inserts it
in the PostScript code.
\coor(x1,y1)(x2,y2)...(xn,yn)
Convert one or more PSTricks coordinates to a pair of numbers (using pt units), and insert them in the PostScript code.
\rcoor(x1,y1)(x2,y2)...(xn,yn)
Like \coor, but insert the coordinates in reverse order.
\file{file}
This is like \code, but the raw PostScript is copied verbatim (except
comments delimited by %) from file.
\arrows{arrows}
This defines the PostScript operators ArrowA and ArrowB so that
1
2
x2 y2 x1 y1 ArrowA
x2 y2 x1 y1 ArrowB
each draws an arrow(head) with the tip at (x1,y1) and pointing from
(x2,y2). ArrowA leaves the current point at end of the arrowhead,
where a connect line should start, and leaves (x2,y2) on the stack.
ArrowB does not change the current point, but leaves
1
x2 y2 x1’ y1’
Custom graphics: For hackers only
38
on the stack, where (x1’,y1’) is the point where a connecting line
should join. To give an idea of how this work, the following is
roughly how PSTricks draws a bezier curve with arrows at the end:
3
1
2
2
3
4
1
5
6
\pscustom{
\arrows{|->}
\code{
80 140 5 5 ArrowA
30 -30 110 75 ArrowB
curveto}}
0
0
1
2
3
4
\setcolor{color}
Set the color to color .
Custom graphics: For hackers only
39
V
23
Picture Tools
Pictures
The graphics objects and \rput and its variants do not change TEX’s current
point (i.e., they create a 0-dimensional box). If you string several of these
together (and any other 0-dimensional objects), they share the same coordinate system, and so you can create a picture. For this reason, these macros
are called picture objects.
If you create a picture this way, you will probably want to give the whole
picture a certain size. You can do this by putting the picture objects in a
pspicture environment,10 as in:
\pspicture*[baseline](x0,y0 )(x1,y1)
picture objects
\endpspicture
The picture objects are put in a box whose lower left-hand corner is at
(x0,y0) (by default, (0,0)) and whose upper right-hand corner is at (x1,y1).
By default, the baseline is set at the bottom of the box, but the optional
argument [<baseline>] sets the baseline fraction baseline from the bottom.
Thus, baseline is a number, generally but not necessarily between 0 and 1.
If you include this argument but leave it empty ([]), then the baseline passes
through the origin.
Normally, the picture objects can extend outside the boundaries of the box.
However, if you include the *, anything outside the boundaries is clipped.
Besides picture objects, you can put anything in a \pspicture that does not
take up space. E.g., you can put in font declarations and use \psset, and
you can put in braces for grouping. PSTricks will alert you if you include
something that does take up space.11
10 A
LT
\begin{pspicture} stuff \end{pspicture}
11
When PSTricks picture objects are included in a \pspicture environment, they gobble up any spaces that follow, and any preceding spaces as well, making it less likely that
extraneous space gets inserted. (PSTricks objects always ignore spaces that follow. If you
also want them to try to neutralize preceding space when used outside the \pspicture environment (e.g., in a LATEX picture environment), then use the command \KillGlue. The
command \DontKillGlue turns this behavior back off.)
Picture Tools
40
You can use PSTricks picture objects in a LATEX picture environment, and
you can use LATEX picture objects in a PSTricks pspicture environment.
However, the pspicture environment makes LATEX’s picture environment
obsolete, and has a few small advantages over the latter. Note that the arguments of the pspicture environment work differently from the arguments
of LATEX’s picture environment (i.e., the right way versus the wrong way).
Driver notes:
24
The clipping option (*) uses \pstVerb and \pstverbscale.
Placing and rotating whatever
PSTricks contains several commands for positioning and rotating an HRmode argument. All of these commands end in put, and bear some similarity to LATEX’s \put command, but with additional capabilities. Like LATEX’s
\put and unlike the box rotation macros described in Section 29, these commands do not take up any space. They can be used inside and outside
\pspicture environments.
Most of the PSTricks put commands are of the form:
\put *arg{<rotation>}(<coor>){<stuff>}
With the optional * argument, stuff is first put in a
1
\psframebox*[boxsep=false]{stuff }
thereby blotting out whatever is behind stuff . This is useful for positioning
text on top of something else.
arg refers to other arguments that vary from one put command to another,
The optional rotation is the angle by which stuff should be rotated; this
arguments works pretty much the same for all put commands and is described further below. The (<coor>) argument is the coordinate for positioning stuff , but what this really means is different for each put command.
The (<coor>) argument is shown to be obligatory, but you can actually omit
it if you include the rotation argument.
The rotation argument should be an angle, as described in Section 4, but the
angle can be preceded by an *. This causes all the rotations (except the box
rotations described in Section 29) within which the \rput command is be
nested to be undone before setting the angle of rotation. This is mainly useful for getting a piece of text right side up when it is nested inside rotations.
For example,
Picture Tools: Placing and rotating whatever
41
stuff
1
2
3
\rput{34}{%
\psframe(-1,0)(2,1)
\rput[br]{*0}(2,1){\emph{stuff}}}
There are also some letter abbreviations for the command angles. These
indicate which way is up:
Letter
U
L
D
R
Short for
Up
Left
Down
Right
Equiv. to
0
90
180
270
Letter
N
W
S
E
Short for
North
West
South
East
Equiv. to
*0
*90
*180
*270
This section describes just a two of the PSTricks put commands. The most
basic one command is
\rput*[refpoint ]{rotation}(x,y){stuff }
refpoint determines the reference point of stuff , and this reference point is
translated to (x,y ).
By default, the reference point is the center of the box. This can be changed
by including one or two of the following in the optional refpoint argument:
Horizontal
l Left
r Right
t
b
B
Vertical
Top
Bottom
Baseline
Visually, here is where the reference point is set of the various combinations
(the dashed line is the baseline):
t
tr
l
Bl
B
r
Br
bl
b
br
Here is a marginal note.
tl
There are numerous examples of \rput in this documentation, but for now
here is a simple one:
1
\rput[b]{90}(-1,0){Here is a marginal note.}
Picture Tools: Placing and rotating whatever
42
One common use of a macro such as \rput is to put labels on things.
PSTricks has a variant of \rput that is especially designed for labels:
\uput*{labelsep}[refangle]{rotation}(x,y){stuff }
This places stuff distance labelsep from (x,y ), in the direction refangle.
The default value of labelsep is the dimension register
\pslabelsep
You can also change this be setting the
labelsep=dim
Default: 5pt
parameter (but remember that \uput does have an optional argument for
setting parameters).
Here is a simple example:
(1,1)
1
2
\qdisk(1,1){1pt}
\uput[45](1,1){(1,1)}
Here is a more interesting example where \uput is used to make a pie chart:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
\psset{unit=1.2cm}
\pspicture(-2.2,-2.2)(2.2,2.2)
\pswedge[fillstyle=solid,fillcolor=gray]{2}{0}{70}
\pswedge[fillstyle=solid,fillcolor=lightgray]{2}{70}{200}
\pswedge[fillstyle=solid,fillcolor=darkgray]{2}{200}{360}
\SpecialCoor
\psset{framesep=1.5pt}
\rput(1.2;35){\psframebox*{\small\$9.0M}} \uput{2.2}[45](0,0){Oreos} \rput(1.2;135){\psframebox*{\small\$16.7M}}
\uput{2.2}[135](0,0){Heath}
\rput(1.2;280){\psframebox*{\small\$23.1M}} \uput{2.2}[280](0,0){M\&M} \endpspicture Picture Tools: Placing and rotating whatever 43 Heath Oreos$16.7M
$9.0M$23.1M
M&M
You can use the following abbreviations for refangle, which indicate the
direction the angle points:1213
Letter
r
u
l
d
Short for
right
up
left
down
Equiv. to
0
90
180
270
Letter
Short for
up-right
up-left
down-left
down-right
ur
ul
dl
dr
Equiv. to
45
135
225
315
The first example could thus have been written:
(1,1)
1
2
\qdisk(1,1){1pt}
\uput[ur](1,1){(1,1)}
Driver notes:
25
The rotation macros use \pstVerb and \pstrotate.
Repetition
The macro
12
Using the abbreviations when applicable is more efficient.
There is an obsolete command \Rput that has the same syntax as \uput and that works
almost the same way, except the refangle argument has the syntax of \rput’s refpoint argument, and it gives the point in stuff that should be aligned with (x, y ). E.g.,
13
\qdisk(4,0){2pt}
\Rput[tl](4,0){$(x,y)$}
(x, y)
Here is the equivalence between \uput’s refangle abbreviations and \Rput’s refpoint abbreviations:
\uput
r
u
l
d
ur
ul
dr
dl
\Rput
l
b
r
t
bl
br
tr
rl
Some people prefer \Rput’s convention for specifying the position of stuff over \uput’s.
Picture Tools: Repetition
44
\multirput*[refpoint ]{angle}(x0,y0)(x1,y1){int}{stuff }
is a variant of \rput that puts down int copies, starting at (x0,y0) and advancing by (x1,y1) each time. (x0,y0) and (x1,y1) are always interpreted
as Cartesian coordinates. For example:
**
*
**
*
*
**
**
*
1
\multirput(.5,0)(.3,.1){12}{*}
If you want copies of pure graphics, it is more efficient to use
\multips{angle}(x0,y0)(x1,y1){int}{graphics}
graphics can be one or more of the pure graphics objects described in
Part II, or \pscustom. Note that \multips has the same syntax as \multirput, except that there is no refpoint argument (since the graphics are zero
dimensional anyway). Also, unlike \multirput, the coordinates can be of
any type. An Overfull \hbox warning indicates that the graphics argument
contains extraneous output or space. For example:
1
2
3
multido
\def\zigzag{\psline(0,0)(.5,1)(1.5,-1)(2,0)}%
\psset{unit=.25,linewidth=1.5pt}
\multips(0,0)(2,0){8}{\zigzag}
PSTricks can heavily benefit of a much more general loop macro, called
\multido. You must input the file multido.tex or multido.sty. See the documentation multido.doc for details. Here is a sample of what you can do:
1
2
3
4
5
6
7
8
9
10
11
\begin{pspicture}(-3.4,-3.4)(3.4,3.4)
\definecolor{mygray}{gray}{0}% Initialize ‘mygray’ for benefit
\psset{fillstyle=solid,fillcolor=mygray} % of this line.
\SpecialCoor
\degrees[1.1]
\multido{\n=0.0+0.1}{11}{%
\definecolor{mygray}{gray}{\n}%
\psset{fillcolor=mygray}%
\rput{\n}{\pswedge{3}{-.05}{.05}}
\uput{3.2}[\n](0,0){\small\n}}
\end{pspicture}
Picture Tools: Repetition
45
0.3
0.2
0.4
0.1
0.5
0.0
0.6
1.0
0.7
0.8
0.9
All of these loop macros can be nested.
26
Axes
The axes command described in this section is defined in pst-plot.tex /
pst-plot.sty, which you must input first. pst-plot.tex, in turn, will automatically input multido.tex, which is used for putting the labels on the axes.
pst-plot
The macro for making axes is:
\psaxes*[par ]{arrows}(x0,y0)(x1,y1)(x2,y2)
The coordinates must be Cartesian coordinates. They work the same way
as with \psgrid. That is, if we imagine that the axes are enclosed in a
rectangle, (x1,y1) and (x2,y2) are opposing corners of the rectangle. (I.e.,
the x-axis extends from x1 to x2 and the y-axis extends from y1 to y2 .) The
axes intersect at (x0,y0). For example:
3
2
(x2,y2)
(x0,y0)
1
2
1
\psaxes[linewidth=1.2pt,labels=none,
ticks=none]{<->}(2,1)(0,0)(4,3)
0
0
1
(x1,y1)
2
3
4
If (x0,y0) is omitted, then the origin is (x1,y1). If both (x0,y0) and (x1,y1)
are omitted, (0,0) is used as the default. For example, when the axes enclose
a single orthont, only (x2,y2) is needed:
Picture Tools: Axes
46
1
1
\psaxes{->}(4,2)
0
0
1
2
3
Labels (numbers) are put next to the axes, on the same side as x1 and y1.
Thus, if we enclose a different orthont, the numbers end up in the right
place:
0
1
2
3
0
1
−1
\psaxes{->}(4,-2)
Also, if you set the arrows parameter, the first arrow is used for the tips at
x1 and y1, while the second arrow is used for the tips at x2 and y2 . Thus, in
the preceding examples, the arrowheads ended up in the right place too.14
When the axes don’t just enclose an orthont, that is, when the origin is not at
a corner, there is some discretion as to where the numbers should go. The
rules for positioning the numbers and arrows described above still apply,
and so you can position the numbers as you please by switching y1 and y2 ,
or x1 and x2 . For example, compare
2
1
−2 −1
1
0
1
\psaxes{<->}(0,0)(-2.5,0)(2.5,2.5)
2
with what we get when x1 and x2 are switched:
2
1
−2 −1
0
1
1
\psaxes{<->}(0,0)(2.5,0)(-2.5,2.5)
2
\psaxes puts the ticks and numbers on the axes at regular intervals, using
the following parameters:
14
Including a first arrow in these examples would have had no effect because arrows are
never drawn at the origin.
Picture Tools: Axes
47
Horitontal
Vertical
Dflt
Description
Ox=num
Dx=num
dx=dim
Oy=num
Dy=num
dy=dim
0
1
0pt
Label at origin.
Label increment.
Dist btwn labels.
When dx is 0, Dx\psxunit is used instead, and similarly for dy. Hence, the
default values of 0pt for dx and dy are not as peculiar as they seem.
You have to be very careful when setting Ox, Dx, Oy and Dy to non-integer
values. multido.tex increments the labels using rudimentary fixed-point
arithmetic, and it will come up with the wrong answer unless Ox and Dx,
or Oy and Dy, have the same number of digits to the right of the decimal.
The only exception is that Ox or Oy can always be an integer, even if Dx
or Dy is not. (The converse does not work, however.)15
Note that \psaxes’s first coordinate argument determines the physical position of the origin, but it doesn’t affect the label at the origin. E.g., if the
origin is at (1,1), the origin is still labeled 0 along each axis, unless you
explicitly change Ox and Oy. For example:
3
2
1
\psaxes[Ox=-2](-2,0)(2,3)
1
0
−2
−1
0
1
2
The ticks and labels use a few other parameters as well:
labels=all/x/y/none
Default: all
To specify whether labels appear on both axes, the x-axis, the y-axis,
or neither.
showorigin=true/false
Default: true
If true, then labels are placed at the origin, as long as the label doesn’t
end up on one of the axes. If false, the labels are never placed at the
origin.
ticks=all/x/y/none
Default: all
To specify whether ticks appear on both axes, the x-axis, the y-axis,
or neither.
15
For example, Ox=1.0 and Dx=1.4 is okay, as is Ox=1 and Dx=1.4, but Ox=1.4 and
Dx=1, or Ox=1.4 and Dx=1.15, is not okay. If you get this wrong, PSTricks won’t complain, but you won’t get the right labels either.
Picture Tools: Axes
48
Default: full
tickstyle=full/top/bottom
For example, if tickstyle=top, then the ticks are only on the side of
the axes away from the labels. If tickstyle=bottom, the ticks are on
the same side as the labels. full gives ticks extending on both sides.
Default: 3pt
ticksize=dim
Ticks extend dim above and/or below the axis.
The distance between ticks and labels is \pslabelsep, which you can change
with the labelsep parameter.
The labels are set in the current font (ome of the examples above were
preceded by \small so that the labels would be smaller). You can do fancy
things with the labels by redefining the commands:
\pshlabel
\psvlabel
E.g., if you want change the font of the horizontal labels, but not the vertical
labels, try something like
1
\def\pshlabel#1{\small #1}
You can choose to have a frame instead of axes, or no axes at all (but you
still get the ticks and labels), with the parameter:
axesstyle=axes/frame/none
Default: axes
The usual linestyle, fillstyle and related paremeters apply.
For example:
3
2
1
−1.5 −1.0 −0.5
0
1
\psaxes[Dx=.5,dx=1,tickstyle=top,axesstyle=frame](-3,3)
0
The \psaxes macro is pretty flexible, but PSTricks contains some other
tools for making axes from scratch. E.g., you can use \psline and \psframe
to draw axes and frames, respectively, \multido to generate labels (see the
documentation for multido.tex), and \multips to make ticks.
Picture Tools: Axes
49
VI
27
Text Tricks
Framed boxes
The macros for framing boxes take their argument, put it in an \hbox, and
put a PostScript frame around it. (They are analogous to LATEX’s \fbox).
Thus, they are composite objects rather than pure graphics objects. In addition to the graphics parameters for \psframe, these macros use the following parameters:
framesep=dim
Default: 3pt
Distance between each side of a frame and the enclosed box.
boxsep=true/false
Default: true
When true, the box that is produced is the size of the frame or whatever that is drawn around the object. When false, the box that is
produced is the size of whatever is inside, and so the frame is “transparent” to TEX. This parameter only applies to \psframebox, \pscirclebox, and \psovalbox.
Here are the three box-framing macros:
\psframebox*[par]{stuff }
A simple frame (perhaps with rounded corners) is drawn using \psframe. The * option is of particular interest. It generates a solid
frame whose color is fillcolor (rather than linecolor, as with the
closed graphics objects). Recall that the default value of fillcolor is
white, and so this has the effect of blotting out whatever is behind the
box. For example,
Label
1
2
\pspolygon[fillcolor=gray,fillstyle=crosshatch*](0,0)(3,0)(3,2)(2,2)
\rput(2,1){\psframebox*[framearc=.3]{Label}}
\psdblframebox*[par]{stuff }
This draws a double frame. It is just a variant of \psframebox, defined by
Text Tricks
50
1
\newpsobject{psdblframebox}{psframebox}{doublesep=\pslinewidth}
For example,
1
2
3
\psdblframebox[linewidth=1.5pt]{%
\parbox[c]{6cm}{\raggedright A double frame is drawn
with the gap between lines equal to \texttt{doublesep}}}
A double frame is drawn with the gap
between lines equal to doublesep
This draws a single frame, with a shadow.
Great Idea!!
1
You can get the shadow with \psframebox just be setting the shadowsize parameter, but with \psframebox the dimensions of the box
won’t reflect the shadow (which may be what you want!).
\pscirclebox*[par]{stuff }
This draws a circle. With boxsep=true, the size of the box is close
to but may be larger than the size of the circle. For example:
You are
here
1
\pscirclebox{\begin{tabular}{c} You are \\ here \end{tabular}}
is distributed with
\cput*[par]{angle}(x,y){stuff }
This combines the functions of \pscirclebox and \rput. It is like
1
\rput{angle}(x0,y0){\pscirclebox*[par ]{stuff }}
but it is more efficient. Unlike the \rput command, there is no argument for changing the reference point; it is always the center of
the box. Instead, there is an optional argument for changing graphics
parameters. For example
1
K1
1
\cput[doubleline=true](1,.5){\large $K_1$}
0
0
1
2
Text Tricks: Framed boxes
51
\psovalbox*[par]{stuff }
This draws an ellipse. If you want an oval with square sides and
rounded corners, then use \psframebox with a positive value for
rectarc or linearc (depending on whether cornersize is relative or
absolute). Here is an example that uses boxsep=false:
At the introductory
price of $13.99, it pays to act now! 1 2 3 At the introductory price of \psovalbox[boxsep=false,linecolor=darkgray]{\$13.99},
it pays to act now!
\psdiabox*[par]{stuff }
\psdiabox draws a diamond.
Happy?
1
\pstribox*[par]{stuff }
\pstribox draws a triangle.
Begin
1
\pstribox[trimode=R,framesep=5pt]{\Large\textbf{Begin}}
The triangle points in the direction:
trimode=*U/D/R/L
Default: U
If you include the optional *, then an equilateral triangle is drawn,
otherwise, you get the minimum-area isosceles triangle.
1
\pstribox[trimode=*U]{\Huge Begin}
Begin
You can define variants of these box framing macros using the \newpsobject command.
If you want to control the final size of the frame, independently of the material inside, nest stuff in something like LATEX’s \makebox command.
Text Tricks: Framed boxes
52
28
Clipping
The command
\clipbox[dim]{stuff }
puts stuff in an \hbox and then clips around the boundary of the box, at a
distance dim from the box (the default is 0pt).
The \pspicture environment also lets you clip the picture to the boundary.
The command16 :
\psclip{graphics} … {} \endpsclip
sets the clipping path to the path drawn by the graphics object(s), until the
\endpsclip command is reached. \psclip and \endpsclip must be properly
nested with respect to TEX grouping. Only pure graphics (those described
in Part II and \pscustom) are permitted. An Overfull \hbox warning indicates that the graphics argument contains extraneous output or space. Note
that the graphics objects otherwise act as usual, and the \psclip does not
otherwise affect the surrounded text. Here is an example:
\parbox{4.5cm}{%
\psclip{\psccurve[linestyle=none](-3,-2)(0.3,-1.5)(2.3,-2)
(4.3,-1.5)(6.3,-2)(8,-1.5)(8,2)(-3,2)}
“One of the best new plays I have seen all year: cool,
poetic, ironic \ldots” proclaimed \emph{The Guardian} upon
the London premiere of this extraordinary play about a Czech
director and his actress wife, confronting exile in America.%
\vspace{-1cm}
\endpsclip}
1
“One of the best new plays I
have seen all year: cool, poetic, ironic … ” proclaimed The
Guardian upon the London premiere of this extraordinary play
about a Czech director and his
2
3
4
5
6
7
8
9
If you don’t want the outline to be painted, you need to include linestyle=none
in the parameter changes. You can actually include more than one graphics
object in the argument, in which case the clipping path is set to the intersection of the paths.
\psclip can be a useful tool in picture environments. For example, here it
is used to shade the region between two curves:
EX users can write \begin{psclip} … \end{psclip} instead.
16 A
LT
Text Tricks: Clipping
53
1
4
2
3
3
4
5
6
2
7
8
1
9
10
0
11
0
1
2
3
4
12
\psclip{%
\pscustom[linestyle=none]{%
\psplot{.5}{4}{2 x div}
\lineto(4,4)}
\pscustom[linestyle=none]{%
\psplot{0}{3}{3 x x mul 3 div sub}
\lineto(0,0)}}
\psframe*[linecolor=gray](0,0)(4,4)
\endpsclip
\psplot[linewidth=1.5pt]{.5}{4}{2 x div}
\psplot[linewidth=1.5pt]{0}{3}{3 x x mul 3 div sub}
\psaxes(4,4)
This is important to clearly understand this mechanism, so we give here the
various steps of how it works in the preceding example:
1
2
3
4
5
6
7
8
9
10
11
12
\pspicture(-0.5,-1)(4,4)
\psaxes(4,4)
\psplot{0.5}{4}{2 x div}
\psplot{0}{3}{3 x x mul 3 div sub}
\endpspicture
\hfill
\pspicture(-0.5,-1)(4,4)
\psframe*[linecolor=lightgray](4,4)
\psaxes(4,4)
\psplot{0}{3}{3 x x mul 3 div sub}
\psplot{0.5}{4}{2 x div}
\endpspicture
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
\pspicture(-0.5,-1)(4,4)
\psaxes(4,4)
\pscustom[linecolor=red]{%
\psplot{0.5}{4}{2 x div}
\lineto(4,4)}
\pscustom[linecolor=blue]{%
\psplot{0}{3}{3 x x mul 3 div sub}
\lineto(0,0)}
\endpspicture
\hfill
\pspicture(-0.5,-1)(4,4)
\psaxes(4,4)
\psclip{\pscustom[linecolor=red]{%
\psplot{0.5}{4}{2 x div}
\lineto(4,4)}
\pscustom[linecolor=blue]{%
\psplot{0}{3}{3 x x mul 3 div sub}
\lineto(0,0)}}
\psframe*[linecolor=lightgray](4,4)
\endpsclip
\endpspicture
35
36
\pspicture(-0.5,-1)(4,4)
Text Tricks: Clipping
54
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
\psaxes(4,4)
\psclip{\pscustom[linecolor=red]{%
\psplot{0.5}{4}{2 x div}
\lineto(4,4)}
\pscustom[linecolor=blue]{%
\psplot{0}{3}{3 x x mul 3 div sub}
\lineto(0,0)}}
\psframe*[linecolor=lightgray](4,4)
\endpsclip
\psplot{0}{3}{3 x x mul 3 div sub}
\psplot{0.5}{4}{2 x div}
\endpspicture
\hfill
\pspicture(-0.5,-1)(4,4)
\psaxes(4,4)
\psclip{\pscustom[linestyle=none]{%
\psplot{0.5}{4}{2 x div}
\lineto(4,4)}
\pscustom[linestyle=none]{%
\psplot{0}{3}{3 x x mul 3 div sub}
\lineto(0,0)}}
\psframe*[linecolor=lightgray](4,4)
\endpsclip
\psplot{0}{3}{3 x x mul 3 div sub}
\psplot{0.5}{4}{2 x div}
\endpspicture
4
4
3
3
2
2
1
1
0
0
0
1
2
3
4
4
4
3
3
2
2
1
1
0
0
1
2
3
4
0
1
2
3
4
0
0
1
2
Text Tricks: Clipping
3
4
55
4
4
3
3
2
2
1
1
0
0
0
1
2
3
4
0
1
2
3
4
Driver notes: The clipping macros use \pstverbscale and \pstVerb. Don’t be
surprised if PSTricks’s clipping does not work or causes problem—it is never robust. \endpsclip uses initclip. This can interfere with other clipping operations,
and especially if the TEX document is converted to an Encapsulated PostScript
file. The command \AltClipMode causes \psclip and \endpsclip to use gsave
and grestore instead. This bothers some drivers, especially if \psclip and \endpsclip do not end up on the same page.
29
Rotation and scaling boxes
There are versions of the standard box rotation macros:
\rotateleft{stuff }
\rotateright{stuff }
\rotatedown{stuff }
Right
Left
stuff is put in an \hbox and then rotated or scaled, leaving the appropriate
amount of spaces. Here are a few uninteresting examples:
1
\Large\bfseries\rotateleft{Left}\rotatedown{Down}\rotateright{Right}
There are also two box scaling macros:
\scalebox{num1 num2}{stuff }
If you give two numbers in the first argument, num1 is used to scale
horizontally and num2 is used to scale vertically. If you give just one
number, the box is scaled by the same in both directions. You can’t
scale by zero, but negative numbers are OK, and have the effect of
flipping the box around the axis. You never know when you need to
do something like siht (\scalebox{-1 1}{this}).
Text Tricks: Rotation and scaling boxes
56
Down
\scaleboxto(x,y){stuff }
This time, the first argument is a (Cartesian) coordinate, and the box
is scaled to have width x and height (plus depth) y . If one of the
dimensions is 0, the box is scaled by the same amount in both directions. For example:
Big andlong
1
\scaleboxto(4,2){Big and long}
PSTricks defines LR-box environments for all these box rotation and scaling commands:
1
2
3
4
5
\pslongbox{Rotateleft}{\rotateleft}
\pslongbox{Rotateright}{\rotateright}
\pslongbox{Rotatedown}{\rotatedown}
\pslongbox{Scalebox}{\scalebox}
\pslongbox{Scaleboxto}{\scaleboxto}
Here is an example where we \Rotatedown for the answers to exercises:
Question: How do
Democrats organize a
1
Question: How do Democrats organize a firing squad?
2
3
4
5
\begin{Rotatedown}
\parbox{\hsize}{Answer: First they get in a circle, \ldots\hss}%
\end{Rotatedown}
See the documentation of the ‘fancybox’ package for tips on rotating a
LATEX table or figure environment, and other boxes.
Text Tricks: Rotation and scaling boxes
57
a circle, …
VII
pst-node
Nodes and Node Connections
All the commands described in this part are contained in the file pst-node.tex
/ pst-node.sty.
The node and node connection macros let you connect information and
place labels, without knowing the exact position of what you are connecting
or of where the lines should connect. These macros are useful for making
graphs and trees, mathematical diagrams, linguistic syntax diagrams, and
connecting ideas of any kind. They are the trickiest tricks in PSTricks!
The node and node connection macros let you connect information and
place labels, without knowing the exact position of what you are connecting
or where the lines should connect. These macros are useful for making
graphs and trees, mathematical diagrams, linguistic syntax diagrams, and
connecting ideas of any kind. They are the trickiest tricks in PSTricks!
There are three components to the node macros:
Node definitions The node definitions let you assign a name and shape to
an object. See Section 30.
Node connections The node connections connect two nodes, identified by
their names. See Section 31.
Node labels The node label commands let you affix labels to the node connections. See Section 32.
You can use these macros just about anywhere. The best way to position
them depends on the application. For greatest flexibility, you can use the
nodes in a \pspicture, positioning and rotating them with \rput. You can
also use them in alignment environments. pst-node.tex contains a special alignment environment, \psmatrix, which is designed for positioning
nodes in a grid, such as in mathematical diagrams and some graphs. \psmatrix is described in Section 35. pst-node.tex also contains high-level
macros for trees. These are described in Part VIII.
But don’t restrict yourself to these more obvious uses. For example:
I made the file symbol a
node. Now I can draw an
arrow so that you know
1
2
3
4
5
\rnode{A}{%
\parbox{4cm}{\raggedright
I made the file symbol a node. Now I can draw an
arrow so that you know what I am talking about.}}
\ncarc[nodesep=8pt]{->}{A}{file}
Nodes and Node Connections
58
30
Nodes
Nodes have a name. a boundary and a center.
PS
Warning: The name is for refering to the node when making
node connections and labels. You specify the name as an argument to the node commands. The name must contain only
letters and numbers, and must begin with a letter. Bad node
names can cause PostScript errors.
The center of a node is where node connections point to. The boundary
is for determining where to connect a node connection. The various nodes
differ in how they determine the center and boundary. They also differ in
what kind of visable object they create.
Here are the nodes:
\rnode[refpoint ]{name}{stuff }
\rnode puts stuff in a box. The center of the node is refpoint , which
you can specify the same way as for \rput.
\Rnode*[par]{name}{stuff }
\Rnode also makes a box, but the center is set differently. If you
align \rnode’s by their baseline, differences in the height and depth
of the nodes can cause connecting lines to be not quite parallel, such
as in the following example:
1
sp
Bit
2
3
\Large
\rnode{A}{sp} \hskip 2cm \rnode{B}{Bit}
\ncline{A}{B}
With \Rnode, the center is determined relative to the baseline:
1
sp
Bit
2
3
\Large
\Rnode{A}{sp} \hskip 2cm \Rnode{B}{Bit}
\ncline{A}{B}
You can usually get by without fiddling with the center of the node,
but to modify it you set the
href=num
vref=dim
Default: 0
Default: .7ex
parameters. In the horizontal direction, the center is located fraction
href from the center to the edge. E.g, if href=-1, the center is on
the left edge of the box. In the vertical direction, the center is located
distance vref from the baseline. The vref parameter is evaluated each
Nodes and Node Connections: Nodes
59
time \Rnode is used, so that you can use ex units to have the distance
adjust itself to the size of the current font (but without being sensitive
to differences in the size of letters within the current font).
\pnode(x,y ){name}
This creates a zero dimensional node at (x,y ).
This draws a circle. Here is an example with \pnode and \cnode:
1
2
3
\cnode(0,1){.25}{A}
\pnode(3,0){B}
\ncline{<-}{A}{B}
\Cnode*[par](x,y ){name}
This is like \cnode, but the radius is the value of
Default: .25cm
This is convenient when you want many circle nodes of the same
\circlenode*[par]{name}{stuff }
This is a variant of \pscirclebox that gives the node the shape of the
circle.
\cnodeput*[par]{angle}(x,y ){name}{stuff }
This is a variant of \cput that gives the node the shape of the circle.
That is, it is like
1
\rput{angle}(x,y ){\circlenode{name}{stuff }}
\ovalnode*[par]{name}{stuff }
This is a variant of \psovalbox that gives the node the shape of an
ellipse. Here is an example with \circlenode and \ovalnode:
Circle and Oval
1
2
\circlenode{A}{Circle} and \ovalnode{B}{Oval}
\ncbar[angle=90]{A}{B}
\dianode*[par]{name}{stuff }
This is like \diabox.
\trinode*[par]{name}{stuff }
This is like \tribox.
Nodes and Node Connections: Nodes
60
Diamond
1
2
3
\rput[tl](0,3){\dianode{A}{Diamond}}
\rput[br](4,0){\trinode[trimode=L]{B}{Triangle}}
\nccurve[angleA=-135,angleB=90]{A}{B}
Triangle
\dotnode*[par](x,y ){name}
This is a variant of \psdot. For example:
+
1
2
3
\dotnode[dotstyle=triangle*,dotscale=2 1](0,0){A}
\dotnode[dotstyle=+](3,2){B}
\ncline[nodesep=3pt]{A}{B}
u
\fnode*[par](x,y ){name}
The f stands for “frame”. This is like, but easier than, putting a \psframe in an \rnode.
1
2
3
\fnode{A}
\fnode*[framesize=1 5pt](2,2){B}
\ncline[nodesep=3pt]{A}{B}
There are two differences between \fnode and \psframe:
• There is a single (optional) coordinate argument, that gives the
center of the frame.
• The width and height of the frame are set by the
framesize=dim1 ‘dim2’
Default: 10pt
parameter. If you omit dim2 , you get a square frame.
31
Node connections
All the node connection commands begin with nc, and they all have the
same syntax:17,18
1
\nodeconnection[par ]{arrows}{nodeA}{nodeB}
17
The node connections can be used with \pscustom. The beginning of the node connection is attached to the current point by a straight line, as with \psarc.
18
See page 145 if you want to use the nodes as coordinates in other PSTricks macros.
Nodes and Node Connections: Node connections
61
A line of some sort is drawn from nodeA to nodeB . Some of the node connection commands are a little confusing, but with a little experimentation
you will figure them out, and you will be amazed at the things you can do.
When we refer to the A and B nodes below, we are referring only to the
order in which the names are given as arguments to the node connection
macros.19
The node connections use many of the usual graphics parameters, plus a
few special ones. Let’s start with one that applies to all the node connections:
nodesep=dim
Default: 0pt
nodesep is the border around the nodes that is added for the purpose of
determining where to connect the lines.
For this and other node connection parameters, you can set different values
for the two ends of the node connection. Set the parameter nodesepA for
the first node, and set nodesepB for the second node.
The first two node connections draw a line or arc directly between the two
nodes:
\ncline*[par]{arrows}{nodeA}{nodeB}
This draws a straight line between the nodes. For example:
Idea 2
1
2
3
\rput[bl](0,0){\rnode{A}{Idea 1}}
\rput[tr](4,3){\rnode{B}{Idea 2}}
\ncline[nodesep=3pt]{<->}{A}{B}
Idea 1
\ncarc*[par]{arrows}{nodeA}{nodeB}
This connects the two nodes with an arc.
Y
1
2
3
4
5
X
\cnodeput(0,0){A}{X}
\cnodeput(3,2){B}{Y}
\psset{nodesep=3pt}
\ncarc{->}{A}{B}
\ncarc{->}{B}{A}
19
When a node name cannot be found on the same page as the node connection command,
you get either no node connection or a nonsense node connection. However, TEX will not
report any errors.
Nodes and Node Connections: Node connections
62
The angle between the arc and the line between the two nodes is20
arcangle=angle
Default: 8
\ncline and \ncarc both determine the angle at which the node connections
join by the relative position of the two nodes. With the next group of node
connections, you specify one or both of the angles in absolute terms, by
setting the
angle=angle
Default: 0
(and angleA and angleB) parameter.
You also specify the length of the line segment where the node connection
joins at one or both of the ends (the “arms”) by setting the
arm=dim
Default: 10pt
(and armA and armB) parameter.
These node connections all consist of several line segments, including the
arms. The value of linearc is used for rounding the corners.
Here they are, starting with the simplest one:
\ncdiag*[par]{arrows}{nodeA}{nodeB}
An arm is drawn at each node, joining at angle angleA or angleB,
and with a length of armA or armB. Then the two arms are connected by a straight line, so that the whole line has three line segments. For example:
Node A
1
2
3
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\rput[br](4,0){\ovalnode{B}{Node B}}
\ncdiag[angleA=-90, angleB=90, arm=.5, linearc=.2]{A}{B}
Node B
You can also set one or both of the arms to zero length. For example,
if you set arm=0, the nodes are connected by a straight line, but you
get to determine where the line connects (whereas the connection
point is determined automatically by \ncline). Compare this use of
\ncdiag with \ncline in the following example:
20
Rather than using a true arc, \ncarc actually draws a bezier curve. When connecting
two circular nodes using the default parameter values, the curve will be indistinguishable
from a true arc. However, \ncarc is more flexible than an arc, and works right connecting
nodes of different shapes and sizes. You can set arcangleA and arcangleB separately, and
you can control the curvature with the ncurv parameter, which is described on page ??.
Nodes and Node Connections: Node connections
63
XX
1
2
Root
3
4
5
YY
\rput[r](4,1){\ovalnode{R}{Root}}
\cnodeput(1,2){A}{XX}
\cnodeput(1,0){B}{YY}
\ncdiag[angleB=180, arm=0]{<-}{A}{R}
\ncline{<-}{B}{R}
(Note that in this example, the default value angleA=0 is used.)
\ncdiagg*[par]{arrows}{nodeA}{nodeB}
\ncdiagg is similar to \ncdiag, but only the arm for node A is drawn.
The end of this arm is then connected directly to node B. Compare
\ncdiagg with \ncdiag when armB=0:
\ncdiagg
H
1
2
3
4
\ncdiag
T
5
\cnode(0,0){12pt}{a}
\rput[l](3,1){\rnode{b}{H}}
\rput[l](3,-1){\rnode{c}{T}}
\ncdiagg[angleA=180, armA=1.5, nodesepA=3pt]{b}{a}
\ncdiag[angleA=180, armA=1.5, armB=0, nodesepA=3pt]{c}{a}
You can use \ncdiagg with armA=0 if you want a straight line that
joins to node A at the angle you specify, and to node B at an angle
that is determined automatically.
\ncbar*[par]{arrows}{nodeA}{nodeB}
This node connection consists of a line with arms dropping “down”,
at right angles, to meet two nodes at an angle angleA. Each arm is at
least of length armA or armB, but one may be need to be longer.
1
Connect some words!
2
3
\rnode{A}{Connect} some \rnode{B}{words}!
\ncbar[nodesep=3pt,angle=-90]{<-**}{A}{B}
\ncbar[nodesep=3pt,angle=70]{A}{B}
Generally, the whole line has three straight segments.
\ncangle*[par]{arrows}{nodeA}{nodeB}
Now we get to a more complicated node connection. \ncangle typically draws three line segments, like \ncdiag. However, rather than
fixing the length of arm A, we adjust arm A so that the line joining
the two arms meets arm A at a right angle. For example:
Node A
1
2
3
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\rput[br](4,0){\ovalnode{B}{Node B}}
\ncangle[angleA=-90,angleB=90,armB=1cm]{A}{B}
Node B
Nodes and Node Connections: Node connections
64
Now watch what happens when we change angleA:
Node A
angleA
1
}
2
armB
3
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\rput[br](4,0){\ovalnode{B}{Node B}}
\ncangle[angleA=-70,angleB=90,armB=1cm,linewidth=1.2pt]{A}{B}
Node B
\ncangle is also a good way to join nodes by a right angle, with just
two line segments, as in this example:
Node A
1
2
3
Node B
\rput[tl](0,2){\rnode{A}{\psframebox{Node A}}}
\rput[br](4,0){\ovalnode{B}{Node B}}
\ncangle[angleB=90, armB=0, linearc=.5]{A}{B}
\ncangles*[par]{arrows}{nodeA}{nodeB}
\ncangles is similar to \ncangle, but the length of arm A is fixed
by he armA parameter. Arm A is connected to arm B by two line
segments that eet arm A and each other at right angles. The angle
at which they join arm B, and the length of the connecting segments,
depends on the positions of the two arms. \ncangles generally draws
a total of four line segments.21 For example:
Node A
1
2
3
\rput[tl](0,4){\rnode{A}{\psframebox{Node A}}}
\rput[br](4,0){\ovalnode{B}{Node B}}
\ncangles[angleA=-90, armA=1cm, armB=.5cm, linearc=.15]{A}{B}
Node B
Let’s see what happens to the previous example when we change
angleB:
21
Hence there is one more angle than \ncangle, and hence the s in \ncangles.
Nodes and Node Connections: Node connections
65
Node A
armA
{
angleA
1
2
3
angleB
4
\rput[tl](0,4){\rnode{A}{\psframebox{Node A}}}
\rput[br](4,0){\ovalnode{B}{Node B}}
\ncangles[angleA=-90, angleB=135, armA=1cm, armB=.5cm,
linearc=.15]{A}{B}
armB
Node B
\ncloop*[par]{arrows}{nodeA}{nodeB}
\ncloop is also in the same family as \ncangle and \ncangles, but
now typically 5 line segments are drawn. Hence, \ncloop can reach
around to opposite sides of the nodes. The lengths of the arms are
fixed by armA and armB. Starting at arm A, \ncloop makes a 90
degree turn to the left, drawing a segment of length
loopsize=dim
Default: 1cm
loopsize
This segment connects to arm B the way arm A connects to arm B
with \ncline; that is, two more segments are drawn, which join the
first segment and each other at right angles, and then join arm B. For
example:
A loop
1
2
\rnode{a}{\psframebox{\Huge A loop}}
\ncloop[angleB=180,loopsize=1,arm=.5,linearc=.2]{->}{a}{a}
In this example, node A and node B are the same node! You can do
this with all the node connections (but it doesn’t always make sense).
loopsize
Here is an example where \ncloop connects two different nodes:
1
Begin
End
2
3
4
5
\parbox{3cm}{%
\rnode{A}{\psframebox{\large\textbf{Begin}}}
\vspace{1cm}\hspace*{\fill}
\rnode{B}{\psframebox{\large\textbf{End}}}
\ncloop[angleA=180,loopsize=.9,arm=.5,linearc=.2]{->}{A}{B}}
The next two node connections are a little different from the rest.
\nccurve*[par]{arrows}{nodeA}{nodeB}
\nccurve draws a bezier curve between the nodes.
Node B
1
2
3
\rput[bl](0,0){\rnode{A}{\psframebox{Node A}}}
\rput[tr](4,3){\ovalnode{B}{Node B}}
\nccurve[angleB=180]{A}{B}
Node A
Nodes and Node Connections: Node connections
66
You specify the angle at which the curve joins the nodes by setting
the angle (and angleA and angleB) parameter. The distance to the
control points is set with the
ncurv=num
Default: .67
(and ncurvA and ncurvB) parameter. A lower number gives a tighter
curve. (The distance between the beginning of the arc and the first
control point is one-half ncurvA times the distance between the two
endpoints.)
\nccircle draws a circle, or part of a circle, that, if complete, would
pass through the center of the node counterclockwise, at an angle of
angleA.
1
2
back
3
\rnode{A}{\textbf{back}}
\nccircle[nodesep=3pt]{->}{A}{.7cm}
\kern 5pt
\nccircle can only connect a node to itself; it is the only node connection with this property. \nccircle is also special because it has an
The last two node connections are also special. Rather than connecting the
nodes with an open curve, they enclose the nodes in a box or curved box.
You can think of them as variants of \ncline and \ncarc. In both cases, the
half the width of the box is
boxsize=dim
Default: .4cm
You have to set this yourself to the right size, so that the nodes fit inside the
box. The boxsize parameter actually sets the boxheight and boxdepth
parameters. The ends of the boxes extend beyond the nodes by nodesepA
and nodesepB.
\ncbox*[par]{nodeA}{nodeB}
\ncbox encloses the nodes in a box with straight sides. For example:
Idea 2
1
2
3
Idea 1
4
\rput[bl](.5,0){\rnode{A}{Idea 1}}
\rput[tr](3.5,2){\rnode{B}{Idea 2}}
\ncbox[nodesep=.5cm,boxsize=.6,linearc=.2,
linestyle=dashed]{A}{B}
Nodes and Node Connections: Node connections
67
\ncarcbox*[par]{nodeA}{nodeB}
\ncarcbox encloses the nodes in a curved box that is arcangleA
away from the line connecting the two nodes.
2
1
2
3
4
1
\rput[bl](.5,0){\rnode{A}{1}}
\rput[tr](3.5,2){\rnode{B}{2}}
\ncarcbox[nodesep=.2cm,boxsize=.4,linearc=.4,
arcangle=50]{<->}{A}{B}
The arc is drawn counterclockwise from node A to node B.
There is one other node connection parameter that applies to all the node
connections, except \ncarcbox:
offset=dim
Default: 0pt
(You can also set offsetA and offsetB independently.) This shifts the point
where the connection joins up by dim (given the convention that connections go from left to right).
There are two main uses for this parameter. First, it lets you make two
parallel lines with \ncline, as in the following example:
Y
1
2
3
4
X
5
\cnodeput(0,0){A}{X}
\cnodeput(3,2){B}{Y}
\psset{nodesep=3pt,offset=4pt,arrows=->}
\ncline{A}{B}
\ncline{B}{A}
Second, it lets you join a node connection to a rectangular node at a right
angle, without limiting yourself to positions that lie directly above, below,
or to either side of the center of the node. This is useful, for example, if
you are making several connections to the same node, as in the following
example:
1
Word1 and Word2 and Word3
2
3
\rnode{A}{Word1} and \rnode{B}{Word2} and \rnode{C}{Word3}
\ncbar[offsetB=4pt,angleA=-90,nodesep=3pt]{->}{A}{B}
\ncbar[offsetA=4pt,angleA=-90,nodesep=3pt]{->}{B}{C}
Sometimes you might be aligning several nodes, such as in a tree, and you
want to ends or the arms of the node connections to line up. This won’t
happen naturally if the nodes are of different size, as you can see in this
example:
Nodes and Node Connections: Node connections
68
1
2
3
4
5
H
a
6
7
\Huge
\cnode(1,3){4pt}{a}
\rput[B](0,0){\Rnode{b}{H}}
\rput[B](2,0){\Rnode{c}{a}}
\psset{angleA=90,armA=1,nodesepA=3pt}
\ncdiagg{b}{a}
\ncdiagg{c}{a}
If you set the nodesep or arm parameter to a negative value, PSTricks
will measure the distance to the beginning of the node connection or to the
end of the arm relative to the center of the node, rather than relative to the
boundary of the node or the beginning of the arm. Here is how we fix the
previous example:
1
2
3
4
5
H
a
6
7
\Huge
\cnode(1,3){4pt}{a}
\rput[B](0,0){\Rnode{b}{H}}
\rput[B](2,0){\Rnode{c}{a}}
\psset{angleA=90,armA=1,YnodesepA=12pt}
\ncdiagg{b}{a}
\ncdiagg{c}{a}
Note also the use of \Rnode.
One more parameter trick: By using the border parameter, you can create
the impression that one node connection passes over another.
The node connection commands make interesting drawing tools as well, as
an alternative to \psline for connecting two points. There are variants of
the node connection commands for this purpose. Each begins with pc (for
“point connection”) rather than nc. E.g.,
1
\pcarc{<->}(3,4)(6,9)
gives the same result as
1
2
3
\pnode(3,4){A}
\pnode(6,9){B}
\pcarc{<->}{A}{B}
Only \nccircle does not have a pc variant:
Nodes and Node Connections: Node connections
69
Command
\pcline{arrows}(x1,y1)(x2,y2)
\pccurve{arrows}(x1,y1)(x2,y2)
\pcarc{arrows}(x1,y1)(x2,y2)
\pcbar{arrows}(x1,y1)(x2,y2)
\pcdiag{arrows}(x1,y1)(x2,y2)
\pcdiagg{arrows}(x1,y1)(x2,y2)
\pcangle{arrows}(x1,y1)(x2,y2)
\pcangles{arrows}(x1,y1)(x2,y2)
\pcloop{arrows}(x1,y1)(x2,y2)
\pcbox(x1,y1)(x2,y2)
\pcarcbox(x1,y1)(x2,y2)
32
Corresponds to:
\ncline
\nccurve
\ncarc
\ncbar
\ncdiag
\ncdiagg
\ncangle
\ncangles
\ncloop
\ncbox
\ncarcbox
Node connections labels: I
Now we come to the commands for attaching labels to the node connections. The label command must come right after the node connection to
which the label is to be attached. You can attach more than one label to a
node connection, and a label can include more nodes.
The node label commands must end up on the same TEX page as the node
connection to which the label corresponds.
There are two groups of connection labels, which differ in how they select
the point on the node connection. In this section we describe the first group:
\ncput*[par ]{stuff }
\naput*[par ]{stuff }
\nbput*[par ]{stuff }
These three command differ in where the labels end up with respect to the
line:
\ncput
\naput
\nbput
on the line
above the line
below the line
(using the convention that node connections go from left to right).
Here is an example:
Nodes and Node Connections: Node connections labels: I
70
1
2
above
3
4
5
on
6
7
8
below
9
10
11
\cnode(0,0){.5cm}{root}
\cnode*(3,1.5){4pt}{A}
\cnode*(3,0){4pt}{B}
\cnode*(3,-1.5){4pt}{C}
\psset{nodesep=3pt}
\ncline{root}{A}
\naput{above}
\ncline{root}{B}
\ncput*{on}
\ncline{root}{C}
\nbput{below}
\naput and \nbput use the same algorithm as \uput for displacing the labels, and the distance beteen the line and labels is labelsep (at least if the
lines are straight).
\ncput uses the same system as \rput for setting the reference point. You
change the reference point by setting the
ref=ref
Default: c
parameter.
Rotation is also controlled by a graphics parameter:
nrot=rot
Default: 0
rot can be in any of the forms suitable for \rput, and you can also use the
form
1
{:angle}
The angle is then measured with respect to the node connection. E.g., if the
angle is {:U}, then the label runs parallel to the node connection. Since the
label can include other put commands, you really have a lot of control over
the label position.
The next example illustrates the use {:<angle>}, the offset parameter, and
\pcline:
gth
Len
1
2
3
\pspolygon(0,0)(4,2)(4,0)
\pcline[offset=12pt]{|-|}(0,0)(4,2)
\ncput*[nrot=:U]{Length}
Here is a repeat of an earlier example, now using {:<angle>}:
Nodes and Node Connections: Node connections labels: I
71
1
2
ve
abo
3
4
5
on
6
7
bel
ow
8
9
10
11
\cnode(0,0){.5cm}{root}
\cnode*(3,1.5){4pt}{A}
\cnode*(3,0){4pt}{B}
\cnode*(3,-1.5){4pt}{C}
\psset{nodesep=3pt,nrot=:U}
\ncline{root}{A}
\naput{above}
\ncline{root}{B}
\ncput*{on}
\ncline{root}{C}
\nbput{below}
The position on the node connection is set by the
Default:
npos=num
parameter, roughly according to the following scheme: Each node connection has potentially one or more segments, including the arms and connecting lines. A number npos between 0 and 1 picks a point on the first
segment from node A to B (fraction npos from the beginning to the end
of the segment), a number between 1 and 2 picks a number on the second
segment, and so on.
Each node connection has its own default value of npos. If you leave the
npos parameter value empty (e.g., [npos=]), then the default is substituted.
This is the default mode.
Here are the details for each node connection:
Connection
\ncline
\nccurve
\ncarc
\ncbar
\ncdiag
\ncdiagg
\ncangle
\ncangles
\ncloop
\nccircle
\ncbox
\ncarcbox
Segments
Range
Default
1
1
1
3
3
2
3
4
5
1
4
4
0≤ pos≤ 1
0≤ pos≤ 1
0≤ pos≤ 1
0≤ pos≤ 3
0≤ pos≤ 3
0≤ pos≤ 2
0≤ pos≤ 3
0≤ pos≤ 4
0≤ pos≤ 5
0≤ pos≤ 1
0≤ pos≤ 4
0≤ pos≤ 4
0.5
0.5
0.5
1.5
1.5
0.5
1.5
1.5
2.5
0.5
0.5
0.5
Here is an example:
Nodes and Node Connections: Node connections labels: I
72
Node A
1
d
2
par
3
4
5
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\rput[br](3.5,0){\ovalnode{B}{Node B}}
\ncangles[angleA=-90,arm=.4cm,linearc=.15]{A}{B}
\ncput*{d}
\nbput[nrot=:D,npos=2.5]{par}
Node B
With \ncbox and \ncarcbox, the segments run counterclockwise, starting
with the lower side of the box. Hence, with \nbput the label ends up outside
the box, and with \naput the label ends up inside the box.
II
1
2
2
3
4
5
1
6
set
\rput[bl](.5,0){\rnode{A}{1}}
\rput[tr](3.5,2){\rnode{B}{2}}
\ncarcbox[nodesep=.2cm,boxsize=.4,linearc=.4,
arcangle=50,linestyle=dashed]{<->}{A}{B}
\nbput[nrot=:U]{set}
\nbput[npos=2]{II}
If you set the parameter
shortput=none/nab/tablr/tab
Default: none
to nab, then immediately following a node connection or another node connection label you can use ^ instead of \naput and _ instead of \nbput.
x
1
2
3
4
5
y
6
\cnode(0,0){.5cm}{root}
\cnode*(3,1.5){4pt}{A}
\cnode*(3,-1.5){4pt}{C}
\psset{nodesep=3pt,shortput=nab}
\ncline{root}{A}^{$x$}
\ncline{root}{C}_{$y$}
You can still have parameter changes with the short ^ and _ forms. Another
example is given on page 78.
If you have set shortput=nab, and then you want to use a true ^ or _
character right after a node connection, you must precede the ^ or _ by {}
so that PSTricks does not convert it to \naput or \nbput.
You can change the characters that you use for the short form with the
\MakeShortNab{char1}{char2}
command.22
22
You can also use \MakeShortNab if you want to use ^ and _ with non-standard category codes. Just invoke the command after you have made your \catcode changes.
Nodes and Node Connections: Node connections labels: I
73
The shortput=tablr and shortput=tab options are described on pages 75
and ??, respectively.
33
Node connection labels: II
Now the second group of node connections:
\tvput*[par ]{stuff }
\tlput*[par ]{stuff }
\trput*[par ]{stuff }
\thput*[par ]{stuff }
\taput*[par ]{stuff }
\tbput*[par ]{stuff }
The difference between these commands and the \n*put commands is that
these find the position as an intermediate point between the centers of the
nodes, either in the horizontal or vertical direction. These are good for
trees and mathematical diagrams, where it can sometimes be nice to have
the labels be horizontally or vertically aligned. The t stands for “tree”.
You specify the position by setting the
Default: .5
tpos=num
parameter.
\tvput, \tlput and \trput find the position that lies fraction tpos in the vertical direction from the upper node to the lower node. \thput, \taput and
\tbput find the position that lies fraction tpos in the horizontal direction
from the left node to the right node. Then the commands put the label on
or next to the line, as follows:
Command
Direction
Placement
\tvput
vertical
vertical
vertical
horizontal
horizontal
horizontal
middle
left
right
middle
above
below
\tlput
\trput
\thput
\taput
\tbput
Here is an example:
1
2
3
4
$\setlength{\arraycolsep}{1.1cm} \begin{array}{cc} \Rnode{a}{(X-A)} & \Rnode{b}{A} \\[1.5cm] Nodes and Node Connections: Node connection labels: II 74 \Rnode{c}{x} & \Rnode{d}{\tilde{X}} \end{array} \psset{nodesep=5pt,arrows=->} \everypsbox{\scriptstyle} \ncline{a}{c}\tlput{r} \ncline{a}{b}\taput{u} \ncline[linestyle=dashed]{c}{d}\tbput{b} \ncline{b}{d}\trput{s} 5 6 7 8 9 10 11 12 13$
(X − A)
u
r
s
x
b
u
(X − A)
A
a
s
r
x
X̃
b
X̃
On the left is the diagram with \tlput, \trput \tbput and \Rnode, as shown
in the code. On the right is the same diagram, but with \naput \nbput and
\rnode.
These do not have a rotation argument or parameter. However, you can
rotate stuff in 90 degree increments using box rotations (e.g., \rotateleft).
If you set shortput=tablr, then you can use the following single-character
abbreviations for the t put commands:
Char.
Short for:
^
\taput
_
\tbput
<
\tlput
>
\trput
You can change the character abbreviations with
\MakeShortTablr{char1}{char2}{char3}{char4}
The t put commands, including an example of shortput=tablr, will be
shown further when we get to mathematical diagrams and trees.
Driver notes:
34
The node macros use \pstVerb and \pstverbscale.
Attaching labels to nodes
The command
\nput*[par ]{refangle}{name}{stuff }
Nodes and Node Connections: Attaching labels to nodes
75
affixes stuff to node name. It is positioned distance labelsep from the
node, in the direction refangle from the center of the node. The algorithm
is the same as for \uput. If you want to rotate the node, set the
rot=rot
Default: 0
parameter, where rot is a rotation that would be valid for \rput.23 The position of the label also takes into account the offsetA parameter. If labelsep
is negative, then the distance is from the center of the node rather than from
the boundary, as with nodesep.
Here is how I used \nput to mark an angle in a previous example:
Node A
1
2
angleA
3
4
5
6
Node B
35
7
\rput[br](4,0){\ovalnode{B}{Node B}}
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\nput[labelsep=0]{-70}{A}{%
\psarcn(0,0){.4cm}{0}{-70}
\uput{.4cm}[-35](0,0){\texttt{angleA}}}
\ncangle[angleA=-70,angleB=90,armB=1cm,linewidth=1.2pt]{A}{B}
\ncput[nrot=:U,npos=1]{\psframe[dimen=middle](0,0)(.35,.35)}
Mathematical diagrams and graphs
For some applications, such as mathematical diagrams and graphs, it is
useful to arrange nodes on a grid. You can do this with alignment environments, such as TEX’s \halignprimitive, LATEX’s tabular environment, and
AMS-TEX’s \matrix, but PSTricks contains its own alignment environment
that is especially adapted for this purpose24
\psmatrix{} ... \endpsmatrix
Here is an example
A
1
2
3
B
E
C
4
5
6
7
D
$\psmatrix[colsep=1cm,rowsep=1cm] & A \\ B & E & C \\ & D & \endpsmatrix$
As an alignment environment, \psmatrix is similar to AMS-TEX’s \matrix.
There is no argument for specifying the columns. Instead, you can just use
23
Not to be confused with the nput parameter.
24 A
LT
\begin{psmatrix} stuff \end{psmatrix}
Nodes and Node Connections: Mathematical diagrams and graphs
76
as many columns as you need. The entries are horizontally centered. Rows
are ended by \\. \psmatrix can be used in or out of math mode.
Our first example wasn’t very interesting, because we didn’t make use of
the nodes. Actually, each entry is a node. The name of the node in row
row and column col is {<row>,<col>}, with no spaces. Let’s see some node
connections:
1
2
3
4
X
5
6
f
g
7
8
9
Y
h
Z
10
11
12
13
14
$\psmatrix[colsep=1cm] & X \\ Y & Z \endpsmatrix \everypsbox{\scriptstyle}% \psset{nodesep=3pt,arrows=->} \ncline{1,2}{2,1} \tlput{f} \ncline{1,2}{2,2} \trput{g} \ncline[linestyle=dotted]{2,1}{2,2} \tbput{h}$
You can include the node connections inside the \psmatrix, in the last entry and right before \endpsmatrix. One advantage to doing this is that
shortput=tab is the default within a \psmatrix.
1
$\begin{psmatrix} U \\ & X\times_Z Y & X \\ & Y & Z \psset{arrows=->,nodesep=3pt} \everypsbox{\scriptstyle} \ncline{1,1}{2,2}_{y} \ncline[doubleline=true,linestyle=dashed]{-}{1,1}{2,3}^{x} \ncline{2,2}{3,2}<{q} \ncline{2,2}{2,3}_{p} \ncline{2,3}{3,3}>{f} \ncline{3,2}{3,3}_{g} \end{psmatrix} 2 3 U 4 x 5 6 y 7 X ×Z Y p X 8 9 q f 10 11 Y g Z 12 13 14 15$
You can change the kind of nodes that are made by setting the
mnode=type
Default: R
parameter. Valid types are R, r, C, f, p, circle, oval, dia, tri, dot and
none, standing for \Rnode, \rnode, \Cnode, \fnode, \pnode, \circlenode, \ovalnode, \dotnode and no node, respectively. Note that for circles,
Nodes and Node Connections: Mathematical diagrams and graphs
77
For example:
1
2
A
3
g
4
B
b
5
e
f
E
6
a
C
7
8
9
d
c
10
11
12
D
13
14
\psmatrix[mnode=circle,colsep=1]
& A \\
B & E & C \\
& D &
\endpsmatrix
\psset{shortput=nab,arrows=->,labelsep=3pt}
\small
\ncline{2,2}{2,3}^[npos=.75]{a}
\ncline{2,2}{2,1}^{b}
\ncline{3,2}{2,1}^{c}
\ncarc[arcangle=-40,border=3pt]{3,2}{1,2}
_[npos=.3]{d}^[npos=.7]{e}
\ncarc[arcangle=12]{1,2}{2,1}^{f}
\ncarc[arcangle=12]{2,1}{1,2}^{g}
Note that a node is made only for the non-empty entries. You can also
specify a node for the empty entries by setting the
emnode=type
Default: none
parameter.
You can change parameters for a single entry by starting this entry with
the parameter changes, enclosed in square brackets. Note that the changes
affect the way the node is made, but not contents of the entry (use \psset
for this purpose). For example:
1
2
X
3
4
5
6
7
Y
Z
8
9
10
$\psmatrix[colsep=1cm] & [mnode=circle] X \\ Y & Z \endpsmatrix \psset{nodesep=3pt,arrows=->} \ncline{1,2}{2,1} \ncline{1,2}{2,2} \ncline[linestyle=dotted]{2,1}{2,2}$
If you want your entry to begin with a [ that is not meant to indicate parameter changes, the precede it by {}.
You can assign your own name to a node by setting the
name=name
Default:
parameter at the beginning of the entry, as described above. You can still
refer to the node by {<row>,<col>}, but here are a few reasons for giving
your own name to a node:
Nodes and Node Connections: Mathematical diagrams and graphs
78
• The name may be easier to keep track of;
• Unlike the {<row>,<col>} names, the names you give remain valid
• The names remain valid even when you start a new \psmatrix that
reuses the {<row>,<col>} names.
Here a few more things you should know:
• The baselines of the nodes pass through the centers of the nodes.
\psmatrix achieves this by setting the
Default: false
nodealign=true/false
parameter to true. You can also set this parameter outside of \psmatrix when you want this kind of alignment.
• You can left or right-justify the nodes by setting the
mcol=l/r/c
Default: c
parameter. l, r and c stand for left, right and center, respectively.
• The space between rows and columns is set by the
rowsep=dim
colsep=dim
Default: 1.5cm
Default: 1.5cm
parameters.
• If you want all the nodes to have a fixed width, set
mnodesize=dim
Default: -1pt
to a positive value.
• If \psmatrix is used in math mode, all the entries are set in math
mode, but you can switch a single entry out of math mode by starting
and ending the entry with . • The radius of the c mnode (corresponding to \cnode) is set by the radius parameter. • Like in LATEX, you can end a row with \<dim>] to insert an extra space dim between rows. • The command \psrowhookii is executed, if defined, at the beginning of every entry in row ii (row 2), and the command \pscolhookv is executed at athe beginning of every entry in column v (etc.). You can use these hooks, for example, to change the spacing between two columns, or to use a special mnode for all the entries in a particular row. Nodes and Node Connections: Mathematical diagrams and graphs 79 • An entry can itself be a node. You might do this if you want an entry to have two shapes. • If you want an entry to stretch across several (int ) columns, use the \psspan{int} at the end of the entry. This is like P LAIN TEX’s \multispan, or LATEX’s \multicolumn, but the template for the current column (the first column that is spanned) is still used. If you want wipe out the template as well, use \multispan{<int>} at the beginning of the entry instead. If you just want to wipe out the template, use \omit before the entry. • \psmatrix can be nested, but then all node connections and other references to the nodes in the {<row>,<col>} form for the nested matrix must go inside the \psmatrix. This is how PSTricks decides which matrix you are referring to. It is still neatest to put all the node connections towards the end; just be sure to put them before \endpsmatrix. Be careful also not to refer to a node until it actually appears. The whole matrix can itself go inside a node, and node connections can be made as usual. This is not the same as connecting nodes from two different \psmatrix’s. To do this, you must give the nodes names and refer to them by these names. 36 Complex examples As this environment is very powerful and can be used for a lot of structured graphics (those of grid-like types), we give here two more complex examples. First, a complex mathematical commutative diagram (rewritten from [17]): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 \psmatrix[rowsep=1,colsep=1] % Nodes % First line & [name=SL] \Sigma^L & & & & [name=SR] \Sigma^R\\[0cm] % Second line [name=L] L & & [name=Lr] L_r & & [name=R] R\\[1.5cm] % Third line [name=Lm] L_m & & [name=Krm] K_{r,m} & & [name=Rm] R_{m^*}\\ & [name=SG] \Sigma^G & & & & [name=SH] \Sigma^H\\[0cm] % Fourth line [name=G] G & & [name=Gr] G_{r^*} Nodes and Node Connections: Complex examples 80 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 & & [name=H] H % % Links \everypsbox{\scriptstyle} \psset{arrows=->,nodesep=2mm,border=3pt}% \ncline{Lr}{R} ^{r} \ncline{Krm}{Rm} ^{r} \ncline{Gr}{H} _{r^*} \ncline{Lr}{L} ^[tpos=0.3]{i_1} \ncline{Krm}{Lm} ^[tpos=0.3]{i_3} \ncline{Gr}{G} _{i_5} \ncline{SL}{SR} ^{\varphi^r} \ncline{SG}{SH} _{\varphi^{r^*}} \ncline{SR}{SH} >{\varphi^{m^*}} \ncline{SL}{SG} <{\varphi^m} \ncline{Lm}{G} <{m} \ncline{Krm}{Lr} >{i_4} \ncline{Rm}{H} >[tpos=0.3]{m^*} \ncline{Lm}{L} <{i_2} \ncline{Krm}{Gr} >[tpos=0.3]{m} \ncline{Rm}{R} >{i_6} \ncline{L}{SL} <[tpos=0.3]{\lambda^L} \ncline{R}{SR} >[tpos=0.6]{\lambda^R} \ncline{G}{SG} <[tpos=0.3]{\lambda^G} \ncline[linestyle=dashed]{H}{SH} >[tpos=0.6]{\lambda^H} \endpsmatrix ϕr ΣL ΣR λL λR i1 L r Lr ϕm i2 R i4 i3 Lm Kr,m r Rm∗ m m∗ ΣG m ϕr λG ∗ ϕm i6 ΣH ∗ λH G i5 Gr ∗ r∗ H And second, a general connection diagram: 1 2 \newcommand{\PstComputingServer}{% \psovalbox[fillstyle=solid,fillcolor=Orange]{% Nodes and Node Connections: Complex examples 81 3 \shortstack{Computing\\Server}}} 4 5 6 7 \newcommand{\PstUnicoreClient}{% \psframebox[fillstyle=solid,fillcolor=Pink]{% \shortstack{Unicore\\Client}}} 8 9 10 11 \newcommand{\PstVisualizationServer}{% \psovalbox[fillstyle=solid,fillcolor=LemonChiffon]{% \shortstack{Visualization\\Server}}} 12 13 14 15 \newcommand{\PstCorbaNameServer}{% \pscirclebox[fillstyle=solid,fillcolor=cyan,framesep=0.02]{% \bfseries\shortstack{CORBA\\Name\\Server}}} 16 17 18 19 \newcommand{\PstComputingClient}{% \psovalbox[fillstyle=solid,fillcolor=PaleGreen]{% \shortstack{Computing\\Client}}} 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 \rput[l](-0.5,6){% \footnotesize \shortstack[l]{% \psline[linewidth=0.05,linecolor=black](-0.6,0.1)(-0.1,0.1) Program interactions\\ \psline[linestyle=dashed,linecolor=red](-0.6,0.08)(-0.1,0.08) Name Server interactions}} % \begin{psmatrix}[colsep=-0.5,rowsep=-0.5] & & [name=ComputingServer] \PstComputingServer\\[1cm] [name=Unicore] \PstUnicoreClient\\ & & & \psframebox{% \begin{psmatrix}[colsep=-0.7,rowsep=0] & [name=Visualization]\PstVisualizationServer\\[5mm] [name=CORBA] \PstCorbaNameServer \end{psmatrix}}\\ & [name=ComputingClient] \PstComputingClient \end{psmatrix} % \ncline[arrowscale=1.5,linewidth=0.05]{<->} {ComputingServer}{ComputingClient} \ncline[arrowscale=1.5,linewidth=0.05,offsetA=0.35,offsetB=0.5, nodesepA=-0.35,nodesepB=0.2]{->} {ComputingClient}{Visualization} \psset{linestyle=dashed,linecolor=red,arrowscale=1.3,labelsep=0.06}% \ncline[offsetA=0.08,nodesepA=0.07]{<->}{Unicore}{CORBA} \naput[npos=0.6,nrot=:U]{\footnotesize status} \nbput[npos=0.41,nrot=:U]{\footnotesize references \ \ cleaning} \ncline[nodesepB=-0.2]{->}{ComputingServer}{CORBA} \naput[npos=0.3,nrot=:U]{\footnotesize registration} \ncline[nodesepB=-0.15]{->}{Visualization}{CORBA} \naput{\footnotesize registration} \ncline[offsetA=0.2,nodesepA=-0.05,nodesepB=-0.14]{<->} {ComputingClient}{CORBA} Nodes and Node Connections: Complex examples 82 55 \nbput[nrot=:U]{\footnotesize inquiry} Program interactions Name Server interactions Computing Server istr reg n atio Unicore Client Visualization Server refe ren ces s cle tatus ani ng registration CORBA Name Server Computing Client inquiry Nodes and Node Connections: Complex examples 83 VIII 37 pst-tree Trees Overview The node and node connections are perfect tools for making trees, but positioning the nodes using \rput would be rather tedious.25 The file pstree.tex / pstree.sty contains a high-level interface for making trees. The tree commands are \pstree{root}{successors} \psTree{root} successors \endpsTree These do the same thing, but just have different syntax. \psTree is the “long” version.26 These macros make a box that encloses all the nodes, and whose baseline passes through the center of the root. Most of the nodes described in Section 30 has a variant for use within a tree. These variants are called tree nodes, and are described in Section 38. Trees and tree nodes are called tree objects. The root of a tree should be a single tree object, and the successors should be one or more tree objects. Here is an example with only nodes: root 1 \pstree[radius=3pt]{\Toval{root}}{\TC* \TC* \TC* \TC*} There is no difference between a terminal node and a root node, other than their position in the \pstree command. Here is an example where a tree is included in the list of successors, and hence becomes subtree: 25 Unless you have a computer program that generates the coordinates. EX users can write \begin{psTree} and \end{psTree} instead. 26 A LT Trees 84 1 2 3 4 38 \pstree[radius=3pt]{\Tp}{% \TC* \pstree{\TC}{\TC* \TC*} \TC*} Tree Nodes For most nodes described in Section 30, there is a variant for use in trees, called a tree node. In each case, the name of the tree node is formed by omitting node from the end of the name and adding T at the beginning. For example, \ovalnode becomes \Toval. Here is the list of such tree nodes: \Tp*[par ] \Tc*[par ]{dim} \TC*[par ] \Tf*[par ] \Tdot*[par ] \Tr*[par ]{stuff } \TR*[par ]{stuff } \Tcircle*[par ]{stuff } \TCircle*[par ]{stuff } \Toval*[par ]{stuff } \Tdia*[par ]{stuff } \Ttri*[par ]{stuff } The syntax of a tree node is the same as of its corresponding “normal” node, except that: • There is always an optional argument for setting graphics parameters, even if the original node did not have one; • There is no argument for specifying the name of the node; • There is never a coordinate argument for positioning the node; and • To set the reference point with \Tr, set the ref parameter. Figure 1 gives a reminder of what the nodes look like. The difference between \Tr and \TR (variants of \rnode and \Rnode, respectively) is important with trees. Usually, you want to use \TR with vertical trees because the baselines of the text in the nodes line up horizontally. For example: Trees: Tree Nodes 85 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \small \psset{armB=1cm, levelsep=3cm, treesep=-3mm, angleB=-90, angleA=90, nodesepA=3pt} \def\s#1{#1~{\tt\string#1}} \def\b#1{#1{\tt\string#1}} \def\psedge#1#2{\ncangle{#2}{#1}} \psTree[treenodesize=1cm]{\Toval{Tree nodes}} \s\Tp \Tc{.5}~{\tt\string\Tc} \s\TC \psTree[levelsep=4cm,armB=2cm]{\Tp[edge=\ncline]} \b\Tcircle \s\Tdot \TCircle[radius=1]{\tt\string\TCircle} \Tn \b\Toval \b\Ttri \b\Tdia \endpsTree \s\Tf \b\Tr \b\TR \endpsTree Tree nodes \TR \Tr \Tp \Tc \Tcircle b \TCircle \TC \Tf \Toval \Ttri \Tdia \Tdot Figure 1: The tree nodes. Trees: Tree Nodes 86 1 X 2 3 4 5 ˜ X̃ x y 6 \pstree[nodesepB=3pt]{\Tcircle{X}}{% \TR{\tilde{\tilde{X}}} \TR{x} \TR{y}} Compare with this example, which uses \Tr: X 1 2 3 4 5 ˜ X̃ y x 6 \pstree[nodesepB=3pt]{\Tcircle{X}}{% \Tr{\tilde{\tilde{X}}} \Tr{x} \Tr{y}} There is also a null tree node: \Tn It is meant to be just a place holder. Look at the tree in Figure page ??. The bottom row has a node missing in the middle. \Tn was used for this missing node. There is also a special tree node that doesn’t have a “normal” version and that can’t be used as the root node of a whole tree: \Tfan*[par ] This draws a triangle whose base is fansize=dim Default: 1cm and whose opposite corner is the predecessor node, adjusted by the value of nodesepA and offsetA. For example: 11 1 2 ⊕ ⊕ 3 4 5 \pstree[dotstyle=oplus,dotsize=8pt,nodesep=2pt] {\Tcircle{11}}{% \Tdot \pstree{\Tfan}{\Tdot} \pstree{\Tdot}{\Tfan[linestyle=dashed]}} ⊕ Trees: Tree Nodes 87 39 Tree orientation Trees can grow down, up, right or left, depending on the treemode=D/U/R/L Default: D parameter. Here is what the previous example looks like when it grows to the right: ⊕ 1 ⊕ 11 2 3 4 ⊕ 5 \pstree[dotstyle=oplus,dotsize=8pt,nodesep=2pt,treemode=R] {\Tcircle{11}}{% \Tdot \pstree{\Tfan}{\Tdot} \pstree{\Tdot}{\Tfan[linestyle=dashed]}} You can change the treemode in the middle of the tree. For example, here is a tree that grows up, and that has a subtree which grows to the left: 3 4 1 1 2 ⊗ ⊗ 3 4 2 5 \footnotesize \pstree[treemode=U,dotstyle=otimes,dotsize=8pt,nodesep=2pt] {\Tdot}{% \pstree[treemode=L]{\Tdot}{\Tcircle{1} \Tcircle{2}} \pstree{\Tdot}{\Tcircle{3} \Tcircle{4}}} b Since you can change a tree’s orientation, it can make sense to include a tree (treeB ) as a root node (of treeA). This makes a single logical tree, whose root is the root of treeB , and that has successors going off in different directions, depending on whether they appear as a successor to treeA or to treeB . root B 1 2 3 A1 \pstree{\pstree[treemode=L]{\Tcircle{root}}{\Tr{B}}}{% \Tr{A1} \Tr{A2}} A2 When the tree grows up or down, the successors are lined up from left to right in the order they appear in \pstree. When the tree grows to the left or right, the successors are lined up from top to bottom. As an afterthought, you might want to flip the order of the nodes. The Trees: Tree orientation 88 treeflip=true/false Default: false let’s you do this. For example: 3 4 1 2 2 ⊗ ⊗ 3 4 1 5 \footnotesize \pstree[treemode=U,dotstyle=otimes,dotsize=8pt, nodesep=2pt,treeflip=true]{\Tdot}{% \pstree[treemode=R]{\Tdot}{\Tcircle{1} \Tcircle{2}} \pstree{\Tdot}{\Tcircle{3} \Tcircle{4}}} b Note that I still have to go back and change the treemode of the subtree that used to grow to the left. 40 The distance between successors The distance between successors is treesep=dim Default: .75cm The rest of this section describes ways to fine-tune the spacing between successors. You can change the method for calculating the distance between subtrees by setting the treefit=tight/loose Default: tight parameter. Here are the two methods: tight When treefit=tight, which is the default, treesep is the minimum distance between each of the levels of the subtrees. loose When treefit=loose, treesep is the distance between the subtrees’ bounding boxes. Except when you have large intermediate nodes, the effect is that the horizontal distance (or vertical distance, for horizontal trees) between all the terminal nodes is the same (even when they are on different levels).27 Compare: 27 When all the terminal nodes are on the same level, and the intermediate nodes are not wider than the base of their corresponding subtrees, then there is no difference between the two methods. Trees: The distance between successors 89 With treefit=loose, trees take up more space, but sometimes the structure of the tree is emphasized. Sometimes you want the spacing between the centers of the nodes to be regular even though the nodes have different sizes. If you set treenodesize=dim Default: -1pt to a non-negative value, then PSTricks sets the width (or height+depth for vertical trees) to treenodesize, for the purpose of calculating the distance between successors. DG: It seems that there is a bug here... For example, ternary trees look nice when they are symmetric, as in the following example: 1 2 3 4 x=y x1 = y1 x11 = y11 \pstree[nodesepB=-8pt,treenodesize=0.85]{\Tc{3pt}}{% \TR{x=y} \TR{x_1=y_1} \TR{x_{11}=y_{11}}} Compare with this example, where the spacing varies with the size of the nodes: 1 2 3 4 x=y x1 = y1 x11 = y11 \pstree[nodesepB=-8pt]{\Tc{3pt}}{% \TR{x=y} \TR{x_1=y_1} \TR{x_{11}=y_{11}}} Finally, if all else fails, you can adjust the distance between two successors by inserting \tspace{dim} Trees: The distance between successors 90 between them: 1 2 3 4 foo and bar 41 5 \pstree{\Tc{3pt}}{% \Tdia{foo} \tspace{-0.5} \Toval{and} \Ttri{bar}} Spacing between the root and successors The distance between the center lines of the tree levels is: Default: 2cm levelsep=*dim If you want the spacing between levels to vary with the size of the levels, use the * convention. Then levelsep is the distance between the bottom of one level and the top of the next level (or between the sides of the two levels, for horizontal trees). Note: PSTricks has to write some information to your .aux file if using LATEX, or to \jobname.pst otherwise, in order to calculate the spacing. You have to run your input file a few times before PSTricks gets the spacing right. You are most likely to want to set varlevelsep to true in horizontal trees. Compare the following example: 1 2 3 4 5 \def\psedge#1#2{\ncdiagg[nodesep=3pt,angleA=180,armA=0]{#2}{#1}} \pstree[treemode=R,levelsep=*1cm] {\TR{George Alexander Kopf VII}}{% \pstree[ref=c]{\Tr{Barry Santos}}{\Tr{James Kyle} \Tr{Ann Ada}} \pstree[ref=c]{\Tr{Terri Maloney}}{\Tr{Uwe Kopf} \Tr{Vera Kan}}} James Kyle Barry Santos Ann Ada George Alexander Kopf VII Uwe Kopf Terri Maloney Vera Kan with this one, were the spacing between levels is fixed: 1 2 3 \def\psedge#1#2{\ncdiagg[nodesep=3pt,angleA=180,armA=0]{#2}{#1}} \pstree[treemode=R,levelsep=3cm] {\Tr{George Alexander Kopf VII}}{% Trees: Spacing between the root and successors 91 \pstree[ref=c]{\Tr{Barry Santos}}{\Tr{James Kyle} \Tr{Ann Ada}} \pstree[ref=c]{\Tr{Terri Maloney}}{\Tr{Uwe Kopf} \Tr{Vera Kan}}} 4 5 James Kyle Barry Santos Ann Ada George Alexander Kopf VII Uwe Kopf Terri Maloney Vera Kan 42 Edges Right after you use a tree node command, \pssucc is equal to the name of the node, and \pspred is equal to the name of the node’s predecessor. Therefore, you can draw a line between the node and its predecessor by inserting, for example, \ncline{\pspred}{\pssucc} 1 To save you the trouble of doing this for every node, each tree node executes \psedge{\pspred}{\pssucc} 1 The default definition of \psedge is \ncline, but you can redefine it as you please with \def or LATEX’s \renewcommand. For example, here I use \ncdiag, with armA=0, to get all the node connections to emanate from the same point in the predecessor:28 K L \def\psedge{\ncdiag[armA=0,angleB=180,armB=1]} \pstree[treemode=R,levelsep=3.5,framesep=2pt] {\Tc{6pt}}{% \small \Tcircle{K} \Tcircle{L} \Tcircle{M} \Tcircle{N}} 1 2 3 M 4 N 28 A LT EX users can instead type: \renewcommand{\psedge}{\ncdiag[armA=0,angleB=180,armB=1cm]} Trees: Edges 92 Here is an example with \ncdiagg. Note the use of a negative armA value so that the corners of the edges are vertically aligned, even though the nodes have different sizes: 1 2 3 4 5 6 7 8 9 10 \def\psedge#1#2{% \ncdiagg[angleA=180,armA=-3,nodesep=4pt]{#2}{#1}} % Or: \renewcommand{\psedge}[2]{ ... } \pstree[treemode=R,levelsep=5]{\Tc{3pt}}{% \Tr{z_1\leq y} \Tr{z_1<y\leq z_2} \Tr{z_2<y\leq x} \Tr{x<y}} z1 ≤ y z1 < y≤ z2 z2 < y≤ x x<y Another way to define \psedge is with the edge=command Default: \ncline parameter. Be sure to enclose the value in braces {} if it contains commas or other parameter delimiters. This gets messy if your command is long, and you can’t use arguments like in the preceding example, but for simple changes it is useful. For example, if I want to switch between a few node connections frequently, I might define a command for each node connection, and then use the edge parameter. 1 2 3 4 5 \def\dedge{\ncline[linestyle=dashed]} \pstree[treemode=U,radius=2pt]{\Tc{3pt}}{% \TC*[edge=\dedge] \pstree{\Tc{3pt}}{\TC*[edge=\dedge] \TC*} \TC*} You can also set edge=none to suppress the node connection. If you want to draw a node connection between two nodes that are not direct predecessor and successor, you have to give the nodes a name that you can Trees: Edges 93 refer to, using the name parameter. For example, here I connect two nodes on the same level: nature 1 2 3 4 \pstree[nodesep=3pt,radius=2pt]{\Toval{nature}}{% \pstree{\Tc[name=top]{3pt}}{\TC* \TC*} \pstree{\Tc[name=bot]{3pt}}{\TC* \TC*}} \ncline[linestyle=dashed]{top}{bot} We conclude with the more examples. X 1 root Y 2 3 \def\psedge{\nccurve[angleB=180,nodesepB=3pt]} \pstree[treemode=R,treesep=1.5,levelsep=3.5]% {\Toval{root}}{\Tr{X} \Tr{Y} \Tr{Z}} Z 1 root 2 3 4 5 6 x y z 7 \pstree[arrows=->,nodesepB=3pt,xbbl=15pt,xbbr=15pt, levelsep=2.5cm]{\Tdia{root}}{% \TR[edge={\ncbar[angle=180]}]{x} \TR{y} \TR[edge=\ncbar]{z} } root 1 2 3 4 43 \psset{arrows=<-,armB=1,levelsep=3,treesep=1, angleB=-90,angleA=90,nodesepA=3pt} \def\psedge#1#2{\ncangle{#2}{#1}} \pstree[radius=2pt]{\Ttri{root}}{\TC* \TC* \TC* \TC*} Edge and node labels Right after a node, an edge has typically been drawn, and you can attach labels using \ncput \tlput, etc. Trees: Edge and node labels 94 With \tlput, \trput, \taput and \tbput, you can align the labels vertically or horizontally, just like the nodes. This can look nice, at least if the slopes of the node connections are not too different. 1 k r m 2 3 4 5 6 j i 7 \pstree[radius=2pt]{\Tp}{% \psset{tpos=0.6} \TC* \tlput{k} \pstree{\Tc{3pt} \tlput[labelsep=3pt]{r}}{% \TC* \tlput{j} \TC* \trput{i}} \TC* \trput{m}} Within trees, the tpos parameter measures this distance from the predecessor to the successor, whatever the orientation of the true. (Outside of trees it measures the distance from the top to bottom or left to right nodes.) PSTricks also sets shortput=tab within trees. This is a special shortput option that should not be used outside of trees. It implements the following abbreviations, which depend of the orientation of the true: Char. Short for: Vert. Horiz. ^ \tlput \taput _ \trput \tbput (The scheme is reversed if treeflip=true.) left right 1 2 3 above 4 5 above 6 7 8 \psset{tpos=0.6} \pstree[treemode=R,thistreesep=1,thislevelsep=3, radius=2pt]{\Tc{3pt}}{% \pstree[treemode=U,xbbr=20pt]{\Tc{3pt}^{above}}{% \TC*^{left} \TC*_{right}} \TC*^{above} \TC*_{below}} below You can change the character abbreviations with \MakeShortTab{char1}{char2} The \n*put commands can also give good results: Trees: Edge and node labels 95 ve abo above 1 2 3 4 belo w 5 \psset{npos=0.6,nrot=:U} \pstree[treemode=R,thistreesep=1,thislevelsep=3cm]{\Tc{3pt}}{% \Tc{3pt}\naput{above} \Tc*{2pt}\naput{above} \Tc*{2pt}\nbput{below}} You can put labels on the nodes using \nput. However, \pstree won’t take these labels into account when calculating the bounding boxes. There is a special node label option for trees that does keep track of the bounding boxes: ~*[par ]{stuff } Call this a “tree node label”. Put a tree node label right after the node to which it applies, before any node connection labels (but node connection labels, including the short forms, can follow a tree node label). The label is positioned directly below the node in vertical trees, and similarly in other trees. For example: root 1 2 h i j \pstree[radius=2pt]{\Tc{3pt}\nput{45}{\pssucc}{root}}{% \TC*~{h} \TC*~{i} \TC*~{j} \TC*~{k}} k Note that there is no “long form” for this tree node label. However, you can change the single character used to delimit the label with \MakeShortTnput{char1} If you find it confusing to use a single character, you can also use a command sequence. E.g., 1 \MakeShortTnput{\tnput} You can have multiple labels, but each successive label is positioned relative to the bounding box that includes the previous labels. Thus, the order in which the labels are placed makes a difference, and not all combinations will produce satisfactory results. You will probably find that the tree node label works well for terminal nodes, without your intervention. However, you can control the tree node labels be setting several parameters. To position the label on any side of the node (left, right, above or below), set: Trees: Edge and node labels 96 Default: tnpos=l/r/a/b root 1 2 3 4 h \psframebox{% \pstree{\Tc{3pt}~[tnpos=a,tndepth=0,radius=4pt]{root}}{% \TC*~[tnpos=l]{h} \TC*~[tnpos=r]{i}}} i When you leave the argument empty, which is the default, PSTricks chooses the label position is automatically. To change the distance between the node and the label, set tnsep=dim Default: When you leave the argument empty, which is the default, PSTricks uses the value of labelsep. When the value is negative, the distance is measured from the center of the node. When labels are positioned below a node, the label is given a minimum height of tnheight=dim Default: \ht\strutbox Thus, if you add labels to several nodes that are horizontally aligned, and if either these nodes have the same depth or tnsep is negative, and if the height of each of the labels is no more than tnheight, then the labels will also be aligned by their baselines. The default is \ht\strutbox, which in most TEX formats is the height of a typical line of text in the current font. Note that the value of tnheight is not evaluated until it is used. The positioning is similar for labels that go below a node. The label is given a minimum depth of tndepth=dim Default: \dp\strutbox For labels positioned above or below, the horizontal reference point of the label, i.e., the point in the label directly above or below the center of the node, is set by the href parameter. When labels are positioned on the left or right, the right or left edge of the label is positioned distance tnsep from the node. The vertical point that is aligned with the center of the node is set by tnyref=num Default: When you leave this empty, vref is used instead. Recall that vref gives the vertical distance from the baseline. Otherwise, the tnyref parameter works like the yref parameter, giving the fraction of the distance from the bottom to the top of the label. Trees: Edge and node labels 97 44 Framing The \pstreeframe and \pstreecurve macros allow to frame trees or subtrees: 1 2 3 1 2 3 4 5 6 \pstreeframe{\pstree{\Tc{3pt}}{\Tc{3pt}\Tc{3pt}}} \hspace{1cm} \pstreecurve{\pstree{\Tc{3pt}}{\Tc{3pt}\Tc{3pt}}} \pstreecurve[fillstyle=solid,fillcolor=PaleGreen,framesep=0.6]{% \pstree[nodesep=3pt,framearc=0.2]{\TR{William}}{% \pstreeframe[fillstyle=solid,fillcolor=Pink]{% \pstree{\TR{Georges}}{\TR{Paul}\TR{Alan}}} \pstreeframe[fillstyle=solid,fillcolor=LemonChiffon]{% \pstree{\TR{Richard}}{\TR{John}\TR{Peter}\TR{Jack}}}}} William Georges Paul Alan Richard John Peter Jack Note that the bounding boxes does not include the frame (at opposite that if we frame the tree with a macro like \psframebox), and that macros like \psframebox does not allow to frame subtrees. 45 Details PSTricks does a pretty good job of positioning the nodes and creating a box whose size is close to the true bounding box of the tree. However, PSTricks does not take into account the node connections or labels when calculating the bounding boxes, except the tree node labels. If, for this or other reasons, you want to fine tune the bounding box of the nodes, you can set the following parameters: Trees: Framing 98 bbl=dim bbr=dim bbh=dim bbd=dim xbbl=dim xbbr=dim xbbh=dim xbbd=dim Default: Default: Default: Default: Default: 0 Default: 0 Default: Default: The x versions increase the bounding box by dim, and the others set the bounding box to dim. There is one parameter for each direction from the center of the node, left, right, height, and depth. These parameters affect trees and nodes, and subtrees that switch directions, but not subtrees that go in the same direction as their parent tree (such subtrees have a profile rather than a bounding box, and should be adjusted by changing the bounding boxes of the constituent nodes). Save any fiddling with the bounding box until you are otherwise finished with the tree. You can see the bounding boxes by setting the showbbox=true/false Default: false parameter to true. To see the bounding boxes of all the nodes in a tree, you have to set this parameter before the tree. In the following example, the labels stick out of the bounding box: foo bar 1 left right 2 3 4 \psset{tpos=0.6,showbbox=true} \pstree[treemode=U]{\Tc{5pt}}{% \TR{foo}^{left} \TR{bar}_{right}} Here is how we fix it: foo bar 1 left right 2 3 4 \psset{tpos=0.6,showbbox=true} \pstree[treemode=U,xbbl=8pt,xbbr=14pt]{\Tc{5pt}}{% \TR{foo}^{left} \TR{bar}_{right}} Now we can frame the tree: Trees: Details 99 foo left 1 bar 2 3 right 4 5 6 7 \psframebox[fillstyle=solid,fillcolor=lightgray,framesep=14pt, linearc=14pt,cornersize=absolute,linewidth=1.5pt]{% \psset{tpos=0.6,border=1pt,nodesepB=3pt} \pstree[treemode=U,xbbl=8pt,xbbr=14pt]{% \Tc[fillcolor=white,fillstyle=solid]{5pt}}{% \TR*{foo}^{left} \TR*{bar}_{right}}} We would have gotten the same result by changing the bounding box of the two terminal nodes. To skip levels, use \skiplevel*[par ]{nodes or subtrees} \skiplevels*[par ]{int} nodes or subtrees \endskiplevels These are kind of like subtrees, but with no root node. 1 2 3 4 5 6 7 8 9 \pstree[treemode=R,levelsep=1.8,radius=2pt]{\Tc{3pt}}{% \skiplevel{\Tfan} \pstree{\Tc{3pt}}{% \TC* \skiplevels{2} \pstree{\Tc{3pt}}{\TC* \TC*} \TC* \endskiplevels \pstree{\Tc{3pt}}{\TC* \TC*}}} The profile at the missing levels is the same as at the first non-missing level. You can adjust this with the bounding box parameters. You get greatest control if you use nested \skiplevel commands instead of \skiplevels. 1 2 \large \psset{radius=6pt,dotsize=4pt} Trees: Details 100 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 \pstree[thislevelsep=0,edge=none,levelsep=2.5cm]{\Tn}{% \pstree{\TR{Player 1}}{\pstree{\TR{Player 2}}{\TR{Player 3}}} \psset{edge=\ncline} \pstree {\pstree[treemode=R]{\TC}{\Tdot ~{(0,0,0)} ^{N}}}{% \pstree{\TC[name=A] ^{L}}{% \Tdot ~{(-10,10.-10)} ^{l} \pstree{\TC[name=C] _{r}}{% \Tdot ~{(3,8,-4)} ^{c} \Tdot ~{(-8,3,4)} _{d}}} \pstree{\TC[name=B] _{R}}{% \Tdot ~{(10,-10.0)} ^{l} \pstree{\TC[name=D]_{r}}{% \Tdot ~{(4,8,-3)} ^{c} \Tdot ~{(0,-5,0)} _{d}}}}} \ncbox[linearc=0.3,boxsize=0.3,linestyle=dashed,nodesep=0.4]{A}{B} \ncarcbox[linearc=0.3,boxsize=0.3,linestyle=dashed,arcangle=25, nodesep=0.4]{D}{C} N Player 1 L b (0,0,0) R Player 2 l Player 3 r l b b (-10,10.-10) (10,-10.0) c 46 r d c d b b b b (3,8,-4) (-8,3,4) (4,8,-3) (0,-5,0) The scope of parameter changes edge is the only parameter which, when set in a tree node’s parameter argument, affects the drawing of the node connection (e.g., if you want to change the nodesep, your edge has to include the parameter change, or you have to set it before the node). As noted at the beginning of this section, parameter changes made with \pstree affect all subtrees. However, there are variants of some of these Trees: The scope of parameter changes 101 parameters for making local changes, i.e, changes that affects only the current level: thistreesep=dim thistreenodesize=dim thistreefit=tight/loose thislevelsep=dim Default: Default: Default: Default: For example: 1 2 3 \pstree[thislevelsep=0.5,thistreesep=2,radius=2pt]{\Tc*{3pt}}{% \pstree{\TC*}{\TC* \TC*} \pstree{\TC*}{\TC* \TC*}} There are some things you may want set uniformly across a level in the tree, such as the levelsep. At level n, the command \pstreehook<roman(n)> (e.g., \pstreehookii) is executed, if it is defined (the root node of the whole tree is level 0, the successor tree objects and the node connections from the root node to these successors is level 1, etc.). In the following example, the levelsep is changed for level 2, without having to set the thislevelsep parameter for each of the three subtrees that make of level 2: 1 \[ \def\pstreehookiii{\psset{thislevelsep=3cm}} \pstree[treemode=R,levelsep=1cm,radius=2pt]{\Tc{4pt}}{% \pstree{\TC*}{% \pstree{\TC*}{\Tr{X_1} \Tr{X_2}} \pstree{\TC*}{\Tr{Y_1} \Tr{Y_2}}} \pstree{\TC*}{% \pstree{\TC*}{\Tr{K_1} \Tr{K_2}} \pstree{\TC*}{\Tr{J_1} \Tr{J_2}}}} 2 3 4 5 6 7 8 9 10 Trees: The scope of parameter changes 102 X1 X2 Y1 Y2 K1 K2 J1 J2 47 Complex examples As trees are a very often representation structure used in many areas, we give here three more complex examples. First a general organization tree: 1 2 % Connection style \def\psedge#1#2{\ncangle[angleA=90,angleB=-90]{#2}{#1}} 3 4 5 6 7 8 9 10 \def\DirBa#1{\Tr{\psshadowbox{\footnotesize #1}}} \def\DirBx#1#2{% \pstree[thislevelsep=#2,treenodesize=0.6]{\Tn}{\DirBa{#1}}} \def\DirBb#1{\DirBx{#1}{1.5}} \def\DirBc#1{\DirBx{#1}{3}} \def\DirBd#1{\DirBx{#1}{4.5}} \def\DirBe#1{\DirBx{#1}{6}} 11 12 \psset{levelsep=3,armB=1.5}% 13 14 15 16 17 18 19 20 21 22 23 \rotateleft{% \scaleboxto(22,7){% \psframebox[framesep=0.8,framearc=0.2]{% \pstree[xbbd=2.5]{\DirBa{\large Benchs 98}} {\pstree[treenodesize=0.3] {\DirBa{\large Low-Level}% \nput[labelsep=10.5]{-90}{\pssucc}{% \psline[linewidth=0.1]{<->}(-7,1)(13.5,1) \Huge 16 codes}} {\pstreeframe*[linecolor=Thistle]{% Trees: Complex examples 103 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 \pstree{\DirBa{Architecture}} {\DirBa{Paranoia} \DirBb{Elefunt}}} \pstreeframe*[linecolor=LemonChiffon]{% \pstree{\DirBa{System}} {\DirBa{Stream} \DirBb{CacheBench} \DirBa{Iozone} \DirBb{Bonnie}}} \pstreeframe*[linecolor=PaleGreen]{% \pstree{\DirBa{Network}} {\DirBa{FTP} \DirBb{MLTTCP} \DirBa{Netpipe}}} \pstreeframe*[linecolor=Pink]{% \pstree[treenodesize=0.6]{\DirBa{Applications}} {\DirBa{EuroBen} \DirBb{F90} \DirBa{Livermore} \DirBb{PBLL} \DirBa{SKaMPI} \DirBb{Testmpio} \DirBa{IOD}}}} \pstree{\DirBa{\large Applications}% \nput[labelsep=10.5]{-90}{\pssucc}{% \psline[linewidth=0.1]{<->}(-19,1)(22,1) \Huge 25 codes}} {\pstreeframe*[linecolor=LightBlue]{% \pstree[thislevelsep=0]{\Tn} {\DirBa{LMDZ} \DirBb{OPA} \DirBc{BOA} \DirBd{Convect} \DirBa{SPEC3D} \DirBb{NS-P1P2} % ... \DirBb{CPMD}}}} \tspace{17} \DirBa{\large Workload}}}}} Trees: Complex examples 104 Trees: Complex examples Benchs 98 Applications Low-Level System Architecture Applications Network LMDZ OPA Paranoia Stream Elefunt Iozone CacheBench FTP Bonnie Netpipe MLTTCP EuroBen Livermore F90 SKaMPI PBLL IOD Testmpio NTMIX SPEC3D NS-P1P2 BOA COSMO3D AVBP Workload ES1D ZPZM3 NSMD Convect EMI2D-V KE-3D 25 codes CHARMM H2P EMI2D-P NASTI 16 codes U1 MDVPL ASTERIX GAUSSIAN EGEN CPMD RURA 105 And, second, an example of a complex genealogical tree, coming from Françoise Coustillas and Louis Rigot. 1 2 % Defaut edge \renewcommand{\psedge}{\ncangle[angleA=-90]} 3 4 5 6 7 8 % Macro to define one person \newcommand{\Person}[3][]{% \TR[#1]{% \setlength{\tabcolsep}{0mm}% \begin{tabular}[t]{#2}#3\end{tabular}}} 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 % Definition of people \newcommand{\CatherineVerrier}{% \Person{c}{% \rnode{NodeTempA}{% Catherine V\textsc{errier} (\oldstylenums{1741}, Feyzin – \oldstylenums{1826}, Lyon)\hspace{1mm}}\\ fille de Marin et de Beno^^eete Langlois, domestique\\ \rnode{NodeTempB}{% \hspace{1mm}x \oldstylenums{1764}, V^^e9nissieux}\\ Jean-Baptiste B\textsc{uffard}\\ (v. \oldstylenums{1739}, Ardon, auj. Ch^^e2tillon-en-Michaille ? –\\ \oldstylenums{1777}, La Guilloti^^e8re, auj. Lyon)\\ domestique, postillon, m\textsuperscript{d} ^^e9picier, revendeur}} 24 25 26 27 28 \newcommand{\MarieVerrier}{% \Person[edge={\ncangle[angleA=0]}]{c}{% Marie V\textsc{errier}\\ % ... 29 30 31 32 33 34 \newcommand{\MadeleineBuffard}{% \Person[edge={\ncangles[angleA=180,armA=2.2cm]}]{c}{% Magdelaine B\textsc{uffard}\\ % ... \scriptsize 35 36 37 {\Large Parent^^e9 avec Paul Vigi^^e8re d’Anval} {\Large des parties signataires de son acte de bapt^^eame} 38 39 40 41 42 43 44 45 46 47 48 49 \fbox{\makebox[\textwidth]{% \pstree[levelsep=*1.5\baselineskip,treesep=-0.1, armB=0.6\baselineskip,angleB=90,linewidth=0.015] {\CatherineVerrier \gdef\pssucc{NodeTempB}} {\pstree{\MadeleineBuffard} {\ClaudeMorenne} \pstree[thistreesep=1mm] {\AntoinetteBuffard \gdef\pssucc{NodeTempC}} {\AndreCreuzet Trees: Complex examples 106 50 51 52 53 54 55 56 \gdef\pspred{NodeTempD}% \FleuryDumas \pstree[levelsep=*4\baselineskip] {\ClarisseDumas} {\PaulVigiere}} \gdef\pspred{NodeTempA}% \MarieVerrier}}} Parenté avec Paul Vigière d’Anval des parties signataires de son acte de baptême Catherine VERRIER (, Feyzin – , Lyon) fille de Marin et de Benoîte Langlois, domestique x , Vénissieux Jean-Baptiste BUFFARD (v. , Ardon, auj. Châtillon-en-Michaille ? – , La Guillotière, auj. Lyon) domestique, postillon, md épicier, revendeur Magdelaine BUFFARD (, La Guillotière – , St -Cyr-au-Mt -d’Or) x ... ... ... Jean-Marie MORENNE (, Lyon St -Paul ? – av. --) commissaire national Antoinette BUFFARD Marie VERRIER (, La Guillotière – (, La Guillotière – , Lyon er ) , Lyon er ) brodeuse x , Lyon x o , Lyon St -Polycarpe Jacques TROUVÉ Joseph CREUZET (, Lyon St -Pierre (, La Guillotière – St -Saturnin – , Lyon Nord) , Lyon er ) négt , md fabr. brodeur vernisseur et x o , Lyon Nord décorateur, André DUMAS ptaire rentier (, Lyon St -Georges – , Lyon) négt , ptaire rentier Claude MORENNE (, Lyon – , St -Cyrau-Mt -d’Or) prêtre André CREUZET Fleury DUMAS Clarisse DUMAS (, Lyon Nord – (, Lyon – (, Lyon – , Tiviers) , id.) , St -Rambertoff. de la L.H., député rentier l’Île-Barbe, auj. Lyon) au corps législatif, mbre s.a. x , Lyon du cons. gén. du Cantal, Camille VIGIÈRE D ’ANVAL ss-préfet, maire de St -Flour (, Lyon Nord – et de Tiviers, ptaire rentier , St -Flour, Cantal) x , Lyon ptaire rentier, Adèle VIGIÈRE D ’ANVAL fils de Jean-Fran(xc, yc)ois, (, St -Didier-au-Mt -d’Or – négt , ptaire rentier, , St -Flour, Cantal) et de Marie Perrochia fille de Jean-Fran(xc, yc)ois, négt , ptaire rentier, et de Marie Perrochia Paul VIGIÈRE D ’ANVAL (, Lyon – , Belleville, Rhône) cher de la L.H., capne adj.-major x , Lyon e Louise VITTON (, Chaneins – , Lyon e ) fille de Constant, avocat, ptaire rentier, et d’Émilie Charvériat Trees: Complex examples 107 1 2 3 4 5 6 \def\MyNodeA{\@ifnextchar[{\MyNodeA@i}{\MyNodeA@i[]}} \def\MyNodeA@i[#1]#2{\Tr[#1]{\psframebox{#2}}} \def\MyNodeB{\@ifnextchar[{\MyNodeB@i}{\MyNodeB@i[]}} \def\MyNodeB@i[#1]#2{\TR[#1]{\psframebox{#2}}} \def\MyNodeC{\@ifnextchar[{\MyNodeC@i}{\MyNodeC@i[]}} \def\MyNodeC@i[#1]#2#3{\Tr[#1]{\rnode[b]{#2}{\psframebox{#3}}}} 7 8 \SpecialCoor 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 \pstree[arrows={-*},arrowscale=2,nodesepB=0.1] {\MyNodeA[ref=b]{matrix package}} {\pstree[treesep=-2,levelsep=1.5] {\MyNodeC[ref=t]{Types}{matrix types}} {\psset{levelsep=0.8,labelsep=0.1}% \def\pspred{Types}% \MyNodeB[href=-0.4]{% \Rnode[href=-0.4]{Dense}{dense matrices}} \tlput[tpos=0.44]{0.7} \skiplevels{1} \MyNodeB{\Rnode{Sparse}{sparse matrices}} \tlput[tpos=0.58]{0.3} \endskiplevels \pspolygon*([nodesep=3.3]{\pspred}Dense)(\pspred) ([nodesep=2.8]{\pspred}Sparse) \skiplevels{2} \MyNodeB[href=0.3]{% \Rnode[href=0.3]{Real}{real matrices}} \tlput[tpos=0.65]{0.7} \endskiplevels \skiplevels{3} \MyNodeB[href=0.3]{% \Rnode[href=0.3]{Complex}{complex matrices}} \tlput[tpos=0.7]{0.3} \endskiplevels \pspolygon*([nodesep=2.75]{\pspred}Real)(\pspred) ([nodesep=2.3]{\pspred}Complex) \skiplevels{4} \MyNodeB[href=0.4]{rectangular matrices} \endskiplevels \psset{arrows={-o},tpos=0.78}% \skiplevels{5} \MyNodeB[href=0.4]{symmetric matrices} \tlput[tpos=0.74]{0.3} \endskiplevels \skiplevels{6} \MyNodeB[href=0.5]{diagonal matrices} \tlput{0.3} \endskiplevels \skiplevels{7} \MyNodeB[href=0.5]{triangular matrices} \tlput{0.3} \endskiplevels Trees: Complex examples 108 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 \skiplevels{8} \MyNodeB[href=1]{band matrices} \tlput[labelsep=0]{0.1} \endskiplevels \tspace{6}\Tn} \pstree[treesep=-3.5,levelsep=1.5] {\MyNodeC[ref=t]{Computation}{% matrix computation types}} {\def\pspred{Computation}% \MyNodeB[href=0.6]{factorizations} \psset{levelsep=0.8,labelsep=0.05,tpos=0.8}% \skiplevels{1} \MyNodeB[href=-0.4]{% \Rnode[href=-0.4]{Linear}{linear systems}} \tlput[tpos=0.7]{0.3} \endskiplevels \skiplevels{2} \MyNodeB[href=-0.6]{least squares} \tlput[tpos=0.75]{0.2} \endskiplevels \skiplevels{3} \MyNodeB[href=-0.6]{eigenvalues} \tlput{0.2} \endskiplevels \skiplevels{4} \MyNodeB[href=-0.8]{% \Rnode[href=-0.8]{Iterative}{iterative methods}} \tlput{0.2} \endskiplevels \pnode([nodesep=0.8]{\pspred}Linear){LinearB} \pnode([nodesep=3.3]{\pspred}Iterative){IterativeB} \pscustom*[arrows=-]{% \psline(IterativeB)(\pspred)(LinearB) \ncarc[arcangle=40]{LinearB}{IterativeB}}}} Trees: Complex examples 109 matrix package matrix types matrix computation types 0.7 dense matrices 0.3 sparse matrices 0.7 real matrices 0.2 0.3 0.2 complex matrices 0.2 0.3 rectangular matrices factorizations 0.3 linear systems least squares eigenvalues iterative methods 0.3 symmetric matrices 0.3 diagonal matrices 0.1 triangular matrices band matrices Trees: Complex examples 110 IX 48 Filling and Tiling 29 Overview The file pst-fill.tex/pst-fill.sty contains a high-level interface for simple drawing of various kinds of filling and area tiling. pst-fill We use the word filling to describe the operation which consists of filling a defined area by a pattern (or a composition of patterns), and tiling as the operation which is like filling, but with control of the starting point (we use the upper left corner), where the pattern is positioned relative to this point. There is an essential difference between the two modes, as without control of the starting point we cannot create the tilings (sometimes called tesselations) used in many fields of Art and Science. Tilings are a wide and difficult field of mathematics,30 and this package is limited to simple ones, mainly monohedral tilings with one prototile (which nevertheless can be composite). With some experience and wiliness we can do more, and easily obtain quite sophisticated results, but obviously hyperbolic tilings like the famous Escher ones or aperiodic tilings like the Penrose ones are not within the capabilities of this package. For more complex needs, we must use low level and more painfull techniques, with the basic \multido and \multirput macros. This package defines two modes are defined, called respectively manual and automatic. For both, the pattern is generated on contiguous positions in a large area which includes the region to fill, which is later cut to the required dimensions by a clipping mechanism. In the first mode, the pattern is explicitely inserted in the PostScript output file each time. In the second, the result is the same but with a single insertion of the pattern and a repetition done by PostScript. Control over the starting point was lost, so it allowed only filling a region and not to tiling it. Using the following utility macro: 1 2 \def\Square{% \pspicture(0.5,0.5)\psframe[dimen=middle](0.5,0.5)\endpspicture} 29 This chapter is an adaptation of the documentation for this package written in 1997 by Denis Girou. 30 For an extensive presentation of tilings, in their history and usage in many fields, see the reference book by Branko Grünbaum and Geoffrey Shephard, Tilings and Patterns [28]. Filling and Tiling 111 the difference between the two modes is shown here; filling: 1 \psboxfill{\Square} 2 3 4 5 6 7 8 9 \begin{pspicture}(2,2) \psframe[fillstyle=boxfill](2,2) \end{pspicture} \hspace{5mm} \begin{pspicture}(2,2) \psframe[fillstyle=boxfill](2,2) \end{pspicture} where, as you can see, the initial position is arbitrary and depends on the current point, and tiling: 1 2 \psboxfill{\Square} \psframe[fillstyle=boxfill](2,2) It is clear that filling is very restrictive compared to tiling, as the desired effect very often requires the possibility of controlling the starting point. To load the extended mode, LATEX users must load the package with the tiling parameter and plain TEX and ConTEXt users must define the following macro after loading the package: \def\PstTiling{true} There is little reason to use the manual mode, apart very special cases where the automatic one cannot work, because it has the very big disadvantage of requiring very large resources, in disk space and subsequently in printing time (a small tiling can sometimes require several megabytes in manual mode!) Only one case is known, when some kinds of EPS files are used, such as the ones produced by partial screen dumps. Note that in all of our next examples, we will always use tiling mode, and also that tilings are drawn from left to right and top to bottom, which can have be important in some circumstances. And PostScript programmers may be interested to know that, even in automatic mode, the iterations of the pattern are managed directly by the PostScript code of the package, which uses only PostScript Level 1 operators. The special ones introduced in Level 2 for drawing patterns are not used. 49 Usage To do a tiling, we just have to define the pattern with the \psboxfill macro and to use the fillstyle boxfill. Filling and Tiling: Usage 112 First, for convenience, we define a simple \Tiling macro, which will simplify our next examples: 1 2 3 4 5 6 7 8 9 \def\Tiling#1#2{% \edef\Temp{#1}% \pspicture#2 \ifx\Temp\empty \psframe[fillstyle=boxfill]#2 \else \psframe[fillstyle=boxfill,#1]#2 \fi \endpspicture} There are several parameters available to change the way the filling/tiling is defined, and one debugging option. Default: 0 fillangle=angle The rotation applied to the patterns. In this case, we must force the tiling area to be noticeably larger than the area to cover, to be sure that the defined area will be covered after rotation. 1 \psboxfill{\Square} 2 3 4 5 \Tiling{fillangle=45}{(2,2)} \hspace{5mm} \Tiling{fillangle=-60}{(2,2)} fillsepx=dim Default: 0pt The value of the horizontal separation between consecutive patterns.31 fillsepy=dim Default: 0pt The value of the vertical separation between consecutive patterns.31 fillsep=dim Default: 0pt The value of the horizontal and vertical separations between consecutive patterns.32 These values can be negative, which allow the tiles to overlap. 31 32 This option is only available in the tiling mode. More precisely, the default value is 0pt in tiling mode and 2pt in filling mode. Filling and Tiling: Usage 113 1 2 3 4 5 \psboxfill{\Square} \Tiling{fillsepx=2mm}{(2,2)}\hfill \Tiling{fillsepy=1mm}{(2,2)}\hfill \Tiling{fillsep=0.5}{(2,2)}\hfill \Tiling{fillsep=-0.25}{(2,2)} Default: 0 fillcyclex=num The shift coefficient applied to each row.31 Default: 0 fillcycley=num The shift coefficient applied to each collumn.31 fillcycle=num Default: 0 The shift coefficient applied both to each row and each collumn. For instance, if fillcyclex is 2, the second row of patterns will be horizontally shifted by a factor of 12 = 0.5, and by a factor of 0.333 if fillcyclex is 3, etc. These values must be integers and can be negative. 1 \psboxfill{\Square} 2 3 4 5 6 \Tiling{}{(2,2)}\hfill \Tiling{fillcyclex=1}{(2,2)}\hfill \Tiling{fillcyclex=2}{(2,2)}\hfill \Tiling{fillcyclex=3}{(2,2)} 7 8 9 10 11 12 \vspace{3mm} \Tiling{fillcyclex=-3}{(2,2)}\hfill \Tiling{fillcycley=2}{(2,2)}\hfill \Tiling{fillcycley=-3}{(2,2)}\hfill \Tiling{fillcycle=2}{(2,2)}\hfill Filling and Tiling: Usage 114 fillmovex=dim Default: 0pt The value of the horizontal move between consecutive patterns.31 fillmovey=dim Default: 0pt The value of the vertical move between consecutive patterns.31 fillmove=dim Default: 0pt The value of the horizontal and vertical move between consecutive patterns.31 These parameters allow the patterns to overlap and to draw some special kinds of tilings. Their values can be negative. In some cases, the effect of these parameters will be the same as that with the fillcycle? ones, but this is not true for all values. 1 2 3 4 5 \psboxfill{\Square} \Tiling{fillmovex=0.25}{(2,2)}\hfill \Tiling{fillmovey=0.25}{(2,2)}\hfill \Tiling{fillmove=0.25}{(2,2)}\hfill \Tiling{fillmove=-0.25}{(2,2)} fillsize=auto/{(x0,y0)(x1,y1)} Default: auto The choice of automatic mode or the size of the area in manual mode. If first pair values are not given, (0,0) is used. The default value is auto in tiling mode, (-15cm,-15cm)(15cm,15cm) otherwise. As explained in the overview, the manual mode can use up a large amount of computer resources, so it’s usage is therefore discouraged in favour of automatic mode, unless special circumstances when some kinds of EPS files are used (see such an example Section 50). fillloopaddx=num Default: 0 The number of times the pattern is added on left and right positions.31 fillloopaddy=num Default: 0 The number of times the pattern is added on top and bottom positions.31 Filling and Tiling: Usage 115 Default: 0 fillloopadd=num The number of times the pattern is added on left, right, top and bottom positions.31 These parameters (exclusively for the tiling mode) are only useful in special circumstances, such as in complex patterns when the size of the rectangular box used to tile the area does not correspond to the pattern itself and also sometimes when the size of the pattern is not a divisor of the size of the area to fill and when the number of loop repeats is not properly computed, which can occur (see such an example Section 50). Default: 0 PstDebug=num To be able to see the exact tiling done, without clipping.31 This parameter must be set to 1 to be activated. This is mainly useful for debugging or to understand better how the tilings are done. 1 2 3 4 5 50 \psboxfill{\Square} \psset{unit=0.5,dimen=middle,linewidth=1mm,PstDebug=1} \Tiling{}{(2,2)}\hspace{1cm} \Tiling{fillcyclex=2}{(2,2)}\hspace{3cm} \Tiling{fillmove=0.5}{(2,2)} Examples The single \psboxfill macro has many variations and different uses. We will try here to demonstrate many of them: 50.1 Kind of tiles Since we can access all the power of PSTricks macros to define the tiles (patterns) used, very complicated ones can be created. Here we give four Archimedian tilings (those built with only some regular polygons) from the eleven known, first discovered completely by Johanes Kepler at the beginning of 17th century, the two regular ones with the tiling by squares, formed by a single regular polygon, and two formed by two different regular polygons. Filling and Tiling: Examples 116 1 2 3 4 5 6 7 8 \def\Triangle{% \pspicture(1,1)\pstriangle[dimen=middle](0.5,0)(1,1)\endpspicture} \def\Hexagon{% \pspicture(0.866,0.75)% sin(60)=0.866 \SpecialCoor \pspolygon[dimen=middle](0.5;30)(0.5;90)(0.5;150) (0.5;210)(0.5;270)(0.5;330)%Hexagon \endpspicture} 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 \psset{unit=0.5} \psboxfill{\Triangle} \Tiling{}{(4,4)}\hfill % The two other regular tilings \Tiling{fillcyclex=2}{(4,4)}\hfill \psboxfill{\Hexagon} \Tiling{fillcyclex=2,fillloopaddy=1}{(5,5)} \def\ArchimedianA{% Archimedian tiling 3^2.4.3.4 \psset{dimen=middle}% \pspicture(1.866,1.866)% sin(60)=0.866 \psframe(1,1) \psline(1,0)(1.866,0.5)(1,1) (0.5,1.866)(0,1)(-0.866,0.5) \psline(0,0)(0.5,-0.866) \endpspicture} 9 10 11 12 13 14 15 16 17 \def\ArchimedianB{% Archimedian tiling 4.8^2 \psset{dimen=middle,unit=1.5}% \pspicture(1.3066,0.6533)% cos(22.5) + sin(22.5) = 1.3066 % cos(22.5) - sin(22.5) = 0.6533 \SpecialCoor \pspolygon(0.5;22.5)(0.5;67.5)(0.5;112.5)(0.5;157.5)(0.5;202.5) (0.5;247.5)(0.5;292.5)(0.5;337.5)% Octogon \endpspicture} 18 19 20 21 22 23 \psset{unit=0.5} \psboxfill{\ArchimedianA} \Tiling{fillmove=0.5}{(7,7)}\hfill \psboxfill{\ArchimedianB} \Tiling{fillcyclex=2,fillloopaddy=1}{(7,7)} Filling and Tiling: Examples 117 We can of course tile an arbitrarily defined area; with the addfillstyle parameter, we can easily mix the boxfill style with another one. 1 2 3 4 5 6 \psset{unit=0.5,dimen=middle} \psboxfill{% \pspicture(1,1) \psframe(1,1) \pscircle(0.5,0.5){0.25} \endpspicture} 7 8 9 10 11 12 13 14 15 \begin{pspicture}(4,6) \pspolygon[fillstyle=boxfill,fillsep=0.25](0,1)(1,4)(4,6)(4,0)(2,1) \end{pspicture} \hspace{2cm} \begin{pspicture}(4,4) \pscircle[linestyle=none,fillstyle=solid,fillcolor=yellow,fillsep=0.5, addfillstyle=boxfill](2,2){2} \end{pspicture} Various effects can be obtained; sometimes complicated ones are surprisingly easy, as in this example reproduced from one by Slavik Jablan in the field of OpTiles, inspired by Op-art: 1 2 3 4 5 6 7 8 \def\ProtoTile{% \pspicture(1,1) \psset{linestyle=none,linewidth=0,hatchwidth=0.08333\psunit, hatchsep=0.08333\psunit}% 1/12=0.08333 \psframe[fillstyle=solid,fillcolor=black,addfillstyle=hlines, hatchcolor=white](1,1) \pswedge[fillstyle=solid,fillcolor=white,addfillstyle=hlines]{1}{0}{90} \endpspicture} 9 10 \def\BasicTile{% Filling and Tiling: Examples 118 11 12 13 14 \pspicture(2,1) \rput[lb](0,0){\ProtoTile} \rput[lb](1,0){\rotateleft{\ProtoTile}} \endpspicture} 15 16 17 18 \ProtoTile\hfill\BasicTile\hfill \psboxfill{\BasicTile} \Tiling{fillcyclex=2}{(4,4)} It is also possible to superimpose several different tilings. Here is the splendid visual proof of the Pythagore theorem done by the Arab mathematician Annairizi around the year 900, given by superposition of two tilings by squares of different sizes. 1 2 3 4 5 6 7 8 9 10 11 12 \psset{unit=1.5,dimen=middle} \pspicture*(2,2) \psboxfill{\pspicture(1,1) \psframe(1,1) \endpspicture} \psframe[fillstyle=boxfill](2,2) \psboxfill{\pspicture(1,1) \rput{-37}{\psframe[linecolor=red](0.8,0.8)} \endpspicture} \psframe[fillstyle=boxfill](3,4) \pspolygon[fillstyle=hlines,hatchangle=90](1,2)(1.64,1.53)(2,2) \endpspicture In a same way, it is possible to build tilings based on figurative patterns, in the style of the famous Escher ones. Following an example of André Deledicq, the next example shows a simple tiling of the p1 category (according to the international classification of the 17 symmetry groups of the plane, first discovered by the Russian crystalographer Jevgraf Fedorov at the end of the 19th century). Filling and Tiling: Examples 119 1 2 3 4 5 6 7 8 9 10 11 12 \def\SheepHead#1{% \pspicture(3,1.5) \pscustom[liftpen=2,fillstyle=solid,fillcolor=#1]{% \pscurve(0.5,-0.2)(0.6,0.5)(0.2,1.3)(0,1.5)(0,1.5)(0.4,1.3)(0.8,1.5) (2.2,1.9)(3,1.5)(3,1.5)(3.2,1.3)(3.6,0.5)(3.4,-0.3)(3,0) (2.2,0.4)(0.5,-0.2)} \pscircle*(2.65,1.25){0.12\psunit} % Eye \psccurve*(3.5,0.3)(3.35,0.45)(3.5,0.6)(3.6,0.4)% Muzzle \pscurve(3,0.35)(3.3,0.1)(3.6,0.05) % Mouth \pscurve(2.3,1.3)(2.1,1.5)(2.15,1.7) \pscurve(2.1,1.7)(2.35,1.6)(2.45,1.4) % Ear \endpspicture} 13 14 15 \psboxfill{\psset{unit=0.4}\SheepHead{yellow}\SheepHead{cyan}} \Tiling{fillcyclex=2,fillloopadd=1}{(10,5)} The next example shows a tiling of the pg category (the code for the kangaroo itself is too long to be shown here, but has no difficulties).33 ; the kangaroo is reproduced from an original picture by Raoul Raba and here is a translation into PSTricks from the one drawn by Emmanuel Chailloux and Guy Cousineau for their MLgraph system [6] 1 2 3 4 5 6 7 8 9 \psboxfill{% \psset{unit=0.4}% \Kangaroo{yellow}\Kangaroo{red}% \Kangaroo{cyan}\Kangaroo{green}% \scalebox{-1 1}{% \rput(1.235,4.8){% \Kangaroo{green}\Kangaroo{cyan}% \Kangaroo{red}\Kangaroo{yellow}}}} \Tiling{fillloopadd=1}{(10,6)} 33 You will find it in the source code of this documentation. Filling and Tiling: Examples 120 And now a Wang tiling [84], based on very simple tiles in the form of a square and composed of four colored triangles. Such tilings are simply built with a matching color constraint. Despite its simplicity, it is an important kind of tiling, as Wang and others used them to study the special class of aperiodic tilings, and also because it was shown that (surprisingly) this tiling is similar to a Turing machine. 1 2 3 4 5 6 7 \def\WangTile#1#2#3#4{% \pspicture(1,1) \pspolygon*[linecolor=#1](0,0)(0,1)(0.5,0.5) \pspolygon*[linecolor=#2](0,1)(1,1)(0.5,0.5) \pspolygon*[linecolor=#3](1,1)(1,0)(0.5,0.5) \pspolygon*[linecolor=#4](1,0)(0,0)(0.5,0.5) \endpspicture} 8 9 10 11 \def\WangTileA{\WangTile{cyan}{yellow}{cyan}{cyan}} \def\WangTileB{\WangTile{yellow}{cyan}{cyan}{red}} \def\WangTileC{\WangTile{cyan}{red}{yellow}{yellow}} 12 13 14 15 16 17 18 19 20 \def\WangTiles#1{% \pspicture(3,3) \psset{ref=lb}% \rput(0,2){\WangTileB}\rput(1,2){\WangTileA}\rput(2,2){\WangTileC} \rput(0,1){\WangTileC}\rput(1,1){\WangTileB}\rput(2,1){\WangTileA} \rput(0,0){\WangTileA}\rput(1,0){\WangTileC}\rput(2,0){\WangTileB} #1 \endpspicture} 21 22 23 \WangTileA\hfill\WangTileB\hfill\WangTileC\hfill \WangTiles{\psgrid[subgriddiv=0,gridlabels=0](3,3)} 24 25 26 27 28 \vspace{2mm} \psset{unit=0.4} \psboxfill{\WangTiles{}} \Tiling{}{(12,12)} Filling and Tiling: Examples 121 50.2 External graphic files We can fill an arbitrary area with an external PostScript image. We have only, as usual, to worry about the BoundingBox definition if there is not one provided or if it is inaccurate, as in the case of the well known tiger picture (part of the Ghostscript distribution). 1 2 3 4 \psboxfill{% \raisebox{-1cm}{% \includegraphics[bb=17 176 562 740,width=3cm]{tiger}}} \Tiling{}{(6,6.2)} Be warned there are some types of PostScript file for which the automatic mode does not work, specifically those produced by a screen dump. This is demonstrated in the next example, where a picture was reduced before Filling and Tiling: Examples 122 H e N a y Ne w Y ea ar! Ha ppy N e N w e r! H pp N ew e a a N w Ye r! H pp y N ew ew Y ar H ap y e w Ye ear! ! H app py N New w Y Y Y ar H ap y e e Ye ear ! H app py Ne w Y Yea ar! ! H a p y N w e r! a ea r! H ap py N ew Ye ar H r! a p N ew Y ar ! H ap H p y e e ! a p H app py N New w Y Yea ar! H Hap pp a H pp y N ew Y ea r! H ap py ap y e r py N w Ye ear! ! H app py ew Y ar H ap y Ne N y e Y ea ! a py N N w r H p e N ew Ye ear! ! H app py N New w ew Y ar H ap y e Y ear ! H ap py Ne w Ye Ye ear ! H app py Ne w Y Yea ar! ! a N w e ar! Ha pp y N ew Y ea r! ea ar! H Hap ppy y N ew Ye ear r! H r! a p N ew Y ar ! H ap H p y e e ! a p H app py N New w Y Yea ar! H Hap pp H app y N ew Y ea r! H ap py ap y e r py N w Ye ear! ! H app py N ew Ye ar! H app y N Ne N ew Y ar H ap y e N ew Ye ear! ! H app py N New w ew Y ar H ap y e Y ear ! H ap py Ne w Ye Ye ear ! H app py Ne w Y Yea ar! ! a N w ea ar! H Hap ppy y N ew Ye ear r! r! a p N ew Y ar ! H H p y e e ! a H ap py Ne w Ye ar! Ha pp H app py N New w Y Yea ar! H Hap pp ap y e r py N w Ye ear! ! H app py N e a y Ne w Y Yea ar! Ha ppy y N e N w e r! H pp N ew ew Y ar H ap y e Ye ear ! H app py Ne w Y ar ! H ap y Ne w ! H ap py N w Ye e ar ap p ! p conversion to the Encapsulated PostScript format by a screen dump utility. In this case, use of the manual mode is the only alternative, at the price of real multiple inclusion of the EPS file. We must take care to specify the correct fillsize parameter, because otherwise the default values are large and will load the file too many times, perhaps just actually using a few occurrences as the other ones are clipped away… 1 2 3 4 1 2 3 4 5 6 7 8 9 1 2 3 \psboxfill{\includegraphics{flowers}} \pspicture(8,4) \psellipse[fillstyle=boxfill,fillsize={(8,4)}](4,2)(4,2) \endpspicture 50.3 Tiling of characters We can also use the \psboxfill macro to fill the interior of characters for special effects like the following: \DeclareFixedFont{\Sf}{T1}{phv}{b}{n}{5cm} \DeclareFixedFont{\Rm}{T1}{ptm}{m}{n}{3mm} \psboxfill{\Rm Happy New Year!} \pspicture*(10.8,3.8) \rput(5.4,0.1){% \pscharpath[fillstyle=gradient,gradangle=-45,gradmidpoint=0.5, addfillstyle=boxfill,fillangle=45,fillsep=0.7mm] {\rput[b](0,0){\Sf 2003}}} \endpspicture \DeclareFixedFont{\Rmm}{T1}{ptm}{m}{n}{3cm} \psboxfill{% \psset{unit=0.2,linewidth=0.2pt}% Filling and Tiling: Examples 123 4 5 6 7 8 9 10 11 12 13 14 \Kangaroo{PeachPuff}\Kangaroo{PaleGreen}% \Kangaroo{LightBlue}\Kangaroo{LemonChiffon}% \scalebox{-1 1}{% \rput(1.235,4.8){% \Kangaroo{LemonChiffon}\Kangaroo{LightBlue}% \Kangaroo{PaleGreen}\Kangaroo{PeachPuff}}}} % A kangaroo of kangaroos... \begin{pspicture}(11.6,2.7) \pscharpath[linestyle=none,fillloopadd=1,fillstyle=boxfill] {\rput[b](5.8,0){\Rmm Kangaroo}} \end{pspicture} 50.4 “Dynamic” tiling In some cases, tilings use non-static tiles, that is to say the prototile(s), even if unique, can have several forms, for instance specified by different colors or rotations, not fixed before generation, or varying each time. We present here as an example the so-called Truchet tiling, which is in fact better called Lewthwaite-Pickover-Truchet (LPT) tiling.34 The single prototile is just a square with two opposing circle arcs. This tile obviously has two positions, if we rotate it through 90 degrees (see the two tiles on the next figure). A LPT tiling is a tiling with randomly oriented LPT tiles. We can see that even if it is very simple in it principle, it draws sophisticated curves with strange properties. Unfortunately, the ‘pst-fill’ package does not work in a straightforward manner, because the \psboxfill macro stores the content of the tile in a TEX box, which is static. So the call of the random function is done only once, which explains why only one rotation of the tile is used for all the tiling. Only one of the two rotations can differ from one drawing to the next… 1 2 3 4 5 6 7 \def\ProtoTileLPT{{% LPT prototile \psset{dimen=middle}% \pspicture(1,1) \psframe(1,1) \psarc(0,0){0.5}{0}{90} \psarc(1,1){0.5}{-180}{-90} \endpspicture}} 34 For description of the context, history and references about Sébastien Truchet and this tiling, see the article by Philippe Esperet and Denis Girou in Les Cahiers GUTenberg [13]. Filling and Tiling: Examples 124 8 9 \newcount\Boolean 10 11 12 13 14 15 16 17 \def\BasicTileLPT{% LPT tile \setrannum{\Boolean}{0}{1}% From random.tex (Donald Arseneau) \ifnum\Boolean=0 \ProtoTileLPT% \else \rotateleft{\ProtoTileLPT}% \fi} 18 19 20 21 22 23 \ProtoTileLPT\hfill \rotateleft{\ProtoTileLPT}\hfill \psset{unit=0.5}% \psboxfill{\BasicTileLPT} \Tiling{}{(5,5)} For simple cases, there is a solution to this problem using a mixture of PSTricks and PostScript programming. Here the PSTricks construction \pscustom{\code{...}} allows us to insert PostScript code inside the LATEX+ PSTricks one. The programming is less straightforward than to solve this problem using the basic PSTricks \multido macro, but it has also the advantages of being noticeably faster, since all tilings operations are done in PostScript, and we are not limited by TEX memory. Note also that \pslbrace and \psrbrace are PSTricks macros which insert the { and } characters. 1 2 3 4 5 \def\ProtoTileLPT{{% \psset{dimen=middle}% \psframe(1,1) \psarc(0,0){0.5}{0}{90} \psarc(1,1){0.5}{-180}{-90}}} 6 7 \newcount\InitCounter% Counter to change the random seed 8 9 10 11 12 13 14 15 16 \def\BasicTileLPT{% LPT tile \InitCounter=\the\time \pscustom{\code{rand \the\InitCounter\space sub 2 mod 0 eq \pslbrace}} \pspicture(1,1)\ProtoTileLPT\endpspicture% \pscustom{\code{\psrbrace \pslbrace}} \rotateleft{\ProtoTileLPT}% \pscustom{\code{\psrbrace ifelse}}} 17 Filling and Tiling: Examples 125 18 19 20 \psset{unit=0.4,linewidth=0.4pt} \psboxfill{\BasicTileLPT} \Tiling{}{(15,15)} Using the very surprising fact that the coloring of these tiles does not depend on their neighbors (even if it is difficult to believe as the opposite seems obvious!) but only on the parity of the value of row and column positions, we can directly program in the same way a colored version of the LPT tiling. The ‘pst-fill’ package has in tiling mode two accessible PostScript variables, row and column,33 which can be useful in some circumstances, like this one. 1 2 3 4 5 6 \def\ProtoTileLPT#1#2{% LPT prototile \psset{dimen=middle,linestyle=none,fillstyle=solid}% \psframe[fillcolor=#1](1,1) \psset{fillcolor=#2}% \pswedge(0,0){0.5}{0}{90} \pswedge(1,1){0.5}{-180}{-90}} 7 8 \newcount\InitCounter% Counter to change the random seed 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \def\BasicTileLPT#1#2{% LPT tile \InitCounter=\the\time \pscustom{\code{rand \the\InitCounter\space sub 2 mod 0 eq \pslbrace row column add 2 mod 0 eq \pslbrace}} \pspicture(1,1)\ProtoTileLPT{#1}{#2}\endpspicture% \pscustom{\code{\psrbrace \pslbrace}} \ProtoTileLPT{#2}{#1}% \pscustom{\code{\psrbrace ifelse \psrbrace \pslbrace row column add 2 mod 0 eq \pslbrace}} \rotateleft{\ProtoTileLPT{#2}{#1}}% \pscustom{\code{\psrbrace \pslbrace}} \rotateleft{\ProtoTileLPT{#1}{#2}}% \pscustom{\code{\psrbrace ifelse \psrbrace ifelse}}} 23 Filling and Tiling: Examples 126 24 25 26 27 28 29 \psboxfill{\BasicTileLPT{red}{yellow}} \Tiling{}{(4,4)} \hfill \psset{unit=0.4} \psboxfill{\BasicTileLPT{blue}{cyan}} \Tiling{}{(15,15)} Another classic example is generation of coordinates and labelling for a grid. Of course, it is possible to do it directly in PSTricks using nested \multido commands, and it would clearly be easy to program. Nevertheless, for users who have a little knowledge of PostScript programming, this method offers an alternative which is useful for large cases, because it will be noticeably faster and use less computer resources. Remember here that the tiling is drawn from left to right, and top to bottom, and note that the PostScript variable x2 contains the total number of columns. 1 2 % \Escape will be the \ character {\catcode‘\!=0\catcode‘\\=11!gdef!Escape{\}} 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 \def\ProtoTile{% \pspicture(1,1)\psframe[dimen=middle](1,1)\endpspicture% \pscustom{% \moveto(-0.9,0.75)% In PSTricks units \code{/Times-Italic findfont 8 scalefont setfont (\Escape() show row 3 string cvs show (,) show column 3 string cvs show (\Escape)) show} \moveto(-0.5,0.25)% In PSTricks units \code{/Times-Bold findfont 18 scalefont setfont 1 0 0 setrgbcolor% red color /center {dup stringwidth pop 2 div neg 0 rmoveto} def row 1 sub x2 mul column add 3 string cvs center show}}} \psboxfill{\ProtoTile} \Tiling{}{(6,4)} Filling and Tiling: Examples 127 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 1 2 3 4 5 6 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 7 8 (3,1) (3,2) 9 10 11 12 (3,3) (3,4) (3,5) (3,6) 13 14 15 16 17 18 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 19 20 21 22 23 24 Filling and Tiling: Examples 128 X 51 Three Dimensional Graphics Overview The file pst-3d.tex/pst-3d.sty contains a macro to add a shadow to some text, two macros to angle objects into the third dimension and a general macro to put objects into three dimensional space. This last command is powerful but supports only parallel (isometric) perspective, and not other kinds of perspective like linear point perspective or spherical perspective,37 nor hidden-line removal or lighting of objects. pst-3d 52 36 Usage \psshadow[par]{stuff } is a macro to draw a text with a shadow. Shadow 1 \psshadow{\Huge Shadow} The Tshadowangle parameter specifies the angle of the shadow in degrees (do not use a value of 0 or 180). Tshadowangle=num 1 Catherine March 25 Default: 60 \psshadow[Tshadowangle=120]{Catherine} 2 3 \psshadow[Tshadowangle=-45]{March 25} The Tshadowsize parameter specifies the size of the shadow. Tshadowsize=dim No! 1 No! Lewis Lewis Carroll Carroll Default: 1 \psshadow[Tshadowsize=4]{No!} 2 3 \psshadow[Tshadowangle=-45,Tshadowsize=0.5]{Lewis Carroll} 36 This chapter is merely an adaptation of the documentation for this package written in 1998 by Manuel Luque. 37 For management of these kinds of perspective representations, you can refer to the developments of Manuel Luque. Three Dimensional Graphics 129 The Tshadowcolor parameter specifies the color of the shadow. Tshadowcolor=color Good morning! Good morning! 1 Default: lightgray \psshadow[Tshadowsize=2,Tshadowcolor=red]{Good morning!} Note that the result will be incorrect if you change the color of the text itself from black (then the shadow will be the same color as the text). \pstilt[par]{angle}{stuff } is a macro which angles an object into the third dimension (do not use an angle of 0 or 180). The world is slanted 1 \pstilt{45}{The world is slanted} 1 \pstilt{60}{% \begin{tabular}{|l|c|c|} \hline January & 250 & 90 \\\hline February & 320 & 20 \\\hline March & 200 & -40 \\\hline \end{tabular}} 2 January 250 90 February 320 20 March 200 -40 3 4 5 6 7 \psTilt[par]{angle}{stuff } is a macro which angles an object into the third dimension (do not use an angle of 0 or 180). The world is slanted 0 0 1 \psTilt{45}{The world is slanted} 1 \psTilt{-60}{% \begin{pspicture}(2,2) \psaxes{<->}(2,2) \end{pspicture}} 1 1 2 3 4 The difference between \pstilt and \psTilt is that \pstilt keeps the length of the objects constant while \psTilt keeps the height of the objects constant as shown in the following example: 1 \def\Bar{\psframe*(-0.25,0)(0.25,2)} 2 3 4 5 6 % Additional information is superimposed on the drawing \rput(1,0){\Bar} \rput(3,0){\psTilt{30}{\Bar}} \rput(7,0){\pstilt{30}{\Bar}} Three Dimensional Graphics: Usage 130 2cm 4cm 2cm 30o \psTilt{30}{\Bar} 30o \pstilt{30}{\Bar} These two effects can now easily be understood: 1 2 \psframebox[framesep=0]{\Huge\sffamily\bfseries% A\psTilt{20}{A}\pstilt{20}{A}} A A A \ThreeDput[par](x0 , y0 , z0 ){stuff } is a generic macro which puts objects into three dimensional space. Everything belonging to a plane can be shown in three dimensional space. If this is not the case, as for a cylinder, a sphere, etc., then it is necessary to decompose the surface into smaller planes of juxtaposed tiles (more planes will produce a more realistic result). z55 z 4 4 3 3 1 y 5 ve bo 3 4 5 % The three colored grids are previously drawn \ThreeDput{\psframe*[linecolor=green](2,2)} \ThreeDput(1,1,0){\LARGE Below} \ThreeDput(0,0,2){\psframe*[linecolor=cyan](2,2)} \ThreeDput(1,1,2){\LARGE Above} 2 1 1 B ow el 0 0 0 0 3 4 3 2 1 1 y5 4 A 2 2 2 00 1 1 2 2 3 3 4 4 x5 x5 The viewpoint parameter specifies the direction of the observer as shown in the following diagram: viewpoint=vx vy vz Default: 1 -1 1 (vx vy vz ) are the coordinates of a vector pointing from the origin O to the observers eye. In fact, it defines the direction of the projection Three Dimensional Graphics: Usage 131 z 1.5 Firs choo s ge ’ packa ‘pst-3d 0 x 1 e t he t: view p oint! 0.5 y Figure 2: How to choose the viewpoint for the \ThreeDput macro. PS on the horizontal plane. As the vector norm has no importance, it is not necessary to take a unit vector. We must simply choose the coordinates according to the view point that we must have on the object. In figure 2, this vector has (1 0.5 1.5) for coordinates.38 Warning: Take care to not use one of the coordinates equal to 0, as this will generate a PostScript error. Nevertheless, we can use a very small value, like 0.001 for instance. Other divisions by 0 can occur in very special circumstances, but in this case it is enough to slightly modify the values used. The cube shown next has its faces drawn in the following order: Face A (yellow), Face B (blue), Face C (green) then face marked ABOVE (gray). The various objects are drawn one after the other and there is no management of hidden-line removal. You can see that the order used is very important and must sometimes be changed according to the viewpoint chosen (see the fourth of the following examples). 38 But the figure itself is not drawn with this value, because we would only see a single point, at the end of the arrow! Three Dimensional Graphics: Usage 132 z44 z 3 3 1 y 3 2 1 0 0 0 0 2 Be y4 c3aF 2 eA Fac 1 1 4 E V O B A 2 2 3 4 \psset{viewpoint=1 -1 1}% Default value \ShowPartialCube % Note that Face A on the left side is partially covered % and that Face B is totally covered eC Fac 1 00 1 1 2 2 3 3 x4 x4 z4 4z 3 3 2 2 E OV AB 1 1 0 2 \psset{viewpoint=1 1.5 1} \ShowPartialCube 0Fa0ce B 1 1 1 2 2 3 3 x4 3 4 y 2 4x 1 2 3 1 Fac eA 0 Fac eC 0 0 y4 z4 4z 3 3 2 2 1 1 0 0 0 A 1 1 1 B C e c a F 2 3 1 y4 2 Fa ce 3 1 2 AB 0 OVE Fa ce 0 0 y4 2 \psset{viewpoint=1 0.5 2} \ShowPartialCube 2 3 3 x4 x 4 Three Dimensional Graphics: Usage 133 44z 1 E x4 OV3 B A z 33 4x 3 aF 1 caF Ae 4 11 6 \psset{viewpoint=-1 0.5 1} \ShowPartialCube % Note that as the order of drawing is faces A, B and C. % C partially covers the previously drawn B. % This illustrates the importance of the order in which the % different objects of a three dimensional scene are drawn. 0 0 00 0 1 0 B 3 5 2 1 Fa ce 22 2 c Ce 2 2 1 3 2 3 y4 4y The viewangle parameter specifies the clockwise rotation applied from the view point. viewangle=angle Default: 0 4z z4 3 3 2 2 1 EB OV AB 2 y4 00 2 y4 2 1 00 1 1 1 Face A 3 ecaF 0 0 3 \psset{viewangle=30} \ShowPartialCube 11 Face C 22 33 z4 4 x4x 3 4z 2 3 2 1 0 ace B 0F 2 3 y4 1 2 0 0 1 0 0 3 AB OV E Face A 1 y4 1 2 \psset{viewpoint=1 1.5 1,viewangle=-45} \ShowPartialCube 1 1 Face C 2 2 3 3 4x x4 Three Dimensional Graphics: Usage 134 The normal parameter specifies the normal vector. normal=nx ny nz Default: 0 0 1 z44 z 3 3 1 y 4 3 2 1 1 2 1 De c1aF y4 3 E V O B A 2 2 0 0 0 0 \def\Face#1#2{\psframe*[linecolor=#1](2,2)\rput(1,1){#2}} 2 3 4 5 eC Fac 6 % The three colored grids are previously drawn \ThreeDput[normal=0 1 0](2,0,0){\Face{Pink}{Face D}} \ThreeDput[normal=1 0 0](2,0,0){\Face{PaleGreen}{Face C}} \ThreeDput[normal=0 0 1](0,0,2){\Face{lightgray}{ABOVE}} 00 1 1 2 2 3 3 x4 x4 We will demonstrate how the normal is to be computed on the example of a rectangle parallelopiped, where we will define only the visible faces from the (default) view point chosen (see the next drawing). nx = 1 The normal to the face ABCD has the coordinates: ny = 0 nz = 0 These are the coordinates of a vector which must be perpendicular to the plane that we want to draw. These coordinates are given in the reference landmark Oxyz. It is not necessary that this be a unit vector. nx = 0 The normal to the face ADHE has the coordinates: ny = 0 nz = 1 nx = 0 The normal to the face AEFB has the coordinates: ny = −1 nz = 0 etc. 1 2 3 4 % % % % The three visible faces of the rectangle parallelopiped (note that each time we will call the grid macro twice once for the grid itself and secondly for the labels, because we do not want to label the extreme values) 5 6 7 8 9 10 11 \def\FaceABCD{% \psgrid[gridlabels=0](0,0)(-4,-2)(4,2) \psgrid[gridwidth=0](0,0)(-3,-1)(3,1) \uput[-45](-4,2){A} \uput[45](-4,-2){B} \uput[135](4,-2){C} Three Dimensional Graphics: Usage 135 12 \uput[225](4,2){D}} 13 14 15 16 17 18 19 20 \def\FaceADHE{% \psgrid[gridlabels=0](0,0)(-2,-4)(2,4) \psgrid[gridwidth=0](0,0)(-1,-3)(1,3) \uput[135](2,-4){A} \uput[225](2,4){D} \uput[-45](-2,4){H} \uput[45](-2,-4){E}} 21 22 23 24 25 26 27 28 \def\FaceABFE{% \psgrid[gridlabels=0](0,0)(-2,-2)(2,2) \psgrid[gridwidth=0](0,0)(-1,-1)(1,1) \uput[225](2,2){A} \uput[135](2,-2){B} \uput[45](-2,-2){F} \uput[-45](-2,2){E}} 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 \pspicture(-4.2,-4.1)(5.3,4.3) \psset{dimen=middle,subgriddiv=0,arrows=->,arrowscale=2}% % % Face ABCD \ThreeDput[normal=1 0 0](2,0,0){\FaceABCD} % % Normal for the plane ABCD. % In its center, we draw the plane where it is placed. % This is the plane parallel to Oxy placed in (2,0,0) % for which the normal is parallel to Oz. \ThreeDput[normal=0 0 1](2,0,0){% \psline[linecolor=red,linewidth=0.1](1,0) \psline(3,0)\uput[0](3,0){x$}} % % Face ADHE \ThreeDput[normal=0 0 1](0,0,2){\FaceADHE} % % Normal for the plane ADHE. % In its center, we draw the plane where it is placed. % This is the plane parallel to Oyz placed in (0,0,2) % for which the normal is parallel to Ox. \ThreeDput[normal=1 0 0](0,0,2){% \psline[linecolor=red,linewidth=0.1](0,1) \psline(0,3)\uput[0](0,3){$z$}} % % Face ABFE \ThreeDput[normal=0 -1 0](0,-4,0){\FaceABFE} % % Normal for the plane ABFE. % In its center, we draw the plane where it is placed. % This is the plane parallel to Oxy placed in (0,-4,0) % for which the normal is parallel to Oy. \ThreeDput[normal=0 0 -1](0,-4,0){% \psline[linecolor=red,linewidth=0.1](0,1)} % Three Dimensional Graphics: Usage 136 65 66 67 68 % Oy axis \ThreeDput[normal=0 0 1](0,4,0){% \psline(0,3)\uput[0](0,3){$y$}} \endpspicture z H 3 y 2 D 1 D -1 0 0 -1 1 -2 E -3 E 3 1 A 1 0 A A -1 -1 0 -2 0 -1 -3 1 1 C 0 -1 x F 2 B B Let us suppose that we wish to draw a chamfered edge according to the edge AD. The normal for the chamfer has the coordinates: nx = 1 x0 = 1.5 n = 0 and the origin of this plane has the coordinates: y0 = 0 y nz = 1 z0 = 1.5 √ The dimensions of this chamfered edge are L = 8, l = 2 = 1.414. We will draw the chamfer with its normal. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 \pspicture(-3.6,-3.4)(4.8,4.9) \psset{dimen=middle,subgriddiv=0,arrows=->,arrowscale=2, viewpoint=1 -2 0.75}% % % Oy axis \ThreeDput[normal=0 0 1](0,4,0){% \psline(0,5)\uput[0](0,5){$y$}} % \ThreeDput[normal=1 0 0](2,0,0){% \psgrid[gridlabels=0](0,0)(-4,-2)(4,1) \psgrid[gridwidth=0](0,0)(-3,-1)(3,0)} % \ThreeDput[normal=0 0 1](2,0,0){% \psline[linecolor=red,linewidth=0.1](1,0) \psline(3,0)\uput[0](3,0){$x$}} % \ThreeDput[normal=0 0 1](0,0,2){% \psgrid[gridlabels=0](0,0)(-2,-4)(1,4) \psgrid[gridwidth=0](0,0)(-1,-3)(1,3)} Three Dimensional Graphics: Usage 137 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 % \ThreeDput[normal=1 0 0](0,0,2){% \psline[linecolor=red,linewidth=0.1](0,1) \psline(0,3)\uput[0](0,3){$z}} % \ThreeDput[normal=0 -1 0](0,-4,0){% \psclip{\pspolygon(-2,-2)(-2,2)(1,2)(2,1)(2,-2)} \psgrid[gridlabels=0](0,0)(-2,-2)(2,2) \psgrid[gridwidth=0](0,0)(-1,-1)(1,1) \endpsclip} % \ThreeDput[normal=0 0 -1](0,-4,0){% \psline[linecolor=red,linewidth=0.1](0,1)} % % The chamfered edge \ThreeDput[normal=1 0 1](1.5,0,1.5){% \psclip{\psframe[fillstyle=solid](-4,-0.707)(4,0.707)} \psgrid(0,0)(-4,-0.707)(4,0.707) \endpsclip} % % The normal vector to this chamfer \ThreeDput[normal=0 1 0](1.5,0,1.5){% \psline[linecolor=blue,linewidth=0.1](-0.707,0.707)} \endpspicture z 3 y 2 1 -1 -1 0 0 1 0 0 -1 -3 1 -4 -2 -3 -1 0 1 1 -1 0 0 -3 -2 3 2 1 -2 -1 0 1 4 2 3 x -1 -1 The embedangle parameter rotates the object about the normal in a counter clockwise (if embedangle > 0) direction. embedangle=angle Default: 0 Three Dimensional Graphics: Usage 138 1 2 3 4 5 6 7 1 er pt ha y r C M ge un yo 8 \def\BookChapter#1#2#3#4{% \psframe[style=#4](2,2) \rput(1,1){% \begin{minipage}{1.5cm} \centering \textcolor{#3}{Chapter #1}\\ #2 \end{minipage}}} 9 10 11 \newpsstyle{SolidCyan}{fillstyle=solid,fillcolor=cyan} \newpsstyle{SolidYellow}{fillstyle=solid,fillcolor=yellow} 12 Chap te My a r 2 dult life 13 14 \ThreeDput(-2,-2,0){% \BookChapter{1}{My younger}{black}{SolidCyan}} 15 16 17 1 2 3 4 \ThreeDput[embedangle=30](-2,-2,-3){% \BookChapter{2}{My adult life}{black}{SolidYellow}} \newpsstyle{TransparencyRed}{fillstyle=vlines,hatchcolor=red, hatchwidth=0.1\pslinewidth,hatchsep=1\pslinewidth} \newpsstyle{TransparencyBlue}{fillstyle=vlines,hatchcolor=blue, hatchwidth=0.1\pslinewidth,hatchsep=1\pslinewidth} 5 6 7 % Underlaying grid \ThreeDput{\psgrid[subgriddiv=0](-1,0)(4,3)} 8 9 10 11 12 3 13 2 15 1 14 Chap ter 1 My young er Chap te My a r 2 dult life 17 un yo 0 1 er pt ha y r C M ge 0 -1 16 1 2 2 er t pt ul ha d C ya e M lif 18 19 20 3 21 4 22 23 24 % embedangle=0 \ThreeDput{% \BookChapter{1}{My younger}{black}{SolidYellow}} \ThreeDput(2,0,0){% \BookChapter{2}{My adult life}{black}{SolidYellow}} \bgroup \psset{embedangle=30}% % embedangle=30 \ThreeDput{% \BookChapter{1}{\textcolor{gray}{My younger}} {gray}{TransparencyRed}} \ThreeDput(2,0,0){% \BookChapter{2}{\textcolor{gray}{My adult life}} {gray}{TransparencyBlue}} \egroup 25 26 27 28 29 30 % Normals \ThreeDput[normal=0 1 0]{% \psline[linewidth=0.1,linecolor=red](0,4)} \ThreeDput[normal=0 1 0](2,0,0){% \psline[linewidth=0.1,linecolor=blue](0,4)} It is not really possible to use this option on complex scenes, with composite objects, because the behavior is not equivalent to applying a global change. This is especially important when a scene includes Three Dimensional Graphics: Usage 139 objects with different normals, because if each object turns around its normal by the same angle, this is not equivalent to turning the whole composite object, as illustrated in the next example. 1 2 \psset{unit=0.3,dimen=middle,framesep=0.15,viewpoint=1 1 1} \SpecialCoor 3 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ce! ce! hoi rc ou ou 0 2 1 8 7 9 8 4 6 4 3 2 9 7 5 3 2 2 0 5 4 3 1 1 0 5 6 3 7 5 4 3 4 3 53 6 hoi rc ou y ke Ma 4 6 6 5 7 5 9 8 9 8 7 y ke Ma 0 1 y ke Ma ce! hoi rc 0 12 7 6 9 8 11 8 9 10 2 8 1 7 9 1 6 \multido{\iEmbedAngle=0+36}{3}{% \pspicture(-5.2,-3)(5.2,8.3) \ThreeDput{% \pscircle*[linecolor=PaleGreen]{4.5} \multido{\iNum=0+1,\iAngle=0+36,\iRot=-90+36}{10}{% \rput{\iRot}(2.7;\iAngle){% \pscirclebox[fillstyle=solid,fillcolor=lightgray]{% \small\iNum}}}} \ThreeDput[embedangle=\iEmbedAngle]{% \pscircle[linewidth=1.4,linecolor=yellow]{4.5} \multido{\iNum=0+1,\iAngle=0+36,\iRot=-90+36, \nHue=0.0+0.1}{10}{% \definecolor{ColorNumber}{hsb}{\nHue,1,1}% \rput{\iRot}(4.5;\iAngle){% \pscirclebox[fillstyle=solid,fillcolor=ColorNumber]{% \small\iNum}}}} \ThreeDput[normal=0 1 0]{% \psline[linewidth=0.1](0,7) \rput(0,7){% \psframebox[fillstyle=solid,fillcolor=green,framearc=.5]{% \textcolor{red}{Make your choice!}}}} \endpspicture \hfill} 2 5 0 4 More details The macro \ThreeDput[normal=nx ny nz ](Ωx Ωy Ωz ) allows us to mathematically define the plane by a vector normal to this plane and by a point Ω belonging to this plane. This point Ω is considered as the origin of the axes system (ΩXY ), on which all the positioning of the points on this plane are entered. This landmark is automatically defined by the \ThreeDput macro. In the next drawing, the normal vectors to the three faces are shown with both of their associated landmarks. It is important to notice the continuity Three Dimensional Graphics: More details 140 of the orientation of the faces if we turn the cube around. Also, if we apply a three dimensional rotation to the upper face of the cube so that the Xabove axis is parallel to the XB axis of face B, we can see that the two faces are aligned. 1 2 3 4 5 6 ~na 7 b ov 8 e 9 10 11 13 Y ab o ve E OV AB X ab o ve YB 12 14 15 16 17 Fa ce 18 B ~nB YA ce A Fa 19 20 21 22 XA XB 23 24 25 26 ~n A 27 28 29 30 31 32 33 34 \psset{viewpoint=1 1.5 1,arrows=->,arrowinset=0, gridlabels=0,subgriddiv=0} % Grids \ThreeDput[normal=0 0 1]{% Oxy plane \psgrid[gridcolor=red](5,5) \psline[linewidth=3pt,linecolor=blue](4,4)(4,5.5) \uput[90](4,5.5){% \rotateleft{\textcolor{blue}{\vec{n}_A$}}}} \ThreeDput[normal=0 -1 0]{% Oxz plane \psgrid[gridcolor=green](5,5) \psline[linewidth=3pt,linecolor=green](4,0)(5.5,0) \uput[90](5.5,0){% \scalebox{-1 1}{\textcolor{green}{$\vec{n}_B$}}}} \ThreeDput[normal=1 0 0]{% Oyz plane \psgrid[gridcolor=blue](5,5) \psline[linewidth=3pt](0,4)(0,5.5) \uput[0](0,5.5){$\vec{n}_{above}$}} % Cube and axes \psset{linewidth=2pt} \ThreeDput[normal=0 0 1](0,0,4){% \psframe*[linecolor=lightgray](4,4) \rput(2,2){\Huge\textbf{ABOVE}} \psline(4,0)\uput[90](3,0){X$_{above}$} \psline(0,4)\uput[0](0,3){Y$_{above}$}} \ThreeDput[normal=0 1 0](4,4,0){% \psframe*[linecolor=LightBlue](4,4) \rput(2,2){\Huge\textbf{Face A}} \psline(4,0)\uput[90](3,0){X$_{A}$} \psline(0,4)\uput[0](0,3){Y$_{A}$}} \ThreeDput[normal=1 0 0](4,0,0){% \psframe*[linecolor=PaleGreen](4,4) \rput(2,2){\Huge\textbf{Face B}} \psline(4,0)\uput[90](3,0){X$_{B}$} \psline(0,4)\uput[0](0,3){Y$_{B}$}} What are the orientation rules? Take for instance the face B. If Ω is the point of coordinates (1,0,0) in the landmark Oxyz, then Ω XB ,Ω YB ,~nB produces a direct trihedral. From a practical point of view, we must have (the three fingers of your right hand producing a trihedral): • thumb = Ω XB • forefinger = Ω YB • long finger = ~nB All the faces obey to this rule. Imagine standing on a face of the cube with Three Dimensional Graphics: More details 141 the heels of your feet meeting at one corner, your right foot will be facing Ox, your left foot will be facing Oy and you will be standing in the ~n (the normal) direction. You can write onto the face in the direction that your right foot points toward. How to represent the intersection of the unit cube with the plane h defined by: • 0≤ x≤ 4 • 0≤ y≤ 4 • 0≤ z≤ 4 where h = x + y + z with 0 < h < 12? We will define this plane by its normal and the origin Ω of the new landmark in this plane. A plane of Cartesian equation ax + by + cz = d owns ~n(a, b, c) as its normal vector. In this case, we can then take ~n(1, 1, 1), and easily verify that the h h h point Ω( , , ) is a point of this plane. This is the foot of the perpen3 3 3 dicular of O to this plane. And we can define this plane by the macro h h h \ThreeDput[normal=1 1 1]( , , ) 3 3 3 The next examples are related respectively to h=3, h=6 (regular hexagon) and h=7. But, first, we must compute the coordinates of the vertex of the polygons (triangle or hexagon), intersections of the plane with the edges of the cube (this package does not do it, but we can easily code the computations in PostScript). After that we can draw the polygon by the usual \pspolygon macro. Three Dimensional Graphics: More details 142 1 2 3 4 z5 5z 5 4 4 7 3 3 9 6 8 10 11 2 2 12 13 1 1 14 0 17 18 3 4 3 19 4 2 2 3 1 1 2 0 4 4 20 5 y x5 5x 16 1 3 0 0 1 2 15 0 0 y5 21 22 23 24 25 26 27 28 1 2 z5 5z 3 4 4 4 5 3 3 7 6 8 2 2 9 10 11 1 1 12 14 15 16 17 4 5 y 3 4 2 3 1 2 0 0 1 0 1 2 3 3 1 0 4 x5 5x 4 2 13 0 0 y5 18 19 20 21 22 23 24 \SpecialCoor \psset{viewpoint=1 1.5 1,arrows=->,arrowscale=2,subgriddiv=0} % Grids and axes \ThreeDput[normal=0 0 1]{% Oxy plane \psgrid[gridcolor=red](5,5) \psline(0,5)\uput[180](0,5){\textcolor{red}{$y$}} \psline(5,0)\uput[-90](5,0){\textcolor{red}{$x$}}} \ThreeDput[normal=0 -1 0]{% Oxz plane \psgrid[gridcolor=green](5,5) \psline(0,5)\uput[180](0,5){\textcolor{green}{$z$}} \psline(5,0)\uput[-90](5,0){\textcolor{green}{$x$}}} \ThreeDput[normal=1 0 0](0,0,0){% Oyz plane \psgrid[gridcolor=blue](5,5) \psline(0,5)\uput[180](0,5){\textcolor{blue}{$z$}} \psline(5,0)\uput[-90](5,0){\textcolor{blue}{$y$}}} % Intersection of the plane x+y+z=h with the cube for h=3 % Radius = h*sqrt(2/3) = 3*0.8465 = 2.4495 \ThreeDput[normal=1 1 1](1,1,1){% (h/3,h/3,h/3) \pscustom[fillstyle=hlines,hatchwidth=0.1pt,hatchsep=2pt]{% \code{/h 3 def /Radius h 2 3 div sqrt mul def}% \pspolygon(! Radius dup -30 cos mul exch -30 sin mul) (! Radius dup 90 cos mul exch 90 sin mul) (! Radius dup 210 cos mul exch 210 sin mul)}} % Cube \psset{linewidth=0.05} \ThreeDput[normal=0 0 1](0,0,4){\psframe(4,4)} \ThreeDput[normal=0 1 0](4,4,0){\psframe(4,4)} \ThreeDput[normal=1 0 0](4,0,0){\psframe(4,4)} \SpecialCoor \psset{viewpoint=1 1.5 1,arrows=->,arrowscale=2,subgriddiv=0} % Grids and axes % ... % Polygons \ThreeDput[normal=1 1 1](2,2,2){% (h/3,h/3,h/3) % Triangle \pscustom[linecolor=magenta]{% \code{/h 6 def /Radius h 2 3 div sqrt mul def}% \pspolygon(! Radius dup -30 cos mul exch -30 sin mul) (! Radius dup 90 cos mul exch 90 sin mul) (! Radius dup 210 cos mul exch 210 sin mul)} % Intersection of the plane x+y+z=h with the cube for h=6 % Radius = h/3*sqrt(2) = 6/3*1.414 = 2.828 \pscustom[fillstyle=hlines,hatchwidth=0.1pt,hatchsep=2pt]{% \code{/h 6 def /Radius h 3 div 2 sqrt mul def}% \pspolygon(! Radius dup 0 cos mul exch 0 sin mul) (! Radius dup 60 cos mul exch 60 sin mul) (! Radius dup 120 cos mul exch 120 sin mul) (! Radius dup 180 cos mul exch 180 sin mul) (! Radius dup 240 cos mul exch 240 sin mul) (! Radius dup 300 cos mul exch 300 sin mul)}} % Cube % ... Three Dimensional Graphics: More details 143 z5 5z 4 4 3 3 1 2 2 2 3 4 5 1 1 6 0 8 1 9 3 4 3 11 4 2 2 10 3 1 1 2 0 4 5 y x5 5x 2 3 4 0 0 1 7 0 0 12 y5 1 2 z5 5z 3 4 4 5 4 6 3 3 7 8 9 2 2 10 11 1 1 12 0 15 16 17 4 18 5 y 3 4 2 3 1 2 0 1 2 3 4 4 1 14 1 x5 5x 3 2 13 0 0 0 0 \SpecialCoor \psset{viewpoint=1 1.5 1,arrows=->,arrowscale=2,subgriddiv=0} % Grids and axes % ... % Intersection of the plane x+y+z=h with the cube for h=7 \def\Radius{2.9439}% \ThreeDput[normal=1 1 1](2.33,2.33,2.33){% (h/3,h/3,h/3) \pspolygon[fillstyle=hlines,hatchwidth=0.1pt,hatchsep=2pt] (\Radius;43.9)(\Radius;136.1)(\Radius;163.9) (\Radius;256.1)(\Radius;283.9)(\Radius;376.1)} % Cube % ... y5 19 20 21 22 23 24 \SpecialCoor \psset{viewpoint=1 1.5 1,arrows=->,arrowscale=2,subgriddiv=0} % Grids and axes % ... % Intersection of the plane x+y+z=h with the cube for h=7 \def\Radius{2.9439}% \ThreeDput[normal=1 1 1](2.33,2.33,2.33){% (h/3,h/3,h/3) \pspolygon[fillstyle=hlines,hatchwidth=0.1pt,hatchsep=2pt, hatchcolor=yellow] (\Radius;43.9)(\Radius;136.1)(\Radius;163.9) (\Radius;256.1)(\Radius;283.9)(\Radius;376.1)} % % On the face A, this is a triangle with edges % of coordinates (4,0)(1,0)(4,3) \ThreeDput[normal=0 1 0](4,4,0){% \pspolygon[fillstyle=solid,fillcolor=LightBlue](4,0)(1,0)(4,3)} % On the face B, this is a triangle with edges % of coordinates (0,0)(0,3)(3,0) \ThreeDput[normal=1 0 0](4,0,0){% \pspolygon[fillstyle=solid,fillcolor=PaleGreen](0,0)(0,3)(3,0)} % On the upper face, this is a triangle with edges % of coordinates (0,0)(3,0)(0,3) \ThreeDput[normal=0 0 1](0,0,4){% \pspolygon[fillstyle=solid,fillcolor=Pink](0,0)(3,0)(0,3)} Three Dimensional Graphics: More details 144 XI 54 Other features Special coordinates The command \SpecialCoor enables a special feature that lets you specify coordinates in a variety of ways, in addition to the usual Cartesian coordinates. Processing is slightly slower and less robust, which is why this feature is available on demand rather than by default, but you probably won’t notice the difference. Here are the coordinates you can use: (x,y) The usual Cartesian coordinate. E.g., (3,4). (r;a) Polar coordinate, with radius r and angle a. The default unit for r is unit. E.g., (3;110). 1 b 0b b b b -1 b b -1 b b b b b b 0 b b b b b b b 1 2 \SpecialCoor \multido{\iAngle=0+18}{20}{\psdot(1;\iAngle)} 1 (!ps) Raw PostScript code. ps should expand to a coordinate pair. The units xunit and yunit are used. For example, if we want to use polar coordinates (2, 45) and (1.5, 70) that are scaled along with xunit and yunit, we can write: 3 1 b u 2 b u 1 2 3 4 5 6 7 0 0 1 2 \SpecialCoor \psset{dotscale=2,xunit=2,yunit=1.5}% \psdot(2;45) \psdot[linecolor=cyan](! 2 45 cos mul 2 45 sin mul) \psset{dotstyle=triangle*}% \psdot(1.5;70) \psdot[linecolor=cyan](! 1.5 70 cos mul 1.5 70 sin mul) 3 A lot of things can be done with some PostScript programming, and sometimes in an easiest way than at the TEX level. Note also that some PostScript code can be executed in addition to the computation Other features 145 of the coordinates. In the next example, eighty dots of random colors (using the HSB color model) are put at random coordinates, in the square (5,5):39 b b b b b 4 bb b bb b b b b b b b b b 3 b b b b b bb bb b b bb b bbb bbb b b 2 b bbbb bb b bb b b bb b b b bb b 1 b b b b b b bb bbb b b 0 b b bb 5 1 0 2 3 4 1 2 3 4 5 \SpecialCoor \psset{dotscale=2}% \multips(0,0){80}{% \psdot(! rand 501 mod 100 div rand 501 mod 100 div rand 101 mod 100 div 1 1 sethsbcolor)} 5 (coor1|coor2) The x coordinate from coor1 and the y coordinate from coor2 . coor1 and coor2 can be any other coordinates for use with \SpecialCoor. 3 2 b 1 1 2 3 \SpecialCoor \Cnode*(2,2){A} \psdot[linecolor=cyan,dotscale=3](A|1in;30) 0 0 1 2 3 (node) The center of node. E.g., (A). ([par]node) The position relative to node determined using the angle, nodesep and offset optional parameters. E.g., ([angle=45]A). Using both nodesep and offset allow to define relative moves (nodesep for horizontal and offset for vertical) from an existing node. 4 bA 3 1 2 3 2 4 5 1 6 \SpecialCoor \pnode(3,3){A}\psdot[dotscale=2](A)\uput[45](A){A} \psline([nodesep=1]A) \psline[linestyle=dashed]([nodesep=-1]A) \psline[linestyle=dotted,linewidth=0.08]([offset=1]A) \psline[linewidth=0.08]([nodesep=-1,offset=-1]A) 0 0 1 2 3 4 39 The rand PostScript operator generate an integer random number between 0 and 231 –1, 501 mod allow to restrict it between 0 and 500 and 100 div to transform it in a real number between 0 and 5. Then we use the sethsbcolor operator to fix the color of the dot, fixing randomly between 0 and 1 the Hue composante value (see [51] for more details.) Other features: Special coordinates 146 4 A 3 b 1 2 3 2 4 5 1 6 7 \SpecialCoor \pnode(3,3){A}\psdot[dotscale=2](A)\uput[135](A){A} \pscircle[linestyle=dotted](A){1} \psline([nodesep=1,angle=-45]A) \psline[linestyle=dashed]([nodesep=-1,angle=-45]A) \psline[linestyle=dotted,linewidth=0.08]([offset=1,angle=-45]A) \psline[linewidth=0.08]([offset=1,angle=135]A) 0 0 1 2 3 4 ([par]{nodeB}nodeA) The position relative to nodeA, on the virtual line joining nodeA and nodeB , determined using the angle, nodesep, Xnodesep, Ynodesep and offset optional parameters. Xnodesep and Ynodesep allows to specify vertical and horizontal increments. 5 bB 4 1 2 bA 3 3 4 5 2 6 7 8 1 9 \SpecialCoor \pnode(3,3){A}\psdot[dotscale=2](A)\uput[45](A){A} \pnode(0,5){B}\psdot[dotscale=2](B)\uput[45](B){B} \psline[linestyle=dashed,dash=0.4 0.1,linecolor=red] (B)([nodesep=-2.5]{B}A) \psline(A) \psline[linestyle=dashed]([nodesep=-1]{B}A) \psline[linewidth=0.08]([Ynodesep=-1]{B}A) \psline[linestyle=dotted,linewidth=0.08]([Xnodesep=-1]{B}A) 0 0 1 2 3 4 5 \SpecialCoor also lets you specify angles in several ways: num A number, as usual, with units given by the \degrees command. (coor) A coordinate, indicating where the angle points to. Be sure to include the (), in addition to whatever other delimiters the angle argu- ment uses. For example, the following are two ways to draw an arc of .8 inch radius from 0 to 135 degrees: 1 2 3 \SpecialCoor \psarc(0,0){.8in}{0}{135} \psarc(0,0){.8in}{0}{(-1,1)} !ps Raw PostScript code. ps should expand to a number. The same units are used as with num. The command \NormalCoor Other features: Special coordinates 147 disables the \SpecialCoor features. Here is an example for geometric drawing, which use some PostScript computations and node references.40 1 \SpecialCoor 2 3 4 5 6 B 2 7 A 8 9 1 10 Z 0 0 1 2 3 C 11 4 12 13 14 15 16 17 18 55 pst-coil \pnode(0,2){A}\uput[-135](A){A} \pnode(4,2){B}\uput[90](B){B} \pnode(4,0){C}\uput[45](C){C} \pspolygon(A)(B)(C) % Angle = atan(2/4) = 26.57 \pnode(! /LengthA 4 def /LengthB 2 def /Angle LengthB LengthA atan def LengthA Angle cos dup mul mul LengthB Angle cos Angle sin LengthA mul mul sub){Z}\uput[-135](Z){Z} \psline[linecolor=red,linestyle=dashed](Z)(B) \psset{linecolor=blue}% % sqrt(0.3*0.3 + 0.3*0.3) = 0.42 and 45 - 26.57 = 18.43 \psline(Z)([nodesep=0.3]{B}Z)([nodesep=0.42,angle=18.43]Z) ([nodesep=0.3]{C}Z) Coils and zigzags The file pst-coil.tex/pst-coil.sty (along with the header file pst-coil.pro) defines the following graphics objects for coils and zigzags: \pscoil*[par ]{arrows}(x0,y0)(x1,y1) \psCoil*[par ]{angle1}{angle2} \pszigzag*[par ]{arrows}(x0,y0)(x1,y1) These graphics objects use the following parameters: coilwidth=dim coilheight=num coilarm=dim coilaspect=angle coilinc=angle Default: 1cm Default: 1 Default: .5cm Default: 45 Default: 10 All coil and zigzag objects draw a coil or zigzag whose width (diameter) is coilwidth, and with the distance along the axes for each period (360 degrees) equal to 40 For such Euclidian geometric drawings, the ‘pst-eucl’ contribution package from Dominique Rodriguez [59] offer many high level and powerful functions. Other features: Coils and zigzags 148 coilheight x coilwidth. Both \pscoil and \psCoil draw a “3D” coil, projected onto the xz-axes. The center of the 3D coil lies on the yz-plane at angle coilaspect to the z-axis. The coil is drawn with PostScript’s lineto, joining points that lie at angle coilinc from each other along the coil. Hence, increasing coilinc makes the curve smoother but the printing slower. \pszigzag does not use the coilaspect and coilinc parameters. \pscoil and \pszigzag connect (x0,y0) and (x1,y1), starting and ending with straight line segments of length coilarmA and coilarmB, resp. Setting coilarm is the same as setting coilarmA and coilarmB. Here is an example of \pscoil: 1 \pscoil[coilarm=.5cm,linewidth=1.5pt,coilwidth=.5cm]{<-|}(4,2) Here is an example of \pszigzag: 1 \pszigzag[coilarm=.5,linearc=.1]{<->}(4,0) Note that \pszigzag uses the linearc parameters, and that the beginning and ending segments may be longer than coilarm to take up slack. \psCoil just draws the coil horizontally from angle1 to angle2 . Use \rput to rotate and translate the coil, if desired. \psCoil does not use the coilarm parameter. For example, with coilaspect=0 we get a sine curve: 1 2 pst-node \psCoil[coilaspect=0,coilheight=1.33, coilwidth=.75,linewidth=1.5pt]{0}{1440} pst-coil.tex also contains coil and zigzag node connections. You must also load pst-node.tex/pst-node.sty to use these. The node connections are: \nccoil*[par ]{arrows}{nodeA}{nodeB} \nczigzag*[par ]{arrows}{nodeA}{nodeB} \pccoil*[par ]{arrows}(x1,y1)(x2,y2) \pczigzag*[par ]{arrows}(x1,y1)(x2,y2) The end points are chosen the same as for \ncline and \pcline, and otherwise these commands work like \pscoil and \pszigzag. For example: Other features: Coils and zigzags 149 \cnode(.5,.5){.5}{A} \cnode[fillstyle=solid,fillcolor=lightgray](3.5,2.5){.5}{B} \nccoil[coilwidth=.3]{<->}{A}{B} 1 2 3 56 Overlays Overlays are mainly of interest for making slides, and the overlay macros described in this section are mainly of interest to TEX macro writers who want to implement overlays in a slide macro package. For example, Seminar [78], a LATEX document class for slides and notes, uses PSTricks to implement overlays. Overlays are made by creating an \hbox and then outputting the box several times, printing different material in the box each time. The box is created by the commands41 \overlaybox stuff \endoverlaybox The material for overlay string should go within the scope of the command \psoverlay{string} string can be any string, after expansion. Anything not in the scope of any \psoverlay command goes on overlay main, and material within the scope of \psoverlayall goes on all the overlays. \psoverlay commands can be nested and can be used in math mode. The command \putoverlaybox{string} then prints overlay string . Here is an example: 1 2 3 4 \overlaybox \psoverlay{all} \psframebox[framearc=.15,linewidth=1.5pt]{% \psoverlay{main} 41 A LT EX users can instead write: \begin{overlaybox} stuff \end{overlaybox} Other features: Overlays 150 5 6 7 8 \parbox{3.5cm}{\raggedright Foam Cups Damage Environment {\psoverlay{one} Less than Paper Cups,} Study Says.}} \endoverlaybox 9 10 \putoverlaybox{main}\hspace{.5in}\putoverlaybox{one} Foam Cups Damage Environment Study Says. Less than Paper Cups, Driver notes: 57 pst-grad Overlays use \pstVerb and \pstverbscale. The gradient fill style The file pst-grad.tex/pst-grad.sty, along with the PostScript header file pst-grad.pro, defines the gradient fillstyle, for gradiated shading.42 This fillstyle uses the following parameters: gradbegin=color Default: 0 .1 .95 The starting and ending color (default color is a dark blue). gradend=color Default: 0 1 1 The color at the midpoint (default color is cyan). gradlines=int Default: 500 The number of lines. More lines means finer gradiation, but slower printing. gradmidpoint=num Default: .9 The position of the midpoint, as a fraction of the distance from top to bottom. num should be between 0 and 1. gradangle=angle Default: 0 The image is rotated by angle. 42 The ‘pst-slpe’ contribution package from Martin Giese [64] offer extended functionalities, like radial and concentric gradients and multicolored ones (for rainbow effects.) Other features: The gradient fill style 151 gradbegin and gradend should preferably be rgb colors, but gray and cmyk colors should also work. The definitions of the colors gradbegin and gradend are: 1 2 gradbegin = 0 0.1 0.95 gradend = 0 1 1 Here are two ways to change the gradient colors: 1 \psset{gradbegin=blue} or, with P LAIN TEX and LATEX (using the ‘color’ package): 1 \definecolor{rgb}{gradbegin}{1,0.4,0} and with ConTEXt: 1 \definecolor{gradbegin}{r=1,g=0.4,b=0} Try these examples: 1 \psframe[fillstyle=gradient,gradmidpoint=1,gradangle=45](4,2) 1 \psellipse[linestyle=none,fillstyle=gradient,gradmidpoint=0.5, gradangle=90,gradbegin=Pink,gradend=red](2,1)(2,1) 2 58 pst-text Typesetting text along a path The file pst-text.tex/pst-text.sty defines the command \pstextpath, for typesetting text along a path. It is a remarkable trick, but there are some caveats: • ‘pst-text’ only works with certain DVI-to-PS drivers. Here is what is currently known: – It works with Rokicki’s dvips. – “Does not work” means that it has no effect, for better or for worse. Other features: Typesetting text along a path 152 – This may work with other drivers. The requirement is that the driver only use PostScript’s show operator, unbound and unloaded, to show characters. • You must also have installed the PostScript header file pst-text.pro, and \pstheader must be properly defined in pstricks.con for your driver. • Like other PSTricks that involve rotating text, this works best with PostScript (outline) fonts. • PostScript rendering with ‘pst-text’ is slow. Here is the command: \pstextpath[pos](x,y){graphics object}{text} text is placed along the path, from beginning to end, defined by the PSTricks graphics object. (This object otherwise behaves normally. If you don’t want it to appear, set linestyle=none.) text can only contain characters. No TeX rules, no PSTricks, and no other \special’s. (These things don’t cause errors; they just don’t work right.) Math mode is OK, but math operators that are built from several characters (e.g., large integral signs) may break. Entire boxes (e.g., \parbox) are OK too, but this is mainly for amusement. l pos is either c r justify on beginning of path center on path justify on end of path. The default is l. (<x>,<y>) is an offset. Characters are shifted by distance x along path, and are shifted up by y . “Up” means with respect to the path, at whatever point on the path corresponding to the middle of the character. (<x>,<y>) must be Cartesian coordinates. Both coordinates use \psunit as the default. The default coordinate is (0,\TPoffset), where \TPoffset a command whose default value is -.7ex. This value leads to good spacing of the characters. Remember that ex units are for the font in effect when \pstextpath occurs, not inside the text argument. More things you might want to know: • Like with \rput and the graphics objects, it is up to you to leave space for \pstextpath. • Results are unpredictable if text is wider than length of path. • \pstextpath leaves the typesetting to TEX. It just intercepts the show operator to remap the coordinate system. Other features: Typesetting text along a path 153 1 2 3 4 \pstextpath[c]% {\pscurve[linecolor=gray](0,1)(4,3)(6,2)(9,0)(11,1)}% {$S_\alpha=\Omega(\gamma_\beta)$is a connected snarf and$B=(\otimes,\rightarrow,\theta)$is Boolean left subideal.} nected snarf a con nd a B ) is Sα = γβ Ω( = (⊗ ,→ ,θ )i sB oo l ea n l e ft id s ub eal . Cen t la de R ech que National re 2 3 4 \LARGE \psset{linestyle=none}% \pstextpath[c]{\psarcn(0,0){1.8}{180}{0}}{Centre National de la} \pstextpath[c]{\psarc(0,0){1.8}{180}{0}}{Recherche Scientifique} ifi e rch 1 e S ci e n t ci p l e, it is p o pr i n ss n I u se p ar b o x , b u t le io t b le what really happe t ’s n see ems hard to beli s. e e s v It someone would w e ant that this. o d to 1 2 3 4 5 \pstextpath[c](0,0){\psarcn[linestyle=none](0,-6){4}{180}{0}}% {\parbox{4cm}{% In principle, it is possible to use parbox, but let’s see what really happens. It seems hard to believe that someone would want to do this.}} And, last, a peom of the calligramme form, La colombe poignardée et le jet d’eau, by the french poet Guillaume Appolinaire [3], re-typeset from the original43 and first published in Les Cahiers GUTenberg in 1994 [22]. 1 2 3 4 5 6 7 8 9 \small \psset{linestyle=none}% \pstextpath[r]{\pscurve(1.5,8)(3,9)(4.45,6.5)} {Tous les souvenirs de nagu^^e8re} \pstextpath[r]{\pscurve(1,7)(2,7.5)(4.45,6)} {O mes amis partis en guerre} \pstextpath[r]{\pscurve(1,6)(2,6.7)(4.45,5.2)} {Jaillissent vers le firmament} % ... 43 Only the code for few verses is shown here, but the complete code will be found in the source file of this documentation. Other features: Typesetting text along a path 154 10 11 12 13 \pstextpath[c]{\pscurve(2.1,1.2)(4.5,0.8)(6.9,1.3)} {Le soir tombe \textbf{\Huge O} sanglante mer} \pstextpath[c]{\pscurve(0,1)(4.5,0)(9,1)} {Jardins o^^f9 saigne abondamment le laurier rose fleur guerri^^e8re} Do Où nt s les ont R ay n na s de nir ve les sou us o T D illy alize B l s amis p e mélanco me art ss lis m is en o en t n e t s s n v s g a u n d i e l e u r s l s a i e p l r e fi s Ja rm re de e a r d s a tz qui s’e en l m eg en omm emni ng ’ea sr ag r o ud v C ea t o m t s n é r l e e ma anc r ù s l i oli m t eu o rts d qu nt son M em Braque et être rs mon âm éjà s l t e i M ee tax nt Peu veni st p on Jac u s o lei s is o u c r gr e e o ù l m x p s b m u u e u ne rm e l’a O x ye D d’ea a u u a be pei t n i ne ra De ? ère nagu se égli Le je O Et t C O CEUX ONT QUI S J ar d i 59 pst-char ns o ù E R R E AU N O R D S E À LA GU BAT T E NT M PA RT IS AINT L e s oi r tom b e sa i g n e abon O s a n gl er an te m damment le laurier r ur g ose fle u e rr i E NA N T èr e Stroking and filling character paths The file pst-char.tex/pst-char.sty defines the command: \pscharpath*[par ]{text} It strokes and fills the text character paths using the PSTricks linestyle and fillstyle. The restrictions on DVI-to-PS drivers listed on page 152 for \pstextpath apply to \pscharpath. Furthermore, only outline (PostScript) fonts are affected. 1 2 \DeclareFixedFont{\Sf}{T1}{phv}{b}{n}{3.5cm} \DeclareFixedFont{\Rm}{T1}{ptm}{m}{n}{3mm} 3 4 5 \pscharpath[linestyle=none,fillstyle=gradient,gradmidpoint=0.5, gradbegin=PaleGreen,gradend=ForestGreen]{\Sf TeX} Other features: Stroking and filling character paths 155 With the optional *, the character path is not removed from the PostScript environment at the end. This is mainly for special hacks. For example, you can use \pscharpath* in the first argument of \pstextpath, and thus typeset text along the character path of some other text. However, you cannot combine \pscharpath and \pstextpath in any other way. E.g., you cannot typeset character outlines along a path, and then fill and stroke the outlines with \pscharpath. i PSTr ri ksP cksP ST ri ric ST sP ic k sPS T k P S Tr i c s ck s P S Tr ck Tri PS cks STr ck s STricksPSTricks r Tr i c k s P ic sPSTr P S ci ksPSTric k cksP PS ciks PS PST PST icksPSTri STr ksPST ri cksPSTricksPST S Tr i c k s sP ric ic k S T S ric ksP ks ric rkicsP ST STr ic k ksP s ric sPST icksPSTri r ksP T ricks P S T r k s P S T ksP PSTri PS ic PSTr s Tr ks ic Tric k STrick sPSTricksPSTric STric k ri cksPSTricksP ksP ST ricksPSTricksPSTri cks PSTricksPSTric 3 \pstextpath(0,-2mm){\pscharpath*[fillstyle=gradient, gradangle=45,gradmidpoint=0.5]{\Sf LaTeX}}% {\Rm\multido{\i=1+1}{60}{PSTricks}} sPST 2 cksP 1 Trick The command44 \pscharclip*[par ]{text} ... \endpscharclip works just like \pscharpath, but it also sets the clipping path to the character path. You may want to position this clipping path using \rput inside \pscharclip’s argument. Like \psclip and \endpsclip, \pscharclip and \endpscharclip should come on the same page and should be properly nested with respect to TEX groups (unless \AltClipMode is in effect).45 1 2 3 4 5 6 7 \begin{pscharclip}[linewidth=3pt]{\rput[t](0,0){\Sf ConTeXt}} \rput{58}{% \color{red} \begin{minipage}{11cm} \multido{\i=1+1}{220}{PSTricks } \end{minipage}} \end{pscharclip} 44 A LT EX users can instead write: \begin{pscharclip}*[par]{text} ... \end{pscharclip} 45 Another way to do this is to use the \pscharpath macro with the \psboxfill one (see Section 50.3.) Other features: Stroking and filling character paths 156 PS rick PS PS Trick s PS T PS Trick s PS Trick PS Trick s PS Trick s PS Trick s PS Trick s Tri s T ck PS rick s s T r ic P S r ic s P ric ks P Tric ks P ST S ks S k PS Trick s PS T PS Trick s PS T PS Trick s PS Trick PS Trick s PS Trick s Tri s PS Tric s c ric ks P Tric ks S ric ks P Tric ks P S k ric s P Tric ks P ST S ks S k PS Trick s PS T PS Trick s PS Trick PS Trick s PS Trick s Tri s PS Tric s c ric ks P Tric ks S ric ks P Tric ks P ST k ST ks s r ic ks PST ricks PST PS rick PS PS Trick s PS Trick PS Trick s PS Trick s PS Trick s PS Trick s Tri s T ck PS rick s s T r ic P S r ic s P ric ks P Tric ks P ST S ric ks P Tric ks P ST ST ks S k PS rick s PS T T PS rick s PS Trick PS Trick s PS Trick s Tri s T ck PS rick s s T s 60 Importing EPS files PSTricks does not come with any facility for including Encapsulated PostScript files, because there are other very good and well-tested macros for exactly that, specially the graphicx package for LATEX, usable also with TEX. What PSTricks is good for is embellishing your EPS picture. You can include an EPS file in the argument of \rput, as in 1 \rput(3,3){\includegraphics{myfile}} and hence you can include an EPS file in the \pspicture environment. Turn on \psgrid, and you can find the coordinates for whatever graphics or text you want to add. This works even when the picture has a weird bounding box, because with the arguments to \pspicture you control the bounding box from TEX’s point of view.46 1 2 3 4 \begin{pspicture}(5,5) \rput[bl](0,0){\includegraphics[scale=0.25]{tiger}} \psgrid[subgriddiv=0] \end{pspicture} 5 4 3 2 1 0 0 1 2 3 4 5 If you do not want to adjust the dimension of the pspicture environments by tries and errors, you can store the image in a TEX box (\pst@boxg is 46 Of course, with ConTEXt, use the P LAIN TEX syntax for the \pspicture environment and the macro \externalfigure. Other features: Importing EPS files 157 the name of an internal temporary PSTricks box), and ask for it width and height: 1 2 3 4 5 \savebox{\pst@boxg}{\includegraphics[scale=0.25]{tiger}} \begin{pspicture}(\wd\pst@boxg,\ht\pst@boxg) \rput[bl](0,0){\usebox{\pst@boxg}} \psgrid[subgriddiv=0] \end{pspicture} 5 4 3 2 1 0 0 1 2 3 4 5 6 1 2 3 4 5 \begin{pspicture}(5,5) \rput[bl](0,0){\includegraphics[scale=0.25]{tiger}} \psset{linewidth=0.1,arrows=->,arrowscale=2}% \psline(6,3)(4,4.6)\uput[-45](6,3){Ear} \psline(6,1.5)(2,1.5)\uput[0](6,1.5){Mouth} \end{pspicture} Ear Mouth This isn’t always the best way to work with an EPS file, however. If the PostScript file’s bounding box is the size you want the resulting picture to be, after your additions, then try 1 \hbox{picture objects \includegraphics{file}} This will put all your picture objects at the lower left corner of the EPS file. Other features: Importing EPS files 158 If you need to determine the bounding box of an EPS file, then you can try of the automatic bounding box calculating programs, such as bbfig (distributed with Rokicki’s dvips). However, all such programs are easily fooled; the only sure way to determine the bounding box is visually. \psgrid is a good tool for this. 61 pst-eps Exporting EPS files You must load pst-eps.tex/pst-eps.sty to use the PSTricks macros described in this section. Exporting a PSTricks graphic as an EPS file is specially useful in some circumstances (to put such graphic on a Web page, after conversion of the EPS file in JPEG or PNG format, to generate animated graphics (see the Section B), etc.) If you want to export an EPS file that contains both graphics and text, you must use the TeXtoEPS environment and a DVI-to-PS driver that suports such a feature. If you just want to export pure graphics, then you can use the \PSTtoEPS command. Both of these options are described in this section. Rokicki’s dvips support an -E option for creating EPS files from TEX .dvi files. E.g., dvips foo.dvi -E -o foo.eps 1 Your document should be a single page (do not forget to suppress the header, footer, page number, etc. to do not include extra material in the resulting file!) dvips will find a tight bounding box that just encloses the printed characters on the page. This works best with outline (PostScript) fonts, so that the EPS file is scalable and resolution independent. There are two inconvenient aspects of this method. You may want a different bounding box than the one calculated by dvips (in particular, dvips ignores all the PostScript generated by PSTricks when calculating the bounding box), and you may have to go out of your way to turn off any headers and footers that would be added by output routines. PSTricks contains an environment that tries to get around these two problems47 : \TeXtoEPS stuff \endTeXtoEPS 47 A LT EX users can instead write: \begin{TeXtoEPS} stuff \end{TeXtoEPS} Other features: Exporting EPS files 159 This is all that should appear in your document, but headers and whatever that would normally be added by output routines are ignored. dvips will again try to find a tight bounding box, but it will treat stuff as if there was a frame around it. Thus, the bounding box will be sure to include stuff , but might be larger if there is output outside the boundaries of this box. If the bounding box still isn’t right, then you will have to edit the 1 %%BoundingBox llx lly urx ury specification in the EPS file by hand. If your goal is to make an EPS file for inclusion in other documents, then dvips -E is the way to go. However, it can also be useful to generate an EPS file from PSTricks graphics objects and include it in the same document,48 rather than just including the PSTricks graphics directly, because TEX gets involved with processing the PSTricks graphics only when the EPS file is initially created or updated. Hence, you can edit your file and preview the graphics, without having to process all the PSTricks graphics each time you correct a typo. This speed-up can be significant with complex graphics such as \listplot’s with a lot of data. To create an EPS file from PSTricks graphics objects, use \PSTtoEPS[par ]{file}{graphics objects} The file is created immediately, and hence you can include it in the same document (after the \PSTtoEPS command) and as many times as you want. Unlike with dvips -E, only pure graphics objects are processed (e.g., \rput commands have no effect). \PSTtoEPS cannot calculate the bounding box of the EPS file. You have to specify it yourself, by setting the following parameters: bbllx=dim bblly=dim bburx=dim bbury=dim Default: Default: Default: Default: 0pt 0pt 0pt 0pt Note that if the EPS file is only to be included in a PSTricks picture with \rput you might as well leave the default bounding box. \PSTricksEPS also uses the following parameters: makeeps=none/new/all/all* Default: new This parameter determines which \PSTtoEPS commands just skip over their arguments, and which create files, as follows: 48 See the preceding section on importing EPS files. Other features: Exporting EPS files 160 none No files are created. new Only those files not found anywhere on the system are created (take care that you must remove the files to re-create them!) all All files are created. all* All files are created, but you are asked for approval before exist- ing files are deleted. headerfile=files Default: This parameter is for specifying PostScript header files that are to be included in the EPS file. The argument should contain one or more file names, separated by commas. If you have more than one file, however, the entire list must be enclosed in braces {}. headers=none/all/user Default: none When none, no header files are included. When all, the header files used by PSTricks plus the header files specified by the headerfile parameter are included. When user, only the header files specified by the headerfile parameter are included. If the EPS file is to be included in a TEX document that uses the same PSTricks macros and hence loads the relevant PSTricks header files anyway (in particular, if the EPS file is to be included in the same document), then headers should be none or user. You can either store the graphic in an unique EPS file: 3 5 \includegraphics[angle=45,scale=0.5]{Frame} 0 0 1 1 \PSTtoEPS[bbllx=-0.2,bblly=-0.2,bburx=5,bbury=3]{Frame.eps}{% \psgrid[subgriddiv=0](5,3) \psframe[linecolor=blue,linewidth=0.1](1,1)(4,2)} 4 2 2 3 3 4 5 1 2 or put the content in a personal header file, using the \psNewHeader and \psDefineProc macros in the preamble of the file, and reusing it later (in the same source file or, of course, in another TEX file), using the \psUseHeader and \psUseProc macros. \psNewHeader{header file}{content} \psDefineProc{procedure name}{graphics objects} \psUseHeader{header file} \psUseProc[par ]{procedure name} Other features: Exporting EPS files 161 There are four special parameters to specify how to handle the graphic when it is reused: GraphicsRef={x0,y0} Default: none The reference point to use (the coordinates must be given between braces.) These values will be set by the origin parameter. Translation={x1,y1} Default: none The point where the graphic will be translated (the coordinates must be given between braces.) Rotation=num Default: none The angle to use. Scale=num1 num2 Default: none The scaling factors to use (if only one number is given, it will be used both for horizontal and vertical scalings.) 1 2 3 4 5 \psNewHeader{Frame.pro}{% \psDefineProc{Frame}{% \psset{linewidth=0.1}% \psframe[linecolor=blue](3,1) \pstriangle[linecolor=red](0.25,0)(0.5,1)}} 6 7 \psUseHeader{Frame.pro} 8 9 % ... 10 11 %\begin{document} 12 13 % ... 14 15 16 17 18 19 \psUseProc{Frame} \psUseProc[Rotation=-90,Scale=0.5]{Frame} \psUseProc[Translation={4.5,0}]{Frame} \psUseProc[Translation={2,-1},Rotation=-25,Scale=0.5]{Frame} \psUseProc[Translation={7,1},Rotation=-90]{Frame} Other features: Exporting EPS files 162 XII Writing high-level macros 49 This chapter is intended only for advanced users who want to develop new high-level macros or new specialized packages. It is a detailed tutorial which progressively introduces many techniques which are commonly used in PSTricks packages. 62 Overview The file pst-key.tex/pst-key.sty, written by David Carlisle in 1997, defines an interface between PSTricks and the ‘keyval’ package [35], written too by David Carlisle, which implements a general mechanism to flexibly manage the parameters of a macro. It uses the key=value syntax and is a generic implementation of the original internal mechanism which PSTricks uses to handle parameters. pst-key This package can be used with P LAIN TEX, LATEX and ConTEXt. Developers are strongly encouraged to create packages that are generic, not limited to LATEX or another TEX flavor. Use of the ‘pst-key’ package will make it easier for this to be done. Of course, other precautions must also be taken to ensure that packages are generic. The ‘keyval’ prefix used by ‘pst-key’ is psset, so the macro 1 \setkeys{psset}{param1=value1,...,paramN=valueN} will initialize the defined parameters, inside the TEX group where it is called. To manage parameters globally or locally to a macro, the general method is the following (sometimes, the grouping mechanism must be done otherwise –see for instance the \PstDotsScaled macro in Section 63.5): 1 \setkeys{psset}{...}% Assignment of global parameters 2 3 \def\PstXxxx{\def\pst@par{}\pst@object{PstXxxx}} 4 5 \def\PstXxxx@i{{% Two braces, because parameter 49 This chapter was written in 2003 by Denis Girou. Writing high-level macros 163 6 7 8 9 10 11 % assignments must be local \use@par% Assignment of local parameters % The code itself, which can of course include calls % to auxiliary macros % ... }} The \pst@object macro will assign the optional parameter to the \pst@par macro. The code above is essentially the same as the following code, which lacks only management of the * convention: 1 \setkeys{psset}{...}% Assignment of global parameters 2 3 4 5 \def\PstXxxx{% % Test for optional parameters \@ifnextchar[{\PstXxxx@i}{\PstXxxx@i[]}} 6 7 8 9 10 11 \def\PstXxxx@i[#1]{{% Two braces, because parameter % assignments must be local \setkeys{psset}{#1}% Assignment of local parameters % ... }} Take special care with naming conventions and try to choose a consistent naming scheme! As in the next examples, a good programming practice is to start the names of all the macros and parameters relative to the same subject with a common prefix. Additionally, it is good practive to use the @ character in the names of macros which are not intended for direct access by users. 63 Usage Most often, we need to define integer, real, string, boolean, length or coordinate optional parameters. TEX registers are a scarce resource. Care should always be taken to avoid using a register to store a value if it can be stored in a macro instead. Integer, real, string, and length parameters, aside from some exceptional cases, can be stored in macros. When computations must be done on integer or dimension parameters which are stored in macros, the macros can be evaluated and the values assigned to temporary count or dimension registers. PSTricks provides six temporary count registers (\pst@cnta,. . . ,\pst@cnth) and six temporary dimension registers (\pst@dima,. . . ,\pst@dimh) for this purpose. Computations can then be carried out using the temporary registers. Since PSTricks also uses these temporary registers to carry out some of its internal computations, care Writing high-level macros: Usage 164 must be taken to avoid using temporary registers whose values might be altered the particular PSTricks macros which are used. There are many examples in the code which follows in this section and in the PSTricks code itself of the use of macros for storing integer and real values and temporary registers for manipulating these values. 63.1 Integer parameters For integer parameters, use the \pst@getint macro to assign the value to a personal macro. Do not define new TEX counters, which are a scare resource. See the examples below and the PSTricks code itself for more details. \define@key{psset}{Integer}{\pst@getint{#1}{\PstXxxx@Integer}} 1 Here is an example which prints a partial multiplication table. 1 2 3 4 5 % “Start”, “End” and “Value” parameters \define@key{psset}{Start}{\pst@getint{#1}{\MultTable@Start}} \define@key{psset}{End}{\pst@getint{#1}{\MultTable@End}} \define@key{psset}{Value}{\pst@getint{#1}{\MultTable@Value}} \setkeys{psset}{Start=1,End=5,Value=2}% Default values 6 7 8 % Main macro for “multiplication table” object \def\MultTable{\def\pst@par{}\pst@object{MultTable}} 9 10 11 12 13 14 15 16 17 18 19 \def\MultTable@i{{% \use@par% Assignment of local parameters \pst@cnth=\MultTable@End \advance\pst@cnth-\MultTable@Start \advance\pst@cnth\@ne \multido{\iValue=\MultTable@Start+\@ne}{\pst@cnth}{% \pst@cntg=\iValue \multiply\pst@cntg\MultTable@Value \iValue$\times$\MultTable@Value = \the\pst@cntg \ifnum\multidocount=\pst@cnth\else; \fi}}} 20 21 \MultTable 22 23 \MultTable[Value=9] 24 25 \setkeys{psset}{Value=6} 26 27 \MultTable[Start=6,End=11] 28 29 \MultTable[Start=19742,End=19742] Writing high-level macros: Usage 165 1×2 = 2; 2×2 = 4; 3×2 = 6; 4×2 = 8; 5×2 = 10 1×9 = 9; 2×9 = 18; 3×9 = 27; 4×9 = 36; 5×9 = 45 6×6 = 36; 7×6 = 42; 8×6 = 48; 9×6 = 54; 10×6 = 60; 11×6 = 66 19742×6 = 118452 We can also handle a special behavior with the * convention. Here, the result of the multiplication is put in a colored circle. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 \def\MultTable@i{{% \use@par% Assignment of local parameters \pst@cnth=\MultTable@End \advance\pst@cnth-\MultTable@Start \advance\pst@cnth\@ne \multido{\iValue=\MultTable@Start+\@ne}{\pst@cnth}{% \pst@cntg=\iValue \multiply\pst@cntg\MultTable@Value \iValue$\times$\MultTable@Value = \if@star {\pscirclebox*[fillstyle=solid,fillcolor=red,framesep=0.02]{% \textcolor{yellow}{\the\pst@cntg}}}% \else \the\pst@cntg \fi \ifnum\multidocount=\pst@cnth\else; \fi}}} 17 18 \MultTable[Value=13,Start=7,End=10] 19 20 \MultTable*[Value=13,Start=7,End=10] 7×13 = 91; 8×13 = 104; 9×13 = 117; 10×13 = 130 7×13 = 91 ; 8×13 = 104 ; 9×13 = 117 ; 10×13 = 130 63.2 Real parameters real parameters (used to define scales, ratios, etc.) and dimension parameters should be stored in macros in order to avoid consuming scarce resources. See the examples below and the PSTricks code itself for more details. So, define a real value by: 1 \define@key{psset}{Real}{\pst@checknum{#1}{\PstXxxx@Real}} if this will be “truly” a real, as the \pst@checknum macro allow in supplement to check that the number is correctly formatted. Writing high-level macros: Usage 166 Lengths are a special case. They can be real values, in which case the current unit will be used, or they can be dimensions, with a unit specified. The \pst@getlength macro allow to scale the “real” values with the current unit. The result will be given in TEX points, without the pt unit, so take care to add it (it is better to use the \p@ macro for that) each time you will use this variable. 1 2 \define@key{psset}{Length}{% \pst@getlength{#1}{\PstXxxx@Length}} Nevertheless, take care to the pitfall that with \pst@getlengththe values are scaled at assignation. The line \PstXxxx[unit=0.2,Length=1] will use a length of 2mm (if the current unit was of 1cm), as expected. But the construction 1 2 3 \setkeys{psset}{Length=3} ... \PstXxxx[unit=0.2] will use a length of 1cm, as it assignemt as been done before. So, if such order of assignement is expected, it it better to define the length parameter as a real value, and to use internally the \pssetlength macro. It does the same thing than \pst@getlength, but on dimensions, not macros. And the \psaddtolength macro allow to add a value to such dimension, scaled too by the current unit. Angles are another special case. Angle parameters are real values, but they must be defined with the \pst@getangle macro so that “special” definitions (based on PostScript computations, for example, as in Section 54) can be used. 1 \define@key{psset}{Angle}{\pst@getangle{#1}{\PstXxxx@Angle}} Here is an example which draws a bar and a wall one unit to the right, with the length of the bar being a parameter. It can either take an integer real or length value (we can verify on the picture that when we use an integer or real value, the current unit is taken in account, as for all PSTricks dimensions. This is not true if we use a value explicitely associated to a unit length, as expected.) Note also the usage of the \psaddtolength macro to increase or decrease a length, which allows it to be scaled according to the current unit. Writing high-level macros: Usage 167 1 2 3 % “Length” parameter: length of the bar \define@key{psset}{Length}{\edef\PstBar@Length{#1}} \setkeys{psset}{Length=3}% Default value Wall 4 5 6 % Main macro for “bar” object \def\PstBar{\def\pst@par{}\pst@object{PstBar}} 7 8 9 10 Wall 11 12 13 14 15 16 17 Wall 18 19 20 \def\PstBar@i{{% \setkeys{psset}{framesep=1pt}% \use@par% Assignment of local parameters \psframe(\PstBar@Length,\@ne) \pssetlength{\pst@dima}{\PstBar@Length}% \psaddtolength{\pst@dima}{\@ne}% \psline[linewidth=0.08](\pst@dima,-0.5)(\pst@dima,1.5) \pst@dimb=\pst@dima \psaddtolength{\pst@dimb}{0.5}% \psframe[linestyle=none,fillstyle=hlines] (\pst@dima,-0.5)(\pst@dimb,1.5) \psaddtolength{\pst@dima}{0.25}% \rput*{90}(\pst@dima,0.5){Wall}}} 21 22 23 24 \rput(-2,3){\PstBar[Length=4.5]} \rput(-2,0){\PstBar[Length=1.65cm]} \rput(-2,-3){\PstBar[unit=1.5,Length=4cm]} 63.3 String parameters String parameters should also be stored as personal macros using either: 1 \define@key{psset}{String}{\edef\PstXxxx@String{#1}} or 1 \define@key{psset}{String}{\def\PstXxxx@String{#1}} If the value of #1 can be evaluated correctly at the time of definition, the \edef alternative should be used, because it avoid side effects due to later expansion, as in the following case where the \PstObject called in the last line will have OLD for value of the String parameter if \edef is used, which is the original content at the time of the assignment of the parameter, rather than NEW which will be the result if \def is used. 1 2 3 4 5 \def\MyString{OLD} \setkeys{psset}{String=\MyString} ... \def\MyString{NEW} \PstObject Writing high-level macros: Usage 168 In some cases, however, expansion at the point of definition is not desired and the \def alternative must be used. One typical case is when a font specification is in the definition, such as String={\Large text}, which cannot be evaluated at the point of definition. If the string is used to define a specific macro, a powerful solution is to dynamically define the macro name according to the value of the string parameter given (for such an example, see how the Form parameter of the test tube in Section 64.2 is defined): 1 2 \define@key{psset}{String}{% \def\PstXxxx@Macro{\@nameuse{PstXxxx@Macro@#1}}} 3 4 \setkeys{psset}{String=BBBB}% Default value 5 6 7 8 9 % Macros for possible values \def\PstXxxx@Macro@AAAA{...} \def\PstXxxx@Macro@BBBB{...} \def\PstXxxx@Macro@CCCC{...} 10 11 \def\PstXxxx{\def\pst@par{}\pst@object{PstXxxx}} 12 13 14 15 16 17 \def\PstXxxx@i{{% % ... \expandafter\PstXxxx@Macro % ... }} 1 2 Support 3 % “Label” parameter: label to legend the support \define@key{psset}{Label}{\def\PstBar@Label{#1}} \setkeys{psset}{Label=Wall}% Default value 4 5 6 7 \def\PstBar@i{{% % ... \rput*{90}(\pst@dima,0.5){\PstBar@Label}}} 8 9 \rput(-2,0){\PstBar[Label=\textcolor{red}{Support}]} 63.4 Boolean parameters Boolean parameters should be defined using the \newif TEX macro. Using the associated \PstXxxx@Booleantrue and \PstXxxx@Booleanfalse macros, the parameter can be set to true or false. The value inside square brackets below is the default setting of the parameter, set when the parameter is defined (so, Boolean would be equivalent to Boolean=true). This is optional, but obviously the usual convention will be to have true as the Writing high-level macros: Usage 169 default value, and not false, which would be the case if we do not explicitly define the default value to true. \newif\ifPstXxxx@Boolean \define@key{psset}{Boolean}[true]{% \@nameuse{PstXxxx@Boolean#1}} 1 2 3 1 2 3 4 % “ThreeD” parameter: to emulate or not a 3d bar \newif\ifPstBar@ThreeD \define@key{psset}{ThreeD}[true]{% \@nameuse{PstBar@ThreeD#1}} 5 6 \setkeys{psset}{ThreeD=false}% Default value 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 \def\PstBar@i{{% \setkeys{psset}{framesep=1pt}% \use@par% Assignment of local parameters \psframe(\PstBar@Length,\@ne) \pssetlength{\pst@dima}{\PstBar@Length}% \ifPstBar@ThreeD \pst@dimb=\pst@dima \psaddtolength{\pst@dimb}{0.3}% \psline(0,1)(0.3,1.3)(\pst@dimb,1.3) (\pst@dimb,0.3)(\PstBar@Length,0) \psline(\PstBar@Length,1)(\pst@dimb,1.3) \fi \psaddtolength{\pst@dima}{\@ne}% \psline[linewidth=0.08](\pst@dima,-0.5)(\pst@dima,1.5) \pst@dimb=\pst@dima \psaddtolength{\pst@dimb}{0.5}% \psframe[linestyle=none,fillstyle=hlines] (\pst@dima,-0.5)(\pst@dimb,1.5) \psaddtolength{\pst@dima}{0.25}% \rput*{90}(\pst@dima,0.5){\PstBar@Label}}} 28 Wall 31 \rput(-7.5,0){\PstBar} \rput(-2.5,0){\PstBar[ThreeD=true]} \rput(3,0){\PstBar[unit=1.5,Length=1,Label=Support,ThreeD=true]} Support 30 Wall 29 63.5 Coordinate arguments A coordinate is a special kind of argument. We use the term argument rather than the term parameter because coordinates do not use the ‘pst- Writing high-level macros: Usage 170 key’ package and are not usually handled by the methods described above. Nevertheless, as they are of common use, we will explain the main ways to manage them. Two features are important: first, if possible, not only cartesian coordinates, but also all the special forms defined (see the Section 54) should be managed; and second, it is often necessary to manage unknown numbers of coordinates, of the (x0 ,y0 )(x1,y1)… (xn,yn) form. We need to distinguish low-level (also called basic) objects using coordinates from high-level ones. You will probably not need to define new basic objects, as the existing ones cover the great majority of the foreseeing needs. Nevertheless, we will briefly explain here how to build them, using the examples (not very useful in practical life!) of randomized lines, polygons and dots.50 Low-level objects Four special kinds of macros are available to help build low-level objects, which allow management of open (two kinds of them, one with and one without optional arrows), closed and special objects. The four corresponding pair of macros are: 1 2 3 4 \begin@OpenObj ... \end@OpenObj \begin@AltOpenObj ... \end@OpenObj \begin@ClosedObj ... \end@ClosedObj \begin@SpecialObj ... \end@SpecialObj We will give examples for the first, third and fourth ones (the second is obviousy very similar to the first one.) First we define a real value parameter which is used to control the extent of the randomness effect: 1 2 3 % Random coefficient parameter \define@key{psset}{RandomCoefficient}{% \pst@checknum{#1}{\PstRandomLine@RandomCoefficient}} 4 5 \setkeys{psset}{RandomCoefficient=1}% Default value Then we define a macro \PstRandomLine which will be an open basic object, with possible arrows, that will be adapted from the \psline macro. After dealing with the optional parameters, as usual, the \PstRandomLine@i macro is called. The management of the optional arrows is done by the 50 For complementary information, see in [79] the detailed explanation of how the \pspolygon macro is defined. Writing high-level macros: Usage 171 \pst@getarrows macro. Then the \begin@OpenObj macro initializes various things for this kind of object and the \pst@getcoors macro allows man- agement of a sequence of coordinates of unknown length, which could simply be cartesian but also can be any kind of the special coordinates, accumulating their PostScript definitions in an internal variable (\pst@coors.) The \PstRandomLine@ii macro stores the PostScript code which defines the Lineto PostScript operator which will join two points (in the \psline macro, it is simply the standard lineto operator, but if the linearc parameter has been set, it will be a special form of an arc). Then the \tx@Line macro is inserted, which calls the Line PostScript operator, defined in the PSTricks header file pstricks.pro, which will do the real work of looping through the points and joining them. Finally, to finish the work, the macro \end@OpenObj is called, which carries out various tasks like managing the border, doubleline and shadow effects, visualizing the points themselves if the showpoints parameter has been set to true, etc. and writing the accumulated PostScript code. The main task of the \PstRandomLine@iii macro is to define the Lineto PostScript operator which will be used to join the points. Here, we simply define it as lineto, but before applying this operator we add a random noise to both the horizontal and vertical coordinates (note that we will not do this for the first and last coordinates.) For this, we add to each component a value called RandomValue, computed by generating an integer random number between 1 and 231 –1, mapping it to the range 0 and 100 by applying the 101 mod modulo operator, then to a real number between 0 and 1 by using the 100 div operator, then to a real number between -0.5 and 0.5 by subtracting 0.5 by the 0.5 sub operator, then multiplying it by the current value of the unit parameter, then multiplying it by the RandomCoefficient value that we have defined. 1 \def\PstRandomLine{\pst@object{PstRandomLine}} 2 3 4 5 6 \def\PstRandomLine@i{% \pst@getarrows{% \begin@OpenObj \pst@getcoors[\PstRandomLine@ii}} 7 8 9 10 \def\PstRandomLine@ii{% \addto@pscode{\pst@cp \PstRandomLine@iii \tx@Line}% \end@OpenObj} 11 12 13 14 15 16 17 \def\PstRandomLine@iii{% /RandomValue {rand 100 mod 100 div 0.5 sub \pst@number{\psunit} mul \PstRandomLine@RandomCoefficient\space mul} def /Lineto {exch RandomValue add exch RandomValue add lineto}def \ifshowpoints true \else false \fi} 18 19 \pspicture(7,6)\psgrid[subgriddiv=0] Writing high-level macros: Usage 172 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 \PstRandomLine[showpoints=true,dotscale=2](1,1)(2,4)(5,5)(6,2) \PstRandomLine[linestyle=dashed](1,1)(2,4)(5,5)(6,2) \PstRandomLine[linestyle=dotted](1,1)(2,4)(5,5)(6,2) \endpspicture \hfill \pspicture(7,6)\psgrid[subgriddiv=0] \SpecialCoor \pnode(5,2){Node} \PstRandomLine[arrowscale=3,showpoints=true,dotscale=2] {->}(2,4)(3,3)(Node)(6,5) \PstRandomLine[linestyle=dashed,RandomCoefficient=2] (2,4)(3,3)(Node)(6,5) \PstRandomLine[linestyle=dotted,RandomCoefficient=0.5] (2,4)(3,3)(Node)(6,5) \PstRandomLine[xunit=0.5,linecolor=red,showpoints=true, dotstyle=square,dotscale=2, RandomCoefficient=3](2,4)(3,3)(Node)(6,5) \endpspicture 6 6 b 5 b 4 rs 5 rs 4 3 b srb 2 b 1 b rs 3 2 b 1 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Closed objects will be illustrated by a variation of the \pspolygon nmacro. After dealing with the optional parameters, the \PstRandomPolygon@i macro initiates the closed object by calling the \begin@ClosedObj macro, then reading and accumulating the coordinates by the \pst@getcoors macro as in the preceding randomized line example. Then the \PstRandomPolygon@ii macro calls the Polygon PostScript operator (using the \tx@Polygon TEX macro), which is defined in the PostScript header file pstricks.pro. It uses a Lineto macro, which will take to be the same as in the previous example, using the macro \PstRandomLine@iii. To finish, the type of the line is set by the linetype parameter as a “closed curve with no particular symmetry”, and finally the \end@ClosedObj macro is called. 1 \def\PstRandomPolygon{\pst@object{PstRandomPolygon}} 2 3 4 \def\PstRandomPolygon@i{% \begin@ClosedObj Writing high-level macros: Usage 173 5 6 \def\pst@cp{}% \pst@getcoors[\PstRandomPolygon@ii} 7 8 9 10 11 \def\PstRandomPolygon@ii{% \addto@pscode{\PstRandomLine@iii \tx@Polygon}% \def\pst@linetype{1}% \end@ClosedObj} 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 \pspicture(7,6)\psgrid[subgriddiv=0] \pspolygon[linecolor=cyan,showpoints=true,dotscale=2] (1,1)(2,4)(5,5)(6,2) \PstRandomPolygon(1,1)(2,4)(5,5)(6,2) \PstRandomPolygon[linestyle=dashed](1,1)(2,4)(5,5)(6,2) \PstRandomPolygon[linestyle=dotted](1,1)(2,4)(5,5)(6,2) \endpspicture \hfill \pspicture(7,6)\psgrid[subgriddiv=0] \SpecialCoor \pnode(5,2){Node} \PstRandomPolygon[showpoints=true,dotscale=2](2,4)(2,2)(Node) (6,5) \PstRandomPolygon[linestyle=dashed,RandomCoefficient=2] (2,4)(2,2)(Node)(6,5) \PstRandomPolygon[linestyle=dotted,RandomCoefficient=0.5] (2,4)(2,2)(Node)(6,5) \PstRandomPolygon[xunit=0.5,linecolor=red,showpoints=true, dotstyle=square,dotscale=2, RandomCoefficient=3](2,4)(2,2)(Node)(6,5) \endpspicture 6 6 b 5 b 4 4 3 b rs 5 rs b rs b 1 2 3 b 2 2 b 1 rsb 1 0 0 0 1 2 3 4 5 6 7 0 3 4 5 6 7 Special objects will be illustrated by a variation of the \psdots macro. After dealing with the optional parameters, the \PstRandomDots@i macro initiates the special object by calling the \begin@SpecialObj macro, then reading and accumulating the coordinates by the \pst@getcoors macro, as in the randomized line example above. Then the \PstRandomDots@ii macro calls the NArray PostScript operator (using the \tx@NArray TEX macro), Writing high-level macros: Usage 174 which is defined in the PostScript header file pstricks.pro. It handles the array of coordinates by applying the \PstRandomDots@iii macro, which specifies the style and size to use for the dots and calls the Dot PostScript operator, also defined in the header file pstricks.pro. As before, we just add a random noise to the coordinates before calling the macro which typesets the dot. Finally, the \end@SpecialObj macro is called. 1 \def\PstRandomDots{\pst@object{PstRandomDots}} 2 3 4 5 \def\PstRandomDots@i{% \begin@SpecialObj \pst@getcoors[\PstRandomDots@ii} 6 7 8 9 \def\PstRandomDots@ii{% \addto@pscode{false \tx@NArray \PstRandomDots@iii}% \end@SpecialObj} 10 11 12 13 14 15 16 17 18 19 \def\PstRandomDots@iii{% \psk@dotsize \@nameuse{psds@\psk@dotstyle} newpath /RandomValue {rand 10 mod 10 div 0.5 sub \pst@number{\psunit} mul \PstRandomLine@RandomCoefficient\space mul} def n { transform floor 0.5 add exch floor 0.5 add exch itransform exch RandomValue add exch RandomValue add Dot } repeat} 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 \pspicture(7,6)\psgrid[subgriddiv=0] \psset{dotscale=2}% \psdots(1,1)(2,4)(5,5)(6,2) \PstRandomDots[dotstyle=triangle](1,1)(2,4)(5,5)(6,2) \PstRandomDots[dotstyle=square](1,1)(2,4)(5,5)(6,2) \PstRandomDots[dotstyle=diamond](1,1)(2,4)(5,5)(6,2) \endpspicture \hfill \pspicture(7,6)\psgrid[subgriddiv=0] \SpecialCoor \psset{dotscale=2}% \pnode(4,2){Node} \psdots(1,4)(3,3)(Node)(6,5) \PstRandomDots[dotstyle=triangle](1,4)(3,3)(Node)(6,5) \PstRandomDots[dotstyle=square,RandomCoefficient=2] (1,4)(3,3)(Node)(6,5) \PstRandomDots[dotstyle=diamond,RandomCoefficient=0.5] (1,4)(3,3)(Node)(6,5) \endpspicture Writing high-level macros: Usage 175 6 6 d rs l tb u 5 5 ursb t d l 4 3 4 lb d rs u t 2 t u 1 rs 3 rl sb d rs t bu d l ul t db 2 sr db u l t 1 0 t bl du rs 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 High-level objects New high-level objects, which can also use coordinates, are much more frequently needed than new low-level objects in new developments. The first illustration is a high-level object used to draw a sequence of dots, each having a different scale. Of course, we can use a list of \psdot[scale=?](x0,y0) macros, but if we want to have a macro to handle such a case in one call, we must do something like the \PstDotsScaled macro. After dealing with the optional parameters, the \PstDotsScaled@i macro creates a group, to ensure that the change of parameters will be local to the macro, activates the modified parameters, then calls the \PstDotsScaled@GetCoordinate macro without argument. This one will read the two next arguments, one as a coordinate inside parentheses and one as a scale value inside brackets. Here we have to avoid reading two values for each coordinate, as this would prohibit the usage of special ones and prevent managing the scaling factor as the third value of the same set. So, it is clear that a syntax like: \PstDotsScaled(x0,y0,1.5)(x1,y1,2)(x2,y2,5)(x3,y3,2.8) 1 which could seem easier to read, must be avoided. The \@ifnextchar macro allows determing if there is another coordinate to manage by testing if the next character to read is an open parenthesis. If it is, the \PstDotsScaled@GetCoordinate macro is called again, otherwise the opened group is closed. This is a simple and powerful mechanism to deal with an unknown number of arguments. 1 \def\PstDotsScaled{\def\pst@par{}\pst@object{PstDotsScaled}} 2 3 4 5 6 \def\PstDotsScaled@i{% \begingroup \use@par% Assignment of local parameters \PstDotsScaled@GetCoordinate} Writing high-level macros: Usage 176 7 8 9 10 \def\PstDotsScaled@GetCoordinate(#1)#2{% \psdot[dotscale=#2](#1) \@ifnextchar({\PstDotsScaled@GetCoordinate}{\endgroup}} 11 12 13 14 15 16 17 18 19 \pspicture(5,3)\psgrid[subgriddiv=0] \SpecialCoor \pnode(2.5,2.5){Node} % “rand 5 mod” return an integer between 0 and 5 and % “rand 3 mod” return an integer between 0 and 3 \PstDotsScaled(0.5,0.5){1.5}(Node){2} (! rand 5 mod rand 3 mod){5}(5;18){2.8} \endpspicture 3 b 2 b 1 b 0 0 1 2 3 b 4 5 In the same way, we will now define a macro to draw a series of dots and an error bar for each of them, using two additional parameters. 1 2 3 % Style of error bars parameter \define@key{psset}{StyleBars}{% \edef\PstDataWithErrorBars@StyleBars{#1}} 4 5 6 \newpsstyle{StyleBars@Default}{arrows=|-|} \setkeys{psset}{StyleBars=StyleBars@Default}% Default value 7 8 9 \def\PstDataWithErrorBars{% \def\pst@par{}\pst@object{PstDataWithErrorBars}} 10 11 12 13 14 \def\PstDataWithErrorBars@i{% \begingroup \use@par% Assignment of local parameters \PstDataWithErrorBars@GetCoordinate} 15 16 17 18 \def\PstDataWithErrorBars@GetCoordinate(#1,#2)#3#4{% \PstDataWithErrorBars@DoCoordinate(#1,#2){#3}{#4}% \@ifnextchar({\PstDataWithErrorBars@GetCoordinate}{\endgroup}} 19 20 21 22 23 \def\PstDataWithErrorBars@DoCoordinate(#1,#2)#3#4{% \psline[style=\PstDataWithErrorBars@StyleBars] (! #1 #2 #3 add)(! #1 #2 #4 add) \psdot(#1,#2)} 24 25 \SpecialCoor 26 Writing high-level macros: Usage 177 \psset{dotscale=1.5}% 27 28 \pspicture(5,5)\psgrid[subgriddiv=0] \PstDataWithErrorBars(0.5,0.5){-0.2}{0.2}(1.2,1){0}{0.5} (2.7,2.4){-1.2}{0.3}(3.5,1){-0.5}{0.1}(4.3,3.7){-0.4}{0.8} \endpspicture \hfill % \newpsstyle{MyStyleBars}{linecolor=red,arrows=[-],arrowscale=1.5} \psset{xunit=0.5,yunit=0.8}% \pspicture(5,5)\psgrid[subgriddiv=0] \PstDataWithErrorBars[dotstyle=o,StyleBars=MyStyleBars] (0.5,0.5){-0.2}{0.2}(1.2,1){0}{0.5} (2.7,2.4){-1.2}{0.3}(3.5,1){-0.5}{0.1}(4.3,3.7){-0.4}{0.8} \endpspicture 29 30 31 32 33 34 35 36 37 38 39 40 41 5 4 5 b 4 3 b 2 bc 3 c b 2 b 1 b 1 b 0 0 0 1 2 3 4 5 c b c b bc 0 1 2 3 4 5 Here, we deal with each coordinate as two parameters separated by a comma, so this will work only for cartesian coordinates. To manage special ones, we must of course use only one argument, then call the \pst@getcoor macro which will return the two coordinates of the point, even if it is a node or the result of a PostScript computation. But we must rescale these values at the TEX level, as the error values are defined in the TEX world unit system and the result of \pst@getcoor at the PostScript one. This is why we divide the horizontal coordinate by \psxunit and the vertical one by \psyunit. And to avoid computing them twice, we store these values in PostScript variables, using the \pst@Verb macro. 1 2 3 \def\PstDataWithErrorBars@GetCoordinate(#1)#2#3{% \PstDataWithErrorBars@DoCoordinate(#1){#2}{#3}% \@ifnextchar({\PstDataWithErrorBars@GetCoordinate}{\endgroup}} 4 5 6 7 8 9 10 \def\PstDataWithErrorBars@DoCoordinate(#1)#2#3{% \pst@getcoor{#1}{\pst@temph}% \pst@Verb{% /XCoor {\pst@temph pop \pst@number{\psxunit} div} def /YCoor {\pst@temph exch pop \pst@number{\psyunit} div} def} \psline[style=\PstDataWithErrorBars@StyleBars] Writing high-level macros: Usage 178 (! XCoor YCoor #2 add)(! XCoor YCoor #3 add) \psdot(#1)} 11 12 13 \SpecialCoor 14 15 \psset{dotscale=1.5}% 16 17 \pspicture(5,5)\psgrid[subgriddiv=0] \pnode(2.7,2.4){Node} \PstDataWithErrorBars(0.5,0.5){-0.2}{0.2}(1.2,1){0}{0.5} (Node){-1.2}{0.3}(! 2 1.5 add 1){-0.5}{0.1} (5.3;32){-0.4}{0.8} \endpspicture \hfill % \newpsstyle{MyStyleBars}{linecolor=red,arrows=[-],arrowscale=1.5} \psset{xunit=0.5,yunit=0.8}% \pspicture(5,5)\psgrid[subgriddiv=0] \pnode(2.7,2.4){Node} \PstDataWithErrorBars[dotstyle=o,StyleBars=MyStyleBars] (0.5,0.5){-0.2}{0.2}(1.2,1){0}{0.5}(Node){-1.2}{0.3} (! 2 1.5 add 1){-0.5}{0.1} (! 5.3 32 cos mul 5.3 32 sin mul){-0.4}{0.8} \endpspicture 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 5 4 5 4 3 b b 2 3 b 1 b 1 b 0 0 0 1 2 3 4 5 bc c b 2 c b c b bc 0 1 2 3 4 5 Sometimes, we need to plot data produced by external programs. There are several ways to handle this. One way is to require that these files be written with some specific TEX instructions, then use the \input macro or directly code the input/output operations using the appropriate TEX macros. An easier way uses raw data files (the err-bars.dat file that we will use in the next example): 1 2 3 4 5 0.7 2.6 3.2 4.1 4.6 4.1 -0.7 0.6 3.4 -2.1 0.2 2 -1.2 0 4.6 -0.3 0.2 1.4 -0.5 1.8 Writing high-level macros: Usage 179 or (0.7, (2.6, (3.2, (4.1, (4.6, 1 2 3 4 5 4.1, -0.7, 0.6) 3.4, -2.1, 0.2) 2, -1.2, 0) 4.6, -0.3, 0.2) 1.4, -0.5, 1.8) and use the \readdata macro (see the Section 11) to store them in a personal macro (note that only cartesian coordinates can be used in this context.) This will produce a macro with the values separated by a D symbol. We can either use this macro like it as a PostScript argument, defining the D operator to do what we want with the coordinates (this is how the plotting commands like \psplot work), or parse this macro to extract the coordinates. This is what we will do in the next example. 1 2 \def\PstDataFileWithErrorBars{% \def\pst@par{}\pst@object{PstDataFileWithErrorBars}} 3 4 5 6 7 8 9 10 \def\PstDataFileWithErrorBars@i#1{% \begingroup \use@par% Assignment of local parameters % Read the data from the file and put them in a macro \readdata{\PstDataFileWithErrorBars@Data}{#1}% \PstDataFileWithErrorBars@GetCoordinate{% \PstDataFileWithErrorBars@Data}} 11 12 13 \def\PstDataFileWithErrorBars@GetCoordinate#1{% \expandafter\PstDataFileWithErrorBars@GetCoordinate@i#1 } 14 15 16 \def\PstDataFileWithErrorBars@GetCoordinate@i#1{% \PstDataFileWithErrorBars@GetCoordinate@ii#1} 17 18 19 20 21 22 \def\PstDataFileWithErrorBars@GetCoordinate@ii% #1 #2 #3 #4 #5 #6 #7 #8 {% \PstDataFileWithErrorBars@DoCoordinate(#2,#4){#6}{#8}% \@ifnextchar D{\PstDataFileWithErrorBars@GetCoordinate@ii}% {\endgroup}} 23 24 25 \let\PstDataFileWithErrorBars@DoCoordinate \PstDataWithErrorBars@DoCoordinate 26 27 \psset{dotscale=1.5}% 28 29 30 31 32 33 34 \pspicture(5,5)\psgrid[subgriddiv=0] \PstDataFileWithErrorBars[dotstyle=diamond]{err-bars.dat} \endpspicture \hfill % \newpsstyle{MyStyleBars}{linecolor=cyan,arrows=(-),arrowscale=1.5} Writing high-level macros: Usage 180 \psset{xunit=0.8,yunit=0.5} \pspicture(5,5)\psgrid[subgriddiv=0] \PstDataFileWithErrorBars[StyleBars=MyStyleBars]{err-bars.dat} \endpspicture 35 36 37 38 5 d l d l 4 d l 3 5 4 3 2 1 0 d l 2 d l 1 0 0 1 2 3 4 5 b b b b 0 1 2 3 b 4 We finish this section with a more sophisticated example, which draws a general mesh based on triangles, as used in finite elements numerical methods, with an automatic computation of the barycenters of the triangles to position their numbers. We want of course to be as generic as possible, just defining here the points of the mesh (with any number of them, and possibly defined as special coordinates), then the list of the triplets of these points which form the triangles. Note that we store the definition of the points as macros, whose names are suffixed by the rank of the point in the list of coordinates. We do not need here to store them as PSTricks nodes, which would make the resulting PostScript code larger and slower without any benefit. 1 2 3 \def\PstMeshNodes{% \pst@cnth=\z@ \PstMeshNodes@GetCoordinate} 4 5 6 7 8 \def\PstMeshNodes@GetCoordinate(#1){% \advance\pst@cnth\@ne \@namedef{MeshNode\the\pst@cnth}{#1}% \@ifnextchar({\PstMeshNodes@GetCoordinate}{}} 9 10 \def\PstMeshTriangles{\def\pst@par{}\pst@object{PstMeshTriangles}} 11 12 13 14 15 16 17 18 19 \def\PstMeshTriangles@i{% \begingroup \use@par% Assignment of local parameters % PostScript macro to help to compute the barycenter % of the three points \pst@Verb{/ForBarycenter {add 2 div exch dup /X3 ED sub 4 1 roll add 2 div neg exch dup /X6 ED Writing high-level macros: Usage 181 5 20 21 add div dup X6 mul X3 add} def}% \PstMeshTriangles@GetTriangle} 22 23 24 25 26 27 28 29 30 31 32 33 \def\PstMeshTriangles@GetTriangle(#1,#2,#3)#4{% % #1, #2, #3 : first, second and third point numbers % #4 : label to print on the barycenter of this triangle \pspolygon(\@nameuse{MeshNode#1})(\@nameuse{MeshNode#2}) (\@nameuse{MeshNode#3}) \PstMeshPrintNode{\@nameuse{MeshNode#1}}{#1}% \PstMeshPrintNode{\@nameuse{MeshNode#2}}{#2}% \PstMeshPrintNode{\@nameuse{MeshNode#3}}{#3}% \PstMeshTrianglesLabelOnBarycenter{\@nameuse{MeshNode#1}} {\@nameuse{MeshNode#2}}{\@nameuse{MeshNode#3}}{#4}% \@ifnextchar({\PstMeshTriangles@GetTriangle}{\endgroup}} 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 \def\PstMeshTrianglesLabelOnBarycenter#1#2#3#4{% % #1 : coordinates of the first point (A) of the triangle % #2 : coordinates of the second point (B) of the triangle % #3 : coordinates of the third point (C) of the triangle % #4 : label to print on the barycenter \pst@getcoor{#1}{\pst@tempa}% \pst@getcoor{#2}{\pst@tempb}% \pst@getcoor{#3}{\pst@tempc}% \rput(! % To retrieve the X and Y coordinates of the three points \pst@tempa \pst@number{\psyunit} div /YA ED \pst@number{\psxunit} div /XA ED \pst@tempb \pst@number{\psyunit} div /YB ED \pst@number{\psxunit} div /XB ED \pst@tempc \pst@number{\psyunit} div /YC ED \pst@number{\psxunit} div /XC ED XA XB add 2 div XC eq {XA XC XB YA YC YB ForBarycenter} {XC XB XA YC YB YA ForBarycenter} ifelse /ZB ED /ZA ED XA XC add 2 div XB eq {XA XC XB YA YC YB ForBarycenter} {XB XC XA YB YC YA ForBarycenter} ifelse /ZD ED /ZC ED % X = (ZB - ZD) / (ZA - ZC) and Y = ZD - ZC * X ZB ZD sub ZA ZC sub div dup ZC mul neg ZD add) {\PstMeshPrintLabel{#4}}} 61 62 63 % Default format to print the mesh nodes \def\PstMeshPrintNode#1#2{\rput*(#1){\bf\scalebox{2}{#2}}} 64 65 66 % Default format to print the mesh labels on the barycenters \def\PstMeshPrintLabel#1{\it\scalebox{2}{#1}} 67 68 69 % Usage examples % ============= 70 71 72 % Definition of the nodes of the mesh \PstMeshNodes(0,9)(3.4,5.8)(3,9)(0,6)(0,3)(1.5,2.8)(0,0)(3,0) Writing high-level macros: Usage 182 (6,9)(6.6,4.3)(9,9)(9,6)(4.1,2.3)(6,0)(9,0)(9,3) 73 74 75 76 77 78 79 80 % To draw the mesh \newcommand{\PstMeshTrianglesDraw}[1][]{% \PstMeshTriangles[#1](1,2,3){1}(1,2,4){2}(2,4,6){3}(4,5,6){4}(5,6,7){5} (6,7,8){6}(6,8,13){7}(2,6,13){8}(8,13,14){9}(10,13,14){10} (10,14,15){11}(10,15,16){12}(2,10,13){13}(10,12,16){14} (10,11,12){15}(9,10,11){16}(2,9,10){17}(2,3,9){18}} 81 82 83 84 % New format for the label \renewcommand{\PstMeshPrintLabel}[1]{% \Large\textbf{\textcolor{cyan}{#1}}} 85 86 \PstMeshTrianglesDraw 3 1 9 11 18 1 16 2 15 17 4 2 3 5 14 8 6 5 13 12 10 7 6 7 10 13 4 12 16 11 9 8 Writing high-level macros: Usage 14 15 183 9 3 1 11 XVIII I 1 2 XVI II 3 2 4 XVII 5 XV III 4 6 7 6 IV VIII XIII 9 12 10 XIV 5 VII 13 11 12 16 X \makeatletter \renewcommand{\PstMeshPrintLabel}[1]{% \scriptsize\textbf{\textcolor{cyan}{\@Roman{#1}}}} \makeatother 13 XII 14 VI \renewcommand{\PstMeshPrintNode}[2]{% \rput(#1){% \pscirclebox[fillstyle=solid,fillcolor=yellow]{\textcolor{red}{#2}}}} 8 10 V % New definition of the nodes of the mesh \PstMeshNodes(0,12)(4,9)(2,12)(0,7)(0,4)(2,6)(0,0)(2,0) (5,12)(6,5)(8,12)(8,5)(4,3)(5,0)(8,0)(8,3) XI 15 % We use the mesh previously defined \PstMeshTrianglesDraw[xunit=0.5,yunit=0.65] IX 7 8 14 15 63.6 Generic template for a package A generic template for a new specialized package should have the following form:51 1 2 \def\FileVersion{1.2} \def\FileDate{2003/06/22} 3 4 5 6 % To identify the package when it will be loaded \message{‘pst-xxxx’ v\FileVersion, \FileDate\space (FirstName LastName)} 7 8 9 10 11 % To allow other packages to test if this one % was already loaded \csname PstXxxxLoaded\endcsname \let\PstXxxxLoaded\endinput 12 13 14 15 16 17 % Require of course the PSTricks package, % and perhaps other ones \ifx\PSTricksLoaded\endinput\else\input{pstricks}\fi %\ifx\PSTnodesLoaded\endinput\else\input{pst-node}\fi %\ifx\MultidoLoaded\endinput\else\input{multido}\fi 18 19 % David Carlisle interface to the ‘keyval’ package 51 For a short, but complete and pedagogically useful example, you can look at the commented source code of the ‘pst-li3d’ package [62], also described in Section 64.5, which allow to add a lighten effect to text and curves, or to the ‘pst-poly’ package [63],which is used to draw polygons. Writing high-level macros: Usage 184 20 \input{pst-key} 21 22 23 24 % Allow to use the @ character for all internal macros \edef\PstAtCode{\the\catcode‘\@} \catcode‘\@=11\relax 25 26 27 % Definition of the specific parameters % ============================= 28 29 30 % A parameter containing an integer value \define@key{psset}{Integer}{\pst@getint{#1}{\PstXxxx@Integer}} 31 32 33 % A parameter containing a real value \define@key{psset}{Real}{\pst@checknum{#1}{\PstXxxx@Real}} 34 35 36 % A parameter containing a string value \define@key{psset}{String}{\edef\PstXxxx@String{#1}} 37 38 39 40 41 % A parameter containing a boolean value \newif\ifPstXxxx@Boolean \define@key{psset}{Boolean}[true]{% \@nameuse{PstXxxx@Boolean#1}} 42 43 44 % Other parameters % ... 45 46 47 48 % Defaults values for these parameters % ============================== \setkeys{psset}{Integer=10,Real=123.456,String=,Boolean=false} 49 50 51 52 % The macro \PstXxxx, with or without optional parameters % ============================================== \def\PstXxxx{\def\pst@par{}\pst@object{PstXxxx}} 53 54 55 56 57 58 59 60 \def\PstXxxx{{% Two braces, because parameter % assignments must be local \use@par% Assignment of local parameters % The code itself, which can of course include calls % to auxiliary macros % ... }} 61 62 63 % Restore the definition of the @ character \catcode‘\@=\PstAtCode\relax 64 65 \endinput Writing high-level macros: Usage 185 64 Examples This section gives five examples which illustrate the major features of the ‘pst-key’ package and show how to use it to write high-level macros and packages. These examples are explained in step by step detail, trying to illustrate many different techniques which can be put to use by developers. 64.1 Basic example : cogged wheels First, a simple example to define “cogged wheels”. The crucial macro is first developed, than converted afterwards into a PSTricks object. 1 \SpecialCoor 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 \def\PstCoggedWheel#1#2{% % #1 = number of teeth (it must be a divisor of 360!) % #2 = height of the teeth, between 0 and 1 unit \pst@cntc=360 \divide\pst@cntc by #1 \pst@cntd=\pst@cntc \divide\pst@cntd\tw@ \pst@dimd=\psunit \pssetlength{\pst@dimc}{#2}% \advance\pst@dimd-\pst@dimc \pscustom{% \moveto(\pst@dimd;0) \multido{\iAngleA=\z@+\pst@cntc, \iAngleB=\pst@cntd+\pst@cntc, \iAngleC=\pst@cntc+\pst@cntc}{#1}{% \lineto(1;\iAngleA) \lineto(1;\iAngleB) \lineto(\pst@dimd;\iAngleB) \lineto(\pst@dimd;\iAngleC)}}} 22 23 24 25 1 2 3 \rput(-2,4){\PstCoggedWheel{9}{0.3}} \rput(-2,1){\PstCoggedWheel{9}{7mm}} \rput(-2,-3){\psset{unit=2,linecolor=red}\PstCoggedWheel{40}{0.1}} % “TeethNumber”: number of teeth (it must be a divisor of 360!) \define@key{psset}{TeethNumber}{% \pst@getint{#1}{\PstCoggedWheel@TeethNumber}} 4 5 6 7 % “TeethHeight”: height of the teeth, in current unit \define@key{psset}{TeethHeight}{% \edef\PstCoggedWheel@TeethHeight{#1}} 8 9 10 % Default parameters values \setkeys{psset}{TeethNumber=10,TeethHeight=0.2} 11 12 % Main macro for “cogged wheel” object Writing high-level macros: Examples 186 13 \def\PstCoggedWheel{\def\pst@par{}\pst@object{PstCoggedWheel}} 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 \def\PstCoggedWheel@i{{% \use@par% Assignment of local parameters \pst@cntc=360 \divide\pst@cntc\PstCoggedWheel@TeethNumber % Test to verify if the number of teeth is valid \pst@cnth=\pst@cntc \multiply\pst@cnth\PstCoggedWheel@TeethNumber \ifnum\pst@cnth=360 \else \@pstrickserr{TeethNumber (\PstCoggedWheel@TeethNumber) must be a divisor of 360! Results will be inaccurate.}{\@ehpb}% \fi \pst@cntd=\pst@cntc \divide\pst@cntd\tw@ \pst@dimd=\psunit \pssetlength{\pst@dimc}{\PstCoggedWheel@TeethHeight}% \advance\pst@dimd-\pst@dimc \pscustom{% \moveto(\pst@dimd;0) \multido{\iAngleA=\z@+\pst@cntc,\iAngleB=\pst@cntd+\pst@cntc, \iAngleC=\pst@cntc+\pst@cntc}% {\PstCoggedWheel@TeethNumber}{% \lineto(1;\iAngleA) \lineto(1;\iAngleB) \lineto(\pst@dimd;\iAngleB) \lineto(\pst@dimd;\iAngleC)}}}} 41 42 43 44 45 46 47 48 \rput(-4,0){\PstCoggedWheel} \rput(-1.5,0){\PstCoggedWheel[TeethNumber=30,TeethHeight=4mm]} \rput(4,0){% \PstCoggedWheel[unit=2,linecolor=cyan, TeethNumber=36,TeethHeight=0.1]% \rput(2.8;200){% \PstCoggedWheel[linecolor=green,TeethNumber=18]}} Writing high-level macros: Examples 187 64.2 Advanced example: test tube This is a complex example which defines a high level macro to draw a test tube, as used in chemistry.52 We first define a simple tube tube. Note that we use the macro \psellipticarc rather than \psarc(0,0.5){0.5}{180}{0} because it scales correctly if we change the xunit parameter. The \psarc macro scales only with the runit parameter, which is not a logical parameter to use here. 1 2 3 4 5 6 7 \def\PstTestTube{{% Two braces to limit the scope of the % next settings inside the macro only \psset{dimen=middle,linewidth=0.08}% \psline(-0.5,3)(-0.5,0.5) \psellipticarc(0,0.5)(0.5,0.5){180}{0} \psline(0.5,0.5)(0.5,3) \psellipse(0,3)(0.5,0.1)}} 8 9 10 11 \rput(-4,0){\PstTestTube} \rput(-2.8,0){\psset{unit=0.7}\PstTestTube} \rput{30}(0,0){\psset{xunit=1.5}\PstTestTube} To be able to accept later various options, we will transform this macro to allow it to accept optional parameters,as already demonstrated. 1 2 3 4 5 6 7 % Macro for tube (\PstTestTube last macro) \def\PstLaboTestTube@Tube{{% \psset{linewidth=0.08}% \psline(-0.5,3)(-0.5,0.5) \psellipticarc(0,0.5)(0.5,0.5){180}{0} \psline(0.5,0.5)(0.5,3) \psellipse(0,3)(0.5,0.1)}} 8 9 10 11 % Main macro for “test tube” object \def\PstLaboTestTube{% \def\pst@par{}\pst@object{PstLaboTestTube}} 12 13 14 15 16 \def\PstLaboTestTube@i{{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \PstLaboTestTube@Tube}} 17 18 19 \rput{30}(-3,0){\PstLaboTestTube[linecolor=red]} \rput(-1,0){\PstLaboTestTube[unit=2,linecolor=cyan]} As we have seen, we can use as usual the \rput macro to put this objects at specified locations, with an optional rotation. But if we want to be able to 52 This is extracted and adapted from the ‘pst-labo’ package [61] by Manuel Luque and Christophe Jorssen, which define a lot more objects and parameters. Writing high-level macros: Examples 188 specify a coordinate as an optional parameter of the macro (with (0,0) for default, as usual), this is easy to do, using what was previously explained. Nevertheless, note that between \PstLaboTestTube[unit=2](x0,y0)} and \rput(x0,y0){\PstLab there is a difference, because in the first case the change of unit apply to the coordinates too, and not it the second case. It is not useful to allow specification of an angle here because the result will not be correct if we put a liquid in the tube, as we will do later. 1 2 3 4 \def\PstLaboTestTube@i{% % Test for optional coordinate (default = (0,0)) \@ifnextchar({\PstLaboTestTube@ii}% {\PstLaboTestTube@ii(\z@,\z@)}} 5 6 7 8 9 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){\PstLaboTestTube@Tube}}} 10 11 12 \PstLaboTestTube[linecolor=red](-3,0) \PstLaboTestTube[xunit=2](0,1) To be able to use several forms for the tubes, we can define a string parameter, which can take the different values allowed, here straight, roundbottom, erlenmeyer, small (obviously, other ones can be easily added.) The macro \PstLaboTestTube@Tube will be defined in an indirect way, as the macro which will define the tube of the chosen form. So, the \PstLaboTestTube@ii macro does not have to be modified for the moment. This way of proceeding is very flexible, as it allows adding new forms which are immediately usable without modifying any line of the macros themselves. We also move the vertical origin of the tube, to be able to keep the same bottom line, with any rotation applied to it (this will require too that the tube will be moved to this vertical position, to ensure that it basis will be at the (0,0) coordinate.) 1 2 3 4 5 6 \def\PstTestTubeA{{% \psset{dimen=middle,linewidth=0.08}% \psline(-0.5,3)(-0.5,0.5) \psellipticarc(0,0.5)(0.5,0.5){180}{0} \psline(0.5,0.5)(0.5,3) \psellipse(0,3)(0.5,0.1)}} 7 8 9 10 11 12 13 \def\PstTestTubeB{{% \psset{dimen=middle,linewidth=0.08,origin={0,0.5}}% \psline(-0.5,3)(-0.5,0.5) \psellipticarc(0,0.5)(0.5,0.5){180}{0} \psline(0.5,0.5)(0.5,3) \psellipse(0,3)(0.5,0.1)}} 14 15 \rput(1,0){\PstTestTubeA} Writing high-level macros: Examples 189 16 17 \rput{-40}(2.5,0){\PstTestTubeA} \rput{-80}(4,0){\PstTestTubeA} 18 19 20 21 22 23 24 \rput(1,0){\PstTestTubeB} \rput{-40}(2.5,0){\PstTestTubeB} \rput{-80}(4,0){\PstTestTubeB} \rput(8,0.5){\PstTestTubeB} \rput{-40}(9.5,0.5){\PstTestTubeB} \rput{-80}(11,0.5){\PstTestTubeB} 4 3 2 1 0 -1 0 4 1 2 3 4 5 6 7 8 10 11 12 3 2 1 0 -1 0 1 2 3 4 5 6 7 8 9 13 14 The definitions of the six macros \PstLaboTestTube@Height (the height of the tube), \PstLaboTestTube@HeightTop (the height of the bottom part of the tube above the rotation point), \PstLaboTestTube@HeightBottom (the height of the bottom part of the tube below the rotation point), \PstLaboTestTube@WidthBottomHalf (half the width of the bottom part), \PstLaboTestTube@WidthTopHalf (half the width of the top part) and \PstLaboTestTube@W (half the width of the neck) will be used later (to know at which height to put a stopper, for instance). We need also to define the macro \PstLaboTestTube@HeightBottom when the Form parameter is set and not when the macro \PstLaboTestTube@Tube is expanded, because we will need to know it value before invoking the macro defining the kind of tube. Writing high-level macros: Examples 190 1 2 3 4 5 % Form parameter \define@key{psset}{Form}{% \def\PstLaboTestTube@Tube{\@nameuse{PstLaboTestTube@#1}}% \def\PstLaboTestTube@HeightBottom{% \@nameuse{PstLaboTestTube@#1@HeightBottom}}} 6 7 \setkeys{psset}{Form=straight}% Default value 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 % Macro for straight tube (was \PstLaboTestTube@Tube) \def\PstLaboTestTube@straight{{% \gdef\PstLaboTestTube@Height{3}% \gdef\PstLaboTestTube@HeightTop{2.5}% \gdef\PstLaboTestTube@WidthBottomHalf{0.5}% \gdef\PstLaboTestTube@WidthTopHalf{0.5}% \gdef\PstLaboTestTube@WidthNeckHalf{0.5}% \psset{dimen=middle,linewidth=0.08, origin={0,\PstLaboTestTube@straight@HeightBottom}}% \psline(-0.5,3)(-0.5,0.5) \psellipticarc(0,0.5)(0.5,0.5){180}{0} \psline(0.5,0.5)(0.5,3) \psellipse(0,3)(0.5,0.1)}} \def\PstLaboTestTube@straight@HeightBottom{0.5} 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 % Macro for round bottom flask \def\PstLaboTestTube@roundbottom{{% \gdef\PstLaboTestTube@Height{3}% \gdef\PstLaboTestTube@HeightTop{1.8}% \gdef\PstLaboTestTube@WidthBottomHalf{1.15}% \gdef\PstLaboTestTube@WidthTopHalf{0.5}% \gdef\PstLaboTestTube@WidthNeckHalf{0.7}% \psset{dimen=middle,linewidth=0.08,% origin={0,\PstLaboTestTube@roundbottom@HeightBottom}}% \psline(-0.5,2.95)(-0.5,2.15)% \psellipticarc(0,1.15)(1.15,1.15){115}{65}% \psline(0.5,2.15)(0.5,2.95)% \psellipse(0,3)(0.7,0.1)}} \def\PstLaboTestTube@roundbottom@HeightBottom{1.2} 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 % Macro for erlenmeyer flask \def\PstLaboTestTube@erlenmeyer{{% \gdef\PstLaboTestTube@Height{3}% \gdef\PstLaboTestTube@HeightTop{1.5}% \gdef\PstLaboTestTube@WidthBottomHalf{1.3}% \gdef\PstLaboTestTube@WidthTopHalf{0.5}% \gdef\PstLaboTestTube@WidthNeckHalf{0.7}% \psset{dimen=middle,linewidth=0.08,% origin={0,\PstLaboTestTube@erlenmeyer@HeightBottom}}% % Last point required to be able to fill the region correctly \psline(-0.5,2.9)(-0.5,2.2)(-0.5,2.25) \psline[linearc=0.3](-0.5,2.2)(-1.3,0)(1.3,0)(0.5,2.2) \psline(0.5,2.2)(0.5,2.9) \psellipse(0,3)(0.7,0.1)}} Writing high-level macros: Examples 191 53 \def\PstLaboTestTube@erlenmeyer@HeightBottom{1.5} 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 % Macro for small flask \def\PstLaboTestTube@small{{% \gdef\PstLaboTestTube@Height{2}% \gdef\PstLaboTestTube@HeightTop{0.8}% \gdef\PstLaboTestTube@WidthBottomHalf{1}% \gdef\PstLaboTestTube@WidthTopHalf{0.5}% \gdef\PstLaboTestTube@WidthNeckHalf{0.7}% \psset{dimen=middle,linewidth=0.08,% origin={0,\PstLaboTestTube@small@HeightBottom}}% \psline(-0.5,1.9)(-0.5,1.47) \psellipticarc(-0.5,1.1)(0.5,0.4){90}{180} \psline[linearc=0.2](-1,1.1)(-1,0)(1,0)(1,1.1) \psellipticarc(0.5,1.1)(0.5,0.4){0}{90} \psline(0.5,1.47)(0.5,1.9) \psellipse(0,2)(0.7,0.1)}} \def\PstLaboTestTube@small@HeightBottom{1.2} 71 72 73 74 75 76 77 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \rput(0,\PstLaboTestTube@HeightBottom){% \PstLaboTestTube@Tube}}}} 78 79 80 81 82 \PstLaboTestTube(-4.5,0) \PstLaboTestTube[Form=roundbottom](-1.5,0) \PstLaboTestTube[Form=erlenmeyer](1.5,0) \PstLaboTestTube[Form=small](4.5,0) To be able to add a stopper to the tube, we define a boolean parameter to specify whether a stopper should be drawn or not. We also have to verify (as for all new features) that everything is scaled correctly if the unit is changed, at least for unit, because sometimes changing only xunit or yunit leads to incorrect behavior. In this example, it does work as expected. 1 2 3 4 % Stopper parameter \newif\ifPstLaboTestTube@Stopper \define@key{psset}{Stopper}[true]{% \@nameuse{PstLaboTestTube@Stopper#1}} 5 6 \setkeys{psset}{Stopper=false}% Default value Writing high-level macros: Examples 192 7 8 9 10 11 12 13 14 15 16 17 18 19 % Macro for stopper (depends on the height of the tube % and on the width of the neck) \def\PstLaboTestTube@Stopper{% \rput(0,\PstLaboTestTube@HeightTop){% \pscustom[fillstyle=solid,fillcolor=lightgray]{% \psellipticarc(0,0.5)(0.6,0.1){0}{180} \psline(-0.6,0.5)(-0.4,-0.3) \psellipticarc(0,-0.3)(0.4,0.1){180}{0} \psline(0.4,-0.3)(0.6,0.5)} \psellipticarc(0,0.5)(0.6,0.1){180}{0} \psellipticarc[linewidth=0.08] (\PstLaboTestTube@WidthNeckHalf,0.1){180}{0}}} 20 21 22 23 24 25 26 27 28 29 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \rput(0,\PstLaboTestTube@HeightBottom){% \PstLaboTestTube@Tube \ifPstLaboTestTube@Stopper \PstLaboTestTube@Stopper \fi}}}} 30 31 32 33 34 35 \psset{Stopper=true} \rput(-4.5,0){\PstLaboTestTube[unit=0.5]} \rput(-2,0){\PstLaboTestTube[xunit=1.5,Form=small]} \rput(1.5,0){\PstLaboTestTube[yunit=1.5,Form=erlenmeyer]} \rput(4.5,0){\PstLaboTestTube[yunit=0.5,Form=roundbottom]} Now, we will add the possibility of having a small escape tube, straight or bent, through the stopper. For this we define a string parameter, which can take here the values straight, bent or triplebent (it will be easy to add new ones of any kind), and a length parameter (but defined as a macro, as previously explained) which will be the length of the outside part (after the bend for these kinds of escape tubes). We modify also the \PstLaboTestTube@Stopper macro, to allow better visualization of the crossing of the escape tube through the stopper. Writing high-level macros: Examples 193 1 2 3 4 % Escape tube type parameter \define@key{psset}{EscapeTube}{% \def\PstLaboTestTube@EscapeTube{% \@nameuse{PstLaboTestTube@EscapeTube@#1}}} 5 6 7 8 % Escape tube length parameter \define@key{psset}{EscapeTubeLength}{% \edef\PstLaboTestTube@EscapeTubeLength{#1}} 9 10 \setkeys{psset}{EscapeTube=,EscapeTubeLength=3}% Defaults 11 12 13 % Macro for no escape tube \let\PstLaboTestTube@EscapeTube@\relax 14 15 16 17 18 19 20 21 22 % Macro for straight escape tube \def\PstLaboTestTube@EscapeTube@straight{{% \pssetlength{\pst@dimd}{\PstLaboTestTube@HeightTop}% \psaddtolength{\pst@dimd}{\m@ne}% \rput(0,\pst@dimd){% \psline[doubleline=true,doublesep=0.1] (0,\PstLaboTestTube@EscapeTubeLength)} \PstLaboTestTube@EscapeTube@AdjustmentsStopper}} 23 24 25 26 27 28 29 30 31 % Macro for bent escape tube \def\PstLaboTestTube@EscapeTube@bent{{% \pssetlength{\pst@dimd}{\PstLaboTestTube@HeightTop}% \psaddtolength{\pst@dimd}{\m@ne}% \rput(0,\pst@dimd){% \psline[doubleline=true,doublesep=0.1,linearc=0.1] (0,0)(0,3)(\PstLaboTestTube@EscapeTubeLength,3)} \PstLaboTestTube@EscapeTube@AdjustmentsStopper}} 32 33 34 35 36 37 38 39 40 41 42 43 44 % Macro for triple bent escape tube \def\PstLaboTestTube@EscapeTube@triplebent{{% \pssetlength{\pst@dimc}{\PstLaboTestTube@HeightTop}% \psaddtolength{\pst@dimc}{\tw@}% \pssetlength{\pst@dimd}{\PstLaboTestTube@EscapeTubeLength}% \psaddtolength{\pst@dimd}{\@ne}% \psline[doubleline=true,doublesep=0.1,linearc=0.5] (0,0.5)(0,\pst@dimc) (\PstLaboTestTube@EscapeTubeLength,\pst@dimc) (\PstLaboTestTube@EscapeTubeLength,0) (\pst@dimd,0)(\pst@dimd,1) \PstLaboTestTube@EscapeTube@AdjustmentsStopper}} 45 46 47 48 49 50 51 52 % If there is no stopper, redraw of the external neck \def\PstLaboTestTube@EscapeTube@AdjustmentsStopper{% \ifPstLaboTestTube@Stopper \else \psellipticarc[linewidth=0.08](0,\PstLaboTestTube@HeightTop) (\PstLaboTestTube@WidthNeckHalf,0.1){180}{0} \fi} Writing high-level macros: Examples 194 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 \def\PstLaboTestTube@Stopper{% \rput(0,\PstLaboTestTube@HeightTop){% \pscustom[fillstyle=solid,fillcolor=lightgray]{% \psellipticarc(0,0.5)(0.6,0.1){0}{180} \psline(-0.6,0.5)(-0.4,-0.3) \psellipticarc(0,-0.3)(0.4,0.1){180}{0} \psline(0.4,-0.3)(0.6,0.5)} \psellipticarc(0,0.5)(0.6,0.1){180}{0} \psellipticarc[linewidth=0.08] (\PstLaboTestTube@WidthNeckHalf,0.1){180}{0} \if\PstLaboTestTube@EscapeTube\relax \else \let\psfillcolor\psdoublecolor \pscustom[fillstyle=solid]{% \psline[linearc=0.05](-0.07,0.7)(-0.07,0.5)(0.07,0.5)(0.07,0.7)} \fi}} 70 71 72 73 74 75 76 77 78 79 80 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \rput(0,\PstLaboTestTube@HeightBottom){% \expandafter\PstLaboTestTube@Tube \expandafter\PstLaboTestTube@EscapeTube \ifPstLaboTestTube@Stopper \PstLaboTestTube@Stopper \fi}}}} 81 82 83 84 85 86 87 \PstLaboTestTube[Form=roundbottom,EscapeTube=straight](-5,0) \PstLaboTestTube[Stopper=true,EscapeTube=straight, EscapeTubeLength=4](-2.5,0) \PstLaboTestTube[unit=0.5,Stopper=true,EscapeTube=bent](-1,0) \PstLaboTestTube[Form=small,Stopper=true, EscapeTube=triplebent](2,0) We can still easily add various objects to enrich the possibilities. Writing high-level macros: Examples 195 1 2 3 % Clip parameter \newif\ifPstLaboTestTube@Clip \define@key{psset}{Clip}[true]{\@nameuse{PstLaboTestTube@Clip#1}} 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 % Macro for clip \def\PstLaboTestTube@Clip{% % We put the clip at vertical position 0.7*height \pst@dimh=\PstLaboTestTube@HeightTop\psyunit \rput(-0.8,0.72\pst@dimh){% \psset{linewidth=0.05}% \pspolygon[fillstyle=solid,fillcolor=LightOrange] (1.3,0.9)(5.7,0.9)(5.8,0.8)(1.8,0.6)(1.3,0.6) \pspolygon[fillstyle=solid,fillcolor=Brown] (1.3,0.6)(5.8,0.8)(5.8,0.6)(2.8,0.4)(1.8,0.6) \pscustom[fillstyle=solid,fillcolor=LightOrange]{% \pscurve(1.3,0.6)(0.8,0.5)(0.3,0.6) \psline(0.3,0.6)(0,0.6) \psellipticarc(0.3,0.3)(0.32,0.32){180}{270} \psline(0.3,0.3)(3.3,0.3)(3.2,0.4)(1.8,0.6)(1.3,0.6)} \pscustom[fillstyle=solid,fillcolor=LightOrange]{% \psline(0,0.6)(0,0.3) \psellipticarc(0.3,0.3)(0.32,0.32){180}{270} \psline(0.3,0)(3.3,0)(3.3,0.3)(0.3,0.3) \psellipticarcn(0.3,0.6)(0.32,0.32){-90}{180}} \pswedge[fillstyle=solid,fillcolor=LightOrange] (0.27,0.66){0.27}{90}{180} \psellipse[linewidth=1.5\pslinewidth,fillstyle=solid] (1.8,0.6)(0.3,0.1) \psline[linewidth=1.5\pslinewidth](1.5,0.55)(1.2,0.3)(1.2,0)}} 30 31 32 33 34 35 36 37 38 39 40 41 42 43 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \rput(0,\PstLaboTestTube@HeightBottom){% \expandafter\PstLaboTestTube@Tube \expandafter\PstLaboTestTube@EscapeTube \ifPstLaboTestTube@Stopper \PstLaboTestTube@Stopper \fi \ifPstLaboTestTube@Clip \PstLaboTestTube@Clip \fi}}}} 44 45 \PstLaboTestTube[Form=roundbottom,Stopper=true,Clip=true] Writing high-level macros: Examples 196 Then we may want to add a liquid inside the tube. Its level will be specified by real number between 0 and 1. 1 \SpecialCoor 2 3 4 5 % LiquidLevel parameter \define@key{psset}{LiquidLevel}{% \pst@checknum{#1}{\PstLaboTestTube@LiquidLevel}} 6 7 \setkeys{psset}{LiquidLevel=0}% Default value 8 9 10 11 12 % Macro for liquid \def\PstLaboTestTube@Liquid#1{% \psframe[linestyle=none,fillstyle=solid,fillcolor=cyan] (-4,-2)(! 4 \PstLaboTestTube@Height\space #1 mul)} 13 14 15 16 17 18 19 20 21 22 23 24 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \psclip{\pscustom[linestyle=none]{% \expandafter\PstLaboTestTube@Tube}} \PstLaboTestTube@Liquid{\PstLaboTestTube@LiquidLevel} \endpsclip \rput(0,\PstLaboTestTube@HeightBottom){% % ... \fi}}}} 25 26 27 28 29 \PstLaboTestTube[LiquidLevel=0.3](-3,0) \PstLaboTestTube[Form=erlenmeyer,Stopper=true, EscapeTube=bent,LiquidLevel=1,doublecolor=cyan] \rput{-30}(3,0){\PstLaboTestTube[LiquidLevel=0.5]} Writing high-level macros: Examples 197 Nevertheless, we can see in the last previous example that the position of the liquid is not physically significant if the tube is rotated. This is a difficult geometric problem, for which we give here an approximative solution, sufficient for our needs. 1 2 3 % Angle parameter \define@key{psset}{Angle}{% \pst@getangle{#1}{\PstLaboTestTube@Angle}} 4 5 \setkeys{psset}{Angle=0}% Default value 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 % Macro for liquid (#1 = angle, #2 = liquid level) \def\PstLaboTestTube@Liquid#1#2{% \pst@Verb{% /xA {\PstLaboTestTube@WidthBottomHalf\space #1 0 gt {neg} if} def /LiquidHeight {#2 \PstLaboTestTube@Height\space mul #2 \PstLaboTestTube@HeightBottom\space mul #1 sin abs mul sub} def /xA’ {xA #1 cos mul \PstLaboTestTube@Height\space #1 sin mul sub} def #1 0 gt {/Xinf xA’ def /Xsup 2 def} {/Xinf -2 def /Xsup xA’ def} ifelse}% \psframe[linestyle=none,fillstyle=solid,fillcolor=cyan] (! Xinf -2)(! Xsup LiquidHeight)} 21 22 23 24 25 26 27 28 29 30 31 32 33 34 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){{% \psclip{\rput{\PstLaboTestTube@Angle} (0,\PstLaboTestTube@HeightBottom){% \pscustom[linestyle=none]{% \translate(0,-\PstLaboTestTube@HeightBottom) \expandafter\PstLaboTestTube@Tube}}} \PstLaboTestTube@Liquid{\PstLaboTestTube@Angle} {\PstLaboTestTube@LiquidLevel}% \endpsclip \rput{\PstLaboTestTube@Angle} Writing high-level macros: Examples 198 35 36 37 38 (0,\PstLaboTestTube@HeightBottom){% \expandafter\PstLaboTestTube@Tube % ... \fi}}}}} 39 40 41 42 43 \PstLaboTestTube[Angle=70,LiquidLevel=0.3](-4,0) \PstLaboTestTube[Angle=-20,LiquidLevel=0.8](-2.5,0) \PstLaboTestTube[Angle=-30,Form=erlenmeyer,Stopper=true, Clip=true,EscapeTube=straight,LiquidLevel=0.5](0.5,0) We can now parameterize the shading of the liquid. For this, we only have to parameterize the style of the polygon drawn to show the liquid. 1 2 3 % LiquidType parameter \define@key{psset}{LiquidType}{% \def\PstLaboTestTube@LiquidType{#1}} 4 5 6 7 8 9 % Default value (first is the parameter name, % second is the aspect name!) \setkeys{psset}{LiquidType=LiquidType} \newpsstyle{LiquidType}{% linestyle=none,fillstyle=solid,fillcolor=cyan} 10 11 12 13 14 15 16 % Macro for liquid (#1 = angle, #2 = liquid level, #3 = style) \def\PstLaboTestTube@Liquid#1#2#3{% \pst@Verb{% % ... {/Xinf -2 def /Xsup xA’ def} ifelse}% \psframe[style=#3](! Xinf -2)(! Xsup LiquidHeight)} 17 18 19 20 21 22 23 24 25 26 27 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \psclip{\rput{\PstLaboTestTube@Angle} (0,\PstLaboTestTube@HeightBottom){% \pscustom[linestyle=none]{% \translate(0,-\PstLaboTestTube@HeightBottom) \expandafter\PstLaboTestTube@Tube}}} \PstLaboTestTube@Liquid{\PstLaboTestTube@Angle} Writing high-level macros: Examples 199 {\PstLaboTestTube@LiquidLevel} {\PstLaboTestTube@LiquidType} 28 29 30 31 32 \endpsclip % ... \fi}}}} 33 34 35 36 37 38 \newpsstyle{cobalt}{% linestyle=none,fillstyle=solid,fillcolor=NavyBlue} \newpsstyle{diffusion}{% linestyle=none,fillstyle=gradient,gradmidpoint=0} \newpsstyle{oil}{linestyle=none,fillstyle=solid,fillcolor=yellow} 39 40 41 42 43 \PstLaboTestTube[unit=0.75,Form=roundbottom,Stopper=true, Angle=20,LiquidType=cobalt,LiquidLevel=0.7](-3,0) \PstLaboTestTube[LiquidType=oil,LiquidLevel=0.5] \PstLaboTestTube[LiquidType=diffusion,LiquidLevel=0.9](3,0) If we want to manage several liquids (here up to 3), we have only to loop on them. Note that we use a number inside the macro names. We could have use the \@namedef macro for that, but here we want to call the \pst@checknum macro to verify if the value is a well formatted number. pst@checknum does not allow numeric characters inside macro names, so we use use a variation on it, the \@nameedef macro, which does allow numeric characters inside macro names. 1 2 3 4 5 6 7 8 9 10 11 12 13 % LiquidLevel parameters \define@key{psset}{LiquidLevel1}{% \pst@checknum{#1}{\pst@temph}% \expandafter\edef\csname PstLaboTestTube@LiquidLevel1% \endcsname{\pst@temph}} \define@key{psset}{LiquidLevel2}{% \pst@checknum{#1}{\pst@temph}% \expandafter\edef\csname PstLaboTestTube@LiquidLevel2% \endcsname{\pst@temph}} \define@key{psset}{LiquidLevel3}{% \pst@checknum{#1}{\pst@temph}% \expandafter\edef\csname PstLaboTestTube@LiquidLevel3% \endcsname{\pst@temph}} 14 15 16 17 18 % LiquidType parameters \define@key{psset}{LiquidType1}{% \@namedef{PstLaboTestTube@LiquidType1}{#1}} \define@key{psset}{LiquidType2}{% Writing high-level macros: Examples 200 19 20 21 \@namedef{PstLaboTestTube@LiquidType2}{#1}} \define@key{psset}{LiquidType3}{% \@namedef{PstLaboTestTube@LiquidType3}{#1}} 22 23 24 25 % Default values \setkeys{psset}{LiquidType1=LiquidType1,LiquidLevel1=0, LiquidType2=,LiquidLevel2=0,LiquidType3=,LiquidLevel3=0} 26 27 28 29 % Default style \newpsstyle{LiquidType1}{% linestyle=none,fillstyle=solid,fillcolor=cyan} 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \psclip{\rput{\PstLaboTestTube@Angle} (0,\PstLaboTestTube@HeightBottom){% \pscustom[linestyle=none]{% \translate(0,-\PstLaboTestTube@HeightBottom) \expandafter\PstLaboTestTube@Tube}}} \multido{\iLiquid=\@ne+\@ne}{\thr@@}{% \ifdim\@nameuse{PstLaboTestTube@LiquidLevel\iLiquid}\p@>\z@ \PstLaboTestTube@Liquid{\PstLaboTestTube@Angle} {\@nameuse{PstLaboTestTube@LiquidLevel\iLiquid}} {\@nameuse{PstLaboTestTube@LiquidType\iLiquid}} \fi} \endpsclip % ... \fi}}}} 49 50 \newpsstyle{vinegar}{linestyle=none,fillstyle=solid,fillcolor=magenta} 51 52 53 54 55 56 57 \PstLaboTestTube[Form=roundbottom,Stopper=true, LiquidType1=oil,LiquidLevel1=0.6, LiquidType2=vinegar,LiquidLevel2=0.2](-3,0) \PstLaboTestTube[Angle=-20,LiquidType1=cobalt,LiquidLevel1=0.8, LiquidType2=oil,LiquidLevel2=0.7, LiquidType3=vinegar,LiquidLevel3=0.5](3,0) We may want to change the form of the liquid surface. This is easy to do. Writing high-level macros: Examples 201 1 2 3 4 % Liquid surface parameter \define@key{psset}{LiquidSurface}{% \def\PstLaboTestTube@LiquidSurface{% \@nameuse{PstLaboTestTube@LiquidSurface@#1}}} 5 6 7 % Default value \setkeys{psset}{LiquidSurface=straight} 8 9 10 11 12 13 14 15 % Macro for liquid surface (straight) % (#1 = angle, #2 = liquid level, #3 = style) \def\PstLaboTestTube@LiquidSurface@straight#1#2#3{% \pst@Verb{% % ... {/Xinf -2 def /Xsup xA’ def} ifelse}% \psframe[style=#3](! Xinf -2)(! Xsup LiquidHeight)} 16 17 18 19 20 21 22 23 24 25 26 % Macro for liquid surface (wavy) % (#1 = angle, #2 = liquid level, #3 = style) \def\PstLaboTestTube@LiquidSurface@wavy#1#2#3{% \pst@Verb{% % ... {/Xinf -2 def /Xsup xA’ def} ifelse}% \pscustom[style=#3]{% \psline(! Xinf LiquidHeight)(!Xinf -2)(! Xsup -2)(! Xsup LiquidHeight) \pszigzag[linearc=0.1,coilwidth=0.2,coilheight=2.5] (! Xinf LiquidHeight)}} 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \psclip{\rput{\PstLaboTestTube@Angle} (0,\PstLaboTestTube@HeightBottom){% \pscustom[linestyle=none]{% \translate(0,-\PstLaboTestTube@HeightBottom) \expandafter\PstLaboTestTube@Tube}}} \multido{\iLiquid=\@ne+\@ne}{\thr@@}{% \ifdim\@nameuse{PstLaboTestTube@LiquidLevel\iLiquid}\p@>\z@ \expandafter\PstLaboTestTube@LiquidSurface% {\PstLaboTestTube@Angle} {\@nameuse{PstLaboTestTube@LiquidLevel\iLiquid}} {\@nameuse{PstLaboTestTube@LiquidType\iLiquid}} \fi} \endpsclip % ... \fi}}}} 47 48 49 50 51 52 \psset{LiquidSurface=wavy} \PstLaboTestTube[Form=small,Stopper=true, LiquidType1=cobalt,LiquidLevel1=0.3](-3,0) \PstLaboTestTube[Angle=-20,LiquidType1=cobalt,LiquidLevel1=0.8, LiquidType2=oil,LiquidLevel2=0.6, Writing high-level macros: Examples 202 53 LiquidType3=vinegar,LiquidLevel3=0.5](3,0) We can also add various substances inside the tubes. Bubbles and nails are defined below, in random sizes and at random positions. 1 2 3 4 % Substance parameter \define@key{psset}{Substance}{% \def\PstLaboTestTube@Substance{% \@nameuse{PstLaboTestTube@Substance@#1}}} 5 6 7 8 % Substance number parameter \define@key{psset}{SubstanceNumber}{% \pst@getint{#1}{\PstLaboTestTube@SubstanceNumber}} 9 10 11 12 % Substance style parameter \define@key{psset}{SubstanceStyle}{% \edef\PstLaboTestTube@SubstanceStyle{#1}} 13 14 15 % Default values \setkeys{psset}{Substance=,SubstanceNumber=10,SubstanceStyle=} 16 17 18 19 20 21 22 % Macro to draw bubbles of random sizes at random positions \def\PstLaboTestTube@Substance@bubbles{% \PstLaboTestTube@Substance@i{% \psdot[dotstyle=o,dotscale=\pointless\pst@dimh] (! \pst@number{\pst@dimc} \pst@number{\pst@dimd} \@nameuse{PstLaboTestTube@LiquidLevel1} mul)}} 23 24 25 26 27 28 29 30 % Macro to draw colored bubbles of random sizes at random pos \def\PstLaboTestTube@Substance@coloredbubbles{% \PstLaboTestTube@Substance@i{% \pscircle[linewidth=0.5\pslinewidth,fillstyle=ccslope, runit=\pointless\pst@dimh] (! \pst@number{\pst@dimc} \pst@number{\pst@dimd} \@nameuse{PstLaboTestTube@LiquidLevel1} mul){0.06}}} 31 32 33 34 35 36 37 38 % Macro to draw nails of random sizes at random positions \def\PstLaboTestTube@Substance@nails{% \PstLaboTestTube@Substance@i{% \rput{\the\pst@cnth}% (! \pst@number{\pst@dimc} \pst@number{\pst@dimd} \@nameuse{PstLaboTestTube@LiquidLevel1} mul){% \psset{unit=\pointless\pst@dimh}% Writing high-level macros: Examples 203 39 40 \psline(0,0.2) \psellipticarc*(0,0.2)(0.06,0.03){0}{180}}}} 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 % Macro to draw thin objects of random sizes at random pos. \def\PstLaboTestTube@Substance@i#1{% #1 = macro of the object \multido{\iSubstance=\@ne+\@ne} {\PstLaboTestTube@SubstanceNumber}{% \setrandim{\pst@dimc}{-\PstLaboTestTube@WidthBottomHalf\p@} {\PstLaboTestTube@WidthBottomHalf\p@}% For position % For position and size \setrandim{\pst@dimd}{\z@}{\PstLaboTestTube@Height\p@}% \setrannum{\pst@cnth}{\z@}{360}% For angle % The size increase proportionally to the vertical position \pst@dimh=\pst@dimd % And this size must depend of the unit \pst@dimg=0.04\psunit \pst@dimh=\pointless\pst@dimg\pst@dimh \ifx\PstLaboTestTube@SubstanceStyle\@empty \else \setkeys{psset}{style=\PstLaboTestTube@SubstanceStyle}% \fi #1}} 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 \def\PstLaboTestTube@ii(#1){{% \setkeys{psset}{dimen=middle}% \use@par% Assignment of local parameters \rput(#1){% \psclip{\rput{\PstLaboTestTube@Angle} (0,\PstLaboTestTube@HeightBottom){% \pscustom[linestyle=none]{% \translate(0,-\PstLaboTestTube@HeightBottom) \expandafter\PstLaboTestTube@Tube}} % To clip the optional substance by the first liquid \expandafter\PstLaboTestTube@LiquidSurface% {\PstLaboTestTube@Angle} {\@nameuse{PstLaboTestTube@LiquidLevel1}}{none}} % ... \PstLaboTestTube@Substance \endpsclip % ... \fi}}}} 80 81 82 83 84 85 86 \newpsstyle{champagne}{% linestyle=none,fillstyle=solid,fillcolor=LemonChiffon} \newpsstyle{water}{% linestyle=none,fillstyle=solid,fillcolor=LightBlue} \newpsstyle{BubblesChampagne}{% fillstyle=solid,fillcolor=PaleYellow} 87 88 89 90 91 \PstLaboTestTube[Form=roundbottom,Stopper=true, LiquidType1=champagne,LiquidLevel1=0.5, Substance=bubbles](-5,0) \PstLaboTestTube[LiquidType1=champagne, Writing high-level macros: Examples 204 92 93 94 95 96 97 98 99 100 101 LiquidLevel1=0.9,Substance=bubbles,SubstanceNumber=20, SubstanceStyle=BubblesChampagne](-2.5,0) \PstLaboTestTube[Form=erlenmeyer,LiquidType1=water, LiquidLevel1=0.8,Substance=nails,SubstanceNumber=30] \PstLaboTestTube[Stopper=true,LiquidType1=water,LiquidLevel1=0.75, Substance=coloredbubbles,SubstanceNumber=15](2.5,0) \PstLaboTestTube[Form=roundbottom,LiquidType1=oil, LiquidLevel1=0.9,LiquidType2=vinegar,LiquidLevel2=0.3, Substance=coloredbubbles,SubstanceNumber=25, slopebegin=NavyBlue,slopeend=white](5,0) c c b b c bc b c b c cbcb bbcb c bc c cbc b bbcb c bc c bb c c b c b c bc b c b c b c b c b bc c b And we can of course compose several objects to illustrate complex scenes. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 % Macro for becher \def\PstLaboTestTube@becher{{% \gdef\PstLaboTestTube@Height{2.5}% \gdef\PstLaboTestTube@HeightTop{1.275}% \gdef\PstLaboTestTube@WidthBottomHalf{0.55}% \gdef\PstLaboTestTube@WidthTopHalf{0.55}% \gdef\PstLaboTestTube@WidthNeckHalf{0.55}% \psset{dimen=middle,linewidth=0.08,% origin={0,\PstLaboTestTube@becher@HeightBottom}}% \psellipse(0,2.55)(1.1,0.1) \psline[linearc=0.5](-1,2.5)(-1,0)(1,0)(1,2.5) \multido{\nDiv=0.3+0.5}{4}{% \psline[linewidth=0.5\pslinewidth](-0.75,\nDiv)(-0.3,\nDiv)} \multido{\nSubDiv=0.3+0.1}{16}{% \psline[linewidth=0.25\pslinewidth](-0.75,\nSubDiv)(-0.5,\nSubDiv)}}} \def\PstLaboTestTube@becher@HeightBottom{1.275} 17 18 19 20 % Macro for “Bunsen burner” object \def\PstLaboBunsenBurner{% \def\pst@par{}\pst@object{PstLaboBunsenBurner}} 21 22 23 24 25 \def\PstLaboBunsenBurner@i{% % Test for optional angle (default = 0) \@ifnextchar\bgroup{\PstLaboBunsenBurner@ii}% {\PstLaboBunsenBurner@ii{0}}} 26 27 28 29 \def\PstLaboBunsenBurner@ii#1{% #1 = angle % Test for optional coordinate (default = (0,0)) \@ifnextchar({\PstLaboBunsenBurner@iii{#1}}% Writing high-level macros: Examples 205 30 {\PstLaboBunsenBurner@iii{#1}(\z@,\z@)}} 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 \def\PstLaboBunsenBurner@iii#1(#2){{% % #1 = angle, #2 = coordinate \setkeys{psset}{linewidth=0.05}% \use@par% Assignment of local parameters \rput{#1}(#2){% % Basis \pstriangle[fillstyle=solid,fillcolor=darkgray,linewidth=0.5\pslinewidth] (0,0.2)(2.5,0.3) \psframe[fillstyle=solid,fillcolor=darkgray](-1.25,0)(1.25,0.2) % Burner \pscustom[fillstyle=solid,fillcolor=LemonChiffon]{% \psline(-0.25,4)(-0.25,0.45) \psellipticarc(0,0.45)(0.27,0.15){180}{0} \psline(0.25,0.45)(0.25,4)(-0.25,4)} % Regulating flame \psframe[fillstyle=solid,fillcolor=lightgray](-0.5,1)(0.5,2) \psdots[dotstyle=o,dotscale=1.25](-0.3,1.5)(0,1.5)(0.3,1.5) % Small gaz tube \pscustom[fillstyle=solid,fillcolor=Orange]{% \psline(-2.5,0.6)(-0.25,0.6) \psellipticarc(-0.25,0.7)(0.1,0.12){-90}{90} \psline(-0.25,0.8)(-2.5,0.8)} % Flame \rput(0,4){% \psset{linestyle=none,fillstyle=gradient,gradmidpoint=0}% \psclip{\psbezier[gradbegin=LightOrange,gradend=yellow]% (-0.25,0)(-0.35,0.5)(-0.4,0.75) (-0.35,1)(-0.25,1.5)(0.5,2) (0.25,1.5)(0.35,1)(0.4,0.75) (0.35,0.5)(0.25,0)(0,0)} \pspolygon[gradbegin=blue,gradend=white](-0.25,0)(0.25,0)(0,1) \endpsclip}}}} 64 65 66 \newpsstyle{SulphuricAcid}{linestyle=none,fillstyle=solid, fillcolor=LemonChiffon} 67 68 69 \newpsstyle{PotassiumPermanganate}{linestyle=none,fillstyle=gradient, gradmidpoint=1,gradbegin=white,gradend=DarkViolet} 70 71 \newpsstyle{SulphuricDioxyde}{fillstyle=solid,fillcolor=Gold} 72 73 74 75 76 77 78 79 80 81 82 \psset{Substance=coloredbubbles,LiquidSurface=wavy}% % Table \psline[linewidth=0.1](-5,0)(5.7,0) \psframe[linestyle=none,fillstyle=vlines](-5,0)(5.7,-1) % Bunsen burner \PstLaboBunsenBurner(-2.5,0) % Tube on right \PstLaboTestTube[Angle=30, LiquidType1=PotassiumPermanganate,LiquidLevel1=0.5, Substance=coloredbubbles, Writing high-level macros: Examples 206 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 slopebegin=DarkViolet,slopeend=white](5.2,0.1)% % Becher \PstLaboTestTube[yunit=0.8,Form=becher](4.7,0.05)% % Round bottom flask on left \PstLaboTestTube[Form=roundbottom,Angle=-60, Stopper=true,Clip=true, EscapeTube=bent,EscapeTubeLength=8.7,doublecolor=PaleYellow, LiquidType1=SulphuricAcid,LiquidLevel1=0.7, Substance=bubbles,SubstanceNumber=30, SubstanceStyle=SulphuricDioxyde](-2.5,5.1)% % Adjustment to redraw the external neck of the right tube \rput{30}(5.45,0.14){% \psellipticarc[linewidth=0.08](0,3)(0.55,0.1){180}{0}} % Adjustment to redraw the external neck of the becher \rput(4.7,2.055){% \psellipticarc[yunit=0.8,linewidth=0.08](1.1,0.1){180}{0}} % Labels \psset{linewidth=0.05,arrows=->,arrowscale=2}% \psline(-0.8,1.5)(-3,5.8) \uput[-90](-0.8,1.5){% \shortstack{Sulfuric acid\\$\mathrm{H_2SO_4}$}} \psline(1,1.5)(-2.2,6.2) \uput[-90](1,1.5){\shortstack{Sulfur\\$\mathrm{SO}$}} \psline(3.3,6)(3.3,3.8) \uput[90](3.3,6){\shortstack{Sulfur dioxyde\\$\mathrm{SO_2}$}} \psline(5.4,7)(5.4,0.6) \uput[90](5.4,7){% \shortstack{Potassium permanganate\\$\mathrm{KMnO_4}$}} c bcbc cb cbcbcb cb cbbcb bc bc cbc bc cb cbbcb c b c c bc b cb b bc bc bc c b Potassium permanganate KMnO4 Sulfur dioxyde SO2 bc bc bc b cb c Sulfuric acid Sulfur H2 SO4 SO Writing high-level macros: Examples 207 64.3 Advanced example: Gantt charts This is another complex example which builds high-level tools to draw simple Gantt charts. We will define a macro (\PstGanttTask) to describe tasks and will show how to define an environment (PstGanttChart) to manage all these defined tasks. Both must of course accept optional parameters. 1 2 % Parameters definition % ================= 3 4 5 6 7 % Intervals to show? \newif\ifPstGantt@ChartShowIntervals \define@key{psset}{ChartShowIntervals}[true]{% \@nameuse{PstGantt@ChartShowIntervals#1}} 8 9 10 % Style for the tasks \define@key{psset}{TaskStyle}{\edef\PstGantt@TaskStyle{#1}} 11 12 13 14 % Name for unit interval \define@key{psset}{ChartUnitIntervalName}{% \edef\PstGantt@ChartUnitIntervalName{#1}} 15 16 17 18 % Name for basic unit \define@key{psset}{ChartUnitBasicIntervalName}{% \edef\PstGantt@ChartUnitBasicIntervalName{#1}} 19 20 21 22 23 24 % Unit interval for the tasks % (7 for a week, 30 for a month, etc.) % Warning: define it before “TaskUnitType”! \define@key{psset}{TaskUnitIntervalValue}{% \pst@getint{#1}{\PstGantt@TaskUnitIntervalValue}} 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 % Unit type for the tasks % (“UnitIntervalName” or “UnitBasicIntervalName”) \define@key{psset}{TaskUnitType}{% \edef\PstGantt@TaskUnitValue{#1}% % Validation of the parameter \ifx\PstGantt@TaskUnitValue\PstGantt@ChartUnitIntervalName \edef\PstGantt@TaskUnitValue{% \PstGantt@TaskUnitIntervalValue}% \else \ifx\PstGantt@TaskUnitValue% \PstGantt@ChartUnitBasicIntervalName \def\PstGantt@TaskUnitValue{1}% \else {\@pstrickserr{GanttTaskUnitType must be ‘\PstGantt@ChartUnitIntervalName’ Writing high-level macros: Examples 208 or ‘\PstGantt@ChartUnitBasicIntervalName’ (and not ‘\PstGantt@TaskUnitValue’)}\@eha}% 41 42 \fi 43 44 \fi} 45 46 47 48 % Outside label for the tasks \define@key{psset}{TaskOutsideLabel}{% \def\PstGantt@TaskOutsideLabel{#1}} 49 50 51 52 % Inside label for the tasks \define@key{psset}{TaskInsideLabel}{% \def\PstGantt@TaskInsideLabel{#1}} 53 54 55 56 57 % Maximum outside size label for the tasks % (in unit “TaskUnitType” !) \define@key{psset}{TaskOutsideLabelMaxSize}{% \pst@getint{#1}{\PstGantt@TaskOutsideLabelMaxSize}} 58 59 60 61 62 63 64 65 66 67 % Default values % =========== % Don’t show intervals, default task style, unit for tasks % is a week (so 7 days), no outside and inside labels \setkeys{psset}{% ChartShowIntervals=false,TaskStyle=TaskStyleDefault, ChartUnitIntervalName=Week,ChartUnitBasicIntervalName=Day, TaskUnitIntervalValue=7,TaskUnitType=Week,TaskOutsideLabel=, TaskInsideLabel=,TaskOutsideLabelMaxSize=0} 68 69 70 % Task default style is yellow background \newpsstyle{TaskStyleDefault}{fillstyle=solid,fillcolor=yellow} 71 72 73 % The environment PstGanttChart % ========================= 74 75 76 77 78 79 80 % Syntax:\PstGanttChart[parameters]{Nb of tasks}{Nb of days} % \endPstGanttChart % or % \begin{PstGanttChart}[parameters]{Nb of tasks}{Nb of days} % \end{PstGanttChart} \def\PstGanttChart{\def\pst@par{}\pst@object{PstGanttChart}} 81 82 83 84 85 86 \def\PstGanttChart@i#1#2{% \bgroup \setkeys{psset}{unit=0.1}% \use@par% Assignment of local parameters % Writing high-level macros: Examples 209 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 % “pspicture” environment \pst@cnta=\PstGantt@TaskOutsideLabelMaxSize \multiply\pst@cnta\PstGantt@TaskUnitValue % \pst@cntb=#1 \multiply\pst@cntb by 5 \advance\pst@cntb\@ne % \pst@cntc=#2 \multiply\pst@cntc\PstGantt@TaskUnitValue \advance\pst@cntc\tw@ % \ifPstGantt@ChartShowIntervals \pspicture(-\pst@cnta,-\pst@cntb)(\pst@cntc,\@two) \else \pspicture(-\pst@cnta,-\pst@cntb)(\pst@cntc,\z@) \fi \psframe(\z@,-\pst@cntb)(\pst@cntc,\z@) % \ifPstGantt@ChartShowIntervals % We will show the intervals \pst@cnta=#2 \multiply\pst@cnta\PstGantt@TaskUnitValue \divide\pst@cnta\PstGantt@TaskUnitIntervalValue \advance\pst@cnta\@ne % \pst@cntb=#1 \multiply\pst@cntb by 5 \advance\pst@cntb\@ne % \pst@dima=\PstGantt@TaskUnitIntervalValue\p@ \divide\pst@dima\tw@ \advance\pst@dima\@ne\p@ % \multido{\iInterval=\@ne+\@ne, \iIntervalPos=\@ne+ \PstGantt@TaskUnitIntervalValue, \rIntervalPos=\pst@number{\pst@dima}+% \PstGantt@TaskUnitIntervalValue}{\pst@cnta}{% \ifnum\iInterval=\pst@cnta \psline(\iIntervalPos,\z@)(\iIntervalPos,1.5) \psline[linestyle=dotted](\iIntervalPos,-\pst@cntb) (\iIntervalPos,\z@) \else \rput(\rIntervalPos,\@ne){% \PstGantt@ChartUnitIntervalName{} \iInterval} Writing high-level macros: Examples 210 \psline(\iIntervalPos,\z@)(\iIntervalPos,1.5) \psline[linestyle=dotted](\iIntervalPos,-\pst@cntb) (\iIntervalPos,\z@) \fi} 133 134 135 136 137 \fi} 138 139 140 141 \def\endPstGanttChart{% \endpspicture % End of “pspicture” environment \egroup} 142 143 144 % The macro \PstGanttTask % ==================== 145 146 147 \newcount\PstGantt@TaskCnt \PstGantt@TaskCnt=\z@ 148 149 150 % Syntax: \PstGanttTask[parameters]{Start}{Length} \def\PstGanttTask{\def\pst@par{}\pst@object{PstGanttTask}} 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 \def\PstGanttTask@i#1#2{% \advance\PstGantt@TaskCnt\m@ne % To increment globally \bgroup \use@par% Assignment of local parameters % Frame \pst@cnta=\PstGantt@TaskUnitValue \multiply\pst@cnta by #1 \advance\pst@cnta\@ne % \pst@cntb=\PstGantt@TaskUnitValue \multiply\pst@cntb by #2 \advance\pst@cntb\pst@cnta % \pst@cntc=\PstGantt@TaskCnt \multiply\pst@cntc by 5 % \pst@cntd=\pst@cntc \advance\pst@cntd by 4 % \psframe[style=\PstGantt@TaskStyle](\pst@cnta,\pst@cntc) (\pst@cntb,\pst@cntd) % Inside label \ifx\PstGantt@TaskInsideLabel\@empty \else \pst@dima=\pst@cnta\p@ \advance\pst@dima\pst@cntb\p@ \divide\pst@dima\tw@ Writing high-level macros: Examples 211 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 % \pst@dimb=\pst@cntc\p@ \advance\pst@dimb\pst@cntd\p@ \divide\pst@dimb\tw@ % \rput(\pst@number{\pst@dima},\pst@number{\pst@dimb}){% \PstGantt@TaskInsideLabel} \fi % Outside label \ifx\PstGantt@TaskOutsideLabel\@empty \else \pst@dima=\pst@cntc\p@ \advance\pst@dima\pst@cntd\p@ \divide\pst@dima\tw@ \rput[r](-1.5,\pst@number{\pst@dima}){% \PstGantt@TaskOutsideLabel} \fi \egroup} We can now use this new environment to specify Gantt charts, inserting into it as many tasks as we need (we use here the LATEX flavor syntax, which of course must be adapted if P LAIN TEX or ConTEXt is used.) 1 2 \newpsstyle{Important}{fillstyle=solid,fillcolor=Orange} \newpsstyle{NotImportant}{fillstyle=vlines} 3 4 5 Important 6 7 8 9 10 11 1 2 3 Important 4 5 6 7 8 \begin{PstGanttChart}{5}{7} \PstGanttTask{0}{3} \PstGanttTask{2}{1} \PstGanttTask[TaskStyle=Important, TaskInsideLabel=Important]{2}{5} \PstGanttTask[TaskStyle=NotImportant]{4}{2} \PstGanttTask{5}{2} \end{PstGanttChart} \begin{PstGanttChart}[yunit=2]{5}{7}% Same with double “yunit” \PstGanttTask{0}{3} \PstGanttTask{2}{1} \PstGanttTask[TaskStyle=Important, TaskInsideLabel=Important]{2}{5} \PstGanttTask[TaskStyle=NotImportant]{4}{2} \PstGanttTask{5}{2} \end{PstGanttChart} Writing high-level macros: Examples 212 1 \newpsstyle{Important}{fillstyle=solid,fillcolor=red} 2 3 4 5 6 7 8 9 10 11 12 13 \begin{PstGanttChart}[unit=2,TaskOutsideLabelMaxSize=1, ChartShowIntervals=true]{5}{7} \PstGanttTask[TaskOutsideLabel={Task 1}]{0}{3} \PstGanttTask[TaskOutsideLabel={Task 2},TaskUnitType=Day] {15}{3} % 3 days starting at day 15 \PstGanttTask[TaskStyle=Important,TaskOutsideLabel={Task 3}, TaskInsideLabel={\Large\textcolor{white}{\textbf{Important}}}]{2}{5} \PstGanttTask[TaskStyle=NotImportant, TaskOutsideLabel={Task 4}]{4}{2} \PstGanttTask[TaskOutsideLabel={Task 5}]{5}{2} \end{PstGanttChart} Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Task 1 Task 2 Important Task 3 Task 4 Task 5 1 \newpsstyle{TaskStyle}{fillstyle=solid,fillcolor=Pink} 2 3 4 5 6 7 8 9 10 \begin{PstGanttChart}[yunit=2,ChartUnitIntervalName=Month, TaskUnitIntervalValue=30,TaskUnitType=Month, ChartShowIntervals,TaskStyle=TaskStyle]{3}{4} \PstGanttTask[TaskInsideLabel={Task 1}]{0}{1} \PstGanttTask[TaskInsideLabel={Task 2},TaskUnitType=Day] {24}{40} % 40 days starting at day 24 \PstGanttTask[TaskInsideLabel={Task 3}]{2}{2} \end{PstGanttChart} Month 1 Month 2 Month 3 Month 4 Task 1 Task 2 Task 3 Writing high-level macros: Examples 213 1 2 3 4 Year 1 Year 2 Year 3 Year 4 Specif. \newpsstyle{MyTaskStyleA}{fillstyle=gradient,gradmidpoint=0, gradangle=90} \newpsstyle{MyTaskStyleB}{fillstyle=gradient,gradmidpoint=0, gradangle=90,gradbegin=ForestGreen,gradend=white} 5 6 7 Development 8 9 Documentation 10 11 Check 12 13 14 15 16 \begin{PstGanttChart}[yunit=1.5,ChartUnitIntervalName=Year, ChartShowIntervals=true,ChartUnitBasicIntervalName=Month, TaskUnitIntervalValue=12,TaskUnitType=Year, TaskStyle=MyTaskStyleA]{4}{4} \PstGanttTask[TaskInsideLabel={Specif.}]{0}{1} \PstGanttTask[TaskInsideLabel={Development}, TaskUnitType=Month]{6}{24} % 24 months since month 6 \PstGanttTask[TaskStyle=MyTaskStyleB, TaskInsideLabel={Documentation}]{2}{2} \PstGanttTask[TaskInsideLabel={Check}]{3}{1} \end{PstGanttChart} 64.4 Advanced example: overlapped colored surfaces53 Figure 3: Basic drawing of overlapped circles with colors in additive synthesis The problem of drawing the picture of the three circles showing the additive synthesis of primary colors (see Figure 3) is very classic and seems simple at the first glance. Nevertheless, there is no high level macro or environment in PSTricks which can directly handle this problem. As in many algorithmic problems, a lot of solutions exist, but they are not at all equivalent. Even if here criteria like computing ressources (CPU time and memory used) does not matter, the various solutions are very different from the point of view of ease of programming, generality and expressivity. 53 This section benefit of some discussions with Manuel Luque in 1999. Writing high-level macros: Examples 214 We will therefore detail several solutions, from the most basic and natural one, but with strong limitations, to more sophisticated and general ones. In order to simplify the exposition, we will limit our study to the case of three surfaces, as the main difficulty in this problem is in fact due to the necessity to be able to manage several surfaces, which raises complex combinational problems. The code for the general case is much more complex than the one which will be explained here for three surfaces. We can first draw the three colored circles above each others. 1 2 3 4 5 \psset{linestyle=none,fillstyle=solid} % Drawing of the circles \pscircle[fillcolor=red](0,0){2} \pscircle[fillcolor=green](2,0){2} \pscircle[fillcolor=blue](1,2){2} But, of course, if the surfaces are correct, the colors are not the expected ones, as PostScript cannot do the mixture of them on his own... We can then draw the filled circles with the primary colors, then using the arc drawing commands \psarc and \psarcn to redraw the overlapped parts, using the special \pscustom command to fill the regions with the additive resulting color. We obtain the following code (we use polar coordinates here, because this is a lot more easier to do with them): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 \SpecialCoor \psset{linestyle=none,fillstyle=solid} % sqrt(1 + 2) = 1.732 \pscircle[fillcolor=red](1;210){1.732}% Red circle \pscircle[fillcolor=green](1;330){1.732}% Green circle \pscircle[fillcolor=blue](1;90){1.732}% Blue circle % Yellow intersection of Red and Green circles (R + G = Y) \pscustom[fillcolor=yellow]{% \psarc(1;-30){1.732}{180}{240} % B \psarc(1;-150){1.732}{-60}{0} % A \psarcn(1;90){1.732}{300}{240}} % C % Cyan intersection of Green and Blue circles (G + B = C) \pscustom[fillcolor=cyan]{% \psarc(1;90){1.732}{-60}{0} % C \psarc(1;-30){1.732}{60}{120} % B Writing high-level macros: Examples 215 16 17 18 19 20 21 22 23 24 25 26 \psarcn(1;-150){1.732}{60}{0}} % A % Magenta intersection of Red and Blue circles (R + B = M) \pscustom[fillcolor=magenta]{% \psarc(1;90){1.732}{180}{240} % C \psarcn(1;-30){1.732}{180}{120} % B \psarc(1;-150){1.732}{60}{120}} % A % White intersection of Red, Green and Blue circles (R+G+B=W) \pscustom[fillcolor=white]{% \psarc(1;90){1.732}{-120}{-60} % C \psarc(1;-150){1.732}{0}{60} % A \psarc(1;-30){1.732}{120}{180}} % B We can see that this was rather easy to do, but also rather painful, because we must compute all the positions of the points delimiting the various arcs, and we are limited to using predefined resulting colors (that is to say that, concerning the colors, we must know the solution before to start to program!) The kind of surfaces is also completey fixed in the program, so we are completely unable to use it to draw the same figure on rhombs or ellipses, for instance, and we are unable to solve the problem on complex closed surfaces such as general polygons or regions enclosed by a general curve. A very powerful feature of PostScript that we can use with the PSTricks interface (and other general drawing languages) is the clipping mechanism. This allows, in a completely general way, drawing a graphic object clipped by other ones. The following code shows how clipping simplifies our little program: 1 2 3 4 \psset{linestyle=none} \def\PstCircleA{\pscircle(0,0){2}} \def\PstCircleB{\pscircle(2,0){2}} \def\PstCircleC{\pscircle(1,2){2}} 5 6 7 8 9 10 {\psset{fillstyle=solid,fillcolor=red}\PstCircleA}% Red circle {\psset{fillstyle=solid,fillcolor=green}\PstCircleB}% Green circle {\psset{fillstyle=solid,fillcolor=blue}\PstCircleC}% Blue circle % % Yellow intersection of Red and Green circles (R + G = Y) Writing high-level macros: Examples 216 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 \psclip{\PstCircleB} \psset{fillstyle=solid,fillcolor=yellow}\PstCircleA \endpsclip % Cyan intersection of Green and Blue circles (G + B = C) \psclip{\PstCircleB} \psset{fillstyle=solid,fillcolor=cyan}\PstCircleC \endpsclip % Magenta intersection of Red and Blue circles (R + B = M) \psclip{\PstCircleC} \psset{fillstyle=solid,fillcolor=magenta}\PstCircleA \endpsclip % White intersection of Red, Green and Blue circles (R+G+B=W) \psclip{\PstCircleB\PstCircleC} \psset{fillstyle=solid,fillcolor=white}\PstCircleA \endpsclip So, the first problem is solved: we have the genericity for the surfaces. This allows management for any closed surfaces, as we no longer have any coordinates to compute. And this solution is far more simple, due to the powerful clipping mechanism. The remaining weakness is that the resulting colors of the overlapped surfaces must still be known externally. We can build a generalized macro to solve this problem. 1 2 % The three surfaces must be defined as \PstSurfaceA, % \PstSurfaceB and \PstSurfaceC 3 4 5 6 7 8 9 10 11 12 13 \def\PstColorSynthesis{{% \psset{linestyle=none}% {\psset{fillstyle=solid,fillcolor=red}\PstSurfaceA}% Red circle {\psset{fillstyle=solid,fillcolor=green}\PstSurfaceB}% Green circle {\psset{fillstyle=solid,fillcolor=blue}\PstSurfaceC}% Blue circle % % Yellow intersection of Red and Green surfaces (R + G = Y) \psclip{\PstSurfaceB} \psset{fillstyle=solid,fillcolor=yellow}\PstSurfaceA \endpsclip Writing high-level macros: Examples 217 14 15 16 17 18 19 20 21 22 23 24 25 26 % Cyan intersection of Green and Blue surfaces (G + B = C) \psclip{\PstSurfaceB} \psset{fillstyle=solid,fillcolor=cyan}\PstSurfaceC \endpsclip % Magenta intersection of Red and Blue surfaces (R + B = M) \psclip{\PstSurfaceC} \psset{fillstyle=solid,fillcolor=magenta}\PstSurfaceA \endpsclip % White intersection of Red, Green and Blue surfaces % (R + G + B = W) \psclip{\PstSurfaceB\PstSurfaceC} \psset{fillstyle=solid,fillcolor=white}\PstSurfaceA \endpsclip}} 27 28 29 30 \def\PstSurfaceA{\psdiamond(0,0)(1,2)} \def\PstSurfaceB{\psdiamond(1,0)(1,2)} \def\PstSurfaceC{\psdiamond(0.5,2)(1,2)} 31 32 \PstColorSynthesis Now we can transform it in a PSTricks object, as usual. 1 2 3 4 % Surface parameters \define@key{psset}{SurfaceA}{\def\PstColorSynthesis@SurfaceA{#1}} \define@key{psset}{SurfaceB}{\def\PstColorSynthesis@SurfaceB{#1}} \define@key{psset}{SurfaceC}{\def\PstColorSynthesis@SurfaceC{#1}} 5 6 \def\PstColorSynthesis{\def\pst@par{}\pst@object{PstColorSynthesis}} 7 8 9 10 11 12 13 14 15 \def\PstColorSynthesis@i{{% \setkeys{psset}{linestyle=none}% \use@par% Assignment of local parameters \bgroup \setkeys{psset}{fillstyle=solid,fillcolor=red}% \PstColorSynthesis@SurfaceA% Red surface \setkeys{psset}{fillcolor=green}% \PstColorSynthesis@SurfaceB% Green surface Writing high-level macros: Examples 218 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 \setkeys{psset}{fillcolor=blue}% \PstColorSynthesis@SurfaceC% Blue surface \egroup % % Yellow intersection of Red and Green surfaces (R + G = Y) \psclip{\PstColorSynthesis@SurfaceB} \setkeys{psset}{fillstyle=solid,fillcolor=yellow}% \PstColorSynthesis@SurfaceA \endpsclip % Cyan intersection of Green and Blue surfaces (G + B = C) \psclip{\PstColorSynthesis@SurfaceB} \setkeys{psset}{fillstyle=solid,fillcolor=cyan}% \PstColorSynthesis@SurfaceC \endpsclip % Magenta intersection of Red and Blue surfaces (R + B = M) \psclip{\PstColorSynthesis@SurfaceC} \setkeys{psset}{fillstyle=solid,fillcolor=magenta}% \PstColorSynthesis@SurfaceA \endpsclip % White intersection of Red, Green and Blue surfaces % (R + G + B = W) \psclip{\PstColorSynthesis@SurfaceB\PstColorSynthesis@SurfaceC} \setkeys{psset}{fillstyle=solid,fillcolor=white}% \PstColorSynthesis@SurfaceA \endpsclip}} 41 42 43 \PstColorSynthesis[SurfaceA={\psdiamond(1.5,3)}, SurfaceB={\parabola(-1.5,-2)(1,1)},SurfaceC={\psellipse(3,1.5)}] The next step that we can take is to improve the code of the macro, using some standard TEX programming techniques. This is not directly related to PSTricks, and we will not get new functionalities, but using a higher level of abstraction will make the program both shorter and easier to modify later. 1 2 % The seven color names to use \define@key{psset}{ColorA}{\def\PstColorSynthesis@ColorA{#1}} Writing high-level macros: Examples 219 3 4 5 6 7 8 \define@key{psset}{ColorB}{\def\PstColorSynthesis@ColorB{#1}} \define@key{psset}{ColorC}{\def\PstColorSynthesis@ColorC{#1}} \define@key{psset}{ColorD}{\def\PstColorSynthesis@ColorD{#1}} \define@key{psset}{ColorE}{\def\PstColorSynthesis@ColorE{#1}} \define@key{psset}{ColorF}{\def\PstColorSynthesis@ColorF{#1}} \define@key{psset}{ColorG}{\def\PstColorSynthesis@ColorG{#1}} 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 \def\PstColorSynthesis@i{{% \setkeys{psset}{linestyle=none}% \use@par% Assignment of local parameters % The initial surfaces in their original colors \bgroup \setkeys{psset}{fillstyle=solid,fillcolor=\PstColorSynthesis@ColorA}% \PstColorSynthesis@SurfaceA \setkeys{psset}{fillcolor=\PstColorSynthesis@ColorB}% \PstColorSynthesis@SurfaceB \setkeys{psset}{fillcolor=\PstColorSynthesis@ColorC}% \PstColorSynthesis@SurfaceC \egroup % We redraw them in a combinatorial way, with clipping \PstColorSynthesis@ClippedSurfaces{\PstColorSynthesis@SurfaceA} {\PstColorSynthesis@SurfaceB}{}{\PstColorSynthesis@ColorD}% \PstColorSynthesis@ClippedSurfaces{\PstColorSynthesis@SurfaceA} {\PstColorSynthesis@SurfaceC}{}{\PstColorSynthesis@ColorE}% \PstColorSynthesis@ClippedSurfaces{\PstColorSynthesis@SurfaceB} {\PstColorSynthesis@SurfaceC}{}{\PstColorSynthesis@ColorF}% \PstColorSynthesis@ClippedSurfaces{\PstColorSynthesis@SurfaceA} {\PstColorSynthesis@SurfaceB}{\PstColorSynthesis@SurfaceC} {\PstColorSynthesis@ColorG}}} 32 33 34 35 36 37 38 39 \def\PstColorSynthesis@ClippedSurfaces#1#2#3#4{% % We draw the first surface #1 in color #4, clipped by the one % or two others #2 and #3 \psclip{#2#3} \setkeys{psset}{fillstyle=solid,fillcolor=#4}% #1 \endpsclip} 40 41 42 43 44 45 \PstColorSynthesis[SurfaceA={\parabola(-1,-1)(1,2)}, SurfaceB={\pswedge(1,1){2}{-70}{150}}, SurfaceC={\pspolygon[linearc=0.3](-1,-1)(-1,3)(4,-1)(4,3)}, ColorA=red,ColorB=green,ColorC=blue,ColorD=yellow,ColorE=cyan, ColorF=magenta,ColorG=white] Writing high-level macros: Examples 220 So, we have already make huge progress! Moreover, the resulting code is far more general, powerful and in fact easier to write as it involve no manual computations of intersection regions. It is no longer than our first working version. Nevertheless, a major weakness remains: the mixed colors must be manually computed externally and provided as parameters. To solve this problem, we must use other TEX programming technics.54 1 2 3 4 % % % % Additive color synthesis (correct results only for sums of RGB components <= 1) Colors must be defined according the RGB model (so, for instance, to use “black”, it must be redefined in RGB) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \def\PstColorSynthesis@i{{% \setkeys{psset}{linestyle=none}% \use@par% Assignment of local parameters \bgroup \setkeys{psset}{fillstyle=solid,fillcolor=\PstColorSynthesis@ColorA}% \PstColorSynthesis@SurfaceA \setkeys{psset}{fillcolor=\PstColorSynthesis@ColorB}% \PstColorSynthesis@SurfaceB \setkeys{psset}{fillcolor=\PstColorSynthesis@ColorC}% \PstColorSynthesis@SurfaceC \egroup % We redraw them in a combinatorial way, with clipping, % and computing the resulting color of overlapped surfaces % two by two then the three together \PstColorSynthesis@ClippedSurfaces{A}{B}{NoSurface}% \PstColorSynthesis@ClippedSurfaces{A}{C}{NoSurface}% \PstColorSynthesis@ClippedSurfaces{B}{C}{NoSurface}% \PstColorSynthesis@ClippedSurfaces{A}{B}{C}}} 24 25 26 27 % For the cases where there are only two surfaces % in the combination \def\PstColorSynthesis@ColorNoSurface{} 28 29 30 % We draw the first surface #1 clipped by the one % or two others #2 and #3, computing it resulting color 54 Note that the proposed solution here is based on the color package, which can be used with P LAIN TEX and LATEX, but with ConTEXt, modifications must be made to implement color management. Writing high-level macros: Examples 221 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 \def\PstColorSynthesis@ClippedSurfaces#1#2#3{% % We compute the “mixed” color, component by component \def\PstColorSynthesis@MixedColorR{0}% \def\PstColorSynthesis@MixedColorG{0}% \def\PstColorSynthesis@MixedColorB{0}% \PstColorSynthesis@MixedColor{% \csname PstColorSynthesis@Color#1\endcsname}% \PstColorSynthesis@MixedColor{% \csname PstColorSynthesis@Color#2\endcsname}% \PstColorSynthesis@MixedColor{% \csname PstColorSynthesis@Color#3\endcsname}% % We draw the first surface, clipped by the other ones \psclip{\csname PstColorSynthesis@Surface#2\endcsname% \csname PstColorSynthesis@Surface#3\endcsname} \definecolor{MixedColor}{rgb}{\PstColorSynthesis@MixedColorR, \PstColorSynthesis@MixedColorG, \PstColorSynthesis@MixedColorB}% \setkeys{psset}{fillstyle=solid,fillcolor=MixedColor}% \csname PstColorSynthesis@Surface#1\endcsname \endpsclip} 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 \def\PstColorSynthesis@MixedColor#1{% \edef\@tempa{#1}% \ifx\@tempa\@empty \else % We ask for the values of the 3 components of the color. % This is the difficult line: % - in the “color” package, a color is defined by the macro % \color@ColorName, % - so, we must build the macro name \color@#1 and call % the macro \PstColorSynthesis@MixedColor@i with the % result of the execution of it. % % Note also that, if we want to manage too the “cmyk” color % model, this macro and the next one must me modified, as % \color@ColorName will return one argument more: % \pst@expandafter\PstColorSynthesis@MixedColor@i{% % \csname\string\color @#1\endcsname} \@nil % ... % \def\PstColorSynthesis@MixedColor@i#1 #2 #3 #4 #5\@nil{% % \pst@expandafter\PstColorSynthesis@MixedColor@i{% \csname\string\color@#1\endcsname}\@nil \fi} 75 76 77 78 79 80 81 82 83 \def\PstColorSynthesis@MixedColor@i#1 #2 #3 #4\@nil{% % We receive the name of the color model (“rgb” is expected % here) and the three color components. % We add the values to the respective components of the new % color to compute. \PstColorSynthesis@MixedColor@ii{% \PstColorSynthesis@MixedColorR}{#2}% \PstColorSynthesis@MixedColor@ii{% Writing high-level macros: Examples 222 84 85 86 \PstColorSynthesis@MixedColorG}{#3}% \PstColorSynthesis@MixedColor@ii{% \PstColorSynthesis@MixedColorB}{#4}} 87 88 89 90 91 92 93 94 \def\PstColorSynthesis@MixedColor@ii#1#2{% % As these values are real numbers, we use a dimension % register, then we assign the computed value in a macro, % converting it from a dimension to a number \pst@dimg=#1\p@ \advance\pst@dimg by #2\p@ \pst@dimtonum{\pst@dimg}{#1}} 95 96 97 98 \PstColorSynthesis[SurfaceA={\pscircle{2}}, SurfaceB={\pscircle(2,0){2}},SurfaceC={\pscircle(1,2){2}}, ColorA=red,ColorB=green,ColorC=blue] What is still missing is correct automatic computation of the mixed colors, according to the rules of the additive color synthesis, in cases where the sum of individual color components is greater than 1.55 1 2 3 4 % We draw the first surface #1 clipped by the one % or two others #2 and #3, computing it resulting color \def\PstColorSynthesis@ClippedSurfaces#1#2#3{% % We compute the “mixed” color, component by component 55 For a generalized solution to the drawing of overlapped surfaces, you can see the code of the ‘pst-csyn’ contribution package [56], from Denis Girou and Manuel Luque which implement: • several synthesis managements (additive, substractive, average), • several color models (RGB and CMYK), • the management of any number of surfaces (which is in fact the main difficulty in this problem, as it open a combinational problem.), • support both the colors management of the color package with P LAIN TEX and LATEX and the one of ConTEXt. Writing high-level macros: Examples 223 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 \def\PstColorSynthesis@MixedColorR{0}% \def\PstColorSynthesis@MixedColorG{0}% \def\PstColorSynthesis@MixedColorB{0}% % \pst@dimd will contain the maximum value of the three % components. \pst@dimd=\z@ \PstColorSynthesis@MixedColor{% \csname PstColorSynthesis@Color#1\endcsname}% \PstColorSynthesis@MixedColor{% \csname PstColorSynthesis@Color#2\endcsname}% \PstColorSynthesis@MixedColor{% \csname PstColorSynthesis@Color#3\endcsname}% % We must test if the maximum of the new computed % component is greater than 1, in which case we divide all % the three components by this value for additive synthesis. \ifdim\pst@dimd>\@ne\p@ \PstColorSynthesis@MixedColor@iii{% \PstColorSynthesis@MixedColorR}% \PstColorSynthesis@MixedColor@iii{% \PstColorSynthesis@MixedColorG}% \PstColorSynthesis@MixedColor@iii{% \PstColorSynthesis@MixedColorB}% \fi % We draw the first surface, clipped by the other ones \psclip{\csname PstColorSynthesis@Surface#2\endcsname% \csname PstColorSynthesis@Surface#3\endcsname} \definecolor{MixedColor}{rgb}{\PstColorSynthesis@MixedColorR, \PstColorSynthesis@MixedColorG, \PstColorSynthesis@MixedColorB}% \setkeys{psset}{fillstyle=solid,fillcolor=MixedColor}% \csname PstColorSynthesis@Surface#1\endcsname \endpsclip} 37 38 39 40 41 42 43 44 45 46 47 48 \def\PstColorSynthesis@MixedColor@i#1 #2 #3 #4\@nil{% % We receive the name of the color model (“rgb” is expected % here and the three color components.) % We add the values to the respective components of the new % color to compute. \PstColorSynthesis@MixedColor@ii{% \PstColorSynthesis@MixedColorR}{#2}% \PstColorSynthesis@MixedColor@ii{% \PstColorSynthesis@MixedColorG}{#3}% \PstColorSynthesis@MixedColor@ii{% \PstColorSynthesis@MixedColorB}{#4}} 49 50 51 52 53 54 55 56 57 \def\PstColorSynthesis@MixedColor@ii#1#2{% % As these values are real numbers, we use dimension % registers, then we assign the computed value in a macro, % converting it from a dimension to a number. % We also keep in \pst@dimd the maximum of the values. \pst@dimg=#1\p@ \advance\pst@dimg by #2\p@ \pst@dimtonum{\pst@dimg}{#1}% Writing high-level macros: Examples 224 58 59 60 \ifdim\pst@dimg>\pst@dimd \pst@dimd=\pst@dimg \fi} 61 62 63 64 65 66 67 68 \def\PstColorSynthesis@MixedColor@iii#1{% \pst@divide{#1\p@}{\pst@dimd}{#1}% % We must take care of possible rounding problems with % \pst@divide (for instance, 1.8/1.8 give 1.0001) \ifdim#1\p@>\@ne\p@ \def#1{1}% \fi} 69 70 71 72 73 74 75 76 77 78 79 80 81 % We redefine Cyan, Magenta and Yellow in the “rgb” model \definecolor{Cyan}{rgb}{0,1,1}% \definecolor{Magenta}{rgb}{1,0,1}% \definecolor{Yellow}{rgb}{1,1,0}% \PstColorSynthesis[SurfaceA={\pscircle{2}}, SurfaceB={\pscircle(2,0){2}},SurfaceC={\pscircle(1,2){2}}, ColorA=Cyan,ColorB=Magenta,ColorC=Yellow] \PstColorSynthesis[SurfaceA={\psccurve(-3,1)(0,2.5)(2,1.5)(4,3)(4,-1) (3,0)(1,-2.5)(-1,-1)(-3,-3)}, SurfaceB={\psellipticarc(0,-1)(3,1.5){41}{-92}}, SurfaceC={\pstriangle(1,-2)(5,5)}, ColorA=SlateBlue,ColorB=Orange,ColorC=Pink] 64.5 Advanced example: three dimensional lighten effect In this example, we will mainly emphasize how to use doc format, which is a very convenient way to organize and distribute a package, and how to define and use a new PostScript header file, relative to a specialized package. The main purpose to do that is to load some PostScript code only one time and to reuse it as many times as needed in some TEX macros, without duplicate it. This is the general way of how PSTricks works. The new header Writing high-level macros: Examples 225 file must be accessible to the dvi converter, or directly to the compiler if it contain itself a PostScript interpreter, like someones have. We will illustrate this way to proceed on an example which has the only behavior to produce a visual effect, similar to a light on a three dimensional frame of objects. This could be applied to both characters and PSTricks curves. The idea come from a short PostScript code from Peter Kleiweg [36], which create a lighten effect on characters. We interface this PostScript code with TEX,56 give it a PSTricks interface, and extend it to opened or closed curves –but this does not work with most of the line parameters (arrows, linestyle, doubleline, etc.) The code is short but not very simple. Nevertheless, most readers can forgot the difficult parts, just looking at the architecture of the code and at the interaction between the TEX and the PostScript macros. The TEX macros are for a large part an adaptation of the \pscharpath macro from the ‘pstchar’ package (see Section 59.) In addition, we use here the doc format [11] (by convention, these files use the .dtx suffix), which allow to embed in only one file all the various source files of a package, with the user’s documentation and the internal documentation of the source code. This is a LATEX package, but LATEX is only required to generate the documentation and the package itself can be a generic one, working both with P LAIN TEX and ConTEXt, as this is the case here. First we give the driver file ‘pst-li3d.ins’, which will generate the various files of the package when compiling it by TEX. Three files will be created here, pst-li3d.sty (the LATEX wrapper), pst-li3d.tex (the generic TEX file) and pst-li3d.pro (the PostScript header file.) Here, we must take care to do not generate an \endinput line at the end of the PostScript file, which is the default behavior, relevant for all TEX files, but this would cause an error for a non TEX file as this one (we use the \usepostamble macro to change this behavior.) 1 2 3 4 5 6 7 8 9 %% %% %% %% %% %% %% %% %% ‘pst-li3d.ins’ Docstrip installation instruction file for docstyle ‘pst-li3d’ Denis Girou (CNRS/IDRIS - France) <Denis.Girou@idris.fr> and Peter Kleiweg (Rijksuniversiteit Groningen - Nederlands) <kleiweg@let.rug.nl> July 10, 2003 10 11 \def\batchfile{pst-li3d.ins} 56 We keep the same algorithm, but we change in some place the order of the computations to avoid to generate overflow computations in PostScript, which frequently arrived otherwise with the numerical values manipulated by TEX on PostScript fonts. Take care that nevertheless such overflows could still arrive Writing high-level macros: Examples 226 12 13 14 15 16 17 \input docstrip.tex \keepsilent \Msg{*** Generating the ‘pst-li3d’ package ***} \askforoverwritefalse \generate{\file{pst-li3d.tex}{\from{pst-li3d.dtx}{pst-li3d}}} \generate{\file{pst-li3d.sty}{\from{pst-li3d.dtx}{latex-wrapper}}} 18 19 20 21 22 23 % We must not write the “\endinput” line at the end % of this external file! \def\EpsFilePostamble{\MetaPrefix\space End of file ‘\outFileName’.} \usepostamble\EpsFilePostamble \generate{\file{pst-li3d.pro}{\from{pst-li3d.dtx}{postscript-header}}} 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 \ifToplevel{% \Msg{***********************************************************} \Msg{*} \Msg{* To finish the installation you have to move the files} \Msg{* pst-li3d.sty and pst-li3d.tex in a directory/folder searched} \Msg{* by TeX and the file pst-li3d.pro in a directory/folder} \Msg{* searched by the DVI converter or the compiler, depending} \Msg{* of your installation.} \Msg{*} \Msg{* To produce the documentation, run the file ‘pst-li3d.dtx’} \Msg{* through LaTeX.} \Msg{*} \Msg{* If you require the commented code, desactivating the} \Msg{* OnlyDescription macro, you must recompile, execute:} \Msg{* ‘makeindex -s gind.ist pst-li3d’} \Msg{* ‘makeindex -s gglo.ist -o pst-li3d.gls pst-li3d.glo’} \Msg{* and recompile.} \Msg{*} \Msg{***********************************************************} } 45 46 47 48 \endinput %% %% End of file ‘pst-li3d.ins’ Then the core file, called ‘pst-li3d.dtx’. Note that the comment prefix for this file (not for the ones that will be generated!) is ^^A. 1 2 3 4 5 6 7 8 9 10 11 % \iffalse meta-comment, etc. %% %% Package ‘pst-li3d.dtx’ %% %% Denis Girou (CNRS/IDRIS - France) <Denis.Girou@idris.fr> %% and Peter Kleiweg (Rijksuniversiteit Groningen - Nederlands) %% <kleiweg@let.rug.nl> %% %% July 10, 2003 %% %% This program can be redistributed and/or modified under Writing high-level macros: Examples 227 12 13 14 15 16 17 18 19 %% the terms of the LaTeX Project Public License Distributed %% from CTAN archives in directory macros/latex/base/lppl.txt. %% %% DESCRIPTION: %% ‘pst-li3d’ is a PSTricks package for three dimensional %% lighten effect on characters and PSTricks graphics. %% % \fi The \changes macro allow to describe the various releases of the package. 20 % \changes{v1.0}{2003/07/10}{First public release.} The \CheckSum macro offer a simple way to verify the integrity of the .dtx file. It is based on the number of macros used in the file. The exact value will be given after a compilation of the file by LATEX, and is to put as the argument of the macro. 21 % \CheckSum{121} The \DoNotIndex macros allow to give the list of the macros used in the file which are not to be used as entries to generate the index (for the documentation of the source code), as this index is supposed to refer mainly to the new macros defined in the package. And settings the IndexColumns counter to 2 require to format the index on two columns. 22 23 24 25 26 27 28 29 % % % % % % % % \DoNotIndex{\@} \DoNotIndex{\begin,\begin@ClosedObj,\box} ... \DoNotIndex{\use@par,\use@pscode,\usepackage} ^^A For the index and changes log (if source code printed) \setcounter{IndexColumns}{2} \setlength{\columnseprule}{0.6pt} We then define some utility macros convenient to format the documentation of the package. This is mainly some example macros,57 which allow to include only one time the source code of some examples and to format it twice, one time in verbatim mode showing the code and another time as the result produced by the compilation of this code. Such macros are essential to guarantee that the two ones will be synchronised after various updates of the documentation. 57 The ones we use here are built above the ‘fancyvrb’ package [16]. Writing high-level macros: Examples 228 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 % % % % % % % % % % % % % % % ^^A Utility macros \newcommand{\PstLightThreeDPackage}{‘\textsf{pst-li3d}’} ^^A A list of options for a package/class (from ltugboat.cls) \newenvironment{optlist}{\begin{description}% \renewcommand\makelabel[1]{% \descriptionlabel{\mdseries\textsf{##1}}}% \itemsep0.25\itemsep}% {\end{description}} \makeatletter ^^A Example macros ... Then we insert all the user’s documentation of the package, not included here, as we will add it later, but formatted. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ^^A Beginning of the documentation itself \title{The \PstLightThreeDPackage{} package\\ A PSTricks package for three dimensional\\ lighten effect on characters and PSTricks graphics} \author{Denis \textsc{Girou} ... and Peter \textsc{Kleiweg} ...} \date{Version 1.0\\July 10, 2003\\ {\small Documentation revised July 10, 2003}} \maketitle \begin{abstract} This package allow to add a three dimensional lighten effect on characters (PostScript fonts), using the \cs{PstLightThreeDText} macro, and curves (opened or closed), using the \cs{PstLightThreeDGraphic} macro, with various customization parameters. \end{abstract} \tableofcontents \section{Introduction} ... \section{Usage} \section{Examples} ... \StopEventually{} Writing high-level macros: Examples 229 76 77 % % ^^A .................... End of the documentation part .................... 4 Driver file Then we include the driver file which will be used to generate the documentation. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 % \section{Driver file} % % The next bit of code contains the documentation driver file % for \TeX{}, i.e., the file that will produce the documentation % you are currently reading. It will be extracted from this file % by the \texttt{docstrip} program. % % \begin{macrocode} %<*driver> \documentclass{ltxdoc} \GetFileInfo{pst-li3d.dtx} \usepackage{fancyvrb} \usepackage{multido} \usepackage{pstcol} \usepackage{pst-grad} \usepackage{pst-li3d} \usepackage{pst-plot} \usepackage{pst-tree} \usepackage{url} \definecolor{DarkGreen}{cmyk}{1,0,1,0.8} \definecolor{Gold} {rgb}{1,0.84,0} \definecolor{Violet} {cmyk}{0.79,0.88,0,0} \EnableCrossrefs \CodelineIndex \RecordChanges \OnlyDescription % Comment it for implementation details \hbadness=7000 % Over and under full box warnings \hfuzz=3pt \begin{document} \DocInput{pst-li3d.dtx} \end{document} %</driver> % \end{macrocode} 5 ‘pst-li3d’ LATEX wrapper Then we define the short LATEX wrapper file, which will be useful for LATEX users. 1 2 3 % \section{\PstLightThreeDPackage{} \LaTeX{} wrapper} % % \begin{macrocode} Writing high-level macros: Driver file 230 4 5 6 7 8 9 %<*latex-wrapper> \ProvidesPackage{pst-li3d}[2003/07/10 package wrapper for PSTricks pst-li3d.tex] \input{pst-li3d} %</latex-wrapper> % \end{macrocode} And now the generic TEX (and PSTricks) package. The source comments are inside the file, but we just repeat them here to have also them formatted, as when the documented source code is generated. 6 ‘pst-li3d’ code 1 2 3 4 5 % \section{\PstLightThreeDPackage{} code} % % \begin{macrocode} %<*pst-li3d> % \end{macrocode} 6.1 Preambule Who we are. 1 2 3 4 5 6 7 8 9 10 11 12 % \subsection{Preambule} % % Who we are. % % \begin{macrocode} \def\FileVersion{1.0} \def\FileDate{2003/07/10} \message{‘Pst-Light3d’ v\FileVersion, \FileDate\space (Denis Girou and Peter Kleiweg)} \csname PSTLightThreeDLoaded\endcsname \let\PSTLightThreeDLoaded\endinput % \end{macrocode} Require the PSTricks package. 1 2 3 4 5 % Require the PSTricks package. % % \begin{macrocode} \ifx\PSTricksLoaded\endinput\else\input{pstricks}\fi % \end{macrocode} David C ARLISLE interface to the ‘keyval’ package. 1 2 3 % David \textsc{Carlisle} interface to the ‘\textsf{keyval}’ % package. % Writing high-level macros: ‘pst-li3d’ code 231 4 5 6 % \begin{macrocode} \input{pst-key} % \end{macrocode} Catcodes changes. 1 2 3 4 5 6 % Catcodes changes. % % \begin{macrocode} \edef\PstAtCode{\the\catcode‘\@} \catcode‘\@=11\relax % \end{macrocode} We load the PostScript header file. 1 2 3 4 5 % We load the PostScript header file. % % \begin{macrocode} \pstheader{pst-li3d.pro} % \end{macrocode} 6.2 Definition of the parameters LightThreeDXLength will be the horizontal length of the frame added. It is a length value. 1 2 3 4 5 6 7 8 9 % \subsection{Definition of the parameters} % % \texttt{LightThreeDXLength} will be the horizontal length of the % frame added. It is a \emph{length} value. % % \begin{macrocode} \define@key{psset}{LightThreeDXLength}{% \pst@getlength{#1}{\PstLightThreeD@XLength}} % \end{macrocode} LightThreeDYLength will be the vertical length of the frame added. It is a length value. 1 2 3 4 5 6 7 % \texttt{LightThreeDYLength} will be the vertical length of the % frame added. It is a \emph{length} value. % % \begin{macrocode} \define@key{psset}{LightThreeDYLength}{% \pst@getlength{#1}{\PstLightThreeD@YLength}} % \end{macrocode} LightThreeDLength will define both the horizontal and the vertical length of the frame added. It is a length value. Writing high-level macros: ‘pst-li3d’ code 232 1 2 3 4 5 6 7 8 9 % \texttt{LightThreeDLength} will define both the horizontal and % the vertical length of the frame added. It is a \emph{length} % value. % % \begin{macrocode} \define@key{psset}{LightThreeDLength}{% \pst@getlength{#1}{\PstLightThreeD@XLength}% \pst@getlength{#1}{\PstLightThreeD@YLength}} % \end{macrocode} LightThreeSteps will be the number of steps for the light effect. It works like a resolution parameter. It is an integer value. 1 2 3 4 5 6 7 8 % \texttt{LightThreeSteps} will be the number of steps for the % light effect. It works like a resolution parameter. It is an % \emph{integer} value. % % \begin{macrocode} \define@key{psset}{LightThreeDSteps}{% \pst@getint{#1}{\PstLightThreeD@Steps}} % \end{macrocode} LightThreeDAngle will be the angle used. It will act as an angle for the light effect. It is a real value used as an angle. 1 2 3 4 5 6 7 8 % \texttt{LightThreeDAngle} will be the angle used. It will act as % an angle for the light effect. It is a \emph{real} value used as % an \emph{angle}. % % \begin{macrocode} \define@key{psset}{LightThreeDAngle}{% \pst@getangle{#1}{\PstLightThreeD@LightAngle}} % \end{macrocode} LightThreeDColorPsCommand will be the PostScript sequence of com- mands which will define the color of the frame added, which must use the last value of the PostScript stack. Good results are obtained when this value is used with the setgray operator or as the Saturation or Brightness component of the sethsbcolor one, using the HSB color model. It is a string value. 1 2 3 4 5 6 7 8 % % % % % % % % \texttt{LightThreeDColorPsCommand} will be the PostScript sequence of commands which will define the color of the frame added, which must use the last value of the PostScript stack. Good results are obtained when this value is used with the \texttt{setgray} operator or as the Saturation or Brightness component of the \texttt{sethsbcolor} one, using the HSB color model. It is a \emph{string} value. Writing high-level macros: ‘pst-li3d’ code 233 9 10 11 12 13 % % \begin{macrocode} \define@key{psset}{LightThreeDColorPsCommand}{% \edef\PstLightThreeD@ColorPsCommand{#1}} % \end{macrocode} Next, we set the default values for all these new parameters. 1 2 3 4 5 6 7 8 % Next, we set the default values for all these new parameters. % % \begin{macrocode} \setkeys{psset}{% LightThreeDXLength=0.2,LightThreeDYLength=0.3, LightThreeDSteps=40,LightThreeDAngle=45, LightThreeDColorPsCommand=2.5 div setgray} % \end{macrocode} 6.3 Main macros The general \PstLightThreeDGraphic macro to apply the lighten effect on a graphic (an opened or closed curve). This is a PSTricks object. 1 2 3 4 5 6 7 8 9 10 11 12 13 % \subsection{Main macros} % % The general \cs{PstLightThreeDGraphic} macro to apply the % lighten effect on a graphic (an opened or closed curve). % This is a PSTricks object. % % \begin{macro}{\PstLightThreeDGraphic} % \begin{macrocode} \def\PstLightThreeDGraphic{% \def\pst@par{}% \pst@object{PstLightThreeDGraphic}} % \end{macrocode} % \end{macro} Then we define it auxiliary macro which will handle the parameters, if some are used, initialize the PostScript environment and redefine the stroke PostScript operator calling two times the LightThreeDPathForAll PostScript macro defined in the header file. 1 2 3 4 5 6 7 8 9 % Then we define it auxiliary macro which will handle the % parameters, if some are used, initialize the PostScript % environment and redefine the \texttt{stroke} PostScript % operator calling two times the \texttt{LightThreeDPathForAll} % PostScript macro defined in the header file. % % \begin{macro}{\PstLightThreeDGraphic@i} % \begin{macrocode} \def\PstLightThreeDGraphic@i{% Writing high-level macros: ‘pst-li3d’ code 234 10 11 12 13 14 15 16 17 \pst@makebox{% \PstLightThreeD@i{% /LightThreeDDXa LightThreeDDX def /LightThreeDDYa LightThreeDDY def /stroke {gsave reversepath LightThreeDPathForAll grestore LightThreeDPathForAll } def}{end}}} % \end{macrocode} % \end{macro} Now, the general \PstLightThreeDText macro to apply the lighten effect on a text (using PostScript fonts). This is a PSTricks object too. 1 2 3 4 5 6 7 8 9 % Now, the general \cs{PstLightThreeDText} macro to apply the % lighten effect on a text (using PostScript fonts). This is a % PSTricks object too. % % \begin{macro}{\PstLightThreeDText} % \begin{macrocode} \def\PstLightThreeDText{\def\pst@par{}\pst@object{PstLightThreeDText}} % \end{macrocode} % \end{macro} Then we define it auxiliary macro which will handle the parameters, if some are used, initialize the PostScript environment, keep the content of the show PostScript operator, redefine it, calling the LightThreeDPathForAll PostScript macro defined in the header file, redraw a second time the outline path using the charpath operator, and restore the old content of the show operator. In fact, this code is very similar to the one of the \pscharpath macro from the ‘pst-char’ package. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 % Then we define it auxiliary macro which will handle the % parameters, if some are used, initialize the PostScript % environment, keep the content of the \texttt{show} PostScript % operator, redefine it, calling the \texttt{LightThreeDPathForAll} % PostScript macro defined in the header file, redraw a second % time the outline path using the \texttt{charpath} operator, % and restore the old content of the \texttt{show} operator. In fact, % this code is very similar to the one of the \cs{pscharpath} % macro from the ‘\textsf{pst-char}’ package. % % \begin{macro}{\PstLightThreeDText@i} % \begin{macrocode} \def\PstLightThreeDText@i{% \pst@makebox{% \PstLightThreeD@i{% /LightThreeDDXa LightThreeDDX Resolution 100 div mul def /LightThreeDDYa LightThreeDDY VResolution 100 div mul def /tx@LightThreeDSavedShow /show load def /show { dup Writing high-level macros: ‘pst-li3d’ code 235 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 gsave false charpath reversepath LightThreeDPathForAll grestore true charpath} def} {/show /tx@LightThreeDSavedShow load def end}% \begin@ClosedObj \def\use@pscode{% \pst@Verb{% gsave \tx@STV \pst@code grestore CP newpath moveto}% \gdef\pst@code{}}% \end@ClosedObj}} % \end{macrocode} % \end{macro} 6.4 Auxiliary macro Both the \PstLightThreeDGraphic and \PstLightThreeDText macros call the auxiliary \PstLightThreeD@i macro, which assign the local PSTricks parameters initialize the various PostScript variables which depend of the PSTricks parameters that the user can change, draw the content (text or PSTricks graphic) and restore some PostScript operator, if needed. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 % \subsection{Auxiliary macro} % % Both the \cs{PstLightThreeDGraphic} and % \cs{PstLightThreeDText} macros call the auxiliary % \cs{PstLightThreeD@i} macro, which assign the local PSTricks % parameters initialize the various PostScript variables which % depend of the PSTricks parameters that the user can change, % draw the content (text or PSTricks graphic) and restore some % PostScript operator, if needed. % % \begin{macro}{\PstLightThreeD@i} % \begin{macrocode} \def\PstLightThreeD@i#1#2{{% % \end{macrocode} Assignment of local parameters. 1 2 3 4 5 % Assignment of local parameters. % % \begin{macrocode} \use@par % \end{macrocode} Writing high-level macros: ‘pst-li3d’ code 236 Initialization of the various PostScript variables which depend of the PSTricks parameters that the user can change. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 % Initialization of the various PostScript variables which % depend of the PSTricks parameters that the user can change. % % \begin{macrocode} \leavevmode \pstVerb{% tx@LightThreeDDict begin /LightThreeDDX \PstLightThreeD@XLength\space def /LightThreeDDY \PstLightThreeD@YLength\space neg def /LightThreeDSteps \PstLightThreeD@Steps def /LightThreeDAngle \PstLightThreeD@LightAngle def /LightThreeDColorPsCommand {\PstLightThreeD@ColorPsCommand} def /LightThreeDMINangle LightThreeDDY LightThreeDDX atan 180 sub def /LightThreeDMAXangle LightThreeDDY LightThreeDDX atan def #1}% % \end{macrocode} Draw the content (text or PSTricks graphic). 1 2 3 4 5 % Draw the content (text or PSTricks graphic). % % \begin{macrocode} \hbox{\box\pst@hbox}% % \end{macrocode} Restoration, if needed, of some PostScript operator (for texts, the show one, in fact). 1 2 3 4 5 6 7 % Restoration, if needed, of some PostScript operator % (for texts, the “show” one, in fact). % % \begin{macrocode} \pstVerb{#2}}} % \end{macrocode} % \end{macro} 6.5 Closing Catcodes restoration. 1 2 3 4 % \subsection{Closing} % % Catcodes restoration. % Writing high-level macros: ‘pst-li3d’ code 237 5 6 7 1 2 3 % \begin{macrocode} \catcode‘\@=\PstAtCode\relax % \end{macrocode} % \begin{macrocode} %</pst-li3d> % \end{macrocode} And now, to finish, the PostScript header file, with the PostScript macros used,58 which will be put in an header file ‘pst-3dli.pro’.59 We define our new PostScript macros inside a personal dictionary. Four macros are defined, to be able to redefine later the standard basic moveto, lineto, curveto and closepath operators with the pathforall macro, which will allow to draw the current paths in the new way that we program here. 7 ‘pst-li3d’ PostScript header file First, identification and references. 1 2 3 1 2 3 4 5 6 7 8 9 10 % \begin{macrocode} %<*postscript-header> % \end{macrocode} % \begin{macrocode} %! % PostScript header file pst-li3d.pro % Version 1.0, 2003/07/10 % % Adapted from Peter Kleiweg <kleiweg@let.rug.nl> % See http://odur.let.rug.nl/~kleiweg/postscript/postscript.html % (file depth.ps) % % \end{macrocode} The dictionary for this package. 1 2 3 4 5 6 % The dictionary for this package. % % \begin{macrocode} /tx@LightThreeDDict 40 dict def tx@LightThreeDDict begin % \end{macrocode} 58 For explanations of them, see [51] or other references on the PostScript programming language. 59 For instance, with a teTeX distribution, it would be put logically in the TeX hierarchy local to the system, so in the /usr/local/share/texmf/dvips/pstricks subdirectory. Writing high-level macros: ‘pst-li3d’ PostScript header file 238 The LightThreeDMove operator, which will replace the moveto operator in the pathforall call. Syntax is: <x> <y> LightThreeDMove 1 2 3 4 5 6 7 8 9 10 11 12 13 % The \texttt{LightThreeDMove} operator, which will replace the % \texttt{moveto} operator in the \texttt{pathforall} call. % Syntax is: \Verb+<x> <y> LightThreeDMove+ % % \begin{macrocode} /LightThreeDMove { /y0c exch def /x0c exch def /xc x0c def /yc y0c def newpath } def % \end{macrocode} The LightThreeDLine operator, which will replace the lineto operator in the pathforall call. Syntax is: <x> <y> LightThreeDLine 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 % The \texttt{LightThreeDLine} operator, which will replace the % \texttt{lineto} operator in the \texttt{pathforall} call. % Syntax is: \Verb+<x> <y> LightThreeDLine+ % % \begin{macrocode} /LightThreeDLine { /yyc exch def /xxc exch def yyc yc sub xxc xc sub 1 index 0 eq 1 index 0 eq and not { atan /ac exch def ac LightThreeDMINangle le ac LightThreeDMAXangle ge or { ac LightThreeDAngle sub 2 mul cos 1 add LightThreeDColorPsCommand xc yc moveto xxc yyc lineto LightThreeDDXa LightThreeDDYa rlineto xc LightThreeDDXa add yc LightThreeDDYa add lineto closepath fill } if } if /xc xxc def /yc yyc def } def Writing high-level macros: ‘pst-li3d’ PostScript header file 239 32 % \end{macrocode} The LightThreeDCurve operator, which will replace the curveto operator in the pathforall call. Syntax is: <x2> <y2> <x3> <y3> <x4> <y4> LightThreeDCurve 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 % The \texttt{LightThreeDCurve} operator, which will replace the % \texttt{curveto} operator in the \texttt{pathforall} call. % Syntax is: % \Verb+<x2> <y2> <x3> <y3> <x4> <y4> LightThreeDCurve+ % % \begin{macrocode} /LightThreeDCurve { /y4c exch def /x4c exch def /y3c exch def /x3c exch def /y2c exch def /x2c exch def /y1c yc def /x1c xc def % \end{macrocode} It is faster to make some preliminary computations outside the loop, as in the original file from Peter Kleiweg, but with TEX it can generate huge numbers which make the PostScript interpreter crash!60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 % % % % % % % % % % It is faster to make some preliminary computations outside the loop, as in the original file form Peter Kleiweg, but it can generate huge numbers which make the PostScript interpreter crash!\footnote{% It still can occur on some (unknown) circumstances. In such cases, just moving the text or graphinc is generally enough to cure the problem...} \begin{macrocode} Computations order changed from the original file 1 LightThreeDSteps div 1 LightThreeDSteps div 1 { /t exch def 3 t sub x1c mul t 2 sub x2c mul 1 t sub x3c mul add 3 mul add x4c t mul add t mul x2c x1c sub 3 mul add t mul x1c add% X 3 t sub y1c mul t 2 sub y2c mul 60 It still can occur on some (unknown) circumstances. In such cases, just moving the text or graphic is generally enough to cure the problem... Writing high-level macros: ‘pst-li3d’ PostScript header file 240 21 22 23 24 25 26 27 28 DG: Code modified because the original one crash the PostScript interpreter of two printers that I tested, even if GhostScript handle it correctly... 1 t sub y3c mul add 3 mul add y4c t mul add t mul y2c y1c sub 3 mul add t mul y1c add% Y LightThreeDLine } for } def % \end{macrocode} The LightThreeDClose operator, which will replace the closepath operator in the pathforall call. Syntax is: LightThreeDClose 1 2 3 4 5 6 7 8 9 10 11 12 % The \texttt{LightThreeDClose} operator, which will replace % the \texttt{closepath} operator in the \texttt{pathforall} call. % Syntax is: \Verb+LightThreeDClose+ % % \begin{macrocode} /LightThreeDClose { % x0c y0c LightThreeDLine% Anomaly on some printers! x0c 0 eq {x0c} {x0c 1 add} ifelse y0c 0 eq {y0c} {y0c 1 add} ifelse LightThreeDLine newpath } def % \end{macrocode} The LightThreeDPathForAll operator, which will replace the pathforall operator to draw the current path with a three dimensional lighten effect. 1 2 3 4 5 6 7 8 9 % The \texttt{LightThreeDPathForAll} operator, which will % replace the \texttt{pathforall} operator to draw the current % path with a three dimensional lighten effect. % % \begin{macrocode} /LightThreeDPathForAll { { LightThreeDMove} { LightThreeDLine } { LightThreeDCurve } { LightThreeDClose } pathforall} def % \end{macrocode} Then, to finish, we close the dictionary. 1 2 3 4 5 1 2 3 % Then, to finish, we close the dictionary. % % \begin{macrocode} end % \end{macrocode} % \begin{macrocode} %</postscript-header> % \end{macrocode} Writing high-level macros: ‘pst-li3d’ PostScript header file 241 And, at the end, we print the index and the list of changes of the package. % \Finale % \PrintIndex % \PrintChanges % \endinput %% %% End of file ‘pst-li3d.dtx’ 1 2 3 4 5 6 7 Now, the new package can be used! 1 2 1 2 1 2 3 4 1 2 3 4 5 6 \DeclareFixedFont{\Bf}{T1}{ptm}{b}{n}{3cm} \PstLightThreeDText[fillstyle=solid,fillcolor=white]{\Bf Test} \PstLightThreeDText[linestyle=none,fillstyle=solid, fillcolor=darkgray]{\Bf Test} \psset{linestyle=none,fillstyle=solid,fillcolor=darkgray}% \PstLightThreeDText[LightThreeDAngle=0]{\Bf Test} \hfill \PstLightThreeDText[LightThreeDAngle=90]{\Bf Test} \psset{linestyle=none,fillstyle=solid,fillcolor=darkgray}% \PstLightThreeDText[LightThreeDXLength=0.5, LightThreeDYLength=-1]{\Bf Test} \hfill \PstLightThreeDText[LightThreeDXLength=-1, LightThreeDYLength=0.5]{\Bf Test} Writing high-level macros: ‘pst-li3d’ PostScript header file 242 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 1 2 \DeclareFixedFont{\Sf}{T1}{phv}{b}{n}{3cm} \psset{linestyle=none,fillstyle=solid,fillcolor=darkgray}% \PstLightThreeDText[LightThreeDColorPsCommand=% 1.2 div setgray]{\Sf 123} \hfill \PstLightThreeDText[LightThreeDColorPsCommand=% 2.5 div setgray]{\Sf 123} \DeclareFixedFont{\Rm}{T1}{ptm}{m}{n}{3cm} \psset{linestyle=none,fillstyle=solid}% \PstLightThreeDText[fillcolor=Violet, LightThreeDColorPsCommand=% 2.5 div 0.7 exch 0.8 sethsbcolor]{% \Rm 987} \hfill \PstLightThreeDText[fillcolor=DarkGreen, LightThreeDColorPsCommand=% 2 div 0.5 exch 0.2 exch sethsbcolor]{% \Rm 987} \DeclareFixedFont{\Rmb}{T1}{ptm}{m}{n}{4cm} \PstLightThreeDText[linestyle=none,fillstyle=solid,fillcolor=Gold, LightThreeDColorPsCommand=% 1.2 div 0.15 exch 0.7 exch sethsbcolor]{% \Rmb PSTricks} \psset{unit=0.5}% \pspicture(-0.1,-3.5)(7.2,3) Writing high-level macros: ‘pst-li3d’ PostScript header file 243 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 \PstLightThreeDGraphic[LightThreeDXLength=0.4, LightThreeDColorPsCommand=% 1.2 div 0.15 exch 0.7 exch sethsbcolor]{% \pscurve(0,2)(1,-3)(2,2)(4,3)(7,0)} \endpspicture \hfill \pspicture(0,-3.5)(7.7,3) \PstLightThreeDGraphic[LightThreeDXLength=0.8, LightThreeDColorPsCommand=% 2 div 0.35 exch 0.9 exch sethsbcolor]{% \pspolygon(0,2)(1,-3)(2,0)(4,1)(6,1)(7,3)} \endpspicture \hfill \pspicture(0.5,-3.6)(3.8,3) \PstLightThreeDGraphic[LightThreeDColorPsCommand=% 2.6 div 0.12 exch 0.7 exch sethsbcolor]{% \psellipse(2,0)(1.5,3)} \endpspicture Here we draw an ellipse. The second case is more sophisticated, as we will increase continously the starting value of the Brightness component of the HSB color, using a PostScript variable. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 \SpecialCoor \def\PstCoordinates{}% \Multido{\nDistance=0.00+0.02,\iAngle=0+20}{200}{% \edef\PstCoordinates{\PstCoordinates(\nDistance;\iAngle)}} \psset{unit=0.5}% \pspicture(-3.8,-4)(4.1,3.7) \PstLightThreeDGraphic[LightThreeDLength=0.2, LightThreeDColorPsCommand=% 1.2 div 0.3 exch 0.7 exch sethsbcolor]{% \expandafter\pscurve\PstCoordinates} \endpspicture \hfill \pspicture(-3.8,-4)(4.1,3.7) \PstLightThreeDGraphic[LightThreeDLength=0.2, LightThreeDAngle=30,LightThreeDColorPsCommand=% /Counter Counter 0.00005 add def 2 mul Counter exch 0.7 exch sethsbcolor]{% \pstVerb{/Counter 0 def}% \expandafter\pscurve\PstCoordinates} \endpspicture Writing high-level macros: ‘pst-li3d’ PostScript header file 244 1 2 3 Jane 4 5 6 7 8 Marc 9 10 11 12 Bob Ann Peter 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 \PstLightThreeDGraphic[LightThreeDXLength=0.2, LightThreeDYLength=-0.2, LightThreeDColorPsCommand=% 1.2 div 0.65 exch 0.9 sethsbcolor]{% \large \let\TovalORIG\Toval \def\Toval#1{\TovalORIG{\raise2mm\hbox{\hskip2mm#1}}}% \let\TtriORIG\Ttri \def\Ttri#1{\TtriORIG{\raise3mm\hbox{#1}}}% \psset{framesep=0.15,fillstyle=gradient,gradmidpoint=0, gradbegin=cyan,gradend=blue}% \pstree[treesep=0.5]{\Ttri{Jane}} {\psset{framesep=0.25}% \pstree{\Toval{Marc}} {\Toval{Bob}\Toval{Ann}\Toval{Peter}}}} \psset{xunit=8,yunit=3}% \pspicture*(-0.45,-1.6)(1,1.3) \psaxes[Dx=0.2,Oy=-1.2,Dy=0.2,tickstyle=top, axesstyle=frame](0,-1.2)(1,1.2) \rput(-0.3,0.1){\textcolor{red}{$\sin (10 \times x)$}} \rput(-0.3,-0.1){\textcolor{blue}{$\cos (40 \times x) / 2$}} \rput(0.5,-1.5){$x$} \psset{plotpoints=500,LightThreeDXLength=0.3, LightThreeDYLength=-0.3}% \PstLightThreeDGraphic[LightThreeDColorPsCommand=% 1.5 div 0.05 exch 0.8 sethsbcolor]{% \psplot{0}{1}{x 10 mul 57.296 mul sin}}% sin(10 x) \PstLightThreeDGraphic[LightThreeDColorPsCommand=% 1.5 div 0.6 exch 0.8 sethsbcolor]{% \psplot{0}{1}{x 40 mul 57.296 mul cos 2 div}}% cos(40 x) / 2 \endpspicture Writing high-level macros: ‘pst-li3d’ PostScript header file 245 1.2 1.0 0.8 0.6 0.4 sin(10 × x) cos(40 × x)/2 0.2 0.0 −0.2 −0.4 −0.6 −0.8 −1.0 −1.2 0 0.2 0.4 0.6 0.8 1.0 x Writing high-level macros: ‘pst-li3d’ PostScript header file 246 XIII 8 Obsolete commands Color commands This also means that the command \gray (or \red, etc.) can be used much like \rm or \tt, as in {\gray This stuff should be gray.} The commands \gray, \red, etc. can be nested like the font commands as well. There are a few important ways in which the color commands differ from the font commands: 1. The color commands can be used in and out of math mode (there are no restrictions, other than proper TEX grouping). 2. The color commands affect whatever is in their scope (e.g., lines), not simply characters. 3. The scope of the color commands does not extend across pages. 4. The color commands are not as robust as font commands when used inside box macros. See page ?? for details. You can avoid most problems by explicitly grouping color commands (e.g., enclosing the scope in braces {}) whenever these are in the argument of another command.61 You can define or redefine additional colors and grayscales with the following commands. In each case, numi is a number between 0 and 1. Spaces are used as delimiters—don’t add any extraneous spaces in the arguments. \newgray{color}{num} num is the gray scale specification, to be set by PostScript’s setgray operator. 0 is black and 1 is white. For example: 1 61 \newgray{darkgray}{.25} However, this is not necessary with the PSTricks LR-box commands, expect when \psverbboxtrue is in effect. See Section K. Obsolete commands 247 \newrgbcolor{color}{num1 num2 num3} num1 num2 num3 is a red-green-blue specification, to be set by PostScript’s setrgbcolor operator. For example, 1 \newrgbcolor{green}{0 1 0} \newhsbcolor{color}{num1 num2 num3} num1 num2 num3 is an hue-saturation-brightness specification, to be set by PostScript’s sethsbcolor operator. For example, 1 \newhsbcolor{mycolor}{.3 .7 .9} \newcmykcolor{color}{num1 num2 num3 num4} num1 num2 num3 num4 is a cyan-magenta-yellow-black specification, to be set by PostScript’s newcmykcolor operator. For example, 1 \newcmykcolor{hercolor}{.5 1 0 .5} For defining new colors, the rbg model is a sure thing. hsb is not recommended. cmyk is not supported by all Level 1 implementations of PostScript, although it is best for color printing. For more information on color models and color specifications, consult the PostScript Language Reference Manual, 3rd Edition (Red Book), and a color guide. Driver notes: 9 The command \pstVerb must be defined. Put commands This is old documentation, but these commands will continue to be supported. There is also an obsolete command \Lput for putting labels next to node connections. The syntax is 1 \Lput{labelsep}[refpoint]{rotation}(pos){stuff } It is a combination of \Rput and \lput, equivalent to 1 \lput(pos){\Rput{labelsep}[refpoint]{rotation}(0,0){stuff }} \Mput is a short version of \Lput with no {<rotation>} or (<pos>) argument. \Lput and \Mput remain part of PSTricks only for backwards compatibility. Here are the node label commands: Obsolete commands: Put commands 248 \lput*[refpoint ]{rotation}(pos){stuff } The l stands for “label”. Here is an example illustrating the use of the optional star and :<angle> with \lput, as well as the use of the offset parameter with \pcline: gth Len 1 2 3 \pspolygon(0,0)(4,2)(4,0) \pcline[offset=12pt]{|-|}(0,0)(4,2) \lput*{:U}{Length} (Remember that with the put commands, you can omit the coordinate if you include the angle of rotation. You are likely to use this feature with the node label commands.) With \lput and \rput, you have a lot of control over the position of the label. E.g., label 1 2 \pcline(0,0)(4,2) \lput{:U}{\rput[r]{N}(0,.4){label}} puts the label upright on the page, with right side located .4 centimeters “above” the position .5 of the node connection (above if the node connection points to the right). However, the \aput and \bput commands described below handle the most common cases without \rput.62 \aput*[labelsep]{angle}(pos){stuff } stuff is positioned distance \pslabelsep above the node connection, given the convention that node connections point to the right. \aput is a node-connection variant of \uput. For example: se enu t o p Hy 1 2 3 \pspolygon(0,0)(4,2)(4,0) \pcline[linestyle=none](0,0)(4,2) \aput{:U}{Hypotenuse} 62 There is also an obsolete command \Lput for putting labels next to node connections. The syntax is \Lput{labelsep}[refpoint]{rotation}(pos){stuff } It is a combination of \Rput and \lput, equivalent to \lput(pos){\Rput{labelsep}[refpoint]{rotation}(0,0){stuff }} \Mput is a short version of \Lput with no {<rotation>} or (<pos>) argument. \Lput and \Mput remain part of PSTricks only for backwards compatibility. Obsolete commands: Put commands 249 \bput*[labelsep]{angle}(pos){stuff } This is like \aput, but stuff is positioned below the node connection. It is fairly common to want to use the default position and rotation with these node connections, but you have to include at least one of these arguments. Therefore, PSTricks contains some variants: \mput*[refpoint ]{stuff } \Aput*[labelsep]{stuff } \Bput*[labelsep]{stuff } of \lput, \aput and \bput, respectively, that have no angle or positioning argument. For example: 1 1 2 3 4 \cnode*(0,0){3pt}{A} \cnode*(4,2){3pt}{B} \ncline[nodesep=3pt]{A}{B} \mput*{1} Here is another: Label 1 2 10 \pcline{<->}(0,0)(4,2) \Aput{Label} Coordinates commands There is an obsolete command \Polar that causes coordinates in the form (<r>,<a>) to be interpreted as polar coordinates. The use of \Polar is not recommended because it does not allow one to mix Cartesian and polar coordinates the way \SpecialCoor does, and because it is not as apparent when examining an input file whether, e.g., (3,2) is a Cartesian or polar coordinate. The command for undoing \Polar was \Cartesian. It has an optional argument for setting the default units. I.e., 1 \Cartesian(x,y ) has the effect of 1 \psset{xunit=x,yunit=y } \Cartesian can be used for this purpose without using \Polar. Obsolete commands: Coordinates commands 250 Help 63 We try to give in this appendix various hints about both common requirements (PDF output files, animated graphics, etc.), frequently asked questions (FAQ) and various programming technics of common interest. In this last area, some (at least basic) knowledge of both TEX and PostScript as programming languages are required, as PSTricks used both. This is outside the scope of this User’s Guide to explain them, and their basis will be supposed to be known. To learn about TEX as a programming language, there is not currently a specific book or publication on this specific topic. Nevertheless, there are chapters on this subject in some general books about TEX. In a more pedagogical way than in the TEXbook [37], you can consult for instance TEX by Topic, by Victor Eijkhout [12], or The Advanced TEXbook, by David Salomon [77]. To learn about the PostScript language, consult Adobe’s PostScript Language Tutorial and Cookbook (the “Blue Book”) [50], or for instance Henry McGilton and Mary Campione’s PostScript by Example [39], or of course the PostScript Language Reference Manual [51]. You may find that the Appendix of the Blue Book, plus an understanding of how the stack works, is all you need to write simple code for computing numbers (e.g., to specify coordinates or plots using PostScript). A PDF output files DG: This chapter is not yet very stable and it English has not yet been corrected. The Portable Document Format (PDF) [46], a proprietary but public format from Adobe Inc., became these last years well spread and more and more used. Nevertheless, this format does not supercede PostScript, heavily used by PSTricks, and is a description language which does not integrate programming capacities that PostScript have and that PSTricks use. So, there is not an obvious unique way to generate PDF files with PSTricks graphics, but several ones, with various advantages and disadvantages each. Consequently, everyone must made his own choice among the various solutions available. 63 This chapter was rewritten in 2003 by Denis Girou. Help 251 A.1 Compilers with internal support of PSTricks Two currently available compilers, Bakoma TEX [5] from Basil K. Malyshev and VTEX [82] from MicroPress Inc., among those which can directly produce PDF output files, embed a PostScript interpreter (at least all the major parts of the defined language, which allow them to include directly EPS external files and PSTricks graphics). These two softwares are both commercial products for Windows systems, but MicroPress also distribute a free version of VTEX for Linux and some other systems. A.2 PostScript to PDF converters The Acrobat software [1] from Adobe, GhostScript [20] from Aladdin Enterprises and PStill [66] from Frank Siegert allow to translate PostScript files to PDF. The first one exist only for Macintosh and Windows systems and the two other ones for all the major systems. Acrobat is a paying product, GhostScript is a free software and PStill is free for academic usage, and commercial otherwise. A.3 PdfTEX workarounds The PdfTEX compiler [47] does not embed a PostScript interpreter, and consequently cannot include EPS external files without previous conversion of them in another accepted format (which could be done on the fly), nor directly PSTricks graphics. Consequently, if you want to use PdfTEX with PSTricks, you must convert the PSTricks graphics, manually or as an automatic process. Manually, you can store each PSTricks graphic in an external EPS file using either the \PSTtoEPS macro or the TeXtoEPS environment (see section 61), convert these files to another format supported by PdfTEX then include these files in the final document. More easily, you could use either the pdfTricks system [48] developed by Radhakrishnan CV, Rajagopal CV and Antoine Chambert-Loir, or the ps4pdf system [53] developed by Rolf Niepraschk, which both offer a way to automatize this process. They both require to encapsulate the PSTricks graphics in a special environment or macro (and work only for LATEX, not P LAIN TEX). pdfTricks require a TEX implementation based on web2c. It is easier to use if you enable the so-called shell escape feature of the compiler, to allow the execution of external processes during the TEX compilation,64 but it can 64 For security reasons, this is not recommended for computers accessible from outside by the Internet network to have this feature permanent, but better as a temporary opened feature during the time of the compilations. Help: PDF output files 252 work in another way without using this feature, using a Shell script given in the distribution. Here is a simple example of usage: 1 \documentclass{article} 2 3 \usepackage{pdftricks} 4 5 6 7 8 9 \begin{psinputs} \usepackage{times} \usepackage{pstcol} \usepackage{pst-plot} \end{psinputs} 10 11 \begin{document} 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 \begin{pdfpic} \psset{xunit=8,yunit=3}% \begin{pspicture}(-0.45,-1.6)(1.05,1.3) \psaxes[Dx=0.2,Oy=-1.2,Dy=0.2,tickstyle=top, axesstyle=frame](0,-1.2)(1,1.2) \rput(-0.3,0){% \shortstack{\textcolor{red}{$\sin (10 \times x)$}\\ \textcolor{blue}{$\cos (40 \times x) / 2$}}} \rput(-0.3,0){% \shortstack{\textcolor{red}{$\sin (10 \times x)$}\\ \textcolor{blue}{$\cos (40 \times x) / 2$}}} \rput(0.5,-1.5){\shortstack{$x$\\Sample plots}} \psplot[linecolor=red]% 1 radian = 57.296 degrees {0}{1}{x 10 mul 57.296 mul sin}% sin(10 x) \psplot[linecolor=blue,plotpoints=200] {0}{1}{x 40 mul 57.296 mul cos 2 div}% cos(40 x) / 2 \end{pspicture} \end{pdfpic} 31 32 \end{document} which must produce the following result: The command to compile this file, and directly produce the PDF output file, is the following (if the shell escape feature is not enabling by default): 1 pdflatex -shell-escape FileName On it side, ps4pdf require a PostScript to PDF converter like GhostScript. It also need the ‘preview’ package [52] from David Kastrup. With ps4pdf, Help: PDF output files 253 1.2 1.0 0.8 0.6 0.4 sin(10 × x) cos(40 × x)/2 0.2 0.0 −0.2 −0.4 −0.6 −0.8 −1.0 −1.2 0 0.2 0.4 0.6 x Sample plots 0.8 1.0 Figure 4: Output of the example about pdfTricks and ps4pdf usage the preceding example must look like: 1 \documentclass{article} 2 3 4 \usepackage{graphicx} \usepackage{ps4pdf} 5 6 7 8 \PSforPDF{% \usepackage{pstcol} \usepackage{pst-plot}} 9 10 \begin{document} 11 12 13 14 15 16 17 18 19 20 21 22 23 \PSforPDF{% \psset{xunit=8,yunit=3}% \begin{pspicture}(-0.45,-1.6)(1.05,1.3) \psaxes[Dx=0.2,Oy=-1.2,Dy=0.2,tickstyle=top, axesstyle=frame](0,-1.2)(1,1.2) \rput(-0.3,0){% \shortstack{\textcolor{red}{$\sin (10 \times x)$}\\ \textcolor{blue}{$\cos (40 \times x) / 2$}}} \rput(0.5,-1.5){\shortstack{$x$\\Sample plots}} \psplot[linecolor=red]% 1 radian = 57.296 degrees {0}{1}{x 10 mul 57.296 mul sin}% sin(10 x) \psplot[linecolor=blue,plotpoints=200] Help: PDF output files 254 24 25 {0}{1}{x 40 mul 57.296 mul cos 2 div}% cos(40 x) / 2 \end{pspicture}} 26 27 \end{document} And the following sequence of commands must be given to generate the PDF output file (this is of course easier to have a Makefile or a script to do that automatically): 1 2 3 4 latex FileName dvips -Ppdf -G0 -o FileName-pics.ps FileName.dvi ps2pdf FileName-pics.ps pdflatex FileName B Animated graphics Sometimes, graphics are interesting to show the evolution of a phenomena. Of course, it is possible to include in a TEX document several pictures of the phenomena, at different steps, but it could be more convenient to generate real animations to be viewed interactively, using one of the available animated graphics file formats (mainly GIF and MNG (Multiple-image Network Graphics) [44].) Two different cases must be considered: the one of pure PSTricks graphics and the one of non pure graphics. B.1 Pure PSTricks graphics This first case (without texts, \rput macros, etc.) is the easiest, as all the images of the animation can be generated in only one compilation, using a loop at the TEX level on the \PSTtoEPS macro (see section 61), which can dynamically transform each PSTricks graphic computed in an EPS file. We will give an example on waves interferences, a simple but powerful development done by Manuel Luque in 2002. The purpose of this code is to simulate the behavior of one or two waves, and the interferences between them when there are two ones. The physical phenomena of interferences come from the superposition of two vibrating movements generated by two sources which have a constant difference of phase. The code only consist in few PostScript lines, to show the propagation of waves from one source or the interferences between the waves of two sources. There are many parameters which can be changed: Help: Animated graphics 255 Time Time of the observation (real, default=0) X1 Abscissa of the first source, in centimeters (real, default=-2) X2 Abscissa of the second source, in centimeters (real, default=2) Y1 Ordinate of the first source, in centimeters (real, default=0) Y2 Ordinate of the second source, in centimeters (real, default=0) Phase1 Phase of the first source, in degrees (real, default=0) Phase2 Phase of the second source, in degrees (real, default=0) Frequency1 Frequency of the first source, in Hz (real, default=20) Frequency2 Frequency of the second source, in Hz (real, default=20) Amplitude1Coeff Amplitude coefficient first source; a value of 0 mean no first source (real between 0 and 1, default=1) Amplitude2Coeff Amplitude coefficient for the second source; a value of 0 mean no second source (real between 0 and 1, default=1) Amortization Amortization factor (real, default=5) Celerity Speed of the waves, in ms-1 (real, default=0.2) Resolution Scale factor for the image (1 is the more precise resolution) (integer, default=1) Here, we will generate only three images, but it is obviously straightforward to generate as many as we want. We must just take care to generate the image number with the correct left leading zeroes (in our example, we show how to do to generate convenient name files until 99 ones.) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 \define@key{psset}{Amortization}{% \edef\PstWavesInterferences@Amortization{#1}} \define@key{psset}{Amplitude1Coeff}{% \edef\PstWavesInterferences@AmplitudeACoeff{#1}} \define@key{psset}{Amplitude2Coeff}{% \edef\PstWavesInterferences@AmplitudeBCoeff{#1}} \define@key{psset}{Celerity}{% \edef\PstWavesInterferences@Celerity{#1}} \define@key{psset}{Frequency1}{% \edef\PstWavesInterferences@FrequencyA{#1}} \define@key{psset}{Frequency2}{% \edef\PstWavesInterferences@FrequencyB{#1}} \define@key{psset}{Phase1}{% \edef\PstWavesInterferences@PhaseA{#1}} \define@key{psset}{Phase2}{% \edef\PstWavesInterferences@PhaseB{#1}} \define@key{psset}{Resolution}{% \edef\PstWavesInterferences@Resolution{#1}} \define@key{psset}{Time}{\edef\PstWavesInterferences@Time{#1}} \define@key{psset}{X1}{% \edef\PstWavesInterferences@SourceXA{#1}} \define@key{psset}{X2}{% \edef\PstWavesInterferences@SourceXB{#1}} \define@key{psset}{Y1}{% \edef\PstWavesInterferences@SourceYA{#1}} Help: Animated graphics 256 26 27 \define@key{psset}{Y2}{% \edef\PstWavesInterferences@SourceYB{#1}} 28 29 30 31 \setkeys{psset}{Amortization=5,Amplitude1Coeff=1,Amplitude2Coeff=1, Celerity=0.20,Frequency1=20,Frequency2=20,Phase1=0,Phase2=0, Resolution=1,Time=0.20,X1=-2,X2=2,Y1=0,Y2=0} 32 33 34 \def\PstWavesInterferences{% \def\pst@par{}\pst@object{PstWavesInterferences}} 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 \def\PstWavesInterferences@i(#1,#2)(#3,#4){% \pspicture(#1,#2)(#3,#4) \begin@AltOpenObj \addto@pscode{% /AmplitudeMax 0.5 def #1 28.45 mul \PstWavesInterferences@Resolution\space #3 28.45 mul { % Loop on abscissas /abscissept exch def % In points /abscisse abscissept 2845 div def % In meters #2 28.45 mul \PstWavesInterferences@Resolution\space #4 28.45 mul { % Loop on ordinates /ordonneept exch def % In points /ordonnee ordonneept 2845 div def % In meters /d1 abscisse \PstWavesInterferences@SourceXA\space 100 div sub dup mul ordonnee \PstWavesInterferences@SourceYA\space 100 div sub dup mul add sqrt def /d2 abscisse \PstWavesInterferences@SourceXB\space 100 div sub dup mul ordonnee \PstWavesInterferences@SourceYB\space 100 div sub dup mul add sqrt def /yS1 360 \PstWavesInterferences@FrequencyA\space mul \PstWavesInterferences@Time\space d1 \PstWavesInterferences@Celerity\space div sub mul \PstWavesInterferences@PhaseA\space add sin AmplitudeMax 2.71828 d1 neg \PstWavesInterferences@Amortization\space mul exp mul \PstWavesInterferences@AmplitudeACoeff\space mul mul def /yS2 360 \PstWavesInterferences@FrequencyB\space mul \PstWavesInterferences@Time\space d2 \PstWavesInterferences@Celerity\space div sub mul \PstWavesInterferences@PhaseB\space add sin AmplitudeMax 2.71828 d2 neg \PstWavesInterferences@Amortization\space mul exp mul \PstWavesInterferences@AmplitudeBCoeff\space mul mul def yS1 0.5 add yS2 0.5 add 1 setrgbcolor % Color newpath abscissept ordonneept \PstWavesInterferences@Resolution\space 0 360 arc closepath fill } for } for}% Help: Animated graphics 257 \end@OpenObj \endpspicture} 79 80 81 % Generation of the images in EPS format \multido{\nTime=0.20+0.01}{3}{% % As all file names must have the same number of characters, % we must add a 0 for the 9 first ones if we have between % 10 and 99 images \ifnum\multidocount<10\relax\def\Pad{0}\else\def\Pad{}\fi \PSTtoEPS[headerfile=pstricks.pro,headers=user, bbllx=-8,bblly=-4,bburx=8,bbury=4] {WavesInterferences\Pad\the\multidocount.eps}{% \PstWavesInterferences[Amortization=10,Celerity=0.2, Time=\nTime,Frequency1=20,Frequency2=20,Resolution=3, X1=-4,X2=4,Y1=-3,Y2=-3](-8,-4)(8,4)}} 82 83 84 85 86 87 88 89 90 91 92 93 Image 1 Image 2 Image 3 Now, to generate the animated graphic file which concatenate these images, we have to convert each file in a convenient format, then to use a tool to concatenate them. For instance, the convert program from ImageMagick [32] (or the gm one from GraphicsMagick [26]) can do all of these tasks, both for GIF and MNG formats. Nevertheless, take care that sometimes it could generate huge files. For GIF files, the gifsicle [21] application usually produce smaller files. Here we give an example script for Unix systems which allow to automatize all the process. 1 #! /bin/sh 2 3 set -x 4 5 6 # Generation of an animated GIF file # from PSTricks pure graphics 7 if [$# != 2 ]
then echo Syntax: PstAnimatedPureGraphics.sh \
file_without_suffix delay
exit
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fi
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latex $1 15 16 for file1 in$1?*.eps
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do
file2=‘basename $file1 .eps‘ convert$file1 $file2.gif # Convert each file in GIF format done 21 22 23 # Generate the animated GIF file using “gifsicle” gifsicle –delay$2 –loop –colors 256 –output $1.gif$1?*.gif
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# We can also use “convert” from ImageMagick
# (but it could produce in some cases huge files)
# convert -delay $2 -loop 0 -colors 256$1?*.gif $1.gif 28 29 30 # Clean up temporary files rm -f$1?*.{eps,gif} $1.{aux,dvi,log} 31 32 animate$1.gif & # From ImageMagick, or “gifview -a $1.gif” 33 34 exit If this script is named PstAnimatedPureGraphics.sh and our TEX file WavesInterferences.tex, we must just execute the following line (the last number is the delay between images, in cent of second): 1 B.2 PstAnimatedPureGraphics.sh WavesInterferences 20 Non pure PSTricks graphics This case is a little more complicated, because each EPS file must be generated independently by a separate compilation, using the TeXtoEPS environment and a translation from the DVI format to the EPS one (see section 61). Nevertheless, everything can also be automatized using a script. We give here an example based on the ‘pst-eucl’ contribution package [59] from Dominique Rodriguez, for Euclidean geometry drawings. 1 \documentclass{minimal} 2 3 4 \usepackage{pst-eps} \usepackage{pst-eucl} 5 6 7 8 9 10 11 % Utility macro to generate intermediate images, % running parts of the complete code of a macro. % Code #3 will be included if #1 >= #2. \def\IncludeCodeForImage#1#2#3{% \ifnum#2>#1\relax \else Help: Animated graphics 259 #3 12 \fi} 13 14 \def\PstOrthocentre{% \typein[\Image]{^^JWhich image?} \TeXtoEPS \pspicture(-1.5,-1.3)(3.6,2.2) \psset{CodeFig=true}% \IncludeCodeForImage{\Image}{1}{% \pstTriangle[PosAngleA=180](-1,0){A}(3,-1){B}(3,2){C}} \IncludeCodeForImage{\Image}{2}{% \pstProjection[PosAngle=-90]{B}{A}{C}{C’}} \IncludeCodeForImage{\Image}{3}{% \pstProjection{B}{C}{A}{A’}} \IncludeCodeForImage{\Image}{4}{% \pstProjection[PosAngle=90]{A}{C}{B}{B’}} \IncludeCodeForImage{\Image}{5}{% \pstInterLL[PosAngle=135,PointSymbol=square] {A}{A’}{B}{B’}{H}} \endpspicture \endTeXtoEPS} 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 \begin{document} \PstOrthocentre \end{document} 34 35 36 b b C b C C b B′ C B′ b A b A b b A b B Image 1 Image 2 C′ b b b b B Image 3 C′ b A′ A b b B Image 4 b C b A′ b B b C′ b A′ b B A H b b Image 5 C′ rs Here we give an example script for Unix systems which allow to automatize all the process. 1 #! /bin/sh 2 3 set -x 4 5 6 # Generation of an animated GIF file # from PSTricks non pure graphics 7 8 9 10 11 if [$# != 3 ]
then echo Syntax: PstAnimatedNonPureGraphics.sh \
file_without_suffix number_images delay
exit
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declare -i i
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i=1
while [ $i -le$2 ]
do
echo $i | latex Orthocentre if [$i -lt 10 ]
else if [ $i -lt 100 ] then pad=“0” else pad=“” fi fi dvips -E -o$1$pad$i.eps $1.dvi # Convert the file in GIF format convert$1$pad$i.eps $1$pad$i.gif i=$i+1
done
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# Generate the animated GIF file using “gifsicle”
gifsicle –delay 200 –loop –colors 256 \
–output $1.gif$1?*.gif
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# We can also use “convert” from ImageMagick
# (but it could produce in some cases huge files)
# convert -delay 200 -loop 0 -colors 256 $1?*.gif$1.gif
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# Clean up temporary files
rm -f $1?*.{eps,gif}$1.{aux,dvi,log}
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animate $1.gif & # From ImageMagick, or “gifview -a$1.gif”
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exit
If this script is named PstAnimatedNonPureGraphics.sh and our TEX file
Orthocentre.tex, we must just execute the following line (the first number
is the number of images to generate and the second one is the delay between
images, in cent of second):
1
PstAnimatedNonPureGraphics.sh Orthocentre 5 200
C Generation of code by external programs
Several drawing tools (Dia [10], Eukleides [14], gnuplot [24], jPicEdt [34],
etc.) can generate PSTricks output code, that can be later inserted in any
TEX documents.
Help: Generation of code by external programs
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But you can of course write yourself some programs in any scripting or
programming language to generate PSTricks output code for complex tasks.
Here is a rather simple script, written in Perl, which allow to draw disk
file trees of Unix systems, analyzing the subdirectories. The script is rather
short, but nevertheless powerful.
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#! /usr/bin/perl
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use Getopt::Long;
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$TreeDirectory = “.”;# Default directory is the current one$RecursionLevelMax = 10;# Better than infinity!
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if (! -d $TreeDirectory) { print “$TreeDirectory is not a directory!\n”;
exit 0
}
print “\\pstree{\\PstTreeDirectory{$TreeDirectory}}\n {“; &ListSubdirectories($TreeDirectory, 0);
print “\n”;
exit 0;
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# To get list of subdirectories (recursive subprogram)
sub ListSubdirectories {
local ($directory,$recursion_level) = @_;
local ($boolean,$dir_temp, $dir_print_temp, @dir, @subdir, *DIR); 23 24 25 26 27 opendir (DIR,$directory) or return;
@dir = grep {!/\/\.\.?$/} grep { -d } map {“$directory/$_”} readdir (DIR); closedir (DIR); 28 29$recursion_level++;
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if ($recursion_level <=$RecursionLevelMax) {
$boolean = 0; foreach$dir_temp (sort @dir) {# Loop on subdirectories
# For special characters that are a problem for TeX
$dir_print_temp =$dir_temp;
$dir_print_temp =~ s/.*\///, s/[\$,\&,%,\#,\_,\{,\}]/\\\_/g;
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if ($boolean != 0) {print “\n”, “ “ x (2*$recursion_level)}
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# We must see if this directory has subdirectories
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opendir (DIR, “$dir_temp”); @subdir = grep {!/\/\.\.?$/} grep { -d }
map {“$dir_temp/$_”} readdir (DIR);
closedir (DIR);
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if ($#subdir != -1 &&$recursion_level != $RecursionLevelMax) { # At least one subdirectory print “\\pstree{\\PstTreeDirectory{$dir_print_temp}}\n”,
“ “ x (2 * $recursion_level + 1), “{“; } else { print “\\PstTreeDirectory{$dir_print_temp}”;
}
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$boolean = 1; &ListSubdirectories(“$dir_temp”, $recursion_level); 56 57 } 58 59 if ($boolean != 0) {print “}”}
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}
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}
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GetOptions (qw (-d=s -rl=i));# Option definitions
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# Option analysis
if ($opt_d) {$TreeDirectory = $opt_d}; if ($opt_rl) {$RecursionLevelMax =$opt_rl};
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}
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and here are some examples of usage, with various customizations. The
commands given which have generated the files included are shown in the
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\tiny
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% pst-dir.pl -d /usr/share/fonts >dirtree1.tex
\bgroup
\def\PstTreeDirectory#1{\Toval[framesep=0.05]{#1}}%
\psset{treesep=0.1}%
\input{dirtree1.tex}
\egroup
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\bgroup
\def\PstTreeDirectory#1{%
\ifx\pstree@next\relax
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\def\pst@tempa{\psframebox[fillstyle=solid,fillcolor=Gold]{#1}}%
\else
\def\pst@tempa{\psframebox[fillstyle=solid,fillcolor=red]{%
\textcolor{white}{\textbf{#1}}}}%
\fi
\TR{\pst@tempa}}%
\def\psedge{\ncangle[angleB=180]}% Horizontal edges
\psset{treemode=R,treesep=0.3,href=-1,levelsep=*1.2}%
\input{dirtree1.tex}
\egroup
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% pst-dir.pl -d /usr/share/fonts -rl 2 >dirtree2.tex
\bgroup
\psset{treesep=0.1}%
\def\PstTreeDirectory#1{%
\ifx\pstree@next\relax
\def\pst@tempa{LemonChiffon}%
\else
\def\pst@tempa{PaleGreen}%
\fi
\Toval[framesep=0.05,fillstyle=solid,fillcolor=\pst@tempa]{#1}}%
\def\psedge{\ncangles[angleA=-90,angleB=90]}% Horizontal edges
\input{dirtree2.tex}
\egroup
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% pst-dir.pl -d /usr/X11R6 >dirtree3.tex
\bgroup
\psset{treefit=loose,treesep=0.2}%
\def\PstTreeDirectory#1{\Tp}%
\scaleboxto(12,4){\input{dirtree3.tex}}
\egroup
/usr/share/fonts
ISO8859-2
100dpi
Type1
afm
ISO8859-7
misc
100dpi
75dpi
Type1
afms
misc
bitmap-fonts
ja
default
TrueType
Type1
TrueType
pfm
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100dpi
afm
Type1
ISO8859-2
pfm
misc
100dpi
75dpi
ISO8859-7
Type1
/usr/share/fonts
misc
afms
bitmap-fonts
TrueType
default
Type1
ja
TrueType
/usr/share/fonts
ISO8859-2
100dpi
Type1
ISO8859-7
misc
100dpi
75dpi
Type1
afms
misc
bitmap-fonts
ja
default
TrueType
Type1
TrueType
D Loops
Loops are a key basic construction in all programs and are often required
also to buid computational graphics. The macros \multirput, to place multiple copies of texts or graphics at equally spaced positions expressed in
Cartesian coordinates, and \multips for pure PSTricks graphics placed at
equally spaced positions, but not obligatory expressed by Cartesian coordinates, have been described in Section 25.
Help: Loops
265
Examples of usage of the more general ‘multido’ package65 [45] had already been shown in various preceding chapters, but this is important to
emphasize it various features, as it usage is common.66
Refer to it documentation for a complete description, but in few words:
• loops can be nested (the \multido and \mmultido ones, not the \Multido and \MMultido variant ones),
• a same loop can define several counters of different kinds, incremented together,
• increments can be either positive or negative,
• counters can have the integer, real, number (for integer or real numbers, but with the same number of digits for the decimal parts of
starting value and increment)67 or dimension types,
• the \multido macro put it body inside a group, at the opposite of
\Multido,
• the \mmultido and \MMultido variants increment the counters before starting,
• the \multidostop macro allow to interrupt a loop,
• the \multidocount counter store the value of the iteration number.
We give here some other examples, to illustrate the various usages of such
loops. You will still found other ones in the next sections of this chapter
(specially look in the Section G the examples of how to define loops of
undefined lengths and how to stop them with the \multidostop macro when
a predefined condition is reached).
First, a simple example to draw a spiral. Note that:
• the straightforward way to draw a spiral is to use polar plots (see
Section L.15),
• the technique used here to compute coordinates, to store them and
reuse them later is very general,
• we use here the \Multido variant; if we would have used the \multido one, we must have used the \xdef macro to store the coordinates
and not the \edef one, to be able to use it value outside the group
automatically defined in the body of a \multido loop.
65
You can also use the ‘repeat’ package [74] from Victor Eijkhout or, if you use only
EX, the \whiledo macro of the ‘ifthen’ package [31] or the internal LATEX macros \@for,
\@whilenum, etc.
66
Nevertheless, in the restricted cases where it is applicable, the \multips and \multirput
macros are more efficient and produce more compact code than the \multido one.
67
Usage of reals rather than numbers is faster but less precise, with possible rounding
approximations during computations.
LAT
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\SpecialCoor
\psset{unit=0.75}%
\def\PstCoordinates{}%
\Multido{\nDistance=0.00+0.02,\iAngle=0+20}{200}{%
\edef\PstCoordinates{\PstCoordinates(\nDistance;\iAngle)}}
\expandafter\pscurve\PstCoordinates
Then we rebuild the Enigma painting of the French painter Isia Leviant.68
Note the usage of two nested loops, two different indexes by loops and the
usage of the external current indexes in the internal loops.
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\pspicture*(-6,-6)(6,6)
\degrees[240]
\SpecialCoor
\multido{\iAngleA=1+2,\iAngleB=2+2}{120}{%
\pspolygon*(1;\iAngleA)(9;\iAngleA)(9;\iAngleB)(1;\iAngleB)}
\definecolor{MyColor}{hsb}{\nHueB,1,1}%
\endpspicture
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Look at it fixedly for few seconds, and you will see the colored circles turning fast. Of
course, this is an optical illusion...
Help: Loops
267
And, to finish, we redraw a picture of the Italian specialist of vision Baingio
Pinna.69 Note the usage of different kinds of indexes in the same loops and
the change of the degrees parameter between the two loops.
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\def\PstMyDiamond#1#2{{%
\psset{dimen=middle,unit=0.1,linewidth=2\pslinewidth,arrows=c-c}%
\psline(0,-3)(-2,#1)(0,3)
\psline[linecolor=white](0,-3)(2,#2)(0,3)}}
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\pspicture(-5,-5)(5,5)
\SpecialCoor
\psframe*[linecolor=lightgray](-5,-5)(5,5)
\psdot[dotstyle=B+,dotscale=3]
\degrees[48]
\multido{\iAngle=1+2,\nRotation=4.5+2.0}{24}{%
\rput{\nRotation}(3.5;\iAngle){\PstMyDiamond{-1}{1}}}
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Fix the cross in the middle of the figure and put away the paper from your eyes (or
move backward your head if you look at the picture on a screen): you will see the two rings
of diamonds turn in opposite direction. Of course, this is too an optical illusion... You can
easily find in publications, or by asking for Internet references, some explanations on this
phenomena and the preceding one.
Help: Loops
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\degrees[62]
\multido{\iAngle=1+2,\nRotation=-3.5+2.0}{31}{%
\rput{\nRotation}(4.25;\iAngle){\PstMyDiamond{1}{-1}}}
\endpspicture
+
E Recursion
Recursion is a classical way of programming, which consist for a function
to call itself with different parameters. Recursive algorithms are generally
shortest than iterative ones, and are generally considered as elegant. Nevertheless, they are usually less efficient than iterative ones when executed on
a computer and can easily require huge computing resources, both computing time and specially memory. So such programs must be used with care.
But, for some problems, they offer a very attractive and easy way to solve
complex problems.
We give here some classical examples on fractals, for the well-known Sierpinski triangle (see for instance [49]) then for the 13 segments auto-similar
curve shown by Benoit Mandelbrot in his book The Fractal Geometry of
Nature [38].
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3
% From the source of LaTeX 2e (latex.ltx file)
\long\def\@firstoftwo#1#2{#1}
\long\def\@secondoftwo#1#2{#2}
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% The recursion macro used (from David Carlisle)
\def\Recursion#1{%
#1\relax
\expandafter\@firstoftwo
\else
\expandafter\@secondoftwo
\fi}
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\def\PstFractalBegin{}% Default value empty
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% General definition of a fractal
\def\PstFractal{\def\pst@par{}\pst@object{PstFractal}}
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\def\PstFractal@i#1{{%
\use@par% Assignment of local parameters
\PstFractalBegin% The first level can need special thing
\Recursion{\ifnum#1>\@ne}
{\pst@cnth=#1\relax
\PstFractalRepeat{\pst@cnth}}
{\PstFractalDefinition}}}
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% Examples on classical fractals
% ——————————————
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% Sierpinski triangle
\def\PstSierpinskiTriangle#1{%
\def\PstFractalDefinition{%
\pspolygon*[linecolor=\PstSierpinskiExternalColor](1;0)(1;1)(1;2)
\rput{-2}(0,0){%
\pspolygon*[linecolor=\PstSierpinskiInternalColor]
(0.5;0.5)(0.5;1.5)(0.5;2.5)}}%
\def\PstFractalBegin{\PstFractalDefinition}%
\def\PstFractalRepeat##1{%
\rput(0.5;0){\PstFractal[unit=0.5]{##1}}
\rput(0.5;1){\PstFractal[unit=0.5]{##1}}
\rput(0.5;2){\PstFractal[unit=0.5]{##1}}}%
\pspicture(-0.866,-0.5)(0.866,1)
\SpecialCoor
\rput{90}(0,0){%
\degrees[3]
\PstFractal{#1}}
\endpspicture}
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\def\PstMandelbrotCurve#1#2{%
\def\PstFractalDefinition{%
\pscustom[#2]{%
\code{1 setlinejoin}%
\moveto(0,0)
\lineto(0.5,0.9)\lineto(1,1.8)\lineto(2,1.8)\lineto(2.5,0.9)
\lineto(2,1.2)\lineto(1.5,1.5)\lineto(1,1.2)\lineto(1,0.6)
\lineto(2,0.6)\lineto(1.5,0.3)\lineto(1,0)\lineto(2,0)\lineto(3,0)}}%
%
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\def\PstFractalRepeat##1{{%
\psset{fillstyle=solid}%
\rput{60.95}(0,0){%
\scalebox{1 -1}{\PstFractal[unit=0.3432,fillcolor=white]{##1}}}
\rput{60.95}(0.5,0.9){\PstFractal[unit=0.3432,fillcolor=red]{##1}}
\rput{0}(1,1.8){\PstFractal[unit=0.3333,fillcolor=red]{##1}}
\rput{-60.95}(2,1.8){\PstFractal[unit=0.3432,fillcolor=red]{##1}}
\rput{-210.96}(2.5,0.9){\PstFractal[unit=0.1944,fillcolor=red]{##1}}
\rput{-210.96}(2,1.2){%
\scalebox{1 -1}{\PstFractal[unit=0.1944,fillcolor=white]{##1}}}
\rput{-149.04}(1.5,1.5){%
\scalebox{1 -1}{\PstFractal[unit=0.1944,fillcolor=white]{##1}}}
\rput{-90}(1,1.2){%
\scalebox{1 -1}{\PstFractal[unit=0.2,fillcolor=white]{##1}}}
\rput(1,0.6){\PstFractal[unit=0.3333,fillcolor=red]{##1}}
\rput{-149.04}(2,0.6){\PstFractal[unit=0.1944,fillcolor=red]{##1}}
\rput{-149.04}(1.5,0.3){%
\scalebox{1 -1}{\PstFractal[unit=0.1944,fillcolor=white]{##1}}}
\rput(1,0){%
\scalebox{1 -1}{\PstFractal[unit=0.3333,fillcolor=red]{##1}}}
\rput(2,0){\PstFractal[unit=0.3333,fillcolor=red]{##1}}}}%
%
\PstFractal{#1}}
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\bgroup
\def\PstSierpinskiInternalColor{red}%
\def\PstSierpinskiExternalColor{yellow}%
\psset{unit=2}%
\PstSierpinskiTriangle{2}\hfill%
\PstSierpinskiTriangle{3}\hfill%
\PstSierpinskiTriangle{4}
\egroup
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\PstMandelbrotCurve{1}{}
\hspace{2cm}
\PstMandelbrotCurve{2}{fillstyle=solid,fillcolor=red}
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\bgroup
\psset{unit=3}%
\PstMandelbrotCurve{2}{linestyle=none,fillstyle=solid,fillcolor=red}
\PstMandelbrotCurve{3}{}
\egroup
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F
Computations
Computations are permanently required for computational graphics. Of
course, as seen in many examples of this manual, TEX has some capabilities to make computations on integer and real values (for reals, using dimensions), but there are rather huge restrictions. With PSTricks, complicated
computations can be done in PostScript, which has a lot more capabilities
and operands than TEX in this area, but with the restriction that the results of
these computations cannot be used in the TEX code, as they will be known
only during the interpretation of the PostScript code.
Sometimes, it is really needed to make the computations in the TEX code.
PSTricks extend a little the TEX features in this area, adding the \pst@divide
macro to do divisions between two dimensions (that is to say real numbers)
and the \pst@getsinandcos macro (defined in the ‘pst-3d’ package) to return the sinus and cosinus of an angle. If there is more to do, external
packages must be used, as the ‘fltpoint’ [18] or ‘realcalc’ [73] packages.
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272
Nevertheless, in this area, the ‘fp’ package [19] from Michael Mehlich, that
we will use in the next example, is from far the more powerful available.70
We give here an example on the generation of basic auto-similar fractals,
which will used the general \Recursion macro defined in the preceding
section. The code is probably not very straightforward to understand, as it
is a program which generate a program, but it illustrate the great capabilities
of a general purpose programming language for computational graphics. In
fact, it works in two steps: first, the program read the definition of the
pattern of a fractal, which is the list of the segments71 which represent the
fractal at it first iteration. Then it generate the code which define the fractal,
in two parts, one which define the drawing of the fractal itself and the other
which define the recursive code to apply. Then the initial program execute
this generated program.
For the example of the famous Van Koch curve (see for instance [49]), the
initial
pattern
is
(0,0)(1,0)(1.5,0.866)(2,0)(3,0), and we must also give for input data the
scaling factor for this fractal, which is here 13 . Then the generated code for
the definition of the fractal will be simply:72
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7
\pscustom{%
\moveto(0,0)
\lineto(1,0)
\lineto(1.5,0.866)
\lineto(2,0)
\lineto(3,0)
}
and the generated code for the recursion will be:
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\rput{0}(0,0){\PstFractal[unit=0.33333]{#1}}
\rput{59.99927}(1,0){\PstFractal[unit=0.33333]{#1}}
\rput{-59.99927}(1.5,0.866){\PstFractal[unit=0.33333]{#1}}
\rput{0}(2,0){\PstFractal[unit=0.33333]{#1}}
A more sophisticated way to proceed would have been to do not store the
generated codes inside macros but to write them in two files. This would
70
Take care that it has an incompatibility with the ‘multido’ package – see the paragraph M.3 in this chapter for a patch which solve this problem.
71
This version of the code does not support discontinuous segments, as in the Cantor set,
which was historically the probable first fractal discovered, by the German mathematician
Georg Cantor in 1883 (see for instance [49]).
72
This is specially important in such circumstances to use low level macros like the
\moveto and \lineto here, because fractals are complicated graphics which handle many
segments, then can generate very huge files for a significant deep recursion level. For the
next examples, the output file is twice huge if the \psline macro is used!
Help: Computations
273
have the advantage to be able to reuse the generated codes for fractals already handled. This is not really more complicated to program, but the
code is significantly longer, so we will not do it here.
And as the computing of the rotation angle for all the repeated patterns
require some trigonometric computations, we will use the ‘fp’ package [19]
for that (see the macro \PstFractal@GenerateCommands@iii).
1
\def\@enamedef#1{\expandafter\edef\csname #1\endcsname}
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% To compute hypotenuse
\def\FPhypotenuse#1#2#3{%
\global\let\FP@tmp\FP@tmp}%
\let#1\FP@tmp}
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% General definition of a fractal
\def\PstFractal{\def\pst@par{}\pst@object{PstFractal}}
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\def\PstFractal@i#1{{%
\use@par% Assignment of local parameters
\Recursion
{\ifnum#1>\@ne}
{\pst@cnth=#1\relax
\multido{\i=\@ne+\@ne}{20}{% No more than 20 segments expected
\@nameuse{PstFractal@Repeat\i}{\the\pst@cnth}}}
{\pscustom{%
\multido{\i=\@ne+\@ne}{20}{\@nameuse{PstFractal@Definition\i}}}}}}
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% Initialisation of internal macros for the fractal definition
\Multido{\i=1+1}{20}{%
\@namedef{PstFractal@Definition\i}{}%
\@namedef{PstFractal@Repeat\i}#1{}}
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% Macro for automatic generation of auto-similar fractals
% by definition of the pattern only
\def\PstFractal@SelfSimilar{%
\def\pst@par{}%
\pst@object{PstFractal@SelfSimilar}}
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\def\PstFractal@SelfSimilar@i#1#2{%
\use@par% Affectation of local parameters
\def\PstFractal@Deep{#1}%
\def\PstFractal@Scale{#2}%
\PstFractal@GenerateCommands}
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\pst@cnta=\z@% Counter for the number of segments
44
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\def\PstFractal@GenerateCommands(#1){%
\PstFractal@GenerateCommands@ii(#1)
\@ifnextchar({\PstFractal@GenerateCommands}
{\PstFractal{\PstFractal@Deep}}}
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\def\PstFractal@GenerateCommands@ii(#1,#2){%
\ifnum\pst@cnta>\@ne
\PstFractal@GenerateCommands@iii
(\PstFractal@PreviousX,\PstFractal@PreviousY,#1,#2)
\fi
\def\PstFractal@PreviousX{#1}%
\def\PstFractal@PreviousY{#2}}
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\def\PstFractal@GenerateCommands@iii(#1,#2,#3,#4){%
\FPeval{\Xdiff}{abs(#3 - #1)}
\FPeval{\Ydiff}{abs(#4 - #2)}
\FPhypotenuse{\PstFractalHypothenuse}{\Xdiff}{\Ydiff}
% \FPeval easily generate overflows on next computations,
% so we rather use here the \FPupn variant
\FPupn{\PstFractalRotation}
{\PstFractalHypothenuse{} \Xdiff{} / arccos 57.29578 *}
\ifdim#1\p@<#3\p@
\ifdim#2\p@>#4\p@
\FPneg{\PstFractalRotation}{\PstFractalRotation}
\fi
\else
\ifdim#2\p@<#4\p@
\else
\FPsub{\PstFractalRotation}{180}{\PstFractalRotation}
\fi
\FPneg{\PstFractalRotation}{\PstFractalRotation}
\fi
\FPround{\PstFractalRotation}{\PstFractalRotation}{5}
% Using \moveto and \lineto macros rather than \psline will optimize
% resulting file with a noticeable factor (around 2)!
\ifnum\pst@cnta=\tw@
\@enamedef{PstFractal@Definition\the\pst@cnta}{%
\noexpand\moveto(#1,#2)
\noexpand\lineto(#3,#4)}%
\else
\@enamedef{PstFractal@Definition\the\pst@cnta}{%
\noexpand\lineto(#1,#2)
\noexpand\lineto(#3,#4)}%
\fi
\@enamedef{PstFractal@Repeat\the\pst@cnta}##1{%
\noexpand\rput{\PstFractalRotation}(#1,#2){%
\noexpand\PstFractal[unit=\PstFractal@Scale]{##1}}}}
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\def\PstVonKochCurve{%
\@ifnextchar[{\PstVonKochCurve@i}{\PstVonKochCurve@i[]}}
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\def\PstVonKochCurve@i[#1]#2{%
\PstFractal@SelfSimilar[#1]{#2}{0.33333}(0,0)(1,0)(1.5,0.866)(2,0)(3,0)}
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\def\PstVonKochSnake{%
\@ifnextchar[{\PstVonKochSnake@i}{\PstVonKochSnake@i[]}}
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\def\PstVonKochSnake@i[#1]#2{%
\rput(0,0){\PstVonKochCurve[#1]{#2}}
\rput{240}(3,0){\PstVonKochCurve[#1]{#2}}
\scalebox{-1 1}{\rput{240}{\PstVonKochCurve[#1]{#2}}}}
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\def\PstMinkowskiCurve{%
\@ifnextchar[{\PstMinkowskiCurve@i}{\PstMinkowskiCurve@i[]}}
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\def\PstMinkowskiCurve@i[#1]#2{%
\PstFractal@SelfSimilar[#1]{#2}{0.25}%
(0,0)(1,0)(1,1)(2,1)(2,0)(2,-1)(3,-1)(3,0)(4,0)}
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\psset{unit=2}%
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\pspicture(3,0.9)\PstVonKochCurve{1}\endpspicture
\hfill
\pspicture(3,0.9)\PstVonKochCurve{2}\endpspicture
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\pspicture(3,0.9)\PstVonKochCurve{3}\endpspicture
\hfill
\pspicture(3,0.9)\PstVonKochCurve{4}\endpspicture
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\pspicture(0,-2.6)(3,0.9)\PstVonKochSnake{4}\endpspicture
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\pspicture(0,-0.2)(0.8,0.2)\PstMinkowskiCurve[unit=0.2]{1}\endpspicture
\hfill
\pspicture(0,-0.23)(0.8,0.23)\PstMinkowskiCurve[unit=0.2]{2}\endpspicture
\hfill
\pspicture(0,-1.3)(4,1.3)
\PstMinkowskiCurve[linewidth=0.2\pslinewidth]{4}
\endpspicture
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G
Storing and retrieving data in arrays
For some applications, it is very convenient to manage data in arrays, in the
meaning of the classical programming languages. For that, the ‘arrayjob’
package [4] from Zhuhan Jiang is very well adapted and powerful.73 It
allow to store and retrieve data in mono or bi-dimensional arrays. Here
is an example which allow to build easily a generic macro to draw simple
(without exploded slices, etc.) two dimensional pie charts, just defining
three arrays of data for the values, labels and styles of the slices.74
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\def\PstPieChart#1#2#3#4{%
% #1 = Values, #2 = Labels, #3 = Styles, #4 = Starting angle
\pspicture(-2,-2)(2,2)
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Take care that it has an incompatibility with the ‘array’ LATEX package, with a name
clash on the \array macro that both define... You could find a workaround for this problem
in the pst-user.cls file of this documentation.
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The ‘pst-chrt’ contribution package [57], to draw various kinds of 2d and pseudo-3d
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% To compute in \pst@dimd the sum of all the values
\pst@dimd=\z@
\Multido{\iNbValues=\z@+\@ne}{9999}{%
\csname check#1\endcsname(\multidocount)%
\ifemptydata
\multidostop
\else
\fi}
\degrees[\pst@number{\pst@dimd}]
% To compute the starting angle
\pst@dimh=\pst@dimd
\divide\pst@dimh by 360
\multiply\pst@dimh by #4
% Loop on slices
\multido{}{\iNbValues}{%
% Slice
\pst@dimg=\pst@dimh
\csname check#1\endcsname(\multidocount)%
\csname check#3\endcsname(\multidocount)%
\pswedge[style=\cachedata]{2}
{\pst@number{\pst@dimg}}{\pst@number{\pst@dimh}}
% Label
\divide\pst@dimg\tw@
\uput{2.2}[\pst@number{\pst@dimg}](0,0){%
\large\csname #2\endcsname(\multidocount)}}
\endpspicture}
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\newarray{\Values}
\newarray{\Labels}
\newarray{\Styles}
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\readarray{Values}{32.7 & 19.3 & 12.4 & 27.6 & 6.9}
% Don’t leave blanks between labels and between styles!
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\newpsstyle{}{}% For undefined styles
\newpsstyle{StyleHatchA}{fillstyle=crosshatch}
\newpsstyle{StyleSolidA}{fillstyle=solid,fillcolor=magenta}
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\PstPieChart{Values}{Labels}{Styles}{0}
\hspace{1.5cm}
\Styles(5)={StyleHatchA}
\Values(6)={8.3}\Labels(6)={2002}\Styles(6)={StyleSolidA}
\PstPieChart{Values}{Labels}{Styles}{180}
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Then another example to draw a classical pyramid of ages in a generic way,
automatically computing the size of the graphic and the axes.
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\def\PstPyramidAges#1#2#3#4{{%
% #1 = Values for first set, #2 = Values for second set,
% #3 = Labels, #4 = Styles
\psset{dimen=middle}%
% To store in \pst@tempc the maximum value for the first set
% and in \pst@tempd the maximum value for the second set.
% This will allow to compute the size of the graphic
% and the correct lengths of the axes.
\pst@dimg=\z@
\pst@dimh=\z@
\Multido{\iNbValues=\z@+\@ne}{9999}{%
\csname check#1\endcsname(\multidocount)%
\ifemptydata
\multidostop
\else
\ifdim\pst@dimg<\cachedata\p@
\pst@dimg=\cachedata\p@
\fi
\csname check#2\endcsname(\multidocount)%
\ifdim\pst@dimh<\cachedata\p@
\pst@dimh=\cachedata\p@
\fi
\fi}
\edef\pst@tempc{\pst@number{\pst@dimg}}%
\edef\pst@tempd{\pst@number{\pst@dimh}}%
\pspicture(-\pst@tempc,-2.5)(\pst@tempd,\iNbValues.9)
% The two styles used
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\csname check#4\endcsname(\@ne)%
\let\PstStyleFirstSet\cachedata
\csname check#4\endcsname(\tw@)%
\let\PstStyleSecondSet\cachedata
% Loop on values
\multido{\iValue=\z@+\@ne}{\iNbValues}{%
% First set
\csname check#1\endcsname(\multidocount)%
\psframe[style=\PstStyleFirstSet]
(0,\iValue)(-\cachedata,\multidocount)
% Second set
\csname check#2\endcsname(\multidocount)%
\psframe[style=\PstStyleSecondSet]
(0,\iValue)(\cachedata,\multidocount)}
% Axes
\def\pshlabel##1{%
\ifnum##1<\z@
\pst@cnth=##1
\pst@cnth=-\pst@cnth
\the\pst@cnth
\else
##1
\fi}%
\psaxes[tickstyle=bottom,ticks=x,labels=x,arrowscale=2]
{<->}(0,-0.5)(-\pst@tempc,-0.5)(\pst@tempd,\iNbValues.9)
% Labels and legend
\rput[r](-1,\iNbValues){\csname #3\endcsname(\@ne)}
\rput[l](1,\iNbValues){\csname #3\endcsname(\tw@)}
\rput(0,-2){\csname #3\endcsname(\thr@@)}
\endpspicture}}
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\newarray{\ValuesMen}
\newarray{\ValuesWomen}
\newarray{\Labels}
\newarray{\Styles}
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3.9 & 4.2 & 4.2 & 4.2 & 3.5 & 2.9 & 2.6 & 1.2 & 0.5 & 0.1}
3.7 & 3.9 & 4.2 & 4.2 & 3.5 & 2.9 & 3.0 & 1.8 & 1.2 & 0.2}
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% Don’t leave blanks between labels and between styles!
French population, in millions (1990)}
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\newpsstyle{StyleSolidA}{fillstyle=solid,fillcolor=LightBlue}
\newpsstyle{StyleSolidB}{fillstyle=solid,fillcolor=Pink}
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\psset{yunit=0.6}%
\PstPyramidAges{ValuesMen}{ValuesWomen}{Labels}{Styles}
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Men
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French population, in millions (1990)
4
H Random
Sometimes, it is needed or useful to be able to generate random values.
There are two ways to do it, at the TEX level or at the PostScript one. In
the first case, the ‘random’ package [72] from Donald Arseneau must be
used, which allow to generate integer or real numbers (as numbers or TEX
lengths).
From the usage point of view, an important difference with the PostScript
level is that the graphic will look the same until we recompile the TEX
file, at the opposite to the PostScript generation of the random numbers,
which will generate a different graphic each time the file will be viewed
or printed.75 Another difference is the speed. As TEX is very slow for
computations, it could take a long time to compile the graphic if you must
generate a huge amount of random numbers. Nevertheless, as explained,
these numbers will not be generated again during each interpretation of the
PostScript code.
We give here examples of both usage, first to generate a patchwork of little squares of a random level of gray color. In the TEX version, we cannot use the \multips macro, as we need to generate at each iteration not
only the code of a pure PSTricks graphic object, but also the code defining the new color. In the PostScript version, we must redefine the internal
\pst@usecolor macro.
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\multido{\nXA=0.0+0.5,\nXB=0.5+0.5}{10}{%
\multido{\nYA=0.0+0.5,\nYB=0.5+0.5}{10}{%
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You can verify it calling two times a visualization tool on this file: the first next graphic
will stay the same when the second one will be different.
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\setrandim{\pst@dimh}{0pt}{1pt}%
\definecolor{MyGray}{gray}{\pst@number{\pst@dimh}}%
\psframe*[linecolor=MyGray](\nXA,\nYA)(\nXB,\nYB)}}
\hfill
\multips(0,0.5){10}{%
\multips(0.5,0){10}{%
\def\pst@usecolor#1{rand 101 mod 100 div setgray }%
\psframe*(0.5,0.5)}}
In the next example, we draw colored bubbles in a test tube. The position of
the bubbles is randomly computed, as their sizes, which may also depend
of the value of the current unit, and they also grow according to the vertical
position inside the tube. The color of the bubbles is also set randomly, using
the Brightness component of the HSB color model.
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\def\PstTestTube{%
\psline[linearc=0.5](-0.5,3)(-0.5,0)(0.5,0)(0.5,3)
\psellipse[fillstyle=solid,fillcolor=white](0,3)(0.5,0.1)}
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\def\PstTestTubeBubbles{%
\pspicture(-0.5,0)(0.5,3.1)
\psclip{\pscustom[linestyle=none]{\PstTestTube}}
\multido{}{30}{%
\setrandim{\pst@dimc}{-0.5pt}{0.5pt}% Horizontal coordinate
\setrandim{\pst@dimd}{0pt}{3pt}%
Vertical coordinate
\setrandim{\pst@dimg}{0.5pt}{1pt}%
Color brightness
\definecolor{MyColor}{hsb}{0.15,0.6,\pointless\pst@dimg}%
% The size increase proportionally to the vertical position
\pst@dimh=\pst@dimd
% And depend of the unit
\pst@dimg=0.02\psunit
\pst@dimh=\pointless\pst@dimg\pst@dimh
\psdot[dotscale=\pointless\pst@dimh,linecolor=MyColor]
(! \pst@number{\pst@dimc} \pst@number{\pst@dimd})}
\endpsclip
\PstTestTube
\endpspicture}
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\PstTestTubeBubbles\hfill
{\psset{unit=0.5}\PstTestTubeBubbles}\hfill
{\psset{unit=1.5}\PstTestTubeBubbles}\hfill
{\psset{unit=2}\PstTestTubeBubbles}
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bb bb b
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Now, a macro to draw fuzzy lines, to mimic hand made bars.76 It allow to
draw sticks to show quantities.
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\def\PstLineFuzzy[#1](#2,#3)(#4,#5)(#6,#7)(#8,#9){%
\pscurve[#1](! #2 rand 101 mod 1000 div sub
#3 rand 101 mod 1000 div sub)
(! #4 rand 101 mod 1000 div sub
#5 rand 101 mod 1000 div sub)
(! #6 rand 101 mod 1000 div sub
#7 rand 101 mod 1000 div sub)
(! #8 rand 101 mod 1000 div sub
#9 rand 101 mod 1000 div sub)}
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\def\PstSticks#1{%
\multido{\iStick=0+1,\nXA=0.1+0.1,\nXB=-0.5+0.1,
\nXC=-0.35+0.10,\nXD=-0.15+0.10}{#1}{%
\pst@cnta=\iStick
\pst@cnth=\iStick
\divide\pst@cnth by 5
\multiply\pst@cnth by 5
\ifnum\iStick>0\relax
\ifnum\pst@cnta=\pst@cnth
\PstLineFuzzy[linecolor=red]%
(\nXB,0.2)(\nXC,0.4)(\nXD,0.6)(\nXA,0.8)
\hbox to 0.2\psxunit{}
\fi
\fi
\PstLineFuzzy[](\nXA,0.1)(\nXA,0.4)(\nXA,0.7)(\nXA,1)}}
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The initial idea come from MetaFun [40] from Hans Hagen.
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\pspicture(-0.1,0)(3.6,3)
\psset{unit=3}%
\PstSticks{12}
\endpspicture
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\large
\psset{xunit=0.8,yunit=0.3}%
\begin{tabular}{|l|r|p{5.5cm}|}
\hline
Linux
& 27 & \PstSticks{27} \\ \hline
Mac OS X
& 14 & \PstSticks{14} \\ \hline
Windows XP & 43 & \PstSticks{43} \\ \hline
\end{tabular}
Linux
Mac OS X
Windows XP
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You could find another example of random usage applied on tilings in Section 50.4.
A lot of things can be done with random. To finish this section, we give an
example of how to build a random mosaic,77 of any number of divisions,
from a PSTricks graphic or an external image.78
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\newarray{\PstMosaic@Indexes}
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\def\PstMosaic(#1,#2)(#3,#4)#5#6{{%
% #1,#2 = X and Y dimensions (without unit)
% #3,#4 = horizontal and vertical number of shifts
% #5 = PSTricks graphic code or external image
% #6 = PSTricks parameters for the borders
\expandarrayelementtrue
\dataheight=#3\relax
% Initialization of an array of indexes
\multido{\iX=\@ne+\@ne}{#3}{%
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The initial idea come from MetaFun [40] from Hans Hagen.
Take care that in this last case the image is loaded the number of times corresponding
to the number of cells, which can generate a huge resulting file if the compiler used is not
able to load the file only one time, or if you do not use a special EPS file with a core part
which will be loaded only one time (see the paragraph 15 (in it version 2.0) in the document
of Keith Reickdahl about the insertion of EPS images with LATEX [75]).
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\multido{\iY=\@ne+\@ne}{#4}{%
\PstMosaic@Indexes(\iX,\iY)={(\iX,\iY)}}}
% Shuffling of this array of indexes (50 times must be enough!)
\PstMosaic@IndexesShuffle(#3,#4){50}%
% The mosaic
\pst@dimg=#1\p@
\divide\pst@dimg by #3
\pst@dimh=#2\p@
\divide\pst@dimh by #4
\pst@dimtonum{\pst@dimg}{\pst@tempi}%
\pst@dimtonum{\pst@dimh}{\pst@tempj}%
\pspicture(#1,#2)
\multido{\iX=\@ne+\@ne}{#3}{%
\multido{\iY=\@ne+\@ne}{#4}{%
\checkPstMosaic@Indexes(\iX,\iY)%
\expandafter\PstMosaic@GetIndexes\cachedata
\PstMosaic@Tile(\pst@tempi,\pst@tempj)%
(\pst@tempg,\pst@temph)(\iX,\iY){#5}{#6}}}
\endpspicture}}
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\def\PstMosaic@IndexesShuffle(#1,#2)#3{%
\multido{\iShuffle=\@ne+\@ne}{#3}{%
\setrannum{\pst@cnta}{\@ne}{#1}%
\setrannum{\pst@cntb}{\@ne}{#2}%
\setrannum{\pst@cntc}{\@ne}{#1}%
\setrannum{\pst@cntd}{\@ne}{#2}%
% Exchange of \PstMosaic@Indexes(\pst@cnta,\pst@cntb)
% and \PstMosaic@Indexes(\pst@cntc,\pst@cntd)
\checkPstMosaic@Indexes(\the\pst@cnta,\the\pst@cntb)%
\let\pst@tempg\cachedata
\checkPstMosaic@Indexes(\the\pst@cntc,\the\pst@cntd)%
\PstMosaic@Indexes(\the\pst@cnta,\the\pst@cntb)={\cachedata}%
\PstMosaic@Indexes(\the\pst@cntc,\the\pst@cntd)={\pst@tempg}}}
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\def\PstMosaic@GetIndexes(#1,#2){%
\edef\pst@tempg{#1}%
\edef\pst@temph{#2}}
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\def\PstMosaic@Tile(#1,#2)(#3,#4)(#5,#6)#7#8{%
\PstMosaic@Position{#1}{#3}{\pst@tempa}%
\PstMosaic@Position{#2}{#4}{\pst@tempb}%
\PstMosaic@Position{#1}{#5}{\pst@tempc}%
\PstMosaic@Position{#2}{#6}{\pst@tempd}%
\rput(\pst@tempc,\pst@tempd){%
\psclip{\psframe[linestyle=none](#1,#2)}
\rput(-\pst@tempa,-\pst@tempb){#7}%
\endpsclip
\psframe[dimen=middle,#8](#1,#2)}}
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\def\PstMosaic@Position#1#2#3{%
\pst@dimh=#1\p@
\pst@cnth=#2
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\multiply\pst@dimh\pst@cnth
\pst@dimtonum{\pst@dimh}{#3}}
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% Examples
% ————–
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\def\PstCircle{%
\pscircle[linewidth=0.1,fillstyle=solid,fillcolor=cyan](2,2){1.5}}
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\pspicture(4,4)
\PstCircle
\endpspicture
\hfill
\PstMosaic(4,4)(2,1){\PstCircle}{linecolor=red,linewidth=0.1}
\hfill
\PstMosaic(4,4)(2,2){\PstCircle}{linecolor=red,linewidth=0.1}
\hfill
\PstMosaic(4,4)(3,3){\PstCircle}{linecolor=red,linewidth=0.1}
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\def\PstCircleHue{{%
\psset{unit=3}%
\multido{\nHue=0.0+0.1}{10}{%
\definecolor{MyColor}{hsb}{\nHue,1,1}%
\pscircle[linewidth=0.1,linecolor=MyColor](1,1){\nHue}}}}
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\pspicture(6,6)
\PstCircleHue
\endpspicture
\hfill
\PstMosaic(6,6)(5,3){\PstCircleHue}{linecolor=red,linewidth=0.1}
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\includegraphics{lbrooks}% Louise Brooks (1906-1985)
\hfill
\PstMosaic(5.88,6.84)(3,2){\includegraphics[bb=0 0 1 1]{lbrooks}}
{linestyle=dashed,linewidth=0.1}
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I Coordinates
With it special coordinates (see Section 54), PSTricks offer powerful capabilities to handle coordinates. Nevertheless, one more thing which can be
useful is to be able to handle relative coordinates, both for Cartesian and
polar ones, and also for self defined lengths.
I.1 Relative coordinates
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% D.G. - 1994/1997
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%
%
%
%
Minimal implementation of relative cartesian and polar
coordinates
(n:m) add n units in X direction and m in Y direction
(n!m) add n units in X direction and m degrees of angle
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% New functions
\let\@psunit\psxunit
\afterassignment\pstunit@off
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\afterassignment\pstunit@off
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\def\PstRelativeCartesian@coor#1#2{%
\edef\pst@coor{\pst@number\pst@dimg \pst@number\pst@dimh}}
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\def\PstRelativePolar@coor#1#2{%
\edef\pst@coor{\pst@number\pst@dimg \pst@angle \tx@PtoC}}
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\def\special@@@coor#1;#2;#3\@nil{%
\ifx#3;\relax
\polar@coor{#1}{#2}%
\else
\special@@@@coor#1::\@nil
\fi}
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\def\special@@@@coor#1:#2:#3\@nil{%
\ifx#3:\relax
\PstRelativeCartesian@coor{#1}{#2}%
\else
\special@@@@@coor#1!!\@nil
\fi}
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\def\special@@@@@coor#1!#2!#3\@nil{%
\ifx#3!\relax
\PstRelativePolar@coor{#1}{#2}%
\else
\cartesian@coor#1,\relax,\@nil
\fi}
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\psset{subgriddiv=0,linewidth=0.1,arrowscale=1.5}
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\pspicture(4,4)\psgrid
\psline[linecolor=blue]{->}(2,3)(3,2)(2,0)
\psline[linecolor=red]{->}(0,2)(2:-1)(4,4)(-2:0)
\psline[linecolor=green]{->}(2,2)(-1:-2)(3:2)(-1:1)
\psframe(2,2)(1:1)
\endpspicture
\hfill
\pspicture(4,4)\psgrid
\psset{xunit=2}%
\pspolygon[linecolor=blue](1,3)(1.5,2)(0.5,1)
\pspolygon[linecolor=green](1,2)(-0.5:-2)(1.5:2)(-0.5:1)
\endpspicture
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\pspicture(4,4)\psgrid
\pscurve[linecolor=blue]{->}(2,3)(3,2)(1,1)
\pscurve[linecolor=green]{->}(2,2)(-1:-2)(3:2)(-1:1)
\endpspicture
\hfill
\pspicture(4,4)\psgrid
\psline[linecolor=blue]{->}(2;30)(3;60)(1;30)
\pscurve[linecolor=green]{->}(2;30)(1!30)(-2!-30)
\psline[linecolor=red]{->}(0;0)(3!90)(0!-90)(2!45)
\endpspicture
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\pspicture(4,4)\psgrid
\psline[linecolor=cyan](2;30)(4;60)(1;30)
\psline[linestyle=dotted,linewidth=0.3,dotsep=0.4](2;30)(2!30)(-3!-30)
\endpspicture
\hfill
\pspicture(4,4)\psgrid
\degrees[4]
\psline[linecolor=cyan](3;0)(4;1)(0;2)
\psline[linestyle=dotted,linewidth=0.3,dotsep=0.4](3;0)(1!1)(-4!1)
\endpspicture
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Another wish could be to define relative values of existing real or lengths
parameters. This can be done using a macro like the \Pst@SetAbsOrRelDim@i
one below, that we will illustrate on a modified version of the \PstBar macro
built in the chapter XII, which define it parameters using the interface of the
‘pst-key’ package.
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\define@key{psset}{Length}{%
\Pst@SetAbsOrRelDim@i{\PstBar@Length}#1\@nil}
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\define@key{psset}{Height}{%
\Pst@SetAbsOrRelDim@i{\PstBar@Height}#1\@nil}
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\def\Pst@SetAbsOrRelDim@i#1{%
\@ifnextchar+{\Pst@SetAbsOrRelDim@ii{#1}}
{\Pst@SetAbsOrRelDim@iii{#1}}}
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\def\Pst@SetAbsOrRelDim@ii#1+#2\@nil{%
\pssetlength{\pst@dimh}{#1}%
\edef#1{\the\pst@dimh}}
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\def\Pst@SetAbsOrRelDim@iii#1#2\@nil{\edef#1{#2}}
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\setkeys{psset}{Length=3,Height=1}% Default values
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\def\PstBar{\@ifnextchar[{\PstBar@i}{\PstBar@i[]}}
Help: Coordinates
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21
\def\PstBar@i[#1]{{%
\setkeys{psset}{framesep=1pt,#1}%
\psframe(\PstBar@Length,\PstBar@Height)
\pssetlength{\pst@dima}{\PstBar@Length}%
\pssetlength{\pst@dimc}{\PstBar@Height}%
\psline[linewidth=0.08](\pst@dima,-0.5)(\pst@dima,\pst@dimc)
\pst@dimb=\pst@dima
\psframe[linestyle=none,fillstyle=hlines]
(\pst@dima,-0.5)(\pst@dimb,\pst@dimc)
\pssetlength{\pst@dimc}{\PstBar@Height}%
\divide\pst@dimc\tw@
\rput*{90}(\pst@dima,\pst@dimc){Wall}}}
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\rput(-6,0){\PstBar}
\PstBar[Length=4,Height=0.5]
Wall
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\rput(-6,0){\PstBar[unit=2,Length=1cm,Height=1cm]}
\PstBar[Length=+1cm,Height=+1cm]
Wall
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\rput(-6,0){%
\setkeys{psset}{Length=4}%
\PstBar[Length=+-15mm,Height=+-0.8cm]}
\PstBar[unit=1.5,Length=+-0.8,Height=+-1.4]
Wall
4
Wall
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Wall
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Help: Coordinates
Wall
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291
J
Nodes
Nodes are a very powerful way to handle coordinates.79
Nevertheless, outside their usage as special coordinates (see Section 54),
it is also interesting to know how to retrieve the coordinates of a node and
how to position objects or new nodes relatively to existing ones.
J.1 Getting the coordinates of a node
When nodes are defined, their explicit coordinates cannot be retrieved at the
TEX level, if they are unknown.80 But they can be retrieved at the PostScript
level, requiring to be handled only in this language part, which is often
enough for practical needs. Here is how to proceed, using the GetCenter
PostScript macro and the tx@NodeDict PostScript dictionary.
We use this function here to draw a line from a node to the two thirds of
the virtual line joining this node to another one (the solution shown for that
in the next paragraph is clearly easier and does not require any PostScript
programming, but this is a general way to proceed, for other needs too).
The PostScript sequence /N@NodeNameload GetCenter allow to retrieve
the coordinates of the node specified, leaving them on the stack. So, the
ED (Exchange and Define macro), introduced in the pstricks.pro header
file, allow to store these values in PostScript variables, for later reuse.
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\SpecialCoor
\Cnode*(1,3){A}
\Cnode*[linecolor=red](3.5,1.5){B}
\psline[arrowscale=2]{-|}(A)
(! tx@NodeDict begin% 2/3 of the AB segment
/N@A load GetCenter % Center of node A
/yA ED
/xA ED
/N@B load GetCenter % Center of node B
/yB ED
/xB ED
xB xA sub 0.66667 mul xA add \pst@number\psxunit div
yB yA sub 0.66667 mul yA add \pst@number\psyunit div
end)
79
The contribution packages ‘pst-circ’ [58] from Christophe Jorssen and Herbert Voss,
for electric circuits, and ‘pst-eucl’ [59] from Dominique Rodriguez, for Euclidean geometry
drawings, are good illustrations of which high level generic functions they allow to built.
80
This is because there is no possibility to sent back informations from the PostScript
level to the TEX one during the compilation (the VTEX compiler [82] has such capability,
but using such feature will give a non portable code).
Help: Nodes
292
J.2 Positions relative to nodes
Positioning objects or new nodes relatively to existing ones is sometimes
needed, and is easy to got, with the conjunction of the \pnode and \ncput
macros, together with the tpos parameter.
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\SpecialCoor
\pcline[linecolor=magenta](1,0)(1,8)
\ncput{\pnode{A}}% A is the middle of (1,0) and (1,8) -> (1,4)
\pcline[linecolor=yellow](5,6)(5,8)
\ncput{\pnode{B}}% B is the middle of (5,6) and (5,8) -> (5,7)
\psline[linecolor=green](A)(B)
%
\pnode(1,2){G}
\pnode(6,4){H}
\ncline[linestyle=none]{G}{H}
% Join the middle of the segment joining G and H, with H
\ncput{\psline(H)}
%
% I is the middle of the segment joining G and H
\ncput{\pnode{I}}
% J is the middle of the segment joining G and I
\ncput[npos=0.25]{\pnode{J}}
\psline[linecolor=red](I)(J)
%
\psset{linecolor=cyan}%
\pnode(2,7){R}
\pnode(7,2){S}
\ncline[linestyle=dotted]{R}{S}
% T is the third of the segment joining R and S
\ncput[npos=0.3333]{\pnode{T}}
\psline[linecolor=blue](I)(T)
Help: Nodes
293
b
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bR
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bT
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8
K Boxes
Many of the PSTricks macros have an argument for text that is processed
in restricted horizontal mode (in LATEX parlance, LR-mode) and then transformed in some way. This is always the macro’s last argument, and it is
written {<stuff>} in this User’s Guide. Examples are the framing, rotating, scaling, positioning and node macros. They will be called “LR-box”
macros, and use framing as the leading example in the discussion below.
In restricted horizontal mode, the input, consisting of regular characters and
boxes, is made into one (long or short) line. There is no line-breaking, nor
can there be vertical mode material such as an entire displayed equation.
However, the fact that you can include another box means that this isn’t
really a restriction.
For one thing, alignment environments such as \halign or LATEX’s tabular
are just boxes, and thus present no problem. Picture environments and the
box macros themselves are also just boxes. Actually, there isn’t a single
PSTricks command that cannot be put directly in the argument of an LRbox macro. However, entire paragraphs or other vertical mode material
such as displayed equations need to be nested in a \vbox or LATEX \parbox
or minipage. LATEX users should see the ‘fancybox’ package [15] and its
documentation for extensive tips and tricks for using LR-box commands.
The PSTricks LR-box macros have some features that are not found in most
other LR-box macros, such as the standard LATEX LR-box commands.
With LATEX LR-box commands, the contents is always processed in text
mode, even when the box occurs in math mode. PSTricks, on the other
hand, preserves math mode, and attempts to preserve the math style as
Help: Boxes
294
well. TEX has four math styles: text, display, script and scriptscript. Generally, if the box macro occurs in displayed math (but not in sub- or superscript math), the contents are processed in display style, and otherwise
the contents are processed in text style (even here the PSTricks macros
can make mistakes, but through no fault of their own). If you don’t get
the right style, explicitly include a \textstyle, \displaystyle, \scriptstyle or
\scriptscriptstyle command at the beginning of the box macro’s argument.
In case you want your PSTricks LR-box commands to treat math in the
same as your other LR-box commands, you can switch this feature on and
off with the commands
\psmathboxtrue
\psmathboxfalse
You can have commands (such as, but not restricted to, the math style commands) automatically inserted at the beginning of each LR-box using the
\everypsbox{commands}
command.81
If you would like to define an LR-box environment name from an LR-box
command cmd , use
\pslongbox{name}{cmd}
For example, after
1
\pslongbox{MyFrame}{\psframebox}
you can write82
1
\MyFrame <stuff>\endMyFrame
1
\psframebox{<stuff>}
It is up to you to be sure that cmd is a PSTricks LR-box command; if it
isn’t, nasty errors can arise.
Environments like have nice properties:
81
This is a token register.
82 A
LT
\begin{MyFrame}stuff \end{MyFrame}
Help: Boxes
295
• The syntax is clearer when stuff is long.
• It is easier to build composite LR-box commands. For example, here
is a framed minipage environment for LATEX:
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3
4
\pslongbox{MyFrame}{\psframebox}
\newenvironment{fminipage}%
{\MyFrame\begin{minipage}}%
{\end{minipage}\endMyFrame}
• You include verbatim text and other \catcode tricks in stuff .
The rest of this section elaborates on the inclusion of verbatim text in
LR-box environments and commands, for those who are interested. The
‘fancybox’ package also contains some nice verbatim macros and tricks,
some of which are useful for LR-box commands.
The reason that you cannot normally include verbatim text in an LR-box
commands argument is that TEX reads the whole argument before processing the \catcode changes, at which point it is too late to change the category
codes. If this is all Greek to you,83 then just try this LATEX example to see
the problem:
1
\psframebox{\verb+\foo{bar}+}
The LR-box environments defined with \pslongbox do not have this problem because stuff is not processed as an argument. Thus, this works:
1
2
\pslongbox{MyFrame}{\psframebox}
\MyFrame \verb+\foo{bar}+\endMyFrame
\foo{bar}
The commands
\psverbboxtrue
\psverbboxfalse
switch into and out of, respectively, a special PSTricks mode that lets you
include verbatim text in any LR-box command. For example:
1
2
\psverbboxtrue
\psframebox{\verb+\foo{bar}+}
83
Incidentally, some foreign language macros use \catcode tricks which can cause problems in LR-box macros.
Help: Boxes
296
\foo{bar}
However, this is not as robust. You must explicitly group color commands
in stuff , and LR-box commands that usually ignore spaces that follow
{<stuff>} might not do so when \psverbboxtrue is in effect.
L
DG: This whole section is to recheck.
L.1
How to inactivate the PSTricks macros
To suppress the PostScript code generate by PSTricks macros, put the command
\PSTricksOff
at the beginning of your document. You should then be able to print or
preview drafts of your document (minus the PostScript, and perhaps pretty
strange looking) with any dvi driver.
L.2
Monochrome version of all or some graphics
To generate a monochrome version of a paper, without having some colored
graphics looking bad due to the gray conversion of the colors, it is easier
to redefine the macros which set the colors rather than changing explicitly
all the colors in the PSTricks macros which define them. And, first, if you
use P LAIN TEX or LATEX, use the monochrome parameter of the ‘pstcol’
package (it will just pass this option to the ‘color’ one).
1
\documentclass[...]{...}
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\usepackage[monochrome]{pstcol}
% ...
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\makeatletter
\def\PSTricksMonochrome{%
\def\psset@bordercolor##1{\pst@getcolor{white}{\psbordercolor}}%
\def\psset@doublecolor##1{\pst@getcolor{white}{\psdoublecolor}}%
\def\psset@linecolor##1{\pst@getcolor{black}{\pslinecolor}}%
\def\psset@fillcolor##1{\pst@getcolor{white}{\psfillcolor}}%
\def\psset@gridcolor##1{\pst@getcolor{black}{\psgridcolor}}%
\def\psset@gridlabelcolor##1{\pst@getcolor{black}{\psgridlabelcolor}}%
\def\psset@hatchcolor##1{\pst@getcolor{black}{\pshatchcolor}}%
\def\psset@subgridcolor##1{\pst@getcolor{gray}{\pssubgridcolor}}}
\makeatother
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%\PSTricksMonochrome% To force it on the whole document
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\begin{document}
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\begin{pspicture}(3,3)
\psframe[linecolor=yellow,fillstyle=solid,fillcolor=red](3,3)
\psline[linecolor=blue,linewidth=0.1]{cc-cc}(0,3)(2.9,1)(1,0)
\rput(2,1){\textcolor{green}{Look!}}
\end{pspicture}
\hfill
\begin{pspicture}(3,3)
\PSTricksMonochrome% To force locally monochrome rendering
\psframe[linecolor=yellow,fillstyle=solid,fillcolor=red](3,3)
\psline[linecolor=blue,linewidth=0.1]{cc-cc}(0,3)(2.9,1)(1,0)
\rput(2,1){\textcolor{green}{Look!}}
\end{pspicture}
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\end{document}
Look!
L.3
Look!
How to improve the rendering of halftones?
This can be an important consideration when you have a halftone in the
background and text on top. You can try putting
1
2
\pstverb{106 45 {dup mul exch dup mul add 1.0 exch sub}
setscreen}
before the halftone, or in a header (as in headers and footers, not as in
PostScript header files), if you want it to have an effect on every page.
setscreen is a device-dependent operator.
L.4
Including PostScript code
When you define TEX macros for including PostScript fragments in various
places, all TEX macros are expanded before being passed on to PostScript.
It is not always clear what this means. For example, suppose you write
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\SpecialCoor
\def\mydata{23 43}
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6
You will get a PostScript error in each of the \psline commands. To see
what the argument is expanding to, try use TEX’s \edef and \show. E.g.,
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\def\mydata{23 43}
\show\temp
\show\temp
\show\temp
\show\temp
TEX expands the code, assigns its value to \temp, and then displays the
four samples expand, respectively, to:
1
2
3
4
47
47
47
47
23
23
23
23
All you really wanted was a space between the 43 and add. The command
\space will do the trick:
1
You can include balance braces { }; these will be passed on verbatim to
PostScript. However, to include an unbalanced left or right brace, you have
to use, respectively,
\pslbrace
\psrbrace
Don’t bother trying \} or \{.
Whenever you insert PostScript code in a PSTricks argument, the dictionary on the top of the dictionary stack is tx@Dict, which is PSTrick’s main
dictionary. If you want to define you own variables, you have two options:
Simplest Always include a @ in the variable names, because PSTricks
never uses @ in its variables names. You are at a risk of overflowing the tx@Dict dictionary, depending on your PostScript interpreter.
You are also more likely to collide with someone else’s definitions,
if there are multiple authors contributing to the document.
299
Safest Create a dictionary named TDict for your scratch computations. Be
sure to remove it from the dictionary stack at the end of any code you
insert in an argument. E.g.,
1
TDict 10 dict def TDict begin <your code> end
ConTEXt color macros support
L.5
ConTEXt fully support PSTricks. Nevertheless, as with the ‘color’ package
in LATEX, this is logical to rather use the standard ConTEXt syntax to define
and use colors. For that, a minor adaptation of the \dodefinecolor macro is
needed. We also add the support of the HSB color model with the ConTEXt
syntax, not currently supported by this TEX format.
1
% D.G. - April 2003
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% To allow to define colors in Gray, RGB, CMYK and HSB models,
% using the ConTeXt syntax.
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\def\dodefinecolor[#1][#2]{%
\doifassignmentelse{#2}{\dodefinecolori[#1][#2]#2\relax}{}}
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\def\dodefinecolori[#1][#2]#3#4\relax{%
\edef\tempa{#3}%
\edef\tempb{s}%
\ifx\tempa\tempb% Gray model
\getparameters[pstricks][s=0,#2]%
\expanded{\newgray{#1}{\pstricksg}}%
\else
\edef\tempb{r}%
\ifx\tempa\tempb% RGB model
\getparameters[pstricks][r=0,g=0,b=0,#2]%
\expanded{\newrgbcolor{#1}{{\pstricksr} {\pstricksg} {\pstricksb}}}%
\else
\edef\tempb{c}%
\ifx\tempa\tempb% CMYK model
\getparameters[pstricks][c=0,m=0,y=0,k=0,#2]%
\expanded{\newcmykcolor{#1}{{\pstricksc} {\pstricksm}
{\pstricksy} {\pstricksk}}}%
\else
\edef\tempb{H}%
\ifx\tempa\tempb% HSB model
\getparameters[pstricks][H=0,S=0,B=0,#2]%
\expanded{\newhsbcolor{#1}{{\pstricksH} {\pstricksS} {\pstricksB}}}%
\fi
\fi
\fi
\fi}
35
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% Support of the HSB model
% —————————————
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\def\dododefinecolor#1#2#3#4[#5][#6]% #2==set(g)value #3==set[e|x]value
\doifassignmentelse{#6}
{\@@resetcolorparameters
\getparameters[\??cl @@][#6]%
\doifelse{\@@cl@@r\@@cl@@g\@@cl@@b}
{\@@cl@@z\@@cl@@z\@@cl@@z}
{\doifelse{\@@cl@@c\@@cl@@m\@@cl@@y\@@cl@@k}
{\@@cl@@z\@@cl@@z\@@cl@@z\@@cl@@z}
% D.G. modification begin - May. 26, 2003
{\doifelse{\@@cl@@H\@@cl@@S\@@cl@@B}
{\@@cl@@z\@@cl@@z\@@cl@@z}
% D.G. modification end
{\doifelse\@@cl@@s\@@cl@@z
{\showmessage\m!colors8{{[#6]},#5}%
#3{\??cr#5}{\colorZpattern}}
{#3{\??cr#5}{\colorSpattern}}}
% D.G. modification begin - May. 26, 2003
{#3{\??cr#5}{\colorHpattern}}}
% D.G. modification end
{#3{\??cr#5}{\colorCpattern}}}
{#3{\??cr#5}{\colorRpattern}}}
{\doifdefinedelse{\??cr#6}
{\doifelse{#5}{#6}
{% this way we can freeze
% \definecolor[somecolor][somecolor]
% and still prevent cyclic definitions
\iffreezecolors#3{\??cr#5}{\getvalue{\??cr#6}}\fi}
{\iffreezecolors\@EA#3\else\@EA#2\fi
{\??cr#5}{\getvalue{\??cr#6}}}}
{\showmessage\m!colors3{#5}}}%
\ifcase#4\or
\unexpanded#2{#5}{\switchtocolor[#5]}% \unexpanded toegevoegd
\fi}
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1
\def\colorHpattern{%
0H:\@@cl@@H:\@@cl@@S:\@@cl@@B:\@@cl@@A:\@@cl@@t}
\starttext
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% New colors (in ConTeXt syntax)
\definecolor[ForestGreen][r=0.13,g=0.55,b=0.13]
\definecolor[LemonChiffon][r=1,g=0.98,b=0.8]
\definecolor[LightBlue][r=0.8,g=0.85,b=0.95]
\definecolor[LightGray][s=0.92]
\definecolor[LightOrange][c=0,m=0.2,y=0.4,k=0]
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\pspicture(-1.5,-1.5)(4.7,1.5)
\psset{fillstyle=solid}%
\pscircle[fillcolor=yellow]{1.5}
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\definecolor[LightBlue][r=0.8,g=0.85,b=0.95]
\definecolor[LightOrange][c=0,m=0.2,y=0.4,k=0]
\pscircle[linecolor=LightBlue,fillcolor=LightOrange]
(3.2,0){1.5}
\endpspicture
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\pspicture(-3,-3)(3,3)
\psset{unit=3}%
\multido{\nHue=0.01+0.01}{100}{%
\definecolor[MyColor][H=\nHue,S=1,B=1]
\pscircle[linewidth=0.01,linecolor=MyColor]{\nHue}}
\endpspicture
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L.6
\stoptext
Scope of parameters changes
When parameters are globally changed, using the \psset or the \setkeys
macros, we may want that this change apply to a series of later commands,
but that the previous values will be restored at some point. For that, the
thing to do is not to keep the old values in some new macros and to reset
later the parameters to these values, but to use the common TEX grouping
mechanism.
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L.7
...
\psset{Param=99}% Global change until the end of the file
...
\bgroup
\psset{Param=7.5}% Global change inside the defined group
...
\bgroup
\psset{Param=21}% Global change inside the new group
...
\PstXxxx[Param=-44]% Local change for this macro only
...% Param=21
\egroup
...% Param=7.5
\egroup
...% Param=99
Defining parameters using macros
This is not directly possible to define parameters using macros (such behavior is also not supported by the ‘keyval’ package [35]), as in:
302
\def\PstMyParameters{linecolor=red,fillstyle=solid,fillcolor=yellow}
\psset{\PstMyParameters}
\pscircle{1}
1
2
3
Here is how we can define a \PstSet macro which allow to do that. This
is also possible to change the behavior of the \psset macro to it, and also
to allow to use things like \psframe[\Attributes](2,2). To be able to use it
too with the ‘keyval’ and ‘pst-key’ interface (which is encouraged to be
used for all new PSTricks contribution packages!), we must modify the
\KV@setkeys macro from ‘pst-key’ and restore the PSTricks definition of
the \use@par one.
1
% D.G. - 2001 / 2003
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% New \PstSet macro
\def\PstSet#1{\PstSet@i#1,\@nil\ignorespaces}
\def\PstSet@i#1,{%
\expandafter\PstSet@ii#1,\@nil
\@ifnextchar\@nil{\@gobble}{\PstSet@i}}
\def\PstSet@ii#1,{%
\PstSet@iii#1=\@nil
\@ifnextchar\@nil{\@gobble}{\PstSet@ii}}
\def\PstSet@iii#1=#2\@nil{\pssetMOD{#1=#2}}
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% Redefinition of \psset to accept arguments in macros
\let\@pssetORI\@psset
\def\pssetMOD#1{\@pssetORI#1,\@nil\ignorespaces}
\let\psset\PstSet
\let\@psset\PstSet@i
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% For “keyval” and “pst-key” compatibility
\let\KV@setkeysORIG\KV@setkeys
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\def\KV@setkeys#1#2{%
\edef\@tempa{#1}%
\edef\@tempb{psset}%
\ifx\@tempa\@tempb
\PstSet@i#2,\@nil%
\else
\KV@setkeysORIG{#1}{#2}%
\fi}
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% We must restore the original PSTricks definition of \use@par
\def\use@par{%
\ifx\pst@par\@empty\else
\expandafter\@psset\pst@par,\@nil
\def\pst@par{}%
\fi}
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% Examples with the “pst-key” interface
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\define@key{psset}{Integer}{\pst@getint{#1}{\PstInteger}}
\define@key{psset}{String}{\edef\PstString{#1}}
41
42
43
44
45
46
47
\def\ParametersA{fillstyle=solid,fillcolor=red}
\def\ParametersB{linecolor=red,fillstyle=solid,fillcolor=yellow}
\def\ParametersC{linecolor=magenta,fillstyle=solid,fillcolor=cyan}
\def\ParametersE{Integer=99,String=AAAA}
\def\ParametersF{Integer=1}
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
\psframebox[\ParametersA]{Monday}
\hfill
\psset{\ParametersB}%
\psframebox{Tuesday}
\hfill
\setkeys{psset}{\ParametersC}%
\psframebox{Wednesday}
\hfill
\psframebox[\ParametersD]{Thursday}
\hfill
\setkeys{psset}{\ParametersE}
\psframebox[\ParametersB,fillcolor=green,doubleline=true]{%
\PstString=\PstInteger}
\hfill
\pscircle[\ParametersD,\ParametersF]{\PstInteger}
Monday
L.8
Tuesday
Wednesday
Thursday
AAAA=99
Line type connections
The setlinecap PostScript parameter, which specify how the ends of a line
finish, is accessible in PSTricks with the c and C arrows, which put this
parameter to 1 and 2, respectively. But other PostScript parameters, and
specially the setlinejoin are useful, to change the default behavior for line
connections. Of course, this is still possible to use it, giving the PostScript
code with the \pscustom macro (see Section IV).
This can be seen in such example:
1
2
3
4
5
6
7
8
9
10
11
\psset{linewidth=0.1}
\pspicture(4.5,3)
\pspolygon(0,0)(0,1)(3,1)(3,0)
\pspolygon(0,1)(2.5,3)(4.5,3)(3,1)
\pspolygon(3,0)(3,1)(4.5,3)(4.5,2.2)
\psline[linecolor=lightgray](2.7,2.6)(3.5,2.6)
\psline[linecolor=lightgray](2.55,1.9)(3.25,2.8)
\endpspicture
\hfill
\pspicture(4.5,3)
\pscustom{%
304
12
13
14
15
16
17
18
\code{1 setlinejoin}
\pspolygon(0,0)(0,1)(3,1)(3,0)
\pspolygon(0,1)(2.5,3)(4.5,3)(3,1)
\pspolygon(3,0)(3,1)(4.5,3)(4.5,2.2)}
\psline[linecolor=lightgray](2.7,2.6)(3.5,2.6)
\psline[linecolor=lightgray](2.55,1.9)(3.25,2.8)
\endpspicture
But for intensive usage, it is easier to redefine the PSTricks internal relevant
macro (\psls@solid, for a line of the solid style) and to define the interesting PostScript parameters as PSTricks ones (we add here the setmiterlimit
one too).84
1
% D.G. - May 2003
2
3
4
\def\psset@linecap#1{\pst@getint{#1}{\pslinecap}}
\psset@linecap{0}
5
6
7
\def\psset@linejoin#1{\pst@getint{#1}{\pslinejoin}}
\psset@linejoin{0}
8
9
10
\def\psset@miterlimit#1{\pst@checknum{#1}{\psmiterlimit}}
\psset@miterlimit{10}
11
12
13
14
15
16
\def\psls@solid{%
\pslinejoin\space setlinejoin
\psmiterlimit\space setmiterlimit
\pslinecap\space setlinecap
stroke }
17
18
19
20
21
22
23
24
\def\Test#1#2#3{%
\pspicture(3,3)\psgrid[subgriddiv=0]
\psset{linewidth=1}%
\psline[linecolor=DarkGray](0.5,1)(1.5,2)(2.5,1)
\psline[linecolor=LightGray,linecap=#1,linejoin=#2,miterlimit=#3]
(0.5,1)(1.5,2)(2.5,1)
\endpspicture}
25
26
\Test{0}{0}{1}\hfill\Test{0}{1}{1}\hfill\Test{0}{2}{1}
27
84
To explain the effects of these parameters, we use the same illustration than in the
MetaFun manual [40].
305
\Test{1}{0}{1}\hfill\Test{1}{1}{1}\hfill\Test{1}{2}{1}
28
29
\Test{2}{0}{1}\hfill\Test{2}{1}{1}\hfill\Test{2}{2}{1}
30
31
\Test{0}{0}{1}\hfill\Test{0}{0}{1.5}
32
3
3
3
2
2
2
1
1
1
0
0
0
1
2
3
0
0
1
2
3
3
3
3
2
2
2
1
1
1
0
0
0
1
2
3
1
2
3
3
3
2
2
2
1
1
1
0
0
1
2
3
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
0
3
0
0
0
0
1
2
3
3
3
2
2
1
1
0
0
0
L.9
1
2
3
Boxes of same sizes for trees and diagrams
If we use boxes for entries in a diagram, it could be not very aesthetic to
have various different sizes for them.
1
2
3
4
5
\psmatrix[mnode=r,colsep=-1]
& [name=P]\MyNode{Project Manager} \\[-1cm]
&
& [name=C]\MyNode{Consulting engineer} \\[0pt]
306
6
7
8
9
10
11
12
[name=S1]\MyNode{Subcontractor} & &
[name=S2]\MyNode{Subcontractor}
\endpsmatrix
\ncangle[angleA=-90,angleB=180]{P}{C}
\psset{angleA=-90,angleB=90,armB=0.8}%
\ncangle{P}{S1}
\ncangle{P}{S2}
Project Manager
Consulting engineer
Subcontractor
Subcontractor
The \makebox LATEX macro (of course, the same result can be obtain otherwise with P LAIN TEX and ConTEXt) allow to impose that all the boxes
will have the same size.
1
2
3
4
% We force the boxes to be of the same size using \makebox
\psmatrix[mnode=r,colsep=-1]
% ...
Project Manager
Consulting engineer
Subcontractor
Subcontractor
Obviously, we can do the same thing in other circumstances, as here for
trees (we use also a LATEX syntax to compute the length of the largest label,
but this can be done otherwise in P LAIN TEX and ConTEXt).
1
2
3
4
\def\PstMyNodeA#1{\Tcircle{#1}}
\def\PstMyNodeB#1{\Tcircle{\makebox[1cm]{#1}}}
\newlength{\PstMyLength}
\newcommand{\PstMyNodeC}[1]{\Tcircle{\makebox[\PstMyLength]{#1}}}
5
6
7
8
9
\pstree{\PstMyNodeA{X}}{\PstMyNodeA{XX}\PstMyNodeA{XXX}}
\hfill
\pstree{\PstMyNodeB{X}}{\PstMyNodeB{XX}\PstMyNodeB{XXX}}
\hfill
307
10
11
12
% Using LaTeX syntax and the ‘calc’ package
\settowidth{\PstMyLength}{XXX}%
\pstree{\PstMyNodeC{X}}{\PstMyNodeC{XX}\PstMyNodeC{XXX}}
X
XX
X
XXX
XX
X
XXX
XX
XXX
L.10 Reference points
In structured diagrams built with the \psmatrix environment and trees, the
default usage of the center of the nodes to draw the connections could produce non aesthetic results. In such cases, changing locally the reference
point definition could produce better results.
1
2
3
4
5
6
7
8
9
10
11
\psmatrix[mnode=r]
[name=A] \psframebox{AAAA} & \\
& [name=B] \psframebox{BBBB}
\endpsmatrix
\ncline{A}{B}
\hfill
\psmatrix[mnode=r]
[name=A,ref=br] \psframebox{AAAA} \\
& [name=B,ref=tl] \psframebox{BBBB}
\endpsmatrix
\ncline{A}{B}
AAAA
AAAA
BBBB
1
2
3
4
BBBB
\pstree{\Tcircle{A}}
{\Ttri{A}
\Ttri[fillstyle=solid,fillcolor=yellow]{AAA}
\Ttri{AAA AAA AAA}}
5
6
\newcommand{\PstMyTtri}[2][]{\Tr[ref=t]{\pstribox[#1]{#2}}}
7
8
9
10
11
\pstree[levelsep=1]{\Tcircle{A}}
{\PstMyTtri{A}
\PstMyTtri[fillstyle=solid,fillcolor=yellow]{AAA}
\PstMyTtri{AAA AAA AAA}}
308
12
13
14
15
16
\pstree{\Tcircle{A}}
{\Tr[ref=br]{\pstribox{A}}
\Tr[ref=t]{\pstribox[fillstyle=solid,fillcolor=yellow]{AAA}}
\Tr[ref=bl]{\pstribox{AAA AAA AAA}}}
A
A
AAA
AAA AAA AAA
A
A
AAA
AAA AAA AAA
A
A
AAA AAA AAA
AAA
L.11 Dashed and dotted hatched styles
Predefined hatched styles (see Section III) contains only continuous lines.
It is easy to add dashed ones (as it is more difficult to add dotted ones, we do
not include the necessary code here, which is too long for it little interest).
1
% D.G. - September 2002
2
3
4
5
6
7
8
9
% To define dashed and dotted hatched styles
\def\pshs@solid{0 setlinecap }
\def\pshs@dashed{[ \psk@dash ] 0 setdash }
\def\psset@hatchstyle#1{%
\@ifundefined{pshs@#1}%
{\@pstrickserr{Hatch style ‘#1’ not defined}\@eha}%
{\edef\pshatchstyle{#1}}}
10
11
\psset@hatchstyle{solid}
12
13
14
15
16
17
18
\def\pst@linefill{%
\@nameuse{pshs@\pshatchstyle}
\psk@hatchangle rotate
\psk@hatchwidth SLW
\pst@usecolor\pshatchcolor
\psk@hatchsep
309
19
\tx@LineFill}
20
21
22
23
24
25
\def\TestHatchedStyle#1{%
\pspicture(3,3)
\psframe[#1](3,3)
\pscircle[fillstyle=solid,fillcolor=white](1.5,1.5){0.75}
\endpspicture}
26
27
28
29
30
31
32
\TestHatchedStyle{fillstyle=hlines}
\hfill
\TestHatchedStyle{fillstyle=hlines,hatchstyle=dashed,dash=0.3 0.15}
\hfill
\TestHatchedStyle{fillstyle=hlines,hatchstyle=dashed,dash=0.01 0.10,
hatchsep=0.05}
33
34
35
36
37
38
39
40
\TestHatchedStyle{fillstyle=vlines,hatchstyle=dashed,
hatchsep=0.4,hatchcolor=red}
\hfill
\TestHatchedStyle{fillstyle=vlines,hatchstyle=dashed,
hatchsep=0.05,dash=0.2 0.1,hatchcolor=cyan}
\hfill
\TestHatchedStyle{fillstyle=crosshatch,hatchstyle=dashed,hatchsep=0.5}
L.12 Axes with labels using commas as separators
In some languages, like French and German, this is not the point character which is used to separated the decimal part of a floating point number, but a comma. To change this convention in the \psaxes macro of the
‘pst-plot’ package, the \pshlabel and \psvlabel macros must be redefined,
calling a utility macro which replace the decimal point by a comma (this
\PstLabelComma macro is part of the contribution file ‘pst-plox’ which
contains some extensions of the core file ‘pst-plot’).
310
1
% D.G. - June 1997
2
3
4
5
\def\PstLabelComma#1.#2.#3\@nil{%
\ifx#1\@empty$#1$\else$#1$\fi
\ifx#2\@empty\else\ifnum#2=0\else,$#2$\fi\fi}
6
7
8
9
% To change decimal points by commas in axe labels of \psaxes
\def\pshlabel#1{\expandafter\PstLabelComma#1..\@nil}
\def\psvlabel#1{\expandafter\PstLabelComma#1..\@nil}
10
11
\scriptsize
12
13
14
15
16
17
18
19
\pspicture(-3,-2.2)(3,2.2)
\psaxes[Dx=0.5,Dy=0.5,yunit=2](0,0)(-3,-1)(3,1)
\endpspicture
\hfill
\pspicture(-3,-2.2)(3,2.2)
\psaxes[Dx=0.5,Dy=0.2,yunit=2](0,0)(-3,-1)(3,1)
\endpspicture
1
1
0,8
0,6
0,4
0,2
0,5
−3 −2,5 −2 −1,5 −1 −0,5
−0,5
−1
0,5 1 1,5 2 2,5 3 −3 −2,5 −2 −1,5 −1−0,2
−0,5
−0,4
−0,6
−0,8
−1
0,5 1 1,5 2 2,5 3
L.13 Alphabetic labels on axes
This is easy to use alphabetic labels rather that numeric ones on axes,
redefining the \pshlabel and \psvlabel macros and using the ‘arrayjob’
package [4].
1
2
3
\newarray{\Months}
July&August&September&October&November&December}
4
5
6
\newarray{\Levels}
7
8
9
\def\pshlabel#1{\tiny\Months(#1)}
\psaxes[showorigin=false]{->}(13,4)
10
11
12
\def\psvlabel#1{\tiny\Levels(#1)}
\psaxes[showorigin=false]{->}(13,4)
311
3
2
1
January
February
March
April
May
June
July
August
September October
November December
January
February
March
April
May
June
July
August
September October
November December
High
Medium
Low
L.14 Two different axes
This is also not difficult to put two different axes on the same graph.
1
\psset{xunit=8,yunit=3}%
2
3
4
5
6
7
8
9
10
11
12
13
14
\pspicture(-0.5,-1.5)(1,1.5)
\psaxes[Dx=0.2,Oy=-1,Dy=0.25,tickstyle=top,
axesstyle=frame](0,-1)(1,1)
\rput(0.5,1.3){Curves example}
\rput(-0.3,0){%
\shortstack{\textcolor{green}{$\frac{x}{(x + 0.3)}$}\\
\textcolor{red}{$\sin (10 \times x) / 2$}}}
\rput(0.5,-1.3){$x$}
\psplot[linecolor=red]% 1 radian = 57.296 degrees
{0}{1}{x 10 mul 57.296 mul sin 0.5 mul}% sin(10 x) / 2
\psplot[linecolor=green]{0}{1}{x 0.3 x add div}% x / (x + 0.3)
\endpspicture
15
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18
19
20
21
22
23
24
25
% Same curves, but with different origin and axe for the first plot
\pspicture(-0.5,-1.5)(1,1.5)
\def\psvlabel#1{\small\textcolor{green}{#1}}%
\psaxes[Dx=0.2,Oy=-1,Dy=0.25,tickstyle=top,
axesstyle=frame](0,-1)(1,1)
\def\psvlabel#1{\small\textcolor{blue}{#1}}%
\psaxes[Oy=-1.25,Dy=0.25,tickstyle=bottom,
ticks=y,labels=y](1,-1)(0,1)
\rput(0.5,1.3){%
\shortstack{Curves example\\(with two different axes)}}
312
26
27
28
29
30
31
32
33
34
\rput(-0.3,0){%
\shortstack{\textcolor{green}{$\frac{x}{(x + 0.3)}$}\\
\textcolor{blue}{$\sin (10 \times x) / 2$}}}
\rput(0.5,-1.3){$x$}
\rput(0,0.25){%
\psplot[linecolor=blue]% 1 radian = 57.296 degrees
{0}{1}{x 10 mul 57.296 mul sin 0.5 mul}}% sin(10 x) / 2
\psplot[linecolor=green]{0}{1}{x 0.3 x add div}% x / (x + 0.3)
\endpspicture
Curves example
1.00
0.75
0.50
x
(x+0.3)
sin(10 × x)/2
0.25
0.00
−0.25
−0.50
−0.75
−1
0
0.2
0.4
0.6
0.8
1.0
x
313
Curves example
(with two different axes)
x
(x+0.3)
sin(10 × x)/2
1.00
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00
-0.25
-0.25
-0.50
-0.50
-0.75
-0.75
-1.00
-1
0
0.2
0.4
0.6
0.8
1.0
x
logarithmic axes and
different tick styles,
L.15 Polar Plots
without the too long
code.
Polar plots can be done with a small modification of the \psplot macro.85
1
% D.G. - June 1998 (according the way suggested by Ulrich Dirr)
2
3
4
5
6
% For polar plots
\newif\ifpolarplot
\def\psset@polarplot#1{\@nameuse{polarplot#1}}
\psset@polarplot{false}
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
\def\psplot@i#1#2#3{%
\pst@killglue
\begingroup
\use@par
\@nameuse{beginplot@\psplotstyle}%
\ifpolarplot
\psplot@init
/x #1 def
/x1 #2 def
/dx x1 x sub \psk@plotpoints div def
#3 dup x cos mul exch x sin mul
\pst@number\psxunit mul exch
85
This code was implemented in 1998 according the way suggested by Ulrich Dirr. And
the examples 2, 3 and 4 come also from him.
314
-1.25
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
\pst@number\psyunit mul exch
} def}%
\else
\psplot@init
/x #1 def
/x1 #2 def
/dx x1 x sub \psk@plotpoints div def
/xy {
x \pst@number\psxunit mul
#3 \pst@number\psyunit mul
} def}%
\fi
\gdef\psplot@init{}%
\@pstfalse
\@nameuse{testqp@\psplotstyle}%
\if@pst
\psplot@ii
\else
\psplot@iii
\fi
\endgroup
\ignorespaces}
45
46
\psset{plotpoints=200}%
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
\pspicture(-0.6,-3.3)(5,3.3)
% Cardioide
\psplot[polarplot=true,unit=0.5]{0}{360}{x cos 1 add 5 mul}
\endpspicture
\hfill
\pspicture*(-5,-5)(3,3)
\psaxes[arrowlength=2]{->}(0,0)(-4.99,-4.99)(3,3)
\rput[Br](3,-0.35){$x$}
\rput[tr](-0.15,3){$y$}
\rput[Br](-0.15,-0.35){$0$}
\psset{polarplot=true}%
\psplot{140}{310}{3 neg x sin mul x cos mul
x sin 3 exp x cos 3 exp add div}
\psplot{140}{310}{6 neg x sin mul x cos mul
x sin 3 exp x cos 3 exp add div}
\psplot{140}{310}{9 neg x sin mul x cos mul
x sin 3 exp x cos 3 exp add div}
\endpspicture
66
67
68
69
70
71
72
73
74
\pspicture(-2.5,-2.5)(2.5,2.5)
\psaxes[arrowlength=2]{->}(0,0)(-2.5,-2.5)(2.5,2.5)
\rput[Br](2.5,-0.35){$x$}
\rput[tr](-0.15,2.5){$y$}
\rput[Br](-0.15,-0.35){$0$}
\psset{plotstyle=curve,polarplot=true}%
\psplot{0}{360}{x cos 2 mul x sin mul}
\psplot{0}{360}{x cos 3 mul x sin mul}
315
75
76
77
78
79
80
81
82
83
84
85
\psplot{0}{360}{x cos 4 mul x sin mul}
\endpspicture
\hfill
\psset{unit=0.5}%
\pspicture(-8.5,-8.5)(9,9)
\psaxes[Dx=2,dx=2,Dy=2,dy=2,arrowlength=2]{->}(0,0)(-8.5,-8.5)(9,9)
\rput[Br](9,-0.7){$x$}
\rput[tr](-0.3,9){$y$}
\rput[Br](-0.3,-0.7){$0$}
\psplot[plotstyle=curve,polarplot=true]{0}{720}{8 2.5 x mul sin mul}
\endpspicture
y
2
1
−4
−3
−2
0
−1
−1
1
x
2
−2
−3
−4
y
8
6
4
2
y
2
−8
1
−2
0
−1
−1
1
2
−6
−4
x
0
−2
−2
2
4
6
8
x
−4
−6
−2
−8
316
Another example, using both a polar plot and putting a text around it, with
the \pstextpath macro. As we also want to slightly increase the size
of the characters along the ellipse, we use a generic macro from Juergen
Schlegelmilch to get one character at a time and apply an action on it).
1
2
3
4
5
6
7
8
9
% A \DoPerCharacter macro adapted from Juergen Schlegelmilch
% (posted on comp.text.tex - January 1998)
\def\DoPerCharacter#1#2#3\@nil{%
#1#2%
\edef\@tempa{#3}%
\ifx\@tempa\empty
\else
\DoPerCharacter#1#3\@nil
\fi}
10
11
\def\PerCharacter#1#2{\DoPerCharacter#1#2\@nil}
12
13
\pst@dimh=0.7pt
14
15
16
17
\def\CharacterAction#1{%
\scalebox{1 \pst@number{\pst@dimh}}{#1}
18
3
97
,14
7 9
5
57 1
83
2
932
626433
1592
058
84
3
71693
9
9
3
02 9
59230781640
4
4
9
74
8419
23
28
22
0
21
\pstextpath{\psplot[linestyle=none,polarplot=true,plotpoints=300,unit=5]
{500}{-500}{1 2.7182818 x 200 div exp 1 add div}}% Spiral
{\PerCharacter{\CharacterAction}{%
3,141592653589793238462643383279502884197169399375%
10582097494459230781640}}
358
20
65
19
317
L.16 Non filled arrows
If we want to draw non filled arrows, we can define an arrowfill parameter
(to have it with double arrows require to modify too the psas@>> and
psas@<< macros.)
1
% D.G. - July 1999
2
3
4
5
6
7
% Redefinition of \psset@arrowscale to store the value
% of the X scale factor
\def\psset@arrowscale#1{%
\psset@arrowscale@i#1 \@nil
\pst@getscale{#1}\psk@arrowscale}
8
9
\def\psset@arrowscale@i#1 #2\@nil{\edef\pst@arrowscale{#1}}
10
11
\def\pst@arrowscale{1}% Default value
12
13
14
15
% New parameter \newif\ifpsarrowfill
\def\psset@arrowfill#1{\@nameuse{psarrowfill#1}}
\psset@arrowfill{true}
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
% Modification of the PostScript macro “Arrow” to choose to fill
% or not the arrow (it require to restore the current linewidth,
% despite of the scaling)
\pst@def{Arrow}<{%
CLW mul add dup 2 div
/w ED mul dup
/h ED mul
/a ED
{ 0 h T 1 -1 scale } if
gsave
\ifpsarrowfill
\else
\pst@number{\pslinewidth} \pst@arrowscale\space div
\ifpsdoubleline\space 4 div\fi\space
SLW
\fi
w neg h moveto
0 0 L w h L w neg a neg rlineto
\ifpsarrowfill
fill
\else
closepath stroke
\fi
grestore
0 h a sub moveto}>
42
43
\psset{subgriddiv=0}%
44
45
46
47
\pspicture(3,4)\psgrid
\psset{arrowfill=false,arrows=->,arrowinset=0}%
\psline[arrowsize=0.3](0.5,3.5)(2.5,0.5)
318
\pnode(0.5,0.5){A}
\pnode(2.5,3.5){B}
\ncline[linewidth=0.1,arrowsize=1,doubleline=true]{A}{B}
\endpspicture
\hfill
\psset{subgriddiv=0,arrowscale=3}%
\pspicture(3,4)\psgrid
\psline{->}(2,2)
\parabola[linecolor=red,arrowinset=0]{<->}(0.5,0)(1.5,3)
\endpspicture
\hfill
\pspicture(3,4)\psgrid
\psset{arrowfill=false}%
\psline{->}(2,2)
\parabola[linecolor=red,arrowinset=0]{<->}(0.5,0)(1.5,3)
\endpspicture
\hfill
\pspicture(3,4)\psgrid
\psset{arrowfill=false,arrowsize=0.2}%
\psline{->}(2,2)
\parabola[linecolor=red,arrowinset=0]{<->}(0.5,0)(1.5,3)
\endpspicture
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
1
2
0
3 0
1
2
0
3 0
1
2
0
3 0
1
2
3
L.17 Lines under a curve
Rather than joining the points of a curve, we can draw for each of these
points a vertical line to the horizontal axis. We can still show the points of
the curve, with the showpoints parameter.
1
% D.G. - January 2000
2
3
4
5
6
7
8
\let\beginplot@LineToXAxis\beginplot@line
\def\endplot@LineToXAxis{\psLineToXAxis@ii}
\let\beginqp@LineToXAxis\beginqp@line
\let\doqp@LineToXAxis\doqp@line
\let\endqp@LineToXAxis\endqp@line
\let\testqp@LineToXAxis\testqp@line
9
10
11
\def\psLineToXAxis@ii{%
319
12
\end@OpenObj}
13
14
\def\tx@LineToXAxis{LineToXAxis }
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
% Adapted from the Line PostScript macro
\pst@def{LineToXAxis}<{%
NArray
n 0 eq not
{ n 1 eq { 0 0 /n 2 def } if
ArrowA
/n n 2 sub def
CP 2 copy moveto pop 0 Lineto
n { 2 copy moveto pop 0 Lineto } repeat
CP
4 2 roll
ArrowB
2 copy moveto pop 0
L
pop pop } if}>
31
32
\psset{xunit=0.0333,yunit=2.5}
33
34
35
36
37
38
39
\pspicture(0,-1)(400,1)
\psline{->}(0,0)(400,0)
\psline{->}(0,-1)(0,1)
\psplot[plotstyle=LineToXAxis,plotpoints=20,linestyle=dotted,
showpoints=true,dotstyle=triangle,dotsize=0.2]{0}{360}{x sin}
\endpspicture
40
41
42
43
44
45
46
\pspicture(0,-1)(400,1)
\psline{->}(0,0)(400,0)
\psline{->}(0,-1)(0,1)
\psplot[plotstyle=LineToXAxis,plotpoints=50,linestyle=dashed,
showpoints=true,dotstyle=o,dotsize=0.2]{0}{360}{x sin}
\endpspicture
t
u
t
u
t
u
u
t t
u
u
t
t
u
t
u
t
u
t
u
t
u
t
u
t
u
t
u
t
u
t
u
t
u
t
t u
u
t
u
320
bc
bc
bc
bc
bc
bc
c
b
cb bc
cb bc bc
bc bc bc bc
bc bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc bc
bc bc
bc bc bc
bc
bc bc cb
bc
c
b
c
b
c
b
c
b
c
b
L.18 Dashed lines
We can extend the dashed linestyle to accept dashes defined by two different segments.
1
% D.G. - November 1997
2
3
4
5
\def\psset@dash#1{%
\pst@expandafter\psset@@dash{#1} {\z@} {\z@}
{\pst@missing} {\pst@missing} {}\@nil
6
7
8
9
\edef\psk@dash{%
\pst@number\pst@dimg \pst@number\pst@dimh
\pst@number\pst@dimc \pst@number\pst@dimd}}
10
11
12
13
14
15
\def\psset@@dash#1 #2 #3 #4 #5\@nil{%
\pssetlength{\pst@dimg}{#1}%
\pssetlength{\pst@dimh}{#2}%
\pssetlength{\pst@dimc}{#3}%
\pssetlength{\pst@dimd}{#4}}
16
17
\psset@dash{5pt 3pt}% Default value
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
\pst@def{DashLine}<%
dup 0 gt
{ /a .5 def PathLength exch div }
{ pop /a 1 def PathLength }
ifelse
/b ED
/x1 ED
/y1 ED
/x ED
/y ED
/Coef b a .5 sub 2 mul y mul sub z Div round
z mul a .5 sub 2 mul y mul add b exch Div def
/y y Coef mul def
/x x Coef mul def
/y1 y1 Coef mul def
321
c
b
c
b
35
36
37
38
39
40
41
/x1 x1 Coef mul def
x1 0 gt y1 0 gt x 0 gt y 0 gt and
{ [ y x y1 x1 ] 1 a sub y mul}
{ [ 1 0] 0 }
ifelse
setdash
stroke>
42
43
44
45
46
\def\TestDashedLine[#1]{%
\pspicture(0,-0.08)(10,0.08)
\psline[#1](10,0)
\endpspicture}
47
48
49
50
51
52
53
\TestDashedLine[linestyle=dashed,dash=1 1]
\TestDashedLine[linestyle=dashed,linewidth=1mm,dash=2 0.5]
\TestDashedLine[linestyle=dashed,dash=1 0.2 0.05 0.2]
\TestDashedLine[linestyle=dashed,dash=0.05 0.2 1 0.2]
\TestDashedLine[linestyle=dashed,linewidth=1mm,dash=2 1 1 2]
54
55
56
57
58
59
60
M
\TestDashedLine[linestyle=dashed,dash=1 1]
\TestDashedLine[linestyle=dashed,linewidth=1mm,dash=2 0.5]
\TestDashedLine[linestyle=dashed,dash=1 0.2 0.05 0.2]
\TestDashedLine[linestyle=dashed,dash=0.05 0.2 1 0.2]
\TestDashedLine[linestyle=dashed,linewidth=1mm,dash=2 1 1 2]
Troubleshooting
DG: To complete and
recheck.
M.1
Compatibility problem between PSTricks and the
‘color’ and ‘graphicx’ LATEX packages
The ‘color’ [7] LATEX package (also usable in P LAIN TEX) is the way to use
to define and manage colors in LATEX and P LAIN TEXsince the arrival of
LATEX2e in 1993. Nevertheless, it is not stricly compatible with the color
macros defined in PSTricks, so, to be able to use the ‘color’ package, the
Help: Troubleshooting
322
‘pstcol’ [65] one, also written by David Carlisle, must be used in place of
both ‘color’ and PSTricks (the core pstricks.sty / pstricks.tex file).
Another pitfall is in the usage of the ‘graphicx’ [27] LATEX package (or the
‘graphics’ one), which, even if the ‘color’ package is not used, require that
the ‘pstcol’ one has been loaded before.
In one word: with LATEX always use the ‘pstcol’ package.
M.2
Compatibility problem between PSTricks and the
‘graphicx’ LATEX package for the \scalebox macro
Both PSTricks and the ‘graphicx’ [27] LATEX package define the \scalebox
macro, but with a different syntax. si, the syntax to use depend of the
order of loading of the PSTricks (that is to say, as explained in the previous
paragraph, ‘pstcol’) and ‘graphicx.
M.3
Compatibility problem between the packages ‘fp’
and ‘multido’
The ‘fp’ [19] and ‘multido’ [45] packages both define the \FP@add and
\FP@sub macros, which can lead to a clash if both are used in the same
file (in fact, when using in a \multido loop an index starting with a \n... or
\N.... The following patch allow to solve this problem.
1
% D.G. - March 2002 and July 2003
2
3
\usepackage{multido}
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
% Compatibility clash between ‘fp’ and ‘multido’
% when using \n.. multido indexes
% (to add after ‘multido’ and before ‘fp’)
%
\def\FPsub#1#2{%
\edef\multido@temp{\noexpand\FPsub@#2\noexpand\@empty}%
%
\let\FPsubMultiDo\FPsub
%
\def\multido@init@n#1#2#3{%
\edef#3{#1}%
\ifnum\multido@count<\z@
\expandafter\FPsubMultiDo
\else
\fi
Help: Troubleshooting
323
23
24
{0}{#2}\multido@temp
25
26
\usepackage[nomessages]{fp}
Help: Troubleshooting
324
XIV
Thanks
All the credit for the initiative of merging the different parts of the documentation from the years 1993 and 1994, integrating and repackaging
all the files, is due to Rolf Niepraschk <Rolf.Niepraschk@ptb.de>, who
started this work at the end of 2002.
Special thanks are due to Manuel Luque <MLuque5130@aol.com> who
wrote nearly all the chapter X on the ‘pst-3d’ package, is one of the authors of the ‘pst-labo’ package used in the chapter XII, give an example
used in the Animated graphics section B and sent various remarks and suggestions at the different steps of work in the process of repackaging this
documentation.
Thanks are also due to the persons who correct the English of the new
sections and proofread them (alphabetical order):
• John Frampton <jframpto@lynx.dac.neu.edu>,
• Manjusha Joshi <manjushasj@math.unipune.ernet.in>,
• Anthony Tekatch <anthony@unihedron.com>.
Thanks
325
XV
References
[1] Acrobat.
Systems
Incorporated.
See
[2] AlDraTEX. A high-level programming language for drawing
http://www.cis.ohio-state.edu/~gurari/systems.html
[3] Guillaume Appolinaire, Calligrammes, Gallimard, 1925 (in French).
[4] ‘arrayjob’. Management of arrays in TEX, by Zhuhan Jiang.
CTAN:macros/generic/arrrayjob
[5] Bakoma TEX. TEX implementation, by Basil K. Malyshev (Windows systems only). CTAN:nonfree/systems/win32/bakoma See also
http://www.tex.ac.uk/tex-archive/systems/win32/bakoma
[6] Emmanuel Chailloux, Guy Cousineau and André Suárez, Programmation fonctionnelle de graphismes pour la production d’illustrations
techniques, Technique et science informatique, Volume 15, Number 7,
pages 977–1007, 1996 (in French).
[7] ‘color’. The color package, LATEX Colour interface, by David Carlisle.
CTAN:macros/latex/graphics/color.dtx
[8] ConTEXt.
package.
A
general
purpose
CTAN:macros/context
TeX
See
macro
also
[9] André Deledicq, Le monde des pavages, ACL Éditions, 1997 (in
French).
[10] Dia.
Interactive
diagram
editor.
See
http://www.lysator.liu.se/~alla/dia
[11] ‘docstrip’. The docstrip package, by Frank Mittelbach, Denys
Duchier, Johannes Braams, Marcin Woliński and Mark Wooding.
CTAN:macros/latex/base/docstrip.dtx
[12] Victor Eijkhout, TEX by Topic, Addison-Wesley, 1992.
[13] Philippe Esperet and Denis Girou, Coloriage du pavage
dit
de
Truchet,
Cahiers
GUTenberg,
Number
31,
pages 5–18, Décembre 1998 (in French). Available at
http://www.gutenberg.eu.org/pub/GUTenberg/publicationsPDF/31-girou.pdf
References
326
[14] Eukleides. Euclidean geometry drawing tool, by Christian Obrecht.
[15] ‘fancybox’. Box tips and tricks for LATEX, by Timothy van Zandt.
CTAN:macros/latex/contrib/fancybox
[16] ‘fancyvrb’. Fancy Verbatims in LATEX, by Timothy van Zandt.
CTAN:macros/latex/contrib/fancyvrb
[17] Gabriel Valiente Feruglio, Typesetting commutative diagrams, TUGBoat, Volume 15, Number 4, pages 466–484, 1994.
[18] ‘fltpoint’. Floating point arithmetic with TEX, by Eckhart Guthölrhein.
CTAN:macros/latex/contrib/fltpoint
[19] ‘fp’. Fixed point arithmetic for TEX, by Michael Mehlich.
CTAN:macros/latex/contrib/fp
[20] GhostScript.
See
PostScript
interpreter.
and
http://www.cs.wisc.edu/~ghost
http://sourceforge.net/projects/ghostscript
[21] gifsicle. Generation of gif animated graphic files, by Eddie Kohler.
See http://www.lcdf.org/~eddietwo/gifsicle
[22] Denis Girou, Présentation de PSTricks, Cahiers GUTenberg,
Number 16, pages 21–70, February 1994 (in French). Available at
http://www.gutenberg.eu.org/pub/GUTenberg/publicationsPDF/16-girou.pdf
[23] Denis Girou,
TUG’95,
St
Building high level
Petersburg,
Florida,
objects
1995.
in PSTricks,
Available at
http://www.tug.org/applications/PSTricks/TUG95-PSTricks_4.ps.gz
[24] gnuplot.
Interactive
function
plotting
program.
See
http://www.gnuplot.info
[25] Michel Goossens, Sebastian Rahtz and Frank Mittelbach, The LATEX
[26] GraphicsMagick. Collection of tools and libraries to read, write, and
manipulate images in various formats (formed as a branch from ImageMagick 5.5.2). See http://www.graphicsmagick.org/
[27] ‘graphicx’.
Graphics,
The
graphicx
package,
by
David
Carlisle
and
Enhanced
Sebastian
LATEX
Rahtz.
CTAN:macros/latex/graphics/graphicx.dtx
[28] Branko Grünbaum and Geoffrey Shephard. Tilings and Patterns, Freeman and Company, 1987.
[29] Eitan M. Gurari, TEX and LATEX: Drawing and Literate Programming,
McGraw-Hill, 1994.
[30] Alan Hoenig, TEX Unbound: LATEX & TEX Strategies, Fonts, Graphics,
and More, Oxford University Press, 1998.
[31] ‘ifthen’.
The
ifthen
package,
CTAN:macros/latex/base/ifthen.dtx
by
David
Carlisle.
327
[32] ImageMagick. Collection of tools and libraries to read,
write, and manipulate images in various formats. See
http://www.imagemagick.org/
[33] Laura E. Jackson and Herbert Voß, Die Plot-Funktionen von
PostScript, Die TeXnische Komödie, Volume 2/02, pages 27–34, June
2002 (in German).
[34] jPicEdt. Interactive picture editor,
by Sylvain Reynal. See
http://www.picedt.org
[35] ‘keyval’.
key=value
parser,
by
David
Carlisle.
CTAN:macros/latex/required/graphics/keyval.dtx
[36] Peter
effect
Kleiweg,
PostScript code to create a lighten
on
characters.
See
the
file
depth.ps
at
http://odur.let.rug.nl/~kleiweg/postscript/postscript.html
[37] Donald E. Knuth, Computers and Typesetting, Vol. A, The TEXbook,
[38] Benoit B. Mandelbrot, The Fractal Geometry of Nature, Freeman,
1977.
[39] Henry McGilton and Mary Campione, PostScript by Example,
[40] MetaFun. MetaPost macros for ConTEXt, by Hans
gen.
See
Haand
[41] MetaObj. Very High-Level Objects in MetaPost, by Denis Roegel. See
CTAN:graphics/metapost/contrib/macros/metaobj
[42] MetaPost. A graphics language based on Knuth’s MetaFont, by John D. Hobby. See CTAN:graphics/metapost and
http://cm.bell-labs.com/who/hobby/MetaPost.html
[43] MFpic. A drawing environment for TEX and LATEX, generating Metafont or MetaPost commands, by Dan Luecking. CTAN:graphics/mfpic
[44] MNG.
mat.
Multiple-image
Network
Graphics
See
http://www.libpng.org/pub/mng/
forand
http://www.libpng.org/pub/png/png-sitemap.html#animation
[45] ‘multido’. A loop macro for Generic TEX, by Timothy van Zandt.
CTAN:macros/generic/multido
[46] Portable
by
Document
Systems
Format
Reference,
Incorporated.
See
[47] pdfTEX. Variant of the TEX program, by Hàn Thế Thành. See
http://tug.org/applications/pdftex
328
[48] pdfTricks. PSTricks support in PDF with pdfTEX, by Radhakrishnan CV, Rajagopal CV and Antoine Chambert-Loir.
CTAN:macros/latex/contrib/pdftricks
[49] Heinz-Otto Peitgen, Hartmut Jürgens and Dietmar Saupe, Chaos and
Fractals — New Frontiers of Science, Springer Verlag, 1992.
[50] PostScript
Systems
Language
Tutorial
and
Cookbook,
Incorporated,
1985.
See
[51] PostScript Language Reference Manual, Adobe Systems Incorporated, Addison-Wesley, 3 edition, 1999.
[52] ‘preview’. Extraction
by David Kastrup.
of
previews
from
LATEX
documents,
See
CTAN:macros/latex/contrib/preview
http://preview-latex.sourceforge.net
[53] ‘ps4pdf’. Usage of PostScript commands inside a pdfLATEX processed
document, by Rolf Niepraschk. CTAN:macros/latex/contrib/ps4pdf
[54] ‘pst-3dplot’. PSTricks contribution package for 3d plots, by
http://www.perce.de/LaTeX/pst-3dplot
[55] ‘pst-blur’. PSTricks contribution package for blurred shadows, by
Martin Giese. CTAN:graphics/pstricks/contrib/pst-blur
[56] ‘pst-csyn’. PSTricks contribution package for color synthesis
of overlapped surfaces, by Denis Girou and Manuel Luque.
CTAN:graphics/pstricks/contrib/pst-csyn
[57] ‘pst-chrt’. PSTricks contribution package for business charts, by Denis Girou (unreleased).
[58] ‘pst-circ’.
PSTricks
contribution
package
for
electric
circuits,
by
Christophe
and
Herbert
Voß.
CTAN:graphics/pstricks/contrib/pst-circ
See
also
http://pstcirc.free.fr
[59] ‘pst-eucl’.
clidean
PSTricks
geometry,
contribution
package
by
Dominique
for
EuRodriguez.
http:/dominique.rodriguez.9online.fr/pst-eucl
[60] ‘pst-lens’. PSTricks contribution package for lens, by Denis Girou
and Manuel Luque. CTAN:graphics/pstricks/contrib/pst-lens
[61] ‘pst-labo’. PSTricks contribution package for chemistry experiment
drawings, by Manuel Luque and Christophe Jorssen.
[62] ‘pst-li3d’. PSTricks contribution package for three dimensional
lighten effect on characters and PSTricks graphics, by Denis Girou.
CTAN:graphics/pstricks/contrib/pst-li3d
[63] ‘pst-poly’. PSTricks contribution package for polygons, by Denis
Girou. CTAN:graphics/pstricks/contrib/pst-poly
329
[64] ‘pst-slpe’. PSTricks contribution package for improved gradients, by
Martin Giese. CTAN:graphics/pstricks/contrib/pst-slpe
[65] ‘pstcol’. The pstcol package, PSTricks color compatibility, by David
Carlisle. CTAN:macros/latex/graphics/pstcol.dtx
[66] PStill. PS/EPS to PDF converter,
by Frank Siegert. See
http://www.pstill.com
[67] PSTricks
tutorial,
by
Alex
AJ,
CV
Radhakrishnan and E. Krishnan (for the India TEX Users
http://sarovar.org/projects/pstricks
and
Group)
See
http://www.tug.org.in/tutorial/pstricks
[68] PSTricks
Web
pages,
maintened
by
Denis
Girou.
See
http://www.tug.org/applications/PSTricks
[69] PSTricks Web pages, maintened by Manuel Luque (in French). See
http://members.aol.com/Mluque5130
[70] PSTricks Web pages on the Syracuse site, maintened by Jean-Michel
Sarlat (in French). See http://melusine.eu.org/syracuse/pstricks
[71] PSTricks
Web
pages,
maintened
by
Herbert
Voß.
See
http://www.pstricks.de
[72] ‘random’. Generating “random” numbers in TEX, by Donald Arseneau. CTAN:macros/generic/random.tex
[73] ‘realcalc’. Real arithmetic with big values and high precision, by
Frank Buchholz. CTAN:macros/generic/realcalc
[74] ‘repeat’.
Repeat
loop
macro,
by
Victor
Eijkhout
CTAN:macros/generic/eijkhout/repeat.tex
[75] Using Imported Graphics in LATEX2e, by Keith Reickdahl, December
1997, available on CTAN:info/epslatex.pdf
[76] Denis Roegel, MetaObj: Very High-Level Objects in MetaPost, TUGBoat, Volume 23, Number 1, pages 93–100, 2002.
[77] David Salomon, The Advanced TEXbook, Springer-Verlag, 1995.
[78] ‘Seminar’. A LATEX style for slides and notes, by Timothy van
http://www.tug.org/applications/Seminar
[79] Timothy van Zandt and Denis Girou, Inside PSTricks, TUGBoat, Volume 15, Number 3, pages 239–246, 1994.
[80] ‘Vaucanson-G’. PSTricks contribution package for drawing automata
and graphs (with LATEX), by Sylvain Lombardy and Sylvain Lombardy. See http://www.liafa.jussieu.fr/~lombardy/Vaucanson-G
[81] Herbert Voß and Laura E. Jackson, Die mathemtischen Funktionen
von PostScript, Die TeXnische Komödie, Volume 1/02, pages 40–47,
March 2002 (in german).
330
[82] VTEX.
porated
TEX
implementation,
by
MicroPress
Incor(Linux,
Windows and some other systems).