Multiresolution Modeling

Multiresolution Modeling
Multiresolution Modeling
A Very Brief Introduction
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Spring 2010
Multiresolution Models: Definition
‰A multiresolution model consists of a collection of
g
usuallyy describing
g small
zMesh fragments,
portions of an object with different LOD (i.e.,
level of details)
zSuitable relations that allow selecting a subset
of fragments (according to user
user-defined
defined quality
criteria) and combining them into a mesh that
represents the object.
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Multiresolution Models: LOD
‰There is
‰Th
i no universally
i
ll accepted
d definition
d fi i i for
f
LOD, level of details. In general, more faces
means more details and perhaps higher accuracy
accuracy.
‰Thus, to accurately represent a curvilinear
objects a large number of small faces may be
objects,
needed (i.e., higher LOD or resolution).
‰Not all meshes in a scene require very high
resolution. For example, back faces of an object
or objects very far away from the camera do not
need much details.
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Multiresolution Models:
Approaches 1/2
‰There are in general two different approaches:
) A new mesh with
zOn-the-Flyy ((i.e., real time):
the desired resolution is constructed from
scratch whenever it is needed.
zOff-Line: Design a data structure to collect
the mesh fragments and relations in a
preprocessing step, and generate the new
mesh with a given resolution on-line.
on line.
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Multiresolution Models:
Approaches 2/2
resolution
requirements
q
input model
construction
multi-resolution
model
query
processing
off line on-line
off-line
on line
desired mesh
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Modifications: 1/3
‰A modification
difi ti (of
( f a mesh)
h) M is
i the
th b
basic
i operation
ti
of changing a mesh X1 locally to mesh X2 written
as M:
M X1⇒ X2, or M =(X
(X1, X2).
)
‰A modification is a refinement (resp., coarsening) if
X2 has more (resp., less) faces than X1 has.
the yellow region of X1 is
re-tessellated to yield X2
M
⇒
X1
X2
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Modifications: 2/3
‰Not all modifications are independent of each other.
Mj
Mi
X3
X1
Mj removes some
faces inserted by Mi
X2
X4
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Modifications: 3/3
‰Given two modifications
‰Gi
difi i
Mi=(X
(Xp,X
Xq) and
d
Mj=(Xs,Xt), if modification Mj removes some
faces inserted by Mi, we say Mj directly depends
on Mi, written as Mi < Mj.
‰Given two modifications,
modifications they are either
independent of each other, Mi < Mj or Mj < Mi.
‰We may apply all possible modifications to a
mesh or to its intermediate results until the
simplest mesh is obtained.
‰The modifications may be the Euler operators
used in mesh simplifications.
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Multiresolution DAG: 1/3
‰The base mesh X0, all modifications M1, M2, …,
Mk, and the dependency relation < together
f
form
a multiresolution
i
i model M=[X
M X0,{M
{M1,
M2, …, Mk},<]
‰Why do we keep track modifications rather
than the intermediate results? This is because
we can regenerate them from X0 and the
necessary modifications. Storing intermediate
results may require very high space
consumption.
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Multiresolution DAG: 2/3
‰A directed graph can be constructed as follows:
zThe root is X0, the base mesh
zThe directed arcs from X0 are all
modifications applied to X0
zIf there is a modification Mi < Mj, draw a
directed arc from Mi to Mj.
zIn this way, we have a directed acyclic graph,
DAG So,
DAG.
So those Mi’s are nodes of this DAG!
‡Why is it a DAG?
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Multiresolution DAG: 3/3
‰ With a multiresolution model, we can do the
following:
1. Given a “resolution/LOD” requirement, we
mayy p
perform a depth-first
p
search (DFS) or
any search from the root until an intermediate
result which satisfies the desired resolution.
2. Selected refinement is also possible. Given a
region of a mesh and a “resolution/LOD”
resolution/LOD
requirement, we may perform a search and
oonlyy “refine”
e e the
t e mesh
es in the
t e indicated
d cated region.
eg o .
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The End
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