Abstract
We consider the problem of representing and manipulating nonmanifold objects of any dimension and at multiple resolutions. We present a modeling scheme based on (1) a multiresolution representation, called the vertex-based nonmanifold multitessellation, (2) a compact and dimension-independent data structure, called the Simplified Incidence Graph (SIG), and (3) an atomic mesh update operator, called vertex-pair contraction/vertex expansion. We propose efficient algorithms for performing the vertex-pair contraction on a simplicial mesh encoded as a SIG, and an effective representation for encoding this multiresolution model based on a compact encoding of vertex-pair contractions and vertex expansions.
Issue Section:
Technical Papers
References
1.
Cutler
,
B.
,
Dorsey
,
J.
, and
McMillan
,
L.
,
2004, “Simplification
and Improvement of Tetrahedral Models for Simulation
,”
Proc. ACM/Eurographics Symposium on Geometry Processing
,
Nice, France, ACM
, New
York
.2.
Véron
,
P.
, and
Léon
,
J.-C.
,
2001, “Using Polyhedral
Models to Automatically Sketch Idealized Geometry for Structural
Analysis
,” Eng. Comput.
0177-0667, 17
, pp.
373
–385
.3.
El-Sana
,
J.
, and
Varshney
,
A.
,
1999, “Generalized
View-Dependent Simplification
,” Comput. Graph.
Forum
0167-7055, 18
(3
), pp.
C83
–C94
. 4.
De Floriani
,
L.
,
Greenfieldboyce
,
D.
, and
Hui
,
A.
,
2004, “A Data Structure
for Non-Manifold Simplicial d-Complexes
,” Proc.
ACM/Eurographics Symposium on Geometry Processing
, L.
Kobbelt
et al., eds, Nice, France,
ACM
, New
York
.5.
Edelsbrunner
,
H.
,
1987, Algorithms in
Combinatorial Geometry
,
Springer-Verlag
, Berlin.6.
Gursoz
, E.
L.
, Choi
,
Y.
, and
Prinz
, F.
B.
, 1990,
“Vertex-Based Representation of Non-Manifold
Boundaries
,” Geometric Modeling for Product
Engineering
, M. J.
Wozny
et al., eds,
Elsevier Science
, North-Holland, Amsterdam,
pp. 107
–130
.7.
Lee
, S.
H.
, and Lee
,
K.
,
2001, “Partial-Entity
Structure: A Fast and Compact Non-Manifold Boundary Representation Based on
Partial Topological Entities
,” Proc. 6th ACM
Symposium on Solid Modeling and Applications
, Ann Arbor, Michigan,
ACM
, pp.
159
–170
.8.
Weiler
,
K.
,
1988, “The Radial-Edge
Data Structure: A Topological Representation for Non-Manifold Geometric
Boundary Modeling
,” Geometric Modeling for CAD
Applications
, J. L.
Encarnacao
et al., eds,
Elsevier Science
, North-Holland, Amsterdam,
pp. 3
–36
.9.
De
Floriani
, L.
, and
Hui
,
A.
,
2005, “Data Structures
for Simplicial Complexes: An Analysis and a Comparison
,”
Third Eurographics Symposium on Geometry Processing,
M.
Desbrun
and
H.
Pottmann
, eds, Vienna,
Austria, pp. 119
–128
.10.
Desaulnier
,
H.
, and
Stewart
,
N.
,
1992, “An Extension of
Manifold Boundary Representation to R-sets
,” ACM
Trans. Graphics
0730-0301, 11
(1
), pp.
40
–60
.11.
Rossignac
,
J.
, and
Cardoze
,
D.
,
1999, “Matchmaker:
Manifold BReps for Non-Manifold R-Sets
,” Proc. 5th
Symposium on Solid Modeling and Applications
, W. F.
Bronsvoort
and
D. C.
Anderson
, eds,
ACM
, New
York
, pp.
31
–41
.12.
De Floriani
,
L.
,
Mesmoudi
,
M.
,
Morando
,
F.
, and
Puppo
,
E.
,
2003, “Non-Manifold
Decompositions in Arbitrary Dimensions
,” CVGIP:
Graph. Models Image Process.
1049-9652, 65
(1/3
), pp.
2
–22
.13.
Garland
,
M.
,
1999, “Multi-Resolution
Modeling: Survey and Future Opportunities
,”
Eurographics—State of the Art Reports, Eurographics
Association, pp. 111
–131
.14.
Cignoni
,
P.
,
Costanza
,
D.
,
Montani
,
C.
,
Rocchini
,
C.
, and
Scopigno
,
R.
,
2000, “Simplification of
Tetrahedral Volume Data With Accurate Error Evaluation
,”
Proc. IEEE Visualization 2000
, IEEE
Computer Society
, Los
Alamitos
, pp.
85
–92
.15.
Gross
, M.
H.
, and Staadt
, O.
G.
, 1998,
“Progressive Tetrahedralizations
,” Proc. IEEE
Visualization, IEEE Computer Society, Research Triangle Park, NC, pp.
397
–402
.16.
Dey
,
T.
,
Edelsbrunner
,
H.
,
Guha
,
S.
, and
Nekhayev
,
D.
,
1999, “Topology
Preserving Edge Contraction
,” Publications de l’Institut
Mathematique (Beograd), 60
(80
), pp.
23
–45
.17.
Popovic
,
J.
, and
Hoppe
,
H.
,
1997, “Progressive
Simplicial Complexes
,” ACM Computer Graphics Proc.
Annual Conference Series (SIGGRAPH)
,
ACM
, New
York
, pp.
217
–224
.18.
De Floriani
,
L.
,
Puppo
,
E.
, and
Magillo
,
P.
,
1997, “A Formal Approach
to Multi-Resolution Modeling
,” Geometric Modeling:
Theory and Practice
, W.
Strasser
et al., eds,
Springer-Verlag
, New York, pp.
302
–323
.19.
Luebke
,
D.
, and
Erikson
,
C.
,
1997, “View-Dependent
Simplification of Arbitrary Polygonal Environments
,”
ACM Computer Graphics Proc., Annual Conference Series
(SIGGRAPH)
, ACM
,
New York
, pp.
199
–208
.20.
Cera
, C.
D.
, Braude
,
I.
,
Kim
,
T.
,
Han
,
J.
, and
Regli
,
W.
,
2006, “Hierarchical
Role-Based Viewing for Multi-Level Information Security in Collaborative
CAD
,” J. Comput. Inf. Sci. Eng.
1530-9827,
6
(1
), pp.
2
–10
. 21.
Lee
, S.
H.
, 2005,
“A CAD-CAE Integration Approach Using Feature-Based
Multi-Resolution and Multi-Abstraction Modelling
Techniques
,” Comput.-Aided Des.
0010-4485, 37
(9
), pp.
941
–955
.22.
Lee
, S.
H.
, 2005,
“Feature-Based Multiresolution Modeling of
Solids
,” ACM Trans. Graphics
0730-0301, 24
(4
), pp.
1417
–1441
.23.
De Floriani
,
L.
,
Magillo
,
P.
,
Puppo
,
E.
, and
Sobrero
,
D.
,
2004, “A
Multi-Resolution Topological Representation for Non-Manifold
Meshes
,” Comput.-Aided Des.
0010-4485, 36
(2
), pp.
141
–159
.24.
De Floriani
,
L.
, and
Hui
,
A.
,
2003, “A Scalable Data
Structure for Three-Dimensional Non-manifold Objects
,”
Proc. ACM/Eurographics Symposium on Geometry Processing
,
L.
Kobbelt
et al., eds,
Aachen
, Germany, pp.
73
–83
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
