Transcript Heuristics for 3D model decomposition Presented by Luv Kohli COMP258

Heuristics for 3D model
decomposition
Presented by Luv Kohli
COMP258
December 11, 2002
What is convex decomposition?
• Technique to split up arbitrary
polyhedra into convex pieces
• Many calculations are far easier
between convex objects
– Collision detection, penetration depth,
etc.
How is it done?
• Two broad categories
– Convex solid decomposition
•Has output of size O(n2) –
impractical
– Convex surface decomposition
•Complexity O(r), where r is the
number of reflex edges
Convex surface decomposition
• Space partitioning
• Space sweep
• Flooding
– Traverse the dual graph of the
surface
– Start at some node and collect facets
as long as they form a convex patch
Chazelle, et al.
Flood and Retract
Decomposition in SWIFT++
• Essentially a flooding algorithm using
DFS or BFS
• Uses “cresting” algorithm to determine
seed faces
– Start growing from faces furthest
away from reflex edges
Decomposition in SWIFT++
Cresting
• The cresting technique attempts to
minimize the number of pieces by
allowing them to grow as large as
possible
• There may be other decomposition
algorithms that provide better results
for certain applications
• Equal-sized pieces?
Alg1 – Reverse (& Fwd) cresting
• Uses the same technique of finding
distance from reflex edges (with minor
modifications)
• Prioritizes seed faces in reverse
– Lets smaller pieces grow first so they
are not overwhelmed by larger ones
Alg2 – Reverse (& Fwd) flooding
• Uses potential piece sizes instead of
distances from reflex edges
– For each unvisited face, flood (grow)
while the current piece is still convex
– When growing ceases, record the
piece size for use as priority
Alg3 – Flooding w/ surface area
• Use surface area of flooded pieces to
prioritize growing
• Same idea as before but with different
input to the graph traversal algorithm
swiftdfs
swiftbfs
swiftcrest fwd crest rev crest
avg # of pcs
80.602
78.991
77.834
78.352
78.131
max # of pcs
86
84
81
83
81
min # of pcs
76
76
76
76
75
avg size of pcs
4.1702
4.2548
4.3174
4.2895
4.3011
std dev (pc size)
5.9494
6.3408
6.2917
6.1725
5.9158
avg # of size1 pcs
19.175
18.694
18.136
18.07
18.758
avg # of size2 pcs
31.684
31.106
28.086
29.64
29.896
avg surface area
0.0084
0.0086
0.0087
0.0087
0.0087
std dev (area)
0.0108
0.0112
0.011
0.0108
0.011
floodfacefor floodfacerev floodareafor floodarearev
avg # of pcs
86.004
81.232
84.405
84.454
max # of pcs
95
88
96
97
min # of pcs
81
79
76
77
avg size of pcs
3.9088
4.1377
3.9874
3.9842
std dev (pc size)
5.7004
5.3596
5.6359
5.6305
avg # of size1 pcs
26.577
19.873
23.7
23.769
avg # of size2 pcs
29.563
31.364
31.428
31.367
avg surface area
0.0079
0.0084
0.0081
0.008
std dev (area)
0.0102
0.0105
0.0105
0.0105
Other ideas
• Use some threshold value to stop piece
growing
– Try to keep pieces around the same
size
• Grow in parallel
– Issues with determining how many
pieces to grow from simultaneously
Future work
• Run rigorous timing tests with
SWIFT++ to determine if different
decomposition methods have an effect
on collision detection
• Combination of decomposition
methods?
References
• Ehmann, Stephen A., Lin, Ming C. Accurate and Fast
Proximity Queries Between Polyhedra Using Convex
Surface Decomposition, EUROGRAPHICS 2001.
• Chazelle, B. et al. Strategies for polyhedral surface
decomposition: An experimental study, Comp. Geom.
Theory Appl., 7:327-342, 1997.
• Chazelle, B. Convex Partitions of Polyhedra: A Lower
Bound and Worst-Case Optimal Algorithm, SIAM J.
Comp., Vol. 13, No. 3, August 1984.
• Bajaj, C. L., Dey, T. K., Convex Decomposition of
Polyhedra and Robustness, SIAM J. Comp., Vol. 21, No.
2, April 1992.