Heuristics for 3D model decomposition

1
Heuristics for 3D model decomposition

• Presented by Luv Kohli
• COMP258
• December 11, 2002

2
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.

3
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

4
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

5
Chazelle, et al.Flood and Retract
6
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

7
Decomposition in SWIFT
8
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?

9
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

10
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

11
(No Transcript)
12
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

13
(No Transcript)
14
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

15
Future work

• Run rigorous timing tests with SWIFT to
  determine if different decomposition methods have
  an effect on collision detection
• Combination of decomposition methods?

16
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., 7327-342, 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.