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(n 2 ) – 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

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 Chazelle, B. et al. Strategies for polyhedral surface decomposition: An experimental study, Comp. Geom. Theory Appl., 7: , Chazelle, B. Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm, SIAM J. Comp., Vol. 13, No. 3, August Bajaj, C. L., Dey, T. K., Convex Decomposition of Polyhedra and Robustness, SIAM J. Comp., Vol. 21, No. 2, April 1992.