1. Overview Class #10 (Feb 18) Assignment #2 (due in two weeks) Deformable collision detection Some simulation on graphics hardware... –Thursday: Cem Cebenoyan (NVIDIA)

2. Assignment #2: HAIL STORM! Pelt a banana bicycle seat with hail stones Watch the punishment in slow motion! Given starter Java code to start –Includes Green’s function model & geometry Implement collision & response code How many hail stones you can handle at once?

3. Assignment #2: Java Starter Code Significant starter code to get you going...

4. Deformable Collision Detection Consider spatial subdivision and hierarchical methods for now Others... graphics hardware Similar to nondeformable case fast query times, e.g., O(lgN) for hierarchies But must update structure after deformation various trade-offs typically involves O(N) work for N simplices Methods can be specialized for cloth-like and strand-like objects (more on that later)

5. BVH vs. Spatial Partitioning BVH: SP: - Object centric - Space centric - Spatial redundancy - Object redundancy (Recall from Ming Lin’s notes)

6. BVH vs. Spatial Partitioning BVH: SP: - Object centric - Space centric - Spatial redundancy - Object redundancy (Recall from Ming Lin’s notes)

7. BVH vs. Spatial Partitioning BVH: SP: - Object centric - Space centric - Spatial redundancy - Object redundancy (Recall from Ming Lin’s notes)

8. BVH vs. Spatial Partitioning BVH: SP: - Object centric - Space centric - Spatial redundancy - Object redundancy (Recall from Ming Lin’s notes)

9. Hierarchical Representations Two Common Types: –Bounding volume hierarchies – trees of spheres, ellipses, cubes, axis-aligned bounding boxes (AABBs), oriented bounding boxes (OBBs), K-dop, SSV, etc. –Spatial decomposition - BSP, K-d trees, octrees, MSP tree, R- trees, grids/cells, space-time bounds, etc. Many are inappropriate for deformable models Do very well in “rejection tests” Performance may slow down when the two objects are in close proximity and can have multiple contacts (modified from Ming Lin’s notes)

10. Spatial Data Structures & Subdivision Uniform Spatial Sub Quadtree/Octree kd-tree BSP-tree (modified from Ming Lin’s notes)

11. Uniform Spatial Subdivision Simple but effective idea for real-time deformable collision detection Space-time trade-off Example –Stéphane Cotin and Hervé Delingette and Nicholas Ayache, Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation, IEEE Transactions on Visualization and Computer Graphics, 5 (1), 62—73, 1999.

12. Bounding Volume Hierarchies Model Hierarchy: –each node has a simple volume that bounds a set of triangles –children contain volumes that each bound a different portion of the parent’s triangles –The leaves of the hierarchy usually contain individual triangles A binary bounding volume hierarchy: (Recall from Ming Lin’s notes)

13. Updating Bounding Hierarchies Good BVHs for deformable models Sphere trees [Brown et al.01, Guibas et al.02,... ] AABB-Trees [van den Bergen 97] are designed to be easily updated Illustration on whiteboard Bottom-up BVH update traversal

14. Hybrid AABB-Tree Updating Thomas Larsson and Tomas Akenine-Möller, Collision Detection for Continuously Deforming Bodies, Eurographics 2001.

15. Paper’s example #1: Bumpy spheres (20480 triangles each) 8-ary AABB-Trees 200 time-steps 1 st collision at time step 60 3760 collisions in final time-step Thomas Larsson and Tomas Akenine-Möller, Collision Detection for Continuously Deforming Bodies, Eurographics 2001.

17. Preview: Simulation in Programmable Graphics Hardware Thursday: Cem Cebenoyan (NVIDIA) Two interesting approaches: –standard (functional) simulation GPU (& CPU) compute, e.g., time-step, the simulation from first-principles Fast because the GPU is fast –data-driven simulation Precompute (and measure) data easily synthesized by GPU Very fast because (a) the GPU is fast and (b) precomputation Each has important applications & pros/cons

18. Preview: Data-driven Deformation Models E.g., superposition of displacement fields Important model for hardware Lighting of model requires more than just deformed shape, e.g., normals