1. Wrapped Bounding Sphere Hierarchy for Necklaces Fixed hierarchical structure SOCG 2002

2. WBSH and Motion WBSH has a combinatorial description Each node is defined by O(1) leaf spheres WBSH’s description changes discretely Cascade verification at each time step Reparing WBSH if verification fails

3. Wrapped BSH is Stable before deformationafter deformation Number of combinatorial changes in BSH under motion is small

5. Self Collision Detection using Wrapped Bounding Sphere Hierarchy Subquadratic optimal time bound O( ) in O( ), in, Separating pairs Sphere packing

6. Spanner for Deformable Chain Capture proximity information with a sparse spanner 3HVT

7. The End

10. Wrapped BSH is Tight… The wrapped hierarchy is at most times tighter than the layered hierarchy. Layered hierarchyWrapped hierarchy

11. Collision Detection using Power Diagram (PD) PD captures proximity info of a necklace PD can be maintained using KDS framework PD has small size when necklace is packed