1. Decomposing Polygon Meshes for Interactive Applications Li Xuetao Computer Graphics Laboratory

2. Polygon Mesh

3. Objective Automatically decompose a polygon mesh into meaningful components Polygon MeshDecomposition

4. Issues How to define a component by features on the mesh How to compute these features How to extract components automatically

5. Basic Idea

8. Geometric Function Topological Function Geometric & Topological Functions

9. Profiles of Geometric Function

10. Derivatives of Geometric Function

11. Critical Point & Component Critical Point Component

12. Approach Decomposition Computing SkeletonDefining sweep pathSpace Sweeping Result

13. Approach Skeletonization Sweep Order Space Sweep

14. Skeletonization

15. Related Structures Medial Axis Axis of generalized cylinder Skeletal Curves

16. Simplification

17. Skeletonization based on Simplification

18. Associated Triangle List (ATL) ATL(v 1, v 5 ) = {T 1 } ATL(v 2, v 5 ) = {T 2 } Edge collapse

19. 2D Example V1V1 V2V2 V3V3 V4V4 V5V5 V6V6 V7V7 T1T1 T2T2 T3T3 T4T4 T5T5 V1V1 V2V2 V4V4 V5V5 V6V6 V8V8 T1T1 T4T4 T5T5 V9V9 V4V4 V 10 V8V8 T4T4 V9V9 V8V8 V 11 ATL(V 2,V 8 ) = { T 2 } ATL(V 4,V 8 ) = { T 3 } ATL(V 10,V 11 ) = {T 5,T 4,T 3 } ATL(V 9,V 8 ) = { T 2,T 1 } ATL(V 4,V 8 ) = { T 3 } ATL(V 10,V 8 ) = { T 5 } V4V4 V5V5 V6V6 V8V8 T4T4 T5T5 V9V9

20. 3D Example

21. Skeleton of Polygon Mesh

22. Sweep Order Skeletal tree Traversal order of the skeletal tree

23. Adding Virtual Edges

24. Skeletal Tree

25. Traversal Order u v

26. Skeletal Tree

27. Space Sweep

28. Sweep Plane

29. Sweep Operation Compute –The cross sections –The topological function –The geometric function Check if critical point is reached If reached, extract component. If not, move the sweep plane to the next position

30. Computing Cross Sections Intersecting triangles

31. Computing Cross Sections

32. Computing Geometric Function

33. Computing Topological Function

34. Advancing the Sweep Plane

35. Extracting Components

36. Decomposition Results

40. Conclusion A formal definition of component A framework for decomposing polygon meshes