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Triangle Fixer: Edge-based Connectivity Compression

This article introduces a new edge-based encoding scheme for polygon mesh connectivity, leading to compact mesh representations. The scheme allows for simple implementation and fast decoding, and it also extends to non-triangular meshes and meshes with group or triangle strip information.

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Triangle Fixer: Edge-based Connectivity Compression

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  1. Triangle Fixer:Edge-based Connectivity Compression Martin Isenburg University of North Carolina at Chapel Hill

  2. Introduction A new edge-based encoding schemefor polygon mesh connectivity.

  3. Introduction A new edge-based encoding scheme for polygon mesh connectivity.  compact mesh representations

  4. Introduction A new edge-based encoding scheme for polygon mesh connectivity.  compact mesh representations simple implementation

  5. Introduction A new edge-based encoding scheme for polygon mesh connectivity.  compact mesh representations simple implementation fast decoding

  6. Introduction A new edge-based encoding scheme for polygon mesh connectivity.  compact mesh representations simple implementation fast decoding

  7. Introduction A new edge-based encoding scheme for polygon mesh connectivity.  compact mesh representations simple implementation fast decoding  extends to non-triangular meshes

  8. Introduction A new edge-based encoding scheme for polygon mesh connectivity.  compact mesh representations simple implementation fast decoding  extends to non-triangular meshes extends to meshes with group ortriangle strip information

  9. What are ‘Polygon Meshes’ . . . ?

  10. A Simple Mesh

  11. Mesh with Holes

  12. Mesh with Handle

  13. Mesh with Handle and Holes

  14. How are Polygon Meshes stored . . . ?

  15. Geometry and Connectivity The minimal information we need to store is: • Where are the vertices located ?  mesh geometry • How are the vertices connected ?  mesh connectivity

  16. Standard Representation list of vertices x0 y0 z0 x1 y1 z1 x2 y2 z2 x3 y3 z3 4 x4 y4 z4 6 4 . . . . . xn yn zn

  17. Standard Representation list of vertices list of faces x0 y0 z0 1 4 20 x1 y1 z1 x2 y2 z2 x3 y3 z3 4 x4 y4 z4 6 4 . . . . . xn yn zn

  18. Standard Representation list of vertices list of faces x0 y0 z0 1 4 20 x1 y1 z1 x2 y2 z2 x3 y3 z3 4 x4 y4 z4 6 4 . . . . . xn yn zn

  19. Standard Representation list of vertices list of faces x0 y0 z0 1 4 20 x1 y1 z1 x2 y2 z2 x3 y3 z3 4 x4 y4 z4 6 4 . . . . . xn yn zn

  20. Standard Representation list of vertices list of faces x0 y0 z0 1 4 20 x1 y1 z1 x2 y2 z2 x3 y3 z3 4 x4 y4 z4 6 4 . . . . . xn yn zn

  21. Standard Representation list of vertices list of faces x0 y0 z0 1 4 2 x1 y1 z1 2 3 03 4 x2 y2 z2 u2 v2 w24 0 53 4 x3 y3 z3 u3 v3 w33 4 53 6 4 x4 y4 z4 u4 v4 w45 0 2 . . . . . xn yn zn . . . . . . . . . . . . . . .

  22. Compressing Geometry list of vertices list of faces x0 y0 z0 1 4 2 x1 y1 z1 2 3 0 3 4 x2 y2 z2 u2 v2 w24 0 5 3 4 x3 y3 z3 u3 v3 w33 4 5 3 6 4 x4 y4 z4 u4 v4 w45 0 2 . . . . . xn yn zn . . . . . . . . . . . . . . .

  23. Compressing Connectivity list of vertices list of faces x0 y0 z01 4 2 x1 y1 z12 3 0 3 4 x2 y2 z2u2 v2 w24 0 5 3 4 x3 y3 z3u3 v3 w33 4 5 3 6 4x4 y4 z4u4 v4 w45 0 2 . . . . . xn yn zn . . . . . . . . . . . . . . .

  24. Uncompressed Connectivity 2 1 3 0 6 5 4 7 9 11 8 12 10

  25. Uncompressed Connectivity 0 4 5 2 1 3 0 6 5 4 7 9 11 8 12 10

  26. Uncompressed Connectivity 0 4 5 0 5 1 2 1 3 0 6 5 4 7 9 11 8 12 10

  27. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 2 1 3 0 6 5 4 7 9 11 8 12 10

  28. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 1 3 0 6 5 4 7 9 11 8 12 10

  29. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 2 1 3 0 6 5 4 7 9 11 8 12 10

  30. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 2 1 3 0 6 5 4 7 9 11 8 12 10

  31. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 2 1 3 0 6 5 4 7 9 11 8 12 10

  32. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 2 1 3 0 6 5 4 7 9 11 8 12 10

  33. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 2 1 3 0 6 5 4 7 9 11 8 12 10

  34. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 2 1 3 0 6 5 4 7 9 11 8 12 10

  35. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 2 1 3 0 6 5 4 7 9 11 8 12 10

  36. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 2 1 3 0 6 5 4 7 9 11 8 12 10

  37. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 2 1 3 0 6 5 4 7 9 11 8 12 10

  38. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 11 12 7 2 1 3 0 6 5 4 7 9 11 8 12 10

  39. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 11 12 7 2 1 3 0 6 5 4 7 9 11 8 12 10

  40. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 11 12 7 2 1 3 0 6 5 4 7 9 11 8 12 10

  41. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 11 12 7 2 1 3 0 6 5 4 7 9 11 8 12 10

  42. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 11 12 7 2 1 3 0 6 5 4 7 9 11 8 12 10

  43. Uncompressed Connectivity 0 4 5 0 5 1 5 6 1 1 6 2 2 6 3 4 8 5 8 9 5 5 9 6 9 11 6 6 11 7 6 7 3 8 10 9 9 10 11 11 12 7 6 log(n) bpv 2 1 3 0 6 5 4 7 9 11 8 12 10

  44. Maximum Connectivity Compression for Triangle Meshes

  45. Turan’s observation • The fact that a planar graph can be decomposed into two spanning trees implies that it can be encoded in a constant number of bits.

  46. Turan’s observation • The fact that a planar graph can be decomposed into two spanning trees implies that it can be encoded in a constant number of bits. • The two spanning trees are: • a vertex spanning tree • its dual triangle spanning tree

  47. Turan’s observation • The fact that a planar graph can be decomposed into two spanning trees implies that it can be encoded in a constant number of bits. • The two spanning trees are: • a vertex spanning tree • its dual triangle spanning tree • He gave an encoding that uses 12 bits per vertex (bpv).

  48. Vertex Spanning Tree

  49. Vertex Spanning Tree

  50. Vertex Spanning Tree

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