2. Face Fixer Compressing Polygon Meshes with Properties Martin Isenburg Jack Snoeyink University of North Carolina at Chapel Hill

3. Polygon Models: Triceratops 356triangles 2266quadrangles 140pentagons 63hexagons 10heptagons 7octagons 2undecagons

4. Polygon Models: Others

5. Faces and Corners: Sandal

6. Fewer polygons  less connectivity information Fewer polygons  less connectivity information Polygons tend to be planar & convex  better geometry prediction Polygons tend to be planar & convex  better geometry prediction Better triangle strips Better triangle strips Do not triangulate!

7. Group Structures: Teapot & Cow

8. Group Structures: Others

9. Overview Do not triangulate! Do not triangulate! Connectivity Compression for Manifold Polygon Meshes Connectivity Compression for Manifold Polygon Meshes Compact mesh representations Simple implementation Beyond Faces: Quadrilateral grids Capture Structures! Capture Structures!

10. Previous Work

11. Fast Rendering Fast Rendering Progressive Transmission Progressive Transmission Maximum Compression Maximum Compression

12. Previous Work Fast Rendering Fast Rendering Progressive Transmission Maximum Compression graphics boardmain memory

13. Previous Work Fast Rendering Fast Rendering Progressive Transmission Maximum Compression Triangle Strips [?] Generalized Triangle Mesh[ Deering ] Transparent Vertex Caching[ Hoppe, n VIDIA ]

14. Previous Work Fast Rendering Progressive Transmission Progressive Transmission Maximum Compression Maximum Compression main memorystorage / network

15. Previous Work Fast Rendering Progressive Transmission Progressive Transmission Maximum Compression Progressive Meshes [ Hoppe ] Progressive Forest Split[ Taubin et ] Compressed Progressive Meshes[ Pajarola et ] Progressive Geometry Compression [ Khodakovsky et ]

16. Previous Work Fast Rendering Progressive Transmission Maximum Compression Maximum Compression Topological Surgery [ Taubin, Rossignac ] Triangle Mesh Compression[ Costa, Gotsman ] Edgebreaker[ Rossignac, King et ] Cut-border Machine[ Gumhold, Strasser ]

17. ver 1 (x,y,z) ver 2 (x,y,z) ver 3 (x,y,z) ver n Standard Mesh Representation face 1 1 2 3 4 face 2 3 4 3 face 3 5 2 1 3 face m connectivity n = 10,000 66 KB60 KB n = 100,000 830 KB600 KB n = 1,000,000 10 MB6 MB geometry

18. ver 1 (x,y,z) ver 2 (x,y,z) ver 3 (x,y,z) ver n Standard Mesh Representation face 1 1 2 3 4 face 2 3 4 3 face 3 5 2 1 3 face m nor 1 (x,y,z) nor 2 (x,y,z) nor 3 (x,y,z) nor i tex 1 (u,v) tex 2 (u,v) tex 3 (u,v) tex k col 1 (r,g,b) col 2 (r,g,b) col 3 (r,g,b) col j

19. Face Fixer

21. encoding is a sequence of labels: encoding is a sequence of labels: one label.... per face one label per hole one label per handle labels and fix it all together number of labels = number of edges number of labels = number of edges reverse decoding reverse decoding Face Fixer F4F4 F5F5 R F3F3 LS E HnHn M

22. Encoding

23. F4F4

24. F4F4 F3F3

25. F4F4 F3F3 R

26. F4F4 F3F3 F5F5 R

27. F4F4 F3F3 F5F5 R F5F5

28. F4F4 F3F3 F5F5 R F5F5 R

29. F4F4 F3F3 F5F5 R F5F5 R R

30. Compressing Resulting label sequence: Resulting label sequence: non-uniform label frequencies correlation among subsequent labels Adaptive order-3 arithmetic coding Adaptive order-3 arithmetic coding Compact probability tables Fast bit-operations F4F4 F3F3 F5F5 R F5F5 R F4F4... RR F4F4 R

31. Decoding R

32. R

33. F5F5

34. F5F5

35. R

36. F3F3

37. F4F4

39. +2.0 TG 2.2 2.4 Compression Results Triceratops2.1 Galleon2.6 Cessna2.8 Beethoven2.9 Shark1.7 Cupie2.3 bits vertex model

40. fragmented disks half-disk disk Non-Manifold Meshes (1)

41. Non-Manifold Meshes (2) cut

42. Beyond Faces

43. Extension: Quadrilateral Grids

44. Encoding a Quad Grid right left height

45. Encoding a Quad Grid QG

46. Triceratops1.9-0.2 Galleon2.2-0.4 Beethoven2.6-0.3 Shark1.4-0.3 Teapot1.1-0.6 Trumpet0.6-0.5 bits vertex model Compression with Quad Grids diff

47. Extension: Repeated Patches

48. Structures

49. Extension: Structures

50. case D case B case A case C Super Faces connected by an edge connected by a vertex

51. Encoding a Super Face

53. SF

54. Encoding a Super Face

55. F4F4

56. F4F4 F3F3

57. F4F4 F3F3 R

58. F4F4 F3F3 R F5F5

59. F4F4 F3F3 R F5F5 R

60. F4F4 F3F3 R F5F5 R R

61. F4F4 F3F3 R F5F5 R R F3F3

62. F4F4 F3F3 R F5F5 R R F3F3 R

63. +0.1 +0.2 +0.1 +0.0 +0.1 Compression with Structures bits vertex model diff Triceratops2.4+0.3 Galleon2.7+0.1 Cessna3.5+0.7 Beethoven3.0+0.1 Shark2.0+0.3 Cupie2.3+0.1

64. Summary

65. Summary of Contributions Compress polygonal connectivity Compress polygonal connectivity simpler, more compact, extensions Capture structural information Capture structural information face groupings mesh partitions discontinuity curves Model Libraries Model Libraries “rich” meshes storage / network transmission

66. Current and Future Work Triangle Strip Compression Graphics Interface 2000 Triangle Strip Compression Graphics Interface 2000 Tetrahedral and Hexahedral meshes  “cell fixer” Tetrahedral and Hexahedral meshes  “cell fixer”

67. Acknowledgements Davis King Jarek Rossignac Mike Maniscalco Stefan Gumhold S 6 Viewpoint Datalabs

68. Thank you.

70. Regular  Irregular Connectivity Re-meshable Re-meshable Bunnies, Horses, various Roman Statues, … Highly detailed, dense, scanned data sets Not Re-meshable Not Re-meshable Cessnas, Spanish Galleons, Sandals, … Careful designed meshes with sharp features CAD models, Viewpoint models

71. Predictive Coding good not convex  bad not planar  bad

72. Attaching Geometry