Face Fixer Compressing Polygon Meshes with Properties

2. Face FixerCompressing Polygon Mesheswith Properties Martin Isenburg Jack Snoeyink University of North Carolina at Chapel Hill

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

4. Polygon Models: Others

5. Faces and Corners: Sandal

6. Do nottriangulate! • Fewer polygons less connectivity information • Polygons tend to be planar & convex better geometry prediction • Better triangle strips

7. Group Structures: Teapot & Cow

8. Group Structures: Others

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

10. Previous Work

11. Previous Work • Fast Rendering • Progressive Transmission • Maximum Compression

12. Previous Work • Fast Rendering • Progressive Transmission • Maximum Compression main memory graphics board

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

14. Previous Work • Fast Rendering • Progressive Transmission • Maximum Compression storage / network main memory

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

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

17. connectivity geometry n = 10,000 66 KB 60 KB n = 100,000 830 KB 600 KB n = 1,000,000 10 MB 6 MB Standard Mesh Representation face1 1 2 3 4 face2 3 4 3 face3 5 2 1 3 facem ver1 (x,y,z) ver2 (x,y,z) ver3 (x,y,z) vern

18. nor1 (x,y,z) nor2 (x,y,z) nor3 (x,y,z) nori col1 (r,g,b) col2 (r,g,b) col3 (r,g,b) colj tex1 (u,v) tex2 (u,v) tex3 (u,v) texk Standard Mesh Representation face1 1 2 3 4 face2 3 4 3 face3 5 2 1 3 facem ver1 (x,y,z) ver2 (x,y,z) ver3 (x,y,z) vern

19. Face Fixer

20. Face Fixer

21. R F4 L S E F5 F3 M Hn Face Fixer • 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 • reverse decoding

22. Encoding

23. F4 Encoding

24. F4 F3 Encoding

25. R F4 F3 Encoding

26. R F4 F5 F3 Encoding

27. R F4 F5 F5 F3 Encoding

28. R R F4 F5 F5 F3 Encoding

29. R R R F4 F5 F5 F3 Encoding

30. R R R R R F4 F4 F4 F5 F5 F3 Compressing • Resulting label sequence: • non-uniform label frequencies • correlation among subsequent labels • Adaptive order-3 arithmetic coding • Compact probability tables • Fast bit-operations . . . . . .

31. R Decoding

32. R Decoding

33. F5 Decoding

34. F5 Decoding

35. R Decoding

36. F3 Decoding

37. F4 Decoding

38. Decoding

39. bits vertex Compression Results TG 2.2 2.4 model Triceratops2.1 Galleon 2.6 Cessna 2.8 Beethoven 2.9 Shark 1.7 Cupie 2.3 +2.0 +2.0

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

41. cut cut Non-Manifold Meshes (2)

42. Beyond Faces

43. Extension: Quadrilateral Grids

44. height left right Encoding a Quad Grid

45. QG Encoding a Quad Grid

46. bits vertex Compression with Quad Grids diff model Triceratops1.9 -0.2 Galleon 2.2 -0.4 Beethoven 2.6 -0.3 Shark 1.4 -0.3 Teapot 1.1 -0.6 Trumpet 0.6 -0.5

47. Extension: Repeated Patches

48. Structures

49. Extension: Structures

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