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Early Split Coding of Triangle Mesh Connectivity

Early Split Coding of Triangle Mesh Connectivity

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Early Split Coding of Triangle Mesh Connectivity

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  1. Early Split Coding ofTriangle Mesh Connectivity Jack Snoeyink UNC Chapel Hill Martin Isenburg UC Berkeley

  2. Geometry Connectivity Mesh Compression “Geometry Compression” [Deering, 95] • Efficient Rendering • Progressive Transmission • Compact Storage main memory • Surface Meshes • triangular • polygonal • Volume Meshes • tetrahedral, hexahedral storage / network

  3. each index uses log2(v)bits enumeration of triangulatedplanargraphs  3.24bpv [Tutte 62] Triangle Mesh Connectivity v -9.7 1.6 -0.2 v -6.6 1.4 3.3 v -1.6 1.4 2.3 v -3.3 -1.4 3.0 v 5.6 1.7 4.5 v -6.6 1.4 6.1 v -3.3 –4.4 3.7v -1.6 1.4 2.1 v -5.4 -1.6 6.4 ...f 1 2 3 f 3 2 4 f 2 1 5 f 2 5 4 f 6 4 5 f 6 5 7 f 5 1 8 f 4 8 7 f 7 8 9 f 9 8 10f 10 11 7 ... Geometry  6 log2 (v) bpv Connectivity

  4. “Succinct Representations of Graphs”[Turan ‘84] PlanarGraph Coding “Short encodings of planar graphs”[Keeler & Westbrook ‘95] “Succinct encodings of planar graphs”[He, Yao, & Hu ‘99] “Optimal Coding”[Poulahlon & Schaeffer ‘03] Compression Schemes “Cut-Border Machine”[Gumhold & Strasser ‘98] “Triangle Mesh Compression”[Touma & Gotsman ‘98] “Edgebreaker”[Rossignac ‘99] “Face Fixer”[Isenburg & Snoeyink ‘00] “Valence-Driven Encoding”[Alliez & Desbrun ‘01] Computer Graphics “Angle Analyzer”[Lee, Alliez & Desbrun ‘02] “Degree Duality Coder”[Isenburg ‘02] “Near-optimal Coding”[Khodakovsky et al. ‘02] “Out-of-Core Compression”[Isenburg & Gumhold ‘03] “Delphi Coding”[Coors and Rossignac ‘04] “FreeLence”[Kälberer et al. ‘05]

  5. Connectivity Graph Traversal split offset

  6. Connectivity Graph Traversal

  7. split offset . . . . . . C R C R R S R C R E R C 4 4 4 4 4 4 6 5 • degree-based split offset 3 . . . . . . “Triangle Mesh Compression” [Touma & Gotsman ‘98] S CBM–Edgebreaker–TG coder • label-based “Cut-Border Machine”[Gumhold & Strasser ‘98] “Edgebreaker”[Rossignac ‘99] “Early Split Coding” [this paper]

  8. CBM and Edgebreaker

  9. compression boundary CBM and Edgebreaker 5 unprocessed region processedregion

  10. CBM and Edgebreaker C 5 compression boundary C unprocessed region processedregion

  11. CBM and Edgebreaker C C 5 compression boundary C C unprocessed region processedregion

  12. CBM and Edgebreaker C C R 5 compression boundary R C C unprocessed region processedregion

  13. CBM and Edgebreaker C C R C 5 compression boundary C R C C unprocessed region processedregion

  14. CBM and Edgebreaker C C R C R 5 compression boundary R C R C C unprocessed region processedregion

  15. offset = 11 8 9 7 10 11 6 1 2 3 5 4 CBM and Edgebreaker C C R C R S 5 compression boundary S R C R C C unprocessed region processedregion

  16. CBM and Edgebreaker C C R C R S L offset = 11 5 compression boundary L S R C R C C unprocessed region processedregion

  17. CBM and Edgebreaker C C R C R S L C offset = 11 5 compression boundary C L S R C R C C unprocessed region processedregion

  18. CBM and Edgebreaker C C R C R S L C R offset = 11 5 compression boundary C L R S R C R C C unprocessed region processedregion

  19. CBM and Edgebreaker C C R C R S L C R C offset = 11 5 compression boundary C L C R S R C R C C unprocessed region processedregion

  20. CBM and Edgebreaker C C R C R S L C R C R offset = 11 5 compression boundary C L C R S R R C R C C unprocessed region processedregion

  21. CBM and Edgebreaker C C R C R S L C R C R C offset = 11 5 compression boundary C L C R S R C R C R C C unprocessed region processedregion

  22. CBM and Edgebreaker C C R C R S L C R C R C R offset = 11 5 compression boundary C L C R S R C R R C R C C unprocessed region processedregion

  23. CBM and Edgebreaker C C R C R S L C R C R C R R offset = 11 5 compression boundary C L C R S R C R R R C R C C unprocessed region processedregion

  24. CBM and Edgebreaker C C R C R S L C R C R C R R R offset = 11 5 compression boundary C L C R S R R C R R R C R C C unprocessed region processedregion

  25. CBM and Edgebreaker C C R C R S L C R C R C R R R L offset = 11 5 compression boundary C L C R L S R R C R R R C R C C unprocessed region processedregion

  26. CBM and Edgebreaker C C R C R S L C R C R C R R R L C offset = 11 5 compression boundary C C L C R L S R R C R R R C R C C unprocessed region processedregion

  27. CBM and Edgebreaker C C R C R S L C R C R C R R R L C R offset = 11 5 compression boundary R C C L C R L S R R C R R R C R C C unprocessed region processedregion

  28. CBM and Edgebreaker C C R C R S L C R C R C R R R L C R R offset = 11 R 5 compression boundary R C C L C R L S R R C R R R C R C C unprocessed region processedregion

  29. CBM and Edgebreaker C C R C R S L C R C R C R R R L C R R R offset = 11 R R 5 compression boundary R C C L C R L S R R C R R R C R C C unprocessed region processedregion

  30. offset = 3 1 2 CBM and Edgebreaker C C R C R S L C R C R C R R R L C R R R S offset = 11 R R 5 S compression boundary R C C L C R L S R R C R R R C R C C unprocessed region processedregion

  31. CBM and Edgebreaker offset = 3 C C R C R S L C R C R C R R R L C R R R S R offset = 11 R R R 5 S compression boundary R C C L C R L S R R C R R R C R C C unprocessed region processedregion

  32. CBM and Edgebreaker offset = 3 C C R C R S L C R C R C R R R L C R R R S R E offset = 11 R R R 5 S compression boundary R E C C L C R L S R R C R R R C R C C unprocessed region processedregion

  33. CBM and Edgebreaker offset = 3 C C R C R S L C R C R C R R R L C R R R S R E E offset = 11 R R R 5 S compression boundary R E E C C L C R L S R R C R R R C R C C unprocessed region processedregion

  34. CBM and Edgebreaker offset = 3 +1 +3 = 4 C C R C R S L C R C R C R R R L C R R R S R E E C ... +1 -1 +1 -1 +1 -1 +1 +1 +1 +1 -1 +1 +1 +1 -1 +1 +3 +3 = 12 offset = 11 R R R 5 S compression boundary R E E C C L C R L S R R C C R R R C R C C unprocessed region processedregion

  35. Subsequences of Labels areself-contained Encodings

  36. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible

  37. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible E

  38. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible E E

  39. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R E E

  40. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R E E

  41. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R E E

  42. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R E E

  43. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R E E

  44. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R S E E

  45. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R R S E E

  46. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R R R S E E

  47. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R R R S R E E

  48. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R R R S R E E C

  49. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R R R S R E E C L

  50. Subsequences are self-contained … S L C R C R C R R R L C R R R S R EE … reversible R R R S R E E C L R