1 / 162

Early Split Coding of Triangle Mesh Connectivity

Early Split Coding of Triangle Mesh Connectivity. Jack Snoeyink UNC Chapel Hill. Martin Isenburg UC Berkeley. Geometry. Connectivity. Mesh Compression. “Geometry Compression” [ Deering, 95 ]. Efficient Rendering Progressive Transmission Compact Storage. main memory.

erika
Download Presentation

Early Split Coding of Triangle Mesh Connectivity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related