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Irregular to Completely Regular Meshing in Computer Graphics

This paper discusses the challenges of rendering complex meshes in computer graphics, including rendering speed and quality, storage, transmission, and scalability. It explores techniques such as multiresolution geometry, irregular and completely regular meshes, view-dependent refinement, and texture mapping. The paper also presents progressive mesh representations and selective refinement algorithms. Finally, it addresses the application of these techniques in real-time rendering and the use of new architectures to improve rendering performance.

stephenfrancis
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Irregular to Completely Regular Meshing in Computer Graphics

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  1. Irregular to Completely RegularMeshingin Computer Graphics Hugues Hoppe Microsoft Research International Meshing Roundtable2002/09/17

  2. Complex meshes in graphics (1994) 70,000 faces

  3. Complex meshes in graphics (1997) 860,000 faces

  4. Complex meshes in graphics (2000) 2,000,000,000faces Challenges: - rendering - storage - transmission - scalability [Digital Michelangelo Project]

  5. Multiresolution geometry Irregular Semi-regular Completely regular

  6. Multiresolution geometry • Irregular meshes • Progressive meshes[1996] • View-dependent refinement[1997] • Texture-mapping PM [2001] • Semi-regular meshes • Multiresolution analysis[1995] • Completely regular meshes • Geometry images[2002]

  7. Goals in real-time rendering #1 : Rendering speed • 60-85 frames/second #2 : Rendering quality • geometric “visual” accuracy • temporal continuity Not a Goal: • Mesh “quality”

  8. Not a goal: mesh quality 13,000 faces  1,000 faces

  9. Irregular meshes Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 2 1 3 Face 4 2 3 … Rendering cost = vertex processing + rasterization ~ #vertices ~ constant yuck

  10. Texture mapping Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 2 1 3 Face 4 2 3 … s1 t1 s2 t2 “Visual” accuracy using coarse mesh t normal map s

  11. Goals in real-time rendering #1 : Rendering speed • Minimize #vertices  best accuracy using irregular meshes #2 : Rendering quality • Use texture mapping  parametrization

  12. 13,546 500 152 150 faces Mn M175 M1 M0 ecoln-1 ecol0 ecoli Simplification: Edge collapse ecol

  13. vspl(vs ,vl ,vr, …) ecol vl vr vs Invertible: vertex split transformation

  14. 150 152 500 13,546 M0 M1 M175 Mn M0 Mn vspl0 … vspli … … vspli … vspln-1 vspl0 vspln-1 progressive mesh (PM) representation Progressive mesh

  15. Applications • Continuous LOD • Geomorphs • Progressive transmission demo demo demo

  16. ^ M Progressive Mesh Summary PM V F lossless M0 vspl • single resolution • continuous-resolution • smooth LOD • progressive • space-efficient

  17. coarser finer vspl0 vspl1 vspli-1 vspln-1 M0 View-dependent refinement of PM’s actual view overhead view

  18. vsplit vs vsplit vu vt Parent-child vertex relations

  19. vspl0 vspl1 vspl2 vspl3 vspl4 vspl5 M0 v1 v2 v3 v10 v10 v11 v4 v5 v5 v8 v9 v12 v13 v6 v6 v7 Mn v14 v15 Vertex hierarchy M0 vspl0 vspl1 vspl2 vspl3 vspl4 vspl5 PM: M0 v1 v2 v3

  20. M0 vspl0 vspl0 vspl1 vspl1 vspl2 vspl2 vspl3 vspl3 vspl4 vspl4 vspl5 vspl2 M0 v1 v1 v1 v2 v2 v2 v3 v3 v3 v3 v10 v10 v10 v11 v11 v4 v4 v5 v5 v5 v8 v8 v9 v9 v8 v9 v12 v12 v13 v13 v6 v6 v7 v7 selectively refined mesh v14 v15 Selective refinement

  21. v3 v9 v10 v10 v11 v11 v4 v4 v8 v8 v8 v9 v9 dependency v12 v13 v6 v6 v7 v7 new mesh initial mesh v14 v14 v15 v15 v15 Runtime algorithm M0 v1 v2 v3 v10 v11 v4 v5 v8 v9 v12 v12 v13 v6 v7 v14 v15 • Algorithm: • incremental • efficient • amortizable

  22. DEMO: View-dependent LOD demo

  23. Complex terrain model Puget Sound data 16K x 16K vertices ~537 million triangles 10m spacing, 0.1m resolution 4m demo simpler 10m demo

  24. ^ M V F Selective Refinement Summary PM • continuous-resolution • smooth LOD • space-efficient • progressive M0 vspl • view-dependentrefinement • real-time algorithm M0 v1 v2 ^ M v3 v4 v5 v6 v7 v8

  25. [Sander et al 2001] Texture mapping progressive meshes • Construct texture atlas valid for allM0…Mn. e.g. 1000 faces demo pre-shaded demo

  26. Multiresolution geometry • Irregular meshes • Progressive meshes[1996] • View-dependent refinement[1997] • Texture-mapping PM [2001] • Semi-regular meshes • Multiresolution analysis[1995] • Completely regular meshes • Geometry images[2002]

  27. Semi-regular representations [Eck et al 1995] [Lee et al 1998] [Khodakovsky 2000] [Guskov et al 2000] [Lee et al 2000]… semi-regular irregular base mesh

  28. Challenge: finding domain [Eck et al 1995] [Lee et al 1998] [Khodakovsky 2000] [Guskov et al 2000] [Lee et al 2000]… base domain original surface

  29. Techniques • “Delaunay” partition + parametrization [Eck et al. 1995] • Mesh simplification + … [Lee et al. 1998] [Lee et al. 2000] [Guskov et al. 2000]

  30. Semi-regular: Applications • View-dependent refinement • Texture-mapping • Multiresolution editing • Compression • … [Lounsbery et al. 1994] [Certain et al. 1995] [Zorin et al. 1997] [Khodakovsky et al. 1999]

  31. Multiresolution geometry • Irregular meshes • Progressive meshes[1996] • View-dependent refinement[1997] • Texture-mapping PM [2001] • Semi-regular meshes • Multiresolution analysis[1995] • Completely regular meshes • Geometry images[2002]

  32. Mesh rendering: complicated process Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 2 1 3 Face 4 2 3 … s1 t1 s2 t2 random access! random access!

  33. Current architecture geometry random framebufferZ-buffer GPU $ random $ texture compression random compression 2D image compression ~40M Δ/sec

  34. New architecture framebufferZ-buffer • Minimize #vertices bandwidth,through compression. • Maximize sequential (non-random) access geometry & textureimage GPU sequential ~random great compression compression

  35. [Gu et al 2002] Geometry Image completely regular sampling 3D geometry geometry image257 x 257; 12 bits/channel

  36. Basic idea cut parametrize demo

  37. Basic idea cut sample

  38. Basic idea cut store render [r,g,b] = [x,y,z]

  39. Rendering (65x65 geometry image) demo

  40. Rendering with attributes geometry image 2572 x 12b/ch normal-map image 5122 x 8b/ch rendering

  41. Normal-Mapped Demo geometry image129x129; 12b/ch normal map512x512; 8b/ch demo pre-shaded demo

  42. Advantages for hardware rendering • Regular sampling  no vertex indices. • Unified parametrization  no texture coordinates. Raster-scan traversal of source data  Run-time decompression?

  43. Compression Image wavelet-coder 295 KB  1.5 KB fused cut + topological sideband (12 B)

  44. Compression results 295 KB  1.5 KB 3 KB 12 KB 49 KB

  45. Irregular Semi-regular Completely regular

  46. Texture Mapping Demo 2,000 faces demo

  47. Displaced subdivision surfaces [Lee et al 2000] control mesh surface displaced surface movie movie scalar displacements

  48. Mip-mapping 257x257 129x129 65x65

  49. Some artifacts aliasing anisotropic sampling

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