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Irregular to Completely Regular Meshing in Computer Graphics. Hugues Hoppe Microsoft Research International Meshing Roundtable 2002/09/17. Complex meshes in graphics (1994). 70,000 faces. Complex meshes in graphics (1997). 860,000 faces. Complex meshes in graphics (2000).

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## Irregular to Completely Regular Meshing in Computer Graphics

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**Irregular to Completely RegularMeshingin Computer Graphics**Hugues Hoppe Microsoft Research International Meshing Roundtable2002/09/17**Complex meshes in graphics (1994)**70,000 faces**Complex meshes in graphics (1997)**860,000 faces**Complex meshes in graphics (2000)**2,000,000,000faces Challenges: - rendering - storage - transmission - scalability [Digital Michelangelo Project]**Multiresolution geometry**Irregular Semi-regular Completely regular**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]**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”**Not a goal: mesh quality**13,000 faces 1,000 faces**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**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**Goals in real-time rendering**#1 : Rendering speed • Minimize #vertices best accuracy using irregular meshes #2 : Rendering quality • Use texture mapping parametrization**13,546**500 152 150 faces Mn M175 M1 M0 ecoln-1 ecol0 ecoli Simplification: Edge collapse ecol**vspl(vs ,vl ,vr, …)**ecol vl vr vs Invertible: vertex split transformation**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**Applications**• Continuous LOD • Geomorphs • Progressive transmission demo demo demo**^**M Progressive Mesh Summary PM V F lossless M0 vspl • single resolution • continuous-resolution • smooth LOD • progressive • space-efficient**coarser**finer vspl0 vspl1 vspli-1 vspln-1 M0 View-dependent refinement of PM’s actual view overhead view**vsplit**vs vsplit vu vt Parent-child vertex relations**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**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**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**Complex terrain model**Puget Sound data 16K x 16K vertices ~537 million triangles 10m spacing, 0.1m resolution 4m demo simpler 10m demo**^**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**[Sander et al 2001]**Texture mapping progressive meshes • Construct texture atlas valid for allM0…Mn. e.g. 1000 faces demo pre-shaded demo**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]**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**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**Techniques**• “Delaunay” partition + parametrization [Eck et al. 1995] • Mesh simplification + … [Lee et al. 1998] [Lee et al. 2000] [Guskov et al. 2000]**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]**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]**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!**Current architecture**geometry random framebufferZ-buffer GPU $ random $ texture compression random compression 2D image compression ~40M Δ/sec**New architecture**framebufferZ-buffer • Minimize #vertices bandwidth,through compression. • Maximize sequential (non-random) access geometry & textureimage GPU sequential ~random great compression compression**[Gu et al 2002]**Geometry Image completely regular sampling 3D geometry geometry image257 x 257; 12 bits/channel**Basic idea**cut parametrize demo**Basic idea**cut sample**Basic idea**cut store render [r,g,b] = [x,y,z]**Rendering**(65x65 geometry image) demo**Rendering with attributes**geometry image 2572 x 12b/ch normal-map image 5122 x 8b/ch rendering**Normal-Mapped Demo**geometry image129x129; 12b/ch normal map512x512; 8b/ch demo pre-shaded demo**Advantages for hardware rendering**• Regular sampling no vertex indices. • Unified parametrization no texture coordinates. Raster-scan traversal of source data Run-time decompression?**Compression**Image wavelet-coder 295 KB 1.5 KB fused cut + topological sideband (12 B)**Compression results**295 KB 1.5 KB 3 KB 12 KB 49 KB**Irregular**Semi-regular Completely regular**Texture Mapping Demo**2,000 faces demo**Displaced subdivision surfaces**[Lee et al 2000] control mesh surface displaced surface movie movie scalar displacements**Mip-mapping**257x257 129x129 65x65**Some artifacts**aliasing anisotropic sampling

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