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Irregular to Completely Regular Meshing in Computer Graphics Hugues Hoppe Microsoft Research International Meshing Roundtable 2002/09/17 Hugues Hoppe Microsoft Research International Meshing Roundtable 2002/09/17
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Complex meshes in graphics (1994) 70,000 faces
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Complex meshes in graphics (1997) 860,000 faces
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Complex meshes in graphics (2000) [Digital Michelangelo Project] 2,000,000,000 faces Challenges: - rendering - storage - transmission - scalability
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Multiresolution geometry Semi-regularIrregular Completely regular
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Multiresolution geometry l Irregular meshes n Progressive meshes [1996] n View-dependent refinement [1997] n Texture-mapping PM [2001] l Semi-regular meshes n Multiresolution analysis [1995] l Completely regular meshes n Geometry images [2002] l Irregular meshes n Progressive meshes [1996] n View-dependent refinement [1997] n Texture-mapping PM [2001] l Semi-regular meshes n Multiresolution analysis [1995] l Completely regular meshes n Geometry images [2002]
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Goals in real-time rendering #1 : Rendering speed n 60-85 frames/second #2 : Rendering quality n geometric “visual” accuracy n temporal continuity Not a Goal: l Mesh “quality” #1 : Rendering speed n 60-85 frames/second #2 : Rendering quality n geometric “visual” accuracy n temporal continuity Not a Goal: l Mesh “quality”
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Not a goal: mesh quality 13,000 faces 1,000 faces
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Irregular meshes Vertex 1 x 1 y 1 z 1 Vertex 2 x 2 y 2 z 2 … Face 2 1 3 Face 4 2 3 … Rendering cost = vertex processing + rasterization ~ #vertices ~ constant yuck
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Texture mapping Vertex 1 x 1 y 1 z 1 Vertex 2 x 2 y 2 z 2 … s1 t1s1 t1s2 t2s2 t2s1 t1s1 t1s2 t2s2 t2 normal map s t Face 2 1 3 Face 4 2 3 … “Visual” accuracy using coarse mesh
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Goals in real-time rendering #1 : Rendering speed n Minimize #vertices best accuracy using irregular meshes #2 : Rendering quality n Use texture mapping parametrization #1 : Rendering speed n Minimize #vertices best accuracy using irregular meshes #2 : Rendering quality n Use texture mapping parametrization
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Simplification: Edge collapse 13,546500152 150 faces M0M0M0M0 M1M1M1M1 M 175 ecol 0 ecol i ecol n-1 MnMnMnMn ecol
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Invertible: vertex split transformation vsvsvsvs vlvlvlvl vrvrvrvr vspl(v s,v l,v r, … ) ecol
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150 M0M0M0M0 M1M1M1M1 vspl 0 152 Progressive mesh M 175 500 … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 MnMnMnMn
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ApplicationsApplications l Continuous LOD l Geomorphs l Progressive transmission l Continuous LOD l Geomorphs l Progressive transmission demo
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Progressive Mesh Summary PM VF M^ M0M0M0M0 n continuous-resolution n smooth LOD n progressive n space-efficient lossless n single resolution vspl
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View-dependent refinement of PM’s actual view overhead view finer coarser M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1
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Parent-child vertex relations vsvsvsvs vtvtvtvt vuvuvuvu vsplit vsplit
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v2v2v2v2 Vertex hierarchy vspl 0 M0M0M0M0 vspl 1 vspl 2 vspl 3 vspl 4 vspl 5 v1v1v1v1 v3v3v3v3 M0M0M0M0 v 10 v 11 vspl 3 v1v1v1v1 v2v2v2v2 v4v4v4v4 v5v5v5v5 vspl 0 v8v8v8v8 v9v9v9v9 vspl 2 v3v3v3v3 v6v6v6v6 v7v7v7v7 vspl 1 v5v5v5v5 v 12 v 13 vspl 4 v 10 vspl 5 v 14 v 15 v6v6v6v6 PM: MnMnMnMn M0M0M0M0
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Selective refinement vspl 2 v 11 v1v1v1v1 v2v2v2v2 v4v4v4v4 v8v8v8v8 v9v9v9v9 v3v3v3v3 v7v7v7v7 v5v5v5v5 v 12 v 13 v 10 v 14 v 15 v6v6v6v6 v2v2v2v2 vspl 0 M0M0M0M0 vspl 1 vspl 3 vspl 4 vspl 5 v1v1v1v1 v3v3v3v3 M0M0M0M0 v 10 v 11 vspl 3 v1v1v1v1 v2v2v2v2 v4v4v4v4 v5v5v5v5 vspl 0 v6v6v6v6 v7v7v7v7 vspl 1 v5v5v5v5 v 12 v 13 vspl 4 v 10 selectively refined mesh v8v8v8v8 v9v9v9v9 vspl 2 v3v3v3v3 v8v8v8v8 v9v9v9v9 v3v3v3v3
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initial mesh v5v5v5v5 v 10 v 11 v4v4v4v4 v8v8v8v8 v9v9v9v9 v7v7v7v7 v 12 v 13 v1v1v1v1 v2v2v2v2 v3v3v3v3 Runtime algorithm M0M0M0M0 v6v6v6v6 v 14 v 15 v 12 v 13 v 12 v 10 v 11 v 10 v 11 v4v4v4v4 v4v4v4v4 v6v6v6v6 v 14 v 15 v6v6v6v6 v 14 v 15 v8v8v8v8 v9v9v9v9 v3v3v3v3 v7v7v7v7 v7v7v7v7 v8v8v8v8 v8v8v8v8 v9v9v9v9 v9v9v9v9 new mesh dependency l Algorithm: n incremental n efficient n amortizable
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DEMO: View-dependent LOD demo
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Complex terrain model Puget Sound data 16K x 16K vertices ~537 million triangles 4m demo 4m demo 4m demo 4m demo 10m spacing, 0.1m resolution simpler 10m demo simpler 10m demo simpler 10m demo simpler 10m demo
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Selective Refinement Summary PM VF M^vspl v1v1v1v1 M0M0M0M0 v2v2v2v2 M0M0M0M0 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 v8v8v8v8 M ^ n view-dependent refinement n real-time algorithm n continuous-resolution n smooth LOD n space-efficient n progressive
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Texture mapping progressive meshes l Construct texture atlas valid for all M 0 …M n. e.g. 1000 faces pre-shaded demo pre-shaded demo pre-shaded demo pre-shaded demo [Sander et al 2001]
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Multiresolution geometry l Irregular meshes n Progressive meshes [1996] n View-dependent refinement [1997] n Texture-mapping PM [2001] l Semi-regular meshes n Multiresolution analysis [1995] l Completely regular meshes n Geometry images [2002] l Irregular meshes n Progressive meshes [1996] n View-dependent refinement [1997] n Texture-mapping PM [2001] l Semi-regular meshes n Multiresolution analysis [1995] l Completely regular meshes n Geometry images [2002]
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Semi-regular representations irregular base mesh semi-regular [Eck et al 1995] [Lee et al 1998] [Khodakovsky 2000] [Guskov et al 2000] [Lee et al 2000] …
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Challenge: finding domain [Eck et al 1995] [Lee et al 1998] [Khodakovsky 2000] [Guskov et al 2000] [Lee et al 2000] … original surface base domain
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TechniquesTechniques l “Delaunay” partition + parametrization l Mesh simplification + … [Lee et al. 1998] [Lee et al. 2000] [Eck et al. 1995] [Guskov et al. 2000]
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Semi-regular: Applications l View-dependent refinement l Texture-mapping l Multiresolution editing l Compression l … l View-dependent refinement l Texture-mapping l Multiresolution editing l Compression l … [Lounsbery et al. 1994] [Certain et al. 1995] [Zorin et al. 1997] [Khodakovsky et al. 1999]
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Multiresolution geometry l Irregular meshes n Progressive meshes [1996] n View-dependent refinement [1997] n Texture-mapping PM [2001] l Semi-regular meshes n Multiresolution analysis [1995] l Completely regular meshes n Geometry images [2002] l Irregular meshes n Progressive meshes [1996] n View-dependent refinement [1997] n Texture-mapping PM [2001] l Semi-regular meshes n Multiresolution analysis [1995] l Completely regular meshes n Geometry images [2002]
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Mesh rendering: complicated process Vertex 1 x 1 y 1 z 1 Vertex 2 x 2 y 2 z 2 … random access! s1 t1s1 t1s2 t2s2 t2s1 t1s1 t1s2 t2s2 t2 Face 2 1 3 Face 4 2 3 …
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Current architecture GPUGPU framebuffer Z-buffer geometrygeometry texturetexture $ $ $ $ random random random compression compression 2D image compression ~40M Δ/sec
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New architecture n Minimize #vertices bandwidth, through compression. n Maximize sequential (non-random) access n Minimize #vertices bandwidth, through compression. n Maximize sequential (non-random) access GPUGPU framebuffer Z-buffer geometry & texture image sequential ~random great compression compression
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Geometry Image geometry image 257 x 257; 12 bits/channel 3D geometry completely regular sampling [Gu et al 2002]
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Basic idea demo cut parametrize
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Basic idea cut sample
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cut [r,g,b] = [x,y,z] render store
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RenderingRendering (65x65 geometry image) demo
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rendering geometry image 257 2 x 12b/ch normal-map image 512 2 x 8b/ch Rendering with attributes
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normal map 512x512; 8b/ch Normal-Mapped Demo geometry image 129x129; 12b/ch demo pre-shaded demo pre-shaded demo pre-shaded demo pre-shaded demo
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Advantages for hardware rendering l Regular sampling no vertex indices. l Unified parametrization no texture coordinates. Raster-scan traversal of source data Run-time decompression? Run-time decompression? l Regular sampling no vertex indices. l Unified parametrization no texture coordinates. Raster-scan traversal of source data Run-time decompression? Run-time decompression?
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CompressionCompression 1.5 KB + topological sideband (12 B) fused cut 295 KB Image wavelet-coder
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Compression results 1.5 KB 3 KB 12 KB 49 KB 295 KB
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Semi-regularIrregular Completely regular Flexibility any input mesh subdivision connect. uniform grid Remeshingunnecessaryrequiredrequired Sharp features yesdifficultdifficult Neighborhood / multiresolution irregular, cumbersome mostly regular, but irregular vertices regular, except at “cut” Rendering vertex & tex. caching N-patches simple raster scan Compression poor, delta-encoding fancy wavelets, software easy wavelets, hardware? Element quality good if desired trouble areas
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Texture Mapping Demo 2,000 faces demo
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Displaced subdivision surfaces control mesh displaced surface [Lee et al 2000] scalar displacements surface movie
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Mip-mappingMip-mapping 257x257129x12965x65
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Some artifacts aliasing anisotropic sampling
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