silhouette clipping pedro v. sander xianfeng gu steven j. gortler harvard university pedro v. sander...
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Silhouette ClippingSilhouette ClippingSilhouette ClippingSilhouette Clipping
Pedro V. SanderPedro V. Sander
Xianfeng GuXianfeng Gu
Steven J. GortlerSteven J. Gortler
Harvard UniversityHarvard University
Pedro V. SanderPedro V. Sander
Xianfeng GuXianfeng Gu
Steven J. GortlerSteven J. Gortler
Harvard UniversityHarvard University
Hugues H. HoppeHugues H. Hoppe
John M. SnyderJohn M. Snyder
Microsoft ResearchMicrosoft Research
Hugues H. HoppeHugues H. Hoppe
John M. SnyderJohn M. Snyder
Microsoft ResearchMicrosoft Research
Mesh simplificationMesh simplificationMesh simplificationMesh simplification
original meshoriginal mesh+ texture/bump map+ texture/bump map
poorpoorsilhouettesilhouette
poorpoorsilhouettesilhouette
coarse meshcoarse mesh
silhouette clippedsilhouette clipped
Silhouette clippingSilhouette clippingSilhouette clippingSilhouette clipping
original meshoriginal mesh coarse meshcoarse mesh+ texture/bump map+ texture/bump map
silhouette clippedsilhouette clipped
Silhouette clippingSilhouette clippingSilhouette clippingSilhouette clipping
original meshoriginal mesh coarse meshcoarse mesh+ texture/bump map+ texture/bump map
Silhouette clipping demoSilhouette clipping demoSilhouette clipping demoSilhouette clipping demo
normal maporiginal mesh
rendered
coarse mesh
OverviewOverviewOverviewOverview
[Soucy et al 96][Soucy et al 96][Cignoni et al 98][Cignoni et al 98][Cohen et al 98][Cohen et al 98]
normal map stencil mask
edge hierarchy
original mesh
rendered
coarse hull
2D silhouette
RuntimePreprocess
OverviewOverviewOverviewOverview
normal map silhouetteclipped
edge hierarchy
original mesh
rendered
coarse hull
2D silhouette
RuntimePreprocess
OverviewOverviewOverviewOverview
Major contributionsMajor contributionsMajor contributionsMajor contributions Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Major contributionsMajor contributionsMajor contributionsMajor contributions Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Major contributionsMajor contributionsMajor contributionsMajor contributions Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Major contributionsMajor contributionsMajor contributionsMajor contributions Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Major contributionsMajor contributionsMajor contributionsMajor contributions Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Progressive hullProgressive hull Texture creationTexture creation Silhouette extractionSilhouette extraction Stencil settingStencil setting
Coarse hullCoarse hullCoarse hullCoarse hull
Given mesh, create coarse mesh that encloses it.Given mesh, create coarse mesh that encloses it.
Original meshOriginal mesh Coarse hullCoarse hull
Progressive hullProgressive hullProgressive hullProgressive hull
Progressive mesh sequenceProgressive mesh sequence Every mesh encloses all finer meshes.Every mesh encloses all finer meshes.
Progressive mesh sequenceProgressive mesh sequence Every mesh encloses all finer meshes.Every mesh encloses all finer meshes.
Edge collapseEdge collapseEdge collapseEdge collapse
Perform greedy sequence of collapses.Perform greedy sequence of collapses. Ensure new mesh encloses old mesh:Ensure new mesh encloses old mesh:
Linear programming problem Linear programming problem
Perform greedy sequence of collapses.Perform greedy sequence of collapses. Ensure new mesh encloses old mesh:Ensure new mesh encloses old mesh:
Linear programming problem Linear programming problem
M i M
i-1
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
Linear programming (2D)Linear programming (2D)Linear programming (2D)Linear programming (2D)
new vertexnew vertexpositionposition
Progressive hull demoProgressive hull demoProgressive hull demoProgressive hull demo
Texture creationTexture creationTexture creationTexture creation
normal maporiginal mesh
rendered
coarse hull
[Cignoni et al 98][Cignoni et al 98][Soucy et al 96][Soucy et al 96]
Texture creationTexture creationTexture creationTexture creation
closest-pointclosest-point[Cignoni et al 98][Cignoni et al 98]
vertex normalsvertex normals
normal-shootingnormal-shootingOursOurs
originaloriginal
coarsecoarse
Silhouette extractionSilhouette extractionSilhouette extractionSilhouette extraction
Given mesh and viewpoint, return edges on silhouette.Given mesh and viewpoint, return edges on silhouette.
What is a silhouette edge?What is a silhouette edge?What is a silhouette edge?What is a silhouette edge?
Edge is on silhouette iff Edge is on silhouette iff oneone adjacent adjacent triangle faces towards viewpoint:triangle faces towards viewpoint:
Edge is on silhouette iff Edge is on silhouette iff oneone adjacent adjacent triangle faces towards viewpoint:triangle faces towards viewpoint:
not silhouettenot silhouette silhouettesilhouette
Related schemesRelated schemesRelated schemesRelated schemes Brute force: Brute force: O(edges)O(edges)
but O(edges on silhouette) but O(edges on silhouette) O( O(edges) !edges) ! [Markosian et al 97][Markosian et al 97]
probabilisticprobabilistic [Gooch et al 99] [Gooch et al 99]
assumes orthographic viewassumes orthographic view [Barequet et al 99] [Hertzmann & Zorin 00][Barequet et al 99] [Hertzmann & Zorin 00]
dual-space formulation dual-space formulation
[Kumar et al 96] [Johannsen & Carter 98] [Kumar et al 96] [Johannsen & Carter 98] backface cullingbackface culling
Ours: optimized hierarchy of anchored conesOurs: optimized hierarchy of anchored cones extracts 3,500 sil edges of 10,000 edges at 250 fpsextracts 3,500 sil edges of 10,000 edges at 250 fps
Brute force: Brute force: O(edges)O(edges) but O(edges on silhouette) but O(edges on silhouette) O( O(edges) !edges) !
[Markosian et al 97][Markosian et al 97] probabilisticprobabilistic
[Gooch et al 99] [Gooch et al 99] assumes orthographic viewassumes orthographic view
[Barequet et al 99] [Hertzmann & Zorin 00][Barequet et al 99] [Hertzmann & Zorin 00] dual-space formulation dual-space formulation
[Kumar et al 96] [Johannsen & Carter 98] [Kumar et al 96] [Johannsen & Carter 98] backface cullingbackface culling
Ours: optimized hierarchy of anchored conesOurs: optimized hierarchy of anchored cones extracts 3,500 sil edges of 10,000 edges at 250 fpsextracts 3,500 sil edges of 10,000 edges at 250 fps
Hierarchical cullingHierarchical cullingHierarchical cullingHierarchical culling
Each node contains:Each node contains: cluster of mesh edgescluster of mesh edges spatial culling primitivespatial culling primitive
Each node contains:Each node contains: cluster of mesh edgescluster of mesh edges spatial culling primitivespatial culling primitive
Hierarchical cullingHierarchical cullingHierarchical cullingHierarchical culling
Each node contains:Each node contains: cluster of mesh edgescluster of mesh edges spatial culling primitivespatial culling primitive
Each node contains:Each node contains: cluster of mesh edgescluster of mesh edges spatial culling primitivespatial culling primitive
Spatial culling primitiveSpatial culling primitiveSpatial culling primitiveSpatial culling primitive
Given cluster of edges,Given cluster of edges,check if there are no silhouette edges.check if there are no silhouette edges.
True if adjacent triangles are True if adjacent triangles are all front-facing or all back-facing.all front-facing or all back-facing.
Given cluster of edges,Given cluster of edges,check if there are no silhouette edges.check if there are no silhouette edges.
True if adjacent triangles are True if adjacent triangles are all front-facing or all back-facing.all front-facing or all back-facing.
Spatial culling primitiveSpatial culling primitiveSpatial culling primitiveSpatial culling primitive
Given cluster of edges,Given cluster of edges,check if there are no silhouette edges.check if there are no silhouette edges.
True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or all back-facing. or all back-facing.
Given cluster of edges,Given cluster of edges,check if there are no silhouette edges.check if there are no silhouette edges.
True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or all back-facing. or all back-facing.
Spatial culling primitiveSpatial culling primitiveSpatial culling primitiveSpatial culling primitive
Given cluster of edges,Given cluster of edges,check if there are no silhouette edges.check if there are no silhouette edges.
True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or or all back-facingall back-facing..
Given cluster of edges,Given cluster of edges,check if there are no silhouette edges.check if there are no silhouette edges.
True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or or all back-facingall back-facing..
Anchored cone primitiveAnchored cone primitiveAnchored cone primitiveAnchored cone primitive
front-facingcone
back-facingcone
Anchored cone primitiveAnchored cone primitiveAnchored cone primitiveAnchored cone primitive
Calculate central axisCalculate central axisGilbert’s algorithmGilbert’s algorithm
Calculate cone angleCalculate cone angle
Calculate anchor positionsCalculate anchor positionsLinear programmingLinear programming
Calculate central axisCalculate central axisGilbert’s algorithmGilbert’s algorithm
Calculate cone angleCalculate cone angle
Calculate anchor positionsCalculate anchor positionsLinear programmingLinear programming
Anchored cone primitiveAnchored cone primitiveAnchored cone primitiveAnchored cone primitive
Calculate central axisCalculate central axisGilbert’s algorithmGilbert’s algorithm
Calculate cone angleCalculate cone angle
Calculate anchor positionsCalculate anchor positionsLinear programmingLinear programming
Calculate central axisCalculate central axisGilbert’s algorithmGilbert’s algorithm
Calculate cone angleCalculate cone angle
Calculate anchor positionsCalculate anchor positionsLinear programmingLinear programming
Anchored cone primitiveAnchored cone primitiveAnchored cone primitiveAnchored cone primitive
Calculate central axisCalculate central axisGilbert’s algorithmGilbert’s algorithm
Calculate cone angleCalculate cone angle
Calculate anchor positionsCalculate anchor positionsLinear programmingLinear programming
Calculate central axisCalculate central axisGilbert’s algorithmGilbert’s algorithm
Calculate cone angleCalculate cone angle
Calculate anchor positionsCalculate anchor positionsLinear programmingLinear programming
Hierarchy constructionHierarchy constructionHierarchy constructionHierarchy construction
Bottom-up greedy joiningBottom-up greedy joining Bottom-up greedy joiningBottom-up greedy joining
two clusterstwo clusters
mergemerge adoptadoptparentparent
Hierarchy constructionHierarchy constructionHierarchy constructionHierarchy construction
Each root has probability of culling.Each root has probability of culling. We compute an expected extraction We compute an expected extraction
cost for each root, and the forest.cost for each root, and the forest. Choose next join operation to Choose next join operation to
maximally decrease expected maximally decrease expected extraction cost.extraction cost.
Silhouette extraction videoSilhouette extraction videoSilhouette extraction videoSilhouette extraction video
PerformancePerformancePerformancePerformance
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Total edgesTotal edges 104,511104,511 600,000600,000 65,79965,799 278,784278,784 282,624282,624
Sil edgesSil edges 3,4613,461 23,49323,493 3,2273,227 3,2913,291 1,7371,737
Tested edgesTested edges 10,25610,256 67,93467,934 10,93810,938 13,13413,134 5,9765,976
Time (ms)Time (ms) 4.14.1 28.228.2 4.34.3 7.97.9 3.33.3
PerformancePerformancePerformancePerformance
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Total edgesTotal edges 104,511104,511 600,000600,000 65,79965,799 278,784278,784 282,624282,624
Sil edgesSil edges 3,4613,461 23,49323,493 3,2273,227 3,2913,291 1,7371,737
Tested edgesTested edges 10,25610,256 67,93467,934 10,93810,938 13,13413,134 5,9765,976
Time (ms)Time (ms) 4.14.1 28.228.2 4.34.3 7.97.9 3.33.3
PerformancePerformancePerformancePerformance
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Total edgesTotal edges 104,511104,511 600,000600,000 65,79965,799 278,784278,784 282,624282,624
Sil edgesSil edges 3,4613,461 23,49323,493 3,2273,227 3,2913,291 1,7371,737
Tested edgesTested edges 10,25610,256 67,93467,934 10,93810,938 13,13413,134 5,9765,976
Time (ms)Time (ms) 4.14.1 28.228.2 4.34.3 7.97.9 3.33.3
PerformancePerformancePerformancePerformance
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Total edgesTotal edges 104,511104,511 600,000600,000 65,79965,799 278,784278,784 282,624282,624
Sil edgesSil edges 3,4613,461 23,49323,493 3,2273,227 3,2913,291 1,7371,737
Tested edgesTested edges 10,25610,256 67,93467,934 10,93810,938 13,13413,134 5,9765,976
Time (ms)Time (ms) 4.14.1 28.228.2 4.34.3 7.97.9 3.33.3
PerformancePerformancePerformancePerformance
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Total edgesTotal edges 104,511104,511 600,000600,000 65,79965,799 278,784278,784 282,624282,624
Sil edgesSil edges 3,4613,461 23,49323,493 3,2273,227 3,2913,291 1,7371,737
Tested edgesTested edges 10,25610,256 67,93467,934 10,93810,938 13,13413,134 5,9765,976
Time (ms)Time (ms) 4.14.1 28.228.2 4.34.3 7.97.9 3.33.3
Stencil settingStencil settingStencil settingStencil setting
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Algorithm inspired by Algorithm inspired by concave polygon-filling algorithmconcave polygon-filling algorithm..
Silhouette edges organized in hash table.Silhouette edges organized in hash table. Each contour drawn as fan of triangles:Each contour drawn as fan of triangles:
Triangle front-facing Triangle front-facing stencil stencil ++= 1= 1 Triangle back-facing Triangle back-facing stencil stencil ––= 1= 1
Algorithm inspired by Algorithm inspired by concave polygon-filling algorithmconcave polygon-filling algorithm..
Silhouette edges organized in hash table.Silhouette edges organized in hash table. Each contour drawn as fan of triangles:Each contour drawn as fan of triangles:
Triangle front-facing Triangle front-facing stencil stencil ++= 1= 1 Triangle back-facing Triangle back-facing stencil stencil ––= 1= 1
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting algorithmStencil setting algorithmStencil setting algorithmStencil setting algorithm
Stencil setting videoStencil setting videoStencil setting videoStencil setting video
Silhouette antialiasingSilhouette antialiasingSilhouette antialiasingSilhouette antialiasing
Transfer stencil to alpha buffer:Transfer stencil to alpha buffer: stencil = 0 stencil = 0 alpha = 0.0 alpha = 0.0 stencil = 1 stencil = 1 alpha = 1.0 alpha = 1.0
Render silhouette edges in alpha buffer Render silhouette edges in alpha buffer as antialiased line segments.as antialiased line segments.
Render coarse hull subject to alpha buffer.Render coarse hull subject to alpha buffer.
Transfer stencil to alpha buffer:Transfer stencil to alpha buffer: stencil = 0 stencil = 0 alpha = 0.0 alpha = 0.0 stencil = 1 stencil = 1 alpha = 1.0 alpha = 1.0
Render silhouette edges in alpha buffer Render silhouette edges in alpha buffer as antialiased line segments.as antialiased line segments.
Render coarse hull subject to alpha buffer.Render coarse hull subject to alpha buffer.
Silhouette antialiasing videoSilhouette antialiasing videoSilhouette antialiasing videoSilhouette antialiasing video
Timing analysisTiming analysisTiming analysisTiming analysis
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Faces (original)Faces (original) 69,67469,674 400,000400,000 43,86643,866 185,856185,856 188,416188,416
Rendering timeRendering time 34.734.7 204.7204.7 20.620.6 81.181.1 90.390.3
Faces (coarse)Faces (coarse) 500500 4,0004,000 1,0201,020 928928 500500
Rendering timeRendering time 4.84.8 5.25.2 4.94.9 4.94.9 4.44.4
SC Rendering timeSC Rendering time 7.87.8 50.350.3 6.96.9 10.310.3 5.55.5
Speedup factorSpeedup factor 4.44.4 4.14.1 3.03.0 7.97.9 16.416.4
All times in millisecondsAll times in milliseconds
Timing analysisTiming analysisTiming analysisTiming analysis
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Faces (original)Faces (original) 69,67469,674 400,000400,000 43,86643,866 185,856185,856 188,416188,416
Rendering timeRendering time 34.734.7 204.7204.7 20.620.6 81.181.1 90.390.3
Faces (coarse)Faces (coarse) 500500 4,0004,000 1,0201,020 928928 500500
Rendering timeRendering time 4.84.8 5.25.2 4.94.9 4.94.9 4.44.4
SC Rendering timeSC Rendering time 7.87.8 50.350.3 6.96.9 10.310.3 5.55.5
Speedup factorSpeedup factor 4.44.4 4.14.1 3.03.0 7.97.9 16.416.4
All times in millisecondsAll times in milliseconds
Timing analysisTiming analysisTiming analysisTiming analysis
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Faces (original)Faces (original) 69,67469,674 400,000400,000 43,86643,866 185,856185,856 188,416188,416
Rendering timeRendering time 34.734.7 204.7204.7 20.620.6 81.181.1 90.390.3
Faces (coarse)Faces (coarse) 500500 4,0004,000 1,0201,020 928928 500500
Rendering timeRendering time 4.84.8 5.25.2 4.94.9 4.94.9 4.44.4
SC Rendering timeSC Rendering time 7.87.8 50.350.3 6.96.9 10.310.3 5.55.5
Speedup factorSpeedup factor 4.44.4 4.14.1 3.03.0 7.97.9 16.416.4
All times in millisecondsAll times in milliseconds
Timing analysisTiming analysisTiming analysisTiming analysis
ModelModel BunnyBunny DragonDragon ParasaurParasaur KnotKnot Holes3Holes3
Faces (original)Faces (original) 69,67469,674 400,000400,000 43,86643,866 185,856185,856 188,416188,416
Rendering timeRendering time 34.734.7 204.7204.7 20.620.6 81.181.1 90.390.3
Faces (coarse)Faces (coarse) 500500 4,0004,000 1,0201,020 928928 500500
Rendering timeRendering time 4.84.8 5.25.2 4.94.9 4.94.9 4.44.4
SC Rendering timeSC Rendering time 7.87.8 50.350.3 6.96.9 10.310.3 5.55.5
Speedup factorSpeedup factor 4.44.4 4.14.1 3.03.0 7.97.9 16.416.4
All times in millisecondsAll times in milliseconds
SummarySummarySummarySummary
Silhouette clipping & antialiasingSilhouette clipping & antialiasing Fast silhouette extractionFast silhouette extraction Progressive hullProgressive hull Normal-shooting parametrizationNormal-shooting parametrization
Silhouette clipping & antialiasingSilhouette clipping & antialiasing Fast silhouette extractionFast silhouette extraction Progressive hullProgressive hull Normal-shooting parametrizationNormal-shooting parametrization
Future workFuture workFuture workFuture work
Handle internal silhouettesHandle internal silhouettes Visual hull simplificationVisual hull simplification Silhouette level-of-detailSilhouette level-of-detail
Handle internal silhouettesHandle internal silhouettes Visual hull simplificationVisual hull simplification Silhouette level-of-detailSilhouette level-of-detail