Silhouette Clipping Pedro V. Sander Xianfeng Gu Steven J. Gortler Harvard University Pedro V. Sander Xianfeng Gu Steven J. Gortler Harvard University Hugues.

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]

RuntimePreprocess

normal map stencil mask

edge hierarchy

original mesh

rendered

coarse hull

2D silhouette

RuntimePreprocess


normal map silhouetteclipped

edge hierarchy

original mesh

rendered

coarse hull

2D silhouette

RuntimePreprocess


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 Every mesh enclosesencloses all finer meshes. all finer meshes.

Progressive mesh sequenceProgressive mesh sequence Every mesh Every mesh enclosesencloses all finer meshes. 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)







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

[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 100,000 edges at 250 fpsextracts 3,500 sil edges of 100,000 edges at 250 fps

[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 100,000 edges at 250 fpsextracts 3,500 sil edges of 100,000 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


Hierarchical cullingHierarchical cullingHierarchical cullingHierarchical culling



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.



2D cross-section2D cross-section






2D cross-section2D cross-section








True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or all back-facing. or all back-facing.


True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or all back-facing. or all back-facing.



True if adjacent triangles are True if adjacent triangles are all front-facingall front-facing or or all back-facingall back-facing..


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


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.

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 DragonDragon BunnyBunny ParasaurParasaur KnotKnot Holes3Holes3

Total edgesTotal edges 600,000600,000 104,511104,511 65,79965,799 278,784278,784 282,624282,624

Sil edgesSil edges 23,49323,493 3,4613,461 3,2273,227 3,2913,291 1,7371,737

Tested edgesTested edges 67,93467,934 10,25610,256 10,93810,938 13,13413,134 5,9765,976

Tested conesTested cones 26,29126,291 4,2824,282 3,5383,538 7,9267,926 4,5944,594

Time (ms)Time (ms) 28.228.2 4.14.1 4.34.3 7.97.9 3.33.3







Time (ms)Time (ms) 28.228.2 4.14.1 4.34.3 7.97.9 3.33.3







Time (ms)Time (ms) 28.228.2 4.14.1 4.34.3 7.97.9 3.33.3







Time (ms)Time (ms) 28.228.2 4.14.1 4.34.3 7.97.9 3.33.3







Time (ms)Time (ms) 28.228.2 4.14.1 4.34.3 7.97.9 3.33.3







Time (ms)Time (ms) 28.228.2 4.14.1 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..

Order silhouette edges into loops. Order silhouette edges into loops. Each loop drawn as fan of triangles:Each loop 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..

Order silhouette edges into loops. Order silhouette edges into loops. Each loop drawn as fan of triangles:Each loop 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 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

Silhouette clipping demosSilhouette clipping demosSilhouette clipping demosSilhouette clipping demos

ParasaurParasaur3x speedup3x speedup

KnotKnot8x speedup8x speedup

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


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 Progressive hullProgressive hull Normal-shooting parametrizationNormal-shooting parametrization Fast silhouette extractionFast silhouette extraction

Silhouette clipping & antialiasingSilhouette clipping & antialiasing Progressive hullProgressive hull Normal-shooting parametrizationNormal-shooting parametrization Fast silhouette extractionFast silhouette extraction

Future workFuture workFuture workFuture work

Handle internal silhouettesHandle internal silhouettes Silhouette level-of-detailSilhouette level-of-detail Visual hull simplificationVisual hull simplification

Handle internal silhouettesHandle internal silhouettes Silhouette level-of-detailSilhouette level-of-detail Visual hull simplificationVisual hull simplification

Silhouette Clipping Pedro V. Sander Xianfeng Gu Steven J. Gortler Harvard University Pedro V. Sander Xianfeng Gu Steven J. Gortler Harvard University Hugues.

Documents

silhouette slide

silhouette edges

silhouette clipped silhouette

silhouette extraction

d slide

runtimepreprocess slide

original mesh coarse

fps slide