Silhouette Clipping

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Silhouette Clipping

• Pedro V. Sander
• Xianfeng Gu
• Steven J. Gortler
• Harvard University

Hugues H. Hoppe John M. Snyder Microsoft
Research
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Mesh simplification
original mesh
coarse mesh
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Silhouette clipping
original mesh
coarse mesh
texture/bump map
silhouette clipped
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Silhouette clipping
original mesh
coarse mesh
texture/bump map
silhouette clipped
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Silhouette clipping demo
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Overview
coarse mesh
rendered
original mesh
normal map
Soucy et al 96 Cignoni et al 98 Cohen et al
98
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Overview
coarse hull
rendered
original mesh
normal map
stencil mask
2D silhouette
edge hierarchy
Runtime
Preprocess
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Overview
coarse hull
rendered
silhouetteclipped
original mesh
normal map
2D silhouette
edge hierarchy
Runtime
Preprocess
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Major contributions

• Progressive hull
• Texture creation
• Silhouette extraction
• Stencil setting

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Major contributions

• Progressive hull
• Texture creation
• Silhouette extraction
• Stencil setting

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Major contributions

• Progressive hull
• Texture creation
• Silhouette extraction
• Stencil setting

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Major contributions

• Progressive hull
• Texture creation
• Silhouette extraction
• Stencil setting

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Major contributions

• Progressive hull
• Texture creation
• Silhouette extraction
• Stencil setting

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Coarse hull
Original mesh
Coarse hull
Given mesh, create coarse mesh that encloses it.
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Progressive hull

• Progressive mesh sequence
• Every mesh encloses all finer meshes.

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Edge collapse
M i
M i-1

• Perform greedy sequence of collapses.
• Ensure new mesh encloses old mesh Linear
  programming problem

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Linear programming (2D)
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Linear programming (2D)
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Linear programming (2D)
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Linear programming (2D)
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Linear programming (2D)
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Linear programming (2D)
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Linear programming (2D)
new vertexposition
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Progressive hull demo
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Texture creation
coarse hull
rendered
Cignoni et al 98 Soucy et al 96
original mesh
normal map
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Texture creation
vertex normals
coarse
original
closest-point Cignoni et al 98
normal-shooting Ours
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Silhouette extraction
Given mesh and viewpoint, return edges on
silhouette.
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What is a silhouette edge?

• Edge is on silhouette iff one adjacent triangle
  faces towards viewpoint

not silhouette
silhouette
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Related schemes

• Brute force O(edges) but O(edges on
  silhouette) ? O(?edges) !
• Markosian et al 97 probabilistic
• Gooch et al 99 assumes orthographic view
• Barequet et al 99 Hertzmann Zorin 00
  dual-space formulation
• Kumar et al 96 Johannsen Carter 98
  backface cullingOurs optimized hierarchy of
  anchored cones extracts 3,500 sil edges of
  10,000 edges at 250 fps

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Hierarchical culling

• Each node contains
• cluster of mesh edges
• spatial culling primitive

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Hierarchical culling

• Each node contains
• cluster of mesh edges
• spatial culling primitive

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Spatial culling primitive

• Given cluster of edges,check if there are no
  silhouette edges.
• True if adjacent triangles are all front-facing
  or all back-facing.

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Spatial culling primitive

• Given cluster of edges,check if there are no
  silhouette edges.
• True if adjacent triangles are all front-facing
  or all back-facing.

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Spatial culling primitive

• Given cluster of edges,check if there are no
  silhouette edges.
• True if adjacent triangles are all front-facing
  or all back-facing.

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Anchored cone primitive
front-facing cone
back-facing cone
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Anchored cone primitive

• Calculate central axisGilberts algorithm
• Calculate cone angle
• Calculate anchor positionsLinear programming

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Anchored cone primitive

• Calculate central axisGilberts algorithm
• Calculate cone angle
• Calculate anchor positionsLinear programming

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Anchored cone primitive

• Calculate central axisGilberts algorithm
• Calculate cone angle
• Calculate anchor positionsLinear programming

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Hierarchy construction

• Bottom-up greedy joining

two clusters
merge
adopt
parent
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Hierarchy construction

• Each root has probability of culling.
• We compute an expected extraction cost for each
  root, and the forest.
• Choose next join operation to maximally decrease
  expected extraction cost.

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Silhouette extraction video
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Performance
Model Bunny Dragon Parasaur Knot Holes3
Total edges 104,511 600,000 65,799 278,784 282,624
Sil edges 3,461 23,493 3,227 3,291 1,737
Tested edges 10,256 67,934 10,938 13,134 5,976
Time (ms) 4.1 28.2 4.3 7.9 3.3
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Performance
Model Bunny Dragon Parasaur Knot Holes3
Total edges 104,511 600,000 65,799 278,784 282,624
Sil edges 3,461 23,493 3,227 3,291 1,737
Tested edges 10,256 67,934 10,938 13,134 5,976
Time (ms) 4.1 28.2 4.3 7.9 3.3
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Performance
Model Bunny Dragon Parasaur Knot Holes3
Total edges 104,511 600,000 65,799 278,784 282,624
Sil edges 3,461 23,493 3,227 3,291 1,737
Tested edges 10,256 67,934 10,938 13,134 5,976
Time (ms) 4.1 28.2 4.3 7.9 3.3
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Performance
Model Bunny Dragon Parasaur Knot Holes3
Total edges 104,511 600,000 65,799 278,784 282,624
Sil edges 3,461 23,493 3,227 3,291 1,737
Tested edges 10,256 67,934 10,938 13,134 5,976
Time (ms) 4.1 28.2 4.3 7.9 3.3
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Performance
Model Bunny Dragon Parasaur Knot Holes3
Total edges 104,511 600,000 65,799 278,784 282,624
Sil edges 3,461 23,493 3,227 3,291 1,737
Tested edges 10,256 67,934 10,938 13,134 5,976
Time (ms) 4.1 28.2 4.3 7.9 3.3
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Stencil setting
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Stencil setting algorithm

• Algorithm inspired by concave polygon-filling
  algorithm.
• Silhouette edges organized in hash table.
• Each contour drawn as fan of triangles
• Triangle front-facing ? stencil 1
• Triangle back-facing ? stencil 1

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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting algorithm
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Stencil setting video
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Silhouette antialiasing

• Transfer stencil to alpha buffer stencil 0
  ? alpha 0.0 stencil 1 ? alpha 1.0
• Render silhouette edges in alpha buffer as
  antialiased line segments.
• Render coarse hull subject to alpha buffer.

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Silhouette antialiasing video
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Timing analysis
Model Bunny Dragon Parasaur Knot Holes3
Faces (original) 69,674 400,000 43,866 185,856 188,416
Rendering time 34.7 204.7 20.6 81.1 90.3
Faces (coarse) 500 4,000 1,020 928 500
Rendering time 4.8 5.2 4.9 4.9 4.4
SC Rendering time 7.8 50.3 6.9 10.3 5.5
Speedup factor 4.4 4.1 3.0 7.9 16.4
All times in milliseconds
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Timing analysis
Model Bunny Dragon Parasaur Knot Holes3
Faces (original) 69,674 400,000 43,866 185,856 188,416
Rendering time 34.7 204.7 20.6 81.1 90.3
Faces (coarse) 500 4,000 1,020 928 500
Rendering time 4.8 5.2 4.9 4.9 4.4
SC Rendering time 7.8 50.3 6.9 10.3 5.5
Speedup factor 4.4 4.1 3.0 7.9 16.4
All times in milliseconds
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Timing analysis
Model Bunny Dragon Parasaur Knot Holes3
Faces (original) 69,674 400,000 43,866 185,856 188,416
Rendering time 34.7 204.7 20.6 81.1 90.3
Faces (coarse) 500 4,000 1,020 928 500
Rendering time 4.8 5.2 4.9 4.9 4.4
SC Rendering time 7.8 50.3 6.9 10.3 5.5
Speedup factor 4.4 4.1 3.0 7.9 16.4
All times in milliseconds
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Timing analysis
Model Bunny Dragon Parasaur Knot Holes3
Faces (original) 69,674 400,000 43,866 185,856 188,416
Rendering time 34.7 204.7 20.6 81.1 90.3
Faces (coarse) 500 4,000 1,020 928 500
Rendering time 4.8 5.2 4.9 4.9 4.4
SC Rendering time 7.8 50.3 6.9 10.3 5.5
Speedup factor 4.4 4.1 3.0 7.9 16.4
All times in milliseconds
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Summary

• Silhouette clipping antialiasing
• Fast silhouette extraction
• Progressive hull
• Normal-shooting parametrization

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Future work

• Handle internal silhouettes
• Visual hull simplification
• Silhouette level-of-detail