CONSERVATIVE VOXELIZATION

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CONSERVATIVE VOXELIZATION

• Long Zhang1, Wei Chen1, David Ebert2, Qunsheng
  Peng1
• 1 State Key Lab of CADCG, Zhejiang University,
  Hangzhou, China
• 2 School of Electrical and Computer Engineering,
  Purdue University

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Contents
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Contents
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Voxelization

• Rasterization 2D scan-conversion
• Voxelization 3D scan-conversion

rasterization
Geometry primitive
pixels
voxelization
Surface model
voxels
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Applications
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Hardware-accelerated Voxelization
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Whats Conservative?
standard rasterization
conservative rasterization
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Why Is It Important?

• Example collision detection with

standard rasterization
conservative rasterization
no collision
4 colliding pixels detected
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Contents
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The Main Idea

• Illustration in 2D

Previous approaches
Conservative voxelization
The resulting voxels
rasterization

• Use the depth value of the pixel center
• Generate a single voxel for each pixel

• Compute the depth range in each pixel
• Generate multiple voxels for each pixel

pixels
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Contents
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Computing the Depth Range
Full covered pixels
Partially covered pixels

• Compute the pixel/triangle intersection
• Compute the depth range in the intersection
  region

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The Pixel/Triangle Intersection

• A convex polygon
• The minimal/maximal depth value lies on one of
  its vertices
• The idea
• Compute the depth values at all vertices
• Compare the depth values to get the depth range

• Compute the intersection of two edges of the
  triangle and the pixel

• The depth value can be easily calculated
• Is the condition satisfied?

• The depth value is known
• Is the condition satisfied? (easy to know)

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The Algorithm

• Compute the minimal depth for each pixel
• Compute the maximal depth in the same way

Text
Text

• None of the pixel vertices has the minimal depth
• Compute the intersection points of
  triangle/pixel edges
• Test if any triangle vertices are in the pixel

Text
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The computation is fast
The computation is slow
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Robustness Issues

• Handling special cases
• The result is conservative

Degenerate edges Replace QR with Pj
Intersection of nearly parallel lines Replace
QT with QR
Degenerate triangles Replace v1 with QL
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Accuracy Analysis

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Timing Statistics
voxelization timings in ms.
Performance comparison between Dongs and our
method
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Application to Collision Detection

• Basic idea
• Voxelize two models with a common bounding box
• Compare the resulting volumes
• Evaluation
• Accuracy
• High resolution supported
• Classfication colliding voxels represent
  potentially colliding reg-ions, and noncolliding
  voxels rep-resent non-colliding regions
• Efficiency
• Computation completely in GPU
• Need to traverse eachmodel once
• Support deforming models

Collision detection between the buddha model and
a morphing hand model. The collision detection is
accomplished in approximately 114 ms.
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Demo
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Conclusions

• Technical contributions

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Future Work

• More efficient algorithm
• Using lookup tables
• Need new functionalities of graphics hardware
• More applications
• Solid voxelization

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Thank You !
lzhang_at_cad.zju.edu.cn