C ONSERVATIVE V OXELIZATION

CONSERVATIVE VOXELIZATION

Long Zhang1, Wei Chen1, David Ebert2, Qunsheng Peng1

1 State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China

2 School of Electrical and Computer Engineering, Purdue University

CGI 2007 – Conservative Voxelization

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Contents

Introduction & Previous Work

The Main Idea

Algorithm & Implementation

Experimental Results

Conclusions & Future Work

Contents

Introduction & Previous WorkIntroduction & Previous WorkIntroduction & Previous WorkIntroduction & Previous Work

The Main Idea




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Voxelization

Rasterization – 2D scan-conversion

Voxelization – 3D scan-conversion

rasterization

voxelization

Geometry primitive pixels

Surface model voxels

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Applications

Voxel-ization

3D spatial analysis

volumetric modelling

virtualmedicine

collision detection

physically-based

simulation

haptic rendering

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Hardware-accelerated Voxelization

The basic ideaUse the rasterization functionality (2D scan-conversion) of graphics hardware to accelerate voxel-ization (3D scan-conversion)

Major advantageEfficient

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What’s Conservative?

standard rasterization conservative rasterization

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Why Is It Important?

Example: collision detection withstandard rasterization conservative rasterization

no collision 4 colliding pixels detected

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Contents


The Main IdeaThe Main IdeaThe Main IdeaThe Main Idea




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Illustration in 2D

The Main Idea

The viewing volumeA triangle to be voxelized

The viewing plane

Orthogonal projection

rasterization

pixels

Previous approaches

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

Conservative voxelization

The resulting voxels

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

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Contents


The Main Idea

Algorithm & ImplementationAlgorithm & ImplementationAlgorithm & ImplementationAlgorithm & Implementation



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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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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

The Pixel/Triangle Intersection

• 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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Compute the minimal depth for each pixel

Compute the maximal depth in the same way

The Algorithm

Text

Text

Text

Text

If is inside the triangle

Let be the vertex of the pixel with the minimal depth value

Yes No

Compute the barycentric coordinate

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

=

The computation is fast

The computation is slow

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Handling special cases

The result is conservative

Robustness Issues

Degenerate edges

Replace QR with Pj

Intersection of nearly parallel lines

Replace QT with QR

Degenerate triangles

Replace v1 with Q’L

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Contents


The Main Idea


Experimental ResultsExperimental ResultsExperimental ResultsExperimental Results


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Accuracy Analysis

Theoretically

Accuracy: • A voxel is generated if and only if it intersects with the input model

ConservativeVoxelization

In practice

Slightly over-conservative: • All voxels intersecting the input model are generated• A few voxels not intersecting the input model are also generated

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Timing Statistics

voxelization timings in ms.

Performance comparison between Dong’s and our method

• Efficient for high resolution voxlization• Not very efficient for large model size

Analysis – the major cost lies in computing the depth range for each pixel – the cost is much lower for inner pixels than for boundary pixels – most of the pixels are inner pixels when the resolution is high

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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

Application to Collision Detection

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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Contents


The Main Idea



Conclusions & Future WorkConclusions & Future WorkConclusions & Future WorkConclusions & Future Work

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Conclusions

Technical contributions

1

The ideaWe propose the idea of conservative vox-lization.

2

Algorithm• Fully implemented in the GPU• Conservative• Efficient• Low memory cons-umption• Suitable for def-ormable models

3

ApplicationWe demonstrate the application of our algorithm in collision detection of complex models.

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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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[email protected]

C ONSERVATIVE V OXELIZATION

Documents

depth values

minimal depth

depth rangefull

pixel vertices

pixel center

intersection region

colliding pixels

multiple voxels