Manifold Dual Contouring - ecology...
Transcript of Manifold Dual Contouring - ecology...
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Scott Schaefer
Manifold Dual Contouring
Rice University
Tao Ju
Joe Warren
Washington University
Texas A&M University
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Implicit Modeling
0)( xf
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Dual Contouring[Ju et al 2002]
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Dual Contouring[Ju et al 2002]
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Dual Contouring[Ju et al 2002]
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Sharp Features
[Garland, Heckbert 1998]
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Adaptive Surface Extraction
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Problems with Dual Contouring
Non-Manifold Geometry Conservative Topology Test
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Previous Work
DC with multiple surface components [Varadhan et al 2003], [Ashida et al 2003], [Zhang et al
2004], [Nielson 2004], [Schaefer et al 2004]
Vertex Clustering [Rossignac et al 1993], [Low et al 1997], [Luebke 1997],
[Lindstrom 2000], [Brodsky et al 2000], [Shaffer et al
2001], [Kanaya et al 2005]
Topology-Preserving Contour Simplification [Cohen et al 1996], [Ju et al 2002], [Lewiner et al 2004]
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Manifold Assumption
Original Data MC DC DMC
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Vertex Clustering
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Vertex Clustering
Not sufficient to prevent non-manifold geometry!
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Topological Safety
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Topological Safety
2S
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Topological Safety
2C
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Topological Safety
A surface is a 2-manifold, if for every vertex
The number of intersections of Sv with the
edges of each face of Cv is either 0 or 2
Sv is equivalent to a disk with a single,
connected boundary
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Topological Safety
A surface is a 2-manifold, if for every vertex
The number of intersections of Sv with the
edges of each face of Cv is either 0 or 2
1)()()()( vvvv SFSESVS
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Topological Safety
A surface is a 2-manifold, if for every vertex
The number of intersections of Sv with the
edges of each face of Cv is either 0 or 2
1)()()()( vvvv SFSESVS
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
0k
vkS
0k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
2k
vkS
5k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
4k
vkS
10k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
5k
vkS
14k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
6k
vkS
18k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
7k
vkS
24k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
8k
vkS
30k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
9k
vkS
33k
vkSe
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Recursive Safety Computation
4
)( kv
k
Se
k
vv SS
10k
vkS
36k
vkSe
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Results
Uncollapsed Only Vertex
Clustering
Manifold
Safety Test
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Results
476184 142570 62134 14335 2738 78
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Comparison
Original Shape Dual Contouring Our Method
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Comparison
Original Shape Dual Contouring Extended
Dual Contouring
Our Method
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Performance
Octree
Depth
Base
Polys
Clustering
w/o Manifold
Test
Clustering
w/ Manifold
Test
Poly
Generation
Simplified
Polys
Spring 6 28740 0.254 0.259 0.06 1042
Spider
Web
7 44784 0.459 0.465 0.10 3672
Queen 9 476184 5.58 5.76 1.12 78
Dragon 9 611476 6.65 6.71 1.42 9944
Thai
Statue
9 878368 10.89 10.99 2.01 30002
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Conclusions
Vertex clustering algorithm that allows
multiple components per cell in DC
Simple, recursive test for vertex clustering
that guarantees manifold geometry
3.3%100%