1 displaced subdivision surfaces aaron lee princeton university henry moreton nvidia hugues hoppe...
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Displaced Subdivision SurfacesDisplaced Subdivision Surfaces
Aaron LeePrincetonUniversity
Henry MoretonNvidia
Hugues HoppeMicrosoftResearch
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Triangle MeshesTriangle Meshes
Interactive animation Adaptive rendering Compact storage Transmission
Dataset provided by Cyberware
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Scalable AlgorithmsScalable Algorithms
Multiresolution now well established
subdivision surfacesmesh simplification
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Subdivision SurfacesSubdivision Surfaces
Smooth (C1) with arbitrary topology No stitching of patches
Easy Implementation Simple subdivision rules
Level-of-detail rendering Uniform or adaptive subdivision
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Displacement MappingDisplacement Mapping
Scalar/Vector displacement Cook 84 RenderMan
Mesh approximation Krishnamurthy-Levoy 96, …
Hardware implementation Gumhold-Hüttner 99, …
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Our ApproachOur Approach
Control mesh Domain Surface Displaced Subdivision
surface
DSS = Smooth Domain Scalar Disp Field
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Representation OverviewRepresentation Overview
Control mesh Piecewise-regular mesh of scalar displacement sampling pattern
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Advantages of DSSAdvantages of DSS
Intrinsic parameterization Governed by a subdivision surface No storage necessary Significant computation efficiency Capture detail as scalar displacement
Unified representation Same sampling pattern and subdivision
rules for geometry and scalar displacement field
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Analytic PropertiesAnalytic Properties C1 continuous everywhere except
at extraordinary vertices Surface normals are easy to
evaluatenDPS ˆ
vu PPn
vus SSn
vvvv
uuuu
nDnDPS
nDnDPS
ˆˆ
ˆˆ
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Evaluation of derivativesEvaluation of derivatives
x/6 x/6
P u P v
1 2
-1 0 1
-1-2
P
x/12
1 1
1 6 1
11
2 1
1 0 -1
-2-1
x/2
1 0
0 -2 0
10
0 1
0 -2 0
01
1 1
-1 -2 -1
11x/1x/1
u v
P vv P uvP uu
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Conversion AlgorithmConversion Algorithm
Control mesh creationControl mesh optimizationScalar displacement computationAttribute resampling
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Control Mesh CreationControl Mesh Creation
Mesh Simplification
Original Mesh Initial Control Mesh
[Garland 97] Surface simplification using quadric error metrics
Normal ConeConstraint
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Normal Cone Constraint Normal Cone Constraint
allowable normals on Gauss sphere
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Tracking CorrespondencesTracking Correspondences
Control Mesh Creation mesh simplification
11776 faces 120 faces
[Lee 98] Multiresolution Adaptive Parameterization of Surfaces
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Control Mesh CreationControl Mesh Creation
Mesh Simplification
Original Mesh Initial Control Mesh
Normal ConeConstraint
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Control Mesh OptimizationControl Mesh Optimization
Initial Control Mesh Optimized Control Mesh
GlobalOptimization
[Hoppe 94] Piecewise smooth surface reconstruction
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Scalar Displacement ComputationScalar Displacement Computation
Scalar Displacement Field
Smooth Domain Surface Displaced Subdivision Surface
[Gottschalk, Lin and Manocha 96] OBB-tree
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Attribute ResamplingAttribute Resampling
Original mesh DSS With ScalarDisplacement Field
DSS with Resampled Texture
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ApplicationsApplications
Editing Animation Bump mapping Adaptive tessellation Compression
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EditingEditing
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AnimationAnimation
Smooth Domain Surface(DSS)
Polyhedral Domain Surface(e.g. Gumhold-Hüttner 99)
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Bump MappingBump Mapping
134,656 faces 8,416 faces 526 faces
Explicit geometry Bump map
[Blinn 78] Simulation of wrinkled surfaces
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Adaptive TessellationAdaptive Tessellation
Threshold
4.0 1.3
#Triangles
6,376 22,190
L2 error 0.13 % 0.05 %
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VIDEOVIDEO
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CompressionCompression
Delta encoding
withLinear
Prediction
Scalar Displacement
field
M0
M1
Mk
QuantizerEntropy Coder
QuantizerEntropy Coder
QuantizerEntropy Coder
Bit Allocation
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Compression (Venus)Compression (Venus)
Original Simplified DSS Compression Ratio
Mesh Info
#V=5000
2 #F=1000
00
#V=1000
2 #F=20000
#V=376 #F=748
(sub 4 times)
23 bits L2
0.0014%
0.027% 0.028%
12 bits L2
0.014% 0.03% 0.03%
8 bits L2 0.21% 0.21% 0.15%[Venus Raw Data] 1,800,032 bytesIBM VRML Compressed Binary Format (Draft 4 Implementation)
Kbytes346 75 17 108
Kbytes140 33 16 115
Kbytes69 18 4 410
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ConclusionConclusionDSS Representation:
Unified representation Simple subdivision rules Analytic surface properties
Applications Editing Animation Bump mapping Adaptive tessellation Compression
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Q & AQ & A
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Timings and ResultsTimings and Results
DatasetInput size#triangles
Armadillo 210,944
Venus 100,000
Bunny
# Basedomain
triangles
69,451
Dinosaur 342,138
1306
748
526
1564
Simplification
(mins)
61
28
19
115
Optimization
(mins)
25
11
12
43
Scalar field creation(mins)
2.5
2
1.3
4.6
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DSS Vs Normal MeshesDSS Vs Normal Meshes
+ Single level displacement map Hardware implementation Easy conversion to bump map
+ Displacements strictly scalar No extraordinary vector
displacements
– Less compression Multilevel displacement map