1

Displaced Subdivision SurfacesDisplaced Subdivision Surfaces

Aaron LeePrincetonUniversity

Henry MoretonNvidia

Hugues HoppeMicrosoftResearch

2

Triangle MeshesTriangle Meshes

Interactive animation Adaptive rendering Compact storage Transmission

Dataset provided by Cyberware

3

Scalable AlgorithmsScalable Algorithms

Multiresolution now well established

subdivision surfacesmesh simplification

4

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

5

Displacement MappingDisplacement Mapping

Scalar/Vector displacement Cook 84 RenderMan

Mesh approximation Krishnamurthy-Levoy 96, …

Hardware implementation Gumhold-Hüttner 99, …

6

Our ApproachOur Approach

Control mesh Domain Surface Displaced Subdivision

surface

DSS = Smooth Domain Scalar Disp Field

7

Representation OverviewRepresentation Overview

Control mesh Piecewise-regular mesh of scalar displacement sampling pattern

8

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

9

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

11

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