1 Displaced Subdivision Surfaces Aaron Lee Princeton University Henry Moreton Nvidia Hugues Hoppe Microsoft Research.

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

10

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

12

Control Mesh CreationControl Mesh Creation

Mesh Simplification

Original Mesh Initial Control Mesh

[Garland 97] Surface simplification using quadric error metrics

Normal ConeConstraint

13

Normal Cone Constraint Normal Cone Constraint

allowable normals on Gauss sphere

14

Tracking CorrespondencesTracking Correspondences

Control Mesh Creation mesh simplification

11776 faces 120 faces

[Lee 98] Multiresolution Adaptive Parameterization of Surfaces

15

Control Mesh CreationControl Mesh Creation

Mesh Simplification

Original Mesh Initial Control Mesh

Normal ConeConstraint

16

Control Mesh OptimizationControl Mesh Optimization

Initial Control Mesh Optimized Control Mesh

GlobalOptimization

[Hoppe 94] Piecewise smooth surface reconstruction

17

Scalar Displacement ComputationScalar Displacement Computation

Scalar Displacement Field

Smooth Domain Surface Displaced Subdivision Surface

[Gottschalk, Lin and Manocha 96] OBB-tree

18

Attribute ResamplingAttribute Resampling

Original mesh DSS With ScalarDisplacement Field

DSS with Resampled Texture

19

ApplicationsApplications

Editing Animation Bump mapping Adaptive tessellation Compression

20

EditingEditing

21

AnimationAnimation

Smooth Domain Surface(DSS)

Polyhedral Domain Surface(e.g. Gumhold-Hüttner 99)

22

Bump MappingBump Mapping

134,656 faces 8,416 faces 526 faces

Explicit geometry Bump map

[Blinn 78] Simulation of wrinkled surfaces

23

Adaptive TessellationAdaptive Tessellation

Threshold

4.0 1.3

#Triangles

6,376 22,190

L2 error 0.13 % 0.05 %

24

VIDEOVIDEO

25

CompressionCompression

Delta encoding

withLinear

Prediction

Scalar Displacement

field

M0

M1

Mk

QuantizerEntropy Coder

QuantizerEntropy Coder

QuantizerEntropy Coder

Bit Allocation

26

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

27

ConclusionConclusionDSS Representation:

Unified representation Simple subdivision rules Analytic surface properties

Applications Editing Animation Bump mapping Adaptive tessellation Compression

28

Q & AQ & A

29

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

30

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