Displaced Subdivision Surfaces

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

2
Triangle Meshes

• Interactive animation
• Adaptive rendering
• Compact storage

Dataset provided by Cyberware
3
Scalable Algorithms

• Multiresolution now well established

subdivision surfaces
4
Subdivision Surfaces

• Smooth with arbitrary topology
• No stitching of patches
• Easy Implementation
• Simple subdivision rules
• Level-of-detail rendering
• Uniform or adaptive subdivision

5
Our Approach
DSS Smooth Domain ? Scalar Disp Field
Displaced Subdivision surface
Control mesh
Domain Surface
6
Representation Overview
Piecewise-regular mesh of scalar displacement
sampling pattern
Control mesh
7
Advantages 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

8
Conversion Algorithm

• Control mesh creation
• Control mesh optimization
• Scalar displacement computation
• Attribute resampling

9
Control Mesh Creation
Mesh Simplification
Normal Cone Constraint
Original Mesh
Initial Control Mesh
Garland 97 Surface simplification using quadric
error metrics
10
Normal Cone Constraint

allowable normals

on Gauss sphere

11
Tracking Correspondences

• Control Mesh Creation
• mesh simplification

11776 faces
120 faces
Lee 98 Multiresolution Adaptive
Parameterization of Surfaces
12
Conversion Process
1. Obtain an initial control mesh by simplifying
the original mesh. 2.Globally optimize the
control mesh vertices. 3.Sample the displacement
map and computr the signed displacement .
13
Control Mesh Creation
Mesh Simplification
Normal Cone Constraint
Original Mesh
Initial Control Mesh
14
Control Mesh Optimization
Global Optimization
Initial Control Mesh
Optimized Control Mesh
15
Scalar Displacement Computation
Scalar Displacement Field
Smooth Domain Surface
Displaced Subdivision Surface
16
Attribute Resampling
DSS With Scalar Displacement Field
DSS with Resampled Texture
Original mesh
17
Applications

• Editing
• Animation
• Bump mapping
• Adaptive tessellation
• Compression

18
Editing
19
Animation
Polyhedral Domain Surface (e.g. Gumhold-Hüttner
99)
Smooth Domain Surface (DSS)
20
Animation
21
Bump Mapping

• Explicit geometry
  Bump map

134,656 faces
8,416 faces
526 faces
Blinn 78 Simulation of wrinkled surfaces
22
Adaptive Tessellation
23
Compression
Scalar Displacement field
Quantizer Entropy Coder
M0
Quantizer Entropy Coder
Delta encoding with Linear Prediction
M1
Bit Allocation
Quantizer Entropy Coder
Mk
24
Compression (Venus)
Venus Raw Data 1,800,032 bytes
25
Compression (Dinosour)
26
Conclusion

• DSS Representation
• Unified representation
• Simple subdivision rules
• Analytic surface properties
• Applications
• Editing
• Animation
• Bump mapping
• Adaptive tessellation
• Compression

27
Timings and Results
Scalar field creation
Simplification
Input size
Base
Optimization
Dataset
triangles
domain
(mins)
(mins)
(mins)
triangles
Armadillo
1306
210,944
61
25
2.5
Venus
748
28
11
2
100,000
1.3
Bunny
69,451
526
19
12
4.6
43
342,138
1564
115
Dinosaur
28
over