Shape Deformation

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Shape Deformation

• Reporter Zhang, Lei
• 5/30/2006

2
Stuff

• Vector Field Based Shape Deformation (VFSD)
• Multigrid Alogrithm for Deformation
• Edit Deforming Surface Animation
• Subspace Gradient Domain Mesh Deformation
• J. Huang, X. H. Shi, X. G. Liu, K. Zhou, L. Y.
  Wei, S. H. Teng, H. J. Bao, B. G. Guo and H. Y.
  Shum.

3
Vector Field Based Shape Deformations

• Wolfram von Funck, Holger Theisel, Hans-Peter
  Seidel
• MPI Informatik

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Basic Model
Moving vertex along the deformation orbit
defined by the path lines of a vector field v.
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Path Line of Vector Field
X(t)
X(t0)
t0
t
Given a time-dependent vector field V(X, t), a
Path Line in space is X(t)
OR
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Vector Field Selection

• Deformation Request
• No self-intersection
• Volume-preserving
• Details-preserving
• Smoothness of shape in deformation
• Divergence-free Vector Field V(V1, V2, V3)

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Construction of V

• Divergence-free

p, q two scalar field
2D space
3D space
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Vector Field for Special Deformation

• Constant Vector Field V translation

Deformation
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Vector Field for Special Deformation

• Linear Vector Field V rotation

Deformation
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Piecewise Field for Deformation

• Deformation for a selected region
• Define piecewise continuous field

• Inner region V
• Outer region zero
• Intermediate region blending

Region specified by an implicit function And
thresholds
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Piecewise Field for Deformation
Inner region
Outer region
Intermediate region
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Piecewise Field for Deformation
if
if
if
if
if
if
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Deformation Tools

• Translation constant vector field

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Deformation Tool

• Rotation linear vector field

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Path Line Computation
Runge-Kutta Integration
For each vertex v(x, ti), integrating vector
field above to v(x, ti1)
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Remeshing
Edge Split
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Examples

• Demo

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Examples
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Performance

• Benchmark Test

AMD 2.6GHz 2 GB RAM GeForce 6800 GT GPU
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Conclusion

• Embeded in Vector Field
• FFD
• Parallel processing
• Salient Strength
• No self-intersection
• Volume-preserving
• Details-preserving
• Smoothness of shape in deformation

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A Fast Multigrid Algorithm for Mesh Deformation

• Lin Shi, Yizhou Yu, Nathan Bell, Wei-Wen Feng
• University of Illinois at Urbana-Champaign

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Basic Model

• Two-pass pipeline
• Local Frame Update
• Vertex Position Update
• Multigrid Computation Method

R. Zayer, C. Rossl, Z. Karni and H. P. Seidel.
Harmonic Guidance for Surface Deformation. EG2005.
Y. Lipman, O. Sorkine, D. Levin and D. Cohen-Or.
Linear rotation-invariant coordinates for meshes.
Siggraph2005.
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Discrete Form (SIG05)
First Discrete Form
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Discrete Form (SIG05)
Second Discrete Form
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Local Frame (SIG05)

• Discrete Frame at each vertex

forms a right-hand orthonormal basis.
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First Pass (EG05)

• Harmonic guidance for local frame

Boundary conditions 1 edited vertex 0 fixed
vertex
1
0

• Scaling
• Rotation

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Second Pass (SIG05)

• Solving vertex position

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Second Pass

• Solving vertex position

Normal Equation
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Some Results
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Computation

• First Pass
• Second Pass

Multigrid Method
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Multigrid Method
defect equation
coarsest level
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Performance
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Performance
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Conclusion

• Computation Method for large mesh

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Editing Arbitrary Deforming Surface Animations

• S. Kircher, M. Garland
• University of Illinois at Urbana-Champaign

36
Problem
Deforming Surface
Editing Surface
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(No Transcript)
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Pyramid Scheme

• Quadric Error Metric

M. Garland and P. S. Heckbert. Surface
simplification using quadric error metrics.
SIGGRAPH97.
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Pyramid Scheme
Detail vector
Coarse
Fine
2nd-order divided difference
Sig99
Construct by and adding detail
vectors for level k.
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Adaptive Transform
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Adaptive Transform

• Multilevel Meshes (Sig05)

Reclustering
is generated from by improving its
error with respect to
Swap
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• Basis Smoothing
• Blockification
• Vertex Teleportation

PRE-processing Time-varying multiresolution
transform for a given animation sequence.
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Editing Tool

• Direct Manipulation

level 0
level k
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Editing Tool

• Direct Manipulation

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Editing Tool

• Direct Manipulation

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Multiresolution Embossing
Multiresolution set of Edit
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Conclusion

• Multiresolution Edit

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The End