Shape Deformation Reporter: Zhang, Lei 5/30/2006

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.

Vector Field Based Shape Deformations Wolfram von Funck, Holger Theisel, Hans-Peter Seidel MPI Informatik

Basic Model Moving vertex along the deformation orbit – defined by the path lines of a vector field v.

Path Line of Vector Field X(t 0 ) X(t) Given a time-dependent vector field V(X, t), a Path Line in space is X(t): t0t0 t OR

Vector Field Selection Deformation Request: No self-intersection Volume-preserving Details-preserving Smoothness of shape in deformation Divergence-free Vector Field: V=(V 1, V 2, V 3 )

Construction of V Divergence-free p, q: two scalar field 2D space: 3D space:

Vector Field for Special Deformation Constant Vector Field V : translation Deformation

Vector Field for Special Deformation Linear Vector Field V : rotation Deformation

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

Piecewise Field for Deformation Inner region Intermediate region Outer region

Piecewise Field for Deformation if

Deformation Tools Translation: constant vector field

Deformation Tool Rotation: linear vector field

Path Line Computation Runge-Kutta Integration For each vertex v(x, t i ), integrating vector field above to v(x’, t i+1 )

Remeshing Edge Split

Examples Demo

Examples

Performance Benchmark Test AMD 2.6GHz 2 GB RAM GeForce 6800 GT GPU

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

A Fast Multigrid Algorithm for Mesh Deformation Lin Shi, Yizhou Yu, Nathan Bell, Wei-Wen Feng University of Illinois at Urbana-Champaign

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.

Discrete Form (SIG ’ 05) First Discrete Form

Discrete Form (SIG ’ 05) Second Discrete Form

Local Frame (SIG ’ 05) Discrete Frame at each vertex forms a right-hand orthonormal basis.

First Pass (EG ’ 05) Harmonic guidance for local frame Boundary conditions: 1: edited vertex 0: fixed vertex Scaling Rotation 1 0

Second Pass (SIG ’ 05) Solving vertex position

Second Pass Solving vertex position “Normal Equation”

Some Results

Computation First Pass Second Pass Multigrid Method

defect equation coarsest level

Performance

Conclusion Computation Method for large mesh

Editing Arbitrary Deforming Surface Animations S. Kircher, M. Garland University of Illinois at Urbana-Champaign

Problem Deforming Surface Editing Surface

Pyramid Scheme Quadric Error Metric M. Garland and P. S. Heckbert. Surface simplification using quadric error metrics. SIGGRAPH’97.

Pyramid Scheme CoarseFine 2nd-order divided difference Detail vector Construct by and adding detail vectors for level k. Sig’99

Adaptive Transform

is generated from by improving its error with respect to Adaptive Transform Multilevel Meshes (Sig ’ 05) Reclustering Swap

Basis Smoothing Blockification Vertex Teleportation PRE-processing: Time-varying multiresolution transform for a given animation sequence.

Editing Tool Direct Manipulation level k level 0

Editing Tool Direct Manipulation

Editing Tool Direct Manipulation

Multiresolution Embossing Multiresolution set of Edit

Conclusion Multiresolution Edit

The End