Large Mesh Deformation Using the

Volumetric Graph Laplacian

Large Mesh Deformation Using the

Volumetric Graph Laplacian

Kun Zhou Jin Huang* John Snyder^ Xinguo Liu

Hujun Bao* Baining Guo Heung-Yeung Shum

Microsoft Research Asia

*Zhejiang University

^Microsoft Research

Kun Zhou Jin Huang* John Snyder^ Xinguo Liu

Hujun Bao* Baining Guo Heung-Yeung Shum

Microsoft Research Asia

*Zhejiang University

^Microsoft Research

Mesh DeformationMesh Deformation

• Smooth geometry

– Freeform deformation [Barr84, Singh98, Bendels03]

– Energy minimization [Welch94, Taubin95, Botsch04]

• Detailed geometry

– Multi-resolution editing [Zorin97, Kobbelt98, Guskov99]

– Differential domain methods:

• Poisson mesh editing [Yu04]

• Laplacian surface editing [Sorkine04, Lipman05]

Large Mesh DeformationLarge Mesh Deformation

• Challenge to existing techniques

– Local self-intersection, unnatural volume change

Bending Twisting

Large Mesh DeformationLarge Mesh Deformation

• Challenge to existing techniques

– Local self-intersection, unnatural volume change

Poisson Mesh Editing VGL

Large Mesh DeformationLarge Mesh Deformation

• Challenge to existing techniques

– Local self-intersection, unnatural volume change

Poisson Mesh Editing VGL

Large Deformation: Why Difficult?Large Deformation: Why Difficult?

• Differential domain methods [Yu04, Sorkine04]

Uniform error distribution using least-squares optimization

Only surface details, volume ignored

• Displacement volumes [Botsch03]

Volumetric constraints

Iterative relaxation produces artifacts

Solution: Volumetric Constraints &Least-Squares Optimization

Poisson Mesh EditingPoisson Mesh Editing

Step 1: Specify control curve Step 2: Edit control curve

F

F’

Poisson Mesh EditingPoisson Mesh Editing

Step 3: Propagate local frame transformations

Step 4: Solve Poisson equation

Surface Details & LaplacianSurface Details & Laplacian

N(i)j

jjiiiM pwp)(pL ,-

Surface Details & LaplacianSurface Details & Laplacian

iiiM

ppL

i

2)(min

Surface Details & LaplacianSurface Details & Laplacian

iiiM

ppL

i

2)(min

Volumetric Details & LaplacianVolumetric Details & Laplacian

N(i)j

jjiiiG pwp)(pL ,-

Volumetric Details & LaplacianVolumetric Details & Laplacian

iiiG

ppL

i

2)(min

Quadric Energy FunctionQuadric Energy Function

k

kkGj

jji

iiM δpLqppL222

)()(

Surface Details Volumetric DetailsPosition Constraints

iiiGiM pLpL )( )(

jj qp

kkG pL )(

bxA bAx 1

1. Construct the volumetric graph

2. Compute Laplacian coordinates

3. Compute and apply local transformation

4. Solve the sparse linear system

Deformation Using VGLDeformation Using VGL

kkk δTδ iii T

Volumetric Graph ConstructionVolumetric Graph Construction

Volumetric Graph ConstructionVolumetric Graph Construction

• Construct an inner shell

Volumetric Graph ConstructionVolumetric Graph Construction

• Embed both the mesh and shell in a lattice

Volumetric Graph ConstructionVolumetric Graph Construction

• Build edge connections

Volumetric Graph ConstructionVolumetric Graph Construction

• Simplify and smooth the graph

Not Tetrahedral Mesh

Deformation ComparisonDeformation Comparison

Laplacian surface[Sorkine04]

Poisson mesh [Yu04]

VGL

Poisson mesh [Yu04]

Laplacian surface[Sorkine04]

Deformation ComparisonDeformation Comparison

VGL

Deformation ComparisonDeformation Comparison

Original model Poisson mesh VGL

Deformation InterfaceDeformation Interface

• 3D space manipulation [Yu04]

– Tedious and require artistic skill

• 2D sketch-based interface

– Modeling: Teddy [Igarashi99]

– Editing: [Zelinka04, Kho05, Nealen05]

“Teddy-like” deformation:intuitive and easy to use

2D Sketch-based Deformation2D Sketch-based Deformation

Deformation RetargetingDeformation Retargeting

Deformation RetargetingDeformation Retargeting

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ConclusionConclusion

• Volumetric graph Laplacian (VGL)

– Volumetric constraints

– Least squares minimization

– No tetrahedral mesh construction

• 2D sketch-based deformation system

– “Teddy-like” deformation system

– Cartoon deformation retargeting

Future WorkFuture Work

• Anchor-based deformation

• Dynamic connectivity

• Automatic contour tracking

AcknowledgementAcknowledgement

• Cartoons from Disney Feature Animation and Dongyu Cao

• 3D models from Stanford, MIT, Cyberware

• Xin Sun, Jianwei Han

• Steve Lin, Bo Zhang

• NSFC and 973 Program of China

Thank You !Thank You !