Feature-Based Mesh Editing

Qingnan Zhou 1

Tino Weinkauf 1,2

Olga Sorkine 1,3

1 NYU2 MPII Saarbrücken3 ETH Zürich

Deformation

DeformationDeformation

Deformation

Detail Preserving

Detail Preserving

[Sorkine et al. ARAP Surface Modeling, SGP 07]

Detail Preserving

Detail Preserving

Deformation

Structure PreservingStructure

Preserving

[Gal et al., iWires, SIGGRAPH 2009]

Deformation

Detail Preserving

Detail Preserving

Structure PreservingStructure

Preserving

Feature Preserving

Feature Preserving

Original

[Sorkine et al. ARAP Surface Modeling, SGP 07] Our result

Feature-Based Mesh Editing

Input Feature Extraction Result of feature editing

Features• What are features?

– In words, features are where surface normal changes abruptly.

– In pictures:

Features• What are features?

[Hildebrandt et al., Smooth Feature Lines, SGP05]

– In math: local minimum and maximum of principle curvatures in their corresponding directions.

Local maximum

Cross Section

Features• What are features?

[Hildebrandt et al., Smooth Feature Lines, SGP05]

– In math: local minimum and maximum of principle curvatures in their corresponding directions.

– Zeros of emax that satisfy the following (similar constraints apply to emin)

Extremality:

Salientconstraints:

Features• What are features?

– In practice:

Input Valley lines (blue)Zeros of emin

Ridge lines (yellow)Zeros of emax

Feature-Preserving Optimization• Idea: if curvature values are preserved, so are

their local minima and maxima, and so are the features, right?

Feature-Preserving Optimization• Idea: if curvature values are preserved, so are

their local minima and maxima, and so are the features, right?

– Answer: possibly.

– Concern 1: what about principle curvature directions?

– Concern 2: non-convex energy?

Feature-Preserving Optimization

Energy Formulation:

Feature-Preserving Optimization

Energy Formulation:

Curvature Preservation:

Feature-Preserving Optimization

Energy Formulation:

Conformality:

Feature-Preserving Optimization

Energy Formulation:

Positional constraint:

Feature Manipulation• Feature-preserving deformation:

[Sorkine et al. ARAP Surface

Modeling, SGP 07]

Our result: original curvature preservedOriginal

Feature Manipulation• Feature-preserving deformation:

[Sorkine et al. ARAP Surface

Modeling, SGP 07]

Our result: original curvature preservedOriginal

Feature Manipulation• Feature smoothing and sharpening:

Original Features Our result

Feature Manipulation• Feature smoothing and sharpening:

Original Features smoothed

Original

Features sharpened

Feature Manipulation• Feature creation:

Original Our result

Feature Manipulation• Feature creation:

Original User drawn featuresRed: ridgeBlue: valley

Our result

Summary• We have presented a feature-based deformation

system.

• Our experiments give optimistic results.

• Future work:– Check for conflicting constraints.– Theoretic support of the idea.– Try meshes with less pronounced features.