Multi-Scale Geometry Interpolation

Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mes...

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Veröffentlicht in:Computer graphics forum Jg. 29; H. 2; S. 309 - 318
Hauptverfasser: Winkler, T., Drieseberg, J., Alexa, M., Hormann, K.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford, UK Blackwell Publishing Ltd 01.05.2010
Schlagworte:
Affine transformations
Computer graphics
Curvature
Finite element method
Geometry
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Hierarchy and geometric transformations
Image processing systems
Interpolation
Matching
Mathematical analysis
Preserves
Systems development
Transformations
ISSN:0167-7055, 1467-8659
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Zusammenfassung:Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mesh, model desired interpolations of the affine transformations, and then optimize vertex positions to conform with the desired transformations. However, the local interpolation of the rotational part is non‐trivial for more than two input configurations and ambiguous if the meshes are deformed significantly. We propose a solution to the vertex interpolation problem that starts from interpolating the local metric (edge lengths) and mean curvature (dihedral angles) and makes consistent choices of local affine transformations using shape matching applied to successively larger parts of the mesh. The local interpolation can be applied to any number of input vertex configurations and due to the hierarchical scheme for generating consolidated vertex positions, the approach is fast and can be applied to very large meshes.
Bibliographie:ArticleID:CGF1600
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01600.x