Surface Deformations Driven by Vector-Valued 1-Forms

Abstract

We formulate the problem of surface deformations as the integration in the least square sense of a discrete vectorvalued 1-forms obtained as the result of applying smooth stretching and rotation fields to the discrete differential of the 0-form defined by the vertex coordinates of a polygon mesh graph. Simple algorithms result from this formulation, which reduces to the solution of sparse linear systems. The method handles large angle rotations in one step and is invariant to rotations, translations, and scaling. We also introduce the integration of 1-forms along spanning trees as a heuristic to speed up the convergence of iterative solvers. Keywords-triangle meshes; differential forms; gradient domain; algorithms; discrete differential geometry; surface deformation

DOI: 10.1109/SMI.2010.36

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Cite this paper

@inproceedings{Taubin2010SurfaceDD, title={Surface Deformations Driven by Vector-Valued 1-Forms}, author={Gabriel Taubin and Çagatay Demiralp}, booktitle={Shape Modeling International}, year={2010} }