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As-rigid-as-possible shape interpolation (2000)
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BibTeX
@MISC{Alexa00as-rigid-as-possibleshape,
author = {Marc Alexa and Daniel Cohen-or and David Levin},
title = {As-rigid-as-possible shape interpolation },
year = {2000}
}
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Abstract
We present an object-space morphing technique that blends the interiors of given two- or three-dimensional shapes rather than their boundaries. The morph is rigid in the sense that local volumes are least-distorting as they vary from their source to target configurations. Given a boundary vertex correspondence, the source and target shapes are decomposed into isomorphic simplicial complexes. For the simplicial complexes, we find a closed-form expression allocating the paths of both boundaryand interior vertices from source to target locations as a function of time. Key points are the identification of the optimal simplex morphing and the appropriate definition of an error functional whose minimization defines the paths of the vertices. Each pair of corresponding simplices defines an affine transformation, which is factored into a rotation and a stretching transformation. These local transformations are naturally interpolated over time and serve as the basis for composing a global coherent least-distorting transformation.
Keyphrases
as-rigid-as-possible shape interpolation boundary vertex correspondence target shape local transformation three-dimensional shape local volume global coherent least-distorting transformation key point object-space morphing technique boundaryand interior vertex isomorphic simplicial complex affine transformation simplicial complex stretching transformation optimal simplex morphing appropriate definition closed-form expression
