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As-rigid-as-possible shape interpolation (2000)

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by Marc Alexa , Daniel Cohen-or , David Levin
Citations:187 - 9 self
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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   

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