TY - GEN

T1 - As-Rigid-As-Possible Shape Interpolation

AU - Alexa, Marc

AU - Cohen-Or, Daniel

AU - Levin, David

N1 - Publisher Copyright:
© ACM 2000.

PY - 2000/7/1

Y1 - 2000/7/1

N2 - 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 boundary and 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.

AB - 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 boundary and 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.

KW - compatible triangulation

KW - shape blending

KW - vertex path problem

UR - http://www.scopus.com/inward/record.url?scp=85160313850&partnerID=8YFLogxK

U2 - 10.1145/344779.344859

DO - 10.1145/344779.344859

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AN - SCOPUS:85160313850

T3 - SIGGRAPH 2000 - Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques

SP - 157

EP - 164

BT - SIGGRAPH 2000 - Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques

PB - Association for Computing Machinery, Inc

T2 - 27th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2000

Y2 - 23 July 2000 through 28 July 2000

ER -