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Geometric modeling in shape space

Kilian, M; Mitra, NJ; Pottmann, H; (2007) Geometric modeling in shape space. In: ACM TRANSACTIONS ON GRAPHICS. (pp. ? - ?). ASSOC COMPUTING MACHINERY

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We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes - triangular meshes or more generally straight line graphs in Euclidean space - are treated as points in a shape space. We introduce useful Riemannian metrics in this space to aid the user in design and modeling tasks, especially to explore the space of (approximately) isometric deformations of a given shape. Much of the work relies on an efficient algorithm to compute geodesics in shape spaces; to this end, we present a multi-resolution framework to solve the interpolation problem - which amounts to solving a boundary value problem - as well as the extrapolation problem - an initial value problem - in shape space. Based on these two operations, several classical concepts like parallel transport and the exponential map can be used in shape space to solve various geometric modeling and geometry processing tasks. Applications include shape morphing, shape deformation, deformation transfer, and intuitive shape exploration.

Type: Proceedings paper
Title: Geometric modeling in shape space
Event: ACM SIGGRAPH 2007 Conference
Location: San Diego, CA
Dates: 2007-08-05 - 2008-08-09
DOI: 10.1145/1239451.1239515
Keywords: Riemannian geometry, shape space, geodesic, isometric, deformation, parallel transport, shape exploration., GEODESIC PATHS, MESHES, PARAMETERIZATION, DEFORMATION, MANIFOLDS, METRICS
URI: http://discovery.ucl.ac.uk/id/eprint/1328002
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