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Discrete Critical Values: a General Framework for Silhouettes Computation

Frédéric Chazal 1, * André Lieutier Nicolas Montana
* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : Many shapes resulting from important geometric operations in industrial applications such as Minkowski sums or volume swept by a moving object can be seen as the projection of higher dimensional objects. When such a higher dimensional object is a smooth manifold, the boundary of the projected shape can be computed from the critical points of the projection. In this paper, using the notion of polyhedral chains introduced by Whitney, we introduce a new general framework to define an analogous of the set of critical points of piecewise linear maps defined over discrete objects that can be easily computed. We illustrate our results by showing how they can be used to compute Minkowski sums of polyhedra and volumes swept by moving polyhedra.
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Submitted on : Thursday, January 10, 2013 - 2:35:02 PM
Last modification on : Friday, February 23, 2018 - 2:20:06 PM

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Frédéric Chazal, André Lieutier, Nicolas Montana. Discrete Critical Values: a General Framework for Silhouettes Computation. Computer Graphics Forum, Wiley, 2009, 28 (5), pp.1509-1518. ⟨10.1111/j.1467-8659.2009.01527.x⟩. ⟨hal-00772400⟩

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