Discrete Critical Values: a General Framework for Silhouettes Computation

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dc.contributor.authorChazal, F.en_US
dc.contributor.authorLieutier, A.en_US
dc.contributor.authorMontana, N.en_US
dc.date.accessioned2015-02-23T15:43:33Z
dc.date.available2015-02-23T15:43:33Z
dc.date.issued2009en_US
dc.description.abstractMany 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.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume28en_US
dc.identifier.doi10.1111/j.1467-8659.2009.01527.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1509-1518en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2009.01527.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleDiscrete Critical Values: a General Framework for Silhouettes Computationen_US
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SGP09: Eurographics Symposium on Geometry Processing