A Geometric Construction of Coordinates for Convex Polyhedra using Polar Duals

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dc.contributor.authorJu, Taoen_US
dc.contributor.authorSchaefer, Scotten_US
dc.contributor.authorWarren, Joeen_US
dc.contributor.authorDesbrun, Mathieuen_US
dc.contributor.editorMathieu Desbrun and Helmut Pottmannen_US
dc.date.accessioned2014-01-29T09:31:12Z
dc.date.available2014-01-29T09:31:12Z
dc.date.issued2005en_US
dc.description.abstractA fundamental problem in geometry processing is that of expressing a point inside a convex polyhedron as a combination of the vertices of the polyhedron. Instances of this problem arise often in mesh parameterization and 3D deformation. A related problem is to express a vector lying in a convex cone as a non-negative combination of edge rays of this cone. This problem also arises in many applications such as planar graph embedding and spherical parameterization. In this paper, we present a unified geometric construction for building these weighted combinations using the notion of polar duals. We show that our method yields a simple geometric construction for Wachspress's barycentric coordinates, as well as for constructing Colin de Verdière matrices from convex polyhedra - a critical step in Lovasz's method with applications to parameterizations.en_US
dc.description.seriesinformationEurographics Symposium on Geometry Processing 2005en_US
dc.identifier.isbn3-905673-24-Xen_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP05/181-186en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Geometric algorithms, languages and systemsen_US
dc.titleA Geometric Construction of Coordinates for Convex Polyhedra using Polar Dualsen_US
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