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• W2103878493 abstract "A 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 Verdiere matrices from convex polyhedra---a critical step in Lovasz's method with applications to parameterizations." @default.
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• W2103878493 date "2005-07-04" @default.
• W2103878493 modified "2023-09-28" @default.
• W2103878493 title "A geometric construction of coordinates for convex polyhedra using polar duals" @default.
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• W2103878493 doi "https://doi.org/10.5555/1281920.1281950" @default.
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