Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes
نویسندگان
چکیده
منابع مشابه
Alexandrov’s Theorem, Weighted Delaunay Triangulations, and Mixed Volumes
— We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the defo...
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The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code; It is implemented in cg...
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where i is the linear interpolation of f over the triangle Ti in T and the sum is over all triangles in the triangulation. One may consider changing the triangulation by exchanging two triangles joined by an edge, forming a quadrilateral, by the triangles obtained by switching the diagonal of the quadrilateral; this is called an edge ip or a 2 ! 2 bistellar ip. He showed that the roughness of...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2008
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2358