A variational principle for weighted Delaunay triangulations and hyperideal polyhedra
نویسندگان
چکیده
منابع مشابه
A Variational Principle for Weighted Delaunay Triangulations and Hyperideal Polyhedra
We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted Delaunay triangulations may be interpreted as images of hyperbolic polyhedra with one vertex on and the remaining vertices beyond the infinite boundary of hype...
متن کاملA Monotonicity Property for Weighted Delaunay Triangulations
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...
متن کاملPerturbations for Delaunay and weighted Delaunay 3D triangulations
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...
متن کاملHyperideal polyhedra in hyperbolic manifolds
Let (M, ∂M) be a 3-manifold with incompressible boundary that admits a convex co-compact hyperbolic metric (but is not a solid torus). We consider the hyperbolic metrics on M such that ∂M looks locally like a hyperideal polyhedron, and we characterize the possible dihedral angles. We find as special cases the results of Bao and Bonahon [BB02] on hyperideal polyhedra, and those of Rousset [Rou02...
متن کاملAspects of Convex Geometry Polyhedra, Shellings, Voronoi Diagrams, Delaunay Triangulations
Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed as a tutorial and a set of notes on convex sets, polytopes, polyhedra, combinatorial topology, Voronoi Diagrams and Delaunay Triangulations. It is intended f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2008
ISSN: 0022-040X
DOI: 10.4310/jdg/1203000270