Complexity of Random Delaunay Triangulation in 3D
2018年12月15日 · 1: Nina Amenta, Dominique Attali, and Olivier Devillers. 2007. Complexity of Delaunay triangulation for points on lower-dimensional polyhedra ; 2: R. Dwyer, The expected number of k-faces of a Voronoi diagram, Computers Math. Applications 26 (5) (1993) 3: Jeff Erickson. 2001. Nice point sets can have nasty Delaunay triangulations.
Delauney triangulation in high (>20) dimensions - MathOverflow
I know that its very hard to find the Delauney triangulation of high dimensional spaces, especially if there are several thousand points that need to be triangulated. So I was wondering . . . is it possible to construct a triangulation by choosing the points in the space as we go along?
Delaunay triangulations and convex hulls - MathOverflow
The Delaunay triangulation is brittle, and unless unusual demands on the vertex configurations are made, the combinatorial structure can change with an arbitrarily small perturbation of the metric. I.e., the point set can be arbitrarily close to being degenerate.
How to do an elevated 2D Delaunay triangulation? - MathOverflow
2022年3月5日 · This is what I call an elevated Delaunay triangulation: This is also called a 2.5D Delaunay triangulation. To do it, I simply perform an ordinary 2D Delaunay triangulation with the (x,y)-coordinates, and then I add the z-coordinate to each point. But I'm wondering whether there is a better way. Would you know that?
n-dimensional Delaunay Triangulation of Lattices
(Well, to be precise, the Delaunay "triangulation" of MY lattice is still not a triangulation; in it the unit cube is decomposed into two tetrahedra and one octahedron. But perturbing the coordinates of the basis further, and generically, will produce a …
Calculating a relaxed Delaunay Triangulation - MathOverflow
2023年7月1日 · Does relaxing the definition of Delaunay Triangulations by replacing the term "circumcircle" with "enclosing ellipse of least area" (i.e. the Steiner circumellipse) but keeping the "empty interior" requirement suffice to uniquely define a triangulation or do we have to add a requirement such as that the sum of ellipse-areas be minimal?
Triangulations of point sets — obtuse and acute triangles
2021年5月20日 · It is known that the Delaunay triangulation is the 'fattest' triangulation possible. It is also easily seen that given 7 points with 6 of them close to the vertices of a regular hexagon and the 7th near its center, there is one triangulation where all 6 resulting triangles are acute and another giving all 6 obtuse triangles.
Regularity of Delaunay triangulation of a hypercube
For 4D triangulation, if using Whitney's trick, then 4-manifolds is divided into hypercubical lattices, then each cube is triangulated into 4-simplices. I wanna avoid to get the triangulation like (A) but rather to have triangulation like (B).
Expected Degree of a vertex in Delaunay Triangulations
From this point process we construct the Delaunay triangulation (or the Voronoi tessellation for that matter). It is known [Stoyan et all] that the expected degree of a typical vertex has degree 6. Moreover, there are several results for the average area of …
distributions - Delaunay triangulation, with connected coloring
2020年10月23日 · Delaunay triangulation, with connected coloring. Ask Question Asked 4 years, 1 month ago. Modified 4 years ...