A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a pr...

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We then show that, for any sufficiently regular submanifold of Euclidean space, and app...

We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite configurations called Delaunay stars. A score, which is related to the density of packings, is assigned to each Delaunay star. We conjecture that the score of ev...

In this paper we introduce a new compression technique for a large triangulated terrains using Delaunay triangulation. Our compression technique decomposes a triangulated mesh into two parts. One is a point set whose connecting structure is deened implicitly by Delaunay edges. The other is the set of edges which cannot be recovered by the implicit Delaunay triangulation rule. Thus we only need ...

We characterize the conditions under which completing a Delaunay tessellation produces a connguration that is a nondegenerate Delaunay triangulation of an arbitrarily small perturbation of the original sites. One consequence of this result is a simple postpro-cessing step for resolving degeneracies in Delaunay triangulations that does not require symbolic perturbation of the data. We also give ...

The purpose of this paper is to generalize the Delaunay[13] triangulation onto surfaces. A formal definition and an appropriate algorithm are presented. Starting from a plane domain Delaunay triangulation definition, a theoretical approach is evolved (which is a background for further considerations). It has been proven that, in the case of a plane surface, the introduced Delaunay triangulation...

We present two new Delaunay refinement algorithms, second an extension of the first. For a given input domain (a set of points or a planar straight line graph), and a threshold angle α, the Delaunay refinement algorithms compute triangulations that have all angles at least α. Our algorithms have the same theoretical guarantees as the previous Delaunay refinement algorithms. The original Delauna...