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...

We prove that the expected size of the 3D Delaunay triangulation of n points evenly distributed on a cylinder is Θ(n log n). This shows that the n √ n behavior of the cylinder-example of Erickson [9] is pathological. Key-words: Delaunay triangulation, random distribution, random sample, surface reconstruction Ce travail préliminaire a été joint avec un travail parallèle de Jeff Erickson et sera...

Delaunay tessellations and Voronoi diagrams capture proximity relationships among sets of points. When applied to points representing protein atoms or residue positions, they are used to compute molecular surfaces and protein volumes, to define cavities and pockets, to analyze and score packing interactions, and to find structural motifs. Since atom and residue coordinates are known imprecisely...

Roughly speaking, the rank of a Delaunay polytope (first introduced in [2]) is its number of degrees of freedom. In [3], a method for computing the rank of a Delaunay polytope P using the hypermetrics related to P is given. Here a simpler more efficient method, which uses affine dependencies instead of hypermetrics is given. This method is applied to classical Delaunay polytopes. Then, we give ...

For any nite point set S in Ed, an oriented matroid DOM(S) can be de ned in terms of how S is partitioned by Euclidean hyperspheres. This oriented matroid is related to the Delaunay triangulation of S and is realizable, because of the lifting property of Delaunay triangulations. We prove that the same construction of a Delaunay oriented matroid can be performed with respect to any smooth, stric...