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...

A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construct...

4 We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, 5 we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay 6 triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms 7 run in deterministic linear time on a pointer machine. Our work builds ...

The traditional image matching algorithms adopt more complex strategies when dealing with mismatch caused by a lot of noise. In this paper, a simple, intuitive and effective noise processing algorithm is proposed based on Delaunay triangulation in computational geometry. The algorithm extracts feature points using SIFT method, respectively establishes Delaunay triangulation in multi-spectral an...

We propose a new C++ implementation of the well-known incremental algorithm for the construction of Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons have shown that our implementation outperforms the best currently available codes for convex hulls and Delaunay triangulations, and that it can be used for ...

We develop a theoretical framework for constructing guaranteed quality Delaunay meshes in parallel for general two-dimensional geometries. This paper presents a new approach for constructing graded meshes, i.e., meshes with element size controlled by a user-defined criterion. The sequential Delaunay refinement algorithms are based on inserting points at the circumcenters of triangles of poor qu...

We present an algorithm that takes as input a finite point set in R, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the we...