In this paper, we give the definition for the voronoi diagram and its dual graph – Delaunay triangulation for 3D cuboids. We prove properties of the 3D Delaunay triangulation, and provide algorithms to construct and update the Delaunay triangulation. The Delaunay triangulation data structure is used to perform proximity searches for both static and kinetic cases. We describe experimental result...

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...

Given a set S of points in the plane, a triangulation of S is a partition of the convex hull of S into triangles whose vertices are the points of S. A triangulation of S is said to be Delaunay if no point of S lies inside the triangles’ circumcircles. In this thesis, we study a generalization of these notions to a set S of disjoint segments in the plane. At first, we define a new family of diag...

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...

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...

Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay trian...

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...