Topic
Delaunay triangulation
About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.
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TL;DR: A dual structure of the Voronoi diagram of three-dimensional spheres called a quasi-triangulation is defined and its important properties are presented and a data structure based on arrays is proposed to compactly store the topology of the quasi-Triangulation with a guaranteed query performance.
Abstract: It is well-known that the Voronoi diagram of points and the power diagram for weighted points, such as spheres, are cell complexes, and their respective dual structures, i.e. the Delaunay triangulation and the regular triangulation, are simplicial complexes. Hence, the topologies of these diagrams are usually stored in their dual complexes using a very compact data structure of arrays. The topology of the Voronoi diagram of three-dimensional spheres in the Euclidean distance metric, on the other hand, is stored in a radial edge data structure which is not as compact as the data structure used for the Voronoi diagram of points and the power diagram for weighted points. In this paper, we define a dual structure of the Voronoi diagram of three-dimensional spheres called a quasi-triangulation and present its important properties. Based on the properties of a quasi-triangulation, we propose a data structure, called an interworld data structure, based on arrays to compactly store the topology of the quasi-triangulation with a guaranteed query performance.
79 citations
TL;DR: This paper presents a method for creating a Delaunay triangulation connected to a set of specified points, valid for dimensions 2 and 3, which is simple, robust and well adapted to computation.
Abstract: This paper presents a method for creating a Delaunay triangulation connected to a set of specified points. The theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach, valid for dimensions 2 and 3, which is simple, robust and well adapted to computation. Convex polyhedral and arbitrary polyhedral situations are introduced.
79 citations
TL;DR: An automatic mesh generator providing tetrahedral meshes suitable in general for finite element simulations and recent improvements relative to this a priori well-known method are described.
79 citations
TL;DR: Using hyperelastic materials and unstructured mesh, a level set based topological shape optimization method was developed for geometrically nonlinear structures in total Lagrangian framework as mentioned in this paper.
78 citations
TL;DR: In this article, the problem of finding a minimal triangulation of an undirected graph G = (V, E) is considered, and an algorithm for finding an optimal ordering α which produces a minimal set of "fill-in" is presented.
78 citations