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: An interpolation method is developed which allows a fast and continuous surface-oracle computation which is exploited to efficiently guide a restricted Delaunay triangulation and can be exploited as an effective and high-quality meshing or remeshing tool.
31 citations
TL;DR: An algorithm using internal concavity to segment dot patterns is described, which produces subsets of the Dirichlet tessellation (Delaunay triangulation) of the dot pattern.
Abstract: This correspondence defines a signed distance, called ``internal concavity,'' on paths of the Voronoi diagram of a dot pattern. An algorithm using internal concavity to segment dot patterns is described. The segmentation algorithm produces subsets of the Dirichlet tessellation (Delaunay triangulation) of the dot pattern.
31 citations
25 Aug 1994
TL;DR: A chain decomposition algorithm is proposed and studied, which proves a property on minimum weight triangulations of points in the Euclidean plane, which shows that a special kind of line segments must be in the minimum weight Triangulations and in the greedy triangulation of a given point set.
Abstract: In this paper, a chain decomposition algorithm is proposed and studied. Using this algorithm, we prove a property on minimum weight triangulations of points in the Euclidean plane, which shows that a special kind of line segments must be in the minimum weight triangulations and in the greedy triangulation of a given point set.
31 citations
TL;DR: A new parallel algorithm, featuring overlapping domain decompositions with stereographic projections, is developed for the construction of spherical meshes that can be used in climate simulations and results in speedups for theConstruction of spherical centroidal Voronoi tessellations and spherical Delaunay triangulations.
Abstract: . 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 construction of spherical Delaunay and Voronoi tessellations. The algorithms are then embedded into algorithms for the parallel construction of planar and spherical centroidal Voronoi tessellations that require multiple constructions of Delaunay tessellations. This combination of overlapping domain decompositions with stereographic projections provides a unique algorithm for the construction of spherical meshes that can be used in climate simulations. Computational tests are used to demonstrate the efficiency and scalability of the algorithms for spherical Delaunay and centroidal Voronoi tessellations. Compared to serial versions of the algorithm and to STRIPACK-based approaches, the new parallel algorithm results in speedups for the construction of spherical centroidal Voronoi tessellations and spherical Delaunay triangulations.
31 citations
01 Jan 2002
31 citations