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: This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise flat, triangulated surface and an application to biological membrane growth modeling.
64 citations
TL;DR: The proposed approach to 3-way decision-making results from the analysis of Delaunay graphs as well as friendship network (social) of location-based social network nodes, which results in knowledge granules that are near sets of nodes representing interaction between either casual users or friends in a social network.
Abstract: Proximal 3-way decision-making introduced.Delaunay triangulation meshes used.Computational geometry and near set theory foundation provided.Location-based social networks application included.Human socio-spatial behaviour analysis carried out. This article introduces proximal three-way decision-making. This form of 3-way decision-making stems from the proximity structures that result from endowing each nonempty set of social network triangulation nodes with several proximity relations. A triangulation is obtained by connecting every pair of nearest neighbour nodes with a straight edge. The proposed approach to 3-way decision-making results from the analysis of Delaunay graphs (spatial) as well as friendship network (social) of location-based social network nodes. The knowledge gained from proximal three-way decision-making is in the form of information granules that are near sets of nodes representing interaction between either casual users or friends in a social network. A practical illustration of proximal three-way decision-making is given in terms of a public domain large-scale social network dataset.
63 citations
TL;DR: In this article, the Delaunay triangulation is used to determine the best fit ellipse of a centred ellipsoid using a steepest gradient non-linear least squares algorithm.
63 citations
TL;DR: An algorithm for triangulatingn-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than π/2, and the running time isO(n log2n).
Abstract: We give an algorithm for triangulatingn-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than ?/2. The number of triangles in the triangulation is onlyO(n), improving a previous bound ofO(n2), and the running time isO(n log2n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm.
63 citations
TL;DR: A robust and feature-capturing surface reconstruction and simplification method that turns an input point set into a low triangle-count simplicial complex is introduced and is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries.
Abstract: We introduce a robust and feature-capturing surface reconstruction and simplification method that turns an input point set into a low triangle-count simplicial complex. Our approach starts with a (possibly non-manifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex--both seen as mass distributions. Our approach is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries. Our new feature-sensitive metric between point sets and triangle meshes can also be used as a post-processing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.
63 citations