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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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Journal ArticleDOI
TL;DR: In this article, a cell centred finite volume method based on Roe's approximate Riemann solver across the edges of the cells is presented and the results are compared for first-and second-order accuracy.
Abstract: Numerical modelling of shallow water flow in two dimensions is presented in this work with the results obtained in dam break tests Free surface flow in channels can be described mathematically by the shallow-water system of equations These equations have been discretized using an approach based on unstructured Delaunay triangles and applied to the simulation of two-dimensional dam break flows A cell centred finite volume method based on Roe's approximate Riemann solver across the edges of the cells is presented and the results are compared for first- and second-order accuracy Special treatment of the friction term has been adopted and will be described The scheme is capable of handling complex flow domains as shown in the simulation corresponding to the test cases proposed, ie that of a dam break wave propagating into a 45° bend channel (UCL) and in a channel with a constriction (LNEC-IST) Comparisons of experimental and numerical results are shown

124 citations

Proceedings ArticleDOI
30 Jul 2000
TL;DR: The results show that the similarity retrieval accuracy of the TVPAS method is as good as the other methods, while it has the lowest computational cost for generating the shape signatures of the objects and is the only method that has direct support for RST query types.
Abstract: Besides traditional applications (e.g. CAD/CAM and trademark registry), new multimedia applications, such as structured video, animation and the MPEG-7 standard, require the storage and management of well-defined objects. We focus on shape-based object retrieval and conduct a comparison study on four such techniques: Fourier descriptors (FD), the grid-based (GB) method, Delaunay triangulation (DT) and MBC-TPVAS (minimum bounding circles/touch-point vertex-angle sequence). Our results show that the similarity retrieval accuracy of our method (TVPAS) is as good as the other methods, while it has the lowest computational cost for generating the shape signatures of the objects. Moreover, it has low storage requirements and a comparable computation cost to compute the similarity between two shape signatures. In addition, TPVAS requires no normalization of the objects and is the only method that has direct support for RST (rotation/scaling/translation) query types. In this paper, we also introduce a new shape description taxonomy.

124 citations

Journal ArticleDOI
TL;DR: In this article, a method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed, which works well even in regions of cavities and gaps.
Abstract: A method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed. The prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions, whereas the tetrahedral grid covers the rest of the computational domain. The Delaunay approach for tetrahedral grid generation is used. The proposed prismatic grid is structured in directions normal to the boundary faces, but the number of prisms generated from one boundary face is variable from face to face. Unlike conventional prismatic grid generators, this technique works well even in regions of cavities and gaps. The Delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms. Particular attention is given to the boundary-constraining problem. A robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used. Grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

123 citations

Journal ArticleDOI
TL;DR: Nessary and sufficient conditions for classification of mesh topology on three-dimensional planar geometry are given, as well as a discussion of the more complex case of curved geometry.
Abstract: One approach to fully automatic mesh generation in two and three dimensions is to generate and triangulate a set of points within and on the boundary of a geometry using the properties of the Delaunay triangulation. Because the point data generate mesh topology of greater dimension, it is necessary to insure topological compatibility and perform classification of the resulting mesh with respect to the original geometry. Necessary and sufficient conditions for classification of mesh topology on three-dimensional planar geometry are given, as well as a discussion of the more complex case of curved geometry. This paper also presents conditions to insure topological compatibility along with techniques for identifying and resolving cases of incompatibility.

123 citations

Journal ArticleDOI
TL;DR: The main novelty lies in a structure‐preserving approach where the input point set is first consolidated by structuring and resampling the planar components, before reconstructing the surface from both the consolidated components and the unstructured points.
Abstract: We present a method for reconstructing surfaces from point sets. The main novelty lies in a structure-preserving approach where the input point set is first consolidated by structuring and resampling the planar components, before reconstructing the surface from both the consolidated components and the unstructured points. The final surface is obtained through solving a graph-cut problem formulated on the 3D Delaunay triangulation of the structured point set where the tetrahedra are labeled as inside or outside cells. Structuring facilitates the surface reconstruction as the point set is substantially reduced and the points are enriched with structural meaning related to adjacency between primitives. Our approach departs from the common dichotomy between smooth/piecewise-smooth and primitive-based representations by gracefully combining canonical parts from detected primitives and free-form parts of the inferred shape. Our experiments on a variety of inputs illustrate the potential of our approach in terms of robustness, flexibility and efficiency.

122 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202393
2022203
2021130
2020185
2019204
2018223