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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.


Papers
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01 Jan 2012
TL;DR: In this paper, Voronoi and Delaunay describe the flip-graphs as a triangulation of the triangulated triangulations of triangulates of the tesselations of a tesselated tesselation.
Abstract: Keywords: Voronoi ; Delaunay ; tesselations ; triangulations ; flip-graphs Reference EPFL-CHAPTER-181846 URL: http://www.math.uiuc.edu/documenta/vol-ismp/60_liebling-thomas.html Record created on 2012-10-19, modified on 2016-08-09

35 citations

Proceedings ArticleDOI
28 Jan 2005
TL;DR: An incremental algorithm for constructing the Delaunay overlaid network for virtual collaborative space, where every node uses Delauny triangulation, by using its knowledge of other nodes and cooperatively exchanging information among nodes, which generates and refines overlaid networks.
Abstract: This paper proposes an incremental algorithm for constructing the Delaunay overlaid network for virtual collaborative space. In our algorithm, every node uses Delaunay triangulation, by using its knowledge of other nodes and cooperatively exchanging information among nodes, which generates and refines overlaid networks. On the resultant Delaunay network, nodes communicate with each other over virtual collaborative space, and employ multihopping communication among distant nodes. This algorithm structure has the following advantages: (1) utilization of only the localized nodes, omitting the use of unnecessary distant nodes for communication, (2) scalability through surveillance of nodes by refining and updating the network continuously, (3) two dimensional space organization which allows construction of super nodes that govern regional areas to process geographical range query, and (4) directional communication through a small routing table. The authors believe that this approach is applicable to large-scale virtual collaborative space and location aware system.

35 citations

Journal ArticleDOI
21 Mar 2013-PLOS ONE
TL;DR: In the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction, which has been seen in self-organized animal groups in both experiments and nature.
Abstract: Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual's Voronoi neighbors. The models include a tunable parameter that controls an individual's relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.

35 citations

Journal ArticleDOI
TL;DR: In this article, an improved version of the SimpleX method for radiative transfer on an unstructured Delaunay grid is presented, which is parallellised for distributed memory machines using MPI.
Abstract: Context. We present an improved version of the SimpleX method for radiative transfer on an unstructured Delaunay grid. The grid samples the medium through which photons are transported in an optimal way for fast radiative transfer calculations. Aims. We study the detailed working of SimpleX in test problems and show improvements over the previous version of the method. Methods. We have applied a direction conserving transport scheme that correctly transports photons in the optically thin regime, a regime where the original SimpleX algorithm lost its accuracy. In addition, a scheme of dynamic grid updates is employed to ensure correct photon transport when the optical depth changes during a simulation. For the application to large data sets, the method is parallellised for distributed memory machines using MPI. Results. To test the new method, we have performed standard tests for cosmological radiative transfer. We show excellent correspondence with both the analytical solution (when available) and to the results of other codes compared to the former version of SimpleX, without sacrificing the benefits of the high computational speed of the method.

35 citations

Proceedings ArticleDOI
21 Jun 2005
TL;DR: This work defines a new filtration of the Delaunay triangulation of a finite set of points in /spl Ropf//sup d/, similar to the alpha shape Filtration, but parameterized by a local scale parameter instead of the global scale parameter in alpha shapes.
Abstract: We define a new filtration of the Delaunay triangulation of a finite set of points in /spl Ropf//sup d/, similar to the alpha shape filtration. The new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. Since our approach shares many properties with the alpha shape filtration and the local scale parameter conforms to the local geometry we call it conformal alpha shape filtration. The local scale parameter is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.

35 citations


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