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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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Proceedings ArticleDOI
05 Mar 2008
TL;DR: The experimental results demonstrate the effectiveness of the proposed novel energy-based hierarchical edge clustering method for node-link graphs in clustering edges and providing good high level abstractions of complex graphs.
Abstract: Effectively visualizing complex node-link graphs which depict relationships among data nodes is a challenging task due to the clutter and occlusion resulting from an excessive amount of edges. In this paper, we propose a novel energy-based hierarchical edge clustering method for node-link graphs. Taking into the consideration of the graph topology, our method first samples graph edges into segments using Delaunay triangulation to generate the control points, which are then hierarchically clustered by energy-based optimization. The edges are grouped according to their positions and directions to improve comprehensibility through abstraction and thus reduce visual clutter. The experimental results demonstrate the effectiveness of our proposed method in clustering edges and providing good high level abstractions of complex graphs.

45 citations

Journal ArticleDOI
TL;DR: A robust parallel Delaunay triangulation algorithm for processing billions of points from nonoverlapped block LiDAR files called ParaStream, which targets ubiquitous multicore architectures and exploits most of the computing power of multicore platforms through parallel computing.

45 citations

Journal ArticleDOI
TL;DR: It is demonstrated how weighted triangulations provide a faster and more robust approach to a series of geometry processing applications, including the generation of well-centered meshes, self-supporting surfaces, and sphere packing.
Abstract: In this article we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary triangle meshes and thus extends weighted Delaunay triangulations to surface meshes. We also present alternative characterizations of this primal-dual structure (through combinations of angles, areas, and lengths) and, in the process, uncover closed-form expressions of mesh energies that were previously known in implicit form only. Finally, we demonstrate how weighted triangulations provide a faster and more robust approach to a series of geometry processing applications, including the generation of well-centered meshes, self-supporting surfaces, and sphere packing.

45 citations

Journal ArticleDOI
TL;DR: In this paper, the authors apply the Delaunay Tessellation Field Estimator (DTFE) to reconstruct and analyse the matter distribution and cosmic velocity flows in the local universe on the basis of the PSCz galaxy survey.
Abstract: We apply the Delaunay Tessellation Field Estimator (DTFE) to reconstruct and analyse the matter distribution and cosmic velocity flows in the local Universe on the basis of the PSCz galaxy survey. The prime objective of this study is the production of optimal resolution 3D maps of the volume-weighted velocity and density fields throughout the nearby universe, the basis for a detailed study of the structure and dynamics of the cosmic web at each level probed by underlying galaxy sample. Fully volume-covering 3D maps of the density and (volume-weighted) velocity fields in the cosmic vicinity, out to a distance of 150 h(-1) Mpc, are presented. Based on the Voronoi and Delaunay tessellation defined by the spatial galaxy sample, DTFE involves the estimate of density values on the basis of the volume of the related Delaunay tetrahedra and the subsequent use of the Delaunay tessellation as natural multidimensional (linear) interpolation grid for the corresponding density and velocity fields throughout the sample volume. The linearized model of the spatial galaxy distribution and the corresponding peculiar velocities of the PSCz galaxy sample, produced by Branchini et al., forms the input sample for the DTFE study. The DTFE maps reproduce the high-density supercluster regions in optimal detail, both their internal structure as well as their elongated or flattened shape. The corresponding velocity flows trace the bulk and shear flows marking the region extending from the Pisces-Perseus supercluster, via the Local Superclusters, towards the Hydra-Centaurus and the Shapley concentration. The most outstanding and unique feature of the DTFE maps is the sharply defined radial outflow regions in and around underdense voids, marking the dynamical importance of voids in the local Universe. The maximum expansion rate of voids defines a sharp cut-off in the DTFE velocity divergence probability distribution function. We found that on the basis of this cut-off DTFE manages to consistently reproduce the value of Omega(m) approximate to 0.35 underlying the linearized velocity data set.

45 citations

Journal ArticleDOI
TL;DR: A simple and flexible algorithm for finding zeros of a complex function is presented, based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes, which creates a set of candidate points.
Abstract: A simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points is created, where the signs of the real and imaginary parts of the function change simultaneously. To verify and refine the results, an iterative algorithm is applied. The validity of the presented technique is supported by the results obtained in numerical tests involving three different types of functions.

45 citations


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