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.

A Node Deployment Algorithm Based on Van Der Waals Force in Wireless Sensor Networks

Abstract: The effectiveness of wireless sensor networks (WSN) depends on the regional coverage provided by node deployment, which is one of the key topics in WSN. Virtual force-based algorithms (VFA) are popular approaches for this problem. In VFA, all nodes are seen as points subject to repulsive and attractive force exerted among them and can move according to the calculated force. In this paper, a sensor deployment algorithm for mobile WSN based on van der Waals force is proposed. Friction force is introduced into the equation of force, the relationship of adjacency of nodes is defined by Delaunay triangulation, and the force calculated produce acceleration for nodes to move. An evaluation metric called pair correlation function is introduced here to evaluate the uniformity of the node distribution. Simulation results and comparisons have showed that the proposed approach has higher coverage rate, more uniformity in configuration, and moderate convergence time compared to some other virtual force algorithms.

Optimal Möbius Transformations for Information Visualization and Meshing

Abstract: We give linear-time quasiconvex programming algorithms for finding a Mobius transformation of a set of spheres in a unit ball or on the surface of a unit sphere that maximizes the minimum size of a transformed sphere. We can also use similar methods to maximize the minimum distance among a set of pairs of input points. We apply these results to vertex separation and symmetry display in spherical graph drawing, viewpoint selection in hyperbolic browsing, element size control in conformal structured mesh generation, and brain flat mapping.

Polynomial-size nonobtuse triangulation of polygons

Abstract: We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with O(n2) nonobtuse triangles. We also show that any triangulation (without Steiner points) of a simple polygon has a refinement with O(n4) nonobtuse triangles. Finally we show that a triangulation whose dual is a path has a refinement with only O(n2) nonobtuse triangles.

Unstructured mesh procedures for the simulation of three-dimensional transient compressible inviscid flows with moving boundary components

Abstract: SUMMARY The solution of high-speed transient inviscid compressible flow problems in three dimensions is considered. Discretization of the spatial domain is accomplished by the use of tetrahedral elements generated by Delaunay triangulation with automatic point creation. Methods of adapting the mesh to allow for boundary movement are considered and a strategy for ensuring boundary recovery is proposed. An explicit multistage time-stepping algorithm is employed to advance the flow solution. A number of examples are included to illustrate the numerical performance of the proposed procedures. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 27: 41‐55 (1998)

Computing 2D Constrained Delaunay Triangulation Using the GPU

Abstract: We propose the first graphics processing unit (GPU) solution to compute the 2D constrained Delaunay triangulation (CDT) of a planar straight line graph (PSLG) consisting of points and edges. There are many existing CPU algorithms to solve the CDT problem in computational geometry, yet there has been no prior approach to solve this problem efficiently using the parallel computing power of the GPU. For the special case of the CDT problem where the PSLG consists of just points, which is simply the normal Delaunay triangulation (DT) problem, a hybrid approach using the GPU together with the CPU to partially speed up the computation has already been presented in the literature. Our work, on the other hand, accelerates the entire computation on the GPU. Our implementation using the CUDA programming model on NVIDIA GPUs is numerically robust, and runs up to an order of magnitude faster than the best sequential implementations on the CPU. This result is reflected in our experiment with both randomly generated PSLGs and real-world GIS data having millions of points and edges.