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.

Linear elasticity of planar delaunay networks: Random field characterization of effective moduli

Abstract: A study is conducted of the influence of microscale geometric and physical randomness on effective moduli of a continuum approximation of disordered microstructures. A particular class of microstructures investigated is that of planar Delaunay networks made up of linear elastic rods connected by joints. Three types of networks are considered: Delaunay networks with random geometry and random spring constants, modified Delaunay networks with random geometry and random spring constants, and regular triangular networks with random spring constants. Using a structural mechanics method, a numerical study is conducted of the first and second order characteristics of random fields of effective moduli. In view of duality of the Delaunay triangulations to the Voronoi tessellations, these results provide the basis for development of analytical models of various heterogeneous solids, e.g. granular, fibrous.

The flow complex: a data structure for geometric modeling

Abstract: Structuring finite sets of points is at the heart of computational geometry. Such point sets arise naturally in many applications. Examples in R3 are point sets sampled from the surface of a solid or the locations of atoms in a molecule. A first step in processing these point sets is to organize them in some data structure. Structuring a point set into a simplicial complex like the Delaunay triangulation has turned out to be appropriate for many modeling tasks. Here we introduce the flow complex which is another simplicial complex that can be computed efficiently from a finite set of points. The flow complex turned out to be well suited for surface reconstruction from a finite sample and for some tasks in structural biology. Here we study mathematical and algorithmic properties of the flow complex and show how to exploit it in applications.

On Refinement of Constrained Delaunay Tetrahedralizations

Abstract: This paper discusses the problem of refining constrained Delaunay tetrahedralizations (CDTs) into good quality meshes suitable for adaptive numerical simulations. A practical algorithm which extends the basic Delaunay refinement scheme is proposed. It generates an isotropic mesh corresponding to a sizing function which can be either user-specified or automatically derived from the geometric data. Analysis shows that the algorithm is able to produce provable-good meshes, i.e., most output tetrahedra have their circumradius-to-shortest edge ratios bounded, except those in the neighborhood of small input angles. Good mesh conformity can be obtained for smoothly changing sizing information. The algorithm has been implemented. Various examples are provided to illustrate the theoretical aspects and practical performance of the algorithm.

A Novel Virtual Force Approach for Node Deployment in Wireless Sensor Network

Abstract: The effectiveness of wireless sensor networks (WSN) depends on the coverage and connectivity provided by node deployment, which is one of the key topics in WSN. In this paper, a modified virtual force-based node self-deployment algorithm for nodes with mobility is proposed. In the virtual force-based approach, all nodes are seen as points subject to repulsive and attractive force exerted among them, nodes can move according to the calculated force. In the proposed approach, Delaunay triangulation is formed with these nodes, adjacent relationship is defined if two nodes are connected in the Delaunay diagram. Force can only be exerted from those adjacent nodes within the communication range. Simulation results showed that the proposed approach has higher coverage rate and faster convergence time than traditional virtual force algorithm.

An accelerated triangulation method for computing the skeletons of free-form solid models

Abstract: Shape skeletons are powerful geometric abstractions that provide useful intermediate representations for a number of geometric operations on solid models including feature recognition, shape decomposition, finite element mesh generation, and shape design As a result there has been significant interest in the development of effective methods for skeleton generation of general free-form solids In this paper we describe a method that combines Delaunay triangulation with local numerical optimization schemes for the generation of accurate skeletons of 3D implicit solid models The proposed method accelerates the slow convergence of Voronoi diagrams to the skeleton, which, without optimization, would require impraelically large sample point sets and resulting meshes to attain acceptable accuracy The Delaunay triangulation forms the basis for generating the topological structure of the skeleton The optimization step of the process generates the geometry of the skeleton patches by moving the vertices of Delaunay tetrahedra and relocating their centres to form maximally inscribed spheres The computational advantage of the optimization scheme is that it involves the solution of one small optimization problem per tetrahedron and its complexity is therefore only linear (O(n)) in the number of points used for the skeleton approximation We demonstrate the effectiveness of the method on a number of representative solid models