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.

Meshing Piecewise Linear Complexes by Constrained Delaunay Tetrahedralizations

Abstract: We present a method to decompose an arbitrary 3D piecewise linear complex (PLC) into a constrained Delaunay tetrahedralization (CDT). It successfully resolves the problem of non-existence of a CDT by updating the input PLC into another PLC which is topologically and geometrically equivalent to the original one and does have a CDT. Based on a strong CDT existence condition, the redefinition is done by a segment splitting and vertex perturbation. Once the CDT exists, a practically fast cavity retetrahedralization algorithm recovers the missing facets. This method has been implemented and tested through various examples. In practice, it behaves rather robust and efficient for relatively complicated 3D domains.

Topology control for multihop packet radio networks

Abstract: A distributed topology-control algorithm has been developed for each node in a packet radio network (PRN) to control its transmitting power and logical neighbors for a reliable high-throughput topology. The algorithm first constructs a planar triangulation from locations of all nodes as a starting topology. Then, the minimum angles of all triangles in the planar triangulation are maximized by means of edge switching to improve connectivity and throughput. The resulting triangulation at this stage, the Delaunay triangulation, can be determined locally at each node. The topology is modified by negotiating among neighbors to satisfy a design requirement on the nodal degree parameter. Simulations show that the final topology is degree-bounded, has a rather regular and uniform structure, and has throughput and reliability that are greater than that of a number of alternative topologies. >

A general surface approach to the integration of a set of range views

Abstract: This paper presents a new and general solution to the problem of range view integration. The integration problem consists in computing a connected surface model from a set of registered range images acquired from different viewpoints. The proposed method does not impose constraints on the topology of the observed surfaces, the position of the viewpoints, or the number of views that can be merged. The integrated surface model is piecewise estimated by a set of triangulations modeling each canonical subset of the Venn diagram of the set of range views. The connection of these local models by constrained Delaunay triangulations yields g non-redundant surface triangulation describing all surface elements sampled by the set of range views. Experimental results show that the integration technique can be used to build connected surface models of free-form objects. No integrated models built from objects of such complexity have yet been reported in the literature, It is assumed that accurate range views are available and that frame transformations between all pairs of views can be reliably computed. >

A fast algorithm for bidimensional EMD

Abstract: In this letter, we describe a new method for bidimensional empirical mode decomposition (EMD). This decomposition is based on Delaunay triangulation and on piecewise cubic polynomial interpolation. Particular attention is devoted to boundary conditions that are crucial for the feasibility of the bidimensional EMD. The study of the behavior of the decomposition on a different kind of image shows its efficiency in terms of computational cost, and the decomposition of Gaussian white noises leads to bidimensional selective filter banks.