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Meshing, Geometric Modeling and Numerical Simulation 1
book

Meshing, Geometric Modeling and Numerical Simulation 1

by Houman Borouchaki, Paul Louis George
November 2017
Intermediate to advanced content levelIntermediate to advanced
384 pages
12h 4m
English
Wiley-ISTE
Content preview from Meshing, Geometric Modeling and Numerical Simulation 1

Chapter 5Delaunay Triangulation

Delaunay triangulation is a predilection for several fields of science and computational geometry in particular. Many varied and very interesting reference works in this field (e.g. [Preparata, Shamos-1985], [Boissonnat, Yvinec-1997], [Edelsbrunner-2001], among many others) have dealt with the properties of this triangulation and the complexities of its construction. Paradoxically, the effective implementation of algorithms that make this construction possible has not, at least at the beginning, been of particular concern. From a less dogmatic and greatly more pragmatic point of view, this triangulation and its construction have been simultaneously studied by the engineering community. Delaunay triangulation, as it is or through its many variants, is indeed an essential component used (typically, and beyond its eventual underlying properties as a connector or interpolator of points) by several methods of construction or modification of meshes. These meshes are the spatial supports used in numerical simulations (through the finite element method, though not exclusively using this method) and hence the interest of the numerical engineers for this triangulation and its effective construction.

In this chapter, we first provide a brief historical description. We then give the definition for and recall some properties of Delaunay triangulations. Our definition is based on Delaunay’s lemma, the initial (and historical) version of which is given here, ...

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Publisher Resources

ISBN: 9781786300386Purchase book