Delaunay Mesh Generation

Siu-Wing Cheng, Tamal K. Dey, Jonathan Shewchuk

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December 4, 2012 by Chapman and Hall/CRC
Reference - 410 Pages - 173 B/W Illustrations
ISBN 9781584887300 - CAT# C7303
Series: Chapman & Hall/CRC Computer and Information Science Series

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Features

  • Presents practical algorithms for generating provably good Delaunay meshes
  • Contains a primer on Delaunay triangulations that describes their combinatorial properties and relatives as well as their geometric and topological fidelity as approximations of smooth surfaces
  • Covers challenging problems, including meshing domains with small angles and eliminating hard-to-remove "sliver" tetrahedra
  • Incorporates historical and bibliographical notes that acknowledge pioneers in the field and reference related ideas and publications
  • Includes exercises suitable for graduate-level courses on mesh generation or computational geometry

Summary

Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why these meshing algorithms work.

The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces.

For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future.

For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software.