Delaunay Mesh Generation

ISBN-13: 9781584887300 / Angielski / Twarda / 2012 / 410 str.

Siu-Wing Cheng;Tamal K. Dey;Sartaj Sahni

Opis

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.

Going beyond, yet thoroughly rooted to theory, this book provides a comprehensive look at the algorithms that can produce quality Delaunay meshes through a paradigm called the Delaunay refinement. The authors describe meshing algorithms that can be built on the Delaunay refinement paradigm along with the involved mathematical analysis. In addition to introducing the theoretical foundation of meshing, the text discusses practical issues associated with the use of these algorithms and explores new developments in guaranteed meshing. The book also includes pseudo code as well as downloadable computer programs for meshing.

 

Spis treści

Introduction. Two-Dimensional Delaunay Triangulations. Algorithms for Constructing Delaunay Triangulations. Three-Dimensional Delaunay Triangulations. Algorithms for Constructing Delaunay Triangulations in R³. Delaunay Refinement in the Plane. Voronoi Diagrams and Weighted Complexes. Tetrahedral Meshing of PLCs. Weighted Delaunay Refinement for PLCs with Small Angles. Sliver Exudation. Refinement for Sliver Exudation. Smooth Surfaces and Point Samples. Restricted Delaunay Triangulations of Surface Samples. Meshing Smooth Surfaces and Volumes. Meshing Piecewise Smooth Complexes. Bibliography. Index.