Cheng, Siu-Wing; Dey, Tamal Krishna; Shewchuk, Jonathan Richard Delaunay mesh generation. (English) Zbl 1298.65187 Chapman & Hall/CRC Computer and Information Science Series. Boca Raton, FL: CRC Press (ISBN 978-1-58488-730-0/hbk; 978-1-58488-731-7/ebook). xv, 394 p. (2013). The book gives a deep insight into Delaunay triangulations. It is a valuable source of information for all who wants to apply mesh generation algorithms and for all who wants to learn the mathematical background of these algorithms. In the first eight chapters of the book, algorithms for the construction and refinement of Delaunay triangulations, weighted Delaunay triangulations and constrained Delaunay triangulations for polygonal and polyhedral domains are given and their properties are discussed. In the next three chapters, triangulations of domains with small angles and a sliver exudation technique for removing slivers from a Delaunay triangulation are explained. In the last four chapters, the triangulation of smooth surfaces and volumes as well as piecewise smooth complexes are described. Each chapter ends with historical and bibliographical notes as well as with exercises. Reviewer: Michael Jung (Dresden) Cited in 1 ReviewCited in 32 Documents MSC: 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry Keywords:Delaunay triangulation; triangular meshes; tetrahedral meshes; mesh refinement; Voronoi diagram; domains with acute angles; monograph; mesh generation; algorithm PDFBibTeX XMLCite \textit{S.-W. Cheng} et al., Delaunay mesh generation. Boca Raton, FL: CRC Press (2013; Zbl 1298.65187) Full Text: DOI