Geometry and Topology for Mesh Generation

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1R2. Geometry and Topology for Mesh Generation. Cambridge Monographs on Applied and Computational Mathematics. - H Edelsbrunner (Dept of Comput Sci, Duke Univ, Durham NC). Cambridge UP, Cambridge, UK. 2001. 177 pp. ISBN 0-521-79309-2. $44.95.

Reviewed by DJ Benson (Dept of Appl Mech and Eng Sci, UCSD, 9500 Gilman, La Jolla CA 92093-0411).

This textbook is a slim 177 pages that focuses on automatic triangular and tetrahedral mesh generation. Although one might expect from the title that it would cover a broader range of topics, eg, hexahedral meshes and blending functions, the preface clearly states the author’s intentions.

The book is broken into seven chapters, with the first six chapters representing two weeks of lecture each. The sections within the chapter each represent one 75-minute lecture. The book starts with a discussion of Vornoi and Delaunay triangulations, moves on to algorithms for constructing them, and then discusses algorithms for surface simplification and eliminating/transforming elements with poor aspect ratios. The final chapter discusses unresolved problems, a nice feature that gives those new to the field a perspective on current research. The subject and author indices are thorough.

The book is clearly written with plenty of figures to illustrate its concepts. Each chapter ends with a bibliography and exercises. The bibliography also contains the author’s comments on the different references, a feature rarely found in books and which this reviewer found to be very helpful. Some of the algorithms are expressed in a pseudo-code format with some features particular to C. Those unfamiliar with C should be able to figure out expressions like “n- -” based on their context.

While the target audience is upper division seniors and graduate students, Geometry and Topology for Mesh Generation, should also appeal to those who want to automatically generate triangular and tetrahedral meshes and are looking for more than a cookbook of algorithms. Those seeking a how-to book for commercial mesh generators should look elsewhere. Individuals seeking information on generating logically regular mesh blocks for computational fluid dynamics would be better off with Joe Thompson’s classic book, Handbook of Grid Generation.

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