Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics) [Hardcover]

Herbert Edelsbrunner (Author)

Book Description

ISBN-10: 0521793092 | ISBN-13: 978-0521793094 | Publication Date: May 28, 2001 | Edition: 1

This book combines mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation) in order to solve the conceptual and technical problems in the combining of elements of combinatorial and numerical algorithms. The book develops methods from areas that are amenable to combination and explains recent breakthrough solutions to meshing that fit into this category. It should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, are useful, and interesting.

Editorial Reviews

Review

' a very readable exposition '.Monatshefte fÜr Mathematik --

Book Description

The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting.

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Product Details

• Hardcover: 190 pages
• Publisher: Cambridge University Press; 1 edition (May 28, 2001)
• Language: English
• ISBN-10: 0521793092
• ISBN-13: 978-0521793094
• Product Dimensions: 9 x 6.1 x 0.6 inches
• Shipping Weight: 13.6 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,960,188 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

8 of 12 people found the following review helpful:

5.0 out of 5 stars Excellent read for mathematically inclined reader, July 23, 2004

By 

Herve Bronnimann (New York City, NY USA) - See all my reviews

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This review is from: Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics) (Hardcover)

OK, I must admit, I know the author personally, like his work a lot. And so I can only recommend this book. But that's not what you're looking for in a review, nor am I talking to freinds or collegues who already know hime too. This book will introduce you to simplicial complexes, and deep mathematical constructs, along with some topology and geometry, while at the same time remaining hands-on and simpler. Mostly, the notation is clean, simple, and yet rigorous enough that you'll really be in terrific shape one you integrate it. It's actually amazing that it comes so clean given how powerful it can be. Meshes are the basis for many of the computer graphics and CAD/CAM modern methods, and are an indispensible tool. That's the real value of reading this book: you'll get some real good tools for manipulating meshes (whether what you want to do is the same or different than the author), and especially you'll get a mathematically correct and rigorous treatment.

At the same time this book is quite manageable even (and foremost) if you don't have a PhD in algebraic topology (all you need is a good bachelor in some computational science with good mathematics foundations). Although it might challenge you at times, it is basically self-contained and does not rely on any other book. (Additional knowledge is always useful, but this is a good starting point.)
You'll earn about simplicial complexes not from an abstract algebraic topology point of view (although the author is well-acquainted with them) but as a tool for representing surfaces and solids. The topics revolve around reconstructing a surface from a point cloud (using so-called Delaunay triangulations, which is one of the prevalent methods for that problem). It starts simply with 2D and moves on to 3D. It builds on the research of the author for more than a decade.

I should mention in fine that the author is the creator of Alpha-Shapes(a well known Delaunay-based method for reconstruction) and of the succesful startup Raindrop Geomagic which uses these methods in an essential way. His current interests are linked to biogeometry. Most of the research in this book somehow made it in one way or the other in their products. So this is excellent reading and a must for anyone interested in meshes, whether from computer graphics, CAD/CAM, or scientific computation / finite elements.

5.0 out of 5 stars A very nice, clear book, February 21, 2010

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Narada "the wondering jew" (Princeton, NJ, USA) - See all my reviews
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This review is from: Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics) (Paperback)

And much more pleasant to read than Edelsbrunner's Computational Geometry book. I have very little interest in Mesh Generation, but most of the book is not about that, but is rather a rather lucid introduction to central topics in modern discrete and computational geometry.