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Discrete and Computational Geometry Hardcover – May 1, 2011

by Satyan L. Devadoss (Author), Joseph O'Rourke (Author)

5 customer reviews

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Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.

This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.

The essential introduction to discrete and computational geometry

Covers traditional topics as well as new and advanced material

Features numerous full-color illustrations, exercises, and unsolved problems

Suitable for sophomores in mathematics, computer science, engineering, or physics

Rigorous but accessible

An online solutions manual is available (for teachers only). To obtain access, please e-mail: Vickie_Kearn@press.princeton.edu

Discrete and Computational Geometry

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Product Details

Hardcover: 280 pages
Publisher: Princeton University Press (May 1, 2011)
Language: English
ISBN-10: 0691145539
ISBN-13: 978-0691145532
Product Dimensions: 10.3 x 7.2 x 1 inches
Shipping Weight: 2.2 pounds (View shipping rates and policies)
Average Customer Review: 3.8 out of 5 stars See all reviews (5 customer reviews)
Amazon Best Sellers Rank: #565,972 in Books (See Top 100 in Books)
- #501 in Books > Science & Math > Mathematics > Geometry & Topology
- #2659 in Books > Computers & Technology > Computer Science
- #2872 in Books > Science & Math > Mathematics > Applied

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Customer Reviews

3.8 out of 5 stars

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12 of 13 people found the following review helpful

a beauty!

By pascal vallotton on August 10, 2011

Format: Hardcover

This was the perfect book for me at a perfect time. I have a relatively strong background in image analysis, modelling, and mathematics in general but I had not really peered into computational geometry, except for using a few tricks of the trade such as Delaunay triangulations. This book fixed me (I am a bit more than half way through). It has a delighful deductive and light flow to it. It touches on more advanced subjects in an informative manner and points to interesting current reseach questions. I even surprise myself touching the exercises - many of which are easy enough not to require pen and paper. The illustrations are superb; the layout is magnificent. A few proofs could have been a bit more complete but generally, one is left with the impression that one really understands what is going on. It would be great if the authors could maintain the quality in a significantly expanded future edition (about 250 pages in this one).
I also have Rourke's book on origamis and foldings, which I purchased mostly for the beauty of the drawing and the very interesting topics covered. However, that book is way more difficult to approach than the "discrete and Computational Geometry", which stands out as a gem!

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8 of 9 people found the following review helpful

Good, but not quite what I expected

By Jeremiah LaRocco on August 3, 2012

Format: Kindle Edition Verified Purchase

I really liked the first five chapters of this book. There's no code, or even pseudo code, but I found the algorithm descriptions to be very clear and give an intuitive understanding of how the algorithms work. It doesn't go into too much detail, but the Big-o running time is given for most of the algorithms. I felt that with a bit of work I would be able to implement most of the algorithms.

The last two chapters didn't seem to fit with the first five. They were very abstract, didn't mention running time analysis, and just didn't seem as practically useful as the first part of the book. The explanations in these chapters also weren't as clear, and I doubt I'd be able to implement any of it without another reference.

The later parts of the book also use a lot of more advanced topics without much explanation. There are several sections starting off like "______ is an advanced topic we can't begin to explain here, but ..." and then going on to use some advanced result or theory.

On a positive note, the Kindle version is typeset very well, and even uses color. I read in the browser, on my kindle, and in the iPad kindle reader, and it looked excellent in all three, which is not always the case for technical books with equations and figures.

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8 of 9 people found the following review helpful

Interesting book, but not everything follows

By TheDiscountPundit on August 26, 2012

Format: Hardcover Verified Purchase

Much of the discussion, particularly the central development of the first 4-5 chapters of the book on Delaunay triangulations, Vornoi diagrams, and their applications is very clearly developed. Pointing out unsolved problems related to the development was a refreshing approach. The book also does a very good job of stating when the various parts of the argument were first understood, be it in Ancient Greek times, the turn of the century, or only in the last 20-30 years.

The only reason I didn't give it a top rating is that there doesn't seem to be any way to solve several of the problems based on material in the book. The first of these is how to partition a cube into five tetrahedra.

It was a little surprising to me (a physicist) that the book doesn't ever have dot products or cross products.
Exercise 1.15 goes very quickly with cross products and the notion of directed (signed) area.

But I quibble. It's an interesting book and I read it straight through, doing the 10% exercises which looked to me neither impossible nor trivial. I've been dealing with programs which do automatic mesh generation for finite element analysis, and I now feel I have a deeper understanding of how they operate.

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1 of 1 people found the following review helpful

mixed feelings

By reader on December 11, 2014

Format: Hardcover

on the plus side there are some pretty pictures throughout
but the exposition gets choppy in places and trails off con
siderably toward the end

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0 of 3 people found the following review helpful

Four Stars

By Daniel P. Evans on October 4, 2014

Format: Hardcover Verified Purchase

Very good introduction to computational geometry.

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