Handbook of Discrete and Computational Geometry [Hardcover]

Jacob E. Goodman (Editor), Joseph O'Rourke (Editor)

Book Description

Publication Date: August 20, 1997 | ISBN-10: 0849385245 | ISBN-13: 978-0849385247 | Edition: 1

For the first time discrete geometry, geometric computing, and their many applications in one complete reference. The authors have answered the need for a comprehensive handbook for workers in these and related fields, and for other users of the body of results. The Handbook of Discrete and Computational Geometry brings together, for the first time, all of the major results in both these fields into one volume. Thousands of results theorems, algorithms, and tables throughout the volume definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is presented clearly enough to assist the novice, but in enough depth to appeal to the specialist. Over 200 figures illustrate the concepts presented and provide supporting examples.

Product Details

• Hardcover: 1008 pages
• Publisher: CRC-Press; 1 edition (August 20, 1997)
• Language: English
• ISBN-10: 0849385245
• ISBN-13: 978-0849385247
• Product Dimensions: 10.1 x 7.2 x 2.3 inches
• Shipping Weight: 4.2 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,577,608 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

14 of 14 people found the following review helpful:

4.0 out of 5 stars Very comprehensive overview of computational geometry, March 25, 2001

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
(VINE VOICE)    (HALL OF FAME REVIEWER)    (REAL NAME)   

This review is from: Handbook of Discrete and Computational Geometry (Hardcover)

This book, written by many well-known experts in the field, is a fine compendium of articles on the most active areas of computational geometry. Each article is supplemented with a glossary of terms needed for understanding the relevant concepts and frequently contains a list of open problems. An overview of the convex hull of a collection of random points in Euclidean n-space is given in one of the articles on discrete aspects of stochastic geometry, where also a very interesting discussion of generalizations of the Buffon needle problem is given.

There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject.

The article on shortest paths and networks is somewhat disappointing since there is no in-depth discussion on network routing algorithms.

The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of Mayer-Vietoris sequences to design efficient divide-and-conquer schemes for computing the homology of higher-dimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.

The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraic-geometric codes, which is good considering their importance in applications.

The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed.

A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area.