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Handbook of Discrete and Computational Geometry 1st Edition

4.0 out of 5 stars 1 customer review
ISBN-13: 978-0849385247
ISBN-10: 0849385245
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Product Details

  • Series: Discrete Mathematics and Its Applications
  • Hardcover: 1008 pages
  • Publisher: CRC Press; 1 edition (July 15, 1997)
  • Language: English
  • ISBN-10: 0849385245
  • ISBN-13: 978-0849385247
  • Product Dimensions: 2 x 7.5 x 10.5 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: #3,789,386 in Books (See Top 100 in Books)

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By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on March 25, 2001
Format: 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.
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