Computational Geometry: Algorithms and Applications, Second Edition (Hardcover)

~ Mark de Berg (Author), M. van Krefeld (Author), M. Overmars (Author), O. Schwarzkopf (Author) "Good solutions to algorithmic problems of geometric nature are mostly based on two ingredients..." (more)
Key Phrases: Zone Theorem, Thales's Theorem, Art Gallery Theorem

Editorial Reviews

Product Description

This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.

Product Details

• Hardcover: 379 pages
• Publisher: Springer; 2nd edition (February 18, 2000)
• Language: English
• ISBN-10: 3540656200
• ISBN-13: 978-3540656203
• Product Dimensions: 9.7 x 7.7 x 1 inches
• Shipping Weight: 1.9 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (16 customer reviews)
• Amazon.com Sales Rank: #606,867 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

39 of 39 people found the following review helpful:

4.0 out of 5 stars Good Introduction but look elsewhere for detailed reference, January 30, 2003

By	Jason (Illinios) - See all my reviews

Pro:
(1) Each chapter begins with a practical example. For example, the chapter computing intersections of lines starts with a discussion of a map-making application that goes into enough detail to see how the algorithms they present would be useful. This is a considerable step up from the common practice in algorithms literature of motivation by way of vaguely mentioning some related field (i.e. "These string matching algorithms are useful in computational biology"). This book does a much better job of motivating the material it presents, but if you're primarily interested in the abstract problem, these sections can be skipped.

(2) Each chapter is relatively self-contained. Feel free to skip ahead to subjects that interest you.

(3) Surprisingly readable. Unlike most technical material, one can read an entire chapter in a single sitting without missing much. Generally, each chapter will develop a single algorithm for a single kind of problem.

(4) It's very up to date. This second edition is less than two years old, it includes some new results in the field.

Con:
(1) Algorithms are only given in pseudocode. The emphasis is on describing algorithms and data structures clearly and completely. If you're looking for a "cookbook" with code to copy and paste into an application, perhaps O'Rourke's "Computational Geometry in C" would be a better choice.

(2) There are many important advanced results that are not discussed in the main text. An obvious example is the first chapter, which describes a well-known convex hull algorithm that takes O(n log n) time but algorithms that are faster for most inputs are mentioned only in the "Notes and Comments" at the end of the chapter. Someone interested in lots of gory details would be well-served to combine this book with Boissonnat and Yvinec's more detailed and mathematical "Algorithmic Geometry".

16 of 16 people found the following review helpful:

5.0 out of 5 stars Extremely well written, October 26, 2002

By	Jacob Marner (Denmark) - See all my reviews (REAL NAME)

Algorithm books are often quite hard to understand, but this is not the case with this book. The information is very compact so it is a slow read but due to the high quality of the text this is only an advantage. You are never left wondering what the authors might have meant with a certain statement.

The book focuses solely on theory, so it presents no real source code (only pseudo-code) which I think is good thing since that would otherwise have polluted the clarity of the explanations.

Many of the topics it covers has been a help to me as a programmer. Can be recommended for anyone interested in computation geometry - but it requires some computer science maturity so I don't recommend it unless you have a bachelor's degree in C.S. or something similar.

Jacob Marner, M.Sc.

13 of 14 people found the following review helpful:

5.0 out of 5 stars The best computational geometry book!, May 4, 1999

By A Customer

This review is from: Computational Geometry: Algorithms and Applications (Hardcover)

I also completely disagree with the one-star review below. The "Dutch book" is the clearest, most complete, most up-to-date, best designed, best illustrated computational geometry textbook out there. Some of the material may be a bit advanced for undergraduates (and for those people I would recommend Joe O'Rourke's excellent "Computational Geometry in C"), but for graduate students and other researchers who want to learn computational geometry, this book is absolutely essential.

This is an algorithms textbook, though, not a textbook full of code. You will not find compilable code in the author's favorite programming language du jour -- this may be what the first reviewer meant by "desperately needed details". What you will find is clear, correct, well-motivated explanations of the underlying algorithms, data structures, and mathematics.

The book does have a few faults. The motivating examples are often forced ("mixing things" for convex hulls??). The authors deliberately chose to show only one algorithm for each problem they consider, and occasionally the algorithm they chose is not the simplest or most efficient. But these are minor points.

If you're going to buy just one computational geometry book, this is the one to get.