Algorithmic Geometry [Hardcover]

Jean-Daniel Boissonnat (Author), Mariette Yvinec (Author), Herve Bronniman (Translator)

Book Description

ISBN-10: 0521563224 | ISBN-13: 978-0521563222 | Publication Date: March 13, 1998

The design and analysis of geometric algorithms has seen remarkable growth in recent years, due to their application in computer vision, graphics, medical imaging, and CAD. Geometric algorithms are built on three pillars: geometric data structures, algorithmic data structuring techniques and results from combinatorial geometry. This comprehensive presents a coherent and systematic treatment of the foundations and gives simple, practical algorithmic solutions to problems. An accessible approach to the subject, Algorithmic Geometry is an ideal guide for instructors or for beginning graduate courses in computational geometry.

Editorial Reviews

Review

"This interesting book about computational geometry is a translation of the well known ^Geometrie Algorithmique^...The translation also contains many more concise proofs, new interesting exercises (for instance about data structures), new explanatory figures, and a more extensive index." Mathematical Reviews

"This text book is a careful introduction to this field. It does not aim for completeness, but concentrates on explaining the fundamental ideas, concepts, and structures: deterministic and randomized algorithms, convex hulls, triangulations, arrangements, Voronoi diagrams." Monatshefte fur Mathematik

Language Notes

Text: English (translation)
Original Language: French

See all Editorial Reviews

Product Details

• Hardcover: 541 pages
• Publisher: Cambridge University Press (March 13, 1998)
• Language: English
• ISBN-10: 0521563224
• ISBN-13: 978-0521563222
• Product Dimensions: 9.9 x 6.9 x 1.3 inches
• Shipping Weight: 2.3 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #5,445,970 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

21 of 21 people found the following review helpful:

5.0 out of 5 stars A great graduate book to complement the textbooks!, March 10, 2000

By A Customer

This review is from: Algorithmic Geometry (Paperback)

If you've read computational geometry textbooks (like the Preparata-Shamos, or the recent and great "Dutch" book by de Berg et al.), and liked the material, here's your chance to delve into the more mathematical and analytical aspect of the topic. This book is not for an undergraduate class, but its thorough yet readable treatment of arrangements or Voronoi diagrams will bring you up to speed for reading technical articles or more elaborate references (like Edelsbrunner's monograph). The scope is wider than Edelsbrunner's, even though fewer or less technical results appear. For instance, there is an analysis of the complexity of the union of triangles in space (based on recent research results).

The book takes the viewpoint of randomized algorithms, which are very simple to describe and implement, and provides general tools for their analysis (on-line or off-line dynamic algorithm). It is based in five parts around geometric structures (polytopes, arrangements, Voronoi diagrams) with two introductory parts (algorithms, randomized analysis -- general theorems).

Many of the algorithms and problems stem from robotics and motion planning. There are many exercises, with either an "algorithmic" interface, or a concrete problem-solving presentation.