This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The code in this new edition is significantly improved from the first edition, and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.
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Editorial Reviews
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"This is an applied approach to fundamental concepts in computational geometry and should be read by every serious practitioner....From a pedagogical point of view, this book is an excellent choice for both undergraduate classes (perhaps with more emphasis on the implementations) and graduate classes (considering a number of the exercises) because of the extensive exercises that review, explore details, and encourage further reading." Computing Reviews
"Conveys the feeling that computational geometry is interesting, exciting, important, and very active." SIGACT News
"Anyone who wants to know what this field is all about should read this book!...a pleasure to read, as questions that arise naturally in the reader's mind are answered, in almost all cases, in the following paragraph. The style strikes an ideal balance between rigor and informality. Mr. O'Rourke must be a wonderful teacher and I envy his students." Siam Review
"...the book is an excellent basis for a course on computational geometry; many interesting exercises and hints for further reading give suitable guidance for teachers and for students." Mathematical Reviews
"Conveys the feeling that computational geometry is interesting, exciting, important, and very active." SIGACT News
"Anyone who wants to know what this field is all about should read this book!...a pleasure to read, as questions that arise naturally in the reader's mind are answered, in almost all cases, in the following paragraph. The style strikes an ideal balance between rigor and informality. Mr. O'Rourke must be a wonderful teacher and I envy his students." Siam Review
"...the book is an excellent basis for a course on computational geometry; many interesting exercises and hints for further reading give suitable guidance for teachers and for students." Mathematical Reviews
Book Description
This is the newly revised and expanded edition of the most suitable textbook for introducing undergraduate students in computer science and mathematics to the design of geometry algorithms. Such algorithms lie at the core of a variety of practical areas, including 3D game program design, geographical information systems, manufacturing design, and robotics. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research. Thus, though it is designed for a course at the advanced undergraduate level, it can be used for graduate courses as well. Numerous exercises are provided at the end of every section; a partial solutions manual is available.A novel aspect of the book is the inclusion of working computer programs for many of the algorithms. Students will enjoy the interplay between practical programming issues and the latest theoretical developments; many student projects can be built on the provided code.
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More About the Author
I am a professor of Computer Science and of Mathematics at Smith College in Massachusetts in the USA. More information at my web page: http://cs.smith.edu/~orourke/ .
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Most Helpful Customer Reviews
13 of 13 people found the following review helpful
Format:Paperback
Anyone who is involved in areas such as computer graphics, computational radiology, robot vision, or visualization software should have a copy of this book. The author has done a fine job of introducing the most important algorithms in computational geometry, choosing the C language for their implementation. The choice of C might be somewhat dated now, since C++ is now beginning to dominate computational geometry, but readers who are actually programming these algorithms using C++ can easily extend the ones in the book to C++. Not all of the algorithms in the book are implemented into C, unfortunately, but the clarity of presentation is done well enough to make this implementation a fairly straightforward task. My interest in the book came from a need to design and implement algorithms for polyhedra in VRML and toric varieties in algebraic geometry. This book, along with others, was a great help in that regard. The running time of these algorithms was not really an issue with me, so the detail the author spends on discussing the complexity of the algorithms was not a concern. Readers who need to pay attention to running-time issues will appreciate his discussion of them for the algorithms that are presented.
The ability to visualize objects in an abstract subject like algebraic geometry boils down to, in the case of toric varieties, to a consideration of how to manipulate polytopes geometrically. A major portion of the book, if not all of it, is devoted to the computational geometry of polyhedra. Because it is an introductory book, some more advanced topics, such as Bayesian methods to find similarities between polyhedra, and neural network approaches to classifying polyhedral objects are not treated. Readers who need to do such things will be well-prepared for them after a study of this book. In addition, there are good exercises assigned at the end of each chapter, so the book could be used in the classroom. Some readers will however choose to use it as a reference source, and it would be a good one, for the author gives references to topics that he only touched upon in the book.
Some particular areas that were treated especially well were: 1. The discussion on data structures for surfaces of polyhedra. Although not very general, since he choose to deal with only triangulated polytopes, readers who need to be more general will have a good start in this discussion. 2. The discussion on volume overflow and how to deal with it using robust computation. 3. The discussion, albeit short, of the randomized incremental algorithm. 4. The treatment on the minimum spanning tree and Kruskal's algorithm. Communication network performance optimization is now a major application of this algorithm and others in graph theory, including the author's later discussion of Dijkstra's algorithm.
21 of 24 people found the following review helpful
Format:Paperback
O'Rourke's approach reflects the essence of both "Computational Geometry" and the "C language" --- concise yet profound. The book covers the core subjects of Computational Geometry: polygon partitioning, convex hulls, Voronoi diagrams / Delaunay triangulation, "arrangements" of lines, geometric searching, and motion planning.
The book assumes some familiarity with the C language, but is very readable even for non-C programmers. This is an excellent text for use as an introduction to Computational Geometry, a primer for Preparata & Shamos, while at the same time it's an excellent addendum to that more seminal text. By weaving working code into his presentation, O'Rourke gives traction to the powerful engine of Preparata & Shamos.
40 of 54 people found the following review helpful
Format:Paperback
This book provides a reasonable introduction to the field of computational geometry, although the notation is sometimes sloppy and the author frequently makes inconsistent assumptions about the reader. For example, on the first page he refers to a circle as a "one-dimensonial set of points," which although valid from a toplogical perspective is a little confusing in an introductory text. As another example, the first exercise refers to "every point in dP," presumably meaning just the corner points (otherwise the problem would be unsolvable). The book also sets up a lot of irrelevant mathematical definitions that generally obfuscate the presentation rather than clarifying it. Although not prohibitive for the ambitious reader, these needless hindrances are at best a little annoying.
Secondly, I must criticize the text's scope, in light of the important role computational geometry has played in modern computer graphics. There is no discussion of clipping, culling, occlusion (e.g. BSP, octree, OBB), or even non-polygon primitives -- important topics arguably more useful to the target audience than e.g. convex hulls (to which over 1/4 of the book's pages are devoted).
Regardless, this book (combined with a professor and a course) probably would serve quite well as an undergraduate text. Readers interested in a cookbook of applied graphics algorithms, however, should look elsewhere.
Most Recent Customer Reviews
A great introduction!
A great introduction to computation geometry with some C code samples that actually work. A great introduction for graphics programmers.
Published 7 months ago by emile
Excellent text, obfuscated code
I bought this book to learn about convex hulls, voronoi diagrams and delaunay triangluations, and line arrangements. Read more
Published 23 months ago by Zeljko Vrba
collates useful computational geometric algorithms
If you are perhaps a graphics or robotics programmer, then you will often have need for computing various geometric forms. And the intersections of these forms. Read more
Published on March 15, 2006 by W Boudville
Nice balance of theory with code
This book was pleasantly surprising: I had expected to see code presented with minimal motivation or discussion of the underlying ideas -- something of a "Computational... Read more
Published on February 2, 2003 by Jason
Inside This Book
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First Sentence:
Much of computational geometry performs its computations on geometrical objects known as polygons. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
innermost polytope, monotone mountains, int vnum, reachability region, convex hull code, triangulation code, inf lag, improper intersection, median link, reflex vertex, largest empty circle, grown obstacles, interior cusps, orthogonal polygon, deficiency tree, parabolic front, lower tangent, monotone polygons, convex vertex, planar point location, sweepline algorithm, monotone pieces, polytope hierarchy, highest vertex, longest link Key Phrases - Capitalized Phrases (CAPs): (learn more)
Additional Exercises, Towers of Hanoi, Michael Goodrich, Van Wyk New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Much of computational geometry performs its computations on geometrical objects known as polygons. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
innermost polytope, monotone mountains, int vnum, reachability region, convex hull code, triangulation code, inf lag, improper intersection, median link, reflex vertex, largest empty circle, grown obstacles, interior cusps, orthogonal polygon, deficiency tree, parabolic front, lower tangent, monotone polygons, convex vertex, planar point location, sweepline algorithm, monotone pieces, polytope hierarchy, highest vertex, longest link Key Phrases - Capitalized Phrases (CAPs): (learn more)
Additional Exercises, Towers of Hanoi, Michael Goodrich, Van Wyk New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 52
books:
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9
books
cite this book:
See all 9 books citing this book
- Handbook of Discrete and Computational Geometry, Second Edition (Discrete Mathematics and Its Applications) by Jacob E. Goodman on 7 pages
- Computer Graphics by Acm Press on 7 pages
- Computational Geometry: Algorithms and Applications, Second Edition by Mark de Berg on page 348, Back Matter (1), and Back Matter (2)
- Computational Geometry: An Introduction (Monographs in Computer Science) by Franco P. Preparata on page 347, Back Matter (1), and Back Matter (2)
- Computer Graphics Using Open GL (2nd Edition) by Francis S. Hill on page 348, Back Matter (1), and Back Matter (2)
See all 52 books this book cites
- Level of Detail for 3D Graphics (The Morgan Kaufmann Series in Computer Graphics) by David Luebke on page 148, and Back Matter
- Geometric Tools for Computer Graphics (The Morgan Kaufmann Series in Computer Graphics) by Philip Schneider in Back Matter
- Introduction to Algorithms, Second Edition by Thomas H Cormen in Back Matter
- Environmental Mathematics in the Classroom (Classroom Resource Materials) by B. A. Fusaro on page 228
- The Way of Z: Practical Programming with Formal Methods by Jonathan Jacky in Back Matter
See all 9 books citing this book
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