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'The balanced combination of careful descriptions, examples, algorithms and exercises makes it a pleasure to read …'. Zentralblatt
'Anyone who wants to know what this field is all about should read this book! The book is 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.' Miriam L. Lucian, Society for Industrial and Applied Mathematics
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Much of computational geometry performs its computations on geometrical objects known as polygons. Lesen Sie die erste Seite
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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.
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.
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.
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.
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