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Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.
- The essential introduction to discrete and computational geometry
- Covers traditional topics as well as new and advanced material
- Features numerous full-color illustrations, exercises, and unsolved problems
- Suitable for sophomores in mathematics, computer science, engineering, or physics
- Rigorous but accessible
- An online solutions manual is available (for teachers only). To obtain access, please e-mail: Vickie_Kearn@press.princeton.edu
- Sales Rank: #298656 in Books
- Brand: Brand: Princeton University Press
- Published on: 2011-05-01
- Original language: English
- Number of items: 1
- Dimensions: 10.28" h x .97" w x 7.21" l, 2.21 pounds
- Binding: Hardcover
- 280 pages
- Used Book in Good Condition
Review
"Discrete and Computational Geometry meets an urgent need for an undergraduate text bridging the theoretical sides and the applied sides of the field. It is an excellent choice as a textbook for an undergraduate course in discrete and computational geometry! The presented material should be accessible for most mathematics or computer science majors in their second or third year in college. The book also is a valuable resource for graduate students and researchers."--Egon Schulte, Zentralblatt MATH
"[W]e recommend this book for an undergraduate course on computational geometry. In fact, we hope to use this book ourselves when we teach such a class."--Brittany Terese Fasy and David L. Millman, SigAct News
From the Back Cover
"This book is ideal for people who want to learn about the topic without wading too deeply into technical details. I really like the figures, and the writing style is very nice for students, with frequent jumps into exercises. The book favors topics that are intuitive, engaging, and easily grasped. It could form the basis of an excellent undergraduate-level course for students in computer science, applied mathematics, and pure mathematics."--Samir Khuller, University of Maryland
"I thoroughly enjoyed reading this book. It covers an incredibly diverse set of topics, ranging from elementary objects to deep mathematical concepts and important computational problems. Devadoss and O'Rourke have done a remarkable job of showing off the rich interplay between pure mathematics and computing that drives our research community. There really is nothing else like this on the market."--Jeff Erickson, University of Illinois, Urbana-Champaign
About the Author
Satyan L. Devadoss is associate professor of mathematics at Williams College. Joseph O'Rourke is the Olin Professor of Computer Science and professor of mathematics at Smith College. His books include "Geometric Folding Algorithms: Linkages, Origami, Polyhedra."
Most helpful customer reviews
12 of 13 people found the following review helpful.
a beauty!
By pascal vallotton
This was the perfect book for me at a perfect time. I have a relatively strong background in image analysis, modelling, and mathematics in general but I had not really peered into computational geometry, except for using a few tricks of the trade such as Delaunay triangulations. This book fixed me (I am a bit more than half way through). It has a delighful deductive and light flow to it. It touches on more advanced subjects in an informative manner and points to interesting current reseach questions. I even surprise myself touching the exercises - many of which are easy enough not to require pen and paper. The illustrations are superb; the layout is magnificent. A few proofs could have been a bit more complete but generally, one is left with the impression that one really understands what is going on. It would be great if the authors could maintain the quality in a significantly expanded future edition (about 250 pages in this one).
I also have Rourke's book on origamis and foldings, which I purchased mostly for the beauty of the drawing and the very interesting topics covered. However, that book is way more difficult to approach than the "discrete and Computational Geometry", which stands out as a gem!
9 of 10 people found the following review helpful.
Interesting book, but not everything follows
By TheDiscountPundit
Much of the discussion, particularly the central development of the first 4-5 chapters of the book on Delaunay triangulations, Vornoi diagrams, and their applications is very clearly developed. Pointing out unsolved problems related to the development was a refreshing approach. The book also does a very good job of stating when the various parts of the argument were first understood, be it in Ancient Greek times, the turn of the century, or only in the last 20-30 years.
The only reason I didn't give it a top rating is that there doesn't seem to be any way to solve several of the problems based on material in the book. The first of these is how to partition a cube into five tetrahedra.
It was a little surprising to me (a physicist) that the book doesn't ever have dot products or cross products.
Exercise 1.15 goes very quickly with cross products and the notion of directed (signed) area.
But I quibble. It's an interesting book and I read it straight through, doing the 10% exercises which looked to me neither impossible nor trivial. I've been dealing with programs which do automatic mesh generation for finite element analysis, and I now feel I have a deeper understanding of how they operate.
8 of 9 people found the following review helpful.
Good, but not quite what I expected
By Jeremiah LaRocco
I really liked the first five chapters of this book. There's no code, or even pseudo code, but I found the algorithm descriptions to be very clear and give an intuitive understanding of how the algorithms work. It doesn't go into too much detail, but the Big-o running time is given for most of the algorithms. I felt that with a bit of work I would be able to implement most of the algorithms.
The last two chapters didn't seem to fit with the first five. They were very abstract, didn't mention running time analysis, and just didn't seem as practically useful as the first part of the book. The explanations in these chapters also weren't as clear, and I doubt I'd be able to implement any of it without another reference.
The later parts of the book also use a lot of more advanced topics without much explanation. There are several sections starting off like "______ is an advanced topic we can't begin to explain here, but ..." and then going on to use some advanced result or theory.
On a positive note, the Kindle version is typeset very well, and even uses color. I read in the browser, on my kindle, and in the iPad kindle reader, and it looked excellent in all three, which is not always the case for technical books with equations and figures.
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