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Discrete and Computational Geometry

by Satyan L. Devadoss (Author), Joseph O'Rourke (Author)
4.5 4.5 out of 5 stars 19 ratings
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An essential introduction to discrete and computational geometry

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).
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  1. ISBN-10
    0691145539
  2. ISBN-13
    978-0691145532
  3. Publisher
    Princeton University Press
  4. Publication date
    May 1, 2011
  5. Language
    English
  6. Dimensions
    7 x 0.75 x 10 inches
  7. Print length
    272 pages
  8. See all details
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Editorial Reviews

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"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

Review

"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

Product details

  • Publisher ‏ : ‎ Princeton University Press (May 1, 2011)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 272 pages
  • ISBN-10 ‏ : ‎ 0691145539
  • ISBN-13 ‏ : ‎ 978-0691145532
  • Item Weight ‏ : ‎ 2.22 pounds
  • Dimensions ‏ : ‎ 7 x 0.75 x 10 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 19 ratings

About the authors

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  1. Joseph O'Rourke

    Joseph O'Rourke

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    I am a professor of Computer Science and of Mathematics at Smith College in Massachusetts in the USA. (I previously served as Dean and Provost). My specialty is computational geometry, a mix of algorithms (CS) and geometry (Math). My most recent work and books are focused on folding & unfolding. More information at my web page: http://smith.edu/~jorourke/ .

    See more on the author's page
  2. Satyan L. Devadoss

    Satyan L. Devadoss

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    Full content visible, double tap to read brief content.

    Satyan Linus Devadoss is the Fletcher Jones Professor of Applied Mathematics and Professor of Computer Science at the University of San Diego. Before landing in the west coast, he was a professor of mathematics at Williams College for nearly 15 years, along with holding visiting positions at Stanford, Ohio State, Mathematical Sciences Research Institute, Harvey Mudd, Université Nice, and University of California, Berkeley.

    An inaugural Fellow of the American Mathematical Society, and recipient of two national teaching awards from the Mathematical Association of America, he has a deep passion to make timeless mathematics timely: from building a 2-ton sculpture for Burning Man, to analyzing the genetics of beer, to painting the cartography of unsolved mathematics. His works and thoughts have appeared in venues such as NPR, the Times of London, the Washington Post, and Forbes, with support over the years from the National Science Foundation, the Mellon Foundation, the John Templeton Foundation, and the Department of Defense.

    See more on the author's page
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Customer reviews

4.5 out of 5 stars
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19 global ratings

Top reviews from the United States

Amazon Customer
5.0 out of 5 stars Excellent undergraduate text on Computational Geometry
Reviewed in the United States on February 28, 2018
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Devadoss & O’Rourke serves as a great introduction to Computational Geometry. Understanding algorithmic themes and computational approaches to geometric problems constitute the book’s central focus. Some high-level pseudocode is given for important algorithms.

Good proofs are given, which are crucial, but it is the quality of visualizations that pushes this text into the “great” category for undergraduates.

This text is most properly classified as an undergraduate resource since the pseudocode isn’t overly precise (compare with de Berg, et al or O’Rourke’s Computational Geometry in C), data structures aren’t discussed at an advanced level, and the text assumes little-to-no formal algorithms background. One might argue that such omissions are a benefit to the text, for those who are only seeing Computational Geometry for the first time and/or do not have an advanced background with regards to correctness, running-time, etc. proofs need not get weighed down with too much detail. Alas, such detail is imperative for one to truly understand Computational Geometry, but perhaps one might follow this text with de Berg et al, or another graduate text.
3 people found this helpful
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Amazon Customer
5.0 out of 5 stars Exceptional book.
Reviewed in the United States on February 3, 2018
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Exceptional book on this topic. Wonderful diagrams and illustrations.
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Jeremiah LaRocco
4.0 out of 5 stars Good, but not quite what I expected
Reviewed in the United States on August 4, 2012
Verified Purchase
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.
12 people found this helpful
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Michael Hardy
5.0 out of 5 stars This book not only introduces the topic but starts to acquaint students with research problems.
Reviewed in the United States on July 9, 2016
It has long been universally recognized that one field of mathematics in which unsolved problems can be understood by 12-year-olds even though actually solving them will require rare genius, broad erudition, and hard work, is number theory.

It seems less widely recognized that another such field is discrete geometry.

This is a textbook on discrete geometry. requiring very modest prerequisite material.

Along the way it presents numerous math problems that no one has ever solved, and students with almost no technical background will understand the questions. Perhaps some of them will become the first to solve some of those problems.

The technical background needed to understand this book is very modest, maybe not more than a bit of high-school algebra. Nonetheless, the student will have to work hard.

Two occasions in mathematics where vector spaces over the field of rational numbers are used are proofs of the Buckingham pi theorem of physics (not in this book) and Max Dehn's solution of Hilbert's third problem, which is about dissections of polytopes. Dehn's solution appears in this book.

UNSOLVED PROBLEM 1: Which polyhedra can be partitioned into disjoint tetrahedra?

(Each unsolved problem is labeled "UNSOLVED PROBLEM" in capital letters.)

UNSOLVED PROBLEM 2: For which classes of polygons does the number of triangulations have a closed form?

UNSOLVED PROBLEM 3: Find the smallest triangulation of the n-dimensional cube into n-simplices.

UNSOLVED PROBLEM 6: Can a polygon whose edges are mirrors be covered by only one guard?

UNSOLVED PROBLEM 11: Is there a polynomial-time algorithm for counting the triangulations of a set of points in the plane?

UNSOLVED PROBLEM 12: Is there a polynomial-time algorithm for finding the distance between the nodes of a flip graph?

UNSOLVED PROBLEM 13: Is the flip graph of every point set in 3-space connected?

UNSOLVED PROBLEM 23: Show that flexing a flexible polyhedron does not change its Dehn invariant.

UNSOLVED PROBLEM 29 is the celebrated P = NP problem.
2 people found this helpful
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Walter W. Olson, Ph.D, P.E.
5.0 out of 5 stars An excellent text for the subject
Reviewed in the United States on January 31, 2021
Discrete and Computatuional Geometry by Satyan L. Devadoss and Joseph O'Rourke is the best books in Mathematics that I have read in at at least a decade, and I have read quite a few few!

The book is clearly written with great examples. In addition, the authors state what problems are currently unproven in the field and would make great Ph. D. topics, and might even lead to to a Fields Medal, or more, if solved.

This book can be read and understood by anyone with a knowledge of basic geometry. The format of the book makes the subject palatable to even the those without a background in Mathematics.

Furthermore, the authors provide references to other more in depth texts, some of which I have read. However, this book is much better than those texts as far as understanding the subject area. I would consider this book a model for anyone writing a textbook.
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