Discrete and Computational Geometry by Satyan L. Devadoss (PDF)

Description

An essential introduction to discrete and computational geometryDiscrete 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 geometryCovers traditional topics as well as new and advanced materialFeatures numerous full-color illustrations, exercises, and unsolved problemsSuitable for sophomores in mathematics, computer science, engineering, or physicsRigorous but accessibleAn online solutions manual is available (for teachers only).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐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.

⭐Very nice, well-written and clear, with excellent diagrams. I recommend reading this in conjunction with watching Devadoss’s Great Course The Shape of Nature. That course draws feom this book and gets into knot theory and surfaces and so on. Also there is some material in the book not in the course.

⭐Exceptional book on this topic. Wonderful diagrams and illustrations.

⭐Very good introduction to computational geometry.

⭐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.

Keywords

Free Download Discrete and Computational Geometry in PDF format
Discrete and Computational Geometry PDF Free Download
Download Discrete and Computational Geometry 2011 PDF Free
Discrete and Computational Geometry 2011 PDF Free Download
Download Discrete and Computational Geometry PDF
Free Download Ebook Discrete and Computational Geometry