Customer Reviews (5)

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 Geometry for Dummies" sort of book. That's not the case at all. This is a bona fide textbook on the subject, suitable for an undergraduate course.
It covers all of the the "classical" topics: convex hulls, line segment intersection, polygon triangulation, Voronoi diagrams, motion planning.

The mode of presentation -- supporting a discussion of the theories with implementable code -- is actually a bit refreshing. For comparison: Other books, when discussing the line segment intersection problem (ie: Given a set of line segments, find all of their intersection points) simply assume that computing the intersection of a pair of segments can be done in constant time. This is not an especially difficult problem, but the discussion seems more complete with a brief description of how this might be done. The same can be said about other primitive tests and operations in other algorithms.

Overall, this book can stand alone as an excellent introduction to computational geometry, but a serious student in the subject will want more: perhaps Preparata and Shamos or de Berg et. al.

Very hepful
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.

my rewiew
i think that these website is very.it has everything that i need. all of my books are from amazan. ... Read more

Subjects:  1. C (Computer program language)   2. Data processing   3. Geometry   4. Geometry - General   5. Mathematics   6. Programming Languages - C   7. Science/Mathematics   8. Algorithms & procedures   9. C & Visual C   10. Computers / General   11. Geometry--Data processing   

Customer Reviews (11)

The best computational geometry book!
I also completely disagree with the one-star review below. The "Dutch book" is the clearest, most complete, most up-to-date, best designed, best illustrated computational geometry textbook out there. Some of the material may be a bit advanced for undergraduates (and for those people I would recommend Joe O'Rourke's excellent "Computational Geometry in C"), but for graduate students and other researchers who want to learn computational geometry, this book is absolutely essential.

This is an algorithms textbook, though, not a textbook full of code. You will not find compilable code in the author's favorite programming language du jour -- this may be what the first reviewer meant by "desperately needed details". What you will find is clear, correct, well-motivated explanations of the underlying algorithms, data structures, and mathematics.

The book does have a few faults. The motivating examples are often forced ("mixing things" for convex hulls??). The authors deliberately chose to show only one algorithm for each problem they consider, and occasionally the algorithm they chose is not the simplest or most efficient. But these are minor points.

If you're going to buy just one computational geometry book, this is the one to get.

Interesting read, excellent theory, no code
This book serves as a survey of computational geometry algorithms. The explanations are very readable. The authors have taken special care to prove algorithm correctness and time complexity bounds.

Although I have yet to actually implement one of the algorithms in the book directly, I was exposed to a number of general techniques which I have used, such as randomized techniques to eliminate pathological worst-case performance problems, and various space partitioning techniques.

The algorithms are all presented in pseudocode, unfortunately, which is the reason for only 4 out of 5 stars. Also, some important details are omitted which make a few of their algorithms practically useless (although they are interesting theoritically). For example, there is an algorithm for pathfinding and collision avoidance for a translating (but not ROTATING!) robot.

If you're lookin for a computational geometry bible, this isn't it. But there are certainly some gems in this book and it is a very interesting read.

Good Introduction but look elsewhere for detailed reference
Pro:
(1) Each chapter begins with a practical example. For example, the chapter computing intersections of lines starts with a discussion of a map-making application that goes into enough detail to see how the algorithms they present would be useful. This is a considerable step up from the common practice in algorithms literature of motivation by way of vaguely mentioning some related field (i.e. "These string matching algorithms are useful in computational biology"). This book does a much better job of motivating the material it presents, but if you're primarily interested in the abstract problem, these sections can be skipped.

(2) Each chapter is relatively self-contained. Feel free to skip ahead to subjects that interest you.

(3) Surprisingly readable. Unlike most technical material, one can read an entire chapter in a single sitting without missing much. Generally, each chapter will develop a single algorithm for a single kind of problem.

(4) It's very up to date. This second edition is less than two years old, it includes some new results in the field.

Con:
(1) Algorithms are only given in pseudocode. The emphasis is on describing algorithms and data structures clearly and completely. If you're looking for a "cookbook" with code to copy and paste into an application, perhaps O'Rourke's "Computational Geometry in C" would be a better choice.

(2) There are many important advanced results that are not discussed in the main text. An obvious example is the first chapter, which describes a well-known convex hull algorithm that takes O(n log n) time but algorithms that are faster for most inputs are mentioned only in the "Notes and Comments" at the end of the chapter. Someone interested in lots of gory details would be well-served to combine this book with Boissonnat and Yvinec's more detailed and mathematical "Algorithmic Geometry". ... Read more

Subjects:  1. Algorithms (Computer Programming)   2. Computer Books: General   3. Computer Mathematics   4. Computer Science   5. Computers   6. Data processing   7. Geometry   8. Geometry - General   9. Mathematics   10. Programming - General   

Subjects:  1. Applied   2. Data processing   3. General   4. Geometry - Differential   5. Geometry - General   6. Line geometry   7. Mathematics   8. Probability & Statistics - General   9. Projective Geometry   10. Riemannian Manifolds   11. Science/Mathematics   

Customer Reviews (6)

Symbolic computation
This book explains and illustrates the algorithms used by symbolic math packages such as Mathematica, Maple, CoCoA, MatLab, MuPAD,... to solve problems involving polynomials in many variables, and along the way teaches the elements of real algebraic geometry-- most mathematics texts concentrate on the complex-variable version. It is not just for undergraduates; electrical engineers, for instance, should see it. Lots of pictures!

Easiest introduction to Algebraic Geometry
This is the easiest introduction to algebraic geometry and commutative algebra, the authors had done a great job in writing a book that assume very little from the readers. To learn some algebraic geometry, you can either start with this book, or you can spend a year to read a lot of background materials in algebra and then go to a Graduate Text like Harris' book. Of course, if you want to be an expert in algebra, you eventually need a lot of background, what this book can help you is to offer you a quick start, much quicker than you would ever imagine.

Straightforward and lucidly written
Having just finished using this text in the course of an undergraduate seminar, I can attest to the fact that the authors' style is outstanding - they are able to synthesize an enormous amount of material in this volume and present it in a manner that is highly accessible to almost all students of mathematics. The presentation of important theorems (for example, Hilbert's Nullstellensatz and Basis Theorem) along with just the right amount of copncrete examples makes for a book of superb quality. All-around, I highly recommend this volume to anyone who has an interest in learning about Algebraic Geometry. ... Read more

Subjects:  1. Algebra   2. Algebraic Geometry   3. Commutative algebra   4. Data processing   5. Geometry - Algebraic   6. Geometry, Algebraic   7. Mathematics   8. Science/Mathematics   

Customer Reviews (5)

This book is history
This book is a classic, in fact the author's PhD thesis created this field, but this book is too old for any meaningful graduate work. There are new bounds and algorithms on almost all topics, which makes this a somewhat undesirable book. Also, this book has failed to keep me interested in it, while I am reading it...

Very useful for code development. Very clear and readable.
The ideas and algorithms presented in this book are clear enough for straight implementation in code. I have long experience in developing comercial and production software for VLSI layout applications, which made extensive use of the algorithms presented in this book.
I also use some chapters of this book as a part of a graduate course in VLSI layout algorithms being tought at the Technion, Israel. The contents of this book is well understood by EE and CS students.
I personally love this book, which introduced me into the area of computational geometry and its applications.

Useful but thick
Most of the papers that I've read on computational geometry refer to this text -- and for good reason. There's many good algorithms to be found here.

The book only gets 4 stars because it's hard to read. It took me several tries to pick up the ideas in this text. I think the De Berg text is MUCH easier to read.

The book is also getting a little dated. Some of the topics have come a long way since the 80's.

This book seems to be in most University libraries if you have that option. ... Read more

Subjects:  1. Computer Science   2. Discrete Mathematics   3. Geometry   4. Geometry - General   5. Mathematics   6. Science/Mathematics   

Customer Reviews (1)

Very comprehensive overview of computational geometry
This book, written by many well-known experts in the field, is a fine compendium of articles on the most active areas of computational geometry. Each article is supplemented with a glossary of terms needed for understanding the relevant concepts and frequently contains a list of open problems. An overview of the convex hull of a collection of random points in Euclidean n-space is given in one of the articles on discrete aspects of stochastic geometry, where also a very interesting discussion of generalizations of the Buffon needle problem is given.

There are a few articles overviewing Voronoi diagrams, such as the one on Voronoi diagrams and triangulations. The applications of Voronoi diagrams are many, and include tumour cell diagnosis, biometry, galaxy distributions, and pattern recognition. This article is a little short considering the importance of the subject.

The article on shortest paths and networks is somewhat disappointing since there is no in-depth discussion on network routing algorithms.

The article on computational topology highlights some of the results in this very important area. Many problems in topology have been tackled recently using computers, particularly the work of the mathematician A.T. Fomenko. Computational topology is a relatively young field, having been in existence only since the early 1990's. The applications are enormous, ranging from meshing, morphing, feature extraction, data compression, and in many scientific areas such as computational medicine, chemistry, and astrophysics. It can also be used in computer security via graphical passwords. It is an immense help in visualizing complicated topological objects, such as Lens spaces, horned spheres, and thickened knots. The article does not touch on the use of Mayer-Vietoris sequences to design efficient divide-and-conquer schemes for computing the homology of higher-dimensional complexes. The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.

The last section of the book covers applications with the most interesting article being the one on sphere packing and coding theory. The algorithms in sphere packing have direct applicability to error correctiong codes over the field GF(q). The author of this article does touch briefly on general algebraic-geometric codes, which is good considering their importance in applications.

The last article appropriately discusses available software for computational geometry. Although the list of Web sites is quite extensive, there are many more available since this book was first printed.

A very fine addition to the literature on computational geometry and should be on everyone's shelf who is interested in this important area. ... Read more

Subjects:  1. Applied   2. Combinatorial geometry   3. Data processing   4. Discrete Mathematics   5. Geometry   6. Geometry - General   7. Handbooks, manuals, etc   8. Mathematics   9. Science/Mathematics   

Customer Reviews (4)

Not a self contained book!
I bought this book with the intent of understanding the level set method AND be able to implement it in code. The book fails on the later. He gives you some basic formulas/algorithms to start with, but they are not good enough for most problems. You need to get the references (and the references of those references) to obtain the actual algorithms people use to implement the level set method.

The first six chapters are good for giving you a nice qualitative understanding of the method and the issues of implementing the method. And the rest of the book claims to show you the more advanced techniques, but whenever the nitty gritty details are needed, he refers you to the references.

My advice: just get his references. If you are at a university, then you probably have free access to the online journals that contain his (and others) research articles. In fact, this book is basically a copy-paste of those articles! Literally!

Not for beginners
I am afraid that this book is not for beginners who want to have a clear mind of the level set method. You will have to go to the library quite often to dig out all the references the author mentioned. I would say this book is for experienced researchers only.

Good introduction to level set methods
I use these methods in the context of image analysis, for image segmentation essentially. The book is an inescapable introduction by one of the main inventors of these methods. It is easy to read and relatively complete. Be sure to get the second edition. The only slight problems are the remaining typos. There are quite a few, for a second edition, and they might throw off a beginner. You will need to read some introduction text on finite differences methods at least. The chapter in Numerical Recipes is enough. ... Read more

Subjects:  1. Advanced   2. Applied   3. Level set methods   4. Mathematics   5. Physics   6. Science/Mathematics   7. Calculus & mathematical analysis   8. Mathematics / General   9. Numerical analysis   

Subjects:  1. Applied   2. Differential Equations   3. Geometry   4. Geometry - General   5. Mathematics   6. Numerical grid generation (Num   7. Numerical grid generation (Numerical analysis)   8. Partial Differential Equations   9. Science/Mathematics   10. Topology   11. Topology - General   12. Mathematics / General   13. Numerical analysis   

Subjects:  1. Geometry - General   2. Mathematics   3. Mechanics - General   4. Science/Mathematics   5. Study & Teaching   6. Mathematics / General   7. Numerical analysis   

Customer Reviews (2)

Deja vu?
In 1958, Cornell psychologist Frank Rosenblatt proposed the 'perceptron', one of the first neural networks to become widely known. A retina sensory layer projected to an association layer made up of threshold logic units which in turn connected to the third layer, the response layer. If two groups of patterns are linearly separable then the perceptron network works well in learning to classify them in separate classes. In this reference, Minsky and Papert show that assuming a diameter-limited sensory retina, a perceptron network could not always compute connectedness, ie, determining if a line figure is one connected line or two separate lines. Extrapolating the conclusions of this reference to other sorts of neural networks was a big setback to the field at the time of this reference. However, it was subsequently shown that having an additional 'hidden' layer in the neural network overcame many of the limitations. This reference figures so prominently in the field of neural networks, and is often referred to in modern works. But of even greater significance, the history of the perceptron demonstrates the complexity of analyzing neural networks. Before this reference, artificial neural networks were considered terrific, after this reference limited, and then in the 1980s terrific again. But at the time of this writing, it is realized that despite physiological plausibility, artificial neural networks do not scale well to large or complex problems that brains can easily handle, and artificial neural networks as we know them may actually be not so terrific.

Seminal AI book
This is a seminal work in the field of Artificial Intelligence. Following an initial period of enthusiasm, the field encountered a period of frustration and disrepute. Minksy and Papert's 1969 book summed up this general feeling of frustration among researchers by demonstrating the representational limitations of Perceptrons (used in neural networks). Their arguments were very influential in the field and accepted by most without further analysis.

I found this book to be generally easy to read. Despite being written in 1969, it is still very timely. ... Read more

Subjects:  1. Artificial Intelligence   2. Computer Bks - Communications / Networking   3. Computer Books: General   4. Computer Books: Operating Systems   5. Computer Science   6. Computers   7. Data Processing - Parallel Processing   8. Data processing   9. Geometry   10. Machine learning   11. Networking - General   12. Neural Networks   13. Parallel processing (Electroni   14. Perceptrons   15. Computers / Computer Science   

Subjects:  1. Algorithms (Computer Programming)   2. Computer Bks - General Information   3. Computer Science   4. Data Structures   

Features

• Facsimil

Customer Reviews (4)

A good start
This book is a short introduction of how the programming language C++ can be used to solve various problems in computational geometry. It is modest in its goals, and concentrates mostly on typical "bread-and-butter" topics that would be encountered by someone first encountering the field of computational and discrete geometry. Specialized topics in computational geometry and more modern techniques can then be found in the literature for interested readers who need a more comprehensive treatment.

The first three chapters introduce the reader to the notion of algorithms and data structures. The author uses the boundary-intersection problem to illustrate the main points of the chapter, such as algorithmic paradigms and abstract data types. Complexity measures for algorithms are discussed briefly, along with mathematical induction. The linked list data structures he discusses are very important in computational geometry, especially the pointer-based implementation.

In chapter 4, the author discusses the data structures that are needed for dealing with geometric structures in dimension 2 and 3. After a review of vector algebra he defines the point class and then the vertex class. The latter, along with the polygon class, is used to define polygons as a cycle of vertices which are stored in a circular doubly linked list. These are generalized to 3 dimensions where classes are given for points, triangles, and edges. The author then gives an algorithm for finding the intersection of a line and a triangle, which uses projection, and tests for degeneracy before projecting.

The next part of the book deals with applications of the algorithms, such as finding a star-shaped polygon in a finite set of points, finding the convex hull of a set of points, the decision problem for points inside polygons, the Cyrus-Beck and Sutherland-Hodgman algorithms for clipping geometric objects to convex polygons, and an O(nlogn) algorithm for triangulating a monotone polygon. The treatment is very understandable and should prepare the reader for more advanced reading (especially in computer graphics). The famous gift wrapping algorithm for finding the convex hull is given, along with the Graham scan algorithm. Issues more pertinent to computer graphics, such as rendering are discussed also. The hidden surface removal problem is solved via depth sorting. An algorithm is also given for finding the Delaunay triangulation. In addition, the author does a nice job of showing how to use plane-sweep algorithms for computational geometry problems in the plane. An interesting O((r + n)logn) time algorithm for finding the number r of pairs of n line segments in the plane that intersect. Voronoi diagrams are discussed also, which are extensively used in applications. The latter few chapters are more specialized than the rest of the book, and concentrate on divide and conquer algorithms and binary search trees.

Author's response
...The main objective of my book is to explore someideas that arebasic, interesting, and accessible, without attempting comprehensivetreatment. These objectives are stated clearly in the first paragraph of the book's preface. My intended audience are relative novices who need not have prior experience with algorithms, data structures, or linear algebra, and with only limited experience with C++. The book's intended audience is also clearly framed in my book's preface. Indeed, the objectives and target audience are also evident from the table of contents, which shows that the first half of the book is devoted to fundamentals (the design and analysis of algorithms, and basic data structures) that the typical graduate student, much less professional, would have mastered years earlier.

Are my references deficient because the papers it cites are no less than four years old (relative to the book's release date), and some even date to the 1970s? Most of the methods I present were devised years and even decades ago. I chose these methods to suit the book's purpose and audience; I chose methods that are basic, yet which a less sophisticated reader will find interesting and accessible. Similarly, I chose the book's references so they would be relevant to the book's content and useful to the reader.

The choice of what topics to present is always to some degree at the author's discretion, particularly in a book such as this which explores ideas without attempting comprehensive coverage. Critics can always be found who will take issue at the omission of this topic or the inclusion of that, or with how some topic is presented. But again, I chose the material with my book's objectives and audience in mind.

Relative to the expectations of a computational geometer or a graduate student, my book cannot compare to Preparata and Shamos', or to Mark deBerg's. Their audience doesn't require a book that spends half its time covering such fundamentals as algorithm analysis, lists and stacks, search trees, and elementary sorting and searching methods. Their audience would expect only the most limited coverage of these things, or no coverage at all. In contrast, given my book's target audience, to omit these topics would be to leave out the very background that the rest of the book not only requires, but that the intended reader likely lacks. Omitting such material would be a disservice to the intended reader. Likewise, to include certain more difficult topics which are the meat of these more advanced books would go well beyond the scope of my book, and to do this would also be a disservice to the intended reader. My book differs significantly from these other books in its objectives and its intended audience.

Embarassingly bad
Don't buy this book. It's a bad computer graphics book, a bad computational geometry book, and a bad C++ programming book.

Several fundamental concepts in computational geometry are screwed up or omitted entirely. For example, there is NO discussion of point-line duality, or of the duality between Delaunay triangulations and Voronoi diagrams, or of the simple connection between 2d Delaunay trianglations and 3d convex hulls. The simple primitive "Are these three points in clockwise order?" is explained using trig (compare angles) instead of linear algebra (compare slopes). [These may seem like technical trivia to novices, but that's why you buy books like this -- in the hopes that at least the technical trivia is done right!]

The book describes slow algorithms for problems such as Voronoi diagrams, when equally simple faster algortihms have been known for many years. Despite its 1996 publication date and the rapid development of the field, the book doesn't reference a single paper newer than 1990, and very few newer than 1980!

Inexcusably for a book with hunderds of lines of source code, the code isn't available online, on either the publisher's or the author's web site. For all we know, it doesn't even compile, much less work!

If you want to learn about computational geometry, this is NOT the book to buy. For programmers, Joe O'Rourke's "Computational Geometry in C" is much more readable, accurate, and up to date. For aspiring computational geometers, Mark de Berg et al's "Comptuational Geometry: Algorithms and Applications" is indispensible. Even the old standard by Preprata and Shamos, depite being 15 years out of date, is better than this one. Laszlo's book is just embarassing. ... Read more

Subjects:  1. C++ (Computer program language   2. C++ (Computer program language)   3. Computer Bks - Languages / Programming   4. Computer Graphics - General   5. Computer graphics   6. Programming Languages - C++   7. Science/Mathematics   

Features

• Facsimil

Customer Reviews (2)

Poor Textbook
This book is not suitable for beginners.It doesn't explain some important theorems and rules clearly,especially for "history" data structues , my classmates also can't understand how to implement it in detail ! All materials of this book seems uilding on auther's personal imaging !

very good if a little specialized
An in-depth look at randomized incremental algorithms in computational geometry. Since this appears to be the most successful and practical approach for classic problems like convex hull, Voronoi diagram and polygon triangulation, this would be a good book to own if you own just one. Especially if you are interested in theory. ... Read more

Subjects:  1. Algorithms   2. Algorithms (Computer Programming)   3. Data processing   4. Geometry   5. Geometry - General   6. Mathematics   7. Science/Mathematics   

Subjects:  1. Congresses   2. Data processing   3. Geometry - Algebraic   4. Geometry - General   5. Geometry, Algebraic   6. Mathematics   7. Science/Mathematics   8. Algebra   9. Algebraic geometry   10. Mathematics / Geometry / Algebraic   

Subjects:  1. Advanced   2. Analytic Mechanics (Mathematical Aspects)   3. Level set methods   4. Mathematics   5. Science/Mathematics   6. Interfaces (Physical sciences) - Mathematics   7. Mathematics / General   

Subjects:  1. Computer Architecture - General   2. Computer Bks - General Information   

Subjects:  1. Computer Bks - General Information   2. General   3. Science/Mathematics   

Subjects:  1. Congresses   2. General   3. Geometry   4. Geometry - General   5. Mathematics   6. Mensuration   7. Physical measurements   8. Science/Mathematics   9. Weights & Measures   10. Weights And Measures   

Subjects:  1. Geometry   2. Topology   

Subjects:  1. Congresses   2. Data processing   3. Geometry