Product Description
A basic problem in computer vision is to understand the structure of a real world scene. This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms.First Edition HB (2000): 0-521-62304-9 ... Read more

Customer Reviews (10)

Good book, but....
Great book in this subject. The good things are...
- Clear theoritical introductionwhich many books miss to add
- Great appendixes about some mathematical theories necessary to understand this book
- Great organizaion of book chapters and coherent topics for each
- Bonus: Chapters for estimating hemographies and the math behind that
I cannot see any cons of the boox except that there is no clear road map to go into specific topic. For example, I am interested in multiple view geometry only (Trifocal tensor and above), I cannot figure out what I should read and what I can skip. I have to figure my way through.
After all, the best in the subject. Recommended.

SH*** happens....
There was a failure in the delivery, the mailman gave the package to someone else. I have no way to be refund by post Canada. I did order the book once again and i received it.

Good on the explanations of the theory
This book is very complete and rigorous in its explanations of the theory. However, I just think I like the approach in An Invitation to 3-D Vision a bit better. This book is better illustrated than that one and is more careful in its explanations, but this book just seems more focused on providing complete proofs than giving you a feel for how you would approach a real problem. Even the exercises are more along the lines of proofs. I like how An Invitation to 3-D Vision ends the book with a complete example. In all fairness, though, this book does have quite a bit of Matlab code on its website.

The book begins with some background material on 2D and 3D geometry. Then the author explains single-view geometry and how cameras map an image in 3D space to an image. Two-view geometry is next, with the author describing the epipolar geometry of two cameras ahd projective reconstruction from resulting image map correspondences. Part three of the book extends ideas to three cameras and the resulting trifocal geometry. The final section of the book takes the algorithms of the book to N views. Thus this book has a simple and straightforward structure that belies the complexity of the material.

If you are really researching this subject you should probably have this book for explanation, illustrations, and rigor, and the Invitation book for enlightenment through a good example-based approach. You should also have Introductory Techniques for 3-D Computer Vision as a text on the individual pieces of algorithms involved in 3D vision. And don't even think about getting into this subject unless you already have a firm foundation in linear algebra, image processing, and computer vision in general as found in Computer Vision, which is my favorite introductory computer vision text.

Missing a chapter
I received the fourth printing a few weeks ago.It is missing pages 177-208.That includes all of chapter seven, on camera calibration.Ridiculous.

Valuable and full of useful content
I find the book very useful, it is full of practically useful content. Formulas, theorems, lots of examples and illustrations.Overall very easy to read and understand, though requires you to recall your forgotten mathematical skills. The book does present what it claims on the first pages, so read the abstract and judge for yourself if you need the book.For my purposes, I found it to contain all the material I needed to perform certain image photo transformations and compositions. There is also lots of reference material, in terms definitions, formulas and theorems with proofs.And it's good to have it all in one place.

Overall I would say it is worth the money. ... Read more

Product Description
Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen.

The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. ... Read more

Customer Reviews (5)

Amazing book
Just an all around great book; interesting way to explore geometry, in a format that's easily understandable for both beginning & advanced students.

Good enough
Not as new as I expected. Doesn't have original cover, though I can settle with the enforced hard cover.

forward thinking book about using the computer for mathematics education
Turtle Geometry teaches mathematics and physics via the computer and the Logo programming language. The mathematics covered is pretty advanced, including topology, and general relativity. Yet, through the use of turtle geometry this advanced math and physics becomes accessible to the layperson. Although all of the examples are in the Logo programming language there are listings of Basic routines in the back of the book. With the help of the Basic routines I was able to easily translate the Logo/Basic code to the Python programming language which I choose to use for reading this book. The reviewers of this book mention it as the beginnning of a revolution in mathematics education. It seems though, that this revolution did not come about as computers are still not used very effectively in the classroom. I think this is very sad as the teaching approach used in Turtle Geometry could be very successful in the classroom.

My favorite geometry textbook
I discovered this little gem of a book while exploring the stacks in the library when I was attending a local junior college back in the 80's.The author uses Logo's turtle graphics as a way of exploring the properties ofgeometric space.From very simple beginnings drawing regular polygons andother simple shapes, the book gradually works its way to more and morecomplicated scenarios.After exploring the properties of ordinary turtlegraphics, turtle graphics are tried on the surfaces of spheres and cubes,then on more complicated surfaces.Little by little, concepts ofnon-Euclidean geometry are introduced, until the final chapters in whichthe turtle is used to demonstrate the geometric nature of gravity inEinstein's general theory of relativity.

I strongly recommend this bookto anyone with interests in computer programming, geometry and physics. The unusual approach this book takes to the understanding of curved spaceis deceptively simple and surprisingly powerful.

Very good book to show how to use logo as a tool for math
Anyone interested in logo from beginners to advanced users will benefit from reading this book.It has very easy and simple to understand examples, along with a review, and questions at the end of every chapter.Some solutions are provided at the end of the book, (and their even correct, as opposed to many other text books I've read).The pace of the book gets gradually more difficulst, yet more interesting as you reach the climax at the end.A must read for anyone interested in Mathematics. ... Read more

Product Description

Until recently, all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming.

Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.

Customer Reviews (4)

ok, but...
It's a good book, but the mathematics is poorly treated, not enough rigorous as would be expected.

very good text
This is the text I would first recommend to anyone involved in geometrical programming who would like to learn geometrical algebra.

An excellent introduction to the subject.
The book Geometric Algebra For Computer Science, by Dorst, Fontijne, and Mann has one of the best introductions to the subject that I have seen.

It contains particularly good introductions to the dot and wedge products and how they can be applied and what they can be used to model.After one gets comfortable with these ideas they introduce the subject axiomatically.Much of the pre-axiomatic introductory material is based on the use of the scalar product, defined as a determinant.You'll have to be patient to see where and why that comes from, but this choice allows the authors to defer some of the mathematical learning overhead until one is ready for the ideas a bit better.

Having started study of the subject with papers of Hestenes, Cambridge, and Baylis papers, I found the alternate notation for the generalized dot product (L and backwards L for contraction) distracting at first but adjusting to it does not end up being that hard.

This book has three sections, the first covering the basics, the second covering the conformal applications for graphics, and the last covering implementation.As one reads geometric algebra books it is natural to wonder about this, and the pros, cons and efficiencies of various implementation techniques are discussed.

There are other web resources available associated with this book that are quite good. The best of these is GAViewer, a graphical geometric calculator that was the product of some of the research that generated this book. Performing the GAViewer tutorial exercises is a great way to build some intuition to go along with the math, putting the geometric back in the algebra.

There are specific GAViewer exercises that you can do independent of the book, and there is also an excellent interactive tutorial available.Browse the book website, or Search for '2003 Game Developer Lecture, Interactive GA tutorial. UvA GA Website: Tutorials'.Even if one decided not to learn GA, using this to play with the graphical cross product manipulation, with the ability to rotate viewpoints, is quite neat and worthwhile.

A reader from Los Alamos, NM
Geometric Algebra (GA) is a unifying mathematical language that should be taught instead of or at least in combination with traditional vector analysis. Most other books on GA are aimed at Physicists. This book is a better match for Engineers and Programmers.The authors are all active researchers in applications of GA. They have done a comprehensive and up to date job of collecting, organizing and presenting the material for both beginners and those who follow the development of GA on the web. The examples and problems use GAViewer, an easy to learn programming language with an Open GL view window that can be downloaded for free from the book website. Using GAViewer with the book is very good way to learn GA, especially the 5D Conformal model of 3D space. The authors hold nothing back. Between the book, the code and the website everything is there to make learning GA fun and useful. I highly recommend this book. ... Read more

Product Description
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. ... Read more

Customer Reviews (16)

let my money back assp
I didn't order this book...

furthermore i don't saw this book.

How it can be happen?

Now I can't believe ordering system of amazon...

Let my money back asap!!!

Concise reference for computational geometry
This book covers the concepts and algorithms concisely and hence forms a very handy reference to Computational Geometry. You could use this as the starting point for any Comp Geom application and build on that. I am pretty happy with this buy!

Good book, not for a primer
The subject is not easy, so the book is surely not for a primer on graphical programming, even more for a primer on computation and algorithms.
But if you need some very advanced algorithms to solve any computational geometry problem, you'll find it here. Maybe the very latest advances on subject are not present here (a new revision of this book is available, not much news on that, look for the difference on the web).
Thanks to the author, whom I asked a clarification on an algorithm present in the book, and responded in less than 3 hours.

The definitive guide to computational geometry.
When studying computer science, one will encounter a number of books."The Dinosaur Book", Operating System Concepts (7th Edition), "The White Book", Introduction to Algorithms, "The Green Book", Artificial Intelligence: A Modern Approach (2nd Edition) (Prentice Hall Series in Artificial Intelligence), and a select few more.The best way to articulate my satisfaction with this material is to refer to it as "The Blue and Yellow Book."

Each chapter is introduced with a problem.For example, "How would one install cameras on the inside of an art gallery (represented by a polygon) such that each wall can be observed with as few cameras as possible."The chapter then presents the material in a clear, concise fashion, and applies this newfound information to solve said problem.

It could be argued that the book is math heavy; certainly those with a strong grip on linear algebra and geometry will have an easier time, but those without can still grasp the material enough to benefit.For those interested in proofs, there's no shortage in the book, either.

Strongly recommended and a great deal of fun to read.

Excellent Background
This book is extremely well written, easy to understand, and actually is the standard text for Computational Geometry classes, as far as I know.The only thing I didn't like about it was that there seemed to be a few errors in some of the pseudocode.But, it's to be expected when publishing a textbook, and I think it'll probably be cleared up in future editions.

Overall, great book.I'd recommend it to anyone taking graphics or a computational geometry class. ... Read more

Product Description
This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design.The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron.A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues.The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels.The code in this new edition is significantly improved from the first edition, and four new routines are included.Java versions for this new edition are also available. ... Read more

Customer Reviews (7)

Excellent text, obfuscated code
I bought this book to learn about convex hulls, voronoi diagrams and delaunay triangluations, and line arrangements.So far I have made it through the chapter on 2D convex hulls, and I must say that it is an excellently written book for learning about the covered topics in computational geometry.The text is clear easy to understand; algorithms are sufficiently detailed and illustrated to allow full implementation without needing other resources.Corner cases are meticulously covered.I also like the text because it is straight to the point, i.e., it does not spoon-feed the reader. So, although relatively short book, it contains a lot of densely packed, but still enjoyably readable, information. Illustrations are simple but excellent: they are carefully designed and very helpful for understanding the described algorithms.

I give the book four stars for two reasons.

First, the coverage of floating-poing precision issues is almost non-existant: most of the algorithms are integer-only.A survey chapter over techniques for handling FP precision issues would be *VERY* welcome.(After all, geometric algorithms are most often applied to floating-point data in the real world.)Judging by the quality of existing bibliography, I think the author would make an outstanding job on this topic.(Hint for the 3rd edition :-))

Second, I have strong objections against the coding style used in this book: the presented code is an excellent demonstration of how to obfuscate C programs by using typedefs and hungarian notation (inconsistently!) applied in postfix. (NOTE: I have 10+ years of experience in C and C++ coding, so I'm not just a "little bit confused").

collates useful computational geometric algorithms
If you are perhaps a graphics or robotics programmer, then you will often have need for computing various geometric forms. And the intersections of these forms. Rather than derive algorithms from scratch, you might want to first look here. O'Rourke has collated several useful sets of methods. Germane to two and three dimenions.

Convex hulls are important enough that he devotes 2 chapters to these. While the somewhat related idea of Voronoi diagrams gets its own chapter.

The C code is a nice bonus to some readers. Though if you are experienced enough in another language, you should be able to readily code an algorithm in the book from scratch.

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

Product Description
In the past decade the systematic study of geometric algorithms has evolved to form the very active field of research known as computational geometry. Computational Geometry: An Introduction presents a comprehensive, systematic, and coherent treatment of its subject.

A fundamental task of computational geometry is identifying condepts, properties, and techniques which aid efficient algorithmic implementations from geometric problems. The approach taken here is the presentation of algorithms and the evaluation of their worst-case complexity. The particular classes of problems addressed include geometric searching and retrieval, convex hull construction and related problems, proximity, intersection, and the geometry of rectangles.

Computational Geometry: An Introduction presents its methodology through detailed case studies. The book, primarily conceived as an early graduate text, should also be essential to researchers and professionals in the fields of computer-aided design, computer graphics and robotics. ... Read more

Customer Reviews (6)

Christians fundimentalists have the King James Version, Computational geometrists have...
This book is to computational geometrists what the King James Version of the Bible is to christian fundimenalists.Even though newer translations of the Bible are easier to read, somehow nothing sounds quite so authentically like the voice of God than those Elisibethen cadences, written in an almost archaic language....

...similarly for this book.Many times, the descriptions of algorithms presented in this book are made unnecesarily hard by very arcane langauge.

But this book is authoritative and definitive in a way that no other text on computational geometry is ever likely to achieve.Even though there are any number of books which are newer and easier to read, it seems like this the one book on the shelf of every serious computational geometer I know.

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.

Still interesting after so many years ...
I have just happened to exhume this book from my library, after it spent some years gathering dust above the shelf. In spite of the long time I have not being reading it, it still retains the full meaning it showed me when I was using in calculations relating radar domain definition. May be the textbook wins by far the comparison to the current vague and inflated computer publications, may be it is not a manager-oriented issue but it is for nearly specialistic use, you find in it clearly stated, and straight, answers to the questions you meet, or at least a definite reference where a more detailed explanation can be find. It presents interesting problems, and explains you how to solve them. I think it is the best you can say about a computer science book. ... Read more

Product Description

This book provides an accessible introduction to methods incomputational geometry and computer graphics. It emphasizesthe efficient object-oriented implemenation of geometricmethods with useable C++ code for all methods discussed.

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 screwedup or omitted entirely.For example, there is NO discussion of point-lineduality, or of the duality between Delaunay triangulations and Voronoidiagrams, or of the simple connection between 2d Delaunay trianglations and3d convex hulls.The simple primitive "Are these three points inclockwise order?" is explained using trig (compare angles) instead oflinear algebra (compare slopes).[These may seem like technical trivia tonovices, but that's why you buy books like this -- in the hopes that atleast the technical trivia is done right!]

The book describes slowalgorithms for problems such as Voronoi diagrams, when equally simplefaster algortihms have been known for many years.Despite its 1996publication date and the rapid development of the field, the book doesn'treference a single paper newer than 1990, and very few newer than1980!

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

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

clear book but you'll have to type the code.
This is a clear book on an interesting subject. Computational geometry isa(nother) field where designing object oriented programs is so natural.Examples are clear, explanations also, with a good level of mathematicalformalism.
I deplore however that source code is not provided with thebook on disk or on the internet. You will have to type the code you want totest.
The paper of the cover is too thin to protect the book. ... Read more

Product Description

Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD).

Customer Reviews (1)

Good computer graphics text
This text has a novel approach to entry level computer graphics using homogeneous coordinates entirely.I struggled a bit with the use of these representations in perspective transformations.However once I got it I found the derivations and formulas to be easy to get and easy to use. The book has an extensive set of exercises with complete answers.I deducted one star because the theoretical aspects of homogeneous transformations could use expansion and simplification. ... Read more

Product Description
Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on how to solve challenging problems.The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next, through numerous problem solving techniques.A large collection of problems, varying in level of difficulty, are integrated throughout the text, and suggested hints for the more challenging problems appear in the instructor's solutions manual for use at instructor's discretion. ... Read more

Customer Reviews (4)

Euclidean and Transformational Geometry
"Euclidean and Transformational Geometry: A Deductive Inquiry" is a text that every mathematics teacher should have a copy of.Not only does it provide a comprehensive coverage of geometry, but it reads like a historical journey through the development of mathematics. The order of the topics is so logical that the reader cannot help but leap from theorem to theorem and take wonderful vacations along the way into islands of interesting problems.

This book's major strength is its clever combination of challenge, clarity, and instruction to teach ideas. The concepts are so clearly presented that students can easily learn them and the skillfully done illustrations augment the book's clarity. Each step of instruction is included and labeled so that the student will not miss some crucial step in their thinking. Multiple paths to the solution of a problem are presented so that the student learns alternative ways of thinking about that concept. This variation and the easy to understand style of writing makes this book interesting and an intellectually stimulating read.

As a high school teacher I find this book to be the richest single resource I have. Most of my students are directed to its well-worn pages multiple times throughout their time with me. I send them to read further about something that interests them, or to read an alternate explanation of a concept that they are struggling with, or simply to find some interesting and challenging problems to work on at home. I believe it is my duty to provide each student with problems that challenge them and are attainable at their level. Dr. Libeskind's book provides me with enough material for all of them, even the brightest of my students, from basic Algebra to Calculus. The problems are not necessarily hard, though some are, but more importantly they're interesting. Many students come early to my class or stay after simply to talk with me, or each other about problems they are working on from this book.

I highly recommend "Euclidean and Transformational Geometry" to all math instructors at the middle school, high school and college levels. Not only has reading it and doing the problems myself greatly enhanced my own understanding of geometry, it has made the subject become beautifully alive for me and the students I share it with. It is a book I cannot imagine being without.

Memorable Geometry
Fifteen years ago I was fortunate to be a student in Professor Libeskind's geometry course at the University of Oregon.The problems that he presented to us, and the way that he emphasized multiple approaches and deep understandings, helped shape my career as a high school mathematics teacher more than any other singular experience.I have now been teaching for thirteen years, and geometry is one of my favorite courses to teach.

My experience in Professor Libeskind's class was unforgettable.I wanted to share some of the problems with my honors students, and was overjoyed to discover that the wonderful collection of problems from that course have now been published as a book!I have yet to find a person who has opened this book and is not immediately interested in finding a solution to the famous Treasure Island Problem.The presentation, clarified through ample diagrams, immediately draws one into the world of exploring.Professor Libeskind writes in a style that invites students of all levels, encourages success, and provides support and assistance to those who need it.He patiently allows the student to make the connections first, but his clear explanations that reveal multiple connections between topics ensure that the student will fully understand the depth of the content.

The development of proof is one of the greatest strengths of this book.High school geometry texts typically begin with a list of theorems and then expect students to construct proofs.As a result, many students look at a proof and have no idea how to proceed.In this book, Professor Libeskind guides students through the process of constructing a proof as an extension of an investigation.I strive to teach my students proof through a similar process, and I am eagerly anticipating Professor Libeskind's high school geometry text.

The wide range of topics introduced and the connections developed between them help to foster a passion for mathematics.One of my favorite aspects of the book is the experience of using Geometer's Sketchpad to investigate problems that formerly led me to use reams of paper.Although the same exercises can be completed without Geometer's Sketchpad, it definitely adds to the experience and helps to keep students motivated.I have not found another geometry book that covers as much material and involves the student in learning as much as this one.

Fantastic Resource
As a middle school math teacher, I am constantly struggling to find textbooks that I can use with my advanced students.There is a dearth of high-quality math textbooks aimed at advanced middle school and high school students, and I usually have to create my own lesson plans using bits and pieces from a number of sources.Though Dr. Libeskind's Euclidean and Transformational Geometry is intended to be a college-level text, I have found it a gold mine for for my advanced middle school classes.The format of the text very closely matches the way I present concepts to my students: each section begins with an introduction to new concepts and vocabulary, followed by simple diagrams and illustrations, and then a theorem and its proof.The exercises are designed to tie back into the main text discussion, and each section builds upon concepts that earlier sections have introduced.

Textbooks that I have worked with in the past have rarely given the same level of focus to writing and understanding proofs that this one does.My experience suggests that while many students find thinking about theorems in terms of proofs foreign at first, they quickly acclimate to the process if proofs are readily available for every property that they encounter.Dr. Libeskind's book is fantastic in this respect because he provides proofs for every mathematical relationship that the text proposes.The book is written to actively encourage students to get into the proof mindset so that they can deconstruct problems, and it is the only textbook that I have come across that does this effectively.

I am also impressed with Dr. Libeskind's ability to collect the diverse topics that his book covers and arrange them in a simple and logical way.This book is straightforward and to the point; no time is wasted on extraneous diagrams, pictures, or problems.The content is clear and concise, but unlike many other textbooks it also encourages the reader to think through problems himself rather than simply providing statements.Even the page layout, which separates ancillary discussions and exercises from the main text using color-coded side-bars and subsections, has been designed with simplicity and ease-of-use in mind.

Though my school district mandates the use of particular textbooks for middle school and high school math, I would like to have several copies of this book in my classroom for students to use as a resource.I have found it vastly superior to many other textbooks that cover the same subject, and though it is aimed at college-level courses, it has been very useful in my lesson planning.

Review from Karen
I highly recommend this book by Professor Libeskind, because it has many outstanding features which make it is vastly superior to the typical college geometry textbook.This geometry textbook is a unique and extraordinary resource for students.It is an elegant book, beautifully written and illustrated, that will introduce students to the process of mathematics - that is to say, to explore interesting problems, discover for themselves possible solutions, and to verify a solution through the process of writing a proof.This book will be treasured by students long after they have completed their coursework and will surely be a continuing resource for students who enter the teaching profession.As a high school math teacher, I can also recommend this book for advanced high school geometry students.

With its beautiful illustrations, uncluttered diagrams, and clear writing style, this book will pique interest by offering students intriguing problems to consider.The book incorporates several features that will develop student appreciation for mathematics, including historical notes about mathematicians that give thoughtful glimpses into the personal lives of those who have contributed to the development of mathematics.The multicultural nature of the discipline of mathematics is clearly described in these notes, and in reading these notes, students will gain a deep respect for the contributions other times and cultures to present-day mathematics.

The book contains a wide range of problems designed to challenge students at every level of understanding.The author's clear belief is that all college students can engage in mathematics at a meaningful level, even beginning students.This textbook is written to develop an in-depth understanding of geometry, and also contains material that will challenge advanced students.Traditional geometric constructions with compass and straight-edge are approached as the outcome of exploration and discovery, rather than as mere techniques.Computer geometry software activities are also included in the text (i.e., Geometer Sketchpad).Sections on recursive formulas for evaluating ð, trigonometric functions, isometries, extremal problems, and complex numbers provide options for providing more complex material for advanced students.
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In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr ... Read more

Customer Reviews (2)

Good introduction
Once thought to be high-brow estoeric mathematics, algebraic geometry is now finding applications in a myriad of different areas, such as cryptography, coding algorithms, and computer graphics. This book gives an overview of some of the techniques involved when applying algebraic geometry. The authors gear the discussion to those who are attempting to write computer code to solve polynomial equations and thus the first few chapters cover the algebraic structure of ideals in polynomial rings and Grobner basis algorithms. The reader is expected to have a fairly good background in undergraduate algebra in order to read this book, but the authors do give an introduction to algebra in the first chapter. Many exercises permeate the text, some of which are quite useful in testing the reader's understanding. The Maple symbolic programming language is used to illustrate the main algorithms, and I think effectively so. The authors do mention other packages such as Axiom, Mathematica, Macauley, and REDUCE to do the calculations. The chapter on local rings is the most well-written in the book, as the idea of a local ring is made very concrete in their discussion and in the examples. The strategy of studying properties of a variety via the study of functions on the variety is illustrated nicely with an example of a circle of radius one. Later, in a chapter on free resolutions, the authors discuss the Hilbert function and give a very instructive example of its calculation, that of a twisted cubic in three-dimensional space. They mention the conjecture on graded resolutions of ideals of canonical curves and refer the reader to the literature for more information. Particularly interesting is the chapter on polytopes, where toric varieties are introduced. The authors motivate nicely how some of the more abstract constructions in this subject, such as the Chow ring and the Veronese map, arise. The important subject of homotopy continuation methods is discussed, and this is helpful since these methods have taken on major applications in recent years. In optimization theory, they serve as a kind of generalization of the gradient methods, but do not have the convergence to local minima problems so characteristic of these methods. In addition, one can use homotopy continuation methods to get a computational handle on the Schubert calculus, namely, the problem of finding explicity the number of m-planes that meet a set of linear subspaces in general position. There are some software packages developed in the academic environment that deal with homotopy continuation, such as "Continuum", which is a projective approach based on Bezout's theorem; and "PHC", which is based on Bernstein's theorem, the latter of which the authors treat in detail in the book. My primary reason for purchasing the book was mainly the last chapter on algebraic coding theory. The authors do give an effective presentation of the concepts, including error-correcting codes, but I was disappointed in not finding a treatment of the soft-decision problem in Reed-Solomon codes.

In general this is a good book and worth reading, if one needs an introduction to the areas covered. Students could definitely benefit from its perusal.

Don't bother
I just completed a course that used this book as a...reference.Granted, it is a first edition, but it reads like a rough draft.The presence of three authors is all too obvious in the inconsistent writing of proofs, paragraphs, and even exercises.Some proofs are just plain wrong, and manyhave gaping holes in them.Notation is confusing, and changes withoutwarning or explanation. I will say this much in its favor: many importantresults are presented, although the proofs are absent.It makes a goodsource for named theorems, but that's about it. ... Read more

Product Description
This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition.Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research.Ideal for geometry at an intermediate level. ... Read more

Customer Reviews (1)

Worst math text I ever had
I have an MA in math so I'm not a complete idiot, but I still expect a math text to provide a little in the way of examples of how to do problems before assigning a slew of them.I would at least like a little more discussion of the implications and applications of key theorems but this book has nothing except a brief statement and proof of some key theorems and then a bunch of exercises.

Any help, understanding or discussion of the topics or theorems I get is from web resources. There may not be a lot of geometry texts at the college level, but this is basically useless.Be better off assigning the orginal texts of Euclid and the other roriginators. ... Read more

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Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups. ... Read more

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This book offers a modern approach to computational geo-metry, an area thatstudies the computational complexity ofgeometric problems. Combinatorial investigations play animportant role in this study. ... Read more

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Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures.

*A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision
*Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data
*Includes exercises, examples, and references to related or more advanced work ... Read more

Customer Reviews (2)

An Excellent Book

It is an excellent book for computer science, mathematics, and
engineering researchers. The book can also be used as a very good
textbook for graduate courses and certain sections would be good for
some senior undergraduate courses (for example, the first part of the
book). Focusingon the needs of real world applications, the authors
try to build a solid mathematical foundation for image processing and
computer vision. The relationship between digital geometry and
computational geometry is also well described by the many practical
algorithms from computational geometry that are embedded in digital
geometry. Some computer graphics methods are also covered. Chapters
1-8 cover basic digital geometry; Chapters 9-16 cover special topics.
Chapter 17 deals with the statistical and geometrical properties of
digital pictures and may be treated as an Appendix. All of these
aspects make this book a comprehensive and self-contained.

A great book on Digital Geometry
This is the first comprehensive overview of the research in Digital Geometry. It documents over fifty years of a very active research field. Digital Geometry has resulted and accompanied the research in Computer Vision. The scope of this book is very large; it clarifies, summarizes, and unifies the results reported in over 1000 research papers.
This book is very well written.
The introduction is great, since it shows the connection to other research fields in mathematics and computer science. It also clearly defines the basic concepts of Digital Geometry that are the underlying concepts in image processing, computer vision, and computer graphics. Most books in these fields do not define these concepts at all.

I see this book as very suitable for the first part of courses on Image Processing and Computer Vision, since it provides a clear definition of the underlying structure of digital images.
I also strongly recommend this book to graduate and undergraduate students of Mathematics and Computer Science who want a clearly written introduction to the underlying concepts of computer vision and computer graphics.
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Product Description
Fractal geometry has become popular in the last 15 years,its applicationscan be found in technology, science, oreven arts. Fractal methods andformalism are seen today as ageneral, abstract, but nevertheless practical instrument forthe description of nature in a wide sense. But itwasComputer Graphics which made possible the increasingpopularity offractals several years ago, and long aftertheir mathematical formulation.The two disciplines aretightly linked.The book contains the scientificcontributions presentedin an international workshop in the "Computer GraphicsCenter" in Darmstadt, Germany. Thetarget of the workshop wasto present the wide spectrumof interrelationships and interactions between FractalGeometry and Computer Graphics. The topics vary fromfundamentals and new theoretical results to variousapplications and systems development. All contributions areoriginal, unpublished papers.The presentations have beendiscussed in two working groups; the discussion results,together with actual trends and topics of future research,are reported in the last section.The topics of the book are divides into foursections:Fundamentals, Computer Graphics and Optical Simulation,Simulation of Natural Phenomena, Image Processing and ImageAnalysis. ... Read more

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"Lines and Curves" is a unique adventure in the world of geometry.Originally written in Russian and used in the Gelfand Correspondence School, the book has since become a classic: unlike standard textbooks that use the subject primarily to introduce axiomatic reasoning as illustrated by formal geometric proofs, "Lines and Curves" maintains solid mathematical rigor, but also strikes a balance between whimsical artistry, creative storytelling, and surprising examples of geometric properties.This newly revised and expanded edition includes more than 200 theoretical and practical problems in which formal geometry provides simple and elegant insight, and the book points the reader toward important areas of modern mathematics.

The text focuses on the geometrical properties of paths traced by moving points, the sets of points satisfying given geometric constraints, and questions of maxima and minima; it is, therefore, well positioned for companion use with software packages like Geometry Sketchpad, and can serve as a guidebook for engineers.Its deeper, interdisciplinary treatment of geometry also makes it ideal for those interested in the subject purely for its beauty, and the development of "Lines and Curves" from first principles makes it accessible to high school students, teachers, and puzzle enthusiasts alike.A wide audience will profit from its careful treatment of geometry and its synthesis of many branches of mathematics.

Based on an English translation of the Russian edition by A. Kundu, Saha Istitute of Nuclear Physics, Calcutta, India. ... Read more

Customer Reviews (2)

Excellent Value to Learn Geometry
Victor Gutenmacher's work Lines and Curves has been a valued part of my library for 6 years.The clever problems inside this work have amused and challenged me, and are excellently instructive.

This work takes you right into the details of solving problems relating to lines and curves.The illustrations that helpfully accompany it are useful and relevant and really add to the learning experience.

Topics it covers include: Sets, points, lines, intersections, curves - and that's just getting started!

If you are looking to learn about geometry, or teach a class on the subject, this book is definitely something you would want to consider.It is a great value.

Beyond outstanding
If you read *one* mathematics book in you whole life, this should be it.No, it will not help you do your taxes or win the lottery.It may, however, change the way you look at the world and give you a serious appreciation of what mathematics as a creative endeavor is about."Lines and Curves" is an invitation to Euclidean geometry from a dynamic perspective.It will teach you how to think about points in motion rather than visualizing figures as static entities.The exposition is so clear and the examples so well chosen that the barest background will allow you to follow the entire exposition.If you half-remember the concepts of congruence and similarity of triangles you are well on your way to enjoying the intellectual ride of a lifetime (a very concise appendix summarizes the formal prerequisites).Hundred of exquisite exercises are a pleasure to try, varying in difficulty from easy to moderately difficult.

The style is engaging and entertaining.I invite anyone to read the Introduction (available free from Amazon) to get a taste of the material.To keep my comments concrete, consider Chapter 2, "The Alphabet": no fewer than six different interpretations of a straight line as a geometric locus are explained (and will consistently be used throughout the rest of the book).The same goes for the circle, for which at least four interpretations are given.Other conics (ellipses, parabolas, hyperbolas) are treated similarly in Chapter 6.

A further remarkable feature is the authors' willingness to employ analytic geometry at crucial places where resorting to purely synthetic methods would be cumbersome and not particularly illuminating.The best illustration of this is the "Theorem on the Squares of the Distances" in Chapter 2 (What is the locus of all the points in the plane whose weighted sum of squares of distances to given fixed points is equal to a constant?)Another instance is to be found already in section 0.2 of the Introduction (read it from the links above!)Exercise for the reader of this review: solve 0.2 using no analytic methods, but rather by modifying the argument of 0.1 and using the fact that the compression/dilation by a factor of b/a of a circle of radius a with respect to a diameter is an ellipse of semiaxis lengths a and b.The latter approach will seem natural enough to a reader who has absorbed the main lessons of "Lines and Curves".

I can only assume that readers of this little gem will want to go further.The book does not have a bibliography, but I can offer the following suggestions: "Geometric Transformations" (volumes I-III) by I.M. Yaglom, H.S.M. Coxeter's "Geometry Revisited", and the hard-to-get but delightful monograph "The Kinematic Method in Geometrical Problems" by Lyubich and Shor.

(Note: While my personal favorite is number theory,"Lines and Curves" still holds a special place in my heart fifteen years after reading Mir Publishers' Spanish translation.English readers should feel very fortunate indeed that this 2004 Birkhäuser translation is available.) ... Read more

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During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This volume, which contains 32 papers on a broad range of topics of current interest in the field, is an outgrowth of that synergism.It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. ... Read more

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Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.

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Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, as well as in efficient and versatile algorithms for computer vision and image analysis.

This book provides a coherent integration of algebraic projective geometry and spatial reasoning under uncertainty with applications in computer vision. Beyond systematically introducing the theoretical foundations from geometry and statistics and clear rules for performing geometric reasoning under uncertainty, the author provides a collection of detailed algorithms.

The book addresses researchers and advanced students interested in algebraic projective geometry for image analysis, in statistical representation of objects and transformations, or in generic tools for testing and estimating within the context of geometric multiple-view analysis.