Book 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 (5)

Lots of Good information, not a lot of words
The book has a lot of valuable information for those who are working in computer vision.The book however is fairly terse on many subject and requires careful reading.

excellent book
My lab has the first edition of this book. Everyone likes it. That's why we order a second book. I have not read through the second edition yet, but this book rocks!

Comment on the first edition
The first edition of this book could have been much better written.It took up a lot of topics, but treated each in a summary fashion.In fairness, though, I must say that this may be as good as any other book with its aim and scope, and better than some.Any writer on computer vision faces the problem of guessing who the reader is likely to be and what the reader's background is.Also, each of the various topics really merits a sizable book.In particular, the mathematics needs a truly mathematical treatment in a separate book.I have not seen this second edition, but there was room for improvement over the first edition.

very informative, fairly easy to read
The book succeeds in introducing you to the world of multiple view geometry.Specially the math and geometry concepts associated with it.In my research, I had to work on stereo images and this book provided very good information about it. The algorithms are presented very clearly and have been easy to implement (at least in Matlab).

It's a good reference book to have.

A must for readers in computer vision
It is the best book in this area that I have seen up to now.It is well-organized and all the notations and words are friendly to beginners and even experts in this field.Included materials are really tracing the latest advanced techniques.Actually, it is great that there are a lot of exercises at the ends of each chapters but there is no sufficient solutions or detail explanations to each questions. ... Read more

Book Description
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 workDownload Description
Computer graphics is about taking mathematical representations of objects and transforming them into visual displays. Digital geometry concerns the reverse process; it is about deriving geometric information from digital pictures. There have been over one thousand papers published in the forty-year history of digital geometry, but until now, never a book that defines and covers the field. Digital Geometry: Geometric Methods for Digital Picture Analysis details the concepts, algorithms, and practices of the field. It is a discipline studied by a huge number of researchers in fields such as digital image processing, medical imaging, robotics, and of course computer graphics. However, digital geometry is relatively new and still emerging as a unique field and the lack of books has made it difficult for researchers in many areas (including applied mathematics) to benefit from this work. ... Read more

Customer Reviews (2)

New viewpoint of these area
These mathemaical fields are becoming recently very important.
Because discrete or finite difference methods are essential forsolving methematical problem. Geometry,the origin of it is very old,and basically it is not assuming the usage of the computer.So,we need transform Geometry for using the computer.
This book is fairly good.

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.
... Read more

Book 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. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp. ... Read more

Customer Reviews (6)

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.

okay content, mediocre presentation
This book provides a reasonable introduction to the field of computational geometry, although the notation is sometimes sloppy and the author frequently makes inconsistent assumptions about the reader.For example,on the first page he refers to a circle as a "one-dimensonial set ofpoints," which although valid from a toplogical perspective is alittle confusing in an introductory text.As another example, the firstexercise refers to "every point in dP," presumably meaning justthe corner points (otherwise the problem would be unsolvable).The bookalso sets up a lot of irrelevant mathematical definitions that generallyobfuscate the presentation rather than clarifying it.Although notprohibitive for the ambitious reader, these needless hindrances are at besta little annoying.

Secondly, I must criticize the text's scope, in lightof the important role computational geometry has played in modern computergraphics.There is no discussion of clipping, culling, occlusion (e.g.BSP, octree, OBB), or even non-polygon primitives -- important topicsarguably more useful to the target audience than e.g. convex hulls (towhich over 1/4 of the book's pages are devoted).

Regardless, this book(combined with a professor and a course) probably would serve quite well asan undergraduate text.Readers interested in a cookbook of appliedgraphics algorithms, however, should look elsewhere. ... Read more

Book Description
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2 ... 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

Book 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

Book Description

This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms.

Customer Reviews (15)

A very nice introduction to the field
The authors did a great job of introducing the reader to all the important aspects of the field of computational geometry while keeping it simple and understandable.

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.

good source of many methods
The authors amass an impressive array of algorithms related to finding geometrical properties. Where these algorithms are performed on a computer. The book itself does not advocate any particular programming language. The algorithms are given in pseudocode, and you are expected to manually convert these to code in your choice of language. Given the calibre of the discussion in the text, which suggests that the readers are quite experienced, then this manual step should be easy to most.

There are numerous contexts in which the text might prove useful. Ranging from graphics to GIS to robotics. Thus, there is an entire chapter on the planning of robotic motion. The robot can in general translate and rotate.

Each chapter comes with an exercise set. Which helps make the book suitable as a graduate or even undergraduate text.

Important book but substandard layout and typesetting
This is one of the really few computational geometry books available. It fills a niche and does it decently. However it could be better:

1. The chapter layout is not very good. There are many "revisiting this" and "we saw in chapter so-and-so".

2. The mathematical proofs are often written in a single paragraph full of "English" interspersed with mathematical notation, instead of the tried and true way of numbered equations and one-per explanations. This makes for disconcerting reading.

3. The book in general could have done with more math and code, and less "English", not to mention more and better diagrams -- they tend to be sparsely detailed (ie. a picture is worth only a hundred words). The arrangement of diagrams also needs to be better: some are in the margins, some are in the middle, again not easy and intuitive to follow.

Hopefully a future edition will address this issues.

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

Book 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

Book 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. ... Read more

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

Book Description

Deformable objects are ubiquitous in the world surrounding us, on all levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. In recent years, non-rigid shapes have attracted a growing interest, which has led to rapid development of the field, where state-of-the-art results from very different sciences - theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention a few - are applied to find solutions.

Book Description
Within the last decade, Geometric Algebra (GA) has emerged as a powerful alternative to classical matrix algebra as a comprehensive conceptual language and computational system for computer science. This book will serve as a standard introduction and reference to the subject for students and experts alike. As a textbook, it provides a thorough grounding in the fundamentals of GA, with many illustrations, exercises and applications. Experts will delight in the refreshing perspective GA gives to every topic, large and small.
-David Hestenes, Distinguished research Professor, Department of Physics, Arizona State University

Geometric Algebra is becoming increasingly important in computer science. This book is a comprehensive introduction to Geometric Algebra with detailed descriptions of important applications. While requiring serious study, it has deep and powerful insights into GAs usage. It has excellent discussions of how to actually implement GA on the computer.
-Dr. Alyn Rockwood, CTO, FreeDesign, Inc. Longmont, Colorado

Until recently, almost 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.

Features

Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics.
Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA.
Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space.
Presents effective approaches to making GA an integral part of your programming.
Includes numerous drills and programming exercises helpful for both students and practitioners.
Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter.

About the Authors

Leo Dorst is Assistant Professor of Computer Science at the University of Amsterdam, where his research focuses on geometrical issues in robotics and computer vision. He earned M.Sc. and Ph.D. degrees from Delft University of Technology and received a NYIPLA Inventor of the Year award in 2005 for his work in robot path planning.

Daniel Fontijne holds a Masters degree in artificial Intelligence and is a Ph.D. candidate in Computer Science at the University of Amsterdam. His main professional interests are computer graphics, motion capture, and computer vision.

Stephen Mann is Associate Professor in the David R. Cheriton School of Computer Science at the University of Waterloo, where his research focuses on geometric modeling and computer graphics. He has a B.A. in Computer Science and Pure Mathematics from the University of California, Berkeley, and a Ph.D. in Computer Science and Engineering from the University of Washington.

* The first book on Geometric Algebra for programmers in computer graphics and entertainment computing

* Written by leaders in the field providing essential information on this new technique for 3D graphics

* This full colour book includes a website with GAViewer, a program to experiment with GA ... Read more

Customer Reviews (1)

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

Book Description
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

Book Description
This concise text on geometry with computer modeling presents someelementary methods for analytical modeling and visualization of curvesand surfaces.The author systematicallyexamines such powerful toolsas 2-D and 3-D animation of geometric images, transformations,shadows, and colors, and then further studies more complex problems indifferential geometry.Well-illustrated with more than 350 figures---reproducible using Mapleprograms in the book---the work is devoted to three main areas:curves, surfaces, and polyhedra.Pedagogical benefits can be found inthe large number of Maple programs, some of which are analogous to C++programs, including those for splines and fractals.To avoid tedioustyping, readers will be able to download many of the programs from theBirkhauser web site.Aimed at a broad audience of students, instructors of mathematics,computer scientists, and engineers who have knowledge of analyticalgeometry, i.e., method of coordinates, this text will be an excellentclassroom resource or self-study reference.With over 100 stimulatingexercises, problems and solutions, {\it Geometry of Curves andSurfaces with Maple} will integrate traditional differential and non-Euclidean geometries with more current computer algebra systems in apractical and user-friendly format. ... Read more

Book Description

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.

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ISBN: 0-87567-034-2 ... Read more

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This item bank is a chapter by chapter list of questions provided in the data base, including algorithmically generated questions, and answers to all questions. ... Read more

Book Description
This book offers a modern approach to computational geometry, an area that studies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study. ... Read more