Product Description
This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. ... Read more

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This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2004, held in Tokyo, Japan in October 2004, to honor János Pach on his fiftieth year.

The 20 revised full papers presented were carefully selected during two rounds of reviewing and improvement from over 60 talks at the conference. All current issues in discrete algorithmic geometry are addressed.

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This book is based on a NATO workshop for researchersconcerned with thedesign of intelligent learningenvironments for geometry. Geometry cannot bereduced toprocedural knowledge and its complexity makes it ofinterestfor the development of intelligent tutoring systems. Thecentral theme of the volume is student modeling, which hasthreeaspects: modeling the knowledge domain, modelingstudent knowledge, and designing the didactic interactionand learner control. Four main issues runthrough the papersin the book:- Knowledge about geometry is not real-world knowledge andits computer implementation implies a reificationofgeometry.- The learning of geometry involves conceptualization at anumber of different levels, which must be reflected whenmodeling student knowledge.- The design of the interface and the management ofthedidactic interaction must cope with multiplerepresentations.- Domains of geometry other than plane geometry areconsidered.The bookis part of the NATO Special Programme on AdvancedEducational Technology. ... Read more

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The study of two-dimensional analytic geometry has gone in and out of fashion several times over the past century, however this classic field of mathematics has once again become popular due to the growing power of personal computers and the availability of powerful mathematical software systems, such as Mathematica, that can provide an
interactive environment for studying the field. By combining the power of Mathematica with an analytic geometry software system called Descarta2D, the author has succeeded in meshing an ancient field of study with modern computational tools, the result being a simple, yet powerful, approach to studying analytic geometry. Students, engineers and mathematicians alike who are interested in analytic geometry can use this book and software for the study, research or just plain enjoyment of analytic geometry.

Mathematica provides an attractive environment for studying analytic geometry. Mathematica supports both numeric and symbolic computations meaning that geometry problems can be solved for special cases using numbers, as well as general cases producing formulas. Mathematica also has good facilities for producing graphical plots which are useful for visualizing the graphs of two-dimensional geometry.


* A classic study in analytic geometry, complete with in-line Mathematica dialogs illustrating every concept as it is introduced
* Excellent theoretical presentation
*Fully explained examples of all key concepts
*Interactive Mathematica notebooks for the entire book
* Provides a complete computer-based environment for study of analytic geometry
* All chapters and reference material are provided on CD-ROM in addition to being printed in the book
* Complete software system: Descarta2D
* A software system, including source code, for the underlying computer implementation, called Descarta2D is provided
* Part VII of the book is a listing of the (30) Mathematica files supporting Descarta2D; the source code is also supplied on CD-ROM
* Explorations
* More than 120 challenging problems in analytic geometry are posed;Complete solutions are provided both as interactive Mathematica notebooks on CD-ROM and as printed material in the book
* Mathematica and Descarta2D Hints expand the reader's knowledge and understanding of Descarta2D and Mathematica
* Sortware developed with Mathematica 3.0 and is compatible with Mathematica 4.0
* Detailed reference manual
* Complete documentation for Descarta2D
* Fully integrated into the Mathematica Help Browser ... Read more

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The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research.Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM). ... Read more

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Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse or parabola, or complex problems such as rotating 3D objects about an arbitrary axis.

Customer Reviews (1)

a handbook of formulae
Computer graphics is all about geometry, as you may well imagine, if you have ever had to code in this field. Vince attacks a problem for many such programmers. The field has hundreds (if not thousands) of formulae, for all sorts of conceivable configurations. Yet these formulae are scattered across many texts and research papers and websites. Associated with this is the widely varying levels of explanatory details you will find. And some formulae might actually be wrong! How would you know, for some complicated instances, if your expertise is not deep?

What Vince has done is bring hundreds of useful formulae under one cover. For both 2 and 3 dimensional images. Plus, he explains these in a consistent and lucid manner. And there are examples of usages. More than anything else, the examples can be a quick way to understand and apply the formulae.

It is also no small matter that this is done under Springer. The publisher's technical reputation is a reassuring validation of the book. ... Read more

Customer Reviews (1)

Good introduction to the subject
This is the only elementary, yet not too cursory, introduction to the subject that I have seen.It begins at the level of a lower-division college math student.It is too bad that the publisher let it go out of print.In view of the many other books on the subject of computer graphics and computer vision, there would be many needing this book.It treats more carefully the math that some other books gloss over.

My criticism so far is a minor one of style.The author writes things like, "The line l passing through the point A[4, 4, 1] and B[-2, 0, 2]."That is, he introduces a variable name (A or B) along with the value of the variable, by juxtapostion.This used to be done in high-school level books, but it conflicts with other uses of juxtaposition and so seems slightly nonsensical.I am used to the more accepted style using an equals sign: "The line l passing through the point A = [4, 4, 1] and B = [-2, 0, 2]."However, this is a minor criticism.

Postscript:Since I wrote this, I have become aware of other textbooks on the mathematics of computer graphics and computer vision, some recently published.I recommend _Applied Geometry for Computer Graphics and CAD_ by Duncan Marsh. ... Read more

Product Description

This book constitutes the refereed proceedings of the 12th International Conference on Discrete Geometry for Computer Imagery, DGCI 2005, held in Poitiers, France in April 2005.

The 36 revised full papers presented together with an invited paper were carefully reviewed and selected from 53 submissions. The papers are organized in topical sections on applications, discrete hierarchical geometry, discrete tomography, discrete topology, object properties, reconstruction and recognition, uncertain geometry, and visualization.

Product Description
This book constitutes the refereed proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery, DGCI'99 held in Marne-la-Vallee, France in March 1999. The 24 revised full papers presented were selected from a total of 41 submissions. Also included are four invited papers and seven poster presentations. The volume is divided in topical sections on discrete objects and shapes, planes, surfaces, reconstruction, topology, distance and object recognition, thinning, discretization and visualization. ... Read more

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This book constitutes the refereed proceedings of the 10th International Conference on Digital Geometry for Computer Imagery, DGCI 2002, held in Bordeaux, France, in April 2002. The 22 revised full papers and 13 posters presented together with 3 invited papers were carefully reviewed and selected from 67 submissions. The papers are organized in topical sections on topology, combinatorial image analysis, morphological analysis, shape representation, models for discrete geometry, segmentation and shape recognition, and applications. ... Read more

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The International Workshop CG '88 on "Computational Geometry" was held at the University of Würzburg, FRG, March 24-25, 1988. As the interest in the fascinating field of Computational Geometry and its Applications has grown very quickly in recent years the organizers felt the need to have a workshop, where a suitable number of invited participants could concentrate their efforts in this field to cover a broad spectrum of topics and to communicate in a stimulating atmosphere. This workshop was attended by some fifty invited scientists. The scientific program consisted of 22 contributions, of which 18 papers with one additional paper (M. Reichling) are contained in the present volume. The contributions covered important areas not only of fundamental aspects of Computational Geometry but a lot of interesting and most promising applications: Algorithmic Aspects of Geometry, Arrangements, Nearest-Neighbor-Problems and Abstract Voronoi-Diagrams, Data Structures for Geometric Objects, Geo-Relational Algebra, Geometric Modeling, Clustering and Visualizing Geometric Objects, Finite Element Methods, Triangulating in Parallel, Animation and Ray Tracing, Robotics: Motion Planning, Collision Avoidance, Visibility, Smooth Surfaces, Basic Models of Geometric Computations, Automatizing Geometric Proofs and Constructions. ... Read more

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This text shows students how to translate geometry concepts into computer code so that they can generate pictures representing the relevant concepts.Chapter 1 and Chapters 4 through 5 present the fundamental mathematical concepts needed for two- and three-dimensional computer graphics, including matrices, vector spaces, transformations, and homogeneous coordinates.Chapter 2 presents the various languages in which these ideas are communicated, such as programming languages and page description language. Chapters 3 and 6 present many different ways of describing pictures mathematically.These two chapters also contain many examples of mathematical theories that the student can illustrate using the methods of the book. ... Read more

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Describing the shapes of real objects for the purposes of engineering, architecture, medicine, and a host of other disciplines often requires complicated mathematics and subtle computer techniques. With contributions from eminent authorities in the field, this wide-ranging volume describes the latest research in computer-aided surface geometry and design techniques currently being used and developed.Topics include: The geometry of helical canal surface, optimized triangulation of parametric surfaces, simple singularities in surface-surface intersections, and the volume function, among others. With its technical richness and comprehensive treatment of the subject, the book will appeal to students and researchers working in CAD, CAM, architecture, medical modeling, molecular modeling, geography, cartography, and landscape design. ... Read more

Product Description

This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2002, held in Tokyo, Japan, in December 2002.

The 29 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in discrete algorithmic geometry are addressed.

Product Description

This book constitutes the refereed proceedings of the 13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006, held in Szeged, Hungary in October 2006.

The 28 revised full papers and 27 revised poster papers presented together with 2 invited papers were carefully reviewed and selected from 99 submissions. The papers are organized in topical sections on discrete geometry, discrete tomography, discrete topology, distance, image analysis, shape representation, segmentation, skeletonization, as well as surfaces and volumes.

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The four-volume set comprising LNCS volumes 3951/3952/3953/3954 constitutes the refereed proceedings of the 9th European Conference on Computer Vision, ECCV 2006, held in Graz, Austria, in May 2006.

The 192 revised papers presented were carefully reviewed and selected from a total of 811 papers submitted. The four books cover the entire range of current issues in computer vision. The papers are organized in topical sections on recognition, statistical models and visual learning, 3D reconstruction and multi-view geometry, energy minimization, tracking and motion, segmentation, shape from X, visual tracking, face detection and recognition, illumination and reflectance modeling, and low-level vision, segmentation and grouping.

Product Description

This book constitutes the refereed proceedings of the 11th International Conference on Discrete Geometry for Computer Imagery, DGCI 2003, held in Naples, Italy, in November 2003.

The 49 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 68 submissions. All current issues in discrete geometry for computer imagery are addressed including topology, surfaces and volumes, morphology, shape representation, and shape analysis. ... Read more