Description

Do you spend too much time creating the building blocks of your graphics applications or finding and correcting errors? Geometric Tools for Computer Graphics is an extensive, conveniently organized collection of proven solutions to fundamental problems that you'd rather not solve over and over again, including building primitives, distance calculation, approximation, containment, decomposition, intersection determination, separation, and more.

If you have a mathematics degree, this book will save you time and trouble. If you don't, it will help you achieve things you may feel are out of your reach. Inside, each problem is clearly stated and diagrammed, and the fully detailed solutions are presented in easy-to-understand pseudocode. You also get the mathematics and geometry background needed to make optimal use of the solutions, as well as an abundance of reference material contained in a series of appendices.

Features

  • Filled with robust, thoroughly tested solutions that will save you time and help you avoid costly errors.
  • Covers problems relevant for both 2D and 3D graphics programming.
  • Presents each problem and solution in stand-alone form allowing you the option of reading only those entries that matter to you.
  • Provides the math and geometry background you need to understand the solutions and put them to work.
  • Clearly diagrams each problem and presents solutions in easy-to-understand pseudocode.
  • Resources associated with the book are available at the companion Web site www.mkp.com/gtcg.

Key Features

* Filled with robust, thoroughly tested solutions that will save you time and help you avoid costly errors. * Covers problems relevant for both 2D and 3D graphics programming. * Presents each problem and solution in stand-alone form allowing you the option of reading only those entries that matter to you. * Provides the math and geometry background you need to understand the solutions and put them to work. * Clearly diagrams each problem and presents solutions in easy-to-understand pseudocode. * Resources associated with the book are available at the companion Web site www.mkp.com/gtcg.

Readership

Programmers, software engineers, and technical directors whose work involves 2D or 3D computer graphics for filmmaking including special effects and animation programming, gane development, visualization, medical image analysis, simulation, virtual worlds, and other software development.

Table of Contents

Foreword
Figures
Tables
Preface

Chapter 1 Introduction
1.1 How to Use This Book
1.2 Issues of Numerical Computation
1.2.1 Low-Level Issues
1.2.2 High-Level Issues
1.3 A Summary of the Chapters

Chapter 2 Matrices and Linear Systems
2.1 Introduction
2.1.1 Motivation
2.1.2 Organization
2.1.3 Notational Conventions
2.2 Tuples
2.2.1 Definition
2.2.2 Arithmetic Operations
2.3 Matrices
2.3.1 Notation and Terminology
2.3.2 Transposition
2.3.3 Arithmetic Operations
2.3.4 Matrix Multiplication
2.4 Linear Systems
2.4.1 Linear Equations
2.4.2 Linear Systems in Two Unknowns
2.4.3 General Linear Systems
2.4.4 Row Reductions, Echelon Form, and Rank
2.5 Square Matrices
2.5.1 Diagonal Matrices
2.5.2 Triangular Matrices
2.5.3 The Determinant
2.5.4 Inverse
2.6 Linear Spaces
2.6.1 Fields
2.6.2 Definition and Properties
2.6.3 Subspaces
2.6.4 Linear Combinations and Span
2.6.5 Linear Independence, Dimension, and Basis
2.7 Linear Mappings
2.7.1 Mappings in General
2.7.2 Linear Mappings
2.7.3 Matrix Representation of Linear Mappings
2.7.4 Cramer’s Rule
2.8 Eigenvalues and Eigenvectors
2.9 Euclidean Space
2.9.1 Inner Product Spaces
2.9.2 Orthogonality and Orthonormal Sets

Details

No. of pages:
1056
Language:
English
Copyright:
© 2003
Published:
Imprint:
Morgan Kaufmann
Print ISBN:
9781558605947
Electronic ISBN:
9780080478029

About the editors

Philip Schneider

24 years of professional programming, primarily focused on modeling tools and geometric algorithms. Employers include Digital Equipment Corporation, Apple, Walt Disney Feature Animation, Digital Domain, and Industrial Light + Magic. Formed and lead groups specializing in these areas as well as in physics simulation. Film Credits: Oil & Vinegar, 102 Dalmatians, Disney's Magic Lamp, Mickey's Philharmagic, Reign of Fire, Kangaroo Jack, Chicken Little, Indiana Jones and the Kingdom of the Crystal Skull, Pirates of the Caribbean: Dead Man's Chest, Harry Potter and the Goblet of Fire. ACM Siggraph, IEEE. M.S. in Computer Science, University of Washington.

Affiliations and Expertise

24 years of professional programming, primarily focused on modeling tools and geometric algorithms. Employers include Digital Equipment Corporation, Apple, Walt Disney Feature Animation, Digital Domain, and Industrial Light + Magic. Formed and lead groups specializing in these areas as well as in physics simulation. Film Credits: Oil & Vinegar, 102 Dalmatians, Disney's Magic Lamp, Mickey's Philharmagic, Reign of Fire, Kangaroo Jack, Chicken Little, Indiana Jones and the Kingdom of the Crystal Skull, Pirates of the Caribbean: Dead Man's Chest, Harry Potter and the Goblet of Fire. ACM Siggraph, IEEE. M.S. in Computer Science, University of Washington.

Philip Schneider

24 years of professional programming, primarily focused on modeling tools and geometric algorithms. Employers include Digital Equipment Corporation, Apple, Walt Disney Feature Animation, Digital Domain, and Industrial Light + Magic. Formed and lead groups specializing in these areas as well as in physics simulation. Film Credits: Oil & Vinegar, 102 Dalmatians, Disney's Magic Lamp, Mickey's Philharmagic, Reign of Fire, Kangaroo Jack, Chicken Little, Indiana Jones and the Kingdom of the Crystal Skull, Pirates of the Caribbean: Dead Man's Chest, Harry Potter and the Goblet of Fire. ACM Siggraph, IEEE. M.S. in Computer Science, University of Washington.

Affiliations and Expertise

24 years of professional programming, primarily focused on modeling tools and geometric algorithms. Employers include Digital Equipment Corporation, Apple, Walt Disney Feature Animation, Digital Domain, and Industrial Light + Magic. Formed and lead groups specializing in these areas as well as in physics simulation. Film Credits: Oil & Vinegar, 102 Dalmatians, Disney's Magic Lamp, Mickey's Philharmagic, Reign of Fire, Kangaroo Jack, Chicken Little, Indiana Jones and the Kingdom of the Crystal Skull, Pirates of the Caribbean: Dead Man's Chest, Harry Potter and the Goblet of Fire. ACM Siggraph, IEEE. M.S. in Computer Science, University of Washington.

David Eberly

Dave Eberly is the president of Geometric Tools, Inc. (www.geometrictools.com), a company that specializes in software development for computer graphics, image analysis, and numerical methods. Previously, he was the director of engineering at Numerical Design Ltd. (NDL), the company responsible for the real-time 3D game engine, NetImmerse. He also worked for NDL on Gamebryo, which was the next-generation engine after NetImmerse. His background includes a BA degree in mathematics from Bloomsburg University, MS and PhD degrees in mathematics from the University of Colorado at Boulder, and MS and PhD degrees in computer science from the University of North Carolina at ChapelHill. He is the author of 3D Game Engine Design, 2nd Edition (2006), 3D Game Engine Architecture (2005), Game Physics (2004), and coauthor with Philip Schneider of Geometric Tools for Computer Graphics (2003), all published by Morgan Kaufmann. As a mathematician, Dave did research in the mathematics of combustion, signal and image processing, and length-biased distributions in statistics. He was an associate professor at the University of Texas at San Antonio with an adjunct appointment in radiology at the U.T. Health Science Center at San Antonio. In 1991, he gave up his tenured position to re-train in computer science at the University of North Carolina. After graduating in 1994, he remained for one year as a research associate professor in computer science with a joint appointment in the Department of Neurosurgery, working in medical image analysis. His next stop was the SAS Institute, working for a year on SAS/Insight, a statistical graphics package. Finally, deciding that computer graphics and geometry were his real calling, Dave went to work for NDL (which is now Emergent Game Technologies), then to Magic Software, Inc., which later became Geometric Tools, Inc. Dave’s participation in the newsgroup comp.graphics.algorit

Affiliations and Expertise

President of Geometric Tools, Inc (www.geometrictools.com), a company that specializes in software development for computer graphics, image analysis, and numerical methods. Previously, he was the Director of Engineering at Numerical Design Ltd (NDL), the company responsible for the real-time 3D game engine, Netlmmerse. His background includes a BA in Mathematics from Bloomsburg U, MS and PhD degrees in Mathematics from the U of Colorado at Boulder, and MS and PhD degrees in computer science from the U of North Carolina at Chapel Hill.

Reviews

"An hour of a programmer's time often costs more than the price of a book. By this measure, you hold a volume potentially worth thousands of dollars. That it can be purchased for a fraction of this cost I consider a modern miracle. The amount of information crammed into this book is incredible." --Eric Haines