3D Math Primer for Graphics and Game Development

3D Math Primer for Graphics and Game Development covers fundamental 3D math concepts that are especially useful for computer game developers and programmers. The authors discuss the mathematical theory in detail and then provide the geometric interpretation necessary to make 3D math intuitive. Working C++ classes illustrate how to put the techniques into practice, and exercises at the end of each chapter help reinforce the concepts. This book explains basic concepts such as vectors, coordinate spaces, matrices, transformations, Euler angles, homogenous coordinates, geometric primitives, intersection tests, and triangle meshes; discusses orientation in 3D, including thorough coverage of quaternions and a comparison of the advantages and disadvantages of different representation techniques; describes working C++ classes for mathematical and geometric entities and several different matrix classes, each tailored to specific geometric tasks; includes complete derivations for all the primitive transformation matrices.

Table of Contents

Chapter 1 Introduction
Chapter 2 The Cartesian Coordinate System
Chapter 3 Multiple Coordinate Spaces
Chapter 4 Vectors
Chapter 5 Operations on Vectors
Chapter 6 A Simple 3D Vector Class
Chapter 7 Introduction to Matrices
Chapter 8 Matrices and Linear Transformations
Chapter 9 More on Matrices
Chapter 10 Orientation and Angular Displacement in 3D
Chapter 11 Transformations in C++
Chapter 12 Geometric Primitives
Chapter 13 Geometric Tests
Chapter 14 Triangle Meshes
Chapter 15 3D Math for Graphics
Chapter 16 Visibility Determination
Chapter 17 Afterword
Appendix A Math Review
Appendix B References