How Is This Book Organized?

The first half of this book provides a mathematical foundation for the physics topics discussed in the second half.

Chapter 1 starts with the point and line. Both items are defined in 2D and 3D, and then applications in collision detection are discussed.

Chapter 2 provides a brief overview of geometry topics specific to game programming. The Pythagorean theorem, the distance formula, and the midpoint formula are reviewed. The equations of several geometric shapes, such as circle, parabola, and sphere, are defined. Then these topics are used for more approaches to collision detection.

Chapter 3 provides a brief overview of trigonometry topics that are used frequently in coding games. The six trigonometric functions are defined, along with their identities. In addition, the use of C++ math functions and measuring angles in radians are discussed.

Chapter 4 introduces the concept of using vectors to describe physical quantities. Various vector formats are introduced, and all the necessary mathematical operations for vectors, such as addition/subtraction, scalar multiplication, dot product, cross product, and normalizing, are defined.

Chapter 5 defines a matrix as well as all the mathematical operations used for matrices, including addition/subtraction, scalar multiplication, matrix multiplication, and transpose.

Chapter 6 describes the most common use of matrices—transformations. Matrices can control all the movement of objects in a game, including translation, scaling, and rotation. Great attention is given to optimization techniques for game programming.

Chapter 7 prepares you to deal with the units of physical quantities. Converting all measurements to the same units is critical when coding.

Chapter 8 introduces physics. Velocity, acceleration, and their relationship to time and displacement are defined in terms of one dimension.

Chapter 9 introduces the concept of derivative in terms of velocity and acceleration. It serves as a very brief introduction to derivative calculus.

Chapter 10 expands the topics of the previous two chapters into two and three dimensions. In particular, this chapter pays close attention to projectile motion.

Chapter 11 examines the forces that cause objects to move. Sir Isaac Newton coined three laws that govern almost all motion near the surface of the earth. This chapter links those laws to the earlier chapters that describe how objects move.

Chapter 12 defines two different types of energy. It provides an alternative approach, an energy approach, to modeling the motion of objects in games.

Chapter 13 examines the fun part of games—collisions. Without collisions there would be no interactivity. This chapter discusses how objects should move as a result of hitting each other.

Chapter 14 wraps up with a discussion of rotational motion. Many of the earlier physics topics are then redefined in terms of angular motion as opposed to linear.

Appendix A lists important formulas that are featured throughout the book.

Appendix B is a reference of great resources you can turn to for more information.

Each chapter contains several examples and then provides practice questions with the answers so that you can check your answers. Many of the chapters also contain a "Visualization Experience." These sections each relate to one of the demos provided on the companion CD. Some demos simply illustrate an important concept from the chapter, and others are completely interactive. The C++ code for each demo is also provided so that you can see how they were done.