You’ve already done most of the work to enable you to move from two to three dimensions. The concepts of vectors, forces, energy, and momentum are the same in three dimensions as in two, and collision detection, while more complex, involves all the same techniques as before. In this fourth part of the book, you’ll finish your exploration of mathematical and physical theory by taking this final step into 3-D.

You’ll start by looking at the basics of 3-D space, and how it can be represented on a two-dimensional screen. Then you’ll spend another chapter further extending the vector work you have done up to now, and I’ll introduce the concept of a transform. Chapter 18 deals with collision detection for 3-D shapes, Chapter 19 looks at lighting and shading, and the final chapter covers various 3-D modeling techniques for creating complex objects and moving surfaces, such as waves on water.

3-D is a subject much more widely covered than the more general techniques in this book, and so you won’t retread the ground of many other authors. Most of the topics are dealt with briefly. For a full mathematical treatment, along with much more information on the more obscure topics, it is helpful to consult the references given in the appendices of the book.