Graphics Reference
In-Depth Information
Chapter 7
and the Geometry of
2-Space and 3-Space
Unlike other chapters in this topic, this one covers a great deal of material with
which you may already be familiar in some form. The goals of this organization
of the material are
• To have it all in one place, where you can easily refer to it
• To present it in a way that has a somewhat different approach from
what you may have seen in the past, one that's particularly useful for
graphics
Much of the chapter will be easy reading; the material will look familiar. To
be sure it really is familiar, we include a number of exercises in the chapter itself;
you should work through these exercises to be certain you really are understanding
what you're reading. We assume that you've encountered some linear algebra, and
are familiar with vectors, matrices, linear transformations, and notions like “basis”
and “linear independence.”
One test, as you read this material, is to ask yourself, “Could I write code to
implement this idea?” If the answer is no, you should spend more time under-
standing the concept. This is sufficiently important that we embody it in a prin-
ciple, which one of us first heard expressed by Hale Trotter of Princeton in the
1970s.
T
HE IMPLEMENTATION PRINCIPLE
:
If you understand a mathematical pro-
cess well enough, you can write a program that executes it.
149
