Game Development Reference

In-Depth Information

-1-

Mathematical Background

James M. Van Verth

1.1

Introduction

It has been said that, at its core, all physics is mathematics. While that statement

may be debatable, it is certainly true that a background in mathematics is indis-

pensable in studying physics, and game physics is no exception. As such, a single

chapter cannot possibly cover all that is useful in such a broad and interesting

field. However, the following should provide an essential review of the mathe-

matics needed for the remainder of this topic. Further references are provided at

the end of the chapter for those who wish to study further.

1.2 Vectors and Points

1.2.1 Definitions and Relations

The core elements of any three-dimensional system are points and vectors. Points

represent positions in space and are represented graphically as dots. Vectors rep-

resent direction or rate of change—the amount of change indicated by the length,

or
magnitude
, of the vector—and are presented graphically as arrows. Figure 1.1

Figure 1.1.
Relationship between points and vectors.