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.