Game Development Reference
As a quick reference, the mathematical equations and formulae in the topic are
also collected together in appendix D for easy location when programming a game.
If you are an experienced game developer, then the chances are you will know
a fair amount of three-dimensional (3D) mathematics: vectors, matrices, and linear
algebra. If you are relatively new to games, then these topics may be beyond your
In this topic I will assume you know some mathematics, and I will cover the rest.
If I assume you know something, but you aren't confident in using it, then it would be
worth getting hold of a reference book or looking for a web tutorial before proceeding,
so you can easily follow the text.
T HE M ATH Y OU N EED TO K NOW
I'm going to assume every potential physics developer knows some mathematics.
The most important thing to be comfortable with is algebraic notation. I will
introduce new concepts directly in notation, and if you flick through this topic, you
will see many formulae written into the text.
I'll assume you are happy to read an expression like
sin θ 2
and can understand that x , t ,and θ are variables and how to combine them to get a
I will also assume you know some basic algebra: you should be able to understand
that, if the preceding formula is correct, then
sin θ 2
These kinds of algebraic manipulations will pop up all through the topic without
Finally I'll assume you are familiar with trigonometry and coordinate geometry:
sines, cosines, and tangents, and their relationship to right-angled triangles and to
two-dimensional geometry in general. In particular, you should know that if we have
the triangle shown in figure 1.1, then these formulae hold:
a sin θ
a cos θ
c tan θ