Game Development Reference
T HE M ATHEMATICS
OF R OTATIONS
gine. We have built a sophisticated system capable of simulating particles, ei-
ther individually or connected into aggregates.
We are missing two things:
A robust general-purpose collision detection system (currently we're using
quite an ad hoc system of hard constraints).
The first of these problems is fairly easy to resolve and is the subject of part IV of this
The second is more complex: it is the difference between a complete rigid-body
physics system and the mass-aggregate systems we've seen so far. To add rotations
we'll need to go backward in the capability of our engine. We'll need to remove a
good deal of functionality and rebuild it based on full rotating rigid bodies. This will
take this part and part V—almost the rest of the topic.
This chapter looks at the properties of rotating bodies and the mathematical
structures needed to represent and manipulate them.
So far we have covered almost all there is to know when creating a physics en-
R OTATING O BJECTS IN T WO D IMENSIONS
Before we look at rotations in three dimensions, it is worth understanding them in
two. I will not implement any code from this section, but thinking about the two-
dimensional case is a good analogy for understanding three dimensions.