Game Physics Engine Development, 2nd Edition

488 Chapter 20 Other Types of Physics

20.2 Reduced Coordinate Approaches

Another technique sometimes mentioned in game development circles (although

very rarely implemented) is the reduced coordinate approach.

In our physics engine we’ve given each rigid body 12 degrees of freedom—three

each for position, orientation, velocity, and rotation. The orientation uses four values

but has only three degrees of freedom; the fourth value can always be determined from

the other three (because the size of the quaternion must be 1).

When objects are in contact, or have j oints between them, they are constrained.

They can no longer have any value for each of the 12 degrees of freedom. For exam-

ple: if a nonliftable block is placed on the flat ground, it can on