Game Physics Cookbook

Axis angle rotation

As discussed earlier, we can combine yaw, pitch, and roll using matrix multiplication to create a complete rotation matrix. Creating a rotation matrix by performing each rotation sequentially introduces the possibility of a Gimbal Lock.

We can avoid that Gimbal Lock if we change how a rotation is represented. Instead of using three Euler angles to represent a rotation, we can use an arbitrary axis, and some angle to rotate around that axis.

Given axis , we can define a matrix that will rotate some angle around that axis:

Where