This is an alternative method to get a basis from a quaternion (log quaternion)... or from angle/angle/angle.
This is built by rotating the constant vectors (1,0,0), (0,1,0), (0,0,1) via standard quaternion
rotation, and reducing common factors. The
1s collapse out a lot of the terms of
apply. It ends up being less work to get the 3 vector basis than to rotate a single point;
although if you USE the basis to multiply with the point; that increases the work to excess of
just rotating a vector directly...
This is the base form... the steps will be broken out for phases of substitution. As implemented here https://github.com/d3x0r/STFRPhysics/blob/master/3d/src/dual-quat.js#L347