Problem
1. Write a routine to implement quaternion rotations, tor any specified axis.
2. Derive the transformation matrix for scaling an object by d scaling factor s in a direction defined by the direction angles a, 13, and y.
3. Develop an algorithm for scaling an object defined in an octree representation.
4. Develop a procedure for animating an object by incrementally rotating it about any specified axis Lls.t appropriate approximations to the trigonometric equations to speed up the calculations, and reset the object to N initial position after each complete revolution about the axis.