Commentary on Rotations in 3-Space

The problem of computing rotations in three-dimensional Euclidean space has been widely studied. It arises in many areas of mathematics and computer science, including graphics, robotics, animation, and simulation [Pique 19901. A 3 x 3 rotation matrix R represents a rotation in 3-space about an axis a through an angle 8. The matrix R is orthogonal and has unit determinant. The sign of the angle 8 depends on which of two directions is chosen for the axis, and on whether a reference frame or space rotates.