Rotations in 3D space are made mathematically much more tractable by the use of spherical coordinates. Any rotation in 3D can be characterized by a fixed axis of rotation and an invariant plane perpendicular to that axis. Without loss of generality, we can take the -plane as the invariant plane and the -axis as the fixed axis. Since radial distances are not affected by rotation, we can characterize a rotation by its effect on the unit sphere (2-sphere) by spherical coordinates referred to the fixed axis and invariant plane: