Skew Rotation
In a rigid rotation both the x- and y- axes are rotated by the same angle. In a skew rotation, the coordinate axes may be rotated by a different amount as illustrated in the figure below.
Skew rotation of coordinate frames
If qx and qy are the rotation angles of the x- and y- axes measured from Frame B to Frame A, the coordinates of the point P in Frame A are mapped to the ones in Frame B by:
The coordinates of P in Frame B are mapped to the ones in Frame A by:
Notice that the angles qx and qy are the rotation angles from Frame B to Frame A as measured in Frame B. Frame B must be orthogonal.