# Nonuniform or Skew Rotation

In a nonuniform rotation, each coordinate axis rotates by a different angle. You can think of nonuniform rotation as:

- a rotation by two different angles (θx and θy) or
- a uniform rotation (θ) and an additional skew factor (Q).

The following figure shows a nonuniform rotation of coordinate spaces.

If θx and θy are the two different rotation angles of the x- and y-axes measured from space B to space A, you can map the coordinates of point P in space A to the corresponding points in space B using:

Note that the angles θx and θy are the rotation angles from space B to space A as measured in space B. Coordinate space B must also be orthogonal.

In the second way of thinking about nonuniform rotation, you map points using a matrix that consists of a uniform rotation and an additional skew as follows:

You calculate the skew factor by: