2-d Transformations

Rotation

Every point in the object co-ordinate system is rotated by an angle anti-clockwise around the origin to give .

The equations governing this transformation are:

This pair of equations is derived from the formulas for the sines and cosines of the sums of angles.

The equations describe rotation around the origin. However, a special formula for rotation about an arbitrary point not needed, as this can be achieved by a composition of transformations.

1. Translate all points by . This moves the origin to :



2. Rotate by in the new co-ordinate system.



3. Translate back to the original system:

We can represent this mathematically as a composite transformation, :

where is the translation, is the rotation and is the inverse translation.

The operations are applied left-to-right. This is opposite to the usual mathematical convention for the composition of operators.

From Colin Flanagan -- see details
26.11.1996