Determine the transformation:

Determine the transformation that rotates an object point P (x, y), θ^o around a fix centre of rotation (l, m).

Solution

The transformations RQ, P may be found in the following three steps :

1. translation of point p to centre,

2. rotation of θ^o about the origin, and

3. Translation of point P back to position l, m.

The rotation around point P is get by concatenating the individual transformations.

R_{θ, 0 =} T_{- l , - m}  . R_θ. T_{l. m}