Thread: Transformation matrices

Using homogeneous coordinates, what is the transformation matrix (one matrix) needed to perform a rotation in 2D about point and about 60 degrees?

If you were just rotating about the origin, the transformation matrix would just be your standard



But now you have to perform 3 operations:

1) Make (2;1) the "new" origin by shifting it to be the origin
2) Rotate normally about the origin
3) Translate back to the origin of (2;1)

So your resulting transformation matrix will be the product of these three separate transformation matrices. The second is just the standard rotation matrix above (with theta = 60 degrees in your case).

The first transformation, using homogeneous coordinates, translating (2;1) to be the new origin, is

[1 0 -2
0 1 -1
0 0 1]

And the third transformation, translating the origin to (2,1), is

[1 0 2
0 1 1
0 0 1]

So, multiplying these three matrices together will yield the final transformation matrix.