Rotate Object using rotational matrix around different origin? (java)

Question

I am using the rotation to rotate a rectangle I have displaying on the screen by a degree of θ°. My rectangle matrix of vertices is:

Where the first column is the x values and the second column is the y values. I load my vertices like this: bottomLeft (2,4), topLeft (2,5), topRight (3,5), and finally bottomRight (3,4).

Next I multiply it against the rotation matrix:

Finally once the calculation is done, I get a new set of vertices:

This is great and all but a problem is here, it rotates around the center point of (0,0). I want it to rotate around my bottomLeft vertex (2,4) (the first vertex in my matrix for this rectangle). How do I go about doing this? What do I have to do to rotate it around my bottomLeft vertex (basically change the center point of (0,0) to (2,4) as my center)?

Answer 1

All rotations will be done around the origin, so you have to move your rectangle to the origin, rotate it, then move it back.

If you use Affine Transforms you can do all three with matrix multiplications, and you can have a single matrix that does all three operations at once. If your rotation matrix must stay 2x2 then you'll have to do the translation (i.e. move) manually.

This answer shows how to compose the transforms for a point rotation.