Rotate point P = ( x , y ) in ℝ2, around a point C, as a center of rotation, by an angle θ. Center of rotation C can be either the origin O = (0,0) or some other specified point C = (xc , yc) . Direction of rotation is counterclockwise. For clockwise direction, use negative angle θ. Rotation can be seen as a transformation T : ℝ2 → ℝ2 , such that T (P) = R × (P - C) + C , where R is a rotational matrix R =
