Known values: Point P coordinates x, y on initial coordinate system, translation vector parameters ΔΧ , ΔΥ between origin centers of the two coordinate systems, scale factor s, rotation angle a.
Solution: Point P coordinates X, Y on reference coordinate system.
From the geometry of the scene applies:
X=s⋅(x⋅cosa-y⋅sina)+ΔΧ
Υ=s⋅(x⋅sina+y⋅cosa)+ΔΥ
*Rotation angle a is measured counterclockwise from reference coordinate system XY to initial coordinate system xy.