Known values: Point P coordinates * x*,

*on initial coordinate system, translation vector parameters*

**y***between origin centers of the two coordinate systems, scale factor*

**Î”Î§**,**Î”Î¥***, rotation angle*

**s***.*

**a**

Solution: Point P coordinates ** X, Y** on reference coordinate system.

From the geometry of the scene applies:

X=sâ‹…(xâ‹…cosa-yâ‹…sina)+Î”Î§

Î¥=sâ‹…(xâ‹…sina+yâ‹…cosa)+Î”Î¥

*Rotation angle * a* is measured counterclockwise from reference coordinate system XY to initial coordinate system xy.