The title can not be clear enough as I really don't know how to call this problem. Let me describe it briefly.
I have some points in coordinate system as (x,y). All points have to move to a new coordinate system (translating) for some need (assume that they move to new positions as reinforced). I have some sample values that I know where they have to be in new map. By the help of this information, I would like to be able to calculate new positions of new points on new map. What I want to accomplish is like calculating a formula or something (like regression, least squares fitting) that I can use it to be able to estimate new positions of new points (see the illustration below).
I don't know how to call this in terms of math, I searched but could not get what I want but I am sure there is a solution already to solve this kind of problems.
Thanks in advance.
