Mathematical Iteration for Alignment of 4 Points

[Ashraf_Robot]

What is the mathematical equation or algorithm for alignment of four points in cartesian coordinates (X & Y). Say, we have 4 nominal points (Xn & Yn), and another 4 measured points (Xm & Ym)?. After alignment, what are the new locations of the measured points (Xmn & Ymn)?.

 

[HallsofIvy]

What do you mean by "alignment"? Alignment in what sense? What do you mean by "nominal points"? What is the difference between "nominal points" and "measured points"?

 

[Ashraf_Robot]

Points are located at certain object. Nominal points are the designed point dimensions, in the blue print, related to certain cartesian coordinate, or the dimensions of these points as specified in the CAD drawing. Measured points are the actual measured locations or dimensions in the real world, on the real object. Alignment means trying to align both nominal and measured point locations, as a group but not one by one. As if the location of the nominal point dimensions are drawn on white sheet, and the location of the measured point dimensions are drawn on a transparent sheet. Moving the Transparent sheet on the white sheet to align both points (Nominal and measured) for the minimum error or the least square error. alignment here like a best fit between these point locations.