Best Fit Points to Points

Best-fit transformations are widely used in coordinate metrology to consistently and confidently align measurements into a coordinate frame that is meaningful to a user. The term “best-fit” is a mathematical procedure known as a Linear Least Squares fit that uses an optimization to minimize the square of the distance between corresponding points.

The Best-Fit alignment technique has many applications, but Best-Fit Point to Point is typically performed when there is a need to tie back into a known coordinate system. For instance, you have a network of control points from a previous station measurement, and you would like to continue measuring in that previous coordinate system by aligning to these control points. When performing this alignment, the group of points being aligned to are referred to as the “reference group” or “nominal group” and the points that are being moved are referred to as the “corresponding group” or “measured group”. The Best-Fit Points to Points alignment can, however, be used when aligning two instruments to each other or when alignment imported points or any combination in between. The key idea behind this alignment is that two groups already exist within SA and are to be aligned.

Note that the two groups need not have exactly the same number of points. Any points that don’t have corresponding pairs are simply ignored in the command, although if they are in the moving point group they will be transformed along with the rest of the points in the group.

In order to perform a point-based best-fit transformation, the points involved must meet two prerequisites: