Fitting Points to Lines

The Fitting tool can determine the 3, 4, 5, or 6-degree-of-freedom transformation that best describes the relationship between a set of points and a set of lines. You order the point set and the line set such that they correspond in numerical order. Point 1 corresponds to line 1, point 2 to line 2, and so on.

The Fitting tool considers the best fit transformation to be the transformation that, when applied to the set of points produces a set of points which minimizes the sum of the squares of the distances between each transformed point and the corresponding line.

The figure below shows how the Fitting tool computes the best fit transformation for a set of four points and a set of four lines. After applying the best fit transformation to the set of points (shown in black), the sum of the squares of the distances between the each of the points in the first set and the corresponding line (shown in grey) is minimized.

Best fit transformation relating a point set to a line set

When the Fitting tool calculates the transformation, it does so based on the number of degrees of freedom that you specify.