# Fit three intersecting lines to planar data

Suppose I have three sets of points on the plane. Call them the red set, the blue set and the yellow set.

Assume that each set contains at least two distinct points.

I'd like to find three lines - call them the red line, blue line and yellow line - such that:

i) the red, blue and yellow lines have a common point

ii) the red line "fits" the red set as close as possible

iii) the blue line "fits" the blue set as close as possible

iv) the yellow line "fits" the yellow set as close as possible

In a slight variation to this problem the data is not colored. The goal is still to find a best fit for three lines with a common point.

Note:

I have in mind some kind of least-squares fit but I'm open to other best fit criteria if they lead to a simpler solution (or any solution).

This is actually a slight simplification of the real problem I am encountering which is a higher dimensional version. In that version, the three sets of data lie in space - not merely a plane - and I am trying to fit the data with three planes that share a common line. I suspect that a solution to the lower dimensional version will readily lead to a solution to the higher dimensional version.

• Least squares seems fine to me. For the second question, you may want to see the Hough transform. Sep 9, 2021 at 9:22