Ok, so it didn't work that well, but it seems like it is working now, also with real points.
The subproblem of disallowing the same peak in the hough-space to create multiple lines was solved by maskin out the area such that we are sure there is some minimum distance betwen the lines ( that is distancebetween the a and b parameters )
The two images shows, first the laser line on a dark image, and second the lines detected on a thresholded image.
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