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I have 2 cluster of points, each of which are derived from a RANSAC line fitting (among several points in the set). Solving the system of equations, I can retrieve the parameters for the two lines in least square fashion. I want to determine if these two lines intersect within the set of points or not. If so, I want to determine the intersection point.

I guess I need to do some kind of approximation for estimating the intersection (because unless they are parallel, they will intersect at some point, but I want to determine if that point belongs to the set of points I have). Two cases are shown in (a) & (b) of the figure.

ayan.c
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  • Can you clarify what you mean by belonging to the set of points? What criteria do you want to use? – Codie CodeMonkey Jun 30 '14 at 18:12
  • Imagine a point set approximates two straight lines. Suppose the solution of intersection of these straight lines is (x,y). I want to know if the point belongs to the original set of points or not. I can exhaustively search for the point in the original point set, but least square approximation of the straight lines may not be good to find out the intersection point (a small error will result in huge change in the inclination of the straight lines, resulting a wrong location of intersection point). In figure(a), the intersection point is not contained in the point set,in figure(b), it is. – ayan.c Jul 01 '14 at 00:53

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As I understand your question, you can find the intersection points of your lines, you just need to know if they're near a point that is in one of your sets.

A good way to do this is to put your points in a quadtree before finding any of your intersections. Then you can query the quadtree to find any points nearby.

Codie CodeMonkey
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