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Line segments instersection algorithm

Hi experts!

I wanna study the intersection between line segments (sticks). I wrote a algorithm that generate a matrix, M, with N rows and N columns. The M-element Mij is 1 if stick number 'i' intersect stick number 'j' (obviously M is symmetric).

Given two arbitrary sticks, i need a simple and effective algorithm that determinate if that two sticks are conected by a 'intersected-stick' path.

Any idea for that?

Thanks a lot!