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I have a rectangular plane filled with randomly drawn straight lines (of which i know the vertices coordinates), with different lenghts, and i need to find which triangles can i draw (possibly the biggest ones) inside it that intersecates with the least lines possible, is there an existing algorithm that could work here, or some way that you think i can relate this problem to a more common one? thanks in advice

KylesDev
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    This is a rather ill-defined problem statement. How do you decide that one triangle or a set of triangles is better than another? – n. m. could be an AI Oct 09 '15 at 08:15
  • You're right, my English isn't the best, what I meant is that I need to find the triangles I can draw that intersect the lower number of lines possible, that would result in a single triangle, which would be my final result, or in a collection of different triangles, from which I would choose the one with the biggest surface – KylesDev Oct 09 '15 at 08:30
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    So the answer is one triangle, not a set. It is still not clear how you decide between a bigger triangle that intersects more lines, and a smaller triangle that intersects fewer lines. – n. m. could be an AI Oct 09 '15 at 08:43
  • Yes, in the end I need a single triangle, and between the two I would need the smaller one that has less intersections, as the main priority is to have less intersections as possible – KylesDev Oct 09 '15 at 09:05
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    So in fact you need zero intersections, as it is better than anything with non-zero intersections. – n. m. could be an AI Oct 09 '15 at 09:07
  • You can always draw a triangle far away from all lines. It will have zero intersections and as big area as you want... – Petr Oct 09 '15 at 09:08
  • Yes, but in the case there isn't any possible triangle with zero intersections, I would still want I get the triangle with the less intersections possible – KylesDev Oct 09 '15 at 09:10
  • @xKylesx, you can _always_ have a triangle with zero intersections, just take three points as close to each other as possible. – Petr Oct 09 '15 at 09:11
  • It seems that you do limit the set of triangles under consideration somehow. Can you post some picture and show which triangles are allowed and which not? – Petr Oct 09 '15 at 09:12

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