# Curve intersection criteria

I have two curves, which are given by sets of values:

$C = [( x{_1} ,y{_1}),(x{_2},y{_2}),(x{_3},y{_2}),...,(x{_n},y{_n})]$

$C^' = [( x^'{_1} ,y^'{_1}),(x^'{_2},y^'{_2}),(x^'{_3},y^'{_2}),...,(x^'{_m},y^'{_m})]$

where $m \ne n$

Is there any criteria to determine if these curves are intersects or not (I need to find only fact of intersection). If yes, it would be great to determine if they intersect odd or even times.

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## 2 Answers

This is basically the same as the Polygon intersection problem.

One possible difficulty is how your curves are defined. For example, I can give you two discrete triangles that have overlapping circumcircles.

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Thank you for link! It may be very useful, but here I am expecting math answer without any programming – Anton Semenov Jun 10 '11 at 6:53

One way I can think of is to test if each line segment $(x_i, y_i)$ in the first curve intersects any line segment $(x'_j,y'_j)$

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Yes, it seems to be right answer, but how can I rewrite it in math form? – Anton Semenov Jun 10 '11 at 6:54