How to calculate the intersection of 2 planes from a point cloud

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Hi all and thank you for your time
I have a point cloud representing 2 planes and a line with is their intersection (looks like a flag, i.e all interconnected), I know the coordinates of vertices, connections of faces and the face normals. I need to find the equation of that line. Any ideas for the best way to approach?
Thank you
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Tim Navr
Tim Navr 2016-4-14
编辑:Tim Navr 2016-4-14
Thank you for commenting. What I have is a mesh of triangles created by a 3D scanner and imported as a .stl file. No, all the points do not lie exactly in the same plane, in fact the planes looks like parallelepipeds. The points are scattered amongst 2 parallelepipeds and a cylinder which forms a connection between them. Btw the planes are at 90 to each other. Hope that clarifies it. Please let me know if you have any further questions. Thank you

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