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

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

[Kuifeng]

Interesting question. The optimized/best solution is critical for VR computing speed.

[John D'Errico]

You say that you have two planes, but from what it sounds like, you really have a set of scattered points in plane A, and another set of scattered points in plane B.

However, then you talk about face normals, etc. So it appears as if you have a triangulated set in A, and a triangulated set in B.

There is a significant difference between a pure point cloud and a triangulated surface.

Anyway, are the points that putatively lie in plane A, do they ALL lie EXACTLY in the same plane? Is that also true for plane B? If so, then you need only three points that determine each pane.

These are all important things to understand about your problem, before we can help find an answer.

[Tim Navr]

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

[John D'Errico]

So the planes are not exactly planes. A picture might help.