I have two planes defined by three points each. These planes are "finite", meaning that the three points define their limits. These planes may or may not intersect, if so, the intersection is a finite line.
What's the smartest way to find the two end points of this intersection line?
Example:
planea = {(369.4956, 467.6504, 60.5147), (372.1940, 467.9910, 50.6351), (297.3370, 665.9444, 47.6697)}
planeb = {(198.1879, 626.4104, 59.6933), (199.4659, 620.8089, 38.2796), (398.9405, 661.8527, 62.6248)}
Here's a tedious way - perhaps not the "smartest" but probably quite fast enough in any programming language. It's all standard linear algebra (geometry in three dimensions).
First find the (equation of) the line of intersection of the planes determined by the two triangles.
Then find the (at most four) points where that line meets the edges of the triangles.
Two of those points will be the end points of the segment you seek.
At any stage of the calculation you may be able to conclude that the two triangles don't meet at all.