Consider two 3D polylines, A and B. I am interested in computing a distance/similarity between them (from their current positions, no need to find the "best overlap" first). I have come up with some reasonable approximations (average distance between all points on A to their closest points on B, etc.), but I am surprised to have not been able to find any algorithms that do this more formally. I often seen the Frechet distance (see https://mathoverflow.net/a/199742), but I don't want a maximal distance like that, but rather a "total" distance. It seems to me like we should be trying to find the surface between A and B and finding its area, but I haven't seen any algorithms described that do that. Has anyone seen something like this?
