Would one way to account for this situation is to see whether the slopes of the two lines are different by some threshold (if they are too similar, say that they don't intersect)?
How can you detect this case happening? Do you just check that the slopes are within some small threshold?
If we want to find the intersection of two lines that are almost parallel, can we find the segment of the degenerate intersection and take the midpoint since it is symmetric?
Does this mean that mesh/mesh intersection is really only difficult if the mesh is moving?
Is this easier to do if both lines are stored implicitly?
Would overlapping lines also fall under the degenerate intersection case? since it would cause a change from many intersections to just one.
Can't we project the problem into a different set of coordinates, where the lines are not as parallel and we don't run into floating point numbers, then project back?