This is a fairly complex question, so please bear with me.
I'm attempting to calculate an edge loop based on the intersection of a plane with a mesh, bounded by a sphere.
Here is a mockup of what the expected result might look like:
The black lines represent the intersected mesh, the orange line the result. Blue and cyan lines are vertex and face normals, respectively. The sphere origin would be somewhere inside the mesh. The orange vertices and sphere origin would also be coincident with the plane. Note that the edge loop is not part of the mesh. This is not a mesh split - just a list of vertices forming a loop along it.
Faces included in the edge should be pointed toward the sphere origin side, and any islands should be ignored (greedy), as shown in this mock up:
In the event that a closed loop cannot be found, the function should return null or an empty array.
I'm working on this in Unity, so I will use its API to further illustrate. The signature I expect to use looks like this:
Vector3 CalculateCorridorLoop(Vector3 planeNormal, Vector3 origin, float radius, MeshFilter meshSource)
I've tried a few different approaches, but I'm now leaning toward a more brutal approach. To come up with those mockups I simply used Blender's knife tool, duplicated the edge loop, and then dissolved the edges on the mesh. If I could calculate an edge loop for every face intersecting the plane then project the edges and origin into 2D space using the plane, it simply becomes a problem of finding the outermost loop containing the origin, which is itself contained by the circle.
Of course I get the feeling I've spent so much time on this I've overthought it and missed something simpler - although even that doesn't seem very straightforward. I think I'd need to keep track of which edges belong to which triangles to keep track of which vertex goes with which loop.
I found this paper, Fast Algorithm To Split And Reconstruct Triangular Meshes, which also uses planes for splitting, but seems to integrate the vertices into the mesh as it goes - whereas I just want the resulting edge loops. Though it's entirely possible I'm reading it wrong.