Thank you for providing the visual, TheNut!
I thought about how to determine through which lines the Plane would intersect, and all I could come up with was a brute force search .
In your proposed method of "finding the first intersection point and then follow neighbouring edges to find new intersection data", I am having touble understanding what this means.
The only sense I can make is to pick a direction (CW or CCW) from the Point of Contact (Known Vertex) and calculate the Plane created from the Triangle that's been sliced. Then it's simple algebra.
Programmatically, how do I determine the Vertices of a Triangle that I've intersected, using only 1 point on one of the lines of the Triangle? I'm using DirectX (in case there's a function for this).
If this is not the approach you had in mind, please let me know.
**EDIT - I think I actually got this figured out. I'll get back to you