Checking If A Triangle Is In A Mesh

This may or may not be a simple question, how would i detect if a single triangle is intersecting a mesh? Preferably something cheap to process. At first i was thinking i could check if a point is within a range of a Dot product, but then i realized a mesh could intersect it without having a vertex inside the triangle, so that obviously wouldn’t work. I would simply use the default collision detection, but i want to cycle through certain triangles in a mesh to check for intersection.

I’m sure there are plenty of people out there who know the answer, so could someone give me a general idea of how i would achieve this?

First step is to understand that a mesh is simply a collection of triangles, from here you can turn your mesh into a set of triangles to test against your given collision triangle.

Searching “triangle triangle intersection” on google is yielding some promising results; most immediately this paper:

I’m sure with more googling and asking around on math forums you’ll be able to create something very functional.

Specific to mesh collision, triangle-triangle intersection isn’t going to help if your collision triangle is INSIDE the mesh.