I think you do it like so:
For every line in mesh A:
For every point in mesh B:
Find the plane that passes through these three points.
If every point in mesh A is on one side of this plane,
and every point in mesh B is on the other side of this plane,
then you have found a seperating plane, and the meshes are definitely not intersecting.
Next
Next
Then swap mesh A and B and do it again if you haven't found a seperating plane.
I'm pretty sure this only works for convex meshes. It won't work for concave meshes. You'd have to split the concave meshes into a bunch of convex meshes and test each seperately.
There's probably other methods which work for convex meshes, but are slower.
For every line in mesh A:
For every point in mesh B:
Find the plane that passes through these three points.
If every point in mesh A is on one side of this plane,
and every point in mesh B is on the other side of this plane,
then you have found a seperating plane, and the meshes are definitely not intersecting.
Next
Next
Then swap mesh A and B and do it again if you haven't found a seperating plane.
I'm pretty sure this only works for convex meshes. It won't work for concave meshes. You'd have to split the concave meshes into a bunch of convex meshes and test each seperately.
There's probably other methods which work for convex meshes, but are slower.