def triangle_intersects_plane(mesh, tid, plane):
    """
    Returns true if the given triangle is cut by the plane. This will return
    false if a single vertex of the triangle lies on the plane
    """
    dists = [point_to_plane_dist(mesh.verts[vid], plane)
             for vid in mesh.tris[tid]]
    side = np.sign(dists)
    return not (side[0] == side[1] == side[2])
Returns true if the given triangle is cut by the plane. This will return
    false if a single vertex of the triangle lies on the plane