A plane a*x + b*y + c*z + d = 0 stored as a, b, c, d; normal is the (a, b, c) part and vector4 the four coefficients. plane_dot(plane, point) is the signed distance from the point to the plane when normal has length 1, positive on the side the normal points to.
p := make_plane(xyz(0, 1, 0), xyz(0, 2, 0)); // the plane y = 2
assert(p.d == -2 && p.normal == xyz(0, 1, 0));
assert(plane_dot(p, xyz(5, 3, 5)) == 1);