Do you really need to be that accurate? Poser's rendering engine smooths corners out anyway, so things will usually look better than they are. Unless I misunderstand what you're trying do do an approximation might be good enough. You say that you know the x and y for this new point but need the z. I assume that you are creating a new vertex so that you can get a higher resolution mesh. Incidentally, somebody else has already done a util that does this. Unfortunately I can't remember what it is called. I'll post again if I remember. How about just averaging the z of all the vertices in face F? It won't be far out and it's certainly an easy algorithm. I can't imagine a situation where that would cause a noticeable crease or other artifact.