Bug Alert: The Knot isn't always drawn correctly! A knotty problem that I have been unable to resolve in a reasonable time ... more in the Notes and Credits. Press <M> to switch to manual rotation using the keys below: <Right Arrow> & <Left Arrow> keys to rotate about the Y axis. <Up Arrow> & <Down Arrow> keys to rotate about the X axis. <a> and <z> keys to rotate about the Z axis. Try key combinations to rotate about several axes simultaneously. Press <M> again to return to automatic rotation.
I spent a little bit of time on the issue but I'm still not 100% sure. I think there is something in the sort. The first screen shows the "problem". I've tried to outline Face 9 in orange and Face 4 in black to help see those faces. I'm assuming a larger z value means the z is closer to the viewer. If you scroll down on the Face Draw Order list (go down to around index 43) you can see that it says to draw 9 before 4 even though I think the Depth values say 4 should be drawn before 9. Granted I may have misunderstood the Face Depth values for 4 and 9. If you hit the right arrow the problem goes away because the program correctly draws 4 first and then 9. You can arrow left and right to see the problem come and go. If my Face 9 Depth and Face 4 Depth are the wrong values then it's probably not a sort problem. My other thought was that it was just that the z averages for Face 9 in position 1 of my example happen to average out farther away because of it's shape and the fact that it extends in the z direction farther than Face 4. There might be a problem point where the z averages just do not return satisfactory results, which I think is at least partially what you were referring too in your original notes. This seems like a Painters Algorithm system for surface removal and there are limitations to that process which you may have stumbled across. If you were to calculate the face normal vectors Face 4 would be hidden in both of my positions and you would not have the problem at all. At any rate I'm travelling most of the rest of the day so I doubt I can spend any more time on it and I thought I'd see if you had any thoughts on my findings.