I am trying to draw points of a 3D sphere onto my monitor as if I was looking out into space. Me, the viewer, is at (0, 0, 0). The plane of my monitor is at (x, y, 1) and I have a sphere out in space beyond the screen, off to the side not centered on the Z axis. For each point of the sphere I compute where the point of intersection is between the plane of the monitor and the line between me and the point. What I get is an ellipse. Not surprising since a plane intersecting a cone at an angle would form an ellipse. But if I look at a real sphere off to the side it looks like a sphere and not an ellipsoid. If you draw an ellipse on a roadway and you view it from the correct spot it looks like a circle. I presume you've seen stretched lettering on roads which are readable.
So why when I draw the points of a 3D object exactly at the point of intersection with the line between the point and my eyes doesn't it look right? Or more simply: Given P1 = (0, 0, 0), a plane 0X + 0Y + Z = 1, and P2 at (X2, Y2, Z2) assume Z2 > 1 so that P2 is on the far side of the plane; where do I draw the point on my monitor such that a collection of points forming a sphere actually look like a sphere instead of an ellipsoid? I've been using (X2/Z2, Y2/Z2) assuming the distance between me and the monitor is '1'. But this gives me an ellipse.
