Alan,

Three points do determine a plane. And you can match many subject planes by an appropriate choice of both tilt and swing, but you can't necessarily do it with just a tilt. If you use just a tilt, you can be sure that the subject plane will intersect the film plane (assumed vertical here) in a horizontal line. In that case, two points will completely specify the subject plane. If there were a third point you wanted to be in that plane, either you would have to be lucky or else you would have to use a swing in addition to your tilt to get it there.

Your intuition that not every subject plane is possible is correct. For example, by tilting, you can't have the subject plane pass any closer vertically to the lens than the focal length, and in practice, it will be considerably further away than that. For example, for a 150 mm lens, with a 30 degree tilt, the distance of the subject plane below the lens is 300 mm. 30 degrees is, or course, an enormous tilt, much larger than you would use except in exceptional circumstances. For a more realistic 10 degree tilt, it would be about 864 mm.

With respect to your other point, let me suggest you go back and read carefully what I said. I think you will find we are saying the same thing. You have to remember that, ideally at least, there is one plane where the focus is exact. (In reality things are not that neat, of course, but it is close enough for all practical purposes.) That is going to be true whether you tilt or not. That means that all other points, not in that plane, are going to be out of focus to a greater or lesser degree. The object of selecting the proper f-stop is so that all points within some desired region of space will come into adequate, if not exact, focus. To do that, as I keep pointing out, you have to stop thinking about the original near and far point which are used just to choose the position of the plane of exact focus. You then have to do something else, namely consider points above and below that plane to determine the proper f-stop.

As I noted above, things may not be so simple, because you may want to go back and change the position of the exact plane of focus, either by just shifting the position of the standard or even by changing the tilt. Often it makes sense to start with the upper and lower limits of what you want in exact focus and then to try to position the exact plane of focus about halfway between them. You would then choose your near and far points to set the tilt with that in mind. But unless you separate in your mind the process of determining the tilt angle from the process of determining the f-stop, you are going to run into difficulties in doing either.

John,

I'm not sure just what you are asking, but let's suppose you want the near foreground and objects both 1 mile out and 3 miles out to be in focus. If by foregound, you typically mean something quite close to the lens, with anything but a wide angle lens, chances are you will need a tilt. Then you would choose your near point to be some specific point in the foreground close to the lens that you want in focus. With any lens you were likely to be using, it wouldn't matter if you chose for a far point something one mile out or three miles out, since both would be effectively at infinity. Optically, they could be considered to be at the same distance in the sense that in either case their images would be in exact focus basically at the focal lens distance from the lens.

On the other hand if you considered an analogous situation with more realistic distances, and you had a near point, a middle point and a more distant point you wanted in focus, you could choose either the point in the mid distance or in the far distance as your far point. Probably it would work better using the middle distance point. But in either case, you would choose your exact plane so that it passed through the desired two points and then select your f-stop so the third point came into focus when stopped down. In a situation like that you describe, you probably wouldn't have to stop down very far. Problems arise where there are additional points above and below the plane of exact focus which are quite close to the lens and which you want in focus.