3D visualization of movements

[Leonard Evens]

I am in the process of developing some software (using the program Maple) for making view camera calculations and viewing the results in three dimensions. I have not got too far, but here are some examples of what I've come up with.

The purpose is to visualize a method for using tilt and swing to get a desired subject plane in focus. Assume for simplicty that the lens is approximated by a point, there are no horizontal or vertical shifts, and that tilts and swings are done about axes through the lens. Briefly, you choose three points, two of which project in the image plane to points on a vertical line through the image center. You then tilt so that those two points come into focus, and then swing to bring the remaining point in focus.

I show three views. In each case, there is a blue triangle in the scene which projects to a red triangle in the film plane.

In the first view, the lens plane and the subject plane are parallel to the film plane. The triangle was chosen so that one side projects to a vertical line in the film plane. The diagram doesn't show it, but needless to say, the image triangle would not be in focus.

In the second view, the lens plane has been tilted so that one side of the triangle is in focus. The diagram shows the film plane, the lens plane, and the corresponding subject plane which now contains that side of the triangle. That side of the image triangle would be in focus, but the rest of the triangle would not be. The diagram also shows the vertical plane containing the lens which I'll call the reference plane. Note that the hinge line, its intersersection with the subject plane, is horizontal.

In the third view, the lens plane has been swung so that the entire triangle will be in focus. The diagram shows the film plane, the lens plane, the reference plane, and the subject plane. Note that the subject plane now contains the entire triangle. Note also that the hinge line is tilted upward to the left in the reference plane.

PS: In answer to the inevitable remark that I would be better off taking pictures, let me respond by saying I spend as much time doing that as my arthritic back can manage these days. If you have a cure for that, let me know.

[Kirk Keyes]

Very cool!

[Ralph Barker]

Hmmmm. This software, plus a few small servo motors = auto-focus view camera!

Looks interesting.

Sorry to hear your arthritis is acting up, Leonard.

[Leonard Evens]

Very cool!

In the Maple worksheet, it is beyond cool. I can rotate each of the 3D diagrams in real time. so they can be viewed from different perspectives.

I can also produce an animation going from the first diagram through stages to the last one.

Unfortunately, I don't yet know how to reproduce anything but a static picture outside the Maple environment.

[Kirk Keyes]

I have a demo copy of Maple 13(?) around here. I wish I had the time to play with it...

OK - it was a Mathcad 13 Demo. Still would be fun.

This sounds really neat. I'd love to see some 3-D animations of some common camera setups.