Demonstrate for example if you have an image at 17mm on an APS crop sensor camera what is the right way to calculate the size of the scene as if the shot was taken at say 70mm with the same camera. so I have an image I want to crop away anything thats not viewable if it had been 70mm.

OK how about with a stitched scene with 2 frames joined from the same 17mm how would I show it if it was taken with a 5mm (if there was one)?

If you have the field of view (in degrees) and the distance, then I suppose you could do some math with sinus and cosinus...

17 > 70, crop to 692 × 1038 pixels if it was done on an A700.
Easy to figure out with a CAD program.

Not enough info for the pano question.

No, it's way easier than that; no trigonometry required. All you need is the Theorem of Intersecting Lines---which is nothing but the geometrical version of the Rule of Three (also known as Rule of Proportion; "Dreisatz" in German).

Javelin, if your image taken with a 17 mm lens is X pixels wide and Y pixels high then multiply X and Y by 17, then divide both by 70, to get the pixel dimensions of the crop that shows the same field-of-view as if the original shot had been taken with a 70 mm lens. This calculation is accurate for pictures taken at infinity distance and less accurate for shorter distances but still accurate enough for all practical intents and purposes, except for macro shots.

-- Olaf

Olaf. Thats exactly what I did with a shot and I wasn't sure it looked right. thanks.

Winston: I did lay it out in mastercam to arrive at what Olaf said but I doubted myself because I was assuming the scene didn't matter and doubted that assumtion so I was thinking along the lines of what Bossel was suggesting but not having measure out the scene and knowing the distance between refence points and the angle the camera was at was going to make me crazy and I was pretty sure I didn't need that.

Hang on. Are you not assuming a small angle approximation here as well? Ignoring that puts this comparison about 11% out (could be worse but the errors are in the same direction).

For the second part to the question you need to know the angle of overlap used when stitching.

Harvey

Olaf's method is fine. My CAD method works the same way. It just makes it visually obvious.

The only assumption that might be a problem is that all of the lenses involved are perfectly rectilinear.