conspiratemus1

I read your optical reference. As you say, the difficulty in determining if a photo of a structure shows straight lines or curves as they really are lies in the fact that we don’t know the relationship between the focal plane of the image-gathering surface and the plane of the structure being photographed. If the two planes are not parallel there will be distortion that no amount of fiddling with rulers on the monitor or paper photographic print will correct.

This effect is immediately apparent to anyone who has tried to photograph anything like a building taller than one story or a statue of a general on horseback. When you tilt the camera back “to get it all in”, you invariably find that the building or statue looks like it is falling over backwards in your picture (maybe that is the point with the statue...). Vertical parallel lines no longer look parallel and measuring with a ruler on the print will show them to be not parallel. But we know the building is standing perfectly vertically: the photo of it is not a true image. This effect, and measures to adjust for it, are described in introductory photography texts. The optical characteristics of different lenses are added to this, especially at large apertures.

Curved, raked structures like forks are even more difficult to assess in casual photographs. Perspective of curved things like a bend in the road or the graceful ellipse of a Spitfire’s wing are challenging to draw properly from an oblique view.