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If I have a camera pointing "straight" down towards a table and put a pack of gum on the table, it will look the same no matter where I move the pack of gum in the image. If I put a bottle on the table right in the center of the image, I will only be able to see the cap and the top silhouette of the bottle. If I move the bottle towards the edge of the image, I will begin to see more of the bottle's side and the cap will at some point exit the image because the bottle will look skewed.

What do you call it when the height of an object determines how it will look in a 2D image, and are there formulas to calculate how much the object will get skewed(I am guessing the camera FOV has an impact)?

I realize this might be a math question, but if someone knows what it is called I think I can google it.

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It's just perspective: "the appearance to the eye of objects in respect to their relative distance and positions." It has nothing to do with a camera in particular, nor it's recording in 2D.

In 2D/art perspective is the opposite: "the technique or process of representing on a plane the spatial relation of objects as they might appear to the eye."

The point where the eye and the camera differ in perspective is at short distances (<~ 10ft) where the human's binocular (3D) vision is effective; particularly w/in about arms length. At greater distances human vision becomes essentially 2D and the lens/camera see (and render) a scene the same. Or, if one were to view a scene with one eye/through a monocular it would be in 2D as well.

This is why images taken at short distance are often referred to as having "perspective distortion"... in reality it is not distortion nor distorted; it is simply perspective. It's just that we normally see that scene/situation with binocular vision (parallax, which the brain corrects to a more distant 2D interpretation) and the camera cannot do that.

The primary principles of perspective here is "apparent foreshortening," but "linear perspective" is also relevant. Your best starting point might be references covering "monocular cues for interpreting distance" (aviation/aeromedical).

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I think you mean parallax

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances.

I don't have the math to explain how it actually can be calculated. Wikipedia does, though ;)

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I think it's usually just referred to as "wide-angle distortion". It's just due to rectilinear lenses being at scale for planes in parallel to the camera, so planes facing the camera are increasingly overrepresented in the image width the more you move to the side and the more oblique the planes in parallel to the camera get.

The other extreme to rectilinear lenses are fisheyes. They don't have that kind of distortion but do not render straight lines as straight lines (unless they run through the image center).

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