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Why an object becomes larger when drawn in perspective

As nicely stated by Kevin Reid, the field of view is not accounted for in the figures I uploaded. In order to get the correct coordinates for the projected points on the $x-y$ plane, one should also ...
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Why an object becomes larger when drawn in perspective

If you keep constant the scale at which you view the x-y plane (image plane), while changing the distance of the viewpoint to that plane, then you are not solely changing the viewpoint position; you ...
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