Circle in perspective
I watch a circle.
It appears like an ellipse because of my angle of view.
I measure its apparent width and height in terms of field of view angles.
Is it possible to determine where I am in relation to the circle, in terms of number of radii distance DS from circle center and at what elevation angle above the circle’s plane (angle VSN)?
1) The height angle NVS of the ellipse puts me on the perimeter of a circle around a point above the center of the circle watched.
I know the angle NVS (the apparent height of the ellipse "north to south"). Define radius DE=1. From this I can calculate the entire triangle SDM and hence I know the center and radius of the circle on which V must be (V, S and N are on that same circle so angles DMS=DMN=SVN and radii MV=MS=MN=MB). S South is of course the point on the circle closest to the viewpoint V and point N North is apposed to it on the circle watched.
2) I also know the angle EVW (the apparent width of the ellipse "east to west").
E is on the line VB. It appears as the center of the ellipse because angles SVE=NVE.
Note that the width angle is NOT measured across the diameter of the circle watched! The perspective distortions make me measure the secant EW as being the widest part of the ellipse I see.
So, thanks to the angle NVS (height), I make great progress because I find a circle on which V must be. But how can I benefit from the angle EVW (width) in order to determine exactly where on that circle V must be?