Without any way to quantify just how much is hor + vs. vert -, it's very hard to devise a formula that takes it into account.
I did come up with a hypothesis - that the angle determines a "cone" of FOV, and that what you see is a rectangle inside the circle. Like this:
The circle is the base of the cone, and the rectangle inside is your actual FOV. The triangle is a side cross-section of the cone.
y is one half of the linear vertical span of the FOV. If true hor + is maintained, this will be constant.
x is one half of the linear horizontal span of the FOV. This should increase with the FOV angle.
r is the radius of the circle.
z is the height of the cone, and is constant.
Theta is half the angle of the cone, and corresponds directly to the FOV setting.
And let's call the aspect ratio "w."
So,
tan(Theta) = r/z
z*tan(Theta) = r
x*x + y*y = r*r
w = x/y
x = w/y
(w*w)/(y*y) + y*y = r*r
(w*w)/(y*y) = z*z*tan(Theta)*tan(Theta)
(w*w)/(tan(Theta)*tan(Theta)) = z*z*y*y
So I've been trying to find out the values of "z" and "y" when hor + behavior is maintained by finding multiple w and Theta values that result in hor +'ness. But I need a break now - I'm just frustrating myself. Plus I'm not entirely sure I did the math right (and I have absolutely no clue if this hypothesis is even remotely correct in the first place).
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