# perspective math, calculating horisontal FoV from vertical

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After some searches I think I get the calculations from vertical to horizontal field of view, i just have one question here goes:
width = 2 * tan(hFoV/2)
height = 2 * tan(vFoV/2)
and from what I can guess:
2 * tan(hFoV/2)/width = 2 * tan(vFoV/2)/height
Now is this jump possible because of the fact that both the width and the height have the same size in the view window? I can not see any other reason due to the fact that with and height could have different sizes, but maybe I am just misunderstanding it. The rest of the calculations is easy and understandable. Regards [Edited by - thallish on January 4, 2007 5:51:47 PM]

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You've just rewritten the eqns:

width = 2 * tan(hFoV/2)

->

2 * tan(hFoV/2) / width = 1

I don't really understand your question, what are you confused by/trying to do?

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ahh yeah.. ok I see how it is possible now, as the both equals 1 after rewriting them. doh!! Guess I was tired at that point[smile]

I was trying to understand why I got from the two equations to the one, and I was right, but for the wrong reasons. Thanks for letting me see the light.

Regards

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I'm glad :) Fov V/H & w/h also relate to the aspect ratio of the viewport, it's actually fairly tricky to get the math exactly right (Jim Blinns 'A Trip Down The Graphics Pipeline' has a very good explanation of the differences and mappings between clip, viewport and screen spaces - I'm sure there are others out there). For widescreen support it is important to get these things right so you don't wind up with warped images.

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i'm also interested in the answer.
So what's the formula for the horizontal fov with given vertical fov and aspect ratio?

regards,
m4gnus

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Quote:
 Original post by m4gnusSo what's the formula for the horizontal fov with given vertical fov and aspect ratio?
This pair of functions converts back and forth between horizontal and vertical fields of view (it'll be easier to just paste the functions than to write out the formulas :):
/** Convert horizontal field of view to vertical field of view. */template < typename T >T xfov_to_yfov(T xfov, T aspect) {    return T(2.0 * std::atan(std::tan(xfov * T(.5)) / double(aspect)));}/** Convert vertical field of view to horizontal field of view. */template < typename T >T yfov_to_xfov(T yfov, T aspect) {    return T(2.0 * std::atan(std::tan(yfov * T(.5)) * double(aspect)));}

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Considering that the distance to the near plane (the adjacent side to the FOV angle) stays the same, but the other side (the opposite side from the FOV angle) changes by a ratio of width/height, the tangents must also vary by that same ratio (since tan = opposite/adjacent, and opposite changes)

Therefore, you end up with:
horizontalFov = atan( tan(verticalFov) * width/height )verticalFov = atan( tan(horizontalFov) * height/width )
Though, for most screen aspect ratios, simply using
horizontalFov = verticalFov * width/heightverticalFov   = horizontalFov * height/width
is a really close approximation.

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ok so the formulas are:
horizontalFov = atan( tan(verticalFov) * aspectratio )
verticalFov = atan( tan(horizontalFov) / aspectratio )
thanks that was what i needed.

regards,
m4gnus

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