perspective math, calculating horisontal FoV from vertical

Graphics and GPU Programming Programming

Started by thallish January 04, 2007 04:46 PM

6 comments, last by m4gnus 17 years, 3 months ago

202

Author

January 04, 2007 04:46 PM

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]

regards/thallishI don't care if I'm known, I'd rather people know me

JuNC

236

January 05, 2007 04:05 AM

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?

thallish

202

Author

January 05, 2007 04:53 AM

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

regards/thallishI don't care if I'm known, I'd rather people know me

JuNC

236

January 05, 2007 05:07 AM

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.

m4gnus

240

January 05, 2007 11:35 AM

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

"There are 10 types of people in the world... those who understand binary and those who don't."

Zakwayda

2,389

January 05, 2007 03:02 PM

Quote:Original post by m4gnus
So 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)));}

Drilian

1,067

January 05, 2007 03:09 PM

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.

m4gnus

240

January 06, 2007 06:25 AM

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

regards,
m4gnus

"There are 10 types of people in the world... those who understand binary and those who don't."

perspective math, calculating horisontal FoV from vertical

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