how to calculate virtual screen size of a HMD?

 One Eyed Hopeful
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 Joined: Tue Jan 07, 2014 12:15 am
how to calculate virtual screen size of a HMD?
Hi,guys
I see most HMD manufacturer often refers to a concept called "virtual screen size" when they advertise their products,such as "80 inch screen at 8 feet away",I don't know it's just a feeling or by some calculated.Can anybody help me to understand this?thanks
I see most HMD manufacturer often refers to a concept called "virtual screen size" when they advertise their products,such as "80 inch screen at 8 feet away",I don't know it's just a feeling or by some calculated.Can anybody help me to understand this?thanks

 CertifEyed!
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 Joined: Sun Mar 25, 2012 12:33 pm
Re: how to calculate virtual screen size of a HMD?
It's basic trigonometry. They first measure the Field of View of the device. This is how much of your vision the screen takes up in degrees.
They then let that number be the corner angle of a triangle, and pick an impressive screen size. They then solve the distance from that corner (your eye) to that side of the triangle.
Of course, this takes one number and makes it two, so you have to do trig to get back to a meaningful figure.
Otherwise you end up with claims like "It simulates a screen the size of the solar system at 50 AU."
EDIT: Oh, I'm not sure exactly how one calculates field of view, but it's not an arbitrary measurement. Last time Palmer was asked on this forum about how he did it, I think he declined to answer.
Maybe something more recent's come up? You can probably juryrig a solution by staring at a dot in the middle of a display and locating your blind spot.
They then let that number be the corner angle of a triangle, and pick an impressive screen size. They then solve the distance from that corner (your eye) to that side of the triangle.
Of course, this takes one number and makes it two, so you have to do trig to get back to a meaningful figure.
Otherwise you end up with claims like "It simulates a screen the size of the solar system at 50 AU."
EDIT: Oh, I'm not sure exactly how one calculates field of view, but it's not an arbitrary measurement. Last time Palmer was asked on this forum about how he did it, I think he declined to answer.
Maybe something more recent's come up? You can probably juryrig a solution by staring at a dot in the middle of a display and locating your blind spot.
 cybereality
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Re: how to calculate virtual screen size of a HMD?
Here is a function I made to convert those misleading X inches at X distance to diagonal FOV (in Actionscript, but should be easy to convert to other languages).
The inputs should be in the same measurement (i.e. inches).
The inputs should be in the same measurement (i.e. inches).
Code: Select all
function getFOV(diag:Number, dist:Number):Number {
return toDegrees(Math.atan((diag/2)/dist))*2;
}

 One Eyed Hopeful
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 Joined: Tue Jan 07, 2014 12:15 am
Re: how to calculate virtual screen size of a HMD?
Big thanks,zalozalo wrote:It's basic trigonometry. They first measure the Field of View of the device. This is how much of your vision the screen takes up in degrees.
They then let that number be the corner angle of a triangle, and pick an impressive screen size. They then solve the distance from that corner (your eye) to that side of the triangle.
Of course, this takes one number and makes it two, so you have to do trig to get back to a meaningful figure.
Otherwise you end up with claims like "It simulates a screen the size of the solar system at 50 AU."
EDIT: Oh, I'm not sure exactly how one calculates field of view, but it's not an arbitrary measurement. Last time Palmer was asked on this forum about how he did it, I think he declined to answer.
Maybe something more recent's come up? You can probably juryrig a solution by staring at a dot in the middle of a display and locating your blind spot.
So the screen size is another way to describe field of view,is my understanding right?

 One Eyed Hopeful
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 Joined: Tue Jan 07, 2014 12:15 am
Re: how to calculate virtual screen size of a HMD?
Thankscybereality wrote:Here is a function I made to convert those misleading X inches at X distance to diagonal FOV (in Actionscript, but should be easy to convert to other languages).
The inputs should be in the same measurement (i.e. inches).
Code: Select all
function getFOV(diag:Number, dist:Number):Number { return toDegrees(Math.atan((diag/2)/dist))*2; }

 One Eyed Hopeful
 Posts: 8
 Joined: Fri Dec 27, 2013 2:57 pm
Re: how to calculate virtual screen size of a HMD?
For anyone curious about the trigonometry, we're essentially using the fact that we can break the diagram into 2 right triangles and apply familiar (though easy to forget) trigonometric identities such as those described by the mnemonic device, "SOH CAH TOA!", meaning
sin(theta) = length of opposite leg /hypotenuse,
cos(theta) = length of adjacent leg / hypotenuse
tan(theta) = length of opposite leg / length of adjacent leg.
The diagram attached as a picture should help visualize it. Essentially to calculate virtual screen size we have:
2*distanceToVirtualScreen * tan(FOV) = virtualScreenSize
and to calculate FOV from virtual screen size and the distance to screen its
arctan(virtualScreenSize / 2*distanceToVirtualScreen)
I don't know if this helps, but I hope so!
https://drive.google.com/file/d/0B79kvk ... sp=sharing
edit: "Hypothesis" != "Hypotenuse"
sin(theta) = length of opposite leg /hypotenuse,
cos(theta) = length of adjacent leg / hypotenuse
tan(theta) = length of opposite leg / length of adjacent leg.
The diagram attached as a picture should help visualize it. Essentially to calculate virtual screen size we have:
2*distanceToVirtualScreen * tan(FOV) = virtualScreenSize
and to calculate FOV from virtual screen size and the distance to screen its
arctan(virtualScreenSize / 2*distanceToVirtualScreen)
I don't know if this helps, but I hope so!
https://drive.google.com/file/d/0B79kvk ... sp=sharing
edit: "Hypothesis" != "Hypotenuse"
Last edited by johnfshaughnessy on Thu Jan 09, 2014 3:43 pm, edited 1 time in total.
 Fredz
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Re: how to calculate virtual screen size of a HMD?
s/hypothesis/hypotenuse/

 Cross Eyed!
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Re: how to calculate virtual screen size of a HMD?
I think the OP asked for the relative screen size to a real life TV screen, when watching through a HMD. Not for the FOV.

 One Eyed Hopeful
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 Joined: Tue Jan 07, 2014 12:15 am
Re: how to calculate virtual screen size of a HMD?
Yes!That's what I really want to know.As zalo's reply,the screen size is mostly depend on the FOV,if we give a distance,then we got the size,and the distance is a setting number,not a real feeling.I don't know if I understand right.Attreyu wrote:I think the OP asked for the relative screen size to a real life TV screen, when watching through a HMD. Not for the FOV.

 Cross Eyed!
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 Joined: Sun Jun 02, 2013 4:21 pm
Re: how to calculate virtual screen size of a HMD?
It's all about proportions. The FOV has little to do with it, as long as your eyes can see the lateral margins of the HMD. That's useful for knowing the FOV and it depends on the lens size as well.lionwong wrote:Yes!That's what I really want to know.As zalo's reply,the screen size is mostly depend on the FOV,if we give a distance,then we got the size,and the distance is a setting number,not a real feeling.I don't know if I understand right.Attreyu wrote:I think the OP asked for the relative screen size to a real life TV screen, when watching through a HMD. Not for the FOV.
But for translating the sensation of watching a real TV screen from a certain distance:
If your real TV has the dimensions X and Y (the diagonal being, as Pitagora told us = square root of (X^2 + Y^2)) and the distance from you to the screen is Z, then you can translate the same to a mobile display. You need the mobile display exact dimensions and the distance from the screen to your lenses (eyes).
It's a perception, but it can be precise by all means. I'll make you a correlation between the Rift and a real TV this afternoon, if that's what you're looking for.

 Cross Eyed!
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Re: how to calculate virtual screen size of a HMD?
So, if you have a HMD with a display which has 6", viewed from a 2" distance (lens to screen), what would be the reallife comparisson ?
You take that 2" distance and multiply it with the required factor needed in reality.
http://en.wikipedia.org/wiki/Optimum_HD ... g_distance
The relation between the TV screen size and the viewing distance is 1:15 in the majority of cases.
So if you have a viewing distance of 2", then the perceived screen size on the HMD's display is about 30" for a 40 degree angle.
But with a HMD the FOV is much larger and the image fills the entire display, at between 60" and more than 110" for the Oculus Rift.
So for a HMD with a 6" display and a 2" focal distance, the reallife correspondent would be a 80"100" plasma display viewed from a 7 ft. (approx. 2 metres) distance.
You take that 2" distance and multiply it with the required factor needed in reality.
http://en.wikipedia.org/wiki/Optimum_HD ... g_distance
The relation between the TV screen size and the viewing distance is 1:15 in the majority of cases.
So if you have a viewing distance of 2", then the perceived screen size on the HMD's display is about 30" for a 40 degree angle.
But with a HMD the FOV is much larger and the image fills the entire display, at between 60" and more than 110" for the Oculus Rift.
So for a HMD with a 6" display and a 2" focal distance, the reallife correspondent would be a 80"100" plasma display viewed from a 7 ft. (approx. 2 metres) distance.
 Randomoneh
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Re: how to calculate virtual screen size of a HMD?
Virtual window of this HMD I've read about is 90° wide. How wide my TV has to be, seen from 3 meter distance, to match this FOV?
TV width = (2xdistance) x (tan(angle/2))
TV width = 6 meters.
My TV is 1 meter wide. I wonder how would I have to sit so it would occupy 90 degrees of my hFOV (horizontal field of view)?
Distance = width / (2 x tan(angle/2))
Distance = 0.5 meters
Handy calculator which works in both ways here.
TV width = (2xdistance) x (tan(angle/2))
TV width = 6 meters.
My TV is 1 meter wide. I wonder how would I have to sit so it would occupy 90 degrees of my hFOV (horizontal field of view)?
Distance = width / (2 x tan(angle/2))
Distance = 0.5 meters
Handy calculator which works in both ways here.
This member owns things.