how to calculate virtual screen size of a HMD?

[lionwong]

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

[zalo]

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 jury-rig a solution by staring at a dot in the middle of a display and locating your blind spot.

[cybereality]

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;
}

[lionwong]

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 jury-rig a solution by staring at a dot in the middle of a display and locating your blind spot.

Big thanks,zalo
So the screen size is another way to describe field of view,is my understanding right?

[lionwong]

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;
}

Thanks

[johnfshaughnessy]

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"

[Fredz]

s/hypothesis/hypotenuse/

[Attreyu]

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.

[lionwong]

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.

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]

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.

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.

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.

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.

[Attreyu]

So, if you have a HMD with a display which has 6", viewed from a 2" distance (lens to screen), what would be the real-life 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 real-life correspondent would be a 80"-100" plasma display viewed from a 7 ft. (approx. 2 metres) distance.

[Randomoneh]

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.