General Question Monitor Field of View

[gimp1992]

I apologize now if I have already posted this, but I can't find it by searching. How can I find out the proper field of view to use to match the human eye on a a 24" wide screen monitor?

 

[Skookum]

It all depends on how much peripheral vision you want to include in the screen image (up to 180 degrees for the human eye). I like to match the FOV to the angle created between the two lines drawn from one of my pupils to the edges of of my screen. That way I know that the image displayed on the screen subtends the same angle of view as it would in real life.
Having said all that, I usually play Orbiter on the default 40 degree setting.

 

[4throck]

I'd say that a realistic field of view would be about ~20º to ~25º.
BUT we are all used to see photos on screen, and those have field of view of about 40º. I usually settle for that unless I'm simulating a realistic VC, like Gemini or Apollo. On those i go down to 30º and the spacecraft windows do fill the screen :thumbup:.

 

[Face]

I apologize now if I have already posted this, but I can't find it by searching. How can I find out the proper field of view to use to match the human eye on a a 24" wide screen monitor?

AFAIK the formula would be

              h*d*4
FOV=arctan(-----------)
            d^2*4-h^2

with h being the height of your computer monitor and d being the distance from screen to eye-point.

For example: my monitor is about 30cm high and I'm sitting approx. 50cm away, so it would be approx. 33° FOV for me.

regards,
Face

 

[gimp1992]

Thanks for all the answers. You have all given me very helpful info. Once again Thank you.

 

[Notebook]

This document gives the viewing distance as three times picture height:
http://tech.ebu.ch/docs/techreports/tr005.pdf

I remember a rule of thumb was 5 times picture height for 4:3 aspect ratio monitors in control rooms and transmission areas. Always seemed bit far to me, but 3 times seems a bit close.

N.

 

[gimp1992]

AFAIK the formula would be

              h*d*4
FOV=arctan(-----------)
            d^2*4-h^2

with h being the height of your computer monitor and d being the distance from screen to eye-point.

For example: my monitor is about 30cm high and I'm sitting approx. 50cm away, so it would be approx. 33° FOV for me.

regards,
Face

Face, I'm no good with math so if you would work out for me what would your formula work out to on a monitor with d =30 cm and h = 69 cm with 16:9 ratio? If not Face anyone who knows math Thank you.

 

[RisingFury]

Face, I'm no good with math so if you would work out for me what would your formula work out to on a monitor with d =30 cm and h = 69 cm with 16:9 ratio? If not Face anyone who knows math Thank you.

What? It's too hard to grab a calculator?

 

[martins]

Face, I'm no good with math so if you would work out for me what would your formula work out to on a monitor with d =30 cm and h = 69 cm with 16:9 ratio? If not Face anyone who knows math Thank you.

Not sure about Face's formula, since the denominator can become negative. Here's my offering:
[math]
\mathrm{FOV} = 2 \arctan \frac{h}{2d}
[/math]
Now, since you want to do "math", I guess you spurn the use of calculators and similar cheating devices, so let's do it properly.
With your parameters, the argument works out as h/2d = 1.15. The tricky bit is the arctan. As a first approximation, you can use arctan z = z. Therefore

FOV = 2 * 1.15 * 180/pi.

Let's say pi=3 to avoid complications, so FOV = 138.

Unfortunately, the arctan z = z approximation only works reasonably for small z, which is not the case here. The actual power series expansion for arctan looks like
[math]
\arctan z = z - \frac{z^3}{3} + \frac{z^5}{5} - \frac{z^7}{7} + ...
[/math]
However this is only valid for |z| < 1. But we can use another identity:
[math]
\arctan z = 2 \arctan \frac{z}{1+\sqrt{1+z^2}}
[/math]
With your parameters, the argument on the right works out as
[math]
z' = \frac{1.15}{1+\sqrt{1+1.15^2}} = 0.4556
[/math]
(I've cheated here and used a calculator for the square root, but you can use an iterative method to do it by hand).

Now then, plug z' into the first terms of the power series:
[math]
\arctan z' = 0.4556 - \frac{0.4556^3}{3} + \frac{0.4556^5}{5} - \frac{0.4556^7}{7} = 0.427
[/math]
And therefore
[math]
\arctan 1.15 = 2 \cdot 0.427 = 0.855
[/math]
which is quite different from our first approximation.
Therefore,
[math]
\mathrm{FOV} = 2 \cdot 0.855 \cdot 180/\pi = 99
[/math]
(where I've also used the better approximation of pi=3.1).

Of course, you could have skipped the math, used a calculator and got FOV = 98.0, but where is the fun in that? :lol:

Btw, don't you think you are sitting a bit close to your monitor?

 

[fireballs619]

Not sure about Face's formula, since the denominator can become negative. Here's my offering:
[math]
\mathrm{FOV} = 2 \arctan \frac{h}{2d}
[/math]
Now, since you want to do "math", I guess you spurn the use of calculators and similar cheating devices, so let's do it properly.
With your parameters, the argument works out as h/2d = 1.15. The tricky bit is the arctan. As a first approximation, you can use arctan z = z. Therefore

FOV = 2 * 1.15 * 180/pi.

Let's say pi=3 to avoid complications, so FOV = 138.

Unfortunately, the arctan z = z approximation only works reasonably for small z, which is not the case here. The actual power series expansion for arctan looks like
[math]
\arctan z = z - \frac{z^3}{3} + \frac{z^5}{5} - \frac{z^7}{7} + ...
[/math]
However this is only valid for |z| < 1. But we can use another identity:
[math]
\arctan z = 2 \arctan \frac{z}{1+\sqrt{1+z^2}}
[/math]
With your parameters, the argument on the right works out as
[math]
z' = \frac{1.15}{1+\sqrt{1+1.15^2}} = 0.4556
[/math]
(I've cheated here and used a calculator for the square root, but you can use an iterative method to do it by hand).

Now then, plug z' into the first terms of the power series:
[math]
\arctan z' = 0.4556 - \frac{0.4556^3}{3} + \frac{0.4556^5}{5} - \frac{0.4556^7}{7} = 0.427
[/math]
And therefore
[math]
\arctan 1.15 = 2 \cdot 0.427 = 0.855
[/math]
which is quite different from our first approximation.
Therefore,
[math]
\mathrm{FOV} = 2 \cdot 0.855 \cdot 180/\pi = 99
[/math]
(where I've also used the better approximation of pi=3.1).

Of course, you could have skipped the math, used a calculator and got FOV = 98.0, but where is the fun in that? :lol:

Btw, don't you think you are sitting a bit close to your monitor?

You gotta love Orbiter Forum when you get a response like that :tiphat:

If its worth anything, I use 40 degrees in panels, but about 30, I think, when in virtual cockpit. It gives it a very nice effect. I'm not sure if its realistic to the human eye, though.

 

[Moach]

not every calculator does arctan.... even the windows one, in scientific mode lacks that feature... which is stupid... even a Flash app can do that math...

unfortuanetly, i, myself, cannot, but Flash so happens to be my job, so i had it do it for me... a while back i wrote me up an advanced calculator using adobe AIR to help me with curve functions and other gnarly math stuff i often fumble about :blush:


as a blunt anwer, you FOV, for 30cm distance, and 69cm full screen height, is 100 degrees....

but i don't recommend anyone sit so close to a monitor, you'll burn your eyes out :blink:


60cm away is probably a much more confortable setup... then your FOV for that screen would be 60 degs...


i'd post the calculator app here, but it has no documentation whatsoever :shifty: ... i'll write a guide on how to use it and post it up later... BTW, it's very beta right now, and there's a healthy array of bugs that need straightening out before i can call this a proper tool

 

[orb]

not every calculator does arctan.... even the windows one, in scientific mode lacks that feature... which is stupid...

How about "tan" with "Inv" checkbox marked? It inverts trigonometric functions, so tangent becomes arcus (inverted) tangent. Like hyperbolic functions can be switched with "Hyp" checkbox in the Windows Calculator.

 

[Lucy]

Not sure about Face's formula, since the denominator can become negative. Here's my offering:
[math]
\mathrm{FOV} = 2 \arctan \frac{h}{2d}
[/math]
Now, since you want to do "math", I guess you spurn the use of calculators and similar cheating devices, so let's do it properly.
With your parameters, the argument works out as h/2d = 1.15. The tricky bit is the arctan. As a first approximation, you can use arctan z = z. Therefore

FOV = 2 * 1.15 * 180/pi.

Let's say pi=3 to avoid complications, so FOV = 138.

Unfortunately, the arctan z = z approximation only works reasonably for small z, which is not the case here. The actual power series expansion for arctan looks like
[math]
\arctan z = z - \frac{z^3}{3} + \frac{z^5}{5} - \frac{z^7}{7} + ...
[/math]
However this is only valid for |z| < 1. But we can use another identity:
[math]
\arctan z = 2 \arctan \frac{z}{1+\sqrt{1+z^2}}
[/math]
With your parameters, the argument on the right works out as
[math]
z' = \frac{1.15}{1+\sqrt{1+1.15^2}} = 0.4556
[/math]
(I've cheated here and used a calculator for the square root, but you can use an iterative method to do it by hand).

Now then, plug z' into the first terms of the power series:
[math]
\arctan z' = 0.4556 - \frac{0.4556^3}{3} + \frac{0.4556^5}{5} - \frac{0.4556^7}{7} = 0.427
[/math]
And therefore
[math]
\arctan 1.15 = 2 \cdot 0.427 = 0.855
[/math]
which is quite different from our first approximation.
Therefore,
[math]
\mathrm{FOV} = 2 \cdot 0.855 \cdot 180/\pi = 99
[/math]
(where I've also used the better approximation of pi=3.1).

Of course, you could have skipped the math, used a calculator and got FOV = 98.0, but where is the fun in that? :lol:

Btw, don't you think you are sitting a bit close to your monitor?

... I love this place.

 

[gimp1992]

Very funny Martins, this is why I can't do math it just makes no sense, if you can do it more power to you. I don't own a calculator Rising Fury, and the one in Windows has no arctan, so that did me no good. I also got the d and h mixed up d was 65cm at 30 cm I would be blind. You all have been very helpful and it is nice to see that Martins would answer a question for a dummy like me. Once again thanks all

---------- Post added at 03:36 PM ---------- Previous post was at 03:35 PM ----------

and before anyone says it I obviously do own a calculator if I have Windows

 

[orb]

Very funny Martins, this is why I can't do math it just makes no sense, if you can do it more power to you. I don't own a calculator Rising Fury, and the one in Windows has no arctan, so that did me no good.

Windows' Calculator has arctan. Please (re)read my post:
http://www.orbiter-forum.com/showpost.php?p=189315&postcount=12

 

[Lucy]

Yes, it doesn't have a button specifically labelled "Arctan", but it has the capacity to calculate it.

 

[gimp1992]

How about "tan" with "Inv" checkbox marked? It inverts trigonometric functions, so tangent becomes arcus (inverted) tangent. Like hyperbolic functions can be switched with "Hyp" checkbox in the Windows Calculator.

Never would have figured that out.

 

[Bj]

Never would have figured that out.

If you dont want to use Windows calculator, you can use google...

just google "arctan(2)" for instance. Its answer:
arctan(2) = 1.10714872

 

[fireballs619]

Wolfram Alpha for the win! That's what I use, but I've never tried arctans on it