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?
h*d*4
FOV=arctan(-----------)
d^2*4-h^2
AFAIK the formula would be
with h being the height of your computer monitor and d being the distance from screen to eye-point.Code:h*d*4 FOV=arctan(-----------) d^2*4-h^2
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.
Not sure about Face's formula, since the denominator can become negative. Here's my offering: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?
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.not every calculator does arctan.... even the windows one, in scientific mode lacks that feature... which is stupid...
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?
Windows' Calculator has arctan. Please (re)read my post: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.
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.