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Need slightly more clarification on monitor distance matching


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#1 Kilroy

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Posted 12 February 2017 - 11:44 PM

I have a ton of questions, and I would really appreciate if someone could take some time out of their day to give me a concrete answer.

 

Is it impossible to have a sensitivity at an FOV that perfectly matches a sensitivity at another FOV? Because even if I match monitor distance to 1% for 2 FOVs, I know full well that I won't be doing only 1% distance flicks, and so that'll be on me to try and compensate for a flick at an enemy at the edge of my screen despite not being used to that feeling. This would be more apparent if I were using something with a really low FOV like the CSGO AWP on its second zoom at 10 FOV, because the difference in zoom sensitivities between 0% and 100% is 0.787398 and 1.127085 (even though you wouldn't be able to see the person through the black scope part). If the answer is yes, doesn't that mean that it's impossible to have a 1:1 mouse movement, across even slightly different media? So I simply have to choose based on preference?

 

My next question is a bit crazy, but what if you were able to partially re-mediate this problem using mouse acceleration? This makes sense to me because the further away from the crosshair lies the target, the faster I'd move my mouse, and so this would result in the higher, more correct sensitivity needed to have a 1:1 movement at that specific distance.

 

How does any of this work on a game with a 2D plain, like osu!, LoL or even my windows desktop? How can I get a (pseudo?) 1:1 mouse movement here?

 

Lastly, I don't understand what matching at 0% monitor distance means, because the sensitivity involved in moving the mouse no distance would be irrelevant, right? So how does the calculator give the number it gives?



#2 Drimzi

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Posted 13 February 2017 - 05:40 AM

I can't answer your question but I can tell you my experiences.

 

For 3D, I have found 0% works great, it is how Call of Duty scales their sensitivity every time the FOV changes when aiming down sights. It's not the best but It is what I am use to and feels pretty consistent. You can't really use the same monitor distance across FOVs and expect the exact same speed universally as every FOV will match at a different point on the monitor if the speed was exact.

 

For 2D, I found that that roughly 65% works best for me. I play Aimbooster and Osu! and I can play an intense session of shooting circles in CS:GO or Aim Hero and go straight to Aimbooster or Osu! without feeling discomfort. I came to the conclusion of this percentage match in this post http://www.mouse-sen...op-mode/?p=5804

 

For reference, I can play CS:GO intensive fast aim at 0.3 respawn time, reach 3 minutes + in Aimbooster, and play some 7 star maps with DoubleTime in Osu! and songs like "Call me it. (500 tortures)" which have screen wide jumps.


Edited by GLiSN, 18 February 2017 - 11:58 PM.

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#3 Joshua Willis

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Posted 13 February 2017 - 12:46 PM

Hey I know you want a solid answer right now but I can't be bothered giving you one (at least not now). But just trust me, since I've integrated and found the average value of each FOV from 0 to 150 FOV (150FOV is more than enough) given the equation y=sqrt((1/sinθ)^2-x^2)-sqrt((1/sinθ)^2-1)... and the monitor distance I calculated that we should be using is 25%.

 

I sent a message to GLiSN just now as we were actually discussing this and this is the monitor distance I mathematically decided on.



#4 Kilroy

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Posted 13 February 2017 - 08:46 PM

GLiSN, in that other post you linked me to, what did you mean by 2D edge to edge distance? Did you mean like, the horizontal length of my screen, or did you mean something else? And if so, is it in centimeters?

 

Joshua, I need to actually understand how that formula works before I could trust using the result, but I might anyway. Also when you said that we should use 25%, did you mean that it is perfect value, or that it's the best it can be?



#5 Drimzi

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Posted 14 February 2017 - 01:02 AM

It is the mouse distance (cm) to go across the screen, which can be found using the calculator.


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#6 DNAMTE

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Posted 14 February 2017 - 12:46 PM

IMO the perfect match is with cursor speed rather than monitor distance. Afterall that is essentialy what you are learning, not a distance on a monitor. Your familiarising yourself with the speed your cursor moves from point to point. The better you judge this the faster the movement, the more 'snappy' you can become.

 

Matching cursor speed is also much easier and consistent across ALL FOV or even 2D-3D. If you match your 2D cursor speed to the rotational speed in 3D then the 'feel', the 'speed' of your cursor is the same. You can match this to any FOV and cursor speed will always feel identical.

 

To give a brief example of this: ARC.png

Here we have a monitor distance (in red) and the arc Field of View of 180 degrees in black. (highlighting larger FOV's, the less accurate monitor matching becomes. This is also true when comparing two FOV's, the greater the difference the worse they match)

 

For simplicity, the monitor distance (chord length) is 2 therefore the Arc length is equal to 3.142... A 57% increase in length. This means when matched at 100% monitor distance the 3D 'cursor' must move at 57% greater speed than the 2D cursor.

 

The inaccuracies 'reduce' as you eventually lower FOV as close to zero as possible. Essentially reducing the sample size to something so small the difference appears negligible. IMO not ideal.

 

Making the 100% monitor match value 57% less however places cursor speed identical in both planes... 2D & 3D?

 

 

NOTE: obviously the percent changes with each FOV.

For example 106.26FOV (90 4:3) is 15.8% which equates to roughly 65% on the implemented monitor match calculator.


Edited by DNAMTE, 14 February 2017 - 12:49 PM.

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#7 jabbothehut

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Posted 14 February 2017 - 01:43 PM

Hey I know you want a solid answer right now but I can't be bothered giving you one (at least not now). But just trust me, since I've integrated and found the average value of each FOV from 0 to 150 FOV (150FOV is more than enough) given the equation y=sqrt((1/sinθ)^2-x^2)-sqrt((1/sinθ)^2-1)... and the monitor distance I calculated that we should be using is 25%.

 

I sent a message to GLiSN just now as we were actually discussing this and this is the monitor distance I mathematically decided on.

tried it on siege and it feels really good! 25%is lovely!



#8 Kilroy

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Posted 15 February 2017 - 04:11 AM

My results put me closer to 70%, unless I'm doing this wrong, but it isn't very different anyway.



#9 DNAMTE

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Posted 15 February 2017 - 05:52 AM

Unless your using the minimum, maximum or median of the two (0%, 100% or 50%) given the way arc length changes with FOV you cannot provide a percentage that works accurately for any broad range of FOV.

25% of 150fov versus 25% of 90fov using the same monitor is going to feel vastly different when trying to match with 2D desktop. The cursor speed will be completely different.

Ideally your desktop cursor speed will match the crosshairs speed ingame. that's what matters. You could Project your screen to a cinema sized screen and because your cursor speed remains relative you will be ready to go. distance matching from two different planes IMO has little merit.

#10 Joshua Willis

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Posted 15 February 2017 - 11:15 AM

GLiSN, in that other post you linked me to, what did you mean by 2D edge to edge distance? Did you mean like, the horizontal length of my screen, or did you mean something else? And if so, is it in centimeters?

 

Joshua, I need to actually understand how that formula works before I could trust using the result, but I might anyway. Also when you said that we should use 25%, did you mean that it is perfect value, or that it's the best it can be?

 

Hey, here's a picture that might explain the maths behind what I'm talking about:

http://i.imgur.com/LiDfxls.png

 

LiDfxls.png

 

Basically, the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, so if we simplify the equation in terms of y we can integrate it and find the average value of the equation. But since this is only for a single FOV, we need to create a list of average values for a given range of FOVs and then find the average of all those averages and that will give us the Monitor distance we are looking for. I know this is messy and I should use a triple integral, but I don't know how to do them (can't be bothered to learn how... but creating a list of single integrals and then finding the average of them is precise enough). The given FOV range is something you would be able to change to your liking. Just check this spreadsheet out and you'll find that you can have a FOV range of 172, 150, 126 or 96 (I didn't include anything lower than 96 as most games have at least 90 FOV): https://docs.google....oCQcaBs/pubhtml

 

As you can see, the calculated monitor distances you can choose from are 30%, 25%, 20% or 15%. Since the mouse sensitivity calculator only goes up in increments of 5 and doesn't have decimals, you can only pick one of these 4 monitor distances. I personally chose 25%. I don't really intend to use anything higher than Quake Live's FOV of 130 so 150 FOV is more than enough for me. If I was using a 21:9 monitor and I wanted to go higher than I might consider using 30%. So depending on your circumstances, choose either 25% or 30%.


Edited by Joshua Willis, 15 February 2017 - 11:32 AM.

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#11 Kilroy

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Posted 15 February 2017 - 06:22 PM

So Joshua, I understand next to none of the math, but you're saying that the average monitor match I should use depends on what I consider to be the maximum fov that I normally use? So if I normally use a maximum of 106.26 fov, I should use 15%?

 

Wouldn't it make more sense to linearly (or something like that) decrease the monitor distance I use depending on how low the fov is? Because if a person somehow normally uses 50 fov, according to this, they'd use an even lower MD for the rest of their even lower fovs.


Edited by Kilroy, 15 February 2017 - 06:31 PM.


#12 Joshua Willis

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Posted 15 February 2017 - 06:28 PM

Yeah, but if 106.26 is your max FOV you should use 20%. Since 15%'s max FOV is 96.

#13 Kilroy

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Posted 15 February 2017 - 06:36 PM

Oh I thought you were using the (4:3) fov in that spreadsheet, instead of hfov



#14 Joshua Willis

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Posted 15 February 2017 - 06:42 PM

Yes always assume math is talking about the actual FOV.

#15 DNAMTE

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Posted 16 February 2017 - 10:32 AM

I Dont understand the over complication. You either want to match cursor speed or you don't.

 

Don't forget if you want true 1:1 cursor speed between differing planes its quite simply, cursor speed = distance / time.

 

Averages, especially over such a broad range of FOV will never match anything accurately.
3D and 2D cannot be measured using the same methods, they are not the same. Trying will result in a 'best fit' scenario. ONE sweet spot.

 

As you rotate in-game, the radial speed of the cursor moving should ideally match, exactly, the desktop cursor movement speed. That's the only true 1:1 match.
No average can determine that.

 

Going back to my first post in relation to arc & chord length, using their relationship we can quickly establish 100% monitor match, that is, the start & finish of maximum movement in both rotation (3D) and  length (2D).

 

Using 106.26FOV. 400dpi

Windows / Desktop Distance 16.256cm  (360' / 106.26') = 55.07396950875211cm  (100% Monitor match)

 

That simply mimics the relationship shared between 2D and 3D maximums. Which ultimately is monitor matching '100%'.
Following that its simply allowing for the difference in Arc length (3D) to Chord length (2D) and adjusting as I previously posted to provide 1:1 mouse speed.
 


Edited by DNAMTE, 16 February 2017 - 11:49 AM.


#16 DPI Wizard

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Posted 16 February 2017 - 01:44 PM

There's already a lot of technical answers here, but I'll answer a few of your questions anyway.

 

Is it impossible to have a sensitivity at an FOV that perfectly matches a sensitivity at another FOV? Because even if I match monitor distance to 1% for 2 FOVs, I know full well that I won't be doing only 1% distance flicks, and so that'll be on me to try and compensate for a flick at an enemy at the edge of my screen despite not being used to that feeling. This would be more apparent if I were using something with a really low FOV like the CSGO AWP on its second zoom at 10 FOV, because the difference in zoom sensitivities between 0% and 100% is 0.787398 and 1.127085 (even though you wouldn't be able to see the person through the black scope part). If the answer is yes, doesn't that mean that it's impossible to have a 1:1 mouse movement, across even slightly different media? So I simply have to choose based on preference?

Yes it is impossible. You can to some degree see the difference in movement at the end of the Monitor Distance video, where it shows and 80% movement when the aims are matched at 25%.

 

IMy next question is a bit crazy, but what if you were able to partially re-mediate this problem using mouse acceleration? This makes sense to me because the further away from the crosshair lies the target, the faster I'd move my mouse, and so this would result in the higher, more correct sensitivity needed to have a 1:1 movement at that specific distance.

The problem with acceleration is that it is not consistent. 

 

How does any of this work on a game with a 2D plain, like osu!, LoL or even my windows desktop? How can I get a (pseudo?) 1:1 mouse movement here?

If you are using a 1080p monitor and match 100% monitor distance from Windows to a game, it is calculated what sensitivity is needed to equal 960 counts to move to the edge of the monitor in a game. If you match 50%, it will match 480 counts to 50% of he monitor distance, and so on.

 

Lastly, I don't understand what matching at 0% monitor distance means, because the sensitivity involved in moving the mouse no distance would be irrelevant, right? So how does the calculator give the number it gives?

It basically means matching the smallest movement possible. You can see that the difference between 1% and 0% is virtually nothing, but there is a small difference.



#17 Kilroy

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Posted 16 February 2017 - 06:03 PM

I Dont understand the over complication. You either want to match cursor speed or you don't.

 

Don't forget if you want true 1:1 cursor speed between differing planes its quite simply, cursor speed = distance / time.

 

Averages, especially over such a broad range of FOV will never match anything accurately.
3D and 2D cannot be measured using the same methods, they are not the same. Trying will result in a 'best fit' scenario. ONE sweet spot.

 

As you rotate in-game, the radial speed of the cursor moving should ideally match, exactly, the desktop cursor movement speed. That's the only true 1:1 match.
No average can determine that.

 

Going back to my first post in relation to arc & chord length, using their relationship we can quickly establish 100% monitor match, that is, the start & finish of maximum movement in both rotation (3D) and  length (2D).

 

Using 106.26FOV. 400dpi

Windows / Desktop Distance 16.256cm  (360' / 106.26') = 55.07396950875211cm  (100% Monitor match)

 

That simply mimics the relationship shared between 2D and 3D maximums. Which ultimately is monitor matching '100%'.
Following that its simply allowing for the difference in Arc length (3D) to Chord length (2D) and adjusting as I previously posted to provide 1:1 mouse speed.
 

 

Sorry, I've read both your posts and I'm trying but I really still can't understand how and what you mean by matching cursor speeds in both plains and across fovs. I know that speed is distance over time, but the problem that keeps nagging at me is that the crosshair in-game is fixed to the middle of the screen and as such doesn't have a speed, right? I get that you're supposed to measure rotational speed of the player's view, but I don't get how. I also haven't learned the math that you're using (still in high school), and how it works, so that makes it more complicated for me.

 

 

The problem with acceleration is that it is not consistent. 

 

This guy named povohat made an excellent mouse acceleration driver and this is a link to a blog post by a guy called kovaak that I think argues pretty well that the acceleration used in their driver is actually very consistent.

 

http://mouseaccel.bl...celeration.html

 

Basically what he's saying is that normally, acceleration is done badly, because it's usually like window's enhance pointer precision, where when your mouse reaches a threshold in speed, it suddenly doubles, and easily throws you off. It can also be hard to learn exponential curves like logitech's mouse acceleration. But when it is a linear acceleration, which can be achieved in this driver, and in games like quake and reflex, it can be very easy to learn. So if the target is far away, it is still easy to know how the speed of my mouse will influence the speed of the cursor/ rotation of my view, and since matching at higher monitor distance percentages gives higher sensitivity, this would sort of benefit that, right?

 

I've been using this driver for almost a year, and I can never go back.


Edited by Kilroy, 16 February 2017 - 06:04 PM.


#18 DNAMTE

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Posted 17 February 2017 - 04:25 AM

I've been thinking how I can describe my post in the easiest way possible. Firstly I'd like to start with some basics.

 

Field of View makes up your view window within a game, this measurement (in degrees) is removed from the remainder of your full rotation (360).

 

Obviously your screen window is fixed in size. Hence, when we lower our FOV the image is scaled larger, when we increase our FOV the image is scaled smaller, maintaining the overall boundaries of the original view box.

 

The reason selecting the correct FOV is important, minimize distortion but maintain a reasonable view angle, however that is another topic and I don't want to lead off track.

 

Here's where my creative side attempts to give you an analogy to understand the relationship between your desktop and in game.

 

 

http://coewww.rutger...rack_pinion.gif

 

 

As you can see moving your cursor on desktop is indeed related to how you rotate in game, For every FOV there's only one speed/ sensitivity that is actually 1:1 with your aspect ratio (allowing the gears to mesh perfectly).

As in this example given that the gears interlock perfectly as the gear rotates over the pinion it's clear they move in unison, 1:1 movement. That relationship is outlayed in my previous posts.

 

Here's another example that I'll attempt to explain why IT IS possible to match ALL FOV 1:1.

 

 

 

http://www.f-lohmuel...Chain_043cb.gif

 

 

As you can see we have two gears of dissimilar diameters (simulating different FOV). They both rotate at different speeds, however the chain travels around them at uniform speed, clearly.

 

It does not matter how big the gear/FOV is or how many times it rotates. What matters is that the 'chain' moves between the two perfectly. Essentially adjusting your speed/sensitivity at the desired FOV so the 'gears' match the chain speed PERFECTLY.

 

Answering the above question then YES, it can be perfect. Perfect does not mean every pixel on your screen should move in sync regardless of FOV. That's physically impossible. Different diameters will complete a rotation at different times. The centre of your screen can be perfect and that's the only bit that matters, that's the only part of the screen you used to line up your shots.

 

Moving to your next target is simply a matter of distance / time, the better you judge this the faster you become.


Edited by DNAMTE, 17 February 2017 - 04:28 AM.


#19 Kilroy

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Posted 17 February 2017 - 07:33 PM

Damn, those are some grade a+ analogies, and to be honest if it were me explaining this to you, I would've long ago given up, so thanks for the time. I do strongly believe its possible now, but I still don't exactly know how to calculate it because I went back and read the previous posts, and I'm having trouble with the math. I just need one final thing from you, which is to explain it in a step by step list, and with examples because I'm brain dead stupid. :P



#20 Drimzi

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Posted 17 February 2017 - 11:36 PM

When you move the mouse in a 3D game, you are rotating the viewport. This is essentially a circle. When you move the mouse in a 2D environment, you are just moving a pointer anywhere along a flat surface. This is just a flat line. When you disable mouse acceleration, the speed that the pointer moves and the speed that the viewport rotates is linear. Speed is just distance over time. There is misconception that because 2D is not rotational movement, it has no relationship to 3D movement. The speed of mouse movements in 2D and 3D can actually be related which is demonstrated in this analogy with a rack-and-pinion gearset.
rack_pinion.gif
Since a monitor is a fixed dimension, when you increase the HFOV of the game, the rendered frame is distorted (pincushion) to fit the image onto the display. Everything becomes zoomed out in the center and stretched along the sides. When you decrease the HFOV, the image is less distorted and more zoomed in. The viewport is essentially a dissected circle. Basically a higher FOV makes everything smaller and a lower FOV makes everything bigger. We can picture the differences in FOV and how their rotational speeds relate to each other in this analogy with a bike chain.
 
Bike_Chain_043cb.gif
 
In order to convert between 2D and 3D, you need to know the speed of either the rack or the pinion wheel in the first analogy. If we were to convert from 2D, we would need to know the speed of the rack which is the mouse distance from edge to edge on the desktop. If we were to convert from 3D (to 2D or to another FOV in 3D), we would need to know the speed of the pinion wheel or gear which is the 360 distance at a given HFOV.
 
In this post we are going to convert from 2D to 3D at 106.26 FOV. In this example I have 2560x1440 resolution, 6/11 WPS, acceleration disabled, and 400 mouse DPI. We need to find the 2D distance, which can be found using this formula

resolution width / DPI = 2D distance (inch)

resolution width / DPI * 2.54 = 2D distance (cm)

2560 / 400 * 2.54 = 16.256 cm

We can use this as the base speed of 106.26 HFOV for now by simply figuring out how many times we need to move from one edge to the other to produce a 360 rotation, which is:

360/fov × 2D distance = cm/360

360/106.26 × 16.256 = 55.074 cm

This is what happens when you do a 100% monitor distance match in the calculator from 2D to 3D. We will use the bike chain analogy above to see how this works. Pretend the large gear is already spinning at the correct speed it needs to be. We are figuring out the speed of the small gear. We have done a 100% monitor distance match as a starting point but the chain is not moving properly along these gears yet because this speed is not correct.
 
Since smaller gears need to rotate faster and larger gears need to rotate slower, we need to find the size difference between our base measurement (2D edge to edge mouse distance) and the correct distance for 106.26 FOV. To do this, we look at a circular segment which is an area of a circle that is cut off from the rest of the circle by a chord. Think of the chord ( c ) as the desktop measurement, and the arc ( L ) as the game's measurement.
 
1304848895.png
 
 
The chord is the width of our resolution. In this example I am using 2560 x 1440 resolution, so the chord is 2560. To find the arc, you need to know the hFOV of the game in radians and substitute them into this formula.

chord + chord * (hfovradians - 2 sin(hfovradians/2))/(2 sin(hfovradians/2)) = arc

2560 + 2560 * (1.85459 - 2 sin(1.85459/2))/(2 sin(1.85459/2)) = 2967.34...

Once we have the arc value, we find the percent increase from the chord to the arc.

100 × ((arc - chord) / chord) = percent increase

100 × ((2967.34 - 2560) / 2560) = 15.91171875%

Now we know the correct speed it needs to rotate at 106.26 FOV is 15.91171875% faster than the base speed (2D distance) we used, so we just take the same formula as before, but reduce the distance to go from one edge to the other by this percentage to find the corrected 360.

360/fov × (2D edge-to-edge distance - percent difference) = cm/360

360/106.26 × (16.256 - 15.91171875%) = 46.3108 cm

With this speed, the chain will move perfectly. On the calculator, this is pretty close to a 65% monitor distance match which is what I said in my first post. But as you can tell by now, the speed is unique for every FOV. You can not just use a fixed monitor distance match % every time. Using the calculator to convert monitor distance or 360 distance will not result in a sensitivity match. Joshua's method of averaging the correct monitor distance across ALL FOVs and using that averaged percent for everything will not work either. The only way to match sensitivity is to match the view speed using this method.
 
Games that do not allow you to customize the way they scale the sensitivity with the HFOV usually use 0% match (Call of Duty), 100% match 4:3 which is 75% match at 16:9, or simply 100% match at the correct aspect ratio. You can choose to use this method to get an actual sensitivity match between games, or use one of the above distance matches to replicate the above games if you have developed muscle memory with that system.
 
edit: The above calculation has an error with percentages. The correction is as follows, thanks to Skwuruhl:

360/fovdegrees * desktop distance * chord /(chord + chord (fovradians - 2 sin(fovradians/2))/(2 sin(fovradians/2)))

360/106.26 (2560/400×2.54)×2560/(2560 + 2560×(106.26×π/180 - 2 sin(1/2 (106.26×π/180)))/(2 sin(1/2 (106.26×π/180))))
= 47.5137...

Simplified down to:

(4 π z sin(x/2))/x^2 where x = fov radians and z = desktop distance

(4 π (2560/400×2.54) sin(1/2 (106.26×π/180)))/(106.26×π/180)^2
= 47.5137...

The calculator now supports this mode.


Edited by Drimzi, 17 March 2017 - 11:21 AM.

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