I can't say I have 100% confidence in understanding this, but I'll do my best.
Since the game is rendered into a flat 2D image to be displayed on your screen, which has a fixed width, the higher the FOV, the more warped and zoomed out it becomes to fit that image onto your monitor. Think of the game as the smaller gear in this analogy http://www.f-lohmuel...Chain_043cb.gif. The higher the FOV, the smaller that gear becomes. 2D is the large gear.
What you want to find is the speed that these gears need to move to make that chain move perfectly. You already know the speed that the large gear is moving, which depends on your resolution, mouse DPI and WPS. If you have 2560x1440 resolution and 400 DPI, it takes 16.256cm to move the mouse horizontally from one edge to the other. With acceleration disabled, the speed is linear.
To make the smaller gear rotate at the same exact speed of the larger gear, you simply need to know the FOV of the game to calculate how many times you need to move the cursor from edge-to-edge to produce a 360 rotation.
360/fov × 2D edge-to-edge distance = cm/360
For our example, it is 16.256cm to move across the desktop, and our game is 106.26 actual HFOV, so our 360 in-game will be 55cm and this is the 100% match in the calculator.
360/106.26 × 16.256 = 55.074
However, if the smaller gear is rotating at the same speed as the larger gear, then the chain is not going to move perfectly. The smaller gear needs to rotate faster as the diameter decreases. We need to find out how much faster it needs to rotate. 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, and the arc ( L ) as the game. We want to find how much longer the arc is compared to the chord, to determine the size of the smaller gear. We can find this because we know the angle, which is the actual HFOV of the game, and then measure the percentage increase of the result.
A calculator for this is at http://planetcalc.com/1421/ and all you need to do is input the angle, set decimal places to 10, and calculate the result.
We find the percent increase from the chord length to the arc length like so: https://www.wolframa...545868631691746
Now we know the 3D distance has a 15.91183424841393% increase, this is how much longer the 3D image is and is being distorted and warped to fit onto the monitor in the same aspect ratio as the desktop. The smaller gear needs to rotate 15.91183424841393% faster to make the chain move perfectly.
Now 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 - 15.91183424841393 percent) = 46.3107
On the calculator, this is pretty close to a 65% match. Obviously you can't just use 65% match universally as the arc length changes with the FOV so every FOV will match at a different point on the monitor. So when you want to set the sensitivity for a game that doesn't have 106.26 actual HFOV, you have to redo the calculation to find the arc/chord length percent difference for that specific FOV.
So decide how you want to calculate the sensitivity for other games with different FOVs after you have done the 2D to 3D conversion. If you play games like Call of Duty where the FOV is constantly changing (aiming with different guns), which scale the sensitivity with 0% match, then you may find it better for your muscle memory to match 0% from FOV to FOV. If you play games that scale with 100% 4:3 (75% at 16:9), use that percentage. If you want the true sensitivity match across all of your FOVs and not permanently adjust yourself to the method of one particular game, then redo the calculation to find the 360 for each FOV.
Edited by GLiSN, 18 February 2017 - 11:55 PM.