DNAMTE has come up with another solution for converting sensitivity to different field of views. This time it is independent of the aspect ratio, which is a flaw with viewspeed v1. The aim of this solution is to make the different field of views behave the same visually when moving the mouse, solving any perceptual issues such as feeling like it is slowing down or speeding up. This makes this method especially useful for zoom/ads sensitivities.
The sensitivity scaling is done using two ratios, the circle ratio and the chord ratio.
DNAMTE is unsure on how to do the math for it, so I will do it. In the picture above, he did 90 degrees and 45 degrees for the angle of view, and found a chord ratio of 2.41 and a circle ratio of 1.3.
circle ratio / chord ratio
The chord ratio can be found using:
tan(y * pi/360) / tan(x * pi/360)
Where the variables are the degrees. If we substitute x for 45, and y for 90, we end up with a ratio of 2.41 as shown in the image above.
Scaling the sensitivity by the chord ratio alone would be equal to scaling the sensitivity by the zoom amount.
The circle ratio can be found using:
cos(x * pi/360) / cos(y * pi/360)
If we substitute x for 45, and y for 90, we end up with a ratio of 1.3 as shown in the image above.
Put these two together, and you simply get the sin ratio.
(cos(x * pi/360) / cos(y * pi/360)) / (tan(y * pi/360) / tan(x * pi/360))
= sin(x * pi/360) / sin(y * pi/360)
When substituting the variables with the angles, you want to use the vertical / horizontal angle for the 1:1 aspect ratio.
With this additional option of converting sensitivities, you end up with the options of converting using the tan ratio (mm 0%), sin ratio (viewspeed v2), or matching a screen-space distance using monitor distance match.
Use tan ratio (0%) or 360 distance match for converting hipfire.
Use tan ratio (0%) or sin ratio (viewspeed) for converting zoom/ads.