#Mathematics to determine desktop pointer speed relative to in-game sensitivity

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static gulch
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I am doing an experiment which involves translating the windows pointer speed in the 2D desktop space to the 3D space in-game in order to match the feel as best as possible and allow a seamless transition when going between desktop and in-game to aid consistency.

Using 2 objects between the mouse and looking to a certain object on the map in-game then checking it with the pointer speed by using scoreboard with mouse input enabled, with trial and error I have found 3.5 to 3.75 in-game sensitivity to roughly be the value for 800 CPI at 1920 x 1080 and a FOV of 90.

Can anyone fact check this or know the mathematics behind calculating this in order to find the exact mathematical value that matches 6/11 windows pointer speed in-game with a FOV of 90 and a resolution of 1920 x 1080? Thank you.
(Also I am aware that sensitivity and DPI option is completely preference but I still have an interest in figuring out what is the exact sensitivity in-game to match the desktop at 800dpi)

dusty yarrow
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Well in 3d space you have depth and your mouse velocity is angular

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"How fast" your cursor appears to be moving depends entirely on how far your camera is from the surface you're looking at

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So it's not something you can compare to movement speed on the desktop

strong streamBOT
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*So it's not something

you can compare to movement

speed on the desktop*

dusty yarrow
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Unless you defined a set distance you care about in the 3d space or something

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Without making some kind of compromise like that, you'd be comparing apples to oranges

static gulch
dusty yarrow
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No, you have to pick a depth

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Then it's easy, linear velocity is angular velocity times your depth

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Imagine you have a 5 unit wide object very close to your camera, and the same 5 unit wide object very far away, it'll clearly take a much smaller mouse movement to move from one side of the object to the other when it's farther away compared to when it's close

inland cairn
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Because 2D to 3D isn't linear, you can only have your movements match 1:1 at one specific distance from the center of the screen.

There is math, and you were close.
It's 3.617155 at the center (1 pixel of movement), and about 2.52 from the center to the edge of the screen.

inland cairn
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@static gulch Did you want the math?

static gulch
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Yes

static gulch
static gulch
inland cairn
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It's the distance that a movement on screen (from the center to the edge) will be 1:1 in and out of game

static gulch
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Oh i see

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ngl i had no idea what i was looking at when i opened it