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Name: GloomWood Website: https://store.steampowered.com/app/1150760/Gloomwood/ Status: Early Access Release date: 6th Sep. 2022 Availability: Purchase

It started with the idea of matching "monitor distance" for set mouse movements. For example if a 4cm mouse movement in hipfire would aim at something halfway across your monitor (horizontally) this would be a 50% mouse movement. If you wanted to make it so when you ADS a 4cm flick would move your crosshair halfway across the screen, your desired sensitivity would be 50% mdh. The equation for this is where x is your desired flick distance. There's 2 major problems with this method: 1. A matched distance only works at that single distance and accuracy falls off by the metric of maintaining flick distance as you make flicks different from x. 2. The math completely breaks down if you aren't looking straight forward, as looking up or down changes how mouse movements translate to monitor distance entirely. The first problem was somewhat addressed when people wondered if you could make x 0% to make tracking very accurate. Plugging x into the above equation is undefined, however you can have x approach infinitely close to zero and calculate the result of that. When you do this the equation simplifies to Turns out this worked pretty well and only lost accuracy for very large flicks. Though that still leaves the 2nd issue, and if trying to match exact mouse movements with exact monitor movements was actually the best way to calculate zoom sensitivity. Many people found that 0% md exhibited some nice behaviors that didn't happen at other distances. See this video by @DPI Wizard: To explain what's happening here (assuming bf3 8x, 4x, red dot in order. with 70 fov in settings. Doesn't exactly matter, only the ratios do.) The first scope is standing at some distance with a 6.9x zoom scope. Second Scope is 3.47x at 50% of that distance Third is 1.83x at 21% of that distance. The exact same mouse movement is being used to track the target at each scope/distance combo. Now what's the big deal? You could find some distance to stand at with any scope and sensitivity combo where target tracking would line up. There's two big deals here: 1. Notice how the target is the exact same visual size on all 3 recordings 2. The distances being stood at line up exactly with the ratio of zoom. e.g. 3.47 is half of 6.9. This is pretty big because that means you can make zoom sensitivity scale the exact same way as just standing closer or further from a target. To the point where the right zoom/distance combo completely cancels out and is the same as hipfire. Now the question is how does this happen? What's so special about 0% md that causes this? Well, put simply: it's not because of 0% md per se. Let's back up a bit to zoom ratio. Zoom as a technical term is used for cameras and telescopes comparing the focal length of two different images. If one image was taken with a focal length of 5mm, and another was taken with a focal length of 10mm, there's a factor of 2x zoom going from the 10mm to the 5mm (smaller focal length is more zoomed in). What if we were to scale our zoom sensitivity by this zoom ratio? That seems to make pretty straightforward sense: if my scope has a zoom ratio of 2.0, then my sensitivity should be halved. Well the major hurdle is that games don't measure fov in focal length, they measure it in degrees (or sometimes radians). Luckily there's an equation to convert your camera's focal length to degrees: Where alpha is degrees, d is size of the film, and f is focal length. Though this is to convert from focal length to degrees, we need to solve for f: So we can calculate the horizontal fov of a 23.8" monitor (526.85mm horizontally): If we can calculate the focal length then we can calculate the zoom ratio by dividing the focal length of two different zoom levels (e.g. hipfire and scope), in fact the equation is simplified even further since we have a consistent film size (monitor): And so we've arrived back at the same equation we arrived at with 0% md. But this explains the behaviors related to zoom ratios. Another example of such behavior: https://imgur.com/a/szjlq Scaling by focal length / 0% is the most mathematically sound way of scaling because of all this.

Name: Doom I & Doom 2 Enhanced Website: https://store.steampowered.com/app/2280/DOOM_1993/ & https://store.steampowered.com/app/2300/DOOM_II/ Status: Release Release date: January 9, 2020 Availability: Purchase

Name: Wolfenstein (2009) Website: - Status: Released Release date: August 18, 2009 Availability: Abandonware

There is less degrees on the screen (lower degree/pixel), so if you continue to rotate the same degree/count then you will rotate more pixels. You have to reduce the degree/count to rotate the same degree/pixels, and end up with a longer distance to rotate 360 degrees. Degree/pixels only uses the middle pixels. If you know there is a total of 103 degrees horizontally (Overwatch), which is across 1920 pixels, then you can scale that down to find how many there is in 1 pixel. 2 * atan(1/1920 * tan(103/2 * pi/180)) * 180/pi = ~0.075032 If you drop to 30 degrees vertically (Overwatch Widowmaker), then you end up with less degree/pixel. 2 * atan(1/1080 * tan(30/2 * pi/180)) * 180/pi = ~0.02843 Since the game rotates a fixed amount of degrees/count for each unit of sensitivity, you will want to reduce the sensitivity when you scope in (by ~0.028/0.075) to keep the same pixel ratio. When scoped, you will have to rotate ~38% of the original amount to preserve the sensitivity of the mouse, but you will end up with the inconvenience of a larger distance to turn 360 degrees. (2 * atan(1/1080 * tan(30/2 * pi/180)) * 180/pi) / (2 * atan(1/1920 * tan(103/2 * pi/180)) * 180/pi) = ~0.378909