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This is what I'm trying (badly, I know) to explain with the crappy picture above. You're actually both right. If everything we were doing were a 2D image, which in fact it is because it's on screen, 0%MM would be correct. Heck, that's exactly how 0%MM works, it treats the game world only as it's 2D projection and tells us how much we zoomed it in on our flat screen. But, because of the distortion we experience by viewing it as a 3D scene (but not changing our focal point when we change FOV, ie, sitting in the same place all the time), the image becomes stretched, so the cursor feels like it is moving through the 3D space at a different speed. The nature of that 3D space is determined by the distortion, so the distortion is controlling the 'too fast/too slow' feeling we get. (and it's not necessarily just the distortion of our seating position - here, I am referring to the difference in distortion between two FOVs) There's good reason why gear ratio/1:1/100%VFOV/4:3 feel closer and seem to move the image at a speed that feels right. 0%MM is always exactly right for anything directly under the crosshair. But for anything away from it, 0% is too slow, and the further it is from the crosshair, the more 0% is too slow. As we monitor match further and further from the crosshair, we get higher and higher sensitivity. If we 'monitor match' at 180degrees - even though that's not on the monitor - what we get is a sensitivity divider of 1 - as in, SAME sensitivity, same cm/360, for any FOV. Which is obviously too fast. So, what we have here are two known sensitivities. At the centre of the crosshair, we have 0%MM. This is as slow as it gets. And at the very edge of the game world/our turning circle, we have =cm/360. This is as fast as it gets. And this makes sense. There's no reason we would ever want to go below or above these speeds respectively. So let's graph out a line between those. In my crappy mspaint, it's shaped like a tan curve (inverted at the Y axis because it's more intuitive to think of it as 'left X'' than 'negative X'). Somewhere along that line, is a place where it's a little too fast, but not too close to the =cm/360 extent; and a little too slow, but not too close to the 0%MM extent.. That's the sweet spot.... and those places where drimzi's muh feels and clever LGS script make it seem correct, they seem that way because they're close to that sweet spot. The geogebra demo I did, shows hints of all of this, but it's not always immediately apparent. We can demonstrate it though. I'm still working on being able to show my working and give an exact formula that gives exact sensitivities to use.

In-game and config file calculations for hipfire and ADS added.

First, some background: We set our sensitivity such that a certain amount of mouse movement will result in a certain amount of soldier movement. In it's simplest form, we have our hipfire at some cm/360. If this were real life, when we use a magnified optic, that means that our movement is magnified accordingly. This is why shooters take such measures as controlling their breathing and heart rate. In game, where magnification amounts to a reduced FOV, this is very unwieldly. Having the same cm/360 at all levels of zoom, just doesn't work. As we zoom in, the sensitivity becomes impractically high - it feels too fast. Muh feels. So, we can use some formula, to reduce our sensitivity in proportion with reduced FOV. The math is fairly straightforward in this case, it is what we here refer to as "0% monitor matching". So, we try this.... and it doesn't feel right either. Muh feels. So, we can try to make our 3D game respond as though it were a 2D space like our desktop. This is obviously never going to work because the 3D game world is NOT in 2D no matter how hard we try to treat it as though it is. So, sometimes, it feels right, and other times, not so much. Muh feels. Now, 'muh feels' is a term which often carries negative connotation. The implication of saying 'muh feels' is that the person is ignoring 'muh reals' - ignoring reality in favour of their subjective sensation. I want to state very early on here, that such an attitude is not the point of this thread. On the contrary, it is clear to me that there is a strong reasoning for the way that sensitivity changes across FOV changes are perceived - and this is the golden word here - Perception. These 'muh feels' are not coming from nowhere. Yes, there will be some psychological effects like placebo and memory and many many others, but I don't think that any of us could put all of our observations down to just these effects. What we do know, is that the human brain performs a great deal of work on the image captured by our eyes, to determine relevant data such as distance, angle, size of objects in the game. It should be clear to us all by now, that this image processing performed by our brains, is having an effect on the way our movement feels in-game - otherwise, 0%MM would just work. In other threads, a great deal of work has been done to find a formula which 'feels' right. Just as much of that work has validated previous formulae, I hope that this thread will do the same. However, the intention of this thread is to take a different approach to finding that 'right' formula. Rather than a process of elimination - in other words, trying a formula, and adjusting it according to 'muh feels', until it 'feels' 'right', I want to take a look at WHY it doesn't 'feel' 'right'. I believe that a more scientific approach will be beneficial as a counterpart to the scatter-gun approaches which we have used in these other threads. I also want to be clear that I am by no means an expert on this subject. Human visual perception is kinda rocket science and I warmly welcome any input on this. However, the intention here is not to simply say "it feels too slow", or "it feels too fast", but to figure out WHY. The first step in solving any problem, is to define that problem clearly (Every properly defined question contains it's own answer), and to the best of my knowledge, this has not yet been done. I've collected a fair few documents and videos as a basis for this, and (largely because I have too many tabs open in my browser) I think it's about time I posted these links here for future reference. I hope you might take the time to look these over and give it some thought, and perhaps you might even have some information you could add to the discussion - I need all the help I can get The next post in this thread will be a 'library' of links that we can reference, which I will update over time as more information becomes available, and the following post will be a brief overview of what I've been able to derive from that information, which appears to be related to our perception of the 3D games projected on our 2D displays.

Confirmed!

I'll check how the 3rd person view behaves now and update you.

Updated this game now: Added a special option for 1st or 3rd person. Added normal and ADS sensitivity for both views. Corrected FOV and how it affects sensitivity, along with instructions on what the different steps in the FOV slider means.

Try with 360 distance instead (it's the same as 100% monitor match). It's the slowest possible 2d to 3d matching method.

Crickets... Oh well, I'll go deeper. That should make things much worse. XD First, more food for thought. Do the lines appear to change in length? Some will say it looks like they are, some will say they don't. Last post, I wrapped up by talking about the amount of distortion at our two FOV's... In other threads, up until this day, there has been debate about which FOV should be the basis for the formula - vertical or horizontal. Over in the https://www.mouse-sensitivity.com/forum/topic/720-viewspeed-reworked/ thread, it was pointed out that the projection has the effect of using a set VFOV, and then 'filling out' the horizontal plane, to fill our monitor. This could imply that we should be using the VFOV, since HFOV varies with monitor aspect ratio. This makes sense, seeing as movement from one point to another that is within the VFOV limits, even in the horizontal plane of the world, should require the same amount of movement of the mouse, regardless of how much peripheral vision extends to the sides of the monitor - in other words, given the same VFOV setting, aiming 1cm to the left should feel the same no matter if we have a 16:9 or a 21:9 or a 32:9 monitor ... But that assumes a positive aspect ratio (monitor wider than tall). What if we consider the centre monitor in one of those cool triple-vertical-monitor setups? Better yet, what if we are in an aircraft/spacecraft, and roll it to the side? Our monitor vertical FOV is now in the horizontal plane of the game world, and vice versa, and the amount of distortion in those planes does not vary. Only the visible amount of distortion in the projection to our monitor varies. So, we can just use the vertical FOV again, since it is always the angle which provides the constant amount of distortion no matter the aspect of our screen. However, if we ignore the distortion in the horizontal aspect of the monitor, we are ignoring the very effects upon our perception which render 0%MM ineffective. Consider the aforementioned effect of the Odessa Steps. This same effect would be just as apparent, if we turn our head to the sides. Then again, if we use the horizontal distortion as a basis, we are now including distortion which is not always visible, and in the most common case of a positive aspect ratio monitor positioned horizontally (read: not a vertical screen or a rolled-sideways spacecraft), this distortion is usually not visible. Indeed, it turns out that this is different for different people. Current studies suggest that the difference is caused by ...wait for it... eye pigmentation. Yep, the colour of your eyes makes a difference here. Does this mean we need some kind of coefficient to allow for blue vs brown vs green eyes? Well, fortunately not. See, the different eye pigmentation does appear to effect our perception of the distortion (see https://en.wikipedia.org/wiki/Müller-Lyer_illusion for more info), and other effects have been cited as the reason for the illusion, but all agree that the perception is uniform in manner. This effect does not vary between vertical and horizontal or any diagonal inbetween. This can be seen in the cool animated image at the top of this post. Whether you see growing/shrinking lines, you'll see the same on all of them. Why is this important? Because it tells us that we do not need to account for the differences in individual perception of the distortion. We need only account for the differences between the distortion in each axis. So, once again, analysis of the sciences tells us that the path to an answer, lies in a ratio between the distortion in each FOV. But to what extent do we measure that FOV? The monitor? A square? the vertical square or the horizontal? Maybe a circle?........ And how do we measure the distortion, since it's not the same all the way to the edges but increases as we diverge from the centre? But that's a topic for another post on another day. I have badguys to pewpew

On rectilinear projection, distortion, and forced perspective: So, we know already that a perfect mathematical scaling between FOVs is '0% Monitor Matching': ZoomLevel = tan(HipFOV/2)/tan(ZoomFOV/2) HipFOV = 2*(arctan(ZoomLevel*(tan(ZoomFOV/2)))) ZoomFOV = 2*(arctan(tan(HipFOV/2)/ZoomLevel)) So, let's think about what is actually contained within those images, which influences our perception of the game world, and causes our mouse to require a different scaling algorithm. We can start by looking at the formula for the projection: x=tan(λ) y=tan(Φ)/cos(λ) There are two obvious facets to this. One, is the distortion by the tangent of the angle. The other, is the reduced distortion on the vertical axis, caused by the division by the cosine of the horizontal angle. It is often said that rectilinear projection results in horizontal stretching, but we can see that in fact, it is that both axes are stretched, just, the vertical axis less so. Whatever - the result is that the horizontal axis is more stretched. But, this isn't a stretch that happens evenly across the entire monitor. The stretching distortion will always be at it's minimum at the centre of our screen, and increase from there outward. This is why attempts to treat the game as we would a 2D space, can never work, because a 2D space like our desktop, is evenly stretched from edge to edge. This is why we have n% monitor matching, and why battlefield uses a coefficient, and why CSGO also uses a (fixed at 133% aka 4:3 aspect afaik) coefficient - these are attempts to make such an approach, function - and they will succeed, but ONLY at that exact percentage/coefficient value. So, we have two considerations here which will effect our perception - Increased horizontal stretching compared to the vertical, and increased stretching on both axes, as we diverge from the centre. I will touch on the latter effect only briefly for now - and I'm not shy to say that is because I really don't know how our brains perceive this. The only information I have come across thus far, was this comment by @TheNoobPolice over on the Battlefield forums: https://forums.battlefield.com/en-us/discussion/comment/532023/#Comment_532023 I'm confident that further study of the effect of distortion on our perception will lead me to more solid conclusions, but any further input on this effect would be greatly appreciated. However, much is known about the former effect, the increased stretching in the horizontal plane. This results in an effect known as "forced perspective". You can read all about it from the links in the 'library' post above this, but the basics of it are that the objects appearing wider than they do long, causes our brains to perceive them as being further away. I think it's worth having a read of the wikipedia page on this effect: https://en.wikipedia.org/wiki/Forced_perspective Let's take a few images from that page to demonstrate how this would effect us in-game. Let's imagine that we are standing on the right side of this room, looking along the pews, toward the left side. Now, we want to move our aimpoint to the back of the dais there and look at the painting of Jesus. We will see that *angular distance* (remember this term!), let's say the dais is, what, a few metres deep? So we turn to our right accordingly, and we are now looking at our saviour..... Or are we? Hold on... that's not a few metres deep. It's an illusion, it's maybe ONE metre deep, if that! But it looked MUCH deeper than that, and we turned accordingly. The illusion has caused us to turn too far. This sensitivity formula is too fast! "MUH FEELS!" XD Let's do it again: What's the distance from the big golden cross, to the red-covered lectern on the left there? How about now? MUH FEEEELZ! Now, these examples may not be entirely analogous to the view we have of our game world on our screens, but I'm sure that it is apparent to you by now, that the angles we see, effect our perception of distance, and conversely, the distances we see, effect our perception of the angles. This is probably a good moment to point you toward https://en.wikipedia.org/wiki/Angular_diameter and https://en.wikipedia.org/wiki/Perceived_visual_angle Fortunately for us, we are not at the whim of a clever church architect playing tricks with our mind. We know exactly how far the distances on screen have changed - it is the ratio between the distortion at the two FOVs. Accordingly, we can write formula which allow for this effect. Please, pitch in guys. Share your thoughts, share your fomulas

Library http://www.tawbaware.com/projections.htm http://www.tawbaware.com/ptassembler_mod_rect_projections.pdf http://mathworld.wolfram.com/GnomonicProjection.html - So why is this formula different to the above? Because we're not doing a map projection of the globe. Turns out that the same terms are used both in cartography (maps) and photography - the latter of which is actually relevant to us. https://en.wikipedia.org/wiki/Rectilinear_lens - Note the image here, which shows us why e don't want to avoid the image distortion present in rectilinear projection. That fish-eye effect (known as 'barrel distortion') means that straight lines are no longer straight. This would be very bad in a shooter for example. Speaking for photography and its relevance to us, and distortion... https://en.wikipedia.org/wiki/Distortion_(optics) - but why? Let's look at how the machine creates the image... This can get pretty nerdy and isn't mandatory for understanding of this subject so feel free to skip the computer-stuff. It's the brain stuff that's important here. https://msdn.microsoft.com/en-us/library/windows/desktop/bb147302(v=vs.85).aspx?f=255&MSPPError=-2147217396 https://en.wikipedia.org/wiki/3D_rendering https://en.wikipedia.org/wiki/3D_projection https://en.wikipedia.org/wiki/Field_of_view_in_video_games https://developer.valvesoftware.com/wiki/Field_of_View Of course I should show these excellent examples provided by forum members (guys please take credit here!) And now we get into the real meat and potatoes of this thread, how this effects our perception of the image. Food for thought, let's start with Escher. https://en.wikipedia.org/wiki/Optical_illusion https://en.wikipedia.org/wiki/Perspective_(graphical) http://artsygamer.com/fov-in-games/ https://en.wikipedia.org/wiki/Angle_of_view#Cinematography_and_video_gaming https://en.wikipedia.org/wiki/Focal_length https://en.wikipedia.org/wiki/Normal_lens#Perspective_effects_of_short_or_long_focal-length_lenses https://en.wikipedia.org/wiki/Perspective_distortion_(photography) https://en.wikipedia.org/wiki/Angular_diameter https://en.wikipedia.org/wiki/Perceived_visual_angle https://en.wikipedia.org/wiki/Depth_perception And really, if you only read ONE of these links, this is the one I feel would be most pertinent: https://en.wikipedia.org/wiki/Forced_perspective Look at the CSGO image above, look at the Odessa Steps....