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1. Super simple method: x*2 (or more)
2. The chad curve: sin(x)+2*(x/10)
3. The aggressive chad curve: sin(x*2)+0.1*x (fixed)
4. The wrinkly brain: Don't use an f(x) but instead use the delta value to detect whether or not the change in the analog value is negative or positive, handle 0 state as reset for an up/down counter that you can customize to have desired sensitivity
I know these are mere examples but I wouldn't use any of those 3 unless you're ok with introducing either huge deadzones to your input axis (example 1), or think it's ok to get a 0.9 output with a 1.0 input as in example 3 (sin(2)=0.909).
Delta would be similar to setting the helm/control seat axis to 100% and let that control an up/down counter, or better a custom lua snippet where you can manipulate increase and fallback rates of individual inputs or even combine them (think roll and yaw on planes).
The second one actually goes up to 1.04 and has no deadzones!
I would only have to guess his use cases. If it's anything but throttle, it's generally fine to not hit 1, but you can fix that issue with the aggressive chad curve by doing sin(x*2)+x*0.1.
I would hardly ever use the first one, but as you say they're more examples than perfect implementations.
So I tend to introduce delta as a boolean. Is the control greater than zero? AND is the delta less than zero? AND is the speed greater than zero? That means you are on the brakes and wanting to stop. So simply subtracting 1 from the control when those conditions are true, gives you much sharper braking.