new_curves.md

Existing curves

Retail curve

The joystick curve found in the retail game's source.

n(x) = (9-x)/9
f(I) = I*(s/9)+(I^5)*n(s)

Current curve for Windows version

The Windows version of joy.cpp got a new curve at some point.

f(I) = I^(3-(s/4.5))

Suggestions for new curves

The following curves will be added for testing.

Herra's suggestion

Adapted from http://www.hard-light.net/forums/index.php?topic=67633.msg1336430#msg1336430

f(I) = I^(s/9)*((1-cos(I*π))/2)^((9-s)/9)

Alternatively, a wider range of curves can be achieved by a small change in the last exponent.

f(I) = I^(s/9)*((1-cos(I*π))/2)^((9-s)/4.5)

Exponential curve (WIP)

f(I) = (exp(I)-1)/(exp(1)-1)

NB: Requires sensitivity parameter - might not make the final cut.

Logistic based (sigmoidal):

a = s+1

S(x) = 1/(1+exp((a)*(-x+0.5)))

f(I) = (S(I)-S(0))/(S(1)-S(0))

Yet another Herra suggestion

Starts with an exponential shape at s<5, becomes linear at s=5, then becomes logarithmic at s>5.

f(x) = I^(1+((5-s)/9))

NB: The linear point (5) might be changed.

Polynomial

f(I) = I*I^((9-s)/9)

NB: Redundant. The entire behaviour of this curve can be achieved with a subset of sensitivity settings s on the current Windows curve.

List of symbols

I    : input percent (position of joystick on half-axis).
s    : in-game sensitivity setting [0..9].
f(I) : translation of input percent to output (the result of the curve function).