0 - 1 Remapping Functions: Smooth Step 2

/* remapping functions */

for(i=[-0:1/160:1])translate([i,0])square([1/160,   ( (   smooth2(i) )) ]);
     function smooth2(x,k=5,n=4) =1- (exp( -k*pow(x,n) ));
 

Compared to smooth step

0 - 1 Remapping Functions: Smooth Step

/* remapping functions */

for(i=[-0:1/160:1])translate([i,0])square([1/160, (smooth( (i),2/3,0.1))]);
    function smooth (a) =let (b = clamp(a))(b * b * (3 - 2 * b));
    function clamp(a, b = 0, c = 1) = min(max(a, b), c)
 

Smooth and Gaussian Curve

Takes a linear 0-1 value and apply an S-function. Gauss is the inverse of that S-function.

function smooth_curve(a) =
let (b = clamp(a))(b * b * (3 - 2 * b));

function clamp(a, b = 0, c = 1) = min(max(a, b), c);

function gauss(x) =  
     x + (x - smooth_curve(x));