Remapping and smoothstep functions are ubiquitous in graphics programming.

Smoothstep

GLSL built-in smoothstep(edge0, edge1, x) performs Hermite interpolation:

$$f(t) = 3t^2 – 2t^3$$

float smoothstep(float e0, float e1, float x) { float t = clamp((x - e0) / (e1 - e0), 0.0, 1.0); return t * t * (3.0 - 2.0 * t); }