# Curve interpolation

Back to PastelMath

A curve is a continuous function from a subset of $\mathbb{R}$ to a metric space $M$. If the image of the function intersects with some finite set of points $X \subset M$, then the curve is said to interpolate $X$.

## Theory

In general, the problem of curve interpolation fixes a function class $C$ for the curves and then asks for an algorithm that for a given set $X$ returns an interpolating function from C. In case $X$ does not uniquely determine a function, additional conditions might be imposed for the solution.

## Files

### Smoothstep functions

Cubic, quartic, and quintic smoothstep functions