A curve is a continuous function from a subset of to a metric space . If the image of the function intersects with some finite set of points , then the curve is said to interpolate .
In general, the problem of curve interpolation fixes a function class for the curves and then asks for an algorithm that for a given set returns an interpolating function from C. In case does not uniquely determine a function, additional conditions might be imposed for the solution.
Cubic, quartic, and quintic smoothstep functions