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*