Piecewise polynomials are the models of choice for fitting to arbitrary data because their piecewise character makes them flexible even when one insists that the polynomial pieces join smoothly (to get a spline), while their polynomial pieces are very easy to evaluate.

Construction tools provided are: Interpolation, (weighted) least-squares fitting, and the smoothing spline. More general fitting procedures can be implemented efficiently with the aid of B-spline tools provided. Splines can be vector-valued, for the description of curves, and multivariate, for the description of surfaces.

The resulting splines can be plotted, evaluated, differentiated, integrated, and combined in various ways. In ppform, such a spline can be used in MATLAB independently of the Spline Toolbox.