It can be demonstrated that curves of any complexity can be described by a sequence of segments defined as polynomials. In practice, most real-life curves can be reliably approximated by a sequence of third-order (cubic) polynomials.

For bivariate data sets (correlations that involve two variables), to determine the curve, the spline procedure solves cubic equations for every point at a regular interval (for more information on cubic interpolation, see de Boor, 1978; Johnson and Ries, 1982; Dahlquist and Bjorck, 1976; and Gerald and Wheatley, 1989).

A minimum of at least 3 data points are necessary to perform a spline fit; the algorithm ignores overlapping data points. Note that while other fitting algorithms are dependent on a specified Stiffness parameter (e.g., Distance-Weighted Least Squares fitting and Negative Exponentially-Weighted fitting), the Spline fitting algorithm is not.

See also Exploratory Data Analysis and Data Mining Techniques.