CubicSpline Class

Use the CubicSpline class to interpolate tabulated data, or to approximate a function defined in terms of tabulated data.

A cubic spline is a piecewise curve defined by a third degree polynomial on each interval.

Splines are defined by the data points and some additional conditions. Depending on the nature of these conditions, different types of spline curves arise. There are four kinds of splines. These types are enumerated by the CubicSplineKind type.

A natural spline is a spline curve whose second derivative at the end points are zero. This type of spline tends to minimize the overall curvature of the spline. There is only one natural spline for a given set of data points.

A clamped spline is a spline curve whose slope is fixed at both end points. There is a clamped spline curve for each pair of slopes. Therefore, two parameters must be defined in addition to the data points to specify a clamped spline completely.

Clamped and natural splines have continuous second derivatives.

A cubic Hermite spline is a spline curve whose slope is fixed at each data point. These slopes must be provided by the user. As a result of these additional conditions, the second derivative is no longer continuous.

An Akima spline is a variation of a spline that is robust against outliers. The polynomial on each interval is defined using only a limited number of points. This means that, unlike natural and clamped splines, the effect of an anomalous data point doesn't propagate throughout the curve. Akima splines require only the data points. No other information is needed.