Cubic Spline

A spline is a smooth function that passes through a set of data points. This is useful for interpolating between the data points or for generating a set of equally spaced data points. Equally spaced data points are sometimes needed for numerical integration or digital filtering.

The form on this page accepts data points as two columns which can be input in the lower left text box. When the "Plot Spline" button is pushed, the data points are plotted in red and the natural cubic spline is plotted as a blue line. In a natural spline, the second derivative is zero at the end points. Points along the blue line equally spaced in $x$ appear in the text box at the lower right.



 at $x=$ , $f(x)=$ .

for equally spaced points.

Input: $x$ $f(x)$

Output: $x$ $f(x)$