Spline interpolation

On each subinterval we have a cubic polynomial . To obtain a very smooth, good-looking curve with minimal unwanted oscillations we impose that the function is twice continuously differentiable. This means that we impose the continuity, countinuous first derivative and continuous second derivative conditions at all intermediate points:

The length of the interval is

The piecewise cubic polynomials have the form:

The parameters will be calculated such that the continuity conditions () are satisfied.