Cubic spline interpolation is based on a drafting tool used to draw smooth curves through a number of points. The spline tool consists of weights attached to a flat surface at the points to be connected. A flexible strip is then bent across each of these weights, resulting in a smooth curve.
The cubic spline interpolation is a piecewise continuous curve that passes through each value in the data set. Each interval of the curve has a separate cubic polynomial, each with its own coefficients. These are equivalent to the spline tool's weights. The cubic spline interpolation method considers the entire data set when adjusting outliers and filling in missing values.