Cubic spline interpolation is a mathematical method commonly used to construct new points within the boundaries of a set of known points. These new points are function values of an interpolation function (referred to as *spline*), which itself consists of multiple cubic piecewise polynomials. This article explains how the computation works mathematically.

After an introduction, it defines the properties of a cubic spline, then it lists different boundary conditions (including visualizations), and provides a sample calculation. Furthermore, it acts as a reference for the mathematical background of the cubic spline interpolation tool on tools.timodenk.com which is introduced at the end of the article. Continue reading Cubic Spline Interpolation