A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly set to zero at the endpoints, since this provides a boundary condition that completes the system of m - 2 equations. This produces a so-called "natural" cubic spline and leads to a simple tridiagonal system which can be solved easily to give the coefficients of the polynomials. However, this choice is not the only one possible, and other boundary conditions can be used instead. Cubic splines are implemented in the Wolfram Language as BSplineCurve[pts, SplineDegree -> 3].

Bézier curve | spline | thin plate spline

BSplineCurve