Spline approximation is a mathematical technique used to create a smooth curve that passes through a set of points. It involves using piecewise polynomial functions, called splines, which are defined on intervals between the data points. This method is particularly useful for interpolating data and can provide a more accurate representation of complex shapes compared to simple linear interpolation. The most common type of spline is the cubic spline, which uses third-degree polynomials. Cubic splines ensure that the curve is smooth at the data points, meaning both the curve and its first and second derivatives are continuous. This results in a visually appealing and mathematically robust approximation of the underlying function.