Theory and implementation of splines by Mike Bersch.
Simple polynomial interpolation finds one polynomial that goes through a given set of points. If there are many points, the interpolating polynomial will be of high degree and likely have to bend in non-intuitive ways. Splines are a mathematical method for interpolating a function that uses piecewise defined polynomials. We will review the definition of standard splines, and then discuss monotonic splines. Finally, we discuss bivariate splines.