In the Bivariate platform, the cubic spline method uses a set of third-degree polynomials spliced together such that the resulting curve is continuous and smooth at the splices (knot points). The estimation is done by minimizing an objective function that is a combination of the sum of squared errors and a penalty for curvature integrated over the curve extent. See the paper by Reinsch (1967) or the text by Eubank (1999) for a description of this method.