Bivariate interpolation of extension modified Akima procedure (Q1390148)

Smooth surface fitting is considered. To interpolate inside a mesh, a patch of the surface is expressed in such a way that the surface passes through the four corners of the patch, and at these corners the three partial derivatives are determined locally. A new bridge technique is used to find the first and the second derivative of data points. Recurrence relations are given to calculate the derivatives at the third point for each bridge by the two last previous derivative values. An example is presented. Errors are tabulated for the non-polynomial function \(z(x,y)= e^{-x} \sin(y)+ e^{-y} \cos(x)\) fitted.