FORTRAN Subroutines for Bicubic Spline Interpolation

Two CDC 3800 FORTRAN subroutines BICUB1 and BICUB2 which perform bicubic spline interpolation of a tabulated function of two variables are described. Given the values X1,...,XN and Y1,...,YM of two independent variables and the corresponding function values UI,JfXI, YJ, I1,...,N and J1,...,M and certain normal derivatives optional along the boundaries of the x-y mesh, BICUB1 estimates the derivatives fx, fy, and fxy at each I, J mesh point. If the normal derivatives along the mesh boundaries are unknown, BICUB1 estimates them using a moving third order two dimensional Lagrange interpolating polynomial. Given the coordinates XPT, YPT and the derivatives calculated by BICUB1, BICUB2 obtains the coefficients of the bicubic polynomial for the rectangular region of the mesh containing XPT, YPT and estimates the functional value UPTfXPT,YPT. In effect, the routines pass a twice continuously differentiable piecewise bicubic polynomial, ux,y belongs to C sup 2, through the given functional values.