Biquadratic interpolation

The National Geodetic Survey (NGS) has coded software based tools for both internal and external use since the late 1960s (Coast and Geodetic Survey, 1967; Coast and Geodetic Survey 1970.) Throughout much of that history, the language of choice was FORTRAN, as this was the de facto standard used around the world for scientific computing. As such, scientists within NGS often had a strong combination of both geodetic skills and computer coding skills, and these same scientists were almost always the authors of the software which found its way into the public domain. As part of that scientific software development, it was often important for NGS scientists to creatively design individual computer tasks, from simple subroutines up through programs of hundreds of thousands of lines of code. Within the team of geoid scientists, one small routine was developed in the 1990s which has served in dozens of programs for the last 20+ years, though it was never formally documented: biquadratic interpolation. Because biquadratic interpolation is being implemented in numerous NGS programs as part of the modernized NSRS, and because it appears to be somewhat less well known than either bilinear interpolation or bi-cubic splines, it was felt that a brief explanation should be provided.