The Akima Method

The seminal paper by Hiroshi Akima, A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures is described here and sample calculations of his reference problem are given. This approach has been incorporated in an R library in various stages of development with some copyright issues. It’s therefore not generally available for commercial work, but usable in instances like ours, for Deep Creek Lake. It’s an excellent method that I’ve used for many years.

The method is devised in such a way that the resulting curve will pass through the given points and will appear smooth and natural. It is based on a piecewise function composed of a set of polynomials, each of degree 3 at most, and applicable to successive intervals of the given points.

Members of the R consortium have written a special, unrestricted, library, called ‘interp’, to be backwards compatible with the ‘akima’ library. It contains an extensive set of sample problems from Franke, R., (1979). A critical comparison of some methods for interpolation of scattered data.. Figures xx-yy show a few of the results of its test problems.

PLV: First Published: 1/4/2022