Quadcubic interpolation: a four-dimensional spline method

Abstract

We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically accessible. The specific example of application of this work to a time-varying three-dimensional magnetic field is given, but this method would work equally well for a time-independent four-dimensional field. Implementations of both of these methods in the Python programming language are also available to download.