Quadcubic interpolation: a four-dimensional spline method
Provides a technical interpolation tool for scientists needing smooth 4D interpolation, but is an incremental extension of existing methods.
The paper extends tricubic interpolation to four dimensions, creating a quadcubic spline method with C1 continuity and analytical partial derivatives, demonstrated on a time-varying 3D magnetic field.
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.