Although Fourier series approximation is ubiquitous in computational physics
owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for
the fast evaluation of a three-dimensional truncated Fourier series at a set of
\emph{arbitrary} points are quite rare, especially in MATLAB language. Here we
employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis,
and D. Potts), a C library designed for this purpose, and provide a Matlab and
GNU Octave interface that makes NFFT easily available to the Numerical Analysis
community. We test the effectiveness of our package in the framework of quantum
vortex reconnections, where pseudospectral Fourier methods are commonly used
and local high resolution is required in the post-processing stage. We show
that the efficient evaluation of a truncated Fourier series at arbitrary points
provides excellent results at a computational cost much smaller than carrying
out a numerical simulation of the problem on a sufficiently fine regular grid
that can reproduce comparable details of the reconnecting vortices
