  Estimators for $n$-point clustering statistics in Fourier-space demand that
modern surveys of large-scale structure be transformed to Cartesian coordinates
to perform Fast Fourier Transforms (FFTs). In this work, we explore this
transformation in the context of pixelised line intensity maps (LIM),
highlighting potential biasing effects on power spectrum measurements. Current
analyses often avoid a complete resampling of the data by approximating survey
geometry as rectangular in Cartesian space, an increasingly inaccurate
assumption for modern wide-sky surveys. Our simulations of a
$20\,{\times}\,20\,\text{deg}^2$ 21cm LIM survey at $0.34\,{<}\,z\,{<}\,0.54$
show this assumption biases power spectrum measurements by ${>}\,20\%$ across
all scales. We therefore present a more robust framework for regridding the
voxel intensities onto a 3D FFT field by coordinate transforming large numbers
of Monte-Carlo sampling particles. Whilst this unbiases power spectrum
measurements on large scales, smaller-scale discrepancies remain, caused by
structure smoothing and aliasing from separations unresolved by the grid. To
correct these effects, we introduce modelling techniques, higher-order particle
assignments, and interlaced FFT grids to suppress the aliased power. Using a
Piecewise Cubic Spline (PCS) particle assignment and an interlaced FFT field,
we achieve sub-percent accuracy up to 80% of the Nyquist frequency for our 21cm
LIM simulations. We find a more subtle hierarchical improvement in results for
higher-order assignment schemes, relative to the gains made for galaxy surveys,
which we attribute to the extra complexity in LIM from additional discretising
steps. Python code accompanying this paper is available at
github.com/stevecunnington/gridimp.
