  We describe an algorithm for application of the classic `drizzle' technique
to produce 3d spectral cubes using data obtained from the slicer-type integral
field unit (IFU) spectrometers on board the James Webb Space Telescope. This
algorithm relies upon the computation of overlapping volume elements (composed
of two spatial dimensions and one spectral dimension) between the 2d detector
pixels and the 3d data cube voxels, and is greatly simplified by treating the
spatial and spectral overlaps separately at the cost of just 0.03% in
spectrophotometric fidelity. We provide a matrix-based formalism for the
computation of spectral radiance, variance, and covariance from arbitrarily
dithered data and comment on the performance of this algorithm for the
Mid-Infrared Instrument's Medium Resolution IFU Spectrometer (MIRI MRS). We
derive a series of simplified scaling relations to account for covariance
between cube spaxels in spectra extracted from such cubes, finding
multiplicative factors ranging from 1.5 to 3 depending on the wavelength range
and kind of data cubes produced. Finally, we discuss how undersampling produces
periodic amplitude modulations in the extracted spectra in addition to those
naturally produced by fringing within the instrument; reducing such
undersampling artifacts below 1% requires a 4-point dithering strategy and
spectral extraction radii of 1.5 times the PSF FWHM or greater.

Instrumentation and Methods for Astrophysics