Basically all I want is the functionally of hp.cartview, but I don't want my machine to waste memory plotting the actual map every single time I call the cartview function. How can I obtain a cartesian projection in healpy in the form of a 2d array without having to plot the projection every time?
First, let me point out that reproject might be a better tool for the job.
You can build a WCS object or a FITS header and then reproject your HEALPix map onto that, and subsequently plot it with wcsaxes, which gives you full support for real-world coordinate pixels (instead of pixel coordinates only).
If you really want to use healpy for these cartview cutouts instead, you can use the underlying healpy.projector.CartesianProj class:
from functools import partial
import healpy as hp
import numpy as np
import matplotlib.pyplot as plt
# Build a map
nside = 64
npix = hp.nside2npix(nside)
hpxmap = np.arange(npix)
# Get the cutout via a cartesian projection
lonra = [30, 40]
latra = [-10, 10]
proj = hp.projector.CartesianProj(
lonra=lonra, latra=latra,
coord='G',
xsize=n_pixels, ysize=n_pixels)
reproj_im = proj.projmap(hpxmap, vec2pix_func=partial(hp.vec2pix, nside))
# Plot the cutout
plt.imshow(reproj_im, origin='lower', interpolation='nearest')
Good luck, let me know if you have any follow-up questions!