Orthographic Projection in Healpy

Question

I was trying to work with healpy maps and I am running into a problem with orthographic projections. I want to assign "N" pixels in the healpy mollview projection map with a value of let's say 100. But, when I do an orthographic projection of the map, not all of the "N" pixels here have the value of 100. Can anyone help me here? What is the area of a pixel in orthographic projection in healpy?

Find the pseudo-code below.

import healpy as hp
import numpy as np
import matplotlib.pyplot as plt

nside =64
npix = hp.nside2npix(nside)
hpxmap = np.arange(npix)

theta = np.pi/2. - np.deg2rad(0)
phi = np.deg2rad(35)
vec = hp.ang2vec(theta, phi, lonlat=False)
disc = hp.query_disc(nside, vec, radius=np.radians(10), nest=False)        
hpxmap[disc] = 100
hp.mollview(hpxmap, coord = ['C'], nest = False, cbar = True)
print(len(disc))


orth_proj = hp.orthview(hpxmap, half_sky=True,return_projected_map=True, rot=(0, 0), xsize= 100, norm = 'log', coord=[ 'C'])
orth_proj[np.where(orth_proj == orth_proj[0,0])] = 0
len(np.where(orth_proj == 100)[0][:])

Based on the above-given code, the problem is that the length of the disc and the number of pixels in the orth_proj 2d array that has the value of 100 is not the same. Any thoughts?

Answer 1

When you plot a map, you are reprojecting it, either with mollweide or orthview, you are going to get pixels that have different shape, size and centers, there is no 1-to-1 mapping.

Not sure what the application is, but maybe you can use rectangular pixels, like CAR? In this case, the map needs no reprojection to be plotted. You can use https://github.com/simonsobs/pixell to handle CAR maps, for example if you start from a HEALPix map, you can do hp.map2alm and then pixell has alm2map.