HEALPix pixel shape

pixshape.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import healpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "nside = [1<<i for i in range(15)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "npix = [healpy.nside2npix(n) for n in nside]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pixshape(nside, ipix, step=1):\n",
    "    theta, phi = healpy.pix2ang(nside, ipix)\n",
    "    R = [[np.cos(theta)*np.cos(phi), np.cos(theta)*np.sin(phi), -np.sin(theta)],\n",
    "         [             -np.sin(phi),               np.cos(phi),              0],\n",
    "         [np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi),  np.cos(theta)]]\n",
    "    x = healpy.boundaries(nside, ipix, step=step)\n",
    "    x = np.dot(R, x)\n",
    "    x /= x[2]\n",
    "    return x[0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {