Spherical Projections

Figure 1.14.

Four common full-sky projections. The shaded ellipses represent the distortion across the sky: each is projected from a circle of radius 10 degrees on the sphere. The extent to which these are distorted and/or magnified shows the distortion inherent to the mapping.

Code output:

Python source code:

# Author: Jake VanderPlas
# License: BSD
#   The figure produced by this code is published in the textbook
#   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
#   For more information, see http://astroML.github.com
#   To report a bug or issue, use the following forum:
#    https://groups.google.com/forum/#!forum/astroml-general
import numpy as np
from matplotlib import pyplot as plt
from astroML.plotting import plot_tissot_ellipse

#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX.  This may
# result in an error if LaTeX is not installed on your system.  In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)

#------------------------------------------------------------
# generate a latitude/longitude grid
circ_long = np.linspace(-np.pi, np.pi, 13)[1:-1]
circ_lat = np.linspace(-np.pi / 2, np.pi / 2, 7)[1:-1]
radius = 10 * np.pi / 180.

#------------------------------------------------------------
# Plot the built-in projections
plt.figure(figsize=(5, 4))
plt.subplots_adjust(hspace=0, wspace=0.12,
                    left=0.08, right=0.95,
                    bottom=0.05, top=1.0)

for (i, projection) in enumerate(['Hammer', 'Aitoff', 'Mollweide', 'Lambert']):
    ax = plt.subplot(221 + i, projection=projection.lower())

    ax.xaxis.set_major_locator(plt.FixedLocator(np.pi / 3
                                                * np.linspace(-2, 2, 5)))
    ax.xaxis.set_minor_locator(plt.FixedLocator(np.pi / 6
                                                * np.linspace(-5, 5, 11)))
    ax.yaxis.set_major_locator(plt.FixedLocator(np.pi / 6
                                                * np.linspace(-2, 2, 5)))
    ax.yaxis.set_minor_locator(plt.FixedLocator(np.pi / 12
                                                * np.linspace(-5, 5, 11)))

    ax.grid(True, which='minor')

    plot_tissot_ellipse(circ_long[:, None], circ_lat, radius,
                        ax=ax, fc='k', alpha=0.3, linewidth=0)
    ax.set_title('%s projection' % projection)

plt.show()

[download source: fig_projections.py]