Mercator Projection

Figure1.13.

The Mercator projection. Shown are the projections of circles of constant radius 10 degrees across the sky. Note that the area is not preserved by the Mercator projection: the projection increases the size of finite regions on the sphere, with a magnitude which increases at high latitudes.

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 Mercator projection: we need to set this up manually
def mercator_axes():
    ax = plt.axes(aspect=1.0)
    ax.set_xticks(np.pi / 6 * np.linspace(-5, 5, 11))
    ax.set_yticks(np.pi / 12 * np.linspace(-5, 5, 11))
    for axy in (ax.xaxis, ax.yaxis):
        axy.set_major_formatter(plt.FuncFormatter(lambda s, a: r'$%i^\circ$'
                                                  % np.round(s * 180 / np.pi)))
    ax.set_xlim(-np.pi, np.pi)
    ax.set_ylim(-np.pi / 2, np.pi / 2)

    return ax

plt.figure(figsize=(5, 3.75))
ax = mercator_axes()
ax.grid(True)
plot_tissot_ellipse(circ_long[:, None], circ_lat, radius,
                    ax=ax, fc='k', alpha=0.3, lw=0)
ax.set_title('Mercator projection')

plt.show()

[download source: fig_mercator.py]