How to plot a tissot with cartopy and matplotlib?

Question

For plotting skymaps I just switched from Basemap to cartopy, I like it a lot more .

(The main reason was segfaulting of Basemap on some computers, which I could not fix).

The only thing I struggle with, is getting a tissot circle (used to show the view cone of our telescope.)

This is some example code plotting random stars (I use a catalogue for the real thing):

import matplotlib.pyplot as plt
from cartopy import crs
import numpy as np

# create some random stars:

n_stars = 100
azimuth = np.random.uniform(0, 360, n_stars)
altitude = np.random.uniform(75, 90, n_stars)
brightness = np.random.normal(8, 2, n_stars)

fig = plt.figure()
ax = fig.add_subplot(1,1,1, projection=crs.NorthPolarStereo())
ax.background_patch.set_facecolor('black')

ax.set_extent([-180, 180, 75, 90], crs.PlateCarree())

plot = ax.scatter(
    azimuth,
    altitude,
    c=brightness,
    s=0.5*(-brightness + brightness.max())**2,
    transform=crs.PlateCarree(),
    cmap='gray_r',
)

plt.show()

How would I add a tissot circle with a certain radius in degrees to that image? https://en.wikipedia.org/wiki/Tissot%27s_indicatrix

Answer 1

I keep meaning to go back and add the two functions from GeographicLib which provide the forward and inverse geodesic calculations, with this it is simply a matter of computing a geodetic circle by sampling at appropriate azimuths for a given lat/lon/radius. Alas, I haven't yet done that, but there is a fairly primitive (but effective) wrapper in pyproj for the functionality.

To implement a tissot indicatrix then, the code might look something like:

import matplotlib.pyplot as plt

import cartopy.crs as ccrs
import numpy as np

from pyproj import Geod
import shapely.geometry as sgeom


def circle(geod, lon, lat, radius, n_samples=360):
    """
    Return the coordinates of a geodetic circle of a given
    radius about a lon/lat point.

    Radius is in meters in the geodetic's coordinate system.

    """
    lons, lats, back_azim = geod.fwd(np.repeat(lon, n_samples),
                                     np.repeat(lat, n_samples),
                                     np.linspace(360, 0, n_samples),
                                     np.repeat(radius, n_samples),
                                     radians=False,
                                     )
    return lons, lats


def main():
    ax = plt.axes(projection=ccrs.Robinson())
    ax.coastlines()

    geod = Geod(ellps='WGS84')

    radius_km = 500
    n_samples = 80

    geoms = []
    for lat in np.linspace(-80, 80, 10):
        for lon in np.linspace(-180, 180, 7, endpoint=False):
            lons, lats = circle(geod, lon, lat, radius_km * 1e3, n_samples)
            geoms.append(sgeom.Polygon(zip(lons, lats)))

    ax.add_geometries(geoms, ccrs.Geodetic(), facecolor='blue', alpha=0.7)

    plt.show()


if __name__ == '__main__':
    main()