Polar Stereographic Projection

For convenience, the projections npstere and spstere are provided for easy access to the polar aspect of the stereographic conformal projection.

from mpl_toolkits.basemap import Basemap
import numpy as np
import matplotlib.pyplot as plt
# setup north polar stereographic basemap.
# The longitude lon_0 is at 6-o'clock, and the
# latitude circle boundinglat is tangent to the edge  
# of the map at lon_0. Default value of lat_ts
# (latitude of true scale) is pole.
m = Basemap(projection='npstere',boundinglat=10,lon_0=270,resolution='l')
m.drawcoastlines()
m.fillcontinents(color='coral',lake_color='aqua')
# draw parallels and meridians.
m.drawparallels(np.arange(-80.,81.,20.))
m.drawmeridians(np.arange(-180.,181.,20.))
m.drawmapboundary(fill_color='aqua') 
# draw tissot's indicatrix to show distortion.
ax = plt.gca()
for y in np.linspace(m.ymax/20,19*m.ymax/20,10):
    for x in np.linspace(m.xmax/20,19*m.xmax/20,10):
        lon, lat = m(x,y,inverse=True)
        poly = m.tissot(lon,lat,2.5,100,\
                        facecolor='green',zorder=10,alpha=0.5)
plt.title("North Polar Stereographic Projection")
plt.show()

(Source code)

from mpl_toolkits.basemap import Basemap
import numpy as np
import matplotlib.pyplot as plt
# setup south polar stereographic basemap.
# The longitude lon_0 is at 6-o'clock, and the
# latitude circle boundinglat is tangent to the edge  
# of the map at lon_0. Default value of lat_ts
# (latitude of true scale) is pole.
m = Basemap(projection='spstere',boundinglat=-10,lon_0=90,resolution='l')
m.drawcoastlines()
m.fillcontinents(color='coral',lake_color='aqua')
# draw parallels and meridians.
m.drawparallels(np.arange(-80.,81.,20.))
m.drawmeridians(np.arange(-180.,181.,20.))
m.drawmapboundary(fill_color='aqua') 
# draw tissot's indicatrix to show distortion.
ax = plt.gca()
for y in np.linspace(19*m.ymin/20,m.ymin/20,10):
    for x in np.linspace(19*m.xmin/20,m.xmin/20,10):
        lon, lat = m(x,y,inverse=True)
        poly = m.tissot(lon,lat,2.5,100,\
                        facecolor='green',zorder=10,alpha=0.5)
plt.title("South Polar Stereographic Projection")
plt.show()

(Source code)