This is a very old question, but I thought it would be nice to answer anyway. When you made the curved lines, I assumed that you wanted to draw a great circle . Here is an example of what the basic documentation I modified to make the change a little easier:
from mpl_toolkits.basemap import Basemap import numpy as np import matplotlib.pyplot as plt m = Basemap(projection='cyl') p0_ll = -73.98, 40.78 p1_ll = 0.08, 51.53 m.drawgreatcircle(p0_ll[0], p0_ll[1], p1_ll[0], p1_ll[1], linewidth=2, color='b') m.drawcoastlines() m.fillcontinents() plt.show()

Please note that the large circle method cannot handle the intersection of map edges ( as indicated in the documentation ), which, although clearly documented, is a rather serious drawback of IMHO.
Hope someone helps,
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