Basemap.drawgreatcircle() map border

Hey,

I know that you're not supposed to draw a greatcircle with Basemaps
drawgreatcircle() when it will hit the border of the map. But I think
it works pretty well except for the attempt to connect the line (see
horizontal lines in [1]). Is there a way to not get these horizontal
lines?

Does someone has an idea how to hack drawgreatcircle() accordingly?
Brute force if wanted, I don't care so much about efficiency at this
point. Thanks for reading and possibly helping :wink:

Cheers, Yoshi

[1]: http://rokuko.net/test.png