This is causing so much fuss, I'm starting to feel bad about asking the 
question.  I'll reply in the "uniqueness" thread about the (r,th) 
coordinate system from a mathematical perspective.

 From a matplotlib.pyplot user perspective, however, I think that if it 
is going to misbehave with negative values of r under certain 
circumstances (rgrids() in this case) then it should produce a noisy 
warning as soon as it sees them in *all* circumstances.  So my 
version2.py and version3.py should both produce warnings.

Any how, the answer seems to be "yes I'm using rgrids() correctly, but 
no I'm not using matplotlib-friendly data points".  I shall adjust my 
values of (r,th).

Thank you for all your feedback.

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