[SciPy-user] Getting coordinates of a level (contour) curve

[Zachary Pincus]

>> Following a level curve from an arbitrary function is a bit harder.  
>> If
>> you have the function's gradient, you could in theory just go around
>> in a direction orthogonal to the gradient, but in the real world that
>> wouldn't work with numerical error and finite step sizes. You could
>> probably take steps orthogonal to the gradient, then correct back to
>> the desired level value by stepping along the gradient, and then
>> repeat until you get back near to where you started.
>
> You can do that in many circumstances using Newton's method or
> variants of it. It's called continuation, and it's what packages like
> AUTO, PyCont, MatCont, and Content do as their bread and butter. There
> are several steps to getting it set up properly so that it converges.

Aah, cool... good to know! (I should have mentioned above that I was  
speculating off the top of my head. Makes sense that there would be  
formal numerical methodologies for that.)

A lot of the PyCont, etc., descriptions seem to be wrapped up in  
pretty specialized terminology -- what would an example of tracing a  
level curve look like, given f(x), fprime(x), and some x0?

Zach