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

[Rob Clewley]

> 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?

I can't really explain it easily off the top of my head. It's a lot
like you described, and there are several ways to do it. A popular
method is pseudo-arc length continuation, and the idea for it is
graphically shown on the wiki page for "numerical continuation". It
takes into account how the curve can bend at "fold points," where a
naive method based on parameterization of the curve along one axis
would lead to a singularity (f' = 0 leading to a 1/0 in the
algorithm). You might also read about predictor-corrector methods.
However, I might be able to help you set up an example of applying
PyCont to finding a level curve - it would be valuable tutorial for
the PyCont documentation (I think all our present examples are based
on bifurcations in dynamical systems). There are some good book
references on the wiki page, maybe the most accessible are [B1], [B5]
and [B6] but I don't know a few of them to comment on them all. From
the title, [B12] looks like it might be too.

-Rob