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

[Rob Clewley]

Zach,

>
> 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.

-Rob