Solve with integrating an implicit function

[parisse]

You should not be surprised that plotting an implicit function as such is faster than plotting it as an explicit function, where all calls to fsolve are independant. Hint: near a regular point you know the tangent, if you move a little along say x, you have a good starting point for the solver on the tangent. Singular points are harder to handle. This is the way plotimplicit works, it finds a discretization of the implicit curve, with all points of the discretization approx. solutions to the equation, once computed you can zoom, or compute approx area inside without recomputing. Another method if you want just a plot output would be to compute the sign pixel by pixel. It's probably possible to mix methods. Perhaps jte can summarize how the adv. graph works.