I want to compute the level sets of a Nd scalar function. Furthermore, I would like to be able to access the list of values on the level set. I am looking for suggestions.

I know of the following possibilities:

contour in Plots.jl

contour in Makie.jl

Contour.jl but 2d

Meshing.jl but 3d

At first, I thought it would be possible to make such method using RegionTrees.jl .

Given an initial Nd box X, IntervalConstraintProgramming.jl can give you a set of small boxes that rigorously enclose the part of a level set lying inside X.

I believe this can also be solved by a version of the “parameterization method” used to find stable ame unstable manifolds, in which you stitch together pieces of Taylor polynomials. Cc @lbenet

But actually I’m not sure this is the right tool for the job, since as far as I can see this is just a union of 1D curves (?). @Xing_Shi_Cai pointed me towards Cylindrical Algebraic Decomposition the other day. This can give you all the “pieces” of the solution.