# Nd level sets
**URL:** https://discourse.julialang.org/t/nd-level-sets/38532
**Category:** General Usage
**Tags:** question
**Created:** [May 1, 2020, 6:57am UTC](https://discourse.julialang.org/t/nd-level-sets/38532 "2020-05-01T06:57:23Z")
**Posts on this page:** 15
**Page:** 1
### Author:  [@rveltz](https://discourse.julialang.org/u/rveltz)
#### Post date: [May 1, 2020, 6:57am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/1 "2020-05-01T06:57:23Z")
Hi,
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 `.
Thank you for your help,
Bests
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 1, 2020, 7:04am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/2 "2020-05-01T07:04:47Z")
In general this is, of course, hard problem.
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
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### Author:  [@rveltz](https://discourse.julialang.org/u/rveltz)
#### Post date: [May 1, 2020, 7:53am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/3 "2020-05-01T07:53:41Z")
Thank you for the pointers!
Can you tell how to plot the box in 3d please, the semantic has changed?
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 1, 2020, 1:59pm UTC](https://discourse.julialang.org/t/nd-level-sets/38532/4 "2020-05-01T13:59:47Z")
Oh good question, will have to check that.
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### Author:  [@rveltz](https://discourse.julialang.org/u/rveltz)
#### Post date: [May 4, 2020, 2:24pm UTC](https://discourse.julialang.org/t/nd-level-sets/38532/5 "2020-05-04T14:24:12Z")
I referenced your package in my [docs](https://rveltz.github.io/PseudoArcLengthContinuation.jl/dev/mittelmann/#Analysis-at-the-2d-branch-points-1). If you can do better than what is linked, I am all ears!
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 4, 2020, 3:27pm UTC](https://discourse.julialang.org/t/nd-level-sets/38532/6 "2020-05-04T15:27:33Z")
Those are some pretty amazing and beautiful figures!
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 4, 2020, 7:08pm UTC](https://discourse.julialang.org/t/nd-level-sets/38532/7 "2020-05-04T19:08:16Z")
What is the exact mathematical problem that you want to solve?
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### Author:  [@rveltz](https://discourse.julialang.org/u/rveltz)
#### Post date: [May 4, 2020, 7:22pm UTC](https://discourse.julialang.org/t/nd-level-sets/38532/8 "2020-05-04T19:22:17Z")
Intersect polynomial submanifolds. As of now, it just remains to adapt the 3d part of your docs/code to the new syntax of Makie .
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 4, 2020, 7:54pm UTC](https://discourse.julialang.org/t/nd-level-sets/38532/9 "2020-05-04T19:54:17Z")
Can you provide an explicit example?
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### Author:  [@rveltz](https://discourse.julialang.org/u/rveltz)
#### Post date: [May 5, 2020, 7:16am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/10 "2020-05-05T07:16:32Z")
Can you for example update one of [those](https://github.com/JuliaIntervals/IntervalConstraintProgrammingNotebooks/tree/master/3D) so the 3d plot works please?
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 6, 2020, 1:37am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/11 "2020-05-06T01:37:14Z")
Wow, those are super out of date – they were apparently made for Julia 0.5 or 0.6…
I’m trying to update them to use Makie, but it seems to be broken right now. Hopefully will be working soon!
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 7, 2020, 2:40am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/12 "2020-05-07T02:40:44Z")
Here is an updated example:
>
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 7, 2020, 2:44am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/13 "2020-05-07T02:44:53Z")
Please do let me know if I can help more. I am interested in playing with difficult examples that you have.
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [May 7, 2020, 3:18am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/14 "2020-05-07T03:18:42Z")
Here’s my attempt at drawing what I understand to be the set in your docs:
Unfortunately currently the mechanism for creating separators from functions is broken
([Package is broken due to changes in ModelingToolkit · Issue #162 · JuliaIntervals/IntervalConstraintProgramming.jl · GitHub](https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl/issues/162))
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.
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### Author:  [@rveltz](https://discourse.julialang.org/u/rveltz)
#### Post date: [May 7, 2020, 6:18am UTC](https://discourse.julialang.org/t/nd-level-sets/38532/15 "2020-05-07T06:18:11Z")
This is great !!