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I'm trying to convert a set of nodes of a mesh into a space-filling curves.

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Now, I tried both Morton encoding and Hilbert curve, and the Hilber curve was the one which worked best. But I have the following problem:

It could happen that two nodes are neighbours on the curve, but not in the mesh, and this cannot happen in what I need.

Does there exists some other space-filling curve which can preserve this property? Or does anyone have suggestions on how to deal with this?

Cla
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    This is a well-known problem: [Seven Bridges of Königsberg](https://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg). Your graph has only two vertices with an odd number of edges, so it's possible to find a curve that follows each of the edges of the graph. But that does not mean you can find a curve that hits each vertex only once and follows only edges of the graph. There is some stricter requirement for that. So even if there is a solution for a subset of graphs, the problem cannot be solved in general. – Cris Luengo Jul 23 '20 at 19:07
  • Thanks! Do you know if there are certain proprierties (like the number of refinements of the curves) that can help erase the problem iteratively? Or maybe if certain classes or mesh would not suffer from this ? – Cla Jul 24 '20 at 10:17

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