Implement Iso Delaunay Tessellation

[sfreedman67]

fixes #160

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[videlec]

We are working with a student (Oscar) on using iso-Delaunay and spine to list more efficiently saddle connections. Right now, the code in the branch does not really makes the distinction between

• the tessellation of $\mathbb{H}^2$ which always have infinitely many regions
• the tessellation of $\mathbb{H}^2 / \Gamma$
  To me the IsoDelaunayTessellation should be the first of the two. The fact that it could be used to discover elements in the Veech group is definitely an important feature. But to my mind it would be better not to force such check for each face exploration.

[sfreedman67]

That sounds like an interesting use case for the iso-Delaunay tessellation! Making IsoDelaunayTessellation the former would be consistent with Bowman’s paper. Are there still plans to implement the Veech group element discovery portion of the code?

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On Apr 25, 2024, at 9:07 AM, Vincent Delecroix ***@***.***> wrote: We are working with a student (Oscar) on using iso-Delaunay and spine to list more efficiently saddle connections. Right now, the code in the branch does not really makes the distinction between the tessellation of $\mathbb{H}^2$ which always have infinitely many regions the tessellation of $\mathbb{H}^2 / \Gamma$ To me the IsoDelaunayTessellation should be the first of the two. The fact that it could be used to discover elements in the Veech group is definitely an important feature. But to my mind it would be better not to force such check for each face exploration. — Reply to this email directly, view it on GitHub <#163 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AQGU3UTRQAFJS5E3YGIXJO3Y7D5YJAVCNFSM5UPKMIDKU5DIOJSWCZC7NNSXTN2JONZXKZKDN5WW2ZLOOQ5TEMBXG4YTGOBVGI3Q>. You are receiving this because you were mentioned.

[videlec]

Are there still plans to implement the Veech group element discovery portion of the code?

Yes. This is another important motivation! But for that purpose I would implement a different explore (or possibly a flexible one that supports many usage).

[videlec]

Also, it feels like the IsoDelaunayTessellation._dual_graph would better be implemented as an "embedded graph" rather than just a graph. Namely, we want to record the cyclic ordering of edges around the region.