Is it possible to find what algorithms are used for Delanunay triangulations?

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    $\begingroup$ See also this question. $\endgroup$
    – user21
    Feb 5, 2020 at 6:24

1 Answer 1


IIRC, Mathematica uses TriangleLink for geometric computations in the plane and in particular for Delaunay triangulation. That is an interface to Shewchuk's famous library Triangle.

As quite often (with a few notable exception), Mathematica's documentation is quite mute about such dependencies. For example, the page https://reference.wolfram.com/language/TriangleLink/guide/TriangleLink.html starts with the sentence

Triangle is a quality triangle mesh generator. TriangleLink is a Wolfram System application that uses Wolfram LibraryLink to link to Triangle functions.

That is in no way a proper way for giving credit; neither is the author mentioned, nor is a link to the source given. Heck, they even forgot to put "Triangle" into quotes or italics!

About the notable exceptions: They do exist and are not seldomly written by user21. Here is one example, explicitly citing the author in the context of planar triangulations:


  • $\begingroup$ Thanks, Henrik! I wonder how did you find this fact. $\endgroup$ Feb 4, 2020 at 15:32
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    $\begingroup$ You're welcome, Pavel! I googled "Mathmatica" and "Shewchuk". Indeed, that's the problem: One cannot find it in the docs when one is looking for it. That's my major point of criticism. $\endgroup$ Feb 4, 2020 at 15:35
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    $\begingroup$ Both TriangleLink and TetGenLink are my codes and documentation. I have updated the mentioned guide pages to include the requested links and requested that these changes be merged into the 12.1 branch - I can not guarantee that this change will make it into 12.1 but latest in 12.2 it will be visible. Sorry for the inconvenience and thanks for the kind words for the other cases. $\endgroup$
    – user21
    Feb 5, 2020 at 6:47

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