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Re: [cgal-discuss] Delaunay triangulations of the sphere


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  • From: "Sebastien Loriot (GeometryFactory)" <>
  • To:
  • Subject: Re: [cgal-discuss] Delaunay triangulations of the sphere
  • Date: Tue, 15 Sep 2020 10:00:28 +0200
  • Authentication-results: mail3-smtp-sop.national.inria.fr; spf=None ; spf=Pass ; spf=None
  • Ironport-phdr: 9a23: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
Dear Marc,

it's on its way (API is currently under review and subject to change):

https://github.com/CGAL/cgal/pull/4421

There is nothing on the 3-sphere.

Best regards,

Sebastien.

On 9/15/20 9:47 AM, Marc Alexa ( via cgal-discuss Mailing List) wrote:
Dear all,

I am interested in CGAL implementations for computing the Delaunay
triangulation of points sets on the 2- and 3-sphere. My current way is to
compute the Delaunay triangulations of the points in R^3 resp. R^4 and then
restrict to the simplices connected to the infinite vertex.

This paper

Manuel Caroli, Pedro M. M. de Castro, Sébastien Loriot, Olivier Rouiller,
Monique Teillaud, and Camille Wormser. Robust and Efficient Delaunay
Triangulations of Points on or Close to a Sphere. In 9th International
Symposium on Experimental Algorithms, volume 6049 of Lecture Notes in
Computer Science, pages 462-473, 2010.

explains how to do better than that.

I am wondering if the authors are willing to share their implementation. And
in particular, if there is an extension to tetrahedralizations of the
3-sphere.

Thanks!
-Marc




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