Delaunay triangulations of the sphere

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Delaunay triangulations of the sphere

Marc Alexa
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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Re: Delaunay triangulations of the sphere

Sebastien Loriot (GeometryFactory)
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 ([hidden email] 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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Re: Delaunay triangulations of the sphere

MaelRL
Note that the branch is not guaranteed to be fully functional /
documented / optimized yet. If you run into issues, please report them
and I will look into it

Best,
Mael

On 15/09/2020 10:00, "Sebastien Loriot (GeometryFactory)"
([hidden email] via cgal-discuss Mailing List) wrote:

> 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 ([hidden email] 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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Re: Delaunay triangulations of the sphere

Marc Alexa
Thanks a lot!
-Marc



> On 15. Sep 2020, at 10:11, Mael Rouxel-Labbé <[hidden email]> wrote:
>
> Note that the branch is not guaranteed to be fully functional / documented / optimized yet. If you run into issues, please report them and I will look into it
>
> Best,
> Mael
>
> On 15/09/2020 10:00, "Sebastien Loriot (GeometryFactory)" ([hidden email] via cgal-discuss Mailing List) wrote:
>> 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 ([hidden email] 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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> You are currently subscribed to cgal-discuss.
> To unsubscribe or access the archives, go to
> https://sympa.inria.fr/sympa/info/cgal-discuss
>
>


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