Does power diagrams have differentiability?

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Does power diagrams have differentiability?

Frank Dz
Does power diagrams have differentiability?

How can we build up the connection between a vertex of the diagram and the
seed in Power Diagram?

Best,
Thanks

Frank



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Re: Does power diagrams have differentiability?

Bruno Levy
Hi Frank,

To do that, you can proceed as follows:


1) write the equation of the coordinates of the circumcenter of a
triangle in function of the coordinates of the three vertices of the
triangle

2) compute their derivative


Using matrix derivation rules helps
(https://tminka.github.io/papers/matrix/minka-matrix.pdf)

I did that in the following article (see in particular the appendix)

https://hal.inria.fr/inria-00600251/fr/


Hope this helps,

-- Bruno



On 9/6/20 1:48 PM, Frank Dz ([hidden email] via cgal-discuss Mailing
List) wrote:

> Does power diagrams have differentiability?
>
> How can we build up the connection between a vertex of the diagram and the
> seed in Power Diagram?
>
> Best,
> Thanks
>
> Frank
>
>
>
> -----
> be open, be creative, be critical
> --
> Sent from: http://cgal-discuss.949826.n4.nabble.com/
>

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Re: Does power diagrams have differentiability?

Frank Dz
Dear Bruno,

Wow, Thank you!

But just want to check, is there any library support this?
I searched but found nothing.


Best,
Frank



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Re: Does power diagrams have differentiability?

Marc Alexa
In reply to this post by Bruno Levy
Hi Bruno,

Thanks for the reminder of these results. Do you know any write-up that derives the gradient wrt. the weights in a weighted Delaunay triangulation (away form the discontinuities because of combinatorial changes)?

Thanks!
-Marc



> On 6. Sep 2020, at 14:32, Bruno Levy <[hidden email]> wrote:
>
> Hi Frank,
>
> To do that, you can proceed as follows:
>
>
> 1) write the equation of the coordinates of the circumcenter of a triangle in function of the coordinates of the three vertices of the triangle
>
> 2) compute their derivative
>
>
> Using matrix derivation rules helps (https://tminka.github.io/papers/matrix/minka-matrix.pdf)
>
> I did that in the following article (see in particular the appendix)
>
> https://hal.inria.fr/inria-00600251/fr/
>
>
> Hope this helps,
>
> -- Bruno
>
>
>
> On 9/6/20 1:48 PM, Frank Dz ([hidden email] via cgal-discuss Mailing List) wrote:
>> Does power diagrams have differentiability?
>>
>> How can we build up the connection between a vertex of the diagram and the
>> seed in Power Diagram?
>>
>> Best,
>> Thanks
>>
>> Frank
>>
>>
>>
>> -----
>> be open, be creative, be critical
>> --
>> Sent from: http://cgal-discuss.949826.n4.nabble.com/
>>
>
> --
> 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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