facets in a regular triangulation

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facets in a regular triangulation

BRYang
This post was updated on .
Hi,
I have got a question. For a delaunay triangulation, a facet is incidental
to two cells which share the facet, so a facet in delaunay triangulation has
three vertices.

However, it shows that in a regular triangulation Rt, we can access four
vertices of a facet ffi as follows:
ffi->first->vertex(i)->point(), where ffi is a Finite_facets_iterator and i
\in {0,1,2,3}.

Does that mean that any three of the four vertices could generate
a face with the three vertices in regular triangulation?

Best,
Baorong Yang


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Re: facets in a regular triangulation

Olivier Devillers-2


> Le 8 juil. 2019 à 09:23, BRYang <[hidden email]> a écrit :
>
> Hi,
> I have got a question. For a delaunay triangulation, a facet is incidental
> to two cells which share the facet, so a facet in delaunay triangulation has
> three vertices.
>
> However, it shows that in a regular triangulation Rt, we can access four
> vertices of a facet ffi as follows:
> ffi->first->vertex(i)->point(), where ffi is a Finite_facets_iterator and i
> \in {0,1,2,3}.
>
> Does that mean that any three of the four vertices could generate
> a face with the three vertices in regular triangulation?
>

A facet is a pair (cell, index)

The cell is one of the two cells incident to the facet,
The index tells you which vertex of the cell you have to ignore to get the facet.


(This is in the manual !)

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Re: facets in a regular triangulation

BRYang
Hi, Olivier.  

I think I have mis-understood that ffi->first is the facet which confuse me
with the fourth vertex while actually it is the first cell handle.

Thank you for your kind help and explanation.

Best,

Baorong



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