CGAL users discussion list

[Simon Perkins <>]

Hi Monique

I'm realising the naivety of my approach. I think I went through the same thought process some years ago with 2D Triangulations before deciding to use Constrained Triangulations to read in the points and edges of the faces.

I understand that inserting vertices of the external triangulation via the T.insert* methods is the preferred way of constructing a Triangulation_3. However, if I understand correctly, this will not necessarily preserve the tetrahedrons that I'm trying to represent, because once points are added outside the convex hull for example, CGAL will connect that point to all other points visible from it.


Is there some generally accepted way of preserving this connectivity information during the vertex insertion process? I tried calling T.insert(const Point & p, Face_handle fh) with fh set to the infinite cells that I was trying to "extend" the triangulation into, but  this also seems to exhibit the point connection behaviour for points external to the convex hull.

Am I trying to do something that CGAL's design precludes?

kind regards
  Simon

On Wed, Jul 18, 2012 at 6:49 PM, Monique Teillaud <> wrote:

Hi,

[Reminder: is the up-to-date address for this mailing list.
It replaced the old ]

* Each facet p,q,r of the convex hull is
- the finite facet of an infinite cell p,q,r,inf
- one of the facets of a finite cell p,q,r,s
These two cells must be neighbors in the data structure.
You must be very careful with orientation (see Sec 39.1)

* When two facets p,q,r and p,q,s of the convex hull share a common edge p,q, then their respective infinite cells p,q,r,inf and p,q,s,inf are neighbors through a common facet p,q,inf.
Here again, be careful with orientation.


In fact, it is easier (and safer) to just read the vertices of your external triangulation, and construct a CGAL triangulation from scratch by inserting the corresponding points...

Best,
        Monique Teillaud

Le 18/07/12 17:56, Simon Perkins a écrit :

Hello

I'm writing a loader that will read information from an external file
format into the CGAL Triangulation_3 data structure. One thing that may
be problematic is that the file format doesn't explicitly define the
infinite cells intrinsic to CGAL's representation and so I will have to
create them myself. I don't find this too daunting but I'm not sure how
the neighbours of an infinite cell should be configured. It seems clear
to me that the one can set the neighbour of the infinite vertex to be
the finite cell sharing a facet with the infinite cell, but I'm not sure
how to handle the neighbours of the other three vertices on the facet
itself.

Would it be valid to set them to a random finite cell for example?

kind regards
   Simon

--
Monique Teillaud
INRIA Sophia Antipolis - Méditerranée
http://www.inria.fr/sophia/members/Monique.Teillaud/

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