CGAL users discussion list

[Juan Carlos Lopez Alfonso <>]

Hi Andreas,

Thank you for your answer and I understand your point. But, How Can I solve my problem? I need that when the Jacobian is equal to 0 the CGAL test of coplanar points is satisfied.

Best Regards

Juan Carlos

On Fri, Jan 20, 2012 at 11:58 AM, Andreas Fabri <> wrote:

Hi Juan,

coplanarity should be transitive, and as soon as you introduce
small epsilons there is the risk of trouble.

It's easier to explain for the equality of numbers
(which are also points, but in the 1D space).

Imagine you say that you want to consider two numbers
as equal as soon as their difference is not larger than 1.

Then   7812 and 7813 are "equal",  7813 and 7814 are also equal,
but 7812 and 7814 are not equal.


It is hard to write an always correct Delaunay triangulation
code for a broken coplanarity test.

andreas

On 20/01/2012 11:47, Juan Carlos Lopez Alfonso wrote:

Hi Oliver:

Thank you for your answer. But, maybe you dont understand my point.

How is possible that this points are not coplanar when the jacobian is
exactly equal to 0? and you dont answer my question:  How Can I say to
CGAL when computes the triangualtion that these points are coplanar?  at
least with my criteria!!!

On the other hand, I cant include or remove points, and I need that the
jacobian of each thetraedron is different to 0. I am using MS 10.0 and
the jacobian is equal to 0, how is possible that in CGAL these points
are not coplanar? I cant understand this issue.

In my code I will use the Jacobian and in some case some expressions are
divide by the jacobian, and for this reason I need to have a jacobian
different to 0, while in c++ the jacobian is 0 for CGAL is not.

Regards
Juan Carlos

On Fri, Jan 20, 2012 at 11:32 AM, Olivier Devillers

< <mailto:>> wrote:

   Le 1/20/12 11:13 AM, Juan Carlos Lopez Alfonso a écrit :

       Hi There:

       I have this concrete example:
       ..........

       - How is possible that in CGAL these points are not coplanar?
       because these points are coplanar.

   as already explained your points ARE NOT coplanar,
   they are just almost coplanar (and since the volume is quite small
   you round it t zero)


       - In order that I can't remove points, How Can I say to CGAL
       when computes the triangualtion that these points are coplanar?

   THEY ARE NOT.
   If you can compute another triangulation, but it will not be the
   Delaunay triangulation.


       - I will use the resultant triangulation in other software where
       the jacobian is computed and I can't use the CGAL library. Is
       possible to change the CGAL test of coplanar points when the
       triangulation is computed?

   if you cannot remove points, may be you can add (e.g. using the
   meshing package).

   Olivier


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Andreas Fabri, PhD
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