CGAL users discussion list

[Juan Carlos Lopez Alfonso <>]

Hi Sebastien and Laurent:

First of all, I want to thank for your answers. I have tested the conditions of coplanar points. In CGAL thsi condition (CGAL::orientation(p1, p2, p3, p4) == CGAL::COPLANAR) is not satisfied when the Jacobian is equal to zero, so I have a question:

- I need to use the triangulation and the Jacobian in other software, for this reason I can't use an exact representation of doubles. Therefore, How I can change the CGAL condition to coplanar points? is to say, I need to consider the coplanar condition in CGAL using my Jacobian, is it possible? or is possible to change the coplanar condition in order to obtain thetraedra with more volume?

Thank you in advance

Juan Carlos

On Thu, Jan 19, 2012 at 5:33 PM, Sebastien Loriot (GeometryFactory) <> wrote:

On 01/19/2012 04:13 PM, Juan Carlos Lopez Alfonso wrote:

Hi Sebastien and  Laurent:

Please, see these links below with my code and the input file of 3D points:

http://dl.dropbox.com/u/2516160/main.cpp
http://dl.dropbox.com/u/2516160/CubeSmall.txt

When I run my code, the test (if (CGAL::orientation(p1, p2, p3, p4) ==
CGAL::COPLANAR)) is never satisfied, but when I compute the Jacobian is
equal to 0.000000000000, is to say, that the 4 points of several
thetraedra are coplanar. Maybe Laurent have reason, but How can I solve
this problem? Could you give me suggestions?

This is what Laurent explained you.
The test GAL::orientation uses the kernel
Exact_predicates_inexact_constructions_kernel meaning that predicates
are correctly evaluated. Which also implies that your points are not
collinear.

If you really want to compute the jacobian by hand you need to use an
exact number type such as CGAL::Gmpq.

something like that should work:
typedef CGAL::Simple_cartesian<CGAL::Gmpq> Exact_kernel;
CGAL::Cartesian_converter<K, Exact_kernel> convert;
Exact_kernel::Point_3 p1_exact=convert(p1);
...
...
Exact_kernel::Point_3 p4_exact=convert(p4);

CGAL::Gmpq jacobian = (p2_exact.x() - p1_exact.x()) * ....

if (jacobian ==0) ...

You'll see that jacobian is not 0


See also this FAQ entry:
http://www.cgal.org/FAQ.html#inexact_NT

Sebastien.

Thank you for all and waiting your answer
Juan Carlos

On Thu, Jan 19, 2012 at 3:41 PM, Laurent Rineau (GeometryFactory)
<

<mailto:>> wrote:

   Le jeudi 19 janvier 2012 15:12:16 Juan Carlos Lopez Alfonso a écrit :
    > Hi Sebastien:
    >
    > To detect that points are coplanar, I have computed the jacobian
   of each
    > thetraedra:
    >
    > //for each thetraedra !!!
    > ........
    > Tetrahedron t = T[i];
    >
    > Vertex p1 = cit->vertex(0);
    > Vertex p2 = cit->vertex(1);
    > Vertex p3 = cit->vertex(2);
    > Vertex p4 = cit->vertex(3);
    >
    > double Jacobian =
    > (p2.x - p1.x) * (p3.y - p1.y) * (p4.z - p1.z) + (p3.x - p1.x) *
   (p4.y -
    > p1.y) * (p2.z - p1.z) + (p4.x - p1.x) * (p2.y - p1.y) * (p3.z - p1.z)
    >  - (p4.x - p1.x) * (p3.y - p1.y) * (p2.z - p1.z) - (p3.x - p1.x)
   * (p2.y -
    > p1.y) * (p4.z - p1.z) - (p2.x - p1.x) * (p4.y - p1.y) * (p3.z -
   p1.z);
    > ........

   That way of detecting coplanarity is subject to rounding errors.
   Probably you
   have almost-coplanar points in your data set, but in reality, using a
   certified arithmetic, there are not coplanar.

   --
   Laurent Rineau, PhD
   R&D Engineer at GeometryFactory http://www.geometryfactory.com/
   Release Manager of the CGAL Project http://www.cgal.org/


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