CGAL users discussion list

["Laurent Rineau (GeometryFactory)" <>]

Le Lundi 01 Mars 2010 20:31:59, Panagiotis Foteinos a écrit :
> Hello all.
> 
> I am using the 3D Delaunay Triangulation package with a custom refinement
> algorithm. In my program, there are almost flat elements which I want to
> identify as flat (by checking the volume for example), and leave them alone
> without performing any calculations on them any more. The problem is that
> the calculation of the circumcenter or the radius (and the volume as a
> consequence)

The volume is a not a consequence of the circumcenter or the radius of a 
tetrahedron. The volume is one sixth of the mixed product:
  http://en.wikipedia.org/wiki/Tetrahedron#Volume
  http://en.wikipedia.org/wiki/Mixed_product#Scalar_triple_product

There is no need to compute a division to compute the volume.

In contrary, to compute the circumcenter or the circumradius of a 
tetrahedron, 
the denominator is the mixed product, if I remember well.

Use CGAL::volume(Point_3, Point_3, Point_3, Point_3):
http://www.cgal.org/Manual/last/doc_html/cgal_manual/Kernel_23_ref/Function_volume.html

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