CGAL users discussion list

[Mariette Yvinec <>]

Laurent Rineau (GeometryFactory) wrote:

On Tuesday 19 May 2009 18:20:27 Daniel Russel wrote:
  

 Surface_3 surface(ellipsoid_function, // pointer to function
                 Sphere_3(CGAL::ORIGIN, 3.5)); // bounding sphere
        

Your bounding sphere is defined with a *squared* radius of 3.5, and
clearly
that sphere does not bound the surface. In my opinion, you need at
least 10 as
*squared* radius of the sphere.

http://www.cgal.org/Manual/3.4/doc_html/cgal_manual/Kernel_23_ref/Class_S
phere_3.html
      

As someone who gets bitten by this periodically when using the surface
mesher, I would really appreciate if there is were a test in the code
which could give a better error message if you mess this up.
    

I do not see any way to discover that a user gives an incorrect bounding 
sphere. The bounding is part of the user input itself. What would be doable 
is the detection that the bounding sphere is completely inside the interior of 
the surface (and in that case the mesher fails to discover any initial point).

But that is all. One can, for example, give the equation of a infinite 
implicit surface, such as x^x+y^x-1 = 0, and the bounding sphere gives the 
limit of the output surface mesh (in that case it is very important that the 
tag CGAL::Manifold_with_boundaries_tag is used instead of CGAL::Manifold_tag).

  

I agree that the bounding sphere could be used to clip the surface
to be meshed but this is not really the intention of this bounding sphere...

On the other hand, there is no way to test if the given bounding sphere is really
bounding ... except may be, in case of closed surface,
a statistical test
that amounts to take random point on this sphere
and check that the segments from these point to the center  point intersects the surface.

-- 
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis