CGAL users discussion list

[Mariette Yvinec <>]

I think that there is some mistake.
You are not talking about the same parameter.
Pierre was  obviously talking about the third parameter
in the  creator of the Implicit_surface_3
and not about the third meshing criteria ....

There is a  third parameter in this creator
which sets the precision
with which points on the surface are computed.
Implicit_surface_3<Traits, Function> surface ( Function f, Sphere_3 
bounding_sphere, FT error_bound = FT(1e-3));
This parameter is relative to the radius
of the bounding sphere and has a default value of 1e-03.
Implicit_surface_3<Traits, Function> surface ( Function f, Sphere_3 
bounding_sphere, FT error_bound = FT(1e-3));
You need to take care that  the resulting error bound
(i. e. error_bound times radius of bounding sphere) is no more
than about 1/10 times the distance bound meshing criteria,
and this might be the source of yoour troubles.


Graham Macpherson wrote:
> Hello Pierre,
>
> That parameter was at 0.001 in my initial post, if I change it to 0.0008 it 
> triples the number of points on the surface (they form in clumps, not 
> uniformly distributed), but there is exactly the same magnitude of radius 
> error.
>
> If I make it 0.0005, my PC runs out of memory (8GB RAM) before it completes.
>
> If I make it 0.1, I get essentially the same result as 0.001.
>
> Regards,
>
> Graham
>
>
> On Friday 14 August 2009 14:27:32 Pierre Alliez wrote:
>   
> > hi Graham,
> >
> > have your tried tuning the third parameter if the surface? the relative
> > precision of the dichotomy mechanism to find the intersection?
> >
> > Pierre Alliez
> > INRIA Sophia Antipolis - Mediterranee
> > Project-team GEOMETRICA
> > http://www-sop.inria.fr/members/Pierre.Alliez/
> > Tel: +33 4 92 38 76 77
> > Fax: +33 4 97 15 53 95
> >
> > Graham Macpherson a écrit :
> >     
> > > Hello,
> > >
> > > I'm meshing surfaces using the implicit surface mesher and testing it
> > > with simple smooth shapes.  Using the example
> > >
> > >     examples/Surface_mesher/mesh_an_implicit_function.cpp
> > >
> > > I've created a fairly fine surface of a sphere using the criteria:
> > >
> > >         30.0, // angular bound
> > >         0.01, // radius bound
> > >         0.001  // distance bound
> > >
> > > The surface is not smooth - it has an "orange peel" look.  Plotting the
> > > radius of each vertex of the triangulation shows the magnitude of error
> > > of the triangulation point positions from the expected radius of 1:
> > >
> > >     fineSphereSurfaceWithRadius.png
> > >
> > > Creating a coarse surface with criteria
> > >
> > >         30.0, // angular bound
> > >         0.1, // radius bound
> > >         0.1  // distance bound
> > >
> > > Results in:
> > >
> > >     coarseSphereSurfaceWithRadius.png
> > >
> > > where the magnitude of vertex error is similar, but in the fine case, the
> > > same radial vertex position error in a smaller triangle creates a bigger
> > > error in the normal direction, hence the uneven look.
> > >
> > > Is this the result that is expected? and is there anything that I can do
> > > to improve the conformance of the triangulation points to the expected
> > > sphere function?  Am I missing a tolerance adjustment somewhere?
> > >
> > > It isn't a write precision/truncation problem, as I've set the precision
> > > of the ofstream to 15.
> > >
> > > Thanks,
> > >
> > > Graham
> > >
> > >
> > >
> > >
> > > ------------------------------------------------------------------------
> > >
> > >
> > > ------------------------------------------------------------------------
> > >       
>
>   

--
Mariette Yvinec
Geometrica project team
INRIA  Sophia-Antipolis