CGAL users discussion list

["Laurent Rineau (GeometryFactory)" <>]

On Wednesday 07 October 2009 22:24:01 

 wrote:
> Hi.
> I'm just learning my way around CGAL 3.5-bet1 and I have been experimenting
> with the SurfaceMesher example.

Hi,

CGAL-3.5 is now released, since Monday. You can upgrade. However, as far as I 
know, nothing has been changed (by documentation details), in Surface_mesher. 
See the file CHANGES_from_CGAL-3.5-beta1 which is included in CGAL-3.5 finale 
tarball.

> I would like to work with an implicit representation that defines a surface
>  in terms of both the value of the function and its gradient (magnitude).
> 
> Reading the manual gave me the impression that it would be a 
>  straightforward matter to create a new model of ImplicitSurfaceTraits3 for
>  the SurfaceMesher to use my new oracle, but now that I have waded around
>  in the code a bit I don't quite see how to do it.
> 
> Is this in fact a simple thing to do and if so, would someone point me in
>  the correct direction to get started?

If you want to create a new model for the concept ImplicitSurfaceTraits_3, 
that deals with implicit representation, you can adapt the class template 
Implicit_surface_oracle_3 in 
<CGAL/Surface_mesher/Implicit_surface_oracle_3.h>.

That class is a model of ImplicitSurfaceTraits_3 that works by bissection: it 
assumes the object is fully contained in a given bounding sphere, and, once a 
query segment/ray/line is passed to the sub-functor Intersect_3, the query is 
clipped to the sphere, so that it is always a segment and, if the value of 
the 
function at the extremities of that segment are different, a bissection is 
done on that segment, to find compute an intersection point. The sub-functor 
Construct_initial_points uses Intersect_3 to find initial intersection 
points, 
by throwing random ray queries, until we get a given number of initial 
intersection points.

If you want to adapt that computation to use not only the values of the 
function but also the gradient, you should have a look at, and modify, the 
function Intersect_3::intersect_clipped_segment(...) of the sub-functor 
Intersect_3 of the traits class. That function member is the one that really 
does the bissection once the queries are clipped by the bounding sphere.

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