CGAL users discussion list

[Andreas Fabri <>]

Hello,

CGAL should offe the feature to triangulate the faces of a
Polyhedron. It's on my todo list.

As it currently doesn't, the easiest solution would probably be to
triangulate a face with a Constrained_triangulation
and split the polyhedron faces along edges of the triangulation.

andreas



FEYEL Frederic. wrote:
> Hello,
>
> I made several experiments around your suggestions.
>
> First of all, I really had to use an extended precision kernel,
> otherwise all creation of the second
> nef fail (this is normal, since it describes a thin structure).
>
> Both the constructor (from a Polyhedron) and the OFF_to_nef_3 work.
>
> On my problems, the computation of the substraction (N2-N1) is
> reasonably fast. The creation
> of the Nefs from the Polyhedrons using the constructor is much faster
> that the OFF_to_nef_3 (of course,
> the limitation are more restrictive using the constructor).
>
> So I would say that in my case, the bottleneck is not the boolean
> operation itself, but clearly the
> creation of the Nefs.
>
> Now, I want to mesh the surface of the resulting Nef. I transformed it
> back to a Polyhedron.
>
> I had a look at the mesher class, and a solution would perhaps to define
> an implicit surface (and mesh
> the 0 isovalue) by computing the signed distance (using a projection
> operator) of any point to the polyhedron.
>
> It seems however a little bit complex.
>
> Do you have any ideas to change my Polyhedron so that it contains only
> triangles (and not general N-nodes faces) ?
>
> Thank you for everything !
>
>
>
>
>
>
> Peter Hachenberger a écrit :
> > Hi Frederic,
> >
> > your files do not work for two reasons:
> >
> > 1. If you use the homogeneous kernel and load double coordinates, the
> > coordinates will all be rounded to integers. 
> >
> > 2. We only convert Polyhedron_3 to Nef_polyhedron_3, if the former is a
> > 2-manifold, but your second file consists of several facets, if I see
> > correctly. 
> >
> > You can do the following:
> >
> > - You can try the Kernels Cartesian<Gmpq> and Simple_cartesian<Gmpq>.
> > Unfortunatly, Nef_3 is quite slow in combination with cartesian kernels
> > at the moment. In the next release we will change that. 
> >
> > - You can try the function OFF_to_nef_3 (see documentation). This
> > converter can handle nearly every off file, i.e., it handles double
> > coordinate, wrong orientations, several surfaces with boundary, self
> > intersecting surfaces, etc. Because of it's versatility, this function
> > is not very fast.
> >
> > - We provide further undocumented constructors. Try
> > Polygon_constructor.h for your second file. The usage is shown in
> > examples/Nef_3/polygon_construction.h.
> >
> > -  I just wrote new I/O routines and can now convert coordinates. If I
> > find time, I send you a small program that converts off files with
> > doubles into our nef3 file format with homogeneous integer coordinates
> > as long as the off file is a 2-manifold.
> >
> > Peter
> >
> >