CGAL users discussion list

[Peter Hachenberger <>]

Yes and No. As far as I know, we don't have a 3D counterpart of
Arrangement_2 and the 2D Counterpart of Nef_polyhedron_3 is
Nef_polyhedron_2. While Arrangement_2 is limited to regularized 
Boolean operations, Nef polyhedra are limited to linear geometry.
To phrase it positively, Arrangement_2 can handle planar curves, while
Nef polyhedra are closed under Boolean and topological operations and
can therefore handle lower-dimensional features, unbounded polyhedra,
open and closed boundaries.

Peter

On Fri, 2007-07-20 at 08:14 +0800, LoadCom wrote:
> Hello Peter,
> 
> That means Nef_polyhedron could be regarded as the 3D counterpart of
> Arrangement_2?
> 
> Thanks.
> 
> Max
> 
> 发件人：Peter Hachenberger
> 发送日期：2007-07-19 17:58:36
> 收件人：
> 抄送：
> 主题：Re: Re:[cgal-discuss] Location of point relative to polyhedron
> 
> A Nef_polyhedron is a decomposition of the 3-space into
> vertices, edges, facets, and volumes. That means, the outer volume is
> also modeled as a volume. You can distinguish the inner and outer volume
> by its mark. 
> 
> Volume_handle c;
> Object_handle o;
> o = myNef.locate(Point_3(5,3,2));
> if(assign(c, o))
>   if(c->mark())
>     std::cerr << "found inner volume" << std::endl;
>   else
>     std::cerr << "found outer volume" << std::endl;
> 
> 
> Peter
> 
> On Thu, 2007-07-19 at 07:29 +0200, Thomas Zangl - Home wrote:
> >  Am Wed, 18 Jul 2007 19:43:40 +0200, schrieb "Peter Hachenberger" 
> > <>:
> > >covert Polyedron_3 to Nef_polyedron_3
> > 
> > And how will myNefPolyhedron.locate(myPoint) work? The docs are a bit
> > unclear:
> > 
> > returns a generic handle to the object (vertex, edge, facet or volume) 
> > which contains the point p in its relative interior.
> > 
> > What if the point is not in the Polyhedron? Returns NULL? Please
> > elaborate! 
> > 
> > Thank you in advance,
> > -- 
> > ----------------------------------------------------------------
> > ,yours Thomas Zangl, Bakk.rer.soc.oec. - 
> > 
> >  -
> > - Freelancer - IT Consulting & Software Development -
> > - Student of Software Development-Economy (Master) -
> -- 
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