CGAL users discussion list

[Sebastien Loriot <>]

Using the figure 31.1 on the page
http://www.cgal.org/Manual/3.4/doc_html/cgal_manual/Triangulation_3/Chapter_main.html
should give you the solution as all tetrahedra are oriented the same way.



On Saturday 07 February 2009 01:38:49 am avanindra wrote:
> Hi Sebastian,
>
> Thanks for the reply. Actually, I was talking about 3D convex hulls. The
> Dynamic convex hull construction given in cgal solved my problem.
>
> I need one more solution regarding convex hull only. Now suppose that I
> pick any point(say P) on the Delaunay triangulation, which is a
> point(finite) of infinite cell. I need to calculate average of outward
> normals of all the hull faces meeting at this particular point(P).
>
> The cells are oriented, but it still I believe, does not give outward
> normal in all the cases because cells are oriented with respect to their
> adjacent cells. Many time just taking cross product of sides in the
> orientation gives normal inward the hull. (I am saying this, because I
> displayed the triangulation of implicit surface mesher by calculating
> normals by taking cross product of sides of triangle in the relative
> orientation and I found a large chunk of displayed surface was having
> inward normals).
>
> If anyhow I can get a unit vector or Ray in the direction of the infinite
> point of cell with respect to the finite points of cell, It would resolve
> my problem. I am still searching out Delaunay triangulation reference
> manual to accomplish it.
>
> Please throw light on it.
>
> Thanks
> Avanindra
>
>
>
> -----Original Message-----
> From: Sebastien Loriot 
> [mailto:]>
>  Sent: 
Wednesday, February 04, 2009 4:30 PM
> To: 
> 
> Subject: Re: [cgal-discuss] A point not on convex hull
>
> On Wednesday 04 February 2009 11:38:11 am 
> 
>  wrote:
> > Hi All,
> >
> > I need to find a particular point from a sample of points of which I made
> > convex hull, is on the convex hull or not. I am not finding any
> > particular function for it in manual.
> >
> > Please give right direction, how to do it. I created ch_object of n
>
> points,
>
> > now I don't know which points were involved in making the hull and which
> > were excluded.
> >
> > Thanks
> > Avanindra
>
> Hello,
>
>
> From the manual page
> http://www.cgal.org/Manual/3.4/doc_html/cgal_manual/Convex_hull_2/Chapter_m
>a in.html#Section_11.3
> You can find one example of how to construct the convex hull of a set of
> points. Instead of using the standard input and output like in the example,
> you can use lists or another container.
> Indeed, following the link behind CGAL::ch_graham_andrew, we can see that
> the
> third parameter of CGAL::ch_graham_andrew is an OutputIterator which gives
> you the list of points on the convex hull. A simple equality test then
> solves
> your problem.
>
>
> Another solution is to use the triangulation_2 and the vertices incident to
> the infinite vertex.
>
>
> Sebastien.
> --
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