CGAL users discussion list

["Valdes, Julio" <>]

Hello Dr. Loriot:

Thank you very much for responding my email and for your valuable suggestions.
I shall follow your indications and see if I could produce an implementation 
of the solutions that you provided.
Once again, thank for your time and advice.
Best regards,
jjv

Julio J. Valdés
National Research Council Canada                                    | Conseil 
National de Recherches Canada 
Digital Technologies Research Centre                               | Centre 
de Recherche en Technologies Numériques
Data Science for Complex Systems Group                        | Science des 
Données pour les Systèmes Complexes
M-50, 1200 Montreal Road, Ottawa, Ontario K1A 0R6 | M-50, 1200 chemin 
Montréal, Ottawa, Ontario K1A 0R6 
Canada                                                                        
             | Canada 

tel/tél: (1)613-993-0257

-----Original Message-----
From: 

 
[mailto:]
 On Behalf Of Sebastien Loriot (GeometryFactory)
Sent: Monday, October 28, 2019 5:05 AM
To: 

Subject: Re: [cgal-discuss] a question about some basic algorithms

There might be a simpler and smarter way to do it but using the dD 
triangulation package:

https://doc.cgal.org/latest/Triangulation

You should be able to know if a point location using the locate function:
https://doc.cgal.org/latest/Triangulation/classCGAL_1_1Triangulation.html#af9ea0ceb6cc5c814e4ed63738396a6b6

For the distance to the convex hull, I would first build the triangulation, 
extract the vertices on the convex hull (which are the set of vertices 
incident to the infinite vertex) and build a triangulation out of those 
vertices.

Then doing locate queries, you will


Access the infinite_vertex() using:
https://doc.cgal.org/latest/Triangulation/classCGAL_1_1Triangulation.html#a44e3585e1b8fa31b718310a3f32a92af

Access dimension 1 incident cells (edges):
https://doc.cgal.org/latest/Triangulation/classTriangulationDataStructure.html#a9700c5ae4a6a2af65b002fb1057d47fa

Use the range of vertices in the cells (vertices_begin(),
vertices_end()) + to get the vertex of the edge that is not the infinite
one:
https://doc.cgal.org/latest/Triangulation/classTriangulationDataStructure_1_1FullCell.html


Note that Delaunay_triangulation inherits from Triangulation, that itself 
inherits from the TriangulationDataStructure. The doc of some methods are in 
the Triangulation or TriangulationDataStructure doc only.

Sebastien.

On 10/25/19 5:10 PM, Valdes, Julio wrote:
> Dear Sirs:
> 
> First of all thank you for the formidable effort that represents the work 
> around the CGAL library.
> I am not an expert in computational geometry, but I need to use some basic 
> algorithms and I have not been able to find my way through the 
> documentation.
> Please excuse me if my questions are too trivial for you.
> The algorithms that I am interested in are related to convex hulls (in d > 
> 3 dimensions):
> 1) distance from a point to a convex hull.
> 2) whether a point is inside/outside with respect to a given convex hull.
> 
> I would appreciate if you could direct me to the algorithms in CGAL that 
> approach the aforementioned problems.
> In case that there would not be available algorithms for the general case, 
> references to lower dimension versions would be also helpful.
> Any additional comments that you could provide, given your expertise in the 
> domain would be greatly appreciated.
> Sincerely
> 
> Julio J. Valdés
> National Research Council Canada                                    | 
> Conseil National de Recherches Canada
> Digital Technologies Research Centre                               | Centre 
> de Recherche en Technologies Numériques
> Data Science for Complex Systems Group                        | Science des 
> Données pour les Systèmes Complexes
> M-50, 1200 Montreal Road, Ottawa, Ontario K1A 0R6 | M-50, 1200 chemin 
> Montréal, Ottawa, Ontario K1A 0R6
> Canada                                                                      
>                | Canada
> 
> tel/tél: (1)613-993-0257
> 

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