CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

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
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