CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

On 02/20/2012 06:44 PM, Dragan Vidovic wrote:
> Thank you for your answer Sebastien. I need a triangulation in order to use
> the query functions on a sphere. I need to find out if one point belongs to
> a triangle on the sphere, who's edges are arcs. Actually, I need this
> because I need to find out if a vector connecting that point to the centre
> of the sphere can be represented as a convex combination of vectors
> connecting the triangle vertices with the sphere centre. Moreover, I need to
> search such triangulation until I find a triangle (or a vector triplet) that
> satisfies this condition. The dynamic_hull_3.cpp code copies the boundary of
> a convex hull into a polyhedron, but none of these two structures seem to be
> searchable in this way. On the other hand, I'm not at all familiar with
> regular triangulations, but the paper that you mention seems like what I
> need. Before I dive into the world of regular triangulations, can you please
> confirm that such structure can be used for my search?
Using the regular triangulation should be working. The locate function
will give you the incident tetrahedron you want.To be on the safe side
I would recommend to make the query with a point slightly translated
inside the sphere (slightly depends on the approximation you have, but
radii/2 should be working).

Also to avoid degeneracies, insert the center of the sphere inside the 
triangulation.

> The paper mentions that CGAL needs to be modified in order to use the method
> proposed there. I suppose that these modifications are in the CGAL
> distribution by now?
Unfortunately not, still an experimental package.

Sebastien.

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