CGAL users discussion list

[Pratyush Pranav <>]

Hi Monique,

thanks for the mail. What you suggest sounds good below. Actually, outputting the convex hull as a polyhedron_3 would have made my life much simple. But i think there is a problem. I have additional information stored on the vertices of the triangulation. I guess when I output the convex hull as a polyhedron, i lose this additional information on the vertices?

I would “guess” the opposite, but in general I don’t trust guesses… I trust the manual better, and/or results of experiments. 

While going through the manual, I ahvent encountered the possibility of deriving polyhedron_3 from vertex_with_info_3. As far as I understand, it is only possible to derive the triangulation class from the base class of vertex with info. Any additional cues would be helpful.

I guess i could circumvent this problem if I can also inherit the polyhedron from the vertex_base_with_if_3 class ( the name of the class is not accurate probably, i am spewing it out of my mind). Do you think it is possible to inherit poly from vertex with info? I am sorry, it has been many years since i touched CGAL, and i am on a bit of shaky ground here.

Alternatively, if this is not possible,

to be checked

I guess I can work with the original triangulation by restricting myself to the simplifies on the convex hull only. I think, for this i need to devise a function that checks if a particular simplex is on the convex hull or not. I write below my idea of how to check if a particular simplex is on the hull.

— for a vertex it is trivial, because by design they are al on the surface of the sphere (or do i need additional checks?)

you can check if it is incident to the infinite vertex

can a vertex itself be incident to the infinite vertex? i "guess" again it has to be through a cell or a facet or an edge, isnt it? i wonder what i am missing here.

— for an edge, i plan to circulate over all the incident facets, and if one of the facet is an infinite facet, the edge must be on the convex hull (?)

yes (provided that this edge is not itself infinite, of course)

yes, for this i intend to iterate over only the finite edges of the triangulation.

— i am not sure how to check this for facets. For a particular facet, i could again check for all the edges that constitute it, and look if they are on the convex hull. if all the edges of the facet are on the hull, the facet must be on the hull?

Similar. If the facet is not infinite, and if one of its incident cells is infinite, then the facet is on the convex hull. 

I maybe wrong, but i was not able to find if it is possible to directly access the incident cells to a facet. hence i was going through the route of the "checking the edges of the facets". could you please confirm if it is indeed a possiblitiy to access the cells incident to a facet directly?

pratyush