find the faces/points' ids on the convex hull of a polyhedron

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find the faces/points' ids on the convex hull of a polyhedron

Hello, I have a set of vertices from Polyhrdron_3, the vertices in Polyhedron
are indexed 0,1,...n using id().

Now, I want to find the vertices that are on the convex hull, and return
*the ids of those vertices*, or the best is to return the* ids of faces that
are on the 3D convex hull*.

Simple use of convex_hull_3(pts.begin(),pts.end(),sm) only gives the Point_3
with no id information, and using the convex points' coordinates to match
polyhedron face does not seems to be the right way.

I searched online to do convex hull algorithm with Point that has id, here
is what I found:
it create a new model of convex_hull_2_traits where it defined the new
Point_3 to be std::pair<K::Point_3,unsigned>. this way the id information is
stored in the pair. However, it's done for 2D convex hull algorithm.

I am following the method to create a convex_hull_3_traits, but failed. It
seems convex_hull_3_traits is much harder. I attached my code.

Please help, Thank you so much! convex_hull_3_traits.cpp

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