CGAL users discussion list

[Olivier Devillers <>]

Your problem is highly degenerate, if the points are all on the unit
sphere, ANY triangulation of the convex hull is Delaunay.

Thus what you get using 3D triangulation is just the convex hull
plus a random triangulation (probably depending on how the points
are wrt the sphere since due to rounding errors they are not
exactly on the sphere).


Since you are anyway working in a parameterization of the sphere,
my advice is to work directly in 2D with Delaunay_triangulation_2
but for a non euclidean metric, that is from the metric on the sphere
that you send in 2D by the parameterization.

For that you have to derived a new geometric traits class for triangulation
that change the in circle test and orientation test and give it to the 
2D triangulation.

Triangulation_euclidean_traits_xy_3 is an example of such a traits class
chapter 25.5.2 to see how to use it
and source file Triangulation_euclidean_traits_xy_3.h could be a 
starting point
to write your personnal traits class.

Olivier