Shall we project the points on the sphere before inserting them?

[stla]

Hello,

In this example, the points are projected on the sphere before inserting them in the Delaunay triangulation. Isn't it automatic when we use Projection_on_sphere_traits_3? I mean does the insertion performs the projection when we use this class?

[MaelRL]

The Construct_point_on_sphere_2 of that traits does not project points on the sphere, but merely caches a scaling factor, see: https://github.com/CGAL/cgal/blob/master/Triangulation_on_sphere_2/include/CGAL/Projection_on_sphere_traits_3.h#L157.

The name is somewhat confusing, that's true.

[stla]

Aahh ok now I understand why I got this strange Delaunay ball with my implementation:

The vertices have not been projected as I believed!

[MaelRL]

You can call get_projection() on the objects of type Point_on_sphere_2

[stla]

Are you sure? I don't find this function in the doc, nor with Google.

[MaelRL]

It's an internal function: https://github.com/CGAL/cgal/blob/master/Triangulation_on_sphere_2/include/CGAL/Projection_on_sphere_traits_3.h#L53

[stla]

Ok I get it:

  ......
  Traits ball(SPoint3(O(0), O(1), O(2)), radius);
  // projection on this ball
  Traits::Construct_point_on_sphere_2 projection =
    ball.construct_point_on_sphere_2_object();
  // Rcpp matrix to store the projected vertices
  Rcpp::NumericMatrix Vertices(3, npoints);
  // make Delaunay triangulation
  DToS dtos(ball);
  {
    int i = 0;
    for(const auto& pt : points) {
      Traits::Point_on_sphere_2 pos = projection(pt);
      DToS::Vertex_handle vh = dtos.insert(pos);
      SPoint3 p = projection(pos).get_projection(ball.center(), ball.radius());
      ......

Thanks!

[stla]

ah wait, I don't need projection a second time, surely