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[cgal-discuss] Counting vertices, edges, and cells in 3D Delaunay triangulation


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  • From: Adam Getchell <>
  • To:
  • Subject: [cgal-discuss] Counting vertices, edges, and cells in 3D Delaunay triangulation
  • Date: Tue, 29 Apr 2014 03:44:54 -0700

And in particular, this function:

template <typename T>
void make_S3_simplicial_complex(T* S3, int number_of_simplices, int number_of_timeslices) {
  // Start with a 3D sphere with two simplices
  S3->insert(typename T::Point(0,0,0));
  S3->insert(typename T::Point(1, 0, 0));
  S3->insert(typename T::Point(0, 1, 0));
  S3->insert(typename T::Point(0, 0, 1));
  //S3->insert(typename T::Point(0, 0, -1));
  // /In 3D with an infinite point we'll get 4 vertices, 10 edges
  /// 10 facets and 5 cells. The point at $\infty$ isn't counted
  /// but the edges, facets, and cells generated by it are

  assert(S3->dimension() == 3);

  std::cout  << "Initial seed has " << S3->number_of_vertices()
        << " vertices and "
        << S3->number_of_edges() << " edges and "
        << S3->number_of_facets() << " facets"
        << " and " << S3->number_of_cells() << " cells" << std::endl;

  assert(S3->dimension() == 3);
  assert(S3->is_valid());
}

I will get counts of edges, facets, and cells that represent the ones generated by the infinite 5th point of the 3D simplex. Is this correct behavior, and if so, what should I do to get the correct count of edges, facets, and cells?

Thanks for any pointers,

--
Adam Getchell
"Invincibility is in oneself, vulnerability in the opponent." -- Sun Tzu



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