CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

Can't you use the Mesh_3 package and set a criteria on the size of the 
tetrahedron? The triangulation will not be a regular triangulation
(and not a Delaunay one).

https://doc.cgal.org/latest/Mesh_3

Sebastien.

On 07/16/2018 06:36 PM, Dahn wrote:
> I'd like to create a 3d Delaunay triangulation with a pre-specified
> circumradius bound. At first I thought a dense enough regular grid is a good
> solution, but due to either the perturbation of the grid points or floating
> point arithmetic (which is it?) this creates very large tetrahedra.
>
> Say I want to limit the circumradius to 0.1. With 6000 points, most
> tetrahedra indeed have a circumradius below 0.1. However, a few will have
> circumradii as large as 3. Increasing the number of points won't help, as it
> will only increase the size and number of the tetrahedra with large
> circumradii.
>
> #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
> #include <CGAL/Delaunay_triangulation_3.h>
> #include <CGAL/point_generators_3.h>                      
> #include <vector>
> #include <iostream>
>
> typedef CGAL::Exact_predicates_inexact_constructions_kernel     K;
> typedef K::Point_3                                              Point;
> typedef CGAL::Creator_uniform_3<double, Point>                    Creator;
> typedef std::vector<Point>                                        Vector;
> typedef CGAL::Delaunay_triangulation_3<K>                         Dt;
> typedef Dt::Tetrahedron                                         Tetrahedron;
>
> double circumradius( const Tetrahedron& t) {
>         return
> CGAL::sqrt(CGAL::squared_distance(CGAL::circumcenter(t),t.vertex(0)));
> }
>
>
> int main(){
>         int npts = 6000;
>         //// Create a vector of random points
>         Vector points;
>         CGAL::points_on_cube_grid_3( 1, npts, std::back_inserter(points), 
> Creator()
> );
>
>         //// Create a Delaunay triangulation from those points
>         Dt T;
>         T.insert(points.begin(),points.end());
>
>      /// Write out tetrahedron whose circumradii are too large
>         for (Dt::Finite_cells_iterator cell = T.finite_cells_begin(); cell !=
> T.finite_cells_end(); ++cell) {
>          double circum = circumradius(T.tetrahedron(cell));
>          if (circum > 0.1) {std::cout << circum << std::endl;}
>
>      }
> }
>
>
>
> Thank you for any help!
>
>
>
> --
> Sent from: http://cgal-discuss.949826.n4.nabble.com/