On Wednesday 23 July 2008 03:26:13

[hidden email] wrote:

> Hello,

>

> is it possible to use Regular_triangulation_3 instead of

> Delaunay_triangulation_3 in make_surface_mesh in order to perform Delaunay

> refinement using weighted points?

>

> Thank you!

Hi,

That is possible. The algorithm used by make_surface_mesh is not supposed to

handle with regular triangulations. However, a regular triangulation that has

all its points weights equal to zero is a delaunay triangulation. The

function make_surface_mesh can take use a CGAL::Regular_triangulation_3, but

there is one compilation error: the lack of the following constructor

CGAL::Weighted_point(FT x, FT y, FT z);

I have attached to this mail a modified example

examples/Surface_mesher/mesh_an_implicit_function.cpp. The solution used is

quite inelegant, but that is the easiest one without exposing too many

internal classes of Surface_mesher. I hope that can satisfy nevertheless.

Next release of CGAL should handle such a construction without any trick.

Be warned that all weights of your regular triangulation's vertices must be

equal to zero, so that the regular triangulation is actually a Delaunay

triangulation. Otherwise the algorithm is not guaranteed to finish correctly.

--

Laurent Rineau, PhD

Engineer at GeometryFactory

http://www.geometryfactory.com/--

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