CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

I would recommand to use this package [1] which deals with degenerate 
cases. To build faces, I recommand to use a halfedge_data_structure
instead, as the arrangement is already encoded in the triangulation [2].

For clipping Voronoi bisectors, the intersection function between
an Iso_rectangle_2 and Line_2 or Segment_2 of Ray_2 objects [3].

Sebastien

[1] 
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Voronoi_diagram_2/Chapter_main.html
[2] 
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/HalfedgeDS/Chapter_main.html
[3]http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_23_ref/Function_intersection.html
On 10/24/2012 02:05 PM, Martin Uhrin wrote:
> Dear CGAL community,
>
> I'm using a Delaunay triangulation using vertices with info to 'tag'
> each vertex.  For neighbouring vertices with the same tag I would like
> to join the corresponding Voronoi faces.  Eventually I plan to bound the
> Voronoi diagram along the lines of this example:
>
> http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_2/Chapter_main.html#Subsection_37.5.4
>
> and extract the now bounded polygons corresponding to regions with the
> same tag.
>
> Currently my approach is roughly as follows:
>
> 1) Create triangulation, tagging each vertex
> 2) Create an Arrangement for each tag
> 3) Iterate over all (finite) Delaunay edges
> 4) if the two vertices of the edge do not share the same tag, insert the
> corresponding Voronoi halfedge into the arrangement for each of the two tags
> 5) Iterate over all arrangements extracting the edges to get the joined
> regions of the Voronoi for each tag
>
> My questions are:
>
> a) Is there any more intuitive a way to achieve my goals rather than
> using arrangements?
>
> b) Is there any way to get better performance?  I've had to use an
> Exact_predicates_exact_constructions_kernel because I was getting
> precondition failures with inexact when adding edges to arrangements but
> now this operation is very slow.
>
> c) When I finally add the boundary to the Voronoi resulting in
> (hopefully) there being only bounded polygons in the arrangements will I
> be able to extract these as polygon objects or do I have to somehow
> build the polygons myself?
>
> Many thanks for your help,
> -Maritn
>
> --
> Martin Uhrin                                                  Tel: +44
> 207 679 3466
> Department of Physics & Astronomy               Fax:+44 207 679 0595
> University College London 
>
> <mailto:>
> Gower St, London, WC1E 6BT, U.K. http://www.cmmp.ucl.ac.uk
> <http://www.cmmp.ucl.ac.uk/>