CGAL users discussion list

[Bernhard Kornberger <>]

Am 2010-12-02 00:45, schrieb randooom:
> Hi and thanks for your reply.
>
> I know about the duality of vd and dt, but I don't see how I could achieve
> what I want, without extracting the vd first.
>
> Basically I need to calculate the volume, the width and the surface of all
> Voronoi cells.
> I don't know how I would be able to get this directly out of the duality
> without extraction.
>
> If you know a way, I'm eager to know it, because that would save me the work
> and the program memory :)


As your input is small, you can use this simple solution
for the volume:

a) Extract the tetrahedra incident to a certain vertex of the
triangulation using incident_cells(..).
b) Compute their dual Voronoi vertices
c) Triangulate the Voronoi vertices and sum up the volumes
of the tetrahedra. (remember, a Voronoi cell is convex)

As to the width: You have the Voronoi vertices of the cell.

As to the surface: You can use the vertices to build a polyhedron
and iterate over its triangles. Alternatively, you can get a
Voronoi facet by iterating over the triangulation cells incident
to an edge and taking their dual Voronoi vertices.

Best
Bernhard








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