Surface Area of Voronoi-Tesseled Ellipsoid.

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Surface Area of Voronoi-Tesseled Ellipsoid.

matheus_viana
Hi Guys.

I've implemented a Voronoi Tesselation over a ellipsoid surface, and the result can be seen in the enclosed figure. Now, I'd like to calculate the surface area of each one of these regions. Do you guys have any idea how to tackle this?

Thanks in advance,
Matheus
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Re: Surface Area of Voronoi-Tesseled Ellipsoid.

Alex Malyushytskyy
Does it mean you have triangulated polygon?
Then area of polygon(s) is a sum of area of triangles.

Alex

On Tue, Feb 12, 2013 at 9:18 AM, matheus_viana <[hidden email]> wrote:

> Hi Guys.
>
> I've implemented a Voronoi Tesselation over a ellipsoid surface, and the
> result can be seen in the enclosed figure. Now, I'd like to calculate the
> surface area of each one of these regions. Do you guys have any idea how to
> tackle this?
>
> Thanks in advance,
> Matheus
> <http://vtk.1045678.n5.nabble.com/file/n5718462/VoronoiEllipsoid.png>
>
>
>
> --
> View this message in context: http://vtk.1045678.n5.nabble.com/Surface-Area-of-Voronoi-Tesseled-Ellipsoid-tp5718462.html
> Sent from the VTK - Users mailing list archive at Nabble.com.
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Re: Surface Area of Voronoi-Tesseled Ellipsoid.

matheus_viana
Hi Alex. Thanks for replaying.

Yes, I have triangles, and then I used the method vtkTriangles::TrangleArea(x1,x2,x3) to obtain the area of each polygon. Of course there is a little error in the area of each region, since some triangles are share by more than one region, but the accuracy can be improved by increasing the ellipsoid resolution.

-m