# What is the correct cartographic projection to calculate a Voronoi tesselation?

I have a set of points with known geographic coordinates. I would like to compute a Voronoi tesselation from these points in order to obtain areas of influence. The geometrical area of each Voronoi cell is then to be used to weight measurements obtained at each point.

Albeit area being my main interest, the computation of a Voronoi tesselation is a distance based algorithm. Considering that the set of points of interest cover about 5% of the Earth's surface, distances calculated in a, say, equiareal projection will incur in a relevant error. Conversely, if the option is to compute the Voronoi tesselation with an equidistant projection, the resulting areas will in their turn have relevant imprecisions.

The correct thing to do seems to be: calculate the tesselation with an equidistant projection, send the resulting cells back to the geographic domain, then re-project them with an equiareal projection and finally compute the areas. But this seems all too convoluted, would there be an alternative process of calculating such a Voronoi tesselation with precision?

Unfortunately the equidistant projection do not preserve the distance in all direction from all the points. If you are looking for a rigourous tessellation on a large area, I suggest that you create the Tessellation directly on the Earth surface. (This code could help, but I havn't tested. ) Then you make sure that you densify your lines, and you project your tessellation in an equal area projection for further analysis.

• Thanks for pointing to that software. Calculating distances on a spherical surface may impose larger errors - with the required datum shift - than a computation with an equidistant projection. Commented Aug 22, 2014 at 14:20