# area of voronoi cell

I have a Voronoi diagram that I need to calculate the area of each cell.

This Voronoi diagram is produced by Voronoi command in MATLAB.

To find the vertices of the Voronoi cell I use Voronoin command in MATLAB, but the problem is that the first row of the v is (inf, inf), so the area of all voronoi cells near the boundary of domain are inf, but I need to find the actual area.

If the area of the domain be $|D|$ and area of the voronoi cells be $|D_i|$, I need to find area such that $\sum_i |D_i|=|D|$

• Can you give a concise example of the problem with a handful of points? It seems like you would need to choose a boundary to form the exterior of the region of interest, and if your data is a point cloud, that boundary is arbitrary. Once you have that boundary, you should be able to intersect the boundary Voronoi cells with it and compute their areas/volumes. – Bill Barth Jun 11 '14 at 0:54
• For example when the domain is a unit square, and the nodes are uniformly distribution by distance 0.1, most of the Voroni cells near the boundary are rectangle with area 0.005 – rosa Jun 11 '14 at 4:07
• How could I intersect the boundary Voronoi cells with the domain boundary? – rosa Jun 11 '14 at 4:20