# Computational Geometry – Voronoi Mesh Cell Count Is Too Low

I was trying to solve this issue out of interest and I thought that creating a mesh of Voronoi, cutting it into a circle and coloring the cells of the mesh could work. However, if I ask `VoronoiMesh` create cells for too many points `MeshCellCount[mesh, 2]` (or equivalent `Length @ MeshCells[mesh]`) it returns a number less than the number of points originally provided.

I've tried using different functions to generate the points around which the cells must be constructed, used both exact and real numbers and extracted documentation from `VoronoiMesh` and `MeshRegion`but I'm still not sure what causes it. Are my points just too close for `VoronoiMesh` to only determine a cell for some of them?

The simplest code that reproduces this is:

``````MeshCellCount[
VoronoiMesh[
2]
``````

which should return 36,000 since it is 100 radial points and 360 azimuth points, but instead returns 35,985. For this code, it seems to start when there are about 32,000 elements. If the radial points on the inside `Interval` are set to 87, I get the expected result. If the radial points are set to 88 (with the same 360 ​​azimuth points), I get an unexpected result. For all the small numbers, it seems to work as expected.

For some reason, if I use the following code to determine the number of cells, this difference appears at even smaller numbers of cells.

``````produce[i_] : =
Table[
{r Sin[[Theta]], r Cos[[Theta]]}
{[Theta]0, 359[Pi]/ 180, [Pi]/ 180},
{r, 1/2, (i - 1) + 1/2}
]66 * 360 - MeshCellCount[VoronoiMesh[Flatten[generate[66], 1]], 2]
``````

The result of this code is 2 and I suppose it is zero for all values ​​passed to `produce`.

Does anyone know what I'm doing wrong or if there is a workaround? Or am I just asking too much `VoronoiMesh`?