Voronoi 2D from hexagonal grid

Hi,

So I wanted to create a voronoi with various density which is based on the brightness/darkness of an image. So far I have manage to do it with a definition that I'm not sure is the easiest way to do or not and there are still some problems I can't seem to fix.

The voronoi achieved is too stiff, some of the boxes are squares, I think this is due to the distributions of the point?, so I was thinking if I started of with a hexagonal grid it would help? Is there any other way?

Also in the end, I would like to convert this pattern onto a paper cut therefor I would like to make an offset of the varanoi which is round and smooth, any suggestions?

Many thanks in advance!