I want to make a hexbin map of a particular kind. Hexbins can be used to embrace several points in the same area, like in this example :

Hexbins 1

With this method, a large city can be covered by one hexagon, and several smaller cities can be covered by the same area. But that's not what I'm trying to do.

In fact, I would do my hexbin map with a file of cities in a French district, with adjoining hexagons and one hexagon for one city, without any empty space between hexagons.

The problem is that in this case, every point must be at the same distance from the others. So my issue is that I'm wondering if it's posible to tidy up with QGis a file with polygons' centroids like this into a file with equidistant points:

enter image description here

How can I transform a file with points to obtain a regular pattern without empty spaces, like this example of South China Morning Post ?

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    Welcome to GIS SE. As a new user, please take the Tour. Most questions on whether something is "possible" are too easily answered with an "of course", without any useful detail. Please edit the question to include graphics, specify the GIS software you are using, and your initial attempt to solve the problem. A subset of the ASCII coordinate contents would be necessary if you want anyone to try your code and improve upon it. – Vince Jun 11 '16 at 18:41
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    hexbins are usually defined by a polygon area, so you might turn your 'District' polygon into hexbins, then you would sample an underlying point dataset such as the one you have shown and give those values to the hexbins... – DPSSpatial Jun 11 '16 at 19:32
  • Thanks for your comments, I edited my question once again ! Hope it's more clear now. – Raphadasilva Jun 12 '16 at 18:34
  • It is still unclear to me what you want to do. Do you want a) to move your points to the center of hexbins in order to have a regular pattern b) to minimize the distance between your points and the centroid of hexbins c) remove (or aggregate) points that fall in the same hexbin in order to have maximum one point per hexbin d) find the minimum hexbin size to have a single point per hexbin e) something else ? – radouxju Jun 13 '16 at 10:16
  • Hi radouxju ! Can now put more than two links in my post (Allelujah), so I edited it once again ! – Raphadasilva Jun 14 '16 at 11:54