I want to cover surface of earth with equal sized shapes and count number of points within each cell. shape of cell doesn't matters (triangle, hexagon ...), neither area, but equality of them is essential.

The problem is that I can not do this in a software like ArcGIS and need to calculate it using formula.

Here is what I am thinking:

  1. convert geographic coordinates into Cartesian coordinates,
  2. divide surface of the earth to equally distributed points
  3. round all points to nearest such point.

Problem is step 2. How to distribute points equally? Have any ideas?

  • How do you solve step 1? There is no worldwide cartesian coordinate system with true distance and area.
    – AndreJ
    Jul 24 '14 at 7:48
  • Well I do not need true distance, any R will work (6371 km, 2000 Km), as a only need to compare points within equally divided cells. Jul 24 '14 at 7:54
  • Do you truly need to do this or are you proposing this method as a density estimator (which seems much more likely)? If so, why not just run a kernel density calculation?
    – whuber
    Jul 24 '14 at 15:19

As you mention ArcGIS: You could create a fishnet (Note: the link is for ArcGIS 10.0) for your surface und use the resulting polygons to calculate the number of points inside them. Make sure to choose the right projection, as Andre Joost already pointed out. It sounds like you would need to choose an equal area projection.

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