Cover earth surface with square tiles

I would like to find an efficient method to cover the surface of the earth with square tiles of rough size 1 square mile. Things to note:

(1) The tiles must be square

(2) The tiles must all be the same size in terms of their area, and somewhere in the region of 1 square mile.

(3) It is OK if we end up with a fraction of a square that is not covered by any tile, but it is not OK for any given location on the earth to belong to more than 1 tile.

Thanks very much.

[John D'Errico]

First, how is this a question about MATLAB?

Second, you do recognize this is provably impossible to accomplish a perfect such tiling? And if the tiling is imperfect, then you will need some sort of an optimization, involving how to tradeoff the errors made.

Given that it is not possible to do perfectly, you would need to find some sub-optimal methiod, since an optimal tiling would be a massive task, given the millions of such tiles necessary. A quick check tells me there would be roughly 197 million tiles needed, since the surface area of the earth is roughly 197 million square miles.

Is it vaguely possible you will be overtaxing your capabilities in this? Perhaps you are trying to solve some problem in the wrong way. Such brute force schemes are rarely a good idea. And given there will be errors in your tiling, are you sure this will be worth the incredibly massive effort it would take to work with the immense data structure that will be involved?

I'm sorry, but I think you have not clearly thought out what is involved here.

[I-J]

I understand that this kind of scheme will lead to distortion (both in the sense of overlapping 'squares' and in the sense of slivers which are not covered by any tile). I also understand that any process to accomplish this would necessarily be algorithmic. I was simply trying to see if this type of problem had been encountered/dealt with my someone in the past so I could benefit from their work.

[Torsten]

May I ask what you are aiming at with this covering problem ?

[I-J]

I'm trying to solve a problem where data that is tied to a specific lat+long needs to be aggregated into a geographic region and compared with similar data somewhere else on the globe, that has also been similarly aggregated into a geographic region of the same size (so the comparison is meaningful).

Thus the problem is - before any of this aggregation can be done, there needs to be a way to divide the earth's surface into small geographic regions of the same size. I'm saying square-mile squares simply because that shape is much easier to deal with in numerous ways, and the size is fine-grained enough given the earth's size, that the comparisons become useful.

[Walter Roberson]

Which geoid are you using? WGS-84 ? Or can the Earth be approximated as a sphere for your purposes?

[I-J]

WGS-84 would be quite appropriate. However I guess the problem transcends the issue of geoid....the first question to be answered is, high to algorithmically deal with the 'lots of little square-ish tiles on a sphere(oid)' problem.

[I-J]

Sorry, that's 'how to', not 'high to'...:)

Answer 1

[Sam Chak]

Hi @I-J

Your question is actually unclear. What do you mean by "the efficient method to cover the surface"? Are you looking for the MATLAB code to create a 3D surface plot of Earth covered by the tiny square tiles?

I'm unsure, but I think this is the basic formula to estimate the approximate number of square tiles required to "cover" the entire Earth surface:

.

After conversion, it is 197,000,000 square miles. That means 197 millions square tiles are required.

[I-J]

I was simply trying to see if this type of problem had been encountered/dealt with by someone in the past, so I could benefit from their work.