[OSM-dev] Good explanation of latitude-to-pixel conversion?

David MENTRE dmentre at linux-france.org
Sat May 17 16:11:19 BST 2008


> On Sat, May 17, 2008 at 2:29 PM, Nick Whitelegg
> <Nick.Whitelegg at solent.ac.uk> wrote:
>> I have the code to do this, but I guess I'm one of these people that like
>> to understand what's actually going on :-)

You are not the only one. I followed the same path (pun intended) a few
weeks ago.

>> The specific formula I mean (represented in Java) is:
>> public static int latToY(double lat,int zoom)
>> {
>>                double f = Math.sin((Math.PI/180)*lat);
>>                int y = (int)Math.round
>>                        (Math.pow(2,zoom+7) + 0.5*Math.log((1+f)/(1-f)) *
>> (-Math.pow(2,zoom+8)/(2*Math.PI)));
>>                return y;
>> }

The code you give is to translate a (lat, zoom) to x coordinate, you
have a more direct formula applying the Mercator projection to the lat

In the above page, it helps to know that r_minor and r_major are Earth
Equatorial and Polar radii[1].

The original post helps to understand why taking into account the
variation of radius was necessary:

"OJ W" <ojwlists at googlemail.com> writes:

> e.g. wikipedia will tell you all about how mercator itself works:
> http://en.wikipedia.org/wiki/Mercator_projection

This is a very useful page.

> and for the tiles, alll you do is say "select the bit of
> mercator-projected map between two arbitrary latitudes (which happen
> to be numerically special but you don't need to care about that) and
> call that range the limits of your map in Y.
> you then just start dividing Y into halves and quarters etc. to do the tiles.

In fact, I found explanation in
http://wiki.openstreetmap.org/index.php/Slippy_map_tilenames sufficient
after thinking a little about it.

I hope it helps,

[1]  http://en.wikipedia.org/wiki/Earth

GPG/PGP key: A3AD7A2A David MENTRE <dmentre at linux-france.org>
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