WMTS : Convert geolocation (lat, long) to tile index, at a given zoom level?

Question

I wanted to know how to get the indexes (x,y) of a WMTS tile for a given geolocation (latitude, longitude) and zoom level.

For exemple, I have a POI located at (48.675, 2.7), I want to get the corresponding open-street-map tile for the zoom 10.

Can I do the math ? Do I need a webservice ? Precision : I have to do this programmatically.

Here you go: http://wiki.openstreetmap.org/wiki/Slippy_map_tilenames#Lon..2Flat._to_tile_numbers_2 — John Powell, Feb 06 '15 at 08:38
A useful MSDN Article on the Bing Maps Tiling Scheme also provides a good primer. Both this and the OSM article assume Web Mercator projection, but the principle is the same for other projected co-ordinate systems. — kes, Feb 06 '15 at 14:48

score 39 · Accepted Answer · edited Oct 03 '18 at 23:36

39

Here is the extracted answer (in pseudo code) for quick reference.

Given Longitude/latitude/zoom to tile numbers :

n = 2 ^ zoom
xtile = n * ((lon_deg + 180) / 360)
ytile = n * (1 - (log(tan(lat_rad) + sec(lat_rad)) / π)) / 2

Note that log() in this pseudo code refers to natural log (often "ln()" in common math syntax, but often "log()" in many programming languages).

Given Tile numbers to longitude/latitude :

n = 2 ^ zoom
lon_deg = xtile / n * 360.0 - 180.0
lat_rad = arctan(sinh(π * (1 - 2 * ytile / n)))
lat_deg = lat_rad * 180.0 / π

edited Oct 03 '18 at 23:36

ak112358

answered Feb 07 '15 at 17:26

Neekobus

2

wait, the OSM slippy format is the WMTS tile format? – spy Dec 15 '16 at 01:52
10

Note that the link above has implementations in many languages! (27 currently) – Cyrille Mar 13 '17 at 10:40
1

Be aware that according to this link , latitude goes from 0 to 85.0511 °N (not 90 °N) and from 0 to 85.0511 °S (not 90 °S). The number 85.0511 is the result of arctan(sinh(π)). By using this bound, the entire map becomes a (very large) square – AmirHossein Rezaei Jan 31 '21 at 11:06

1 Answers1