I wonder if there is any API I could query OSM data through, for example; Are (lon_1, lat_1) at land or at sea? Or could it be possible to get an island as a well-defined polygon? The only usage I've seen so far has just been tools for rendering OSM data (generating tiles).
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I've found a great API for reading Openstreetmap data; Mapscript. This is an interface to MapServer, which is able to read *.map and *.shp files. It is able to use a spatial index and is therefore potentially extremely fast. I've done random polygon lookups (checking if a polygon intersects land) of the world coastline shape file in 40 ms.
No one seems to have mentioned here the Leaflet API:
http://leafletjs.com/reference.html
Yes, there is an api and xapi (extended api).
I havent used these yet.
But there is also the cloudmade api to OSM. I played a bit with the python api.
I am not sure, if any of them could help you with your particular problem, but you could search for a coastline near to your point. If your point is within the polygon tagged natural=coastline, you have an island (or a continent)...
I have used CloudMade OSM extracts but had some problems with them. For example, Norway was clipped too tightly, causing some roads on the west coast to disappear.
I now prefer the overpass API.
Put something like this into the query form at http://www.overpass-api.de/query_form.html
Put the bounds of the area you want, in degrees, in the s, n, w and e attributes of the element.
how about http://wiki.openstreetmap.org/wiki/Nominatim? I had used this and setup my own server
Of course, the javascript api is called openlayers.