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I'm trying to write some code that, given a latitude and longitude, will report which ocean (if any) this point is in.

Is there a public resource available that defines the borders of the oceans as a set of lat/long points that I can download?

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This question is I think a bit different from the other one. The resources pointed to in the accepted answer has just two polygons, one for the Caspian Sea and one for the rest of the world, whereas @Dancrumb wants to know which body of water a given point lies in, e.g. North Atlantic, Bering Sea, etc. –  MerseyViking Jan 4 '12 at 18:10
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2 Answers

ESRI's Ocean Basemap might be useful for your task:

http://www.arcgis.com/home/item.html?id=6348e67824504fc9a62976434bf0d8d5

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Ocean polygons available here:

http://www.naturalearthdata.com/downloads/10m-physical-vectors/

or

http://www.naturalearthdata.com/downloads/50m-physical-vectors/

Different resolutions. You can open the shapefiles in QGis and save as any format you want [assuming you're writing a browser based app].

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