[GIS] Convert UTM to Web Mercator

coordinate systemutmweb-mappingweb-mercator

I'm looking to programmatically convert UTM to Web Mercator (a.k.a. Spherical Mercator, EPSG:3857, EPSG:3785, OpenLayers:900913). I'm looking for the algorithm, or something that runs on iOS (Swift, Objective-C or even C). The GDAL C library is not an option to due its huge size (this will be running on a mobile device).

Best Answer

GeographicLib is open source library with implementation in several languages:

C (geodesic routines): documentation, also included with recent versions of proj.4;
Fortran (geodesic routines): documentation;
Java (geodesic routines): Maven Central package, documentation;
JavaScript (geodesic routines): npm package, documentation;
Python (geodesic routines): PyPI package, documentation; Matlab/Octave (geodesic and some other routines): Matlab Central package, documentation;
C# (.NET wrapper for complete C++ library): documentation;
IDL (not part of GeographicLib): solving the inverse geodesic problem in IDL by Sean Elvidge and Chris Mannix;
C# (not part of GeographicLib): GeographicLib (C#) by Surya Pratap (the same capability is provided by the NETGeographicLib);
Mathematica (not part of GeographicLib): mathematica-geodesic by Kei Misawa.

Reference:
http://geographiclib.sourceforge.net/

Related Solutions

GDAL – How to Georeference Web Mercator Tile Correctly Using GDAL

The tile image is already in EPSG:3857. Why not just create a world file to reference it?

http://en.wikipedia.org/wiki/World_file

For the tile that covers N. America at zoom 1, you'd be looking at the following worldfile contents:

78271.517
0
0
-78271.517
-19998372.6
19998372.6

Where those numbers came from:

Line 1: width of an image pixel in world coordinates = 20037508.342789244 meters / 256 pixels.
Line 2 and 3: rotation, so n/a.
Line 4: height of an image pixel in world coordinates. Same as line 1 but negative, because in image files increasing y corresponds to 'down' while in the coordinate system, increasing y corresponds to 'up'.
Line 5: X coordinate in world coordinates of the center of the top-left pixel. This is -20037508.342789244, as reported by the tiles a la carte link, plus 1/2 of a pixel to bring it to the center.
Line 6: Ditto, only Y coordinate of the top left.

GDAL ought to pick up your worldfile (.pgw for the png); you'll still have to tell it EPSG:3857 on the command line.

(Note: didn't have time to test this, so it's all off the cuff... but hopefully correct on the first try anyway! ;)

[GIS] Spherical Mercator projection invented by Google and not conformal

The Mercator projection has been around for a few hundred years. I don't know when the ellipsoidal version of the algorithm came into being (I don't have my reference books at my current location), but certainly the spherical version is quite old. Both versions certainly pre-date the use for web-based map imagery. By ellipsoidal / spherical, I mean that the algorithm supports either an ellipsoidal or a spherical model of the Earth.

Google / Microsoft (and supposedly Yahoo) started using a spherical version of Mercator. For the spherical model of the Earth, they chose to use the semimajor axis of the WGS84/GRS80 ellipsoid, 6378137.0 meters, for the radius. This means that the sphere is much larger than the actual size of the Earth. There are many ways to calculate a sphere that's closer in size and/or shape to the Earth, but the radius value will be closer to 6371000 km.

There are ways to make a 'conformal' sphere from an ellipsoid (and some adjustments to the geodetic latitudes and longitudes), but that's not being done. Thus, the argument runs that the data in EPSG:3857 cannot be considered conformal.

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Related Solutions

GDAL – How to Georeference Web Mercator Tile Correctly Using GDAL

[GIS] Spherical Mercator projection invented by Google and not conformal

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