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I would like to expand my knowledge coordinate systems, projections and reprojecting data, with a view of writing a reprojection engine.

Could you provide me with some resources (books, websites, scrolls) on the maths behind coordinate systems and reprojecting data?

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The reference (in the US, at least) is John Snyder's Map Projections--A Working Manual. The entire monograph is available as a Google book.

Introductory sections give the theory. The theory is accessible to someone with a working knowledge of multivariate calculus. Emphasis is on documenting formulas, primarily series expansions needed for subsequent calculations. Detailed derivations of most formulas are not worked out. (Snyder was not a mathematician and became interested in projections only later in life. His emphasis--given this was written decades ago when one was lucky to have a Fortran compiler available and a few seconds of CPU time on the local mainframe--is on documenting formulas that could be converted to working code.)

The bulk of the book is devoted to describing 26 major projections organized by type: cylindrical, conic, azimuthal, "space map," pseudocylindrical, and miscellaneous.

Each description begins with a bulleted summary of properties and then about a page of historical information. Following this are a narrative of the features of the projection--including a detailed line drawing with a lat-lon graticule--formulas for the sphere (projection and unprojection), and formulas for the ellipsoid.

Appendices include extensive numerical examples of the calculations (108 pages!) and some US-specific information about USGS projections and the State Plane coordinate system.

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I had heard of this book about 6-7 years ago, and failed to get a copy. Thank you very much for the FREE version! I had a feeling you would come to my aid. I don't want to lessen the thank you - except now I'll have to brush up on my calculus ;) –  OptimizePrime Jun 5 '12 at 21:04
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For those that can't get the book from Google Books, you can also get it directly from USGS site. Click on the 'View Document' Link to get the book as a pdf –  Devdatta Tengshe Jun 6 '12 at 6:27
    
Thanks, @Devdatta: that really is the link I was looking for. I would expect it to have higher quality. –  whuber Jun 6 '12 at 14:30
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