coordinate system - Learning about Reprojection?

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?

Answer

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.