This package includes four geodesic projections
* the azimuthal equidistant projection
* the Cassini-Soldner projection
* the transverse Mercator projection
* the ellipsoidal gnomonic projection
These improve upon the projections of the MATLAB mapping toolbox in the
* the azimuthal equidistant and gnomonic projections are generalized
to work with an ellipsoidal model of the earth;
* the domain of applicability of the transverse Mercator and
Cassini-Solder projections is greatly expanded.
The ellipsoidal gnomonic projection is an azimuthal projection about a
center point. All geodesics through the center point are projected into
straight lines with the correct azimuth relative to the center point.
In addition, all geodesics that pass close to the center point are very
nearly straight. It is derived in Section 8 of
C. F. F. Karney, Algorithms for geodesics,
J. Geodesy 87, 43-55 (2013);
The implementation of the transverse Mercator projection is based on
C. F. F. Karney, Transverse Mercator with an accuracy of a few
nanometers, J. Geodesy 85, 475-485 (2011);
The functions provided are EQDAZIM_FWD, EQDAZIM_INV, CASSINI_FWD,
CASSINI_INV, TRANMERC_FWD, TRANMERC_INV, GNOMONIC_FWD, GNOMONIC_INV,
The Cassini-Solder and transverse Mercator projections are useful for
large scale maps. The primary importance of the other two projections
is that they offer a convenient way of solving various geometrical
problems on the ellipsoid. In particular, the azimuthal equidistant
projection allows problems associated with determining maritime
boundaries to be solved easily. Similary the gnomonic projection allows
the intersection of two geodesics to be determined quickly.
This package depends on the MATLAB File Exchange package "Geodesics on
an ellipsoid of revolution" for performing the necessary geodesic
Use GEODPROJ to obtain a more detailed desciption.