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Geodesic projections for an ellipsoid

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Geodesic projections for an ellipsoid

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07 Dec 2012 (Updated )

Four map projections based on geodesics

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Description

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
following respects:

  * 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);
  http://dx.doi.org/10.1007/s00190-012-0578-z
  Addenda: http://geographiclib.sf.net/geod-addenda.html

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);
  Addenda: http://geographiclib.sf.net/tm-addenda.html

The functions provided are EQDAZIM_FWD, EQDAZIM_INV, CASSINI_FWD,
CASSINI_INV, TRANMERC_FWD, TRANMERC_INV, GNOMONIC_FWD, GNOMONIC_INV,
UTM_FWD, UTM_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
computations:

  http://www.mathworks.com/matlabcentral/fileexchange/39108

Use GEODPROJ to obtain a more detailed desciption.

Acknowledgements

Geodesics On An Ellipsoid Of Revolution inspired this file.

MATLAB release MATLAB 7.11.1 (R2010bSP1)
Other requirements http://www.mathworks.com/matlabcentral/fileexchange/39108
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Comments and Ratings (2)
13 Jan 2014 Peter Manley-Cooke

After downloading the earlier submission by this author (as indicated at the bottom of the description), this program provides instant answers. Well Done.

13 Jan 2014 Peter Manley-Cooke

Line one of the Description should contain the information that the mapping toolbox is required for this submission.

Updates
14 Dec 2012

Update to GeographicLib 1.28. Includes minor documentation fixes.

16 Jan 2013

Update journal reference.

02 Jul 2013

Add "acknowledgement" style reference to 39108.

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