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Geodesics on an ellipsoid of revolution

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Geodesics on an ellipsoid of revolution

by Charles Karney

 

20 Nov 2012 (Updated 16 Jan 2013)

Solutions of the direct and inverse geodesic problems

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Description

This package includes three routines GEODDISTANCE, GEODRECKON, and
GEODAREA which solve various problems involving geodesics on the surface
of an ellipsoid of revolution. These are based on the paper

  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

which, in turn, is based on the classic solution of the geodesic
problems pioneered by Legendre (1806), Bessel (1825), and Helmert
(1880).

GEODRECKON solves the direct geodesic problem (determining an end point
given a starting point, range, and bearing). GEODDISTANCE solves the
inverse geodesic problem (determining the shortest distance between two
points). GEODAREA determines the area of a polygon whose edges are
geodesics.

  * The routines are accurate to round off for abs(f) < 1/50. For
    example, for the WGS84 ellipsoid, the error in the distance returned
    by GEODDISTANCE is less then 15 nanometers.
  * The routines work for prolate (as well as oblate) ellipsoids.
  * GEODDISTANCE converges for all inputs.
  * Differential and integral properties of the geodesics are computed.
  * GEODAREA is accurate regardless of the length of the edges of the
    polygon.

Also provided are 3 auxiliary routines, DEFAULTELLIPSOID, ECC2FLAT, and
FLAT2ECC.

Use GEODDOC to obtain a more detailed desciption.

MATLAB release MATLAB 7.11.1 (R2010bSP1)
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area(2), distance(2), earth, ellipsoid, geodesic, geodesy, wgs84
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Comments and Ratings (1)
03 Feb 2013 littyer

nice

Updates
03 Dec 2012

Synchronize files with GeographicLib 1.27.

11 Dec 2012

Update to GeographicLib 1.28. Fixes 2 bugs: (1) incorrect area returned in certain obscure cases; (2) m12 incorrect for meridional geodesics.

16 Jan 2013

Update journal reference.

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