Corpus ID: 117929179

# Geodesics on an ellipsoid of revolution

```@article{Karney2011GeodesicsOA,
title={Geodesics on an ellipsoid of revolution},
author={Charles F. F. Karney},
journal={arXiv: Geophysics},
year={2011}
}```
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems involving geodesics (triangulation, projections, maritime boundaries, and polygonal areas) are investigated.

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#### References

SHOWING 1-10 OF 66 REFERENCES
The computation of long geodesics on the ellipsoid through Gaussian quadrature
Formulas for computing geodesics on the bi-axial ellipsoid through Gaussian quadrature are shown; the estimation of computational errors, truncation and roundoff errors, for the quadrature is carriedExpand
Intersections on the sphere and ellipsoid
Abstract. The problems of intersection on the sphere and ellipsoid are studied. On the sphere, the problem of intersection along great circles is explicitly solved. On the ellipsoid, each of theExpand
DIRECT AND INVERSE SOLUTIONS OF GEODESICS ON THE ELLIPSOID WITH APPLICATION OF NESTED EQUATIONS
AbstractThis paper gives compact formulae for the direct and inverse solutions of geodesics of any length. Existing formulae have been recast for efficient programming to conserve space and reduceExpand
Determination of areas on the plane, sphere and ellipsoid
Abstract This paper shortly reviews various methods to determine the area of a closed polygon on the plane, sphere and ellipsoid. A new method is derived for calculating the area of a geodeticExpand
Total Inverse Solutions for the Geodesic and Great Elliptic.
AbstractThe inverse problem for all possible geodesics on the spheroid is solved in ways that are selected by the programme in a manner appropriate to any two given end positions. The comparatively...
AREA COMPUTATION OF A POLYGON ON AN ELLIPSOID
AbstractA method has been developed for the area computation of a polygon on an ellipsoid. The sides of this polygon may be geodetic lines, loxodromes, great circles or a combination of these lines.
The computation of long geodesics on the ellipsoid by non-series expanding procedure
In this paper the author shows a procedure to settle the computation of very long geodesic lines on the ellipsoid without using the series expansion. The integration of elliptic integrals appearingExpand
F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements
• Mathematics, Physics
• 2010
First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linkedExpand
Direct transformation from geocentric coordinates to geodetic coordinates
Abstract. The transformation from geocentric coordinates to geodetic coordinates is usually carried out by iteration. A closed-form algebraic method is proposed, valid at any point on the globe andExpand
Gnomonic Projection of the Surface of an Ellipsoid
When a surface is mapped onto a plane so that the image of a geodesic arc is a straight line on the plane then the mapping is known as a geodesic mapping. It is only possible to perform a geodesicExpand