# Algorithms for geodesics

```@article{Karney2012AlgorithmsFG,
title={Algorithms for geodesics},
author={Charles F. F. Karney},
journal={Journal of Geodesy},
year={2012},
volume={87},
pages={43-55}
}```
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of geodesics to be computed.
208 Citations
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• Computer Science
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• 2019
This work experimentally studies the accuracy-performance trade-offs of various methods for some basic geodesic problems and can be used as a reference for practitioners that want to use the most efficient method with respect to some given accuracy.
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Geomorphometry on the surface of a triaxial ellipsoid: towards the solution of the problem
• I. Florinsky
• Mathematics, Geology
Int. J. Geogr. Inf. Sci.
• 2018
This article presents analytical and computational solutions, which provide the basis for geomorphometric modelling on the surface of a triaxial ellipsoid, and describes easy-to-code algorithms for derivation of local and non-local morphometric variables from DEMs based on a spheroidal equal angular grid of a three-dimensional ellipSOid.

## References

SHOWING 1-10 OF 30 REFERENCES
Geodesics on an ellipsoid of revolution
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
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 reduce
F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements
• Mathematics
• 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 linked
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 and
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 geodesic
THE CENTRAL PROJECTION OF THE SPHEROID AND SURFACE LINES
AbstractThe gnomonic (central) projection for a sphere is well known ([2] page 596). It has the characteristic that great circles project into straight lines, so that the shortest distance on the
Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen
• Mathematics
• 1825
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is a transcription of F. W. Bessel, Astronomische
Map Projections: A Reference Manual
• Mathematics
• 1995
1.Introduction 2. General Theory of Map Projections 3. Map Projections with Straight Parallels 4. Map Projections with Parallels in the Shape of Concentric Circles 5. Map Projections with Parallels
NIST Handbook of Mathematical Functions
• Mathematics
• 2010
This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.
A Computer Algebra System
Risa/Asir consists of the Risa engine for performing operations on mathematical objects and an interpreter for programs written in the Asir user language. In Risa/Asir, polynomials are represented in