# 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.
172 Citations

#### Paper Mentions

Numerical determination of the geodesic curves: the solution of a two-point boundary value problem
• Mathematics
• 2018
In this paper, we suggest a simple iterative method to find the geodesic path on a surface parameterized byorthogonal curvilinear system between two given points based on solving Boundary ValueExpand
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• Mathematics
• Journal of Applied Geodesy
• 2019
Abstract In this paper we present an approximation method for a geodesic circle passing through three points on an oblate ellipsoid. Our method uses a prolate ellipsoid passing through the threeExpand
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• Vissarion Fisikopoulos
• Mathematics
• ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
• 2019
Abstract. The figure of the Earth can be modelled either by a cartesian plane, a sphere or an (oblate) ellipsoid, in decreasing order with respect to the approximation quality. Based on those models,Expand
Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid
• Mathematics, Computer Science
• ArXiv
• 2016
It is concluded that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished. Expand
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• Acta Geodaetica et Geophysica
• 2021
We present an approximation method for offset curves of polygons on an oblate ellipsoid using implicit algebraic surfaces. The polygon on the ellipsoid is given by a set of vertices, i.e. points onExpand
Multiscale NURBS curves on the sphere and ellipsoid
• Computer Science, Mathematics
• Comput. Graph.
• 2019
A framework that allows NURBS subdivision curves to be defined on the sphere and ellipsoid in a multiscale manner is introduced via modification of a repeated invertible averaging framework for spherical B-Spline curves, which is constructed in terms of spherical linear interpolations. Expand
Geomorphometry on the surface of a triaxial ellipsoid: towards the solution of the problem
• I. Florinsky
• Geology, Computer Science
• 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. Expand
Application of Global Route-Planning Algorithms with Geodesy
• Computer Science
• ArXiv
• 2016
This work presents a novel simulator for GRPA, which compares and evaluates three GRPAs implemented to solve the shortest path problem for points located at different cities: A*, LPA*, and D*Lite. Expand
AN ALGORITHM FOR THE INVERSE SOLUTION OF GEODESIC SAILING WITHOUT AUXILIARY SPHERE – PUBLISHER'S NOTICE
It has been brought to the attention of the publishers that certain sections of Tseng (2014) are remarkably similar to parts of Karney (2013) and have not been adequately attributed. In addition,Expand