# 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

Theory, strict formula derivation and algorithm development for the computation of a geodesic polygon area

- MathematicsJournal of Geodesy
- 2022

The paper presents a coherent, original theory and an effective algorithm to calculate the surface area of a geodesic polygon, i.e. the area on an ellipsoid of revolution limited by geodesics,…

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 Value…

An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere

- MathematicsJournal of Navigation
- 2014

An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse…

An approximation of geodesic circle passing through three points on an ellipsoid

- MathematicsJournal 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 three…

GEODESIC ALGORITHMS: AN EXPERIMENTAL STUDY

- Computer ScienceISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
- 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.

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

- MathematicsArXiv
- 2016

It is concluded that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

Offset approximation of polygons on an ellipsoid

- Geology, MathematicsActa 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 on…

EARTH SECTION PATHS. SOLUTION TO THE INVERSE AND DIRECT PROBLEMS, AND WAYPOINTS WITHOUT ITERATIONS

- GeologyGeodesy and cartography
- 2022

The use of central elliptical sections in the calculation of air and sea routes and normal sections in Geodesy is common. Elliptic sections do not represent the shortest path between two points,…

Geomorphometry on the surface of a triaxial ellipsoid: towards the solution of the problem

- Mathematics, GeologyInt. 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.

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