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. 
Numerical determination of the geodesic curves: the solution of a two-point boundary value problem
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
An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere
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 inverseExpand
An approximation of geodesic circle passing through three points on an ellipsoid
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
GEODESIC ALGORITHMS: AN EXPERIMENTAL STUDY
  • 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
TLDR
It is concluded that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished. Expand
Offset approximation of polygons on an ellipsoid
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
TLDR
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
TLDR
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
TLDR
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
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 22 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 terrestrialExpand
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
F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements
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
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 theExpand
Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen
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, AstronomischeExpand
Map Projections: A Reference Manual
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 ParallelsExpand
NIST Handbook of Mathematical Functions
TLDR
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. Expand
Geometric geodesy, part II
  • Tech rep, Ohio State University
  • 1993
...
1
2
3
...