Geodesics on an ellipsoid of revolution

Abstract

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.

Algorithms for geodesics

“…Several other problems can be readily tackled with this library, e.g., solving other ellipsoidal trigonometry problems and finding the median line and other maritime boundaries. These and other problems are explored in Karney (2011). The web page http://geographiclib.sf.net/geod.html provides additional information, including the Maxima (2009) code used to carry out the Taylor expansions and a JavaScript implementation which allows geodesic problems to be solved on many portable devices.…”

“…( 56), the convergence cri-terion for Newton's method, how to minimize round-off errors in solving the trigonometry problems on the auxiliary sphere, rapidly computing intermediate points on a geodesic by using σ 12 as the metric, etc. I refer the reader to the implementations of the algorithms in GeographicLib (Karney, 2012) for possible ways to address these issues. The C++ implementation has been tested against a large set of geodesics for the WGS84 ellipsoid; this was generated by continuing the series expansions to O(f 30 ) and by solving the direct problem using with high-precision arithmetic.…”

Application of methods for area calculation of geodesic polygons on Polish administrative units

“…He also presented a direct method for numerical integration of the area under the geodesic line. Another solution was proposed by Karney (2011). He extended the method of Danielsen (1989) to higher order of series.…”

Short-Term Predictability of Extreme Rainfall Using Dual-Polarization Radar Measurements

“…To initiate the analysis, radar data expressed as radar-centered spherical coordinate were converted into geographic form as presented by Karney (2011). Non-meteorological data with correlation coefficients (ρ HV ) of below 0.8 and standard deviations of Ψ DP exceeding 4 • were removed (e.g., Ryzhkov and Zrnic 1998).…”