The area of rhumb polygons

Author:

Karney Charles F. F.

Abstract

AbstractThe formula for the area of a rhumb polygon, a polygon whose edges are rhumb lines on an ellipsoid of revolution, is derived and a method is given for computing the area accurately. This paper also points out that standard methods for computing rhumb lines give inaccurate results for nearly east- or west-going lines; this problem is remedied by the systematic use of divided differences.

Publisher

Springer Science and Business Media LLC

Reference16 articles.

1. Botnev V.A. and Ustinov S.M., 2014. Methods for direct and inverse geodesic problems solving with high precision (Metody resheniya pryamoy i obratnoy geodezicheskikh zadach s vysokoy tochnost’yu). St. Petersburg State Polytechnical University Journal 3(198), 49–58, https://infocom.spbstu.ru/en/article/2014.39.5/ (in Russian)

2. Clenshaw C.W., 1955. A note on the summation of Chebyshev series. Math. Comp., 9, 118–120, https://doi.org/10.1090/S0025-5718-1955-0071856-0

3. Danielsen J.S., 1989. The area under the geodesic. Surv. Rev., 30, 61–66, https://doi.org/10.1179/003962689791474267

4. Freire R.R. and de Vasconcello J.C.P., 2010. Geodetic or rhumb line polygon area calculation over the WGS-84 datum ellipsoid. In: XXIV FIG International Congress, https://www.fig.net/resources/proceedings/fig_proceedings/fig2010/papers/fs02c/fs02c_freire_vasconcellos_3868.pdf

5. Ivory J., 1798. A new series for the rectification of the ellipsis. Trans. Roy. Soc. Edinburgh, 4, 177–190, https://doi.org/10.1017/S0080456800030817

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