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

Young Joon Ahn; Christoph Hoffmann

doi:10.1515/jag-2019-0018

Article

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

Young Joon Ahn and Christoph Hoffmann

Published/Copyright: July 31, 2019

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From the journal Journal of Applied Geodesy Volume 13 Issue 4

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 points, and the new approximation curve is the intersection of the oblate and prolate ellipsoids, which can be obtained algebraically without iterations. The advantage of our approximation method is that it yields a significantly smaller approximation error. Compared to the plane section curve passing through the three points on the oblate ellipse, our method reduces the approximation error by at least 98% when the radii of geodesic circles are 100 km∼1000 km on the surface of the Earth. We illustrate the results using numerical examples.

Keywords: geodesic circle; approximation error; oblate ellipsoid; plane section curve; implicit algebraic surface

Funding source: National Research Foundation of Korea

Award Identifier / Grant number: NRF-2017R1D1A1B03032504

Funding source: National Science Foundation

Award Identifier / Grant number: CMMI – 1361783

Funding statement: The first author’s work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03032504). The second author’s work was supported in part by the National Science Foundation under contract CMMI – 1361783.

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Received: 2019-05-05

Accepted: 2019-07-14

Published Online: 2019-07-31

Published in Print: 2019-10-25

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Articles in the same Issue

https://doi.org/10.1515/jag-2019-0018

Keywords for this article

geodesic circle; approximation error; oblate ellipsoid; plane section curve; implicit algebraic surface