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Circle Approximations on Spheroids

Published online by Cambridge University Press:  12 September 2011

Young Joon Ahn ,
Jian Cui  and
Christoph Hoffmann
Young Joon Ahn*
Affiliation:
(Chosun University, South Korea)
Jian Cui
Affiliation:
(Purdue University, USA)
Christoph Hoffmann
Affiliation:
(Purdue University, USA)
*
(Email: [email protected])
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Abstract

We present an approximation method for geodesic circles on a spheroid. Our ap­proximation curve is the intersection of two spheroids whose axes are parallel, and it interpolates four points of the geodesic circle. Our approximation method has two merits. One is that the approximation curve can be obtained algebraically, and the other is that the approximation error is very small. For example, our approximation of a circle of radius 1000 km on the Earth has error 1·13 cm or less. We analyze the error of our approximation using the Hausdorff distance and confirm it by a geodesic distance computation.

Keywords

geodesic circlespheroidgeodesic distancegeodesic path
Type
Research Article
Information
The Journal of Navigation , Volume 64 , Issue 4 , October 2011 , pp. 739 - 749
Copyright
Copyright © The Royal Institute of Navigation 2011

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