Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

This paper1 presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is reduced to finding a real positive root of a sixth degree poly...

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Bibliographic Details
Published in:Computers & geosciences Vol. 142; p. 104551
Main Authors: Diaz–Toca, Gema Maria, Marin, Leandro, Necula, Ioana
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2020
Subjects:
algorithms
Cartesian coordinates
computers
Coordinate transformation
equations
exhibitions
geodesy
Geodetic coordinates
geometry
rooting
roots
Symbolic-numerical computation
Triaxial ellipsoid
Triaxial ellipsoid
Symbolic-numerical computation
Coordinate transformation
Geodetic coordinates
Cartesian coordinates
ISSN:0098-3004, 1873-7803
Online Access:Get full text
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Summary:This paper1 presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is reduced to finding a real positive root of a sixth degree polynomial. The first approach consists of algebraic manipulations of the equations describing the geometry of the problem and the second one uses Gröbner bases. In order to perform numerical tests and accurately compare efficiency and reliability, our algorithms together with the iterative methods presented by M. Ligas (2012) and J. Feltens (2009) have been implemented in C++. The numerical tests have been accomplished by considering 10 celestial bodies, referenced in the available literature. The obtained results show that our algorithms improve the aforementioned, up-to-date reference, iterative methods, in terms of both efficiency and accuracy. •Direct transformation of Cartesian coordinates into geodetic coordinates.•Triaxial reference ellipsoid.•Symbolic-numerical algorithms based on computing unique real positive roots.•Uniqueness of the positive real roots proved by Descartes' rule.•Improving the existing approaches in terms of both efficiency and accuracy.
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ISSN:0098-3004
1873-7803
DOI:10.1016/j.cageo.2020.104551