Direct symbolic transformation from 3D cartesian into hyperboloidal coordinates

Diaz–Toca, Gema M.; Necula, Ioana

doi:10.1016/j.amc.2013.11.099

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Cited by 3 publications

(2 citation statements)

References 7 publications

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“…From the geometric and algebraic points of view, both problems are closely related. This problem hasn't been tackled before and furthermore there are very few approaches for the biaxial case (see (Díaz-Toca and Necula, 2014) for a closed form solution and (Feltens, 2011) for a iterative solution).…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

Diaz–Toca

Marín

Necula

2020

Computers & Geosciences

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Section: Conclusion and Further Workmentioning

confidence: 99%

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

Diaz–Toca

Marín

Necula

2020

Computers & Geosciences

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“…From the geometric and algebraic points of view, both problems are closely related. This problem hasn't been tackled before and furthermore there are very few approaches for the biaxial case (see [8] for a closed form solution and [12] for a iterative solution).…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

Diaz-Toca,

Marin,

Necula

2019

Preprint

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This paper 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 clearly show that our algorithms improve the aforementioned iterative methods, in terms of both efficiency and accuracy.

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Copyright protection method for 3D model of geological body based on digital watermarking technology

Zhang

Shen

2019

Journal of Visual Communication and Image Representation

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Direct symbolic transformation from 3D cartesian into hyperboloidal coordinates

Cited by 3 publications

References 7 publications

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

Copyright protection method for 3D model of geological body based on digital watermarking technology

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