2021
DOI: 10.1515/jogs-2020-0126
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Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates

Abstract: In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the… Show more

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Cited by 5 publications
(2 citation statements)
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“…According to the measured geometrical parameters of the Camellia oleifera flower, the Camellia oleifera flower of the "Sanhua" variety is ellipsoidal during the budding periodthe parameters are simplified for the theoretical calculation and analysis-and the Camellia oleifera flower is simplified to an ellipsoidal model [29,30]. A spatial coordinate system (Oxyz) is established, where the coordinate origin O coincides with the geometric center.…”
Section: Geometric Model Analysis Of Camellia Oleifera Flowersmentioning
confidence: 99%
“…According to the measured geometrical parameters of the Camellia oleifera flower, the Camellia oleifera flower of the "Sanhua" variety is ellipsoidal during the budding periodthe parameters are simplified for the theoretical calculation and analysis-and the Camellia oleifera flower is simplified to an ellipsoidal model [29,30]. A spatial coordinate system (Oxyz) is established, where the coordinate origin O coincides with the geometric center.…”
Section: Geometric Model Analysis Of Camellia Oleifera Flowersmentioning
confidence: 99%
“…rigorous computer methods which determine the quantitative characteristics of features with high accuracy with a practically infinite sum of members in the Taylor series [Karney, 2011;Pędzich & Kuźma, 2012;Karney, 2013;Huang, 2017;Berk & Ferlan, 2018;Setiawan & Sediyono, 2020;Baselga & Olsen, 2021;Marx, 2021;Panou & Korakitis 2021].…”
Section: Introductionmentioning
confidence: 99%