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- W2023339961 abstract "This paper presents a new form of quartic equation based on Lagrange’s extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari’s line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments." @default.
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- W2023339961 date "2013-04-01" @default.
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- W2023339961 title "Explicitly computing geodetic coordinates from Cartesian coordinates" @default.
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- W2023339961 doi "https://doi.org/10.5047/eps.2012.09.009" @default.
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