2020
DOI: 10.1515/jag-2019-0066
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The direct geodesic problem and an approximate analytical solution in Cartesian coordinates on a triaxial ellipsoid

Abstract: In this work, the direct geodesic problem in Cartesian coordinates on a triaxial ellipsoid is solved by an approximate analytical method. The parametric coordinates are used and the parametric to Cartesian coordinates conversion and vice versa are presented. The geodesic equations on a triaxial ellipsoid in Cartesian coordinates are solved using a Taylor series expansion. The solution provides the Cartesian coordinates and the angle between the line of constant v and the geodesic at the end point. An extensive… Show more

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Cited by 6 publications
(3 citation statements)
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“…In order to verify the effectiveness of the algorithm, this paper selects the multi-focus image fusion (NPF) algorithm based on NSCT and pulse coupled neural network (PCNN) [25], the surface wavelet transform (SCT) [26], and the multi-focus image fusion (FGF) algorithm based on fast finite shear wave transform and guided filtering [27] for comparison. Average gradient (AG), spatial frequency (SF), mutual information MI, and edge-preserving information transfer factor QAB/F (high weight evaluation standard) were used for objective evaluation [28,29].…”
Section: Resultsmentioning
confidence: 99%
“…In order to verify the effectiveness of the algorithm, this paper selects the multi-focus image fusion (NPF) algorithm based on NSCT and pulse coupled neural network (PCNN) [25], the surface wavelet transform (SCT) [26], and the multi-focus image fusion (FGF) algorithm based on fast finite shear wave transform and guided filtering [27] for comparison. Average gradient (AG), spatial frequency (SF), mutual information MI, and edge-preserving information transfer factor QAB/F (high weight evaluation standard) were used for objective evaluation [28,29].…”
Section: Resultsmentioning
confidence: 99%
“…In order to verify the effectiveness of the algorithm, this paper selects the multi focus image fusion (NPF) algorithm based on NSCT and pulse coupled neural network (PCNN) [25], the surface wavelet transform (SCT) [26] and the multi focus image fusion (FGF) algorithm based on fast finite shear wave transform and guided filtering [27] for comparison. Average gradient (AG), spatial frequency (SF), mutual information MI and edge preserving information transfer factor QAB/F (high weight evaluation standard) were used for objective evaluation [29][30].…”
Section: Resultsmentioning
confidence: 99%
“…This particular note has remained unpublished since 2007 (available only my website), however it has received several citations (e.g. [1,2,3]). As a result, it now appears on ArXiv for future reference.…”
mentioning
confidence: 99%