Direct transformation from geocentric coordinates to geodetic coordinates

By H. Vermeille. 2002

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Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm (2012, background): “Transformation of the geocentric cartesian coordinates (X, Y, Z) into geodetic coordinates (j, l, h) or vice versa is necessary for solution of many aerospace, geodetic, cartographical, geo-astronomical and horizontal datum problems (Torge, 2001; Vanieek and Krakiwsky, 1986; Vermeille, 2011; Li et a”
Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley’s Method (2006, methodology): “Other methods have been proposed (Lin and Wang 1995; Pollard 2002; Jones 2002; Vermeille 2002, 2004 ).”
Algorithms for geodesics (2011, methodology): “This root can be found by standard methods (Olver et al. , 2010, § 1.11(iii)). to geodetic Equation (55) arises in converting from geocentric co-ordinates, and I use the solution to that problem given by Vermeille (2002).”
Conversion between Cartesian and geodetic coordinates on a rotational ellipsoid by solving a system of nonlinear equations (2011, background): “…(1) (Heiskanen and Moritz, 1967); introducing additional parameters, e.g. parametric latitude (Borkowski, 1987, 1989; Fukushima, 1999, 2006; Vermeille, 2002, 2004), minimizing the distance between a point in space and its projection on the ellipsoid (Hedgley, 1976) as well as vector…”