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 expli...

The inverse transformation of coordinates, from Cartesian to curvilinear geodetic, or symbolically (x,y,z)-(l,j,h) has been extensively researched in the geodetic literature. However, published formulations require that the application must be deterministically implemented point-by-point individually. Recently, and thanks to GPS technology, scientists have made available thousands of determinat...

In the integration of geodetic networks with different geodetic coordinate systems, the similarity transformation seems to be the most suitable method because the geodetic coordinate systems are designated to be Cartesian (orthogonal). However, this method may always not be practical to use in most surveying works demanding such high accuracies as the coordinates used in the transformation are ...

In 1998 Land Information New Zealand introduced New Zealand Geodetic Datum 2000 (NZGD2000) as its new national datum. It is defined as a semi-dynamic datum and incorporates a national deformation model to ensure that the accuracy of the datum is maintained. The deformation model allows observations made at an epoch other than the datum reference epoch of 2000.0 to be modeled so that coordinates...