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3D Geodetic Inverse

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Geodetic forward and inverse computations are traditionally computed on the mathematical ellipsoid. Although software is readily available for those computations, the complexity of the geodetic equations can be intimidating. The 3D global spatial data model (GSDM) provides an alternate method for computing the inverse. Computations in this article start at a specified point and use numeric integration to establish the latitude and longitude of a second point—both on the ellipsoid. That means the geodesic distance is known and can be used to check the GSDM inverse accuracy. With the latitude and longitude of the endpoints known, the geocentric X/Y/Z coordinates of both points are computed and used to obtain the 3D spatial separation—that is, a chord distance. Standard chord/arc equations provide a circular arc distance between the points. For lines of “short” or “moderate” length, this arc distance very nearly approximates the known geodesic distance. A comparison of differences for various geodesic line lengths and configurations is provided. Values for the 3D azimuth are also compared with geodetic line azimuths computed using Clairaut's constant. Validity of the 3D geodetic inverse is established for short and medium length lines. Additional research is needed to establish a reasonable trade-off between possible accuracies for line lengths over about 50 km.
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Document Type: Review Article

Publication date: May 1, 2016

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