ORTHOGONAL DISTANCE FROM AN ELLIPSOID

Abstract

Finding the orthogonal (shortest) distance to an ellipsoid corresponds to the
ellipsoidal height in Geodesy. Despite that the commonly used Earth reference
systems, like WGS-84, are based on rotational ellipsoids, there have also been over
the course of the years permanent scientific investigations undertaken into different
aspects of the triaxial ellipsoid. Geodetic research has traditionally been motivated
by the need to approximate closer and closer the physical reality. Several
investigations have shown that the earth is approximated better by a triaxial
ellipsoid rather than a rotational one Burša and Šima (1980). The problem of finding
the shortest distance is encountered frequently in the Cartesian- Geodetic coordinate
transformation, optimization problem, fitting ellipsoid, image processing, face
recognition, computer games, and so on. We have chosen a triaxial ellipsoid for the
reason that it possesess a general surface. Thus, the minimum distance from
rotational ellipsoid and sphere is found with the same algorithm. This study deals
with the computation of the shortest distance from a point to a triaxial ellipsoid.