Ellipsoidal area computations of large terrestrial objects

Ellipsoidal area computations of large terrestrial objects

Hrvoje Lukatela

Geodyssey Limited

Calgary, Alberta

Link to full paper

The mathematics of area computation on the ellipsoidal planetary surface is straightforward; it is however rarely implemented in its rigorous form. Traditional systems dealing with small two dimensional objects - for instance land parcels in a cadastral registry - treat the area not as a simple derivative of the object definition geometry, but rather as an artifact of it representation in a particular planar representation. This approach fails when no single, canonical planar representation is either practical or desirable, or when the objects exceed the useful planar coverage of the projection.

The Hipparchus geopositioning model represents two dimensional terrestrial objects in context of an irregular spheroidal tessellation. This paper outlines the strategy used by the area computation for such objects. It assumes that the computational efficiency is as important as the precision, and that the objects can be of any size, shape and topological complexity. As a numerical and timing example, the paper presents the computation of the area of world oceanic coverage, as represented by the DCW product.