Construction and computation of geometries on the ellipsoid

This article describes how to construct a wide range of geometry objects (called GeographicGeometry objects) in the coordinate system of an ellipsoid such as the Geographic coordinate system. Each construction process is formulated analytically and algorithmically using a combination of a set of fairly well-known mathematical methods such as ellipsoid geodesic construction functions, spherical trigonometry and iterative refinement methods. Each such geometry object may efficiently be converted to a corresponding Cartesian geometry object in any map projection coordinate system using an approximation algorithm. This property makes them particularly useful as a coordinate-system-independent geometry representation. A geographic geometry object is normally topologically equivalent to its Cartesian geometry counterpart except for some discontinuity and singularity cases.