Construction and computation of geometries on the ellipsoid

Abstract

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.

Keywords:

• GIS
• geometry
• construction
• ellipsoid
• approximation

Acknowledgements

The author thanks Kjetil Reiten Myhra of Kongsberg Defence & Aerospace by for allowing the publication of results from an internal development project, and also for allowing the inclusion of examples derived from screenshots from live and deployed applications. Several colleagues have made valuable contributions in discussions during the development, testing and deployment phase of this project. I am particularly appreciative for the helpful comments of Dr. Tor Lønnestad, and our discussions connected to several draft versions of the paper.