Spherical Projections in WWT

WorldWide Telescope is a viewer for spheres. As a viewer zooms in the spheres are of ever increasing size and resolution. Sometimes, for panoramas and all-sky surveys – WorldWide Telescope renders the inside of a sphere. Other times, for the surfaces of planets and moons, it renders the outside of a sphere. WorldWide Telescope does not model the irregular shape of the Earth usually referred to as an oblate spheroid. The east-west diameter of the earth is 7,926 miles (or 12,756 kilometers), whereas the north-south diameter is slightly shorter at 7,901 miles (or 12,715 kilometers). The program treats the Earth, and other planets and moons, as perfect spheres.

The classic problem with mapping is obtaining a useful 2D flat image of a round 3D surface. There are several well known projection systems, the most popular are briefly discussed here, though all distort areas of the surface to a degree. Distortions which are acceptable to a mapping system designed to show the populated areas of the Earth, are much less acceptable if the object is to display the topography. In WorldWide Telescope the projection of flat images onto a sphere is done using a method called TOAST projection -- a projection system that does not prioritize one area of a sphere over another.

This document provides background information on the theory and practice of TOAST projection. Equirectangular, Mercator and Gnomonic maps can be converted to the TOAST format, and are discussed as source projections.