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This paper defines and discusses a set of rectangular all-sky projectionswhich have no singular points, notably the Tesselated Octahedral AdaptiveSpherical Transformation (or TOAST) developed initially for the WorldWideTelescope (WWT). These have proven to be useful as intermediate representationsfor imaging data where the application transforms dynamically from astandardized internal format to a specific format (projection, scaling,orientation, etc.) requested by the user. TOAST is strongly related to theHierarchical Triangular Mesh (HTM) pixelization and is particularly welladapted to the situations where one wishes to traverse a hierarchy ofincreasing resolution images. Since it can be recursively computed using a verysimple algorithm it is particularly adaptable to use by graphical processingunits.

Octahedron-Based Projections as Intermediate Representations for Computer Imaging: TOAST, TEA and More