octahedron based projections as intermediate representations for computer imaging toast tea and more

• DOI: 10.48550/arxiv.1812.03926
• Publication Date: 2019-01-29
• Authors: Thomas McGlynn; Jonathan Fay; Curtis Wong; Philip Rosenfield
• Keywords: 0103 physical sciences; FOS: Physical sciences; Astrophysics - Instrumentation and Methods for Astrophysics; Instrumentation and Methods for Astrophysics (astro-ph.IM); 01 natural sciences

Abstract This paper defines and discusses a set of rectangular all-sky projections that have no singular points, notably the Tesselated Octahedral Adaptive Spherical Transformation (or TOAST) developed initially for the WorldWide Telescope. These have proven to be useful as intermediate representations for imaging data where the application transforms dynamically from a standardized internal format to a specific format (projection, scaling, orientation, etc.) requested by the user. TOAST is strongly related to the Hierarchical Triangular Mesh pixelization and is particularly well adapted to situations where one wishes to traverse a hierarchy of images increasing in resolution. Because it can be recursively computed using a very simple algorithm it is particularly adaptable to use with graphical processing units.