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Paper: The Quadrilateralized Spherical Cube and Quad-Tree For All Sky Data
Volume: 25, Astronomical Data Analysis Software and Systems I
Page: 379
Authors: White, Richard A.; Stemwedel, Sally W.
Abstract: The quadrilateralized spherical cube (Chan & O'Neill 1975 and O'Neill & Laubscher 1976) is a geometrical projection well suited for mapping all sky data, as well as to the use of the quad-tree nearest neighbor (rather than rasterized) storage scheme for the the archiving and retrieval of data. The celestial sphere is projected onto the six faces of a cube in a tangent plane projection. The lines of latitude and longitude on each face are then curved such that, when the cube face is divided into equally spaced rows and columns of pixels, each pixel is equal in area on the sky to every other pixel. The maps thus preserve photometric integrity. The changes in lines of latitude and longitude result in only minimal distortion of the shape of objects on a single face. The quad-tree pixel numbering scheme, being hierarchical, permits arbitrarily high resolution and allows comparison of maps at differing resolutions in a particularly elegant and straight forward manner. We present the basic geometry of the quadrilateralized spherical cube, the form of the quad-tree structure, and suggest FITS structures and keywords for use in displaying, storing, and transporting data in this form.
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