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Fig. 1

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HEALPix tessellation of the sphere. Each of the four orthographic projections of the sphere shown here display the twelve base resolution HEALPix quadrilaterals shaded with different grey levels. The left most frame shows how the HEALPix tessellation relates to a generic spherical longitude and latitude coordinate system. The second, third, and forth spheres to the right are overlaid with HEALPix grids of orders k = 0, 1, 2 respectively, to illustrate the hierarchical structure of HEALPix where each pixel is divided into four self-similar pixels at each successive order.

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