2004/09/22 by Boudewijn F. Roukema, Roukema, Boudewijn F., Bartosz Lew +1
Computer Science · Physics and Astronomy · Social Sciences · #Astrophysics (astro-ph) #FOS: Physical sciences #Geochemistry and Geologic Mapping #Geographic Information Systems Studies #Image Retrieval and Classification Techniques #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0409533
5 pages, 4 figures
openalex publication_date 2004/09/22 · arxiv created 2004/11/10 · arxiv updated 2009/12/01 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28
Gorski et al (1999b) have earlier presented the outline of a\npixelisation-to-spherical-coordinate transformation scheme which simultaneously\nsatisfies three properties which are especially useful for rapid analyses of\nmaps on a sphere: (i) equal spacing of pixels along lines of constant latitude,\n(ii) equal pixel `areas' (solid angles) and (iii) hierarchical scaling with\nincreasing numbers of pixels. Their outline is based on the division of the\nsphere into twelve regions covering equal solid angles, which are\nhierarchically subdivided in a way compatible with these three criteria. In\nthis paper, a complete derivation of this scheme is presented, including, in\nparticular, (1) the angle theta^* defining the limit between polar and\nequatorial regions, and (2) the transformations from the unit interval [0,1]\n wedge [0,1] to spherical coordinates in a polar region.\n