HEALPix
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HEALPix (sometimes written as Healpix) is an acronym for Hierarchical Equal Area isoLatitude Pixelization of a sphere.[1] It is a scheme for a spherical projection from the sphere to twelve squares on the Euclidean plane, followed by partitioning (or pixelizing) the twelve squares into a set of equal area pixels. The term HEALPix can be used either for the projection and pixelisation together as an algorithm,[2] or for a software package, of the same name, implementing the algorithm,[2] or in the term HEALPix projection for a class of spherical projections generalised from that used in physical cosmology maps of the cosmic microwave background.[3]
The spherical projection combines a cylindrical equal area projection for the equatorial regions of the sphere and a pseudocylindrical equal area projection, the Collignon projection, for the polar regions.
As the name indicates, at a given level in the hierarchy the pixels are of equal area (which is done by bisecting the square) and their centers lie on a discrete number of circles of latitude, with equal spacing on each circle. The pixels are four-sided and the vertices join four pixels, with the exception of eight vertices which join only three pixels, and the two vertices at the poles. The scheme has a number of mathematical properties which make it efficient for certain computations, e.g. spherical harmonic transforms. It has become widely used in cosmology for storing and manipulating maps of the cosmic microwave background.
An alternative hierarchical grid is the Hierarchical Triangular Mesh (HTM)[4]. The pixels at a given level in the hierarchy are of similar but not identical size. The scheme is good at representing complex shapes because the boundaries are all segments of great and small circles.
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[edit] References
- ^ HEALPix software site at JPL
- ^ a b Analysis Issues for Large CMB Data Sets, K.M. Gorski, E. Hivon, B.D. Wandelt, 1998
- ^ Mapping on the HEALPix grid, Calabretta, Roukema, 2005
- ^ [1]
