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98:. This pixelisation can be thought of as mapping the sphere to twelve square facets (diamonds) on the plane followed by the binary division of these facets into pixels, though it can be derived without using the projection. The associated software package HEALPix implements the algorithm. The HEALPix projection (as a general class of spherical projections) is represented by the keyword
32:
90:. Any of these can be followed by partitioning (pixelising) the resulting region of the 2-plane. In particular, when one of these projections (the H=4, K=3 HEALPix projection) is followed by a pixelisation of the 2-plane, the result is generally known as the HEALPix pixelisation, which is widely used in
144:. In the case of the H=4, K=3 projection, the pixels are squares in the plane (which can be inversely projected back to quadrilaterals with non-geodesic sides on the 2-sphere) and every vertex joins four pixels, with the exception of eight vertices which each join only three pixels.
147:
The latitude of transition between equatorial-orthogonal and polar-convergent longitude lines has been selected to allow the folding of the projection into a perfect cube — "cubing the sphere"; indeed in this way the Arctic Circle becomes a square.
136:
in the case of the H=4, K=3 projection) and their centers lie on a discrete number of circles of latitude, with equal spacing on each circle. The scheme has a number of mathematical properties which make it efficient for certain computations, e.g.
450:
Górski, Krzysztof M.; Hivon, Éric; Banday, Anthony J.; Hansen, Frode K.; Wandelt, Benjamin D.; Reinecke, M.; Bartelmann, M. (2005). "HEALPix: A Framework for High-Resolution
Discretization and Fast Analysis of Data Distributed on the Sphere".
511:
173:(HTM). 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
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70:. The pixelisation algorithm was devised in 1997 by Krzysztof M. GĂłrski at the Theoretical Astrophysics Center in Copenhagen, Denmark, and first published as a preprint in 1998.
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used by HEALPix and its subdivision of the sphere, in four different grid refinements. Notice the similarity between the coarsest grid and the
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323:. Proceedings of the MAP/ESO Cosmology Conference 'Evolution of Large-Scale Structure'. Netherlands: PrintPartners Ipskamp. p. 37.
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Roukema, Boudewijn F.; Lew, Bartosz (2004-09-22). "A Solution to the
Isolatitude, Equi-area, Hierarchical Pixel-Coordinate System".
357:
Górski, Krzysztof M.; Wandelt, Benjamin D.; Hansen, Frode K.; Hivon, Éric; Banday, Anthony J. (1999-05-21). "The HEALPix Primer".
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The pixelisation related to the H=4, K=3 projection has become widely used in cosmology for storing and manipulating maps of the
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standard for writing astronomical data files. It was approved as part of the official FITS World
Coordinate System (WCS) by the
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Górski, Krzysztof M.; Hivon, Éric; Wandelt, Benjamin D. (1999). "Analysis Issues for Large CMB Data Sets".
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50:(sometimes written as Healpix), an acronym for Hierarchical Equal Area isoLatitude Pixelisation of a 2-
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with many languages support (C, C++, Fortran90, IDL, Java and Python) for resolutions up to 0.4 mas (
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The 12 "base resolution pixels" of H=4, K=3 HEALPix projection may be thought of as the facets of a
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Szalay, Alex; Jim Gray; Gyorgy Fekete; Peter Kunszt; Peter Kukol; Ani Thakar (September 2005).
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At a given level in the hierarchy the pixels are of equal area (which is done by bisecting the
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is a general class of spherical projections, sharing several key properties, which map the 2-
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of original
Fortran code by Nikolay Kuropatkin, supporting resolutions up to 0.3 arcsec
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380:"A Solution to the Isolatitude, Equi-area, Hierarchical Pixel-Coordinate System"
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The H=6 HEALPix has similarities to another alternative grid based on the
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537:"Gaia Data Release 1: Datamodel description Documentation release 1.2"
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23:
HEALPix H=4, K=3 projection of the world. The lines on the map are a
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321:
Evolution of Large Scale
Structure: From Recombination to Garching
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689:: convert between lonlat and HEALPix coordinates in JavaScript
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583:"Indexing the Sphere with the Hierarchical Triangular Mesh"
695:: An implementation of HEALPix in JavaScript / TypeScript
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optimized to use RangeSet, very good for high resolutions
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uses HEALPix as the basis for source identification.
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of the 2-sphere based on subdivision of a distorted
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561:"SkyServer.org - HTM: Hierarchical Triangular Mesh"
241:Calabretta, Mark R.; Roukema, Boudewijn F. (2007).
378:Roukema, Boudewijn F.; Lew, Bartosz (2004-09-08).
121:, for the equatorial regions of the sphere and a
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177:. Another alternative hierarchical grid is the
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8:
683:: c++ code to transform healpix coordinates
16:Pseudocylindrical equal-area map projection
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119:Lambert cylindrical equal-area projection
169:An alternative hierarchical grid is the
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626:"Welcome to the icosahedron home page"
125:equal area projection, an interrupted
110:FITS Working Group on April 26, 2006.
7:
508:"FITS World Coordinate System (WCS)"
113:The spherical projection combines a
701:: Healpix library written in Julia
677:: BSD-licensed HEALPix for Astropy
14:
1755:Quadrilateralized spherical cube
1435:Quadrilateralized spherical cube
274:10.1111/j.1365-2966.2007.12297.x
179:Quadrilateralized Spherical Cube
108:International Astronomical Union
518:from the original on 2019-08-04
408:from the original on 2019-08-04
1344:Lambert cylindrical equal-area
289:"HEALPix Background - History"
66:, and the associated class of
1:
1792:Interruption (map projection)
243:"Mapping on the HEALPix grid"
1430:Lambert azimuthal equal-area
1226:Guyou hemisphere-in-a-square
1216:Adams hemisphere-in-a-square
171:Hierarchical Triangular Mesh
27:of latitudes and longitudes.
158:cosmic microwave background
117:equal area projection, the
96:cosmic microwave background
74:Projection and pixelisation
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563:. SkyServer. June 6, 2006
129:, for the polar regions.
1231:Lambert conformal conic
647:Official implementation
257:Oxford University Press
205:List of map projections
1364:Tobler hyperelliptical
977:Tobler hyperelliptical
903:Space-oblique Mercator
152:Usage and alternatives
44:
28:
454:Astrophysical Journal
175:circles of the sphere
34:
22:
1740:Cahill–Keyes M-shape
1600:Chamberlin trimetric
293:healpix.jpl.nasa.gov
186:rhombic dodecahedron
127:Collignon projection
64:rhombic dodecahedron
41:rhombic dodecahedron
1807:Tissot's indicatrix
1708:Central cylindrical
1349:Smyth equal-surface
1251:Transverse Mercator
1100:General perspective
855:Smyth equal-surface
807:Transverse Mercator
605:2007cs........1164S
477:2005ApJ...622..759G
402:2004astro.ph..9533R
339:1999elss.conf...37G
265:2007MNRAS.381..865C
1760:Waterman butterfly
1610:Miller cylindrical
1241:Peirce quincuncial
1136:Lambert equal-area
888:Gall stereographic
693:Typescript healpix
587:Microsoft Research
506:Pence, William D.
139:spherical harmonic
92:physical cosmology
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957:Equal Earth
840:Gall–Peters
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681:healpix.cxx
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259:: 865–872.
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1592:Compromise
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1278:Sinusoidal
1261:Equal-area
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610:2007-02-05
596:cs/0701164
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522:2007-01-09
412:2004-09-08
298:2019-06-08
221:References
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80:projection
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835:Behrmann
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516:Archived
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199:See also
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1658:HEALPix
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1168:Wiechel
1070:Chinese
1014:Conical
878:Central
873:Cassini
850:Lambert
747:History
601:Bibcode
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1677:Planar
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591:arXiv
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