HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere. HEALPix—the Hierarchical Equal Area isoLatitude Pixelization—is a versatile structure for the pixelization of data on the sphere. An associated library of computational algorithms and visualization software supports fast scientific applications executable directly on discretized spherical maps generated from very large volumes of astronomical data. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background experiments (e.g., BOOMERANG, WMAP), HEALPix can be expanded to meet many of the profound challenges that will arise in confrontation with the observational output of future missions and experiments, including, e.g., Planck, Herschel, SAFIR, and the Beyond Einstein inflation probe. In this paper we consider the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere. We demonstrate how these are explicitly satisfied by HEALPix.

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  1. Creasey, Peter E.; Lang, Annika: Fast generation of isotropic Gaussian random fields on the sphere (2018)
  2. Holhoş, Adrian; Roşca, Daniela: Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere (2017)
  3. Rosen, A. L.; Krumholz, M. R.; Oishi, J. S.; Lee, A. T.; Klein, R. I.: Hybrid adaptive ray-moment method (HARM$^2$): A highly parallel method for radiation hydrodynamics on adaptive grids (2017)
  4. Bhattacharjee, Satyaki; Matouš, Karel: A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials (2016)
  5. Townsend, Alex; Wilber, Heather; Wright, Grady B.: Computing with functions in spherical and polar geometries. I. The sphere (2016)
  6. Brauchart, Johann S.; Grabner, Peter J.: Distributing many points on spheres: minimal energy and designs (2015)
  7. Starck, Jean-Luc; Murtagh, Fionn; Fadili, Jalal M.: Sparse image and signal processing. Wavelets and related geometric multiscale analysis (2015)
  8. Holhoş, Adrian; Roşca, Daniela: An octahedral equal area partition of the sphere and near optimal configurations of points (2014)
  9. Faÿ, Gilles; Delabrouille, Jacques; Kerkyacharian, Gérard; Picard, Dominique: Testing the isotropy of high energy cosmic rays using spherical needlets (2013)
  10. Wandelt, Benjamin D.: Gaussian random fields in cosmostatistics (2013)
  11. Roşca, Daniela; Plonka, Gerlind: An area preserving projection from the regular octahedron to the sphere (2012)
  12. Coombs, William M.; Crouch, Roger S.: Algorithmic issues for three-invariant hyperplastic critical state models (2011)
  13. Faÿ, Gilles; Guilloux, Frédéric: Spectral estimation on the sphere with needlets: high frequency asymptotics (2011)
  14. Gräf, Manuel; Potts, Daniel: On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms (2011)
  15. Roşca, Daniela; Plonka, Gerlind: Uniform spherical grids via equal area projection from the cube to the sphere (2011)
  16. Vladimirov, A. E.; Digel, S. W.; Jóhannesson, G.; Michelson, P. F.; Moskalenko, I. V.; Nolan, P. L.; Orlando, E.; Porter, T. A.; Strong, A. W.: GALPROP WebRun: an internet-based service for calculating galactic cosmic ray propagation and associated photon emissions (2011)
  17. Starck, Jean-Luc; Murtagh, Fionn; Fadili, Jalal M.: Sparse image and signal processing. Wavelets, curvelets, morphological diversity (2010)
  18. Yershova, Anna; Lavalle, Steven M.; Mitchell, Julie C.: Generating uniform incremental grids on $SO(3)$ using the Hopf fibration (2010)
  19. Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.: Asymptotics for spherical needlets (2009)
  20. Betoule, M.; Pierpaoli, E.; Delabrouille, J.; Le Jeune, M.; Cardoso, J.-F.: Measuring the tensor to scalar ratio from CMB B-modes in the presence of foregrounds (2009)

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