HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
K. M. Gorski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelman
TL;DR
The paper introduces HEALPix, a hierarchical, equal-area, iso-latitude pixelization for the sphere designed to enable fast analysis of large full-sky maps. It details the grid construction, base 12 pixel configuration, and resolution control via N_side, along with ring and nested indexing schemes that support efficient spherical harmonic transforms and neighbor searches. The framework addresses critical needs in CMB and wide-area surveys by minimizing discretization errors while maintaining computational efficiency. HEALPix has become a widely adopted standard for sky maps and associated analysis tools across major cosmology missions and surveys.
Abstract
HEALPix -- the Hierarchical Equal Area iso-Latitude Pixelization -- is a versatile data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable directly on very large volumes of astronomical data and large area surveys in the form of discretized spherical maps. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background (CMB) 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 CMB polarization probe. In this paper we consider the requirements and constraints to be met in order to implement a sufficient framework for the efficient discretization and fast analysis/synthesis of functions defined on the sphere, and summarise how they are satisfied by HEALPix.