1<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"> 2 3<!--Converted with LaTeX2HTML 2018.3 (Released July 19, 2018) --> 4<HTML lang="EN"> 5<HEAD> 6<TITLE>Introduction to HEALPix</TITLE> 7<META NAME="description" CONTENT="Introduction to HEALPix"> 8<META NAME="keywords" CONTENT="intro"> 9<META NAME="resource-type" CONTENT="document"> 10<META NAME="distribution" CONTENT="global"> 11 12<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=utf-8"> 13<META NAME="viewport" CONTENT="width=device-width, initial-scale=1.0"> 14<META NAME="Generator" CONTENT="LaTeX2HTML v2018.3"> 15 <link rel='apple-touch-icon' sizes='180x180' href='images/favicons/apple-touch-icon.png?v=2017'> 16 <link rel='icon' type='image/png' sizes='32x32' href='images/favicons/favicon-32x32.png?v=2017'> 17 <link rel='icon' type='image/png' sizes='16x16' href='images/favicons/favicon-16x16.png?v=2017'> 18 <link rel='manifest' href='images/favicons/manifest.json?v=2017'> 19 <link rel='mask-icon' href='images/favicons/safari-pinned-tab.svg?v=2017' color='#5bbad5'> 20 <link rel='shortcut icon' href='images/favicons/favicon.ico?v=2017'> 21 <meta name='apple-mobile-web-app-title' content='HEALPix'> 22 <meta name='application-name' content='HEALPix'> 23 <meta name='msapplication-config' content='images/favicons/browserconfig.xml?v=2017'> 24 <meta name='theme-color' content='#ffffff'> 25 26<LINK REL="STYLESHEET" HREF="intro.css"> 27 28<LINK REL="next" HREF="intro_TABLE_CONTENTS.htm"> 29</HEAD> 30 31<body text="#000000" bgcolor="#FFFFFA"> 32 33<DIV CLASS="navigation"><!--Navigation Panel--> 34<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev_g.png"> 35<A 36 HREF="main.htm"> 37<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 38<A 39 HREF="intro_TABLE_CONTENTS.htm"> 40<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 41<A ID="tex2html42" 42 HREF="intro_TABLE_CONTENTS.htm"> 43<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 44<BR> 45<B>Up:</B> <A 46 HREF="main.htm">Main Page</A> 47 48<B> Next:</B> <A 49 HREF="intro_TABLE_CONTENTS.htm">TABLE OF CONTENTS</A> 50<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 51<!--End of Navigation Panel--> 52 53<P> 54 55<P> 56<H1 ALIGN=CENTER>The <b>HEALPix</b> Primer</H1> 57<div id=abstract align=center><b>HEALPix</b> is a Hierarchical, Equal Area, and iso-Latitude Pixelation 58of the sphere designed to support efficiently 59(1) local operations on the pixel set, 60(2) a hierarchical tree structure for multi-resolution applications, and 61(3) the global Fast Spherical Harmonic transform. 62<b>HEALPix</b> based mathematical software meets the challenges presented by 63high resolution and large volume data sets, such as 64the WMAP and Planck CMB mission products. 65</div> 66<P ALIGN=CENTER><STRONG>Krzysztof M. Górski, Benjamin D. Wandelt, Eric Hivon, Frode K. Hansen, 67and Anthony J. Banday</STRONG></P> 68<BR><P ALIGN=CENTER><I>Revision: </I>Version 3.50; December 10, 2018</P> 69<P ALIGN=CENTER><A ID="tex2html1" 70 HREF="https://healpix.sourceforge.io">https://healpix.sourceforge.io</A> 71<BR><A ID="tex2html2" 72 HREF="http://healpix.sf.net">http://healpix.sf.net</A></P> 73 74<BR><HR> 75<!--Table of Child-Links--> 76<A ID="CHILD_LINKS"></A> 77 78<UL CLASS="ChildLinks"> 79<LI><A ID="tex2html44" 80 HREF="intro_TABLE_CONTENTS.htm">TABLE OF CONTENTS</A> 81<LI><A ID="tex2html45" 82 HREF="intro_Introduction.htm">Introduction</A> 83<LI><A ID="tex2html46" 84 HREF="intro_Discretisation_Functions_on.htm">Discretisation of Functions on the Sphere</A> 85<LI><A ID="tex2html47" 86 HREF="intro_Geometric_Algebraic_Propert.htm">Geometric and Algebraic Properties of <b>HEALPix</b> </A> 87<UL> 88<LI><A ID="tex2html48" 89 HREF="intro_Geometric_Algebraic_Propert.htm#SECTION410">RING and NESTED numbering schemes</A> 90<LI><A ID="tex2html49" 91 HREF="intro_Geometric_Algebraic_Propert.htm#SECTION420">The Unique Identifier scheme</A> 92</UL> 93<BR> 94<LI><A ID="tex2html50" 95 HREF="intro_HEALPix_Software_Package.htm">The <b>HEALPix</b> Software Package</A> 96<LI><A ID="tex2html51" 97 HREF="intro_HEALPix_conventions.htm"><b>HEALPix</b> conventions</A> 98<UL> 99<LI><A ID="tex2html52" 100 HREF="intro_HEALPix_conventions.htm#SECTION610">Angular power spectrum conventions</A> 101<LI><A ID="tex2html53" 102 HREF="intro_HEALPix_conventions.htm#SECTION620"><b>HEALPix</b> and Boltzmann codes</A> 103<UL> 104<LI><A ID="tex2html54" 105 HREF="intro_HEALPix_conventions.htm#SECTION621">CMBFAST</A> 106<LI><A ID="tex2html55" 107 HREF="intro_HEALPix_conventions.htm#SECTION622">CAMB and CLASS</A> 108</UL> 109<LI><A ID="tex2html56" 110 HREF="intro_HEALPix_conventions.htm#SECTION630">Polarisation convention</A> 111<UL> 112<LI><A ID="tex2html57" 113 HREF="intro_HEALPix_conventions.htm#SECTION631">Internal convention</A> 114<LI><A ID="tex2html58" 115 HREF="intro_HEALPix_conventions.htm#SECTION632">Relation to previous releases</A> 116<LI><A ID="tex2html59" 117 HREF="intro_HEALPix_conventions.htm#SECTION633">Relation with IAU convention</A> 118<LI><A ID="tex2html60" 119 HREF="intro_HEALPix_conventions.htm#SECTION634">How <b>HEALPix</b> deals with these discrepancies: <SPAN CLASS="texttt">POLCCONV</SPAN> keyword</A> 120</UL> 121<LI><A ID="tex2html61" 122 HREF="intro_HEALPix_conventions.htm#SECTION640">Spherical harmonic conventions</A> 123</UL> 124<BR> 125<LI><A ID="tex2html62" 126 HREF="intro_Pixel_window_functions.htm">Pixel window functions</A> 127<LI><A ID="tex2html63" 128 HREF="intro_Comment_on_Random_Number_Ge.htm">A Comment on the Random Number Generator</A> 129<LI><A ID="tex2html64" 130 HREF="intro_Bibliography.htm">Bibliography</A> 131<LI><A ID="tex2html65" 132 HREF="intro_About_this_document.htm">About this document ...</A> 133</UL> 134<!--End of Table of Child-Links--> 135 136<DIV CLASS="navigation"><HR> 137<!--Navigation Panel--> 138<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev_g.png"> 139<A 140 HREF="main.htm"> 141<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 142<A 143 HREF="intro_TABLE_CONTENTS.htm"> 144<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 145<A ID="tex2html42" 146 HREF="intro_TABLE_CONTENTS.htm"> 147<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 148<BR> 149<B>Up:</B> <A 150 HREF="main.htm">Main Page</A> 151 152<B> Next:</B> <A 153 HREF="intro_TABLE_CONTENTS.htm">TABLE OF CONTENTS</A> 154<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 155<!--End of Navigation Panel--> 156<ADDRESS> 157Version 3.50, 2018-12-10 158</ADDRESS> 159</BODY> 160</HTML> 161
