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>pix2xxx, ang2xxx, vec2xxx, nest2ring, ring2nest</TITLE> 7<META NAME="description" CONTENT="pix2xxx, ang2xxx, vec2xxx, nest2ring, ring2nest"> 8<META NAME="keywords" CONTENT="csub"> 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="csub.css"> 27 28<LINK REL="next" HREF="csub_read_healpix_map.htm"> 29<LINK REL="previous" HREF="csub_nside2npix.htm"> 30<LINK REL="next" HREF="csub_read_healpix_map.htm"> 31</HEAD> 32 33<body text="#000000" bgcolor="#FFFFFA"> 34 35<DIV CLASS="navigation"><!--Navigation Panel--> 36<A 37 HREF="csub_nside2npix.htm"> 38<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 39<A 40 HREF="csub_HEALPix_C_subroutines.htm"> 41<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 42<A 43 HREF="csub_read_healpix_map.htm"> 44<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 45<A ID="tex2html48" 46 HREF="csub_Contents.htm"> 47<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 48<BR> 49<B> Previous:</B> <A 50 HREF="csub_nside2npix.htm">nside2npix</A> 51 52<B>Up:</B> <A 53 HREF="csub_HEALPix_C_subroutines.htm">HEALPix/C subroutines</A> 54 55<B> Next:</B> <A 56 HREF="csub_read_healpix_map.htm">read_healpix_map</A> 57<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 58<!--End of Navigation Panel--> 59 60<H1><A ID="SECTION1000"></A> 61<A ID="csub:pix_tools"></A> 62<BR> 63 64</H1> 65 66<P> 67<b><font size=+6><FONT COLOR="#CC0000">pix2xxx, ang2xxx, vec2xxx, nest2ring, ring2nest</FONT></font></b><hr> 68<H3>These subroutines can be used to convert between pixel number in the 69<b>HEALPix</b> map and <SPAN CLASS="MATH"><IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="csub_img5.png" 70 ALT="$(\theta,\phi) $"></SPAN> coordinates on the sphere. This is only a 71subset of the routines equivalent in Fortran90 or in IDL. </H3> 72Location in HEALPix directory tree: <a href="https://sourceforge.net/p/healpix/code/1005/tree/trunk/src/C/subs/chealpix.c"><b>src/C/subs/chealpix.c</b></a> 73 74<P> 75<hr><H1>ARGUMENTS</H1> 76 77<TABLE CELLPADDING=3 BORDER="1"> 78<TR><TH ALIGN="LEFT" VALIGN="TOP" WIDTH=140><SPAN CLASS="textbf">name & dimensionality</SPAN></TH> 79<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=50><SPAN CLASS="textbf">type</SPAN></TH> 80<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=25><SPAN CLASS="textbf">in/out</SPAN></TH> 81<TH ALIGN="LEFT" VALIGN="TOP" WIDTH=235><SPAN CLASS="textbf">description</SPAN></TH> 82</TR> 83<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140> </TD> 84<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50> </TD> 85<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25> </TD> 86<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235> </TD> 87</TR> 88<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140> 89nside</TD> 90<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>long</TD> 91<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>IN</TD> 92<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235><!-- MATH 93 $N_{\mathrm{side}}$ 94 --> 95<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB></SPAN> parameter for the <b>HEALPix</b> map.</TD> 96</TR> 97<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140>ipnest</TD> 98<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>long</TD> 99<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>--</TD> 100<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235>pixel identification number in NESTED scheme over the range {0,<!-- MATH 101 $N_{\mathrm{pix}}-1$ 102 --> 103<SPAN CLASS="MATH"><I>N</I><SUB>pix</SUB>-1</SPAN>}.</TD> 104</TR> 105<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140>ipring</TD> 106<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>long</TD> 107<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>--</TD> 108<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235>pixel identification number in RING scheme over the range {0,<!-- MATH 109 $N_{\mathrm{pix}}-1$ 110 --> 111<SPAN CLASS="MATH"><I>N</I><SUB>pix</SUB>-1</SPAN>}.</TD> 112</TR> 113<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140>theta</TD> 114<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>double</TD> 115<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>--</TD> 116<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235>colatitude in radians measured southward from north pole in [0,<SPAN CLASS="MATH"><IMG STYLE="height: 1.11ex; vertical-align: -0.10ex; " SRC="csub_img2.png" 117 ALT="$\pi$"></SPAN>].</TD> 118</TR> 119<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140>phi</TD> 120<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>double</TD> 121<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>--</TD> 122<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235>longitude in radians, measured eastward in [0,<SPAN CLASS="MATH"><IMG STYLE="height: 1.57ex; vertical-align: -0.10ex; " SRC="csub_img9.png" 123 ALT="$2\pi$"></SPAN>].</TD> 124</TR> 125<TR><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=140>vector</TD> 126<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>double</TD> 127<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=25>--</TD> 128<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=235>3D cartesian position vector <SPAN CLASS="MATH">(<I>x</I>,<I>y</I>,<I>z</I>)</SPAN>. The north pole is <SPAN CLASS="MATH">(0,0,1)</SPAN>. An output vector is normalised to unity.</TD> 129</TR> 130</TABLE> 131 132<P> 133 134<BIG CLASS="LARGE"><SPAN CLASS="textbf">ROUTINES: </SPAN></BIG> 135<BR> 136<TT>void pix2ang_ring(long nside, long ipring, double *theta, double *phi);</TT> 137 138<P> 139<TABLE CELLPADDING=3> 140<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 141<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders <EM>theta</EM> and <EM>phi</EM> coordinates of the nominal pixel center given the pixel number <EM>ipring</EM> and a map resolution parameter <EM>nside</EM>.</TD> 142<TD ALIGN="LEFT"> </TD></TR> 143</TABLE> 144<BR> 145<BR><TT>void pix2vec_ring(long nside, long ipring, double *vector);</TT> 146 147<P> 148<TABLE CELLPADDING=3> 149<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 150<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders cartesian vector coordinates of the nominal pixel center given the pixel number <EM>ipring</EM> and a map resolution parameter <EM>nside</EM>. Optionally renders cartesian vector coordinates of the considered pixel four vertices.</TD> 151<TD ALIGN="LEFT"> </TD></TR> 152</TABLE> 153<BR> 154<BR><TT>void ang2pix_ring(long nside, double theta, double phi, long *ipring);</TT> 155 156<P> 157<TABLE CELLPADDING=3> 158<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 159<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders the pixel number <EM>ipring</EM> for a pixel which, given the map resolution parameter <EM>nside</EM>, contains the point on the sphere at angular coordinates <EM>theta</EM> and <EM>phi</EM>.</TD> 160<TD ALIGN="LEFT"> </TD></TR> 161</TABLE> 162<BR> 163<BR><TT>void vec2pix_ring(long nside, double *vector, long *ipring);</TT> 164 165<P> 166<TABLE CELLPADDING=3> 167<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 168<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders the pixel number <EM>ipring</EM> for a pixel which, given the map resolution parameter <EM>nside</EM>, contains the point on the sphere at cartesian coordinates <EM>vector</EM>.</TD> 169<TD ALIGN="LEFT"> </TD></TR> 170</TABLE> 171<BR> 172<BR><TT>void pix2ang_nest(long nside, long ipnest, double *theta, double *phi);</TT> 173 174<P> 175<TABLE CELLPADDING=3> 176<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 177<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders <EM>theta</EM> and <EM>phi</EM> coordinates of the nominal pixel center given the pixel number <EM>ipnest</EM> and a map resolution parameter <EM>nside</EM>.</TD> 178<TD ALIGN="LEFT"> </TD></TR> 179</TABLE> 180<BR> 181<BR><TT>void pix2vec_nest(long nside, long ipnest, double *vector);</TT> 182 183<P> 184<TABLE CELLPADDING=3> 185<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 186<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders cartesian vector coordinates of the nominal pixel center given the pixel number <EM>ipnest</EM> and a map resolution parameter <EM>nside</EM>. Optionally renders cartesian vector coordinates of the considered pixel four vertices.</TD> 187<TD ALIGN="LEFT"> </TD></TR> 188</TABLE> 189<BR> 190<BR><TT>void ang2pix_nest(long nside, double theta, double phi, long *ipnest);</TT> 191 192<P> 193<TABLE CELLPADDING=3> 194<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 195<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders the pixel number <EM>ipnest</EM> for a pixel which, given the map resolution parameter <EM>nside</EM>, contains the point on the sphere at angular coordinates <EM>theta</EM> and <EM>phi</EM>.</TD> 196<TD ALIGN="LEFT"> </TD></TR> 197</TABLE> 198<BR> 199<BR><TT>void vec2pix_nest(long nside, double *vector, long *ipnest)</TT> 200 201<P> 202<TABLE CELLPADDING=3> 203<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 204<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>renders the pixel number 205 <EM>ipnest</EM> for a pixel which, given the map 206 resolution parameter <EM>nside</EM>, contains the 207 point on the sphere at cartesian coordinates 208 <EM>vector</EM> .</TD> 209<TD ALIGN="LEFT"> </TD></TR> 210</TABLE> 211<BR> 212<BR> 213<P> 214<TT>void nest2ring(long nside, long ipnest, long *ipring);</TT> 215 216<P> 217<TABLE CELLPADDING=3> 218<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 219<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>performs conversion from NESTED to RING pixel number.</TD> 220<TD ALIGN="LEFT"> </TD></TR> 221</TABLE> 222<BR> 223<BR><TT>void ring2nest(long nside, long ipring, long *ipnest);</TT> 224 225<P> 226<TABLE CELLPADDING=3> 227<TR><TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=150> </TD> 228<TD ALIGN="LEFT"> </TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH=350>performs conversion from RING to NESTED pixel number.</TD> 229<TD ALIGN="LEFT"> </TD></TR> 230</TABLE> 231<BR> 232<BR> 233<P> 234<hr><H1>MODULES & ROUTINES</H1><H3>This section lists the modules and routines used by <FONT COLOR="#CC0000">pix2xxx, ang2xxx, vec2xxx, nest2ring, ring2nest</FONT>.</h3> 235 <DL COMPACT><DT> 236<B>mk_pix2xy, mk_xy2pix</B> 237<DD>routines used in the conversion between pixel values and “cartesian” coordinates on the Healpix face. 238 </DL> 239 240<P> 241<hr><H1>RELATED ROUTINES</H1><h3>This section lists the routines related to <b><FONT COLOR="#CC0000">pix2xxx, ang2xxx, vec2xxx, nest2ring, ring2nest</FONT></b></h3> 242 243 <DL COMPACT><DT> 244<B><A HREF="csub_ang2vec.htm#csub:ang2vec">ang2vec</A></B> 245<DD>converts <SPAN CLASS="MATH"><IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="csub_img5.png" 246 ALT="$(\theta,\phi) $"></SPAN> spherical coordinates into <SPAN CLASS="MATH">(<I>x</I>,<I>y</I>,<I>z</I>)</SPAN> cartesian coordinates. 247 <DT> 248<B><A HREF="csub_vec2ang.htm#csub:vec2ang">vec2ang</A></B> 249<DD>converts <SPAN CLASS="MATH">(<I>x</I>,<I>y</I>,<I>z</I>)</SPAN> cartesian coordinates into <SPAN CLASS="MATH"><IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="csub_img5.png" 250 ALT="$(\theta,\phi) $"></SPAN> spherical coordinates. 251 <DT> 252<B><A HREF="csub_nside2npix.htm#csub:nside2npix">nside2npix</A></B> 253<DD>converts number of full sky 254pixels <!-- MATH 255 $N_{\mathrm{pix}}$ 256 --> 257<SPAN CLASS="MATH"><I>N</I><SUB>pix</SUB></SPAN> into resolution parameter <!-- MATH 258 $N_{\mathrm{side}}$ 259 --> 260<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB></SPAN> 261 <DT> 262<B><A HREF="csub_npix2nside.htm#csub:npix2nside">npix2nside</A></B> 263<DD>converts <!-- MATH 264 $N_{\mathrm{side}}$ 265 --> 266<SPAN CLASS="MATH"><I>N</I><SUB>side</SUB></SPAN> into number of 267full sky pixels <!-- MATH 268 $N_{\mathrm{pix}}$ 269 --> 270<SPAN CLASS="MATH"><I>N</I><SUB>pix</SUB></SPAN>. 271 </DL> 272 273<P> 274 275<P> 276 277 278<P> 279 280<P> 281 282<DIV CLASS="navigation"><HR> 283<!--Navigation Panel--> 284<A 285 HREF="csub_nside2npix.htm"> 286<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 287<A 288 HREF="csub_HEALPix_C_subroutines.htm"> 289<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 290<A 291 HREF="csub_read_healpix_map.htm"> 292<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 293<A ID="tex2html48" 294 HREF="csub_Contents.htm"> 295<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 296<BR> 297<B> Previous:</B> <A 298 HREF="csub_nside2npix.htm">nside2npix</A> 299 300<B>Up:</B> <A 301 HREF="csub_HEALPix_C_subroutines.htm">HEALPix/C subroutines</A> 302 303<B> Next:</B> <A 304 HREF="csub_read_healpix_map.htm">read_healpix_map</A> 305<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 306<!--End of Navigation Panel--> 307<ADDRESS> 308Version 3.50, 2018-12-10 309</ADDRESS> 310</BODY> 311</HTML> 312
