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>rotate_coord</TITLE> 7<META NAME="description" CONTENT="rotate_coord"> 8<META NAME="keywords" CONTENT="idl"> 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="idl.css"> 27 28<LINK REL="next" HREF="idl_same_shape_pixels_nest_same.htm"> 29<LINK REL="previous" HREF="idl_reorder.htm"> 30<LINK REL="next" HREF="idl_same_shape_pixels_nest_same.htm"> 31</HEAD> 32 33<body text="#000000" bgcolor="#FFFFFA"> 34 35<DIV CLASS="navigation"><!--Navigation Panel--> 36<A 37 HREF="idl_reorder.htm"> 38<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 39<A 40 HREF="idl_HEALPix_IDL_subroutines.htm"> 41<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 42<A 43 HREF="idl_same_shape_pixels_nest_same.htm"> 44<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 45<A ID="tex2html407" 46 HREF="idl_TABLE_CONTENTS.htm"> 47<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 48<BR> 49<B> Previous:</B> <A 50 HREF="idl_reorder.htm">reorder</A> 51 52<B>Up:</B> <A 53 HREF="idl_HEALPix_IDL_subroutines.htm">HEALPix/IDL subroutines</A> 54 55<B> Next:</B> <A 56 HREF="idl_same_shape_pixels_nest_same.htm">same_shape_pixels_nest & same_shape_pixels_ring</A> 57<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 58<!--End of Navigation Panel--> 59 60<H1><A ID="SECTION6700"></A> 61<A ID="idl:rotate_coord"></A> 62<BR> 63 64</H1> 65 66<P> 67<b><font size=+6><FONT COLOR="#CC0000">rotate_coord</FONT></font></b><hr> 68<H3>This IDL facility provides a means to rotate a set of 3D position 69vectors (and their Stokes parameters <SPAN CLASS="MATH"><I>Q</I></SPAN> and <SPAN CLASS="MATH"><I>U</I></SPAN>) between to astrophysical coordinate systems 70or by an arbitrary rotation. 71</H3> 72Location in HEALPix directory tree: <a href="https://sourceforge.net/p/healpix/code/1005/tree/trunk/src/idl/misc/rotate_coord.pro"><b>src/idl/misc/rotate_coord.pro</b></a> 73 74<P> 75<hr><h1>FORMAT </h1><h3>IDL> 76<A HREF="#idl:rotate_coord:outvec">Outvec</A> = rotate_coord(<A HREF="#idl:rotate_coord:invec">Invec</A> 77[, <A HREF="#idl:rotate_coord:delta_psi">Delta_Psi=</A>, <A HREF="#idl:rotate_coord:euler_matrix">Euler_Matrix=</A>, <A HREF="#idl:rotate_coord:inco">Inco=</A>, <A HREF="#idl:rotate_coord:outco">Outco=</A>, <A HREF="#idl:rotate_coord:stokes_parameters">Stokes_Parameters=</A>, <A HREF="#idl:rotate_coord:free_norm">/free_norm</A>, <A HREF="#idl:rotate_coord:help">/help</A>] ) 78</h3> 79 80<P> 81<hr> 82<H1>QUALIFIERS</H1> 83 84 <DL COMPACT><DT> 85<B>Invec</B> 86<DD><A ID="idl:rotate_coord:invec"></A> input, array of size (n,3) : set of 3D position vectors 87<DT> 88<B>Outvec</B> 89<DD><A ID="idl:rotate_coord:outvec"></A> output, array of size (n,3) : rotated 3D vectors, with the same norms as the input vectors 90<DT> 91<B>Delta_Psi</B> 92<DD><A ID="idl:rotate_coord:delta_psi"></A> output, vector of size (n) containing the change in azimuth <SPAN CLASS="MATH"><IMG STYLE="height: 2.16ex; vertical-align: -0.55ex; " SRC="idl_img106.png" 93 ALT="$\Delta\psi$"></SPAN> in Radians 94 resulting from the rotation 95 (<A HREF="./intro_HEALPix_conventions.htm#intro:fig:reftqu">measured with respect to the local meridian, from South to East</A>), 96 so that for field of spin <SPAN CLASS="MATH"><I>s</I></SPAN> the output <SPAN CLASS="MATH"><I>Q</I>',<I>U</I>'</SPAN> is related to the input <SPAN CLASS="MATH"><I>Q</I>,<I>U</I></SPAN> via 97 <!-- MATH 98 $Q' = Q \cos (s\Delta\psi) - U \sin (s\Delta\psi),\$ 99 --> 100<SPAN CLASS="MATH"><IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="idl_img107.png" 101 ALT="$Q' = Q \cos (s\Delta\psi) - U \sin (s\Delta\psi),\ $"></SPAN> 102 <!-- MATH 103 $U' = U \cos (s\Delta\psi) + Q \sin (s\Delta\psi),$ 104 --> 105<SPAN CLASS="MATH"><IMG STYLE="height: 2.33ex; vertical-align: -0.68ex; " SRC="idl_img108.png" 106 ALT="$U' = U \cos (s\Delta\psi) + Q \sin (s\Delta\psi), $"></SPAN> 107 with <SPAN CLASS="MATH"><I>s</I>=2</SPAN> for polarization Stokes parameters 108(for which the specific <A HREF="#idl:rotate_coord:stokes_parameters">Stokes_Parameters</A> is also available). 109<DT> 110<B>Euler_Matrix=</B> 111<DD><A ID="idl:rotate_coord:euler_matrix"></A> input, array of size (3,3). Euler Matrix 112 describing the rotation to apply to vectors. 113 <b>default:</b>identity : no rotation. 114<BR> 115Can <SPAN CLASS="textit">not</SPAN> be used together with a change in coordinates. 116<DT> 117<B>Inco=</B> 118<DD><A ID="idl:rotate_coord:inco"></A> input, character string (either 'Q' or 'C': equatorial, 119 'G': galactic or 'E': ecliptic) describing the input coordinate system 120<DT> 121<B>Outco=</B> 122<DD><A ID="idl:rotate_coord:outco"></A> input, character string (see above) describing the output 123 coordinate system. 124<BR> 125Can not be used together with <A HREF="#idl:rotate_coord:euler_matrix">Euler_Matrix</A> 126<DT> 127<B>Stokes_Parameters=</B> 128<DD><A ID="idl:rotate_coord:stokes_parameters"></A> input and output, array of size (n, 2) : 129 values of the <SPAN CLASS="MATH"><I>Q</I></SPAN> and <SPAN CLASS="MATH"><I>U</I></SPAN> Stokes parameters on the sphere for each of 130 the input position vector. <A HREF="./intro_HEALPix_conventions.htm#intro:fig:reftqu"><SPAN CLASS="MATH"><I>Q</I></SPAN> and <SPAN CLASS="MATH"><I>U</I></SPAN> are defined wrt the local 131 meridian and parallel</A> and are therefore transformed in a 132 non-trivial way in case of rotation 133</DL> 134 135<P> 136<hr><H1>KEYWORDS</H1> 137 138 <DL COMPACT><DT> 139<B>/free_norm</B> 140<DD><A ID="idl:rotate_coord:free_norm"></A> if set 141 (and <A HREF="#idl:rotate_coord:stokes_parameters">Stokes_Parameters</A> and/or 142 <A HREF="#idl:rotate_coord:delta_psi">Delta_Psi</A> are present) 143 the input (and output) coordinate vectors are <SPAN CLASS="textit">not</SPAN> assumed to be normalized to 1. 144 Using this option is therefore safer, but 20 to 30% slower. 145 (Note that 3D vectors produced by 146 <A HREF="idl_ang2vec.htm#idl:ang2vec"><SPAN CLASS="texttt">ang2vec</SPAN></A>, 147 <A HREF="idl_pix2xxx_ang2xxx_vec2xxx_nes.htm#idl:pix_tools"><SPAN CLASS="texttt">pix2vec_nest</SPAN></A> and 148 <A HREF="idl_pix2xxx_ang2xxx_vec2xxx_nes.htm#idl:pix_tools"><SPAN CLASS="texttt">pix2vec_ring</SPAN></A> <SPAN CLASS="textit">are</SPAN> properly normalized). 149 Ignored when <A HREF="#idl:rotate_coord:stokes_parameters">Stokes_Parameters</A> and 150 <A HREF="#idl:rotate_coord:delta_psi">Delta_Psi</A> are both absent. 151<DT> 152<B>/help</B> 153<DD><A ID="idl:rotate_coord:help"></A> if set, the documentation header is printed and the routine exits 154</DL> 155 156<P> 157<hr> 158<H1>DESCRIPTION</H1> 159<blockquote> 160<FONT COLOR="#CC0000">rotate_coord</FONT> is a generalisation of the Astro library routine <TT>skyconv</TT>. It allows 161a rotation of 3D position vectors between two standard astronomic coordinates 162system but also an arbitrary active rotation described by its Euler Matrix. 163It can also compute how the linear polarization Stokes parameters (<SPAN CLASS="MATH"><I>Q</I></SPAN> and <SPAN CLASS="MATH"><I>U</I></SPAN>, 164expressed in local coordinates system) 165of each input location are affected by the solid body rotation, or equivalently 166it can output the corresponding change in azimuth. 167</blockquote> 168 169<P> 170<hr><H1>RELATED ROUTINES</H1><h3>This section lists the routines related to <b><FONT COLOR="#CC0000">rotate_coord</FONT></b></h3> 171 172 <DL COMPACT><DT> 173<B>idl</B> 174<DD>version 6.4 or more is necessary to run <FONT COLOR="#CC0000">rotate_coord</FONT>. 175 <DT> 176<B><A HREF="idl_euler_matrix_new.htm#idl:euler_matrix_new">euler_matrix_new</A></B> 177<DD>constructs the Euler Matrix for a set of 178 three angles and three axes of rotation 179 <DT> 180<B><A HREF="idl_ang2vec.htm#idl:ang2vec"><SPAN CLASS="texttt">ang2vec</SPAN></A>, <A HREF="idl_pix2xxx_ang2xxx_vec2xxx_nes.htm#idl:pix_tools"><SPAN CLASS="texttt">pix2vec_*</SPAN></A></B> 181<DD>can be used to generate the input 3D vectors 182 </DL> 183 184<P> 185 186<P> 187 188<P> 189 190<DIV CLASS="navigation"><HR> 191<!--Navigation Panel--> 192<A 193 HREF="idl_reorder.htm"> 194<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A> 195<A 196 HREF="idl_HEALPix_IDL_subroutines.htm"> 197<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A> 198<A 199 HREF="idl_same_shape_pixels_nest_same.htm"> 200<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A> 201<A ID="tex2html407" 202 HREF="idl_TABLE_CONTENTS.htm"> 203<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A> 204<BR> 205<B> Previous:</B> <A 206 HREF="idl_reorder.htm">reorder</A> 207 208<B>Up:</B> <A 209 HREF="idl_HEALPix_IDL_subroutines.htm">HEALPix/IDL subroutines</A> 210 211<B> Next:</B> <A 212 HREF="idl_same_shape_pixels_nest_same.htm">same_shape_pixels_nest & same_shape_pixels_ring</A> 213<B> Top:</B> <a href="main.htm">Main Page</a></DIV> 214<!--End of Navigation Panel--> 215<ADDRESS> 216Version 3.50, 2018-12-10 217</ADDRESS> 218</BODY> 219</HTML> 220
