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<h1>sph.h</h1><a href="sph_8h.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*============================================================================</span>
<a name="l00002"></a>00002 <span class="comment"></span>
<a name="l00003"></a>00003 <span class="comment"> WCSLIB 4.8 - an implementation of the FITS WCS standard.</span>
<a name="l00004"></a>00004 <span class="comment"> Copyright (C) 1995-2011, Mark Calabretta</span>
<a name="l00005"></a>00005 <span class="comment"></span>
<a name="l00006"></a>00006 <span class="comment"> This file is part of WCSLIB.</span>
<a name="l00007"></a>00007 <span class="comment"></span>
<a name="l00008"></a>00008 <span class="comment"> WCSLIB is free software: you can redistribute it and/or modify it under the</span>
<a name="l00009"></a>00009 <span class="comment"> terms of the GNU Lesser General Public License as published by the Free</span>
<a name="l00010"></a>00010 <span class="comment"> Software Foundation, either version 3 of the License, or (at your option)</span>
<a name="l00011"></a>00011 <span class="comment"> any later version.</span>
<a name="l00012"></a>00012 <span class="comment"></span>
<a name="l00013"></a>00013 <span class="comment"> WCSLIB is distributed in the hope that it will be useful, but WITHOUT ANY</span>
<a name="l00014"></a>00014 <span class="comment"> WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS</span>
<a name="l00015"></a>00015 <span class="comment"> FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for</span>
<a name="l00016"></a>00016 <span class="comment"> more details.</span>
<a name="l00017"></a>00017 <span class="comment"></span>
<a name="l00018"></a>00018 <span class="comment"> You should have received a copy of the GNU Lesser General Public License</span>
<a name="l00019"></a>00019 <span class="comment"> along with WCSLIB. If not, see <http://www.gnu.org/licenses/>.</span>
<a name="l00020"></a>00020 <span class="comment"></span>
<a name="l00021"></a>00021 <span class="comment"> Correspondence concerning WCSLIB may be directed to:</span>
<a name="l00022"></a>00022 <span class="comment"> Internet email: mcalabre@atnf.csiro.au</span>
<a name="l00023"></a>00023 <span class="comment"> Postal address: Dr. Mark Calabretta</span>
<a name="l00024"></a>00024 <span class="comment"> Australia Telescope National Facility, CSIRO</span>
<a name="l00025"></a>00025 <span class="comment"> PO Box 76</span>
<a name="l00026"></a>00026 <span class="comment"> Epping NSW 1710</span>
<a name="l00027"></a>00027 <span class="comment"> AUSTRALIA</span>
<a name="l00028"></a>00028 <span class="comment"></span>
<a name="l00029"></a>00029 <span class="comment"> Author: Mark Calabretta, Australia Telescope National Facility</span>
<a name="l00030"></a>00030 <span class="comment"> http://www.atnf.csiro.au/~mcalabre/index.html</span>
<a name="l00031"></a>00031 <span class="comment"> $Id: sph.h,v 4.8.1.1 2011/08/15 08:07:06 cal103 Exp cal103 $</span>
<a name="l00032"></a>00032 <span class="comment">*=============================================================================</span>
<a name="l00033"></a>00033 <span class="comment">*</span>
<a name="l00034"></a>00034 <span class="comment">* WCSLIB 4.8 - C routines that implement the spherical coordinate</span>
<a name="l00035"></a>00035 <span class="comment">* transformations used by the FITS World Coordinate System (WCS) standard.</span>
<a name="l00036"></a>00036 <span class="comment">* Refer to</span>
<a name="l00037"></a>00037 <span class="comment">*</span>
<a name="l00038"></a>00038 <span class="comment">* "Representations of world coordinates in FITS",</span>
<a name="l00039"></a>00039 <span class="comment">* Greisen, E.W., & Calabretta, M.R. 2002, A&A, 395, 1061 (Paper I)</span>
<a name="l00040"></a>00040 <span class="comment">*</span>
<a name="l00041"></a>00041 <span class="comment">* "Representations of celestial coordinates in FITS",</span>
<a name="l00042"></a>00042 <span class="comment">* Calabretta, M.R., & Greisen, E.W. 2002, A&A, 395, 1077 (Paper II)</span>
<a name="l00043"></a>00043 <span class="comment">*</span>
<a name="l00044"></a>00044 <span class="comment">* Refer to the README file provided with WCSLIB for an overview of the</span>
<a name="l00045"></a>00045 <span class="comment">* library.</span>
<a name="l00046"></a>00046 <span class="comment">*</span>
<a name="l00047"></a>00047 <span class="comment">*</span>
<a name="l00048"></a>00048 <span class="comment">* Summary of the sph routines</span>
<a name="l00049"></a>00049 <span class="comment">* ---------------------------</span>
<a name="l00050"></a>00050 <span class="comment">* The WCS spherical coordinate transformations are implemented via separate</span>
<a name="l00051"></a>00051 <span class="comment">* functions, sphx2s() and sphs2x(), for the transformation in each direction.</span>
<a name="l00052"></a>00052 <span class="comment">*</span>
<a name="l00053"></a>00053 <span class="comment">* A utility function, sphdpa(), computes the angular distances and position</span>
<a name="l00054"></a>00054 <span class="comment">* angles from a given point on the sky to a number of other points. sphpad()</span>
<a name="l00055"></a>00055 <span class="comment">* does the complementary operation - computes the coordinates of points offset</span>
<a name="l00056"></a>00056 <span class="comment">* by the given angular distances and position angles from a given point on the</span>
<a name="l00057"></a>00057 <span class="comment">* sky.</span>
<a name="l00058"></a>00058 <span class="comment">*</span>
<a name="l00059"></a>00059 <span class="comment">*</span>
<a name="l00060"></a>00060 <span class="comment">* sphx2s() - Rotation in the pixel-to-world direction</span>
<a name="l00061"></a>00061 <span class="comment">* ---------------------------------------------------</span>
<a name="l00062"></a>00062 <span class="comment">* sphx2s() transforms native coordinates of a projection to celestial</span>
<a name="l00063"></a>00063 <span class="comment">* coordinates.</span>
<a name="l00064"></a>00064 <span class="comment">*</span>
<a name="l00065"></a>00065 <span class="comment">* Given:</span>
<a name="l00066"></a>00066 <span class="comment">* eul const double[5]</span>
<a name="l00067"></a>00067 <span class="comment">* Euler angles for the transformation:</span>
<a name="l00068"></a>00068 <span class="comment">* 0: Celestial longitude of the native pole [deg].</span>
<a name="l00069"></a>00069 <span class="comment">* 1: Celestial colatitude of the native pole, or</span>
<a name="l00070"></a>00070 <span class="comment">* native colatitude of the celestial pole [deg].</span>
<a name="l00071"></a>00071 <span class="comment">* 2: Native longitude of the celestial pole [deg].</span>
<a name="l00072"></a>00072 <span class="comment">* 3: cos(eul[1])</span>
<a name="l00073"></a>00073 <span class="comment">* 4: sin(eul[1])</span>
<a name="l00074"></a>00074 <span class="comment">*</span>
<a name="l00075"></a>00075 <span class="comment">* nphi,</span>
<a name="l00076"></a>00076 <span class="comment">* ntheta int Vector lengths.</span>
<a name="l00077"></a>00077 <span class="comment">*</span>
<a name="l00078"></a>00078 <span class="comment">* spt,sxy int Vector strides.</span>
<a name="l00079"></a>00079 <span class="comment">*</span>
<a name="l00080"></a>00080 <span class="comment">* phi,theta const double[]</span>
<a name="l00081"></a>00081 <span class="comment">* Longitude and latitude in the native coordinate</span>
<a name="l00082"></a>00082 <span class="comment">* system of the projection [deg].</span>
<a name="l00083"></a>00083 <span class="comment">*</span>
<a name="l00084"></a>00084 <span class="comment">* Returned:</span>
<a name="l00085"></a>00085 <span class="comment">* lng,lat double[] Celestial longitude and latitude [deg]. These may</span>
<a name="l00086"></a>00086 <span class="comment">* refer to the same storage as phi and theta</span>
<a name="l00087"></a>00087 <span class="comment">* respectively.</span>
<a name="l00088"></a>00088 <span class="comment">*</span>
<a name="l00089"></a>00089 <span class="comment">* Function return value:</span>
<a name="l00090"></a>00090 <span class="comment">* int Status return value:</span>
<a name="l00091"></a>00091 <span class="comment">* 0: Success.</span>
<a name="l00092"></a>00092 <span class="comment">*</span>
<a name="l00093"></a>00093 <span class="comment">*</span>
<a name="l00094"></a>00094 <span class="comment">* sphs2x() - Rotation in the world-to-pixel direction</span>
<a name="l00095"></a>00095 <span class="comment">* ---------------------------------------------------</span>
<a name="l00096"></a>00096 <span class="comment">* sphs2x() transforms celestial coordinates to the native coordinates of a</span>
<a name="l00097"></a>00097 <span class="comment">* projection.</span>
<a name="l00098"></a>00098 <span class="comment">*</span>
<a name="l00099"></a>00099 <span class="comment">* Given:</span>
<a name="l00100"></a>00100 <span class="comment">* eul const double[5]</span>
<a name="l00101"></a>00101 <span class="comment">* Euler angles for the transformation:</span>
<a name="l00102"></a>00102 <span class="comment">* 0: Celestial longitude of the native pole [deg].</span>
<a name="l00103"></a>00103 <span class="comment">* 1: Celestial colatitude of the native pole, or</span>
<a name="l00104"></a>00104 <span class="comment">* native colatitude of the celestial pole [deg].</span>
<a name="l00105"></a>00105 <span class="comment">* 2: Native longitude of the celestial pole [deg].</span>
<a name="l00106"></a>00106 <span class="comment">* 3: cos(eul[1])</span>
<a name="l00107"></a>00107 <span class="comment">* 4: sin(eul[1])</span>
<a name="l00108"></a>00108 <span class="comment">*</span>
<a name="l00109"></a>00109 <span class="comment">* nlng,nlat int Vector lengths.</span>
<a name="l00110"></a>00110 <span class="comment">*</span>
<a name="l00111"></a>00111 <span class="comment">* sll,spt int Vector strides.</span>
<a name="l00112"></a>00112 <span class="comment">*</span>
<a name="l00113"></a>00113 <span class="comment">* lng,lat const double[]</span>
<a name="l00114"></a>00114 <span class="comment">* Celestial longitude and latitude [deg].</span>
<a name="l00115"></a>00115 <span class="comment">*</span>
<a name="l00116"></a>00116 <span class="comment">* Returned:</span>
<a name="l00117"></a>00117 <span class="comment">* phi,theta double[] Longitude and latitude in the native coordinate system</span>
<a name="l00118"></a>00118 <span class="comment">* of the projection [deg]. These may refer to the same</span>
<a name="l00119"></a>00119 <span class="comment">* storage as lng and lat respectively.</span>
<a name="l00120"></a>00120 <span class="comment">*</span>
<a name="l00121"></a>00121 <span class="comment">* Function return value:</span>
<a name="l00122"></a>00122 <span class="comment">* int Status return value:</span>
<a name="l00123"></a>00123 <span class="comment">* 0: Success.</span>
<a name="l00124"></a>00124 <span class="comment">*</span>
<a name="l00125"></a>00125 <span class="comment">*</span>
<a name="l00126"></a>00126 <span class="comment">* sphdpa() - Compute angular distance and position angle</span>
<a name="l00127"></a>00127 <span class="comment">* ------------------------------------------------------</span>
<a name="l00128"></a>00128 <span class="comment">* sphdpa() computes the angular distance and generalized position angle (see</span>
<a name="l00129"></a>00129 <span class="comment">* notes) from a "reference" point to a number of "field" points on the sphere.</span>
<a name="l00130"></a>00130 <span class="comment">* The points must be specified consistently in any spherical coordinate</span>
<a name="l00131"></a>00131 <span class="comment">* system.</span>
<a name="l00132"></a>00132 <span class="comment">*</span>
<a name="l00133"></a>00133 <span class="comment">* sphdpa() is complementary to sphpad().</span>
<a name="l00134"></a>00134 <span class="comment">*</span>
<a name="l00135"></a>00135 <span class="comment">* Given:</span>
<a name="l00136"></a>00136 <span class="comment">* nfield int The number of field points.</span>
<a name="l00137"></a>00137 <span class="comment">*</span>
<a name="l00138"></a>00138 <span class="comment">* lng0,lat0 double Spherical coordinates of the reference point [deg].</span>
<a name="l00139"></a>00139 <span class="comment">*</span>
<a name="l00140"></a>00140 <span class="comment">* lng,lat const double[]</span>
<a name="l00141"></a>00141 <span class="comment">* Spherical coordinates of the field points [deg].</span>
<a name="l00142"></a>00142 <span class="comment">*</span>
<a name="l00143"></a>00143 <span class="comment">* Returned:</span>
<a name="l00144"></a>00144 <span class="comment">* dist,pa double[] Angular distances and position angles [deg]. These</span>
<a name="l00145"></a>00145 <span class="comment">* may refer to the same storage as lng and lat</span>
<a name="l00146"></a>00146 <span class="comment">* respectively.</span>
<a name="l00147"></a>00147 <span class="comment">*</span>
<a name="l00148"></a>00148 <span class="comment">* Function return value:</span>
<a name="l00149"></a>00149 <span class="comment">* int Status return value:</span>
<a name="l00150"></a>00150 <span class="comment">* 0: Success.</span>
<a name="l00151"></a>00151 <span class="comment">*</span>
<a name="l00152"></a>00152 <span class="comment">* Notes:</span>
<a name="l00153"></a>00153 <span class="comment">* sphdpa() uses sphs2x() to rotate coordinates so that the reference point</span>
<a name="l00154"></a>00154 <span class="comment">* is at the north pole of the new system with the north pole of the old</span>
<a name="l00155"></a>00155 <span class="comment">* system at zero longitude in the new. The Euler angles required by</span>
<a name="l00156"></a>00156 <span class="comment">* sphs2x() for this rotation are</span>
<a name="l00157"></a>00157 <span class="comment">*</span>
<a name="l00158"></a>00158 <span class="comment">= eul[0] = lng0;</span>
<a name="l00159"></a>00159 <span class="comment">= eul[1] = 90.0 - lat0;</span>
<a name="l00160"></a>00160 <span class="comment">= eul[2] = 0.0;</span>
<a name="l00161"></a>00161 <span class="comment">*</span>
<a name="l00162"></a>00162 <span class="comment">* The angular distance and generalized position angle are readily obtained</span>
<a name="l00163"></a>00163 <span class="comment">* from the longitude and latitude of the field point in the new system.</span>
<a name="l00164"></a>00164 <span class="comment">* This applies even if the reference point is at one of the poles, in which</span>
<a name="l00165"></a>00165 <span class="comment">* case the "position angle" returned is as would be computed for a reference</span>
<a name="l00166"></a>00166 <span class="comment">* point at (lng0,+90-epsilon) or (lng0,-90+epsilon), in the limit as epsilon</span>
<a name="l00167"></a>00167 <span class="comment">* goes to zero.</span>
<a name="l00168"></a>00168 <span class="comment">*</span>
<a name="l00169"></a>00169 <span class="comment">* It is evident that the coordinate system in which the two points are</span>
<a name="l00170"></a>00170 <span class="comment">* expressed is irrelevant to the determination of the angular separation</span>
<a name="l00171"></a>00171 <span class="comment">* between the points. However, this is not true of the generalized position</span>
<a name="l00172"></a>00172 <span class="comment">* angle.</span>
<a name="l00173"></a>00173 <span class="comment">*</span>
<a name="l00174"></a>00174 <span class="comment">* The generalized position angle is here defined as the angle of</span>
<a name="l00175"></a>00175 <span class="comment">* intersection of the great circle containing the reference and field points</span>
<a name="l00176"></a>00176 <span class="comment">* with that containing the reference point and the pole. It has its normal</span>
<a name="l00177"></a>00177 <span class="comment">* meaning when the the reference and field points are specified in</span>
<a name="l00178"></a>00178 <span class="comment">* equatorial coordinates (right ascension and declination).</span>
<a name="l00179"></a>00179 <span class="comment">*</span>
<a name="l00180"></a>00180 <span class="comment">* Interchanging the reference and field points changes the position angle in</span>
<a name="l00181"></a>00181 <span class="comment">* a non-intuitive way (because the sum of the angles of a spherical triangle</span>
<a name="l00182"></a>00182 <span class="comment">* normally exceeds 180 degrees).</span>
<a name="l00183"></a>00183 <span class="comment">*</span>
<a name="l00184"></a>00184 <span class="comment">* The position angle is undefined if the reference and field points are</span>
<a name="l00185"></a>00185 <span class="comment">* coincident or antipodal. This may be detected by checking for a distance</span>
<a name="l00186"></a>00186 <span class="comment">* of 0 or 180 degrees (within rounding tolerance). sphdpa() will return an</span>
<a name="l00187"></a>00187 <span class="comment">* arbitrary position angle in such circumstances.</span>
<a name="l00188"></a>00188 <span class="comment">*</span>
<a name="l00189"></a>00189 <span class="comment">*</span>
<a name="l00190"></a>00190 <span class="comment">* sphpad() - Compute field points offset from a given point</span>
<a name="l00191"></a>00191 <span class="comment">* ---------------------------------------------------------</span>
<a name="l00192"></a>00192 <span class="comment">* sphpad() computes the coordinates of a set of points that are offset by the</span>
<a name="l00193"></a>00193 <span class="comment">* specified angular distances and position angles from a given "reference"</span>
<a name="l00194"></a>00194 <span class="comment">* point on the sky. The distances and position angles must be specified</span>
<a name="l00195"></a>00195 <span class="comment">* consistently in any spherical coordinate system.</span>
<a name="l00196"></a>00196 <span class="comment">*</span>
<a name="l00197"></a>00197 <span class="comment">* sphpad() is complementary to sphdpa().</span>
<a name="l00198"></a>00198 <span class="comment">*</span>
<a name="l00199"></a>00199 <span class="comment">* Given:</span>
<a name="l00200"></a>00200 <span class="comment">* nfield int The number of field points.</span>
<a name="l00201"></a>00201 <span class="comment">*</span>
<a name="l00202"></a>00202 <span class="comment">* lng0,lat0 double Spherical coordinates of the reference point [deg].</span>
<a name="l00203"></a>00203 <span class="comment">*</span>
<a name="l00204"></a>00204 <span class="comment">* dist,pa const double[]</span>
<a name="l00205"></a>00205 <span class="comment">* Angular distances and position angles [deg].</span>
<a name="l00206"></a>00206 <span class="comment">*</span>
<a name="l00207"></a>00207 <span class="comment">* Returned:</span>
<a name="l00208"></a>00208 <span class="comment">* lng,lat double[] Spherical coordinates of the field points [deg].</span>
<a name="l00209"></a>00209 <span class="comment">* These may refer to the same storage as dist and pa</span>
<a name="l00210"></a>00210 <span class="comment">* respectively.</span>
<a name="l00211"></a>00211 <span class="comment">*</span>
<a name="l00212"></a>00212 <span class="comment">* Function return value:</span>
<a name="l00213"></a>00213 <span class="comment">* int Status return value:</span>
<a name="l00214"></a>00214 <span class="comment">* 0: Success.</span>
<a name="l00215"></a>00215 <span class="comment">*</span>
<a name="l00216"></a>00216 <span class="comment">* Notes:</span>
<a name="l00217"></a>00217 <span class="comment">* sphpad() is implemented analogously to sphdpa() although using sphx2s()</span>
<a name="l00218"></a>00218 <span class="comment">* for the inverse transformation. In particular, when the reference point</span>
<a name="l00219"></a>00219 <span class="comment">* is at one of the poles, "position angle" is interpreted as though the</span>
<a name="l00220"></a>00220 <span class="comment">* reference point was at (lng0,+90-epsilon) or (lng0,-90+epsilon), in the</span>
<a name="l00221"></a>00221 <span class="comment">* limit as epsilon goes to zero.</span>
<a name="l00222"></a>00222 <span class="comment">*</span>
<a name="l00223"></a>00223 <span class="comment">* Applying sphpad() with the distances and position angles computed by</span>
<a name="l00224"></a>00224 <span class="comment">* sphdpa() should return the original field points.</span>
<a name="l00225"></a>00225 <span class="comment">*</span>
<a name="l00226"></a>00226 <span class="comment">*===========================================================================*/</span>
<a name="l00227"></a>00227
<a name="l00228"></a>00228 <span class="preprocessor">#ifndef WCSLIB_SPH</span>
<a name="l00229"></a>00229 <span class="preprocessor"></span><span class="preprocessor">#define WCSLIB_SPH</span>
<a name="l00230"></a>00230 <span class="preprocessor"></span>
<a name="l00231"></a>00231 <span class="preprocessor">#ifdef __cplusplus</span>
<a name="l00232"></a>00232 <span class="preprocessor"></span><span class="keyword">extern</span> <span class="stringliteral">"C"</span> {
<a name="l00233"></a>00233 <span class="preprocessor">#endif</span>
<a name="l00234"></a>00234 <span class="preprocessor"></span>
<a name="l00235"></a>00235
<a name="l00236"></a>00236 <span class="keywordtype">int</span> <a class="code" href="sph_8h.html#bcdbd119e57482315882d849f2b04e91" title="Rotation in the pixel-to-world direction.">sphx2s</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> eul[5], <span class="keywordtype">int</span> nphi, <span class="keywordtype">int</span> ntheta, <span class="keywordtype">int</span> spt, <span class="keywordtype">int</span> sxy,
<a name="l00237"></a>00237 <span class="keyword">const</span> <span class="keywordtype">double</span> phi[], <span class="keyword">const</span> <span class="keywordtype">double</span> theta[],
<a name="l00238"></a>00238 <span class="keywordtype">double</span> lng[], <span class="keywordtype">double</span> lat[]);
<a name="l00239"></a>00239
<a name="l00240"></a>00240 <span class="keywordtype">int</span> <a class="code" href="sph_8h.html#5c0783d56189d48d9f52af05b64a4df6" title="Rotation in the world-to-pixel direction.">sphs2x</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> eul[5], <span class="keywordtype">int</span> nlng, <span class="keywordtype">int</span> nlat, <span class="keywordtype">int</span> sll , <span class="keywordtype">int</span> spt,
<a name="l00241"></a>00241 <span class="keyword">const</span> <span class="keywordtype">double</span> lng[], <span class="keyword">const</span> <span class="keywordtype">double</span> lat[],
<a name="l00242"></a>00242 <span class="keywordtype">double</span> phi[], <span class="keywordtype">double</span> theta[]);
<a name="l00243"></a>00243
<a name="l00244"></a>00244 <span class="keywordtype">int</span> <a class="code" href="sph_8h.html#ec6222fe1e4d807c9b59980b8e548eb0" title="Compute angular distance and position angle.">sphdpa</a>(<span class="keywordtype">int</span> nfield, <span class="keywordtype">double</span> lng0, <span class="keywordtype">double</span> lat0,
<a name="l00245"></a>00245 <span class="keyword">const</span> <span class="keywordtype">double</span> lng[], <span class="keyword">const</span> <span class="keywordtype">double</span> lat[],
<a name="l00246"></a>00246 <span class="keywordtype">double</span> dist[], <span class="keywordtype">double</span> pa[]);
<a name="l00247"></a>00247
<a name="l00248"></a>00248 <span class="keywordtype">int</span> <a class="code" href="sph_8h.html#8ee2e117701f434f0bffbbe52f05d118" title="Compute field points offset from a given point.">sphpad</a>(<span class="keywordtype">int</span> nfield, <span class="keywordtype">double</span> lng0, <span class="keywordtype">double</span> lat0,
<a name="l00249"></a>00249 <span class="keyword">const</span> <span class="keywordtype">double</span> dist[], <span class="keyword">const</span> <span class="keywordtype">double</span> pa[],
<a name="l00250"></a>00250 <span class="keywordtype">double</span> lng[], <span class="keywordtype">double</span> lat[]);
<a name="l00251"></a>00251
<a name="l00252"></a>00252
<a name="l00253"></a>00253 <span class="preprocessor">#ifdef __cplusplus</span>
<a name="l00254"></a>00254 <span class="preprocessor"></span>}
<a name="l00255"></a>00255 <span class="preprocessor">#endif</span>
<a name="l00256"></a>00256 <span class="preprocessor"></span>
<a name="l00257"></a>00257 <span class="preprocessor">#endif </span><span class="comment">/* WCSLIB_SPH */</span>
</pre></div></div>
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