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<h1>PolarStereographic.hpp</h1> </div>
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<a href="PolarStereographic_8hpp.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"> * \file PolarStereographic.hpp</span>
<a name="l00003"></a>00003 <span class="comment"> * \brief Header for GeographicLib::PolarStereographic class</span>
<a name="l00004"></a>00004 <span class="comment"> *</span>
<a name="l00005"></a>00005 <span class="comment"> * Copyright (c) Charles Karney (2008, 2009, 2010) <charles@karney.com></span>
<a name="l00006"></a>00006 <span class="comment"> * and licensed under the LGPL. For more information, see</span>
<a name="l00007"></a>00007 <span class="comment"> * http://geographiclib.sourceforge.net/</span>
<a name="l00008"></a>00008 <span class="comment"> **********************************************************************/</span>
<a name="l00009"></a>00009
<a name="l00010"></a>00010 <span class="preprocessor">#if !defined(GEOGRAPHICLIB_POLARSTEREOGRAPHIC_HPP)</span>
<a name="l00011"></a><a class="code" href="PolarStereographic_8hpp.html#a7450566a6ed1475dc10f7c0dc85f5dd9">00011</a> <span class="preprocessor"></span><span class="preprocessor">#define GEOGRAPHICLIB_POLARSTEREOGRAPHIC_HPP "$Id: PolarStereographic.hpp 6906 2010-12-02 22:10:56Z karney $"</span>
<a name="l00012"></a>00012 <span class="preprocessor"></span>
<a name="l00013"></a>00013 <span class="preprocessor">#include "<a class="code" href="Constants_8hpp.html" title="Header for GeographicLib::Constants class.">GeographicLib/Constants.hpp</a>"</span>
<a name="l00014"></a>00014
<a name="l00015"></a>00015 <span class="keyword">namespace </span>GeographicLib {
<a name="l00016"></a>00016 <span class="comment"></span>
<a name="l00017"></a>00017 <span class="comment"> /**</span>
<a name="l00018"></a>00018 <span class="comment"> * \brief Polar Stereographic Projection</span>
<a name="l00019"></a>00019 <span class="comment"> *</span>
<a name="l00020"></a>00020 <span class="comment"> * Implementation taken from the report,</span>
<a name="l00021"></a>00021 <span class="comment"> * - J. P. Snyder,</span>
<a name="l00022"></a>00022 <span class="comment"> * <a href="http://pubs.er.usgs.gov/usgspubs/pp/pp1395"> Map Projections: A</span>
<a name="l00023"></a>00023 <span class="comment"> * Working Manual</a>, USGS Professional Paper 1395 (1987),</span>
<a name="l00024"></a>00024 <span class="comment"> * pp. 160&ndash;163.</span>
<a name="l00025"></a>00025 <span class="comment"> *</span>
<a name="l00026"></a>00026 <span class="comment"> * This is a straightforward implementation of the equations in Snyder except</span>
<a name="l00027"></a>00027 <span class="comment"> * that Newton's method is used to invert the projection.</span>
<a name="l00028"></a>00028 <span class="comment"> **********************************************************************/</span>
<a name="l00029"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html">00029</a> <span class="keyword">class </span><a class="code" href="classGeographicLib_1_1PolarStereographic.html" title="Polar Stereographic Projection.">PolarStereographic</a> {
<a name="l00030"></a>00030 <span class="keyword">private</span>:
<a name="l00031"></a>00031 <span class="keyword">typedef</span> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> real;
<a name="l00032"></a>00032 <span class="comment">// _Cx used to be _C but g++ 3.4 has a macro of that name</span>
<a name="l00033"></a>00033 <span class="keyword">const</span> real _a, _r, _f, _e2, _e, _e2m, _Cx, _c;
<a name="l00034"></a>00034 real _k0;
<a name="l00035"></a>00035 <span class="keyword">static</span> <span class="keyword">const</span> real tol, overflow;
<a name="l00036"></a>00036 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> numit = 5;
<a name="l00037"></a>00037 <span class="keyword">static</span> <span class="keyword">inline</span> real sq(real x) <span class="keywordflow">throw</span>() { <span class="keywordflow">return</span> x * x; }
<a name="l00038"></a>00038 <span class="comment">// Return e * atanh(e * x) for f >= 0, else return</span>
<a name="l00039"></a>00039 <span class="comment">// - sqrt(-e2) * atan( sqrt(-e2) * x) for f < 0</span>
<a name="l00040"></a>00040 <span class="keyword">inline</span> real eatanhe(real x) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00041"></a>00041 <span class="keywordflow">return</span> _f >= 0 ? _e * <a class="code" href="classGeographicLib_1_1Math.html#a62ae372f983cb076561204be8de263bd">Math::atanh</a>(_e * x) : - _e * std::atan(_e * x);
<a name="l00042"></a>00042 }
<a name="l00043"></a>00043 <span class="keyword">public</span>:
<a name="l00044"></a>00044 <span class="comment"></span>
<a name="l00045"></a>00045 <span class="comment"> /**</span>
<a name="l00046"></a>00046 <span class="comment"> * Constructor for a ellipsoid with</span>
<a name="l00047"></a>00047 <span class="comment"> *</span>
<a name="l00048"></a>00048 <span class="comment"> * @param[in] a equatorial radius (meters)</span>
<a name="l00049"></a>00049 <span class="comment"> * @param[in] r reciprocal flattening. Setting \e r = 0 implies \e r = inf</span>
<a name="l00050"></a>00050 <span class="comment"> * or flattening = 0 (i.e., a sphere). Negative \e r indicates a prolate</span>
<a name="l00051"></a>00051 <span class="comment"> * ellipsoid.</span>
<a name="l00052"></a>00052 <span class="comment"> * @param[in] k0 central scale factor.</span>
<a name="l00053"></a>00053 <span class="comment"> *</span>
<a name="l00054"></a>00054 <span class="comment"> * An exception is thrown if either of the axes of the ellipsoid is</span>
<a name="l00055"></a>00055 <span class="comment"> * not positive \e a or if \e k0 is not positive.</span>
<a name="l00056"></a>00056 <span class="comment"> **********************************************************************/</span>
<a name="l00057"></a>00057 <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a56558071847ee7d71674ac29a23ec653">PolarStereographic</a>(real a, real r, real k0);
<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"> * Set the scale for the projection.</span>
<a name="l00061"></a>00061 <span class="comment"> *</span>
<a name="l00062"></a>00062 <span class="comment"> * @param[in] lat (degrees) assuming \e northp = true.</span>
<a name="l00063"></a>00063 <span class="comment"> * @param[in] k scale at latitude \e lat (default 1).</span>
<a name="l00064"></a>00064 <span class="comment"> *</span>
<a name="l00065"></a>00065 <span class="comment"> * This allows a "latitude of true scale" to be specified. An exception is</span>
<a name="l00066"></a>00066 <span class="comment"> * thrown if \e k is not positive or if \e lat is not in the range (-90,</span>
<a name="l00067"></a>00067 <span class="comment"> * 90].</span>
<a name="l00068"></a>00068 <span class="comment"> **********************************************************************/</span>
<a name="l00069"></a>00069 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a3f957214eb1d1248277a680e4c4ceed5">SetScale</a>(real lat, real k = real(1));
<a name="l00070"></a>00070 <span class="comment"></span>
<a name="l00071"></a>00071 <span class="comment"> /**</span>
<a name="l00072"></a>00072 <span class="comment"> * Forward projection, from geographic to polar stereographic.</span>
<a name="l00073"></a>00073 <span class="comment"> *</span>
<a name="l00074"></a>00074 <span class="comment"> * @param[in] northp the pole which is the center of projection (true means</span>
<a name="l00075"></a>00075 <span class="comment"> * north, false means south).</span>
<a name="l00076"></a>00076 <span class="comment"> * @param[in] lat latitude of point (degrees).</span>
<a name="l00077"></a>00077 <span class="comment"> * @param[in] lon longitude of point (degrees).</span>
<a name="l00078"></a>00078 <span class="comment"> * @param[out] x easting of point (meters).</span>
<a name="l00079"></a>00079 <span class="comment"> * @param[out] y northing of point (meters).</span>
<a name="l00080"></a>00080 <span class="comment"> * @param[out] gamma meridian convergence at point (degrees).</span>
<a name="l00081"></a>00081 <span class="comment"> * @param[out] k scale of projection at point.</span>
<a name="l00082"></a>00082 <span class="comment"> *</span>
<a name="l00083"></a>00083 <span class="comment"> * No false easting or northing is added. \e lat should be in the range</span>
<a name="l00084"></a>00084 <span class="comment"> * (-90, 90] for \e northp = true and in the range [-90, 90) for \e northp</span>
<a name="l00085"></a>00085 <span class="comment"> * = false; \e lon should be in the range [-180, 360].</span>
<a name="l00086"></a>00086 <span class="comment"> **********************************************************************/</span>
<a name="l00087"></a>00087 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a30ef1a1f906ee389e2a5f7e5fd7d8fa4">Forward</a>(<span class="keywordtype">bool</span> northp, real lat, real lon,
<a name="l00088"></a>00088 real& x, real& y, real& gamma, real& k) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00089"></a>00089 <span class="comment"></span>
<a name="l00090"></a>00090 <span class="comment"> /**</span>
<a name="l00091"></a>00091 <span class="comment"> * Reverse projection, from polar stereographic to geographic.</span>
<a name="l00092"></a>00092 <span class="comment"> *</span>
<a name="l00093"></a>00093 <span class="comment"> * @param[in] northp the pole which is the center of projection (true means</span>
<a name="l00094"></a>00094 <span class="comment"> * north, false means south).</span>
<a name="l00095"></a>00095 <span class="comment"> * @param[in] x easting of point (meters).</span>
<a name="l00096"></a>00096 <span class="comment"> * @param[in] y northing of point (meters).</span>
<a name="l00097"></a>00097 <span class="comment"> * @param[out] lat latitude of point (degrees).</span>
<a name="l00098"></a>00098 <span class="comment"> * @param[out] lon longitude of point (degrees).</span>
<a name="l00099"></a>00099 <span class="comment"> * @param[out] gamma meridian convergence at point (degrees).</span>
<a name="l00100"></a>00100 <span class="comment"> * @param[out] k scale of projection at point.</span>
<a name="l00101"></a>00101 <span class="comment"> *</span>
<a name="l00102"></a>00102 <span class="comment"> * No false easting or northing is added. The value of \e lon returned is</span>
<a name="l00103"></a>00103 <span class="comment"> * in the range [-180, 180).</span>
<a name="l00104"></a>00104 <span class="comment"> **********************************************************************/</span>
<a name="l00105"></a>00105 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a01302b8dba43c57e3c3849f94123a157">Reverse</a>(<span class="keywordtype">bool</span> northp, real x, real y,
<a name="l00106"></a>00106 real& lat, real& lon, real& gamma, real& k) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00107"></a>00107 <span class="comment"></span>
<a name="l00108"></a>00108 <span class="comment"> /**</span>
<a name="l00109"></a>00109 <span class="comment"> * PolarStereographic::Forward without returning the convergence and scale.</span>
<a name="l00110"></a>00110 <span class="comment"> **********************************************************************/</span>
<a name="l00111"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html#ac2fe4c9524ec35f8d05336555f96e1b1">00111</a> <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a30ef1a1f906ee389e2a5f7e5fd7d8fa4">Forward</a>(<span class="keywordtype">bool</span> northp, real lat, real lon,
<a name="l00112"></a>00112 real& x, real& y) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00113"></a>00113 real gamma, k;
<a name="l00114"></a>00114 <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a30ef1a1f906ee389e2a5f7e5fd7d8fa4">Forward</a>(northp, lat, lon, x, y, gamma, k);
<a name="l00115"></a>00115 }
<a name="l00116"></a>00116 <span class="comment"></span>
<a name="l00117"></a>00117 <span class="comment"> /**</span>
<a name="l00118"></a>00118 <span class="comment"> * PolarStereographic::Reverse without returning the convergence and scale.</span>
<a name="l00119"></a>00119 <span class="comment"> **********************************************************************/</span>
<a name="l00120"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html#a16572cc552eeb24ebf84319cdcd6652e">00120</a> <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a01302b8dba43c57e3c3849f94123a157">Reverse</a>(<span class="keywordtype">bool</span> northp, real x, real y,
<a name="l00121"></a>00121 real& lat, real& lon) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00122"></a>00122 real gamma, k;
<a name="l00123"></a>00123 <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a01302b8dba43c57e3c3849f94123a157">Reverse</a>(northp, x, y, lat, lon, gamma, k);
<a name="l00124"></a>00124 }
<a name="l00125"></a>00125 <span class="comment"></span>
<a name="l00126"></a>00126 <span class="comment"> /** \name Inspector functions</span>
<a name="l00127"></a>00127 <span class="comment"> **********************************************************************/</span><span class="comment"></span>
<a name="l00128"></a>00128 <span class="comment"> ///@{</span>
<a name="l00129"></a>00129 <span class="comment"></span><span class="comment"> /**</span>
<a name="l00130"></a>00130 <span class="comment"> * @return \e a the equatorial radius of the ellipsoid (meters). This is</span>
<a name="l00131"></a>00131 <span class="comment"> * the value used in the constructor.</span>
<a name="l00132"></a>00132 <span class="comment"> **********************************************************************/</span>
<a name="l00133"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html#ab1746576356a2409f34d9527064adfdd">00133</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#ab1746576356a2409f34d9527064adfdd">MajorRadius</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _a; }
<a name="l00134"></a>00134 <span class="comment"></span>
<a name="l00135"></a>00135 <span class="comment"> /**</span>
<a name="l00136"></a>00136 <span class="comment"> * @return \e r the inverse flattening of the ellipsoid. This is the</span>
<a name="l00137"></a>00137 <span class="comment"> * value used in the constructor. A value of 0 is returned for a sphere</span>
<a name="l00138"></a>00138 <span class="comment"> * (infinite inverse flattening).</span>
<a name="l00139"></a>00139 <span class="comment"> **********************************************************************/</span>
<a name="l00140"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html#a969a21c3df38517a081e233ae90c098e">00140</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a969a21c3df38517a081e233ae90c098e">InverseFlattening</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _r; }
<a name="l00141"></a>00141 <span class="comment"></span>
<a name="l00142"></a>00142 <span class="comment"> /**</span>
<a name="l00143"></a>00143 <span class="comment"> * The central scale for the projection. This is the value of \e k0 used</span>
<a name="l00144"></a>00144 <span class="comment"> * in the constructor and is the scale at the pole unless overridden by</span>
<a name="l00145"></a>00145 <span class="comment"> * PolarStereographic::SetScale.</span>
<a name="l00146"></a>00146 <span class="comment"> **********************************************************************/</span>
<a name="l00147"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html#ad6f7bd8a35208d91706ac8c258387e6f">00147</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#ad6f7bd8a35208d91706ac8c258387e6f">CentralScale</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _k0; }<span class="comment"></span>
<a name="l00148"></a>00148 <span class="comment"> ///@}</span>
<a name="l00149"></a>00149 <span class="comment"></span><span class="comment"></span>
<a name="l00150"></a>00150 <span class="comment"> /**</span>
<a name="l00151"></a>00151 <span class="comment"> * A global instantiation of PolarStereographic with the WGS84 ellipsoid</span>
<a name="l00152"></a>00152 <span class="comment"> * and the UPS scale factor. However, unlike UPS, no false easting or</span>
<a name="l00153"></a>00153 <span class="comment"> * northing is added.</span>
<a name="l00154"></a>00154 <span class="comment"> **********************************************************************/</span>
<a name="l00155"></a><a class="code" href="classGeographicLib_1_1PolarStereographic.html#a2db6bcb1b59a6ddc6087ee04c64c9825">00155</a> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="classGeographicLib_1_1PolarStereographic.html" title="Polar Stereographic Projection.">PolarStereographic</a> <a class="code" href="classGeographicLib_1_1PolarStereographic.html#a2db6bcb1b59a6ddc6087ee04c64c9825">UPS</a>;
<a name="l00156"></a>00156 };
<a name="l00157"></a>00157
<a name="l00158"></a>00158 } <span class="comment">// namespace GeographicLib</span>
<a name="l00159"></a>00159
<a name="l00160"></a>00160 <span class="preprocessor">#endif</span>
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