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<h1>AlbersEqualArea.hpp</h1> </div>
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<a href="AlbersEqualArea_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 AlbersEqualArea.hpp</span>
<a name="l00003"></a>00003 <span class="comment"> * \brief Header for GeographicLib::AlbersEqualArea class</span>
<a name="l00004"></a>00004 <span class="comment"> *</span>
<a name="l00005"></a>00005 <span class="comment"> * Copyright (c) Charles Karney (2010) <charles@karney.com> and licensed under</span>
<a name="l00006"></a>00006 <span class="comment"> * the LGPL. For more information, see http://geographiclib.sourceforge.net/</span>
<a name="l00007"></a>00007 <span class="comment"> **********************************************************************/</span>
<a name="l00008"></a>00008
<a name="l00009"></a>00009 <span class="preprocessor">#if !defined(GEOGRAPHICLIB_ALBERSEQUALAREA_HPP)</span>
<a name="l00010"></a><a class="code" href="AlbersEqualArea_8hpp.html#aa9494d369d907d2b285fcb2f45b4689c">00010</a> <span class="preprocessor"></span><span class="preprocessor">#define GEOGRAPHICLIB_ALBERSEQUALAREA_HPP "$Id: AlbersEqualArea.hpp 6919 2010-12-21 13:23:47Z karney $"</span>
<a name="l00011"></a>00011 <span class="preprocessor"></span>
<a name="l00012"></a>00012 <span class="preprocessor">#include "<a class="code" href="Constants_8hpp.html" title="Header for GeographicLib::Constants class.">GeographicLib/Constants.hpp</a>"</span>
<a name="l00013"></a>00013 <span class="preprocessor">#include <algorithm></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 Albers Equal Area Conic 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. 101&ndash;102.</span>
<a name="l00025"></a>00025 <span class="comment"> *</span>
<a name="l00026"></a>00026 <span class="comment"> * This is a implementation of the equations in Snyder except that divided</span>
<a name="l00027"></a>00027 <span class="comment"> * differences will be [have been] used to transform the expressions into</span>
<a name="l00028"></a>00028 <span class="comment"> * ones which may be evaluated accurately. [In this implementation, the</span>
<a name="l00029"></a>00029 <span class="comment"> * projection correctly becomes the cylindrical equal area or the azimuthal</span>
<a name="l00030"></a>00030 <span class="comment"> * equal area projection when the standard latitude is the equator or a</span>
<a name="l00031"></a>00031 <span class="comment"> * pole.]</span>
<a name="l00032"></a>00032 <span class="comment"> *</span>
<a name="l00033"></a>00033 <span class="comment"> * The ellipsoid parameters, the standard parallels, and the scale on the</span>
<a name="l00034"></a>00034 <span class="comment"> * standard parallels are set in the constructor. Internally, the case with</span>
<a name="l00035"></a>00035 <span class="comment"> * two standard parallels is converted into a single standard parallel, the</span>
<a name="l00036"></a>00036 <span class="comment"> * latitude of minimum azimuthal scale, with an azimuthal scale specified on</span>
<a name="l00037"></a>00037 <span class="comment"> * this parallel. This latitude is also used as the latitude of origin which</span>
<a name="l00038"></a>00038 <span class="comment"> * is returned by AlbersEqualArea::OriginLatitude. The azimuthal scale on</span>
<a name="l00039"></a>00039 <span class="comment"> * the latitude of origin is given by AlbersEqualArea::CentralScale. The</span>
<a name="l00040"></a>00040 <span class="comment"> * case with two standard parallels at opposite poles is singular and is</span>
<a name="l00041"></a>00041 <span class="comment"> * disallowed. The central meridian (which is a trivial shift of the</span>
<a name="l00042"></a>00042 <span class="comment"> * longitude) is specified as the \e lon0 argument of the</span>
<a name="l00043"></a>00043 <span class="comment"> * AlbersEqualArea::Forward and AlbersEqualArea::Reverse functions.</span>
<a name="l00044"></a>00044 <span class="comment"> * AlbersEqualArea::Forward and AlbersEqualArea::Reverse also return the</span>
<a name="l00045"></a>00045 <span class="comment"> * meridian convergence, \e gamma, and azimuthal scale, \e k. A small square</span>
<a name="l00046"></a>00046 <span class="comment"> * aligned with the cardinal directions is projected to a rectangle with</span>
<a name="l00047"></a>00047 <span class="comment"> * dimensions \e k (in the E-W direction) and 1/\e k (in the N-S direction).</span>
<a name="l00048"></a>00048 <span class="comment"> * The E-W sides of the rectangle are oriented \e gamma degrees</span>
<a name="l00049"></a>00049 <span class="comment"> * counter-clockwise from the \e x axis. There is no provision in this class</span>
<a name="l00050"></a>00050 <span class="comment"> * for specifying a false easting or false northing or a different latitude</span>
<a name="l00051"></a>00051 <span class="comment"> * of origin.</span>
<a name="l00052"></a>00052 <span class="comment"> **********************************************************************/</span>
<a name="l00053"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html">00053</a> <span class="keyword">class </span><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html" title="Albers Equal Area Conic Projection.">AlbersEqualArea</a> {
<a name="l00054"></a>00054 <span class="keyword">private</span>:
<a name="l00055"></a>00055 <span class="keyword">typedef</span> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> real;
<a name="l00056"></a>00056 <span class="keyword">const</span> real _a, _r, _f, _fm, _e2, _e, _e2m, _qZ, _qx;
<a name="l00057"></a>00057 real _sign, _lat0, _k0;
<a name="l00058"></a>00058 real _n0, _m02, _nrho0, _k2, _txi0, _scxi0, _sxi0;
<a name="l00059"></a>00059 <span class="keyword">static</span> <span class="keyword">const</span> real eps, epsx, epsx2, tol, tol0, ahypover;
<a name="l00060"></a>00060 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> numit = 5; <span class="comment">// Newton iterations in Reverse</span>
<a name="l00061"></a>00061 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> numit0 = 20; <span class="comment">// Newton iterations in Init</span>
<a name="l00062"></a>00062 <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="l00063"></a>00063 <span class="keyword">static</span> <span class="keyword">inline</span> real hyp(real x) <span class="keywordflow">throw</span>() { <span class="keywordflow">return</span> <a class="code" href="classGeographicLib_1_1Math.html#a0d422863198d4bec2aae6b187a60760c">Math::hypot</a>(real(1), x); }
<a name="l00064"></a>00064 <span class="comment">// atanh( e * x)/ e if f > 0</span>
<a name="l00065"></a>00065 <span class="comment">// atan (sqrt(-e2) * x)/sqrt(-e2) if f < 0</span>
<a name="l00066"></a>00066 <span class="comment">// x if f = 0</span>
<a name="l00067"></a>00067 <span class="keyword">inline</span> real atanhee(real x) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00068"></a>00068 <span class="keywordflow">return</span> _f > 0 ? <a class="code" href="classGeographicLib_1_1Math.html#a62ae372f983cb076561204be8de263bd">Math::atanh</a>(_e * x)/_e :
<a name="l00069"></a>00069 (_f < 0 ? std::atan(_e * x)/_e : x);
<a name="l00070"></a>00070 }
<a name="l00071"></a>00071 <span class="comment">// return atanh(sqrt(x))/sqrt(x) - 1, accurate for small x</span>
<a name="l00072"></a>00072 <span class="keyword">static</span> real atanhxm1(real x) <span class="keywordflow">throw</span>();
<a name="l00073"></a>00073
<a name="l00074"></a>00074 <span class="comment">// Divided differences</span>
<a name="l00075"></a>00075 <span class="comment">// Definition: Df(x,y) = (f(x)-f(y))/(x-y)</span>
<a name="l00076"></a>00076 <span class="comment">// See: W. M. Kahan and R. J. Fateman,</span>
<a name="l00077"></a>00077 <span class="comment">// Symbolic computation of divided differences,</span>
<a name="l00078"></a>00078 <span class="comment">// SIGSAM Bull. 33(3), 7-28 (1999)</span>
<a name="l00079"></a>00079 <span class="comment">// http://doi.acm.org/10.1145/334714.334716</span>
<a name="l00080"></a>00080 <span class="comment">// http://www.cs.berkeley.edu/~fateman/papers/divdiff.pdf</span>
<a name="l00081"></a>00081 <span class="comment">//</span>
<a name="l00082"></a>00082 <span class="comment">// General rules</span>
<a name="l00083"></a>00083 <span class="comment">// h(x) = f(g(x)): Dh(x,y) = Df(g(x),g(y))*Dg(x,y)</span>
<a name="l00084"></a>00084 <span class="comment">// h(x) = f(x)*g(x):</span>
<a name="l00085"></a>00085 <span class="comment">// Dh(x,y) = Df(x,y)*(g(x)+g(y))/2 + Dg(x,y)*(f(x)+f(y))/2</span>
<a name="l00086"></a>00086 <span class="comment">//</span>
<a name="l00087"></a>00087 <span class="comment">// sn(x) = x/sqrt(1+x^2): Dsn(x,y) = (x+y)/((sn(x)+sn(y))*(1+x^2)*(1+y^2))</span>
<a name="l00088"></a>00088 <span class="keyword">static</span> <span class="keyword">inline</span> real Dsn(real x, real y, real sx, real sy) <span class="keywordflow">throw</span>() {
<a name="l00089"></a>00089 <span class="comment">// sx = x/hyp(x)</span>
<a name="l00090"></a>00090 real t = x * y;
<a name="l00091"></a>00091 <span class="keywordflow">return</span> t > 0 ? (x + y) * sq( (sx * sy)/t ) / (sx + sy) :
<a name="l00092"></a>00092 (x - y != 0 ? (sx - sy) / (x - y) : 1);
<a name="l00093"></a>00093 }
<a name="l00094"></a>00094 <span class="comment">// Datanhee(x,y) = atanhee((x-y)/(1-e^2*x*y))/(x-y)</span>
<a name="l00095"></a>00095 <span class="keyword">inline</span> real Datanhee(real x, real y) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00096"></a>00096 real t = x - y, d = 1 - _e2 * x * y;
<a name="l00097"></a>00097 <span class="keywordflow">return</span> t != 0 ? atanhee(t / d) / t : 1 / d;
<a name="l00098"></a>00098 }
<a name="l00099"></a>00099 <span class="comment">// DDatanhee(x,y) = (Datanhee(1,y) - Datanhee(1,x))/(y-x)</span>
<a name="l00100"></a>00100 real DDatanhee(real x, real y) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00101"></a>00101 <span class="keywordtype">void</span> Init(real sphi1, real cphi1, real sphi2, real cphi2, real k1) <span class="keywordflow">throw</span>();
<a name="l00102"></a>00102 real txif(real tphi) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00103"></a>00103 real tphif(real txi) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00104"></a>00104 <span class="keyword">public</span>:
<a name="l00105"></a>00105 <span class="comment"></span>
<a name="l00106"></a>00106 <span class="comment"> /**</span>
<a name="l00107"></a>00107 <span class="comment"> * Constructor with a single standard parallel.</span>
<a name="l00108"></a>00108 <span class="comment"> *</span>
<a name="l00109"></a>00109 <span class="comment"> * @param[in] a equatorial radius of ellipsoid (meters)</span>
<a name="l00110"></a>00110 <span class="comment"> * @param[in] r reciprocal flattening of ellipsoid. Setting \e r = 0</span>
<a name="l00111"></a>00111 <span class="comment"> * implies \e r = inf or flattening = 0 (i.e., a sphere). Negative \e r</span>
<a name="l00112"></a>00112 <span class="comment"> * indicates a prolate ellipsoid.</span>
<a name="l00113"></a>00113 <span class="comment"> * @param[in] stdlat standard parallel (degrees), the circle of tangency.</span>
<a name="l00114"></a>00114 <span class="comment"> * @param[in] k0 azimuthal scale on the standard parallel.</span>
<a name="l00115"></a>00115 <span class="comment"> *</span>
<a name="l00116"></a>00116 <span class="comment"> * An exception is thrown if \e a or \e k0 is not positive or if \e stdlat</span>
<a name="l00117"></a>00117 <span class="comment"> * is not in the range [-90, 90].</span>
<a name="l00118"></a>00118 <span class="comment"> **********************************************************************/</span>
<a name="l00119"></a>00119 <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a10c2ea3bc889d27744a46e12477f418d">AlbersEqualArea</a>(real a, real r, real stdlat, real k0);
<a name="l00120"></a>00120 <span class="comment"></span>
<a name="l00121"></a>00121 <span class="comment"> /**</span>
<a name="l00122"></a>00122 <span class="comment"> * Constructor with two standard parallels.</span>
<a name="l00123"></a>00123 <span class="comment"> *</span>
<a name="l00124"></a>00124 <span class="comment"> * @param[in] a equatorial radius of ellipsoid (meters)</span>
<a name="l00125"></a>00125 <span class="comment"> * @param[in] r reciprocal flattening of ellipsoid. Setting \e r = 0</span>
<a name="l00126"></a>00126 <span class="comment"> * implies \e r = inf or flattening = 0 (i.e., a sphere). Negative \e r</span>
<a name="l00127"></a>00127 <span class="comment"> * indicates a prolate ellipsoid.</span>
<a name="l00128"></a>00128 <span class="comment"> * @param[in] stdlat1 first standard parallel (degrees).</span>
<a name="l00129"></a>00129 <span class="comment"> * @param[in] stdlat2 second standard parallel (degrees).</span>
<a name="l00130"></a>00130 <span class="comment"> * @param[in] k1 azimuthal scale on the standard parallels.</span>
<a name="l00131"></a>00131 <span class="comment"> *</span>
<a name="l00132"></a>00132 <span class="comment"> * An exception is thrown if \e a or \e k0 is not positive or if \e stdlat1</span>
<a name="l00133"></a>00133 <span class="comment"> * or \e stdlat2 is not in the range [-90, 90]. In addition, an exception</span>
<a name="l00134"></a>00134 <span class="comment"> * is thrown if \e stdlat1 and \e stdlat2 are opposite poles.</span>
<a name="l00135"></a>00135 <span class="comment"> **********************************************************************/</span>
<a name="l00136"></a>00136 <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a10c2ea3bc889d27744a46e12477f418d">AlbersEqualArea</a>(real a, real r, real stdlat1, real stdlat2, real k1);
<a name="l00137"></a>00137 <span class="comment"></span>
<a name="l00138"></a>00138 <span class="comment"> /**</span>
<a name="l00139"></a>00139 <span class="comment"> * Constructor with two standard parallels specified by sines and cosines.</span>
<a name="l00140"></a>00140 <span class="comment"> *</span>
<a name="l00141"></a>00141 <span class="comment"> * @param[in] a equatorial radius of ellipsoid (meters)</span>
<a name="l00142"></a>00142 <span class="comment"> * @param[in] r reciprocal flattening of ellipsoid. Setting \e r = 0</span>
<a name="l00143"></a>00143 <span class="comment"> * implies \e r = inf or flattening = 0 (i.e., a sphere). Negative \e r</span>
<a name="l00144"></a>00144 <span class="comment"> * indicates a prolate ellipsoid.</span>
<a name="l00145"></a>00145 <span class="comment"> * @param[in] sinlat1 sine of first standard parallel.</span>
<a name="l00146"></a>00146 <span class="comment"> * @param[in] coslat1 cosine of first standard parallel.</span>
<a name="l00147"></a>00147 <span class="comment"> * @param[in] sinlat2 sine of second standard parallel.</span>
<a name="l00148"></a>00148 <span class="comment"> * @param[in] coslat2 cosine of second standard parallel.</span>
<a name="l00149"></a>00149 <span class="comment"> * @param[in] k1 azimuthal scale on the standard parallels.</span>
<a name="l00150"></a>00150 <span class="comment"> *</span>
<a name="l00151"></a>00151 <span class="comment"> * This allows parallels close to the poles to be specified accurately.</span>
<a name="l00152"></a>00152 <span class="comment"> * This routine computes the latitude of origin and the azimuthal scale at</span>
<a name="l00153"></a>00153 <span class="comment"> * this latitude. If \e dlat = abs(\e lat2 - \e lat1) <= 160<sup>o</sup>,</span>
<a name="l00154"></a>00154 <span class="comment"> * then the error in the latitude of origin is less than</span>
<a name="l00155"></a>00155 <span class="comment"> * 4.5e-14<sup>o</sup>.</span>
<a name="l00156"></a>00156 <span class="comment"> **********************************************************************/</span>
<a name="l00157"></a>00157 <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a10c2ea3bc889d27744a46e12477f418d">AlbersEqualArea</a>(real a, real r,
<a name="l00158"></a>00158 real sinlat1, real coslat1,
<a name="l00159"></a>00159 real sinlat2, real coslat2,
<a name="l00160"></a>00160 real k1);
<a name="l00161"></a>00161 <span class="comment"></span>
<a name="l00162"></a>00162 <span class="comment"> /**</span>
<a name="l00163"></a>00163 <span class="comment"> * Set the azimuthal scale for the projection.</span>
<a name="l00164"></a>00164 <span class="comment"> *</span>
<a name="l00165"></a>00165 <span class="comment"> * @param[in] lat (degrees).</span>
<a name="l00166"></a>00166 <span class="comment"> * @param[in] k azimuthal scale at latitude \e lat (default 1).</span>
<a name="l00167"></a>00167 <span class="comment"> *</span>
<a name="l00168"></a>00168 <span class="comment"> * This allows a "latitude of conformality" to be specified. An exception</span>
<a name="l00169"></a>00169 <span class="comment"> * is thrown if \e k is not positive or if \e lat is not in the range (-90,</span>
<a name="l00170"></a>00170 <span class="comment"> * 90).</span>
<a name="l00171"></a>00171 <span class="comment"> **********************************************************************/</span>
<a name="l00172"></a>00172 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a0c00022edeb6b67dcd4e00f087b412c4">SetScale</a>(real lat, real k = real(1));
<a name="l00173"></a>00173 <span class="comment"></span>
<a name="l00174"></a>00174 <span class="comment"> /**</span>
<a name="l00175"></a>00175 <span class="comment"> * Forward projection, from geographic to Lambert conformal conic.</span>
<a name="l00176"></a>00176 <span class="comment"> *</span>
<a name="l00177"></a>00177 <span class="comment"> * @param[in] lon0 central meridian longitude (degrees).</span>
<a name="l00178"></a>00178 <span class="comment"> * @param[in] lat latitude of point (degrees).</span>
<a name="l00179"></a>00179 <span class="comment"> * @param[in] lon longitude of point (degrees).</span>
<a name="l00180"></a>00180 <span class="comment"> * @param[out] x easting of point (meters).</span>
<a name="l00181"></a>00181 <span class="comment"> * @param[out] y northing of point (meters).</span>
<a name="l00182"></a>00182 <span class="comment"> * @param[out] gamma meridian convergence at point (degrees).</span>
<a name="l00183"></a>00183 <span class="comment"> * @param[out] k azimuthal scale of projection at point; the radial</span>
<a name="l00184"></a>00184 <span class="comment"> * scale is the 1/\e k.</span>
<a name="l00185"></a>00185 <span class="comment"> *</span>
<a name="l00186"></a>00186 <span class="comment"> * The latitude origin is given by AlbersEqualArea::LatitudeOrigin(). No</span>
<a name="l00187"></a>00187 <span class="comment"> * false easting or northing is added and \e lat should be in the range</span>
<a name="l00188"></a>00188 <span class="comment"> * [-90, 90]; \e lon and \e lon0 should be in the range [-180, 360]. The</span>
<a name="l00189"></a>00189 <span class="comment"> * values of \e x and \e y returned for points which project to infinity</span>
<a name="l00190"></a>00190 <span class="comment"> * (i.e., one or both of the poles) will be large but finite.</span>
<a name="l00191"></a>00191 <span class="comment"> **********************************************************************/</span>
<a name="l00192"></a>00192 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#aac57f3a9c0c08fb897a1e37034d127c1">Forward</a>(real lon0, real lat, real lon,
<a name="l00193"></a>00193 real& x, real& y, real& gamma, real& k) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00194"></a>00194 <span class="comment"></span>
<a name="l00195"></a>00195 <span class="comment"> /**</span>
<a name="l00196"></a>00196 <span class="comment"> * Reverse projection, from Lambert conformal conic to geographic.</span>
<a name="l00197"></a>00197 <span class="comment"> *</span>
<a name="l00198"></a>00198 <span class="comment"> * @param[in] lon0 central meridian longitude (degrees).</span>
<a name="l00199"></a>00199 <span class="comment"> * @param[in] x easting of point (meters).</span>
<a name="l00200"></a>00200 <span class="comment"> * @param[in] y northing of point (meters).</span>
<a name="l00201"></a>00201 <span class="comment"> * @param[out] lat latitude of point (degrees).</span>
<a name="l00202"></a>00202 <span class="comment"> * @param[out] lon longitude of point (degrees).</span>
<a name="l00203"></a>00203 <span class="comment"> * @param[out] gamma meridian convergence at point (degrees).</span>
<a name="l00204"></a>00204 <span class="comment"> * @param[out] k azimuthal scale of projection at point; the radial</span>
<a name="l00205"></a>00205 <span class="comment"> * scale is the 1/\e k.</span>
<a name="l00206"></a>00206 <span class="comment"> *</span>
<a name="l00207"></a>00207 <span class="comment"> * The latitude origin is given by AlbersEqualArea::LatitudeOrigin(). No</span>
<a name="l00208"></a>00208 <span class="comment"> * false easting or northing is added. \e lon0 should be in the range</span>
<a name="l00209"></a>00209 <span class="comment"> * [-180, 360]. The value of \e lon returned is in the range [-180, 180).</span>
<a name="l00210"></a>00210 <span class="comment"> * The value of \e lat returned is in the range [-90,90]. If the input</span>
<a name="l00211"></a>00211 <span class="comment"> * point is outside the legal projected space the nearest pole is returned.</span>
<a name="l00212"></a>00212 <span class="comment"> **********************************************************************/</span>
<a name="l00213"></a>00213 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a577a9f43be8c1e238a4d56158acf8625">Reverse</a>(real lon0, real x, real y,
<a name="l00214"></a>00214 real& lat, real& lon, real& gamma, real& k) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00215"></a>00215 <span class="comment"></span>
<a name="l00216"></a>00216 <span class="comment"> /**</span>
<a name="l00217"></a>00217 <span class="comment"> * AlbersEqualArea::Forward without returning the convergence and</span>
<a name="l00218"></a>00218 <span class="comment"> * scale.</span>
<a name="l00219"></a>00219 <span class="comment"> **********************************************************************/</span>
<a name="l00220"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a68a13780a73bcf9c8e50a3ce4eae3086">00220</a> <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#aac57f3a9c0c08fb897a1e37034d127c1">Forward</a>(real lon0, real lat, real lon,
<a name="l00221"></a>00221 real& x, real& y) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00222"></a>00222 real gamma, k;
<a name="l00223"></a>00223 <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#aac57f3a9c0c08fb897a1e37034d127c1">Forward</a>(lon0, lat, lon, x, y, gamma, k);
<a name="l00224"></a>00224 }
<a name="l00225"></a>00225 <span class="comment"></span>
<a name="l00226"></a>00226 <span class="comment"> /**</span>
<a name="l00227"></a>00227 <span class="comment"> * AlbersEqualArea::Reverse without returning the convergence and</span>
<a name="l00228"></a>00228 <span class="comment"> * scale.</span>
<a name="l00229"></a>00229 <span class="comment"> **********************************************************************/</span>
<a name="l00230"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a871246cba03145512f3f12ceb3e3e3a8">00230</a> <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a577a9f43be8c1e238a4d56158acf8625">Reverse</a>(real lon0, real x, real y,
<a name="l00231"></a>00231 real& lat, real& lon) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00232"></a>00232 real gamma, k;
<a name="l00233"></a>00233 <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a577a9f43be8c1e238a4d56158acf8625">Reverse</a>(lon0, x, y, lat, lon, gamma, k);
<a name="l00234"></a>00234 }
<a name="l00235"></a>00235 <span class="comment"></span>
<a name="l00236"></a>00236 <span class="comment"> /** \name Inspector functions</span>
<a name="l00237"></a>00237 <span class="comment"> **********************************************************************/</span><span class="comment"></span>
<a name="l00238"></a>00238 <span class="comment"> ///@{</span>
<a name="l00239"></a>00239 <span class="comment"></span><span class="comment"> /**</span>
<a name="l00240"></a>00240 <span class="comment"> * @return \e a the equatorial radius of the ellipsoid (meters). This is</span>
<a name="l00241"></a>00241 <span class="comment"> * the value used in the constructor.</span>
<a name="l00242"></a>00242 <span class="comment"> **********************************************************************/</span>
<a name="l00243"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a55d5ca45e7c80a96b3faf0094714ac59">00243</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a55d5ca45e7c80a96b3faf0094714ac59">MajorRadius</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _a; }
<a name="l00244"></a>00244 <span class="comment"></span>
<a name="l00245"></a>00245 <span class="comment"> /**</span>
<a name="l00246"></a>00246 <span class="comment"> * @return \e r the inverse flattening of the ellipsoid. This is the</span>
<a name="l00247"></a>00247 <span class="comment"> * value used in the constructor. A value of 0 is returned for a sphere</span>
<a name="l00248"></a>00248 <span class="comment"> * (infinite inverse flattening).</span>
<a name="l00249"></a>00249 <span class="comment"> **********************************************************************/</span>
<a name="l00250"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a1d0ad953a852d4cdb9faa731b5530d70">00250</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#a1d0ad953a852d4cdb9faa731b5530d70">InverseFlattening</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _r; }
<a name="l00251"></a>00251 <span class="comment"></span>
<a name="l00252"></a>00252 <span class="comment"> /**</span>
<a name="l00253"></a>00253 <span class="comment"> * @return latitude of the origin for the projection (degrees).</span>
<a name="l00254"></a>00254 <span class="comment"> *</span>
<a name="l00255"></a>00255 <span class="comment"> * This is the latitude of minimum azimuthal scale and equals the \e stdlat</span>
<a name="l00256"></a>00256 <span class="comment"> * in the 1-parallel constructor and lies between \e stdlat1 and \e stdlat2</span>
<a name="l00257"></a>00257 <span class="comment"> * in the 2-parallel constructors.</span>
<a name="l00258"></a>00258 <span class="comment"> **********************************************************************/</span>
<a name="l00259"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#ad780e943e9a9ba168b350d809d0bfe08">00259</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#ad780e943e9a9ba168b350d809d0bfe08">OriginLatitude</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _lat0; }
<a name="l00260"></a>00260 <span class="comment"></span>
<a name="l00261"></a>00261 <span class="comment"> /**</span>
<a name="l00262"></a>00262 <span class="comment"> * @return central scale for the projection. This is the azimuthal scale</span>
<a name="l00263"></a>00263 <span class="comment"> * on the latitude of origin.</span>
<a name="l00264"></a>00264 <span class="comment"> **********************************************************************/</span>
<a name="l00265"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#af407e835eaf76895ee25ec9e7a9c090c">00265</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#af407e835eaf76895ee25ec9e7a9c090c">CentralScale</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _k0; }<span class="comment"></span>
<a name="l00266"></a>00266 <span class="comment"> ///@}</span>
<a name="l00267"></a>00267 <span class="comment"></span><span class="comment"></span>
<a name="l00268"></a>00268 <span class="comment"> /**</span>
<a name="l00269"></a>00269 <span class="comment"> * A global instantiation of AlbersEqualArea with the WGS84 ellipsoid, \e</span>
<a name="l00270"></a>00270 <span class="comment"> * stdlat = 0, and \e k0 = 1. This degenerates to the cylindrical equal</span>
<a name="l00271"></a>00271 <span class="comment"> * area projection.</span>
<a name="l00272"></a>00272 <span class="comment"> **********************************************************************/</span>
<a name="l00273"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#ae643f7f82f5864f95da4cb14571ccf55">00273</a> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html" title="Albers Equal Area Conic Projection.">AlbersEqualArea</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#ae643f7f82f5864f95da4cb14571ccf55">CylindricalEqualArea</a>;
<a name="l00274"></a>00274 <span class="comment"></span>
<a name="l00275"></a>00275 <span class="comment"> /**</span>
<a name="l00276"></a>00276 <span class="comment"> * A global instantiation of AlbersEqualArea with the WGS84 ellipsoid, \e</span>
<a name="l00277"></a>00277 <span class="comment"> * stdlat = 90<sup>o</sup>, and \e k0 = 1. This degenerates to the</span>
<a name="l00278"></a>00278 <span class="comment"> * Lambert azimuthal equal area projection.</span>
<a name="l00279"></a>00279 <span class="comment"> **********************************************************************/</span>
<a name="l00280"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#ae65fcb68843b36d206751527ebd08f44">00280</a> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html" title="Albers Equal Area Conic Projection.">AlbersEqualArea</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#ae65fcb68843b36d206751527ebd08f44">AzimuthalEqualAreaNorth</a>;
<a name="l00281"></a>00281 <span class="comment"></span>
<a name="l00282"></a>00282 <span class="comment"> /**</span>
<a name="l00283"></a>00283 <span class="comment"> * A global instantiation of AlbersEqualArea with the WGS84 ellipsoid, \e</span>
<a name="l00284"></a>00284 <span class="comment"> * stdlat = -90<sup>o</sup>, and \e k0 = 1. This degenerates to the</span>
<a name="l00285"></a>00285 <span class="comment"> * Lambert azimuthal equal area projection.</span>
<a name="l00286"></a>00286 <span class="comment"> **********************************************************************/</span>
<a name="l00287"></a><a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#aff0ff4e2f162107bd136310b44444cc1">00287</a> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html" title="Albers Equal Area Conic Projection.">AlbersEqualArea</a> <a class="code" href="classGeographicLib_1_1AlbersEqualArea.html#aff0ff4e2f162107bd136310b44444cc1">AzimuthalEqualAreaSouth</a>;
<a name="l00288"></a>00288 };
<a name="l00289"></a>00289
<a name="l00290"></a>00290 } <span class="comment">// namespace GeographicLib</span>
<a name="l00291"></a>00291
<a name="l00292"></a>00292 <span class="preprocessor">#endif</span>
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