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<h1>LambertConformalConic.hpp</h1> </div>
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<a href="LambertConformalConic_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 LambertConformalConic.hpp</span>
<a name="l00003"></a>00003 <span class="comment"> * \brief Header for GeographicLib::LambertConformalConic class</span>
<a name="l00004"></a>00004 <span class="comment"> *</span>
<a name="l00005"></a>00005 <span class="comment"> * Copyright (c) Charles Karney (2010, 2011) <charles@karney.com> and licensed</span>
<a name="l00006"></a>00006 <span class="comment"> * 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_LAMBERTCONFORMALCONIC_HPP)</span>
<a name="l00011"></a><a class="code" href="LambertConformalConic_8hpp.html#aac2fbd995d5b75016781c58b97093c67">00011</a> <span class="preprocessor"></span><span class="preprocessor">#define GEOGRAPHICLIB_LAMBERTCONFORMALCONIC_HPP "$Id: LambertConformalConic.hpp 6937 2011-02-01 20:17:13Z 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 <span class="preprocessor">#include <algorithm></span>
<a name="l00015"></a>00015
<a name="l00016"></a>00016 <span class="keyword">namespace </span>GeographicLib {
<a name="l00017"></a>00017 <span class="comment"></span>
<a name="l00018"></a>00018 <span class="comment"> /**</span>
<a name="l00019"></a>00019 <span class="comment"> * \brief Lambert Conformal Conic Projection</span>
<a name="l00020"></a>00020 <span class="comment"> *</span>
<a name="l00021"></a>00021 <span class="comment"> * Implementation taken from the report,</span>
<a name="l00022"></a>00022 <span class="comment"> * - J. P. Snyder,</span>
<a name="l00023"></a>00023 <span class="comment"> * <a href="http://pubs.er.usgs.gov/usgspubs/pp/pp1395"> Map Projections: A</span>
<a name="l00024"></a>00024 <span class="comment"> * Working Manual</a>, USGS Professional Paper 1395 (1987),</span>
<a name="l00025"></a>00025 <span class="comment"> * pp. 107&ndash;109.</span>
<a name="l00026"></a>00026 <span class="comment"> *</span>
<a name="l00027"></a>00027 <span class="comment"> * This is a implementation of the equations in Snyder except that divided</span>
<a name="l00028"></a>00028 <span class="comment"> * differences have been used to transform the expressions into ones which</span>
<a name="l00029"></a>00029 <span class="comment"> * may be evaluated accurately and that Newton's method is used to invert the</span>
<a name="l00030"></a>00030 <span class="comment"> * projection. In this implementation, the projection correctly becomes the</span>
<a name="l00031"></a>00031 <span class="comment"> * Mercator projection or the polar sterographic projection when the standard</span>
<a name="l00032"></a>00032 <span class="comment"> * latitude is the equator or a pole. The accuracy of the projections is</span>
<a name="l00033"></a>00033 <span class="comment"> * about 10 nm.</span>
<a name="l00034"></a>00034 <span class="comment"> *</span>
<a name="l00035"></a>00035 <span class="comment"> * The ellipsoid parameters, the standard parallels, and the scale on the</span>
<a name="l00036"></a>00036 <span class="comment"> * standard parallels are set in the constructor. Internally, the case with</span>
<a name="l00037"></a>00037 <span class="comment"> * two standard parallels is converted into a single standard parallel, the</span>
<a name="l00038"></a>00038 <span class="comment"> * latitude of tangency (also the latitude of minimum scale), with a scale</span>
<a name="l00039"></a>00039 <span class="comment"> * specified on this parallel. This latitude is also used as the latitude of</span>
<a name="l00040"></a>00040 <span class="comment"> * origin which is returned by LambertConformalConic::OriginLatitude. The</span>
<a name="l00041"></a>00041 <span class="comment"> * scale on the latitude of origin is given by</span>
<a name="l00042"></a>00042 <span class="comment"> * LambertConformalConic::CentralScale. The case with two distinct standard</span>
<a name="l00043"></a>00043 <span class="comment"> * parallels where one is a pole is singular and is disallowed. The central</span>
<a name="l00044"></a>00044 <span class="comment"> * meridian (which is a trivial shift of the longitude) is specified as the</span>
<a name="l00045"></a>00045 <span class="comment"> * \e lon0 argument of the LambertConformalConic::Forward and</span>
<a name="l00046"></a>00046 <span class="comment"> * LambertConformalConic::Reverse functions. There is no provision in this</span>
<a name="l00047"></a>00047 <span class="comment"> * class for specifying a false easting or false northing or a different</span>
<a name="l00048"></a>00048 <span class="comment"> * latitude of origin. However these are can be simply included by the</span>
<a name="l00049"></a>00049 <span class="comment"> * calling function. For example the Pennsylvania South state coordinate</span>
<a name="l00050"></a>00050 <span class="comment"> * system (<a href="http://www.spatialreference.org/ref/epsg/3364/"></span>
<a name="l00051"></a>00051 <span class="comment"> * EPSG:3364</a>) is obtained by:</span>
<a name="l00052"></a>00052 <span class="comment"> \code</span>
<a name="l00053"></a>00053 <span class="comment"> const double</span>
<a name="l00054"></a>00054 <span class="comment"> a = GeographicLib::Constants::WGS84_a<double>(),</span>
<a name="l00055"></a>00055 <span class="comment"> r = 298.257222101, // GRS80</span>
<a name="l00056"></a>00056 <span class="comment"> lat1 = 39 + 56/60.0, lat1 = 40 + 58/60.0, // standard parallels</span>
<a name="l00057"></a>00057 <span class="comment"> k1 = 1, // scale</span>
<a name="l00058"></a>00058 <span class="comment"> lat0 = 39 + 20/60.0, lon0 = 75 + 45/60.0, // origin</span>
<a name="l00059"></a>00059 <span class="comment"> fe = 600000, fn = 0; // false easting and northing</span>
<a name="l00060"></a>00060 <span class="comment"> // Set up basic projection</span>
<a name="l00061"></a>00061 <span class="comment"> const GeographicLib::LambertConformalConic PASouth(a, r, lat1, lat2, k1);</span>
<a name="l00062"></a>00062 <span class="comment"> double x0, y0;</span>
<a name="l00063"></a>00063 <span class="comment"> {</span>
<a name="l00064"></a>00064 <span class="comment"> // Transform origin point</span>
<a name="l00065"></a>00065 <span class="comment"> PASouth.Forward(lon0, lat0, lon0, x0, y0);</span>
<a name="l00066"></a>00066 <span class="comment"> x0 -= fe; y0 -= fn; // Combine result with false origin</span>
<a name="l00067"></a>00067 <span class="comment"> }</span>
<a name="l00068"></a>00068 <span class="comment"> double lat, lon, x, y;</span>
<a name="l00069"></a>00069 <span class="comment"> // Sample conversion from geodetic to PASouth grid</span>
<a name="l00070"></a>00070 <span class="comment"> std::cin >> lat >> lon;</span>
<a name="l00071"></a>00071 <span class="comment"> PASouth.Forward(lon0, lat, lon, x, y);</span>
<a name="l00072"></a>00072 <span class="comment"> x -= x0; y -= y0;</span>
<a name="l00073"></a>00073 <span class="comment"> std::cout << x << " " << y << "\n";</span>
<a name="l00074"></a>00074 <span class="comment"> // Sample conversion from PASouth grid to geodetic</span>
<a name="l00075"></a>00075 <span class="comment"> std::cin >> x >> y;</span>
<a name="l00076"></a>00076 <span class="comment"> x += x0; y += y0;</span>
<a name="l00077"></a>00077 <span class="comment"> PASouth.Reverse(lon0, x, y, lat, lon);</span>
<a name="l00078"></a>00078 <span class="comment"> std::cout << lat << " " << lon << "\n";</span>
<a name="l00079"></a>00079 <span class="comment"> \endcode</span>
<a name="l00080"></a>00080 <span class="comment"> **********************************************************************/</span>
<a name="l00081"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html">00081</a> <span class="keyword">class </span><a class="code" href="classGeographicLib_1_1LambertConformalConic.html" title="Lambert Conformal Conic Projection.">LambertConformalConic</a> {
<a name="l00082"></a>00082 <span class="keyword">private</span>:
<a name="l00083"></a>00083 <span class="keyword">typedef</span> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> real;
<a name="l00084"></a>00084 <span class="keyword">const</span> real _a, _r, _f, _fm, _e2, _e, _e2m;
<a name="l00085"></a>00085 real _sign, _n, _nc, _t0nm1, _scale, _lat0, _k0;
<a name="l00086"></a>00086 real _scbet0, _tchi0, _scchi0, _psi0, _nrho0;
<a name="l00087"></a>00087 <span class="keyword">static</span> <span class="keyword">const</span> real eps, epsx, tol, ahypover;
<a name="l00088"></a>00088 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> numit = 5;
<a name="l00089"></a>00089 <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="l00090"></a>00090 <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="l00091"></a>00091 <span class="comment">// e * atanh(e * x) = log( ((1 + e*x)/(1 - e*x))^(e/2) ) if f >= 0</span>
<a name="l00092"></a>00092 <span class="comment">// - sqrt(-e2) * atan( sqrt(-e2) * x) if f < 0</span>
<a name="l00093"></a>00093 <span class="keyword">inline</span> real eatanhe(real x) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00094"></a>00094 <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="l00095"></a>00095 }
<a name="l00096"></a>00096 <span class="comment">// Divided differences</span>
<a name="l00097"></a>00097 <span class="comment">// Definition: Df(x,y) = (f(x)-f(y))/(x-y)</span>
<a name="l00098"></a>00098 <span class="comment">// See: W. M. Kahan and R. J. Fateman,</span>
<a name="l00099"></a>00099 <span class="comment">// Symbolic computation of divided differences,</span>
<a name="l00100"></a>00100 <span class="comment">// SIGSAM Bull. 33(3), 7-28 (1999)</span>
<a name="l00101"></a>00101 <span class="comment">// http://doi.acm.org/10.1145/334714.334716</span>
<a name="l00102"></a>00102 <span class="comment">// http://www.cs.berkeley.edu/~fateman/papers/divdiff.pdf</span>
<a name="l00103"></a>00103 <span class="comment">//</span>
<a name="l00104"></a>00104 <span class="comment">// General rules</span>
<a name="l00105"></a>00105 <span class="comment">// h(x) = f(g(x)): Dh(x,y) = Df(g(x),g(y))*Dg(x,y)</span>
<a name="l00106"></a>00106 <span class="comment">// h(x) = f(x)*g(x):</span>
<a name="l00107"></a>00107 <span class="comment">// Dh(x,y) = Df(x,y)*g(x) + Dg(x,y)*f(y)</span>
<a name="l00108"></a>00108 <span class="comment">// = Df(x,y)*g(y) + Dg(x,y)*f(x)</span>
<a name="l00109"></a>00109 <span class="comment">// = Df(x,y)*(g(x)+g(y))/2 + Dg(x,y)*(f(x)+f(y))/2</span>
<a name="l00110"></a>00110 <span class="comment">//</span>
<a name="l00111"></a>00111 <span class="comment">// hyp(x) = sqrt(1+x^2): Dhyp(x,y) = (x+y)/(hyp(x)+hyp(y))</span>
<a name="l00112"></a>00112 <span class="keyword">static</span> <span class="keyword">inline</span> real Dhyp(real x, real y, real hx, real hy) <span class="keywordflow">throw</span>()
<a name="l00113"></a>00113 <span class="comment">// hx = hyp(x)</span>
<a name="l00114"></a>00114 { <span class="keywordflow">return</span> (x + y) / (hx + hy); }
<a name="l00115"></a>00115 <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="l00116"></a>00116 <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="l00117"></a>00117 <span class="comment">// sx = x/hyp(x)</span>
<a name="l00118"></a>00118 real t = x * y;
<a name="l00119"></a>00119 <span class="keywordflow">return</span> t > 0 ? (x + y) * sq( (sx * sy)/t ) / (sx + sy) :
<a name="l00120"></a>00120 (x - y != 0 ? (sx - sy) / (x - y) : 1);
<a name="l00121"></a>00121 }
<a name="l00122"></a>00122 <span class="comment">// Dlog1p(x,y) = log1p((x-y)/(1+y)/(x-y)</span>
<a name="l00123"></a>00123 <span class="keyword">static</span> <span class="keyword">inline</span> real Dlog1p(real x, real y) <span class="keywordflow">throw</span>() {
<a name="l00124"></a>00124 real t = x - y; <span class="keywordflow">if</span> (t < 0) { t = -t; y = x; }
<a name="l00125"></a>00125 <span class="keywordflow">return</span> t != 0 ? <a class="code" href="classGeographicLib_1_1Math.html#ac84507dc4df09cf27e831620e8ad8880">Math::log1p</a>(t / (1 + y)) / t : 1 / (1 + x);
<a name="l00126"></a>00126 }
<a name="l00127"></a>00127 <span class="comment">// Dexp(x,y) = exp((x+y)/2) * 2*sinh((x-y)/2)/(x-y)</span>
<a name="l00128"></a>00128 <span class="keyword">static</span> <span class="keyword">inline</span> real Dexp(real x, real y) <span class="keywordflow">throw</span>() {
<a name="l00129"></a>00129 real t = (x - y)/2;
<a name="l00130"></a>00130 <span class="keywordflow">return</span> (t != 0 ? sinh(t)/t : real(1)) * exp((x + y)/2);
<a name="l00131"></a>00131 }
<a name="l00132"></a>00132 <span class="comment">// Dsinh(x,y) = 2*sinh((x-y)/2)/(x-y) * cosh((x+y)/2)</span>
<a name="l00133"></a>00133 <span class="comment">// cosh((x+y)/2) = (c+sinh(x)*sinh(y)/c)/2</span>
<a name="l00134"></a>00134 <span class="comment">// c=sqrt((1+cosh(x))*(1+cosh(y)))</span>
<a name="l00135"></a>00135 <span class="comment">// cosh((x+y)/2) = sqrt( (sinh(x)*sinh(y) + cosh(x)*cosh(y) + 1)/2 )</span>
<a name="l00136"></a>00136 <span class="keyword">static</span> <span class="keyword">inline</span> real Dsinh(real x, real y, real sx, real sy, real cx, real cy)
<a name="l00137"></a>00137 <span class="comment">// sx = sinh(x), cx = cosh(x)</span>
<a name="l00138"></a>00138 <span class="keywordflow">throw</span>() {
<a name="l00139"></a>00139 <span class="comment">// real t = (x - y)/2, c = sqrt((1 + cx) * (1 + cy));</span>
<a name="l00140"></a>00140 <span class="comment">// return (t != 0 ? sinh(t)/t : real(1)) * (c + sx * sy / c) /2;</span>
<a name="l00141"></a>00141 real t = (x - y)/2;
<a name="l00142"></a>00142 <span class="keywordflow">return</span> (t != 0 ? sinh(t)/t : real(1)) * sqrt((sx * sy + cx * cy + 1) /2);
<a name="l00143"></a>00143 }
<a name="l00144"></a>00144 <span class="comment">// Dasinh(x,y) = asinh((x-y)*(x+y)/(x*sqrt(1+y^2)+y*sqrt(1+x^2)))/(x-y)</span>
<a name="l00145"></a>00145 <span class="comment">// = asinh((x*sqrt(1+y^2)-y*sqrt(1+x^2)))/(x-y)</span>
<a name="l00146"></a>00146 <span class="keyword">static</span> <span class="keyword">inline</span> real Dasinh(real x, real y, real hx, real hy) <span class="keywordflow">throw</span>() {
<a name="l00147"></a>00147 <span class="comment">// hx = hyp(x)</span>
<a name="l00148"></a>00148 real t = x - y;
<a name="l00149"></a>00149 <span class="keywordflow">return</span> t != 0 ?
<a name="l00150"></a>00150 <a class="code" href="classGeographicLib_1_1Math.html#ab0998a80c8946d1c016c1bc4810a0698">Math::asinh</a>(x*y > 0 ? t * (x+y) / (x*hy + y*hx) : x*hy - y*hx) / t :
<a name="l00151"></a>00151 1/hx;
<a name="l00152"></a>00152 }
<a name="l00153"></a>00153 <span class="comment">// Deatanhe(x,y) = eatanhe((x-y)/(1-e^2*x*y))/(x-y)</span>
<a name="l00154"></a>00154 <span class="keyword">inline</span> real Deatanhe(real x, real y) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00155"></a>00155 real t = x - y, d = 1 - _e2 * x * y;
<a name="l00156"></a>00156 <span class="keywordflow">return</span> t != 0 ? eatanhe(t / d) / t : _e2 / d;
<a name="l00157"></a>00157 }
<a name="l00158"></a>00158 <span class="keywordtype">void</span> Init(real sphi1, real cphi1, real sphi2, real cphi2, real k1) <span class="keywordflow">throw</span>();
<a name="l00159"></a>00159 <span class="keyword">public</span>:
<a name="l00160"></a>00160 <span class="comment"></span>
<a name="l00161"></a>00161 <span class="comment"> /**</span>
<a name="l00162"></a>00162 <span class="comment"> * Constructor with a single standard parallel.</span>
<a name="l00163"></a>00163 <span class="comment"> *</span>
<a name="l00164"></a>00164 <span class="comment"> * @param[in] a equatorial radius of ellipsoid (meters)</span>
<a name="l00165"></a>00165 <span class="comment"> * @param[in] r reciprocal flattening of ellipsoid. Setting \e r = 0</span>
<a name="l00166"></a>00166 <span class="comment"> * implies \e r = inf or flattening = 0 (i.e., a sphere). Negative \e r</span>
<a name="l00167"></a>00167 <span class="comment"> * indicates a prolate ellipsoid.</span>
<a name="l00168"></a>00168 <span class="comment"> * @param[in] stdlat standard parallel (degrees), the circle of tangency.</span>
<a name="l00169"></a>00169 <span class="comment"> * @param[in] k0 scale on the standard parallel.</span>
<a name="l00170"></a>00170 <span class="comment"> *</span>
<a name="l00171"></a>00171 <span class="comment"> * An exception is thrown if \e a or \e k0 is not positive or if \e stdlat</span>
<a name="l00172"></a>00172 <span class="comment"> * is not in the range [-90, 90].</span>
<a name="l00173"></a>00173 <span class="comment"> **********************************************************************/</span>
<a name="l00174"></a>00174 <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a9270bac79ef919854a4524044128a4dc">LambertConformalConic</a>(real a, real r, real stdlat, real k0);
<a name="l00175"></a>00175 <span class="comment"></span>
<a name="l00176"></a>00176 <span class="comment"> /**</span>
<a name="l00177"></a>00177 <span class="comment"> * Constructor with two standard parallels.</span>
<a name="l00178"></a>00178 <span class="comment"> *</span>
<a name="l00179"></a>00179 <span class="comment"> * @param[in] a equatorial radius of ellipsoid (meters)</span>
<a name="l00180"></a>00180 <span class="comment"> * @param[in] r reciprocal flattening of ellipsoid. Setting \e r = 0</span>
<a name="l00181"></a>00181 <span class="comment"> * implies \e r = inf or flattening = 0 (i.e., a sphere). Negative \e r</span>
<a name="l00182"></a>00182 <span class="comment"> * indicates a prolate ellipsoid.</span>
<a name="l00183"></a>00183 <span class="comment"> * @param[in] stdlat1 first standard parallel (degrees).</span>
<a name="l00184"></a>00184 <span class="comment"> * @param[in] stdlat2 second standard parallel (degrees).</span>
<a name="l00185"></a>00185 <span class="comment"> * @param[in] k1 scale on the standard parallels.</span>
<a name="l00186"></a>00186 <span class="comment"> *</span>
<a name="l00187"></a>00187 <span class="comment"> * An exception is thrown if \e a or \e k0 is not positive or if \e stdlat1</span>
<a name="l00188"></a>00188 <span class="comment"> * or \e stdlat2 is not in the range [-90, 90]. In addition, if either \e</span>
<a name="l00189"></a>00189 <span class="comment"> * stdlat1 or \e stdlat2 is a pole, then an exception is thrown if \e</span>
<a name="l00190"></a>00190 <span class="comment"> * stdlat1 is not equal \e stdlat2.</span>
<a name="l00191"></a>00191 <span class="comment"> **********************************************************************/</span>
<a name="l00192"></a>00192 <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a9270bac79ef919854a4524044128a4dc">LambertConformalConic</a>(real a, real r, real stdlat1, real stdlat2, real k1);
<a name="l00193"></a>00193 <span class="comment"></span>
<a name="l00194"></a>00194 <span class="comment"> /**</span>
<a name="l00195"></a>00195 <span class="comment"> * Constructor with two standard parallels specified by sines and cosines.</span>
<a name="l00196"></a>00196 <span class="comment"> *</span>
<a name="l00197"></a>00197 <span class="comment"> * @param[in] a equatorial radius of ellipsoid (meters)</span>
<a name="l00198"></a>00198 <span class="comment"> * @param[in] r reciprocal flattening of ellipsoid. Setting \e r = 0</span>
<a name="l00199"></a>00199 <span class="comment"> * implies \e r = inf or flattening = 0 (i.e., a sphere). Negative \e r</span>
<a name="l00200"></a>00200 <span class="comment"> * indicates a prolate ellipsoid.</span>
<a name="l00201"></a>00201 <span class="comment"> * @param[in] sinlat1 sine of first standard parallel.</span>
<a name="l00202"></a>00202 <span class="comment"> * @param[in] coslat1 cosine of first standard parallel.</span>
<a name="l00203"></a>00203 <span class="comment"> * @param[in] sinlat2 sine of second standard parallel.</span>
<a name="l00204"></a>00204 <span class="comment"> * @param[in] coslat2 cosine of second standard parallel.</span>
<a name="l00205"></a>00205 <span class="comment"> * @param[in] k1 scale on the standard parallels.</span>
<a name="l00206"></a>00206 <span class="comment"> *</span>
<a name="l00207"></a>00207 <span class="comment"> * This allows parallels close to the poles to be specified accurately.</span>
<a name="l00208"></a>00208 <span class="comment"> * This routine computes the latitude of origin and the scale at this</span>
<a name="l00209"></a>00209 <span class="comment"> * latitude. In the case where \e lat1 and \e lat2 are different, the</span>
<a name="l00210"></a>00210 <span class="comment"> * errors in this routines are as follows: if \e dlat = abs(\e lat2 - \e</span>
<a name="l00211"></a>00211 <span class="comment"> * lat1) <= 160<sup>o</sup> and max(abs(\e lat1), abs(\e lat2)) <= 90 -</span>
<a name="l00212"></a>00212 <span class="comment"> * min(0.0002, 2.2e-6(180 - \e dlat), 6e-8\e dlat<sup>2</sup>) (in</span>
<a name="l00213"></a>00213 <span class="comment"> * degrees), then the error in the latitude of origin is less than</span>
<a name="l00214"></a>00214 <span class="comment"> * 4.5e-14<sup>o</sup> and the relative error in the scale is less than</span>
<a name="l00215"></a>00215 <span class="comment"> * 7e-15.</span>
<a name="l00216"></a>00216 <span class="comment"> **********************************************************************/</span>
<a name="l00217"></a>00217 <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a9270bac79ef919854a4524044128a4dc">LambertConformalConic</a>(real a, real r,
<a name="l00218"></a>00218 real sinlat1, real coslat1,
<a name="l00219"></a>00219 real sinlat2, real coslat2,
<a name="l00220"></a>00220 real k1);
<a name="l00221"></a>00221 <span class="comment"></span>
<a name="l00222"></a>00222 <span class="comment"> /**</span>
<a name="l00223"></a>00223 <span class="comment"> * Set the scale for the projection.</span>
<a name="l00224"></a>00224 <span class="comment"> *</span>
<a name="l00225"></a>00225 <span class="comment"> * @param[in] lat (degrees).</span>
<a name="l00226"></a>00226 <span class="comment"> * @param[in] k scale at latitude \e lat (default 1).</span>
<a name="l00227"></a>00227 <span class="comment"> *</span>
<a name="l00228"></a>00228 <span class="comment"> * This allows a "latitude of true scale" to be specified. An exception is</span>
<a name="l00229"></a>00229 <span class="comment"> * thrown if \e k is not positive or if \e stdlat is not in the range [-90,</span>
<a name="l00230"></a>00230 <span class="comment"> * 90]</span>
<a name="l00231"></a>00231 <span class="comment"> **********************************************************************/</span>
<a name="l00232"></a>00232 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#aac6267f7f970b35043b17e12e4163ff2">SetScale</a>(real lat, real k = real(1));
<a name="l00233"></a>00233 <span class="comment"></span>
<a name="l00234"></a>00234 <span class="comment"> /**</span>
<a name="l00235"></a>00235 <span class="comment"> * Forward projection, from geographic to Lambert conformal conic.</span>
<a name="l00236"></a>00236 <span class="comment"> *</span>
<a name="l00237"></a>00237 <span class="comment"> * @param[in] lon0 central meridian longitude (degrees).</span>
<a name="l00238"></a>00238 <span class="comment"> * @param[in] lat latitude of point (degrees).</span>
<a name="l00239"></a>00239 <span class="comment"> * @param[in] lon longitude of point (degrees).</span>
<a name="l00240"></a>00240 <span class="comment"> * @param[out] x easting of point (meters).</span>
<a name="l00241"></a>00241 <span class="comment"> * @param[out] y northing of point (meters).</span>
<a name="l00242"></a>00242 <span class="comment"> * @param[out] gamma meridian convergence at point (degrees).</span>
<a name="l00243"></a>00243 <span class="comment"> * @param[out] k scale of projection at point.</span>
<a name="l00244"></a>00244 <span class="comment"> *</span>
<a name="l00245"></a>00245 <span class="comment"> * The latitude origin is given by LambertConformalConic::LatitudeOrigin().</span>
<a name="l00246"></a>00246 <span class="comment"> * No false easting or northing is added and \e lat should be in the range</span>
<a name="l00247"></a>00247 <span class="comment"> * [-90, 90]; \e lon and \e lon0 should be in the range [-180, 360]. The</span>
<a name="l00248"></a>00248 <span class="comment"> * error in the projection is less than about 10 nm (true distance) and the</span>
<a name="l00249"></a>00249 <span class="comment"> * errors in the meridian convergence and scale are consistent with this.</span>
<a name="l00250"></a>00250 <span class="comment"> * The values of \e x and \e y returned for points which project to</span>
<a name="l00251"></a>00251 <span class="comment"> * infinity (i.e., one or both of the poles) will be large but finite.</span>
<a name="l00252"></a>00252 <span class="comment"> **********************************************************************/</span>
<a name="l00253"></a>00253 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2bafb6c1a81d4b6cf04f172b9e96278c">Forward</a>(real lon0, real lat, real lon,
<a name="l00254"></a>00254 real& x, real& y, real& gamma, real& k) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00255"></a>00255 <span class="comment"></span>
<a name="l00256"></a>00256 <span class="comment"> /**</span>
<a name="l00257"></a>00257 <span class="comment"> * Reverse projection, from Lambert conformal conic to geographic.</span>
<a name="l00258"></a>00258 <span class="comment"> *</span>
<a name="l00259"></a>00259 <span class="comment"> * @param[in] lon0 central meridian longitude (degrees).</span>
<a name="l00260"></a>00260 <span class="comment"> * @param[in] x easting of point (meters).</span>
<a name="l00261"></a>00261 <span class="comment"> * @param[in] y northing of point (meters).</span>
<a name="l00262"></a>00262 <span class="comment"> * @param[out] lat latitude of point (degrees).</span>
<a name="l00263"></a>00263 <span class="comment"> * @param[out] lon longitude of point (degrees).</span>
<a name="l00264"></a>00264 <span class="comment"> * @param[out] gamma meridian convergence at point (degrees).</span>
<a name="l00265"></a>00265 <span class="comment"> * @param[out] k scale of projection at point.</span>
<a name="l00266"></a>00266 <span class="comment"> *</span>
<a name="l00267"></a>00267 <span class="comment"> * The latitude origin is given by LambertConformalConic::LatitudeOrigin().</span>
<a name="l00268"></a>00268 <span class="comment"> * No false easting or northing is added. \e lon0 should be in the range</span>
<a name="l00269"></a>00269 <span class="comment"> * [-180, 360]. The value of \e lon returned is in the range [-180, 180).</span>
<a name="l00270"></a>00270 <span class="comment"> * The error in the projection is less than about 10 nm (true distance) and</span>
<a name="l00271"></a>00271 <span class="comment"> * the errors in the meridian convergence and scale are consistent with</span>
<a name="l00272"></a>00272 <span class="comment"> * this.</span>
<a name="l00273"></a>00273 <span class="comment"> **********************************************************************/</span>
<a name="l00274"></a>00274 <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a085d37693f5e95fd650b7f59f61ab744">Reverse</a>(real lon0, real x, real y,
<a name="l00275"></a>00275 real& lat, real& lon, real& gamma, real& k) <span class="keyword">const</span> <span class="keywordflow">throw</span>();
<a name="l00276"></a>00276 <span class="comment"></span>
<a name="l00277"></a>00277 <span class="comment"> /**</span>
<a name="l00278"></a>00278 <span class="comment"> * LambertConformalConic::Forward without returning the convergence and</span>
<a name="l00279"></a>00279 <span class="comment"> * scale.</span>
<a name="l00280"></a>00280 <span class="comment"> **********************************************************************/</span>
<a name="l00281"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a14a3757d85e81488afe476f7ceb8a720">00281</a> <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2bafb6c1a81d4b6cf04f172b9e96278c">Forward</a>(real lon0, real lat, real lon,
<a name="l00282"></a>00282 real& x, real& y) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00283"></a>00283 real gamma, k;
<a name="l00284"></a>00284 <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2bafb6c1a81d4b6cf04f172b9e96278c">Forward</a>(lon0, lat, lon, x, y, gamma, k);
<a name="l00285"></a>00285 }
<a name="l00286"></a>00286 <span class="comment"></span>
<a name="l00287"></a>00287 <span class="comment"> /**</span>
<a name="l00288"></a>00288 <span class="comment"> * LambertConformalConic::Reverse without returning the convergence and</span>
<a name="l00289"></a>00289 <span class="comment"> * scale.</span>
<a name="l00290"></a>00290 <span class="comment"> **********************************************************************/</span>
<a name="l00291"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a1bffe1259895569e6834a4b1df9b22ab">00291</a> <span class="keywordtype">void</span> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a085d37693f5e95fd650b7f59f61ab744">Reverse</a>(real lon0, real x, real y,
<a name="l00292"></a>00292 real& lat, real& lon) <span class="keyword">const</span> <span class="keywordflow">throw</span>() {
<a name="l00293"></a>00293 real gamma, k;
<a name="l00294"></a>00294 <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a085d37693f5e95fd650b7f59f61ab744">Reverse</a>(lon0, x, y, lat, lon, gamma, k);
<a name="l00295"></a>00295 }
<a name="l00296"></a>00296 <span class="comment"></span>
<a name="l00297"></a>00297 <span class="comment"> /** \name Inspector functions</span>
<a name="l00298"></a>00298 <span class="comment"> **********************************************************************/</span><span class="comment"></span>
<a name="l00299"></a>00299 <span class="comment"> ///@{</span>
<a name="l00300"></a>00300 <span class="comment"></span><span class="comment"> /**</span>
<a name="l00301"></a>00301 <span class="comment"> * @return \e a the equatorial radius of the ellipsoid (meters). This is</span>
<a name="l00302"></a>00302 <span class="comment"> * the value used in the constructor.</span>
<a name="l00303"></a>00303 <span class="comment"> **********************************************************************/</span>
<a name="l00304"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a21f9bc21f3f40c56d2f5d12fb4b7f75a">00304</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a21f9bc21f3f40c56d2f5d12fb4b7f75a">MajorRadius</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _a; }
<a name="l00305"></a>00305 <span class="comment"></span>
<a name="l00306"></a>00306 <span class="comment"> /**</span>
<a name="l00307"></a>00307 <span class="comment"> * @return \e r the inverse flattening of the ellipsoid. This is the</span>
<a name="l00308"></a>00308 <span class="comment"> * value used in the constructor. A value of 0 is returned for a sphere</span>
<a name="l00309"></a>00309 <span class="comment"> * (infinite inverse flattening).</span>
<a name="l00310"></a>00310 <span class="comment"> **********************************************************************/</span>
<a name="l00311"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2dcd66922112771c232d686e7bcc5f31">00311</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2dcd66922112771c232d686e7bcc5f31">InverseFlattening</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _r; }
<a name="l00312"></a>00312 <span class="comment"></span>
<a name="l00313"></a>00313 <span class="comment"> /**</span>
<a name="l00314"></a>00314 <span class="comment"> * @return latitude of the origin for the projection (degrees).</span>
<a name="l00315"></a>00315 <span class="comment"> *</span>
<a name="l00316"></a>00316 <span class="comment"> * This is the latitude of minimum scale and equals the \e stdlat in the</span>
<a name="l00317"></a>00317 <span class="comment"> * 1-parallel constructor and lies between \e stdlat1 and \e stdlat2 in the</span>
<a name="l00318"></a>00318 <span class="comment"> * 2-parallel constructors.</span>
<a name="l00319"></a>00319 <span class="comment"> **********************************************************************/</span>
<a name="l00320"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a7c589335b43b2274d3a68c0f68f29d77">00320</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a7c589335b43b2274d3a68c0f68f29d77">OriginLatitude</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _lat0; }
<a name="l00321"></a>00321 <span class="comment"></span>
<a name="l00322"></a>00322 <span class="comment"> /**</span>
<a name="l00323"></a>00323 <span class="comment"> * @return central scale for the projection. This is the scale on the</span>
<a name="l00324"></a>00324 <span class="comment"> * latitude of origin.</span>
<a name="l00325"></a>00325 <span class="comment"> **********************************************************************/</span>
<a name="l00326"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2298a4e48e550cfd7346cf5f2dd175ad">00326</a> <a class="code" href="classGeographicLib_1_1Math.html#aeee4778d7cf2f9fb9648efe4911da59d">Math::real</a> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a2298a4e48e550cfd7346cf5f2dd175ad">CentralScale</a>() <span class="keyword">const</span> throw() { <span class="keywordflow">return</span> _k0; }<span class="comment"></span>
<a name="l00327"></a>00327 <span class="comment"> ///@}</span>
<a name="l00328"></a>00328 <span class="comment"></span><span class="comment"></span>
<a name="l00329"></a>00329 <span class="comment"> /**</span>
<a name="l00330"></a>00330 <span class="comment"> * A global instantiation of LambertConformalConic with the WGS84</span>
<a name="l00331"></a>00331 <span class="comment"> * ellipsoid, \e stdlat = 0, and \e k0 = 1. This degenerates to the</span>
<a name="l00332"></a>00332 <span class="comment"> * Mercator projection.</span>
<a name="l00333"></a>00333 <span class="comment"> **********************************************************************/</span>
<a name="l00334"></a><a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a7fbb6973b77593245db52c9759740f9a">00334</a> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html" title="Lambert Conformal Conic Projection.">LambertConformalConic</a> <a class="code" href="classGeographicLib_1_1LambertConformalConic.html#a7fbb6973b77593245db52c9759740f9a">Mercator</a>;
<a name="l00335"></a>00335 };
<a name="l00336"></a>00336
<a name="l00337"></a>00337 } <span class="comment">// namespace GeographicLib</span>
<a name="l00338"></a>00338
<a name="l00339"></a>00339 <span class="preprocessor">#endif</span>
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