/* proj4js.js -- Javascript reprojection library. Authors: Mike Adair madairATdmsolutions.ca Richard Greenwood richATgreenwoodmap.com Didier Richard didier.richardATign.fr Stephen Irons stephen.ironsATclear.net.nz Olivier Terral oterralATgmail.com License: Copyright (c) 2012, Mike Adair, Richard Greenwood, Didier Richard, Stephen Irons and Olivier Terral Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Note: This program is an almost direct port of the C library PROJ.4. */ /* ====================================================================== proj4js.js ====================================================================== */ /* Author: Mike Adair madairATdmsolutions.ca Richard Greenwood rich@greenwoodmap.com License: LGPL as per: http://www.gnu.org/copyleft/lesser.html $Id: Proj.js 2956 2007-07-09 12:17:52Z steven $ */ /** * Namespace: Proj4js * * Proj4js is a JavaScript library to transform point coordinates from one * coordinate system to another, including datum transformations. * * This library is a port of both the Proj.4 and GCTCP C libraries to JavaScript. * Enabling these transformations in the browser allows geographic data stored * in different projections to be combined in browser-based web mapping * applications. * * Proj4js must have access to coordinate system initialization strings (which * are the same as for PROJ.4 command line). Thes can be included in your * application using a def is a CS definition in PROJ.4 WKT format, for example: +proj="tmerc" //longlat, etc. +a=majorRadius +b=minorRadius +lat0=somenumber +long=somenumber */ Proj4js.defs = { // These are so widely used, we'll go ahead and throw them in // without requiring a separate .js file 'WGS84': "+title=long/lat:WGS84 +proj=longlat +ellps=WGS84 +datum=WGS84 +units=degrees", 'EPSG:4326': "+title=long/lat:WGS84 +proj=longlat +a=6378137.0 +b=6356752.31424518 +ellps=WGS84 +datum=WGS84 +units=degrees", 'EPSG:4269': "+title=long/lat:NAD83 +proj=longlat +a=6378137.0 +b=6356752.31414036 +ellps=GRS80 +datum=NAD83 +units=degrees", 'EPSG:3875': "+title= Google Mercator +proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +no_defs" }; Proj4js.defs['EPSG:3785'] = Proj4js.defs['EPSG:3875']; //maintain backward compat, official code is 3875 Proj4js.defs['GOOGLE'] = Proj4js.defs['EPSG:3875']; Proj4js.defs['EPSG:900913'] = Proj4js.defs['EPSG:3875']; Proj4js.defs['EPSG:102113'] = Proj4js.defs['EPSG:3875']; Proj4js.common = { PI : 3.141592653589793238, //Math.PI, HALF_PI : 1.570796326794896619, //Math.PI*0.5, TWO_PI : 6.283185307179586477, //Math.PI*2, FORTPI : 0.78539816339744833, R2D : 57.29577951308232088, D2R : 0.01745329251994329577, SEC_TO_RAD : 4.84813681109535993589914102357e-6, /* SEC_TO_RAD = Pi/180/3600 */ EPSLN : 1.0e-10, MAX_ITER : 20, // following constants from geocent.c COS_67P5 : 0.38268343236508977, /* cosine of 67.5 degrees */ AD_C : 1.0026000, /* Toms region 1 constant */ /* datum_type values */ PJD_UNKNOWN : 0, PJD_3PARAM : 1, PJD_7PARAM : 2, PJD_GRIDSHIFT: 3, PJD_WGS84 : 4, // WGS84 or equivalent PJD_NODATUM : 5, // WGS84 or equivalent SRS_WGS84_SEMIMAJOR : 6378137.0, // only used in grid shift transforms // ellipoid pj_set_ell.c SIXTH : .1666666666666666667, /* 1/6 */ RA4 : .04722222222222222222, /* 17/360 */ RA6 : .02215608465608465608, /* 67/3024 */ RV4 : .06944444444444444444, /* 5/72 */ RV6 : .04243827160493827160, /* 55/1296 */ // Function to compute the constant small m which is the radius of // a parallel of latitude, phi, divided by the semimajor axis. // ----------------------------------------------------------------- msfnz : function(eccent, sinphi, cosphi) { var con = eccent * sinphi; return cosphi/(Math.sqrt(1.0 - con * con)); }, // Function to compute the constant small t for use in the forward // computations in the Lambert Conformal Conic and the Polar // Stereographic projections. // ----------------------------------------------------------------- tsfnz : function(eccent, phi, sinphi) { var con = eccent * sinphi; var com = .5 * eccent; con = Math.pow(((1.0 - con) / (1.0 + con)), com); return (Math.tan(.5 * (this.HALF_PI - phi))/con); }, // Function to compute the latitude angle, phi2, for the inverse of the // Lambert Conformal Conic and Polar Stereographic projections. // ---------------------------------------------------------------- phi2z : function(eccent, ts) { var eccnth = .5 * eccent; var con, dphi; var phi = this.HALF_PI - 2 * Math.atan(ts); for (var i = 0; i <= 15; i++) { con = eccent * Math.sin(phi); dphi = this.HALF_PI - 2 * Math.atan(ts *(Math.pow(((1.0 - con)/(1.0 + con)),eccnth))) - phi; phi += dphi; if (Math.abs(dphi) <= .0000000001) return phi; } alert("phi2z has NoConvergence"); return (-9999); }, /* Function to compute constant small q which is the radius of a parallel of latitude, phi, divided by the semimajor axis. ------------------------------------------------------------*/ qsfnz : function(eccent,sinphi) { var con; if (eccent > 1.0e-7) { con = eccent * sinphi; return (( 1.0- eccent * eccent) * (sinphi /(1.0 - con * con) - (.5/eccent)*Math.log((1.0 - con)/(1.0 + con)))); } else { return(2.0 * sinphi); } }, /* Function to eliminate roundoff errors in asin ----------------------------------------------*/ asinz : function(x) { if (Math.abs(x)>1.0) { x=(x>1.0)?1.0:-1.0; } return Math.asin(x); }, // following functions from gctpc cproj.c for transverse mercator projections e0fn : function(x) {return(1.0-0.25*x*(1.0+x/16.0*(3.0+1.25*x)));}, e1fn : function(x) {return(0.375*x*(1.0+0.25*x*(1.0+0.46875*x)));}, e2fn : function(x) {return(0.05859375*x*x*(1.0+0.75*x));}, e3fn : function(x) {return(x*x*x*(35.0/3072.0));}, mlfn : function(e0,e1,e2,e3,phi) {return(e0*phi-e1*Math.sin(2.0*phi)+e2*Math.sin(4.0*phi)-e3*Math.sin(6.0*phi));}, srat : function(esinp, exp) { return(Math.pow((1.0-esinp)/(1.0+esinp), exp)); }, // Function to return the sign of an argument sign : function(x) { if (x < 0.0) return(-1); else return(1);}, // Function to adjust longitude to -180 to 180; input in radians adjust_lon : function(x) { x = (Math.abs(x) < this.PI) ? x: (x - (this.sign(x)*this.TWO_PI) ); return x; }, // IGNF - DGR : algorithms used by IGN France // Function to adjust latitude to -90 to 90; input in radians adjust_lat : function(x) { x= (Math.abs(x) < this.HALF_PI) ? x: (x - (this.sign(x)*this.PI) ); return x; }, // Latitude Isometrique - close to tsfnz ... latiso : function(eccent, phi, sinphi) { if (Math.abs(phi) > this.HALF_PI) return +Number.NaN; if (phi==this.HALF_PI) return Number.POSITIVE_INFINITY; if (phi==-1.0*this.HALF_PI) return -1.0*Number.POSITIVE_INFINITY; var con= eccent*sinphi; return Math.log(Math.tan((this.HALF_PI+phi)/2.0))+eccent*Math.log((1.0-con)/(1.0+con))/2.0; }, fL : function(x,L) { return 2.0*Math.atan(x*Math.exp(L)) - this.HALF_PI; }, // Inverse Latitude Isometrique - close to ph2z invlatiso : function(eccent, ts) { var phi= this.fL(1.0,ts); var Iphi= 0.0; var con= 0.0; do { Iphi= phi; con= eccent*Math.sin(Iphi); phi= this.fL(Math.exp(eccent*Math.log((1.0+con)/(1.0-con))/2.0),ts) } while (Math.abs(phi-Iphi)>1.0e-12); return phi; }, // Needed for Gauss Schreiber // Original: Denis Makarov (info@binarythings.com) // Web Site: http://www.binarythings.com sinh : function(x) { var r= Math.exp(x); r= (r-1.0/r)/2.0; return r; }, cosh : function(x) { var r= Math.exp(x); r= (r+1.0/r)/2.0; return r; }, tanh : function(x) { var r= Math.exp(x); r= (r-1.0/r)/(r+1.0/r); return r; }, asinh : function(x) { var s= (x>= 0? 1.0:-1.0); return s*(Math.log( Math.abs(x) + Math.sqrt(x*x+1.0) )); }, acosh : function(x) { return 2.0*Math.log(Math.sqrt((x+1.0)/2.0) + Math.sqrt((x-1.0)/2.0)); }, atanh : function(x) { return Math.log((x-1.0)/(x+1.0))/2.0; }, // Grande Normale gN : function(a,e,sinphi) { var temp= e*sinphi; return a/Math.sqrt(1.0 - temp*temp); }, //code from the PROJ.4 pj_mlfn.c file; this may be useful for other projections pj_enfn: function(es) { var en = new Array(); en[0] = this.C00 - es * (this.C02 + es * (this.C04 + es * (this.C06 + es * this.C08))); en[1] = es * (this.C22 - es * (this.C04 + es * (this.C06 + es * this.C08))); var t = es * es; en[2] = t * (this.C44 - es * (this.C46 + es * this.C48)); t *= es; en[3] = t * (this.C66 - es * this.C68); en[4] = t * es * this.C88; return en; }, pj_mlfn: function(phi, sphi, cphi, en) { cphi *= sphi; sphi *= sphi; return(en[0] * phi - cphi * (en[1] + sphi*(en[2]+ sphi*(en[3] + sphi*en[4])))); }, pj_inv_mlfn: function(arg, es, en) { var k = 1./(1.-es); var phi = arg; for (var i = Proj4js.common.MAX_ITER; i ; --i) { /* rarely goes over 2 iterations */ var s = Math.sin(phi); var t = 1. - es * s * s; //t = this.pj_mlfn(phi, s, Math.cos(phi), en) - arg; //phi -= t * (t * Math.sqrt(t)) * k; t = (this.pj_mlfn(phi, s, Math.cos(phi), en) - arg) * (t * Math.sqrt(t)) * k; phi -= t; if (Math.abs(t) < Proj4js.common.EPSLN) return phi; } Proj4js.reportError("cass:pj_inv_mlfn: Convergence error"); return phi; }, /* meridinal distance for ellipsoid and inverse ** 8th degree - accurate to < 1e-5 meters when used in conjuction ** with typical major axis values. ** Inverse determines phi to EPS (1e-11) radians, about 1e-6 seconds. */ C00: 1.0, C02: .25, C04: .046875, C06: .01953125, C08: .01068115234375, C22: .75, C44: .46875, C46: .01302083333333333333, C48: .00712076822916666666, C66: .36458333333333333333, C68: .00569661458333333333, C88: .3076171875 }; /** datum object */ Proj4js.datum = Proj4js.Class({ initialize : function(proj) { this.datum_type = Proj4js.common.PJD_WGS84; //default setting if (proj.datumCode && proj.datumCode == 'none') { this.datum_type = Proj4js.common.PJD_NODATUM; } if (proj && proj.datum_params) { for (var i=0; i 3) { if (proj.datum_params[3] != 0 || proj.datum_params[4] != 0 || proj.datum_params[5] != 0 || proj.datum_params[6] != 0 ) { this.datum_type = Proj4js.common.PJD_7PARAM; proj.datum_params[3] *= Proj4js.common.SEC_TO_RAD; proj.datum_params[4] *= Proj4js.common.SEC_TO_RAD; proj.datum_params[5] *= Proj4js.common.SEC_TO_RAD; proj.datum_params[6] = (proj.datum_params[6]/1000000.0) + 1.0; } } } if (proj) { this.a = proj.a; //datum object also uses these values this.b = proj.b; this.es = proj.es; this.ep2 = proj.ep2; this.datum_params = proj.datum_params; } }, /****************************************************************/ // cs_compare_datums() // Returns TRUE if the two datums match, otherwise FALSE. compare_datums : function( dest ) { if( this.datum_type != dest.datum_type ) { return false; // false, datums are not equal } else if( this.a != dest.a || Math.abs(this.es-dest.es) > 0.000000000050 ) { // the tolerence for es is to ensure that GRS80 and WGS84 // are considered identical return false; } else if( this.datum_type == Proj4js.common.PJD_3PARAM ) { return (this.datum_params[0] == dest.datum_params[0] && this.datum_params[1] == dest.datum_params[1] && this.datum_params[2] == dest.datum_params[2]); } else if( this.datum_type == Proj4js.common.PJD_7PARAM ) { return (this.datum_params[0] == dest.datum_params[0] && this.datum_params[1] == dest.datum_params[1] && this.datum_params[2] == dest.datum_params[2] && this.datum_params[3] == dest.datum_params[3] && this.datum_params[4] == dest.datum_params[4] && this.datum_params[5] == dest.datum_params[5] && this.datum_params[6] == dest.datum_params[6]); } else if ( this.datum_type == Proj4js.common.PJD_GRIDSHIFT || dest.datum_type == Proj4js.common.PJD_GRIDSHIFT ) { alert("ERROR: Grid shift transformations are not implemented."); return false } else { return true; // datums are equal } }, // cs_compare_datums() /* * The function Convert_Geodetic_To_Geocentric converts geodetic coordinates * (latitude, longitude, and height) to geocentric coordinates (X, Y, Z), * according to the current ellipsoid parameters. * * Latitude : Geodetic latitude in radians (input) * Longitude : Geodetic longitude in radians (input) * Height : Geodetic height, in meters (input) * X : Calculated Geocentric X coordinate, in meters (output) * Y : Calculated Geocentric Y coordinate, in meters (output) * Z : Calculated Geocentric Z coordinate, in meters (output) * */ geodetic_to_geocentric : function(p) { var Longitude = p.x; var Latitude = p.y; var Height = p.z ? p.z : 0; //Z value not always supplied var X; // output var Y; var Z; var Error_Code=0; // GEOCENT_NO_ERROR; var Rn; /* Earth radius at location */ var Sin_Lat; /* Math.sin(Latitude) */ var Sin2_Lat; /* Square of Math.sin(Latitude) */ var Cos_Lat; /* Math.cos(Latitude) */ /* ** Don't blow up if Latitude is just a little out of the value ** range as it may just be a rounding issue. Also removed longitude ** test, it should be wrapped by Math.cos() and Math.sin(). NFW for PROJ.4, Sep/2001. */ if( Latitude < -Proj4js.common.HALF_PI && Latitude > -1.001 * Proj4js.common.HALF_PI ) { Latitude = -Proj4js.common.HALF_PI; } else if( Latitude > Proj4js.common.HALF_PI && Latitude < 1.001 * Proj4js.common.HALF_PI ) { Latitude = Proj4js.common.HALF_PI; } else if ((Latitude < -Proj4js.common.HALF_PI) || (Latitude > Proj4js.common.HALF_PI)) { /* Latitude out of range */ Proj4js.reportError('geocent:lat out of range:'+Latitude); return null; } if (Longitude > Proj4js.common.PI) Longitude -= (2*Proj4js.common.PI); Sin_Lat = Math.sin(Latitude); Cos_Lat = Math.cos(Latitude); Sin2_Lat = Sin_Lat * Sin_Lat; Rn = this.a / (Math.sqrt(1.0e0 - this.es * Sin2_Lat)); X = (Rn + Height) * Cos_Lat * Math.cos(Longitude); Y = (Rn + Height) * Cos_Lat * Math.sin(Longitude); Z = ((Rn * (1 - this.es)) + Height) * Sin_Lat; p.x = X; p.y = Y; p.z = Z; return Error_Code; }, // cs_geodetic_to_geocentric() geocentric_to_geodetic : function (p) { /* local defintions and variables */ /* end-criterium of loop, accuracy of sin(Latitude) */ var genau = 1.E-12; var genau2 = (genau*genau); var maxiter = 30; var P; /* distance between semi-minor axis and location */ var RR; /* distance between center and location */ var CT; /* sin of geocentric latitude */ var ST; /* cos of geocentric latitude */ var RX; var RK; var RN; /* Earth radius at location */ var CPHI0; /* cos of start or old geodetic latitude in iterations */ var SPHI0; /* sin of start or old geodetic latitude in iterations */ var CPHI; /* cos of searched geodetic latitude */ var SPHI; /* sin of searched geodetic latitude */ var SDPHI; /* end-criterium: addition-theorem of sin(Latitude(iter)-Latitude(iter-1)) */ var At_Pole; /* indicates location is in polar region */ var iter; /* # of continous iteration, max. 30 is always enough (s.a.) */ var X = p.x; var Y = p.y; var Z = p.z ? p.z : 0.0; //Z value not always supplied var Longitude; var Latitude; var Height; At_Pole = false; P = Math.sqrt(X*X+Y*Y); RR = Math.sqrt(X*X+Y*Y+Z*Z); /* special cases for latitude and longitude */ if (P/this.a < genau) { /* special case, if P=0. (X=0., Y=0.) */ At_Pole = true; Longitude = 0.0; /* if (X,Y,Z)=(0.,0.,0.) then Height becomes semi-minor axis * of ellipsoid (=center of mass), Latitude becomes PI/2 */ if (RR/this.a < genau) { Latitude = Proj4js.common.HALF_PI; Height = -this.b; return; } } else { /* ellipsoidal (geodetic) longitude * interval: -PI < Longitude <= +PI */ Longitude=Math.atan2(Y,X); } /* -------------------------------------------------------------- * Following iterative algorithm was developped by * "Institut f�r Erdmessung", University of Hannover, July 1988. * Internet: www.ife.uni-hannover.de * Iterative computation of CPHI,SPHI and Height. * Iteration of CPHI and SPHI to 10**-12 radian resp. * 2*10**-7 arcsec. * -------------------------------------------------------------- */ CT = Z/RR; ST = P/RR; RX = 1.0/Math.sqrt(1.0-this.es*(2.0-this.es)*ST*ST); CPHI0 = ST*(1.0-this.es)*RX; SPHI0 = CT*RX; iter = 0; /* loop to find sin(Latitude) resp. Latitude * until |sin(Latitude(iter)-Latitude(iter-1))| < genau */ do { iter++; RN = this.a/Math.sqrt(1.0-this.es*SPHI0*SPHI0); /* ellipsoidal (geodetic) height */ Height = P*CPHI0+Z*SPHI0-RN*(1.0-this.es*SPHI0*SPHI0); RK = this.es*RN/(RN+Height); RX = 1.0/Math.sqrt(1.0-RK*(2.0-RK)*ST*ST); CPHI = ST*(1.0-RK)*RX; SPHI = CT*RX; SDPHI = SPHI*CPHI0-CPHI*SPHI0; CPHI0 = CPHI; SPHI0 = SPHI; } while (SDPHI*SDPHI > genau2 && iter < maxiter); /* ellipsoidal (geodetic) latitude */ Latitude=Math.atan(SPHI/Math.abs(CPHI)); p.x = Longitude; p.y = Latitude; p.z = Height; return p; }, // cs_geocentric_to_geodetic() /** Convert_Geocentric_To_Geodetic * The method used here is derived from 'An Improved Algorithm for * Geocentric to Geodetic Coordinate Conversion', by Ralph Toms, Feb 1996 */ geocentric_to_geodetic_noniter : function (p) { var X = p.x; var Y = p.y; var Z = p.z ? p.z : 0; //Z value not always supplied var Longitude; var Latitude; var Height; var W; /* distance from Z axis */ var W2; /* square of distance from Z axis */ var T0; /* initial estimate of vertical component */ var T1; /* corrected estimate of vertical component */ var S0; /* initial estimate of horizontal component */ var S1; /* corrected estimate of horizontal component */ var Sin_B0; /* Math.sin(B0), B0 is estimate of Bowring aux variable */ var Sin3_B0; /* cube of Math.sin(B0) */ var Cos_B0; /* Math.cos(B0) */ var Sin_p1; /* Math.sin(phi1), phi1 is estimated latitude */ var Cos_p1; /* Math.cos(phi1) */ var Rn; /* Earth radius at location */ var Sum; /* numerator of Math.cos(phi1) */ var At_Pole; /* indicates location is in polar region */ X = parseFloat(X); // cast from string to float Y = parseFloat(Y); Z = parseFloat(Z); At_Pole = false; if (X != 0.0) { Longitude = Math.atan2(Y,X); } else { if (Y > 0) { Longitude = Proj4js.common.HALF_PI; } else if (Y < 0) { Longitude = -Proj4js.common.HALF_PI; } else { At_Pole = true; Longitude = 0.0; if (Z > 0.0) { /* north pole */ Latitude = Proj4js.common.HALF_PI; } else if (Z < 0.0) { /* south pole */ Latitude = -Proj4js.common.HALF_PI; } else { /* center of earth */ Latitude = Proj4js.common.HALF_PI; Height = -this.b; return; } } } W2 = X*X + Y*Y; W = Math.sqrt(W2); T0 = Z * Proj4js.common.AD_C; S0 = Math.sqrt(T0 * T0 + W2); Sin_B0 = T0 / S0; Cos_B0 = W / S0; Sin3_B0 = Sin_B0 * Sin_B0 * Sin_B0; T1 = Z + this.b * this.ep2 * Sin3_B0; Sum = W - this.a * this.es * Cos_B0 * Cos_B0 * Cos_B0; S1 = Math.sqrt(T1*T1 + Sum * Sum); Sin_p1 = T1 / S1; Cos_p1 = Sum / S1; Rn = this.a / Math.sqrt(1.0 - this.es * Sin_p1 * Sin_p1); if (Cos_p1 >= Proj4js.common.COS_67P5) { Height = W / Cos_p1 - Rn; } else if (Cos_p1 <= -Proj4js.common.COS_67P5) { Height = W / -Cos_p1 - Rn; } else { Height = Z / Sin_p1 + Rn * (this.es - 1.0); } if (At_Pole == false) { Latitude = Math.atan(Sin_p1 / Cos_p1); } p.x = Longitude; p.y = Latitude; p.z = Height; return p; }, // geocentric_to_geodetic_noniter() /****************************************************************/ // pj_geocentic_to_wgs84( p ) // p = point to transform in geocentric coordinates (x,y,z) geocentric_to_wgs84 : function ( p ) { if( this.datum_type == Proj4js.common.PJD_3PARAM ) { // if( x[io] == HUGE_VAL ) // continue; p.x += this.datum_params[0]; p.y += this.datum_params[1]; p.z += this.datum_params[2]; } else if (this.datum_type == Proj4js.common.PJD_7PARAM) { var Dx_BF =this.datum_params[0]; var Dy_BF =this.datum_params[1]; var Dz_BF =this.datum_params[2]; var Rx_BF =this.datum_params[3]; var Ry_BF =this.datum_params[4]; var Rz_BF =this.datum_params[5]; var M_BF =this.datum_params[6]; // if( x[io] == HUGE_VAL ) // continue; var x_out = M_BF*( p.x - Rz_BF*p.y + Ry_BF*p.z) + Dx_BF; var y_out = M_BF*( Rz_BF*p.x + p.y - Rx_BF*p.z) + Dy_BF; var z_out = M_BF*(-Ry_BF*p.x + Rx_BF*p.y + p.z) + Dz_BF; p.x = x_out; p.y = y_out; p.z = z_out; } }, // cs_geocentric_to_wgs84 /****************************************************************/ // pj_geocentic_from_wgs84() // coordinate system definition, // point to transform in geocentric coordinates (x,y,z) geocentric_from_wgs84 : function( p ) { if( this.datum_type == Proj4js.common.PJD_3PARAM ) { //if( x[io] == HUGE_VAL ) // continue; p.x -= this.datum_params[0]; p.y -= this.datum_params[1]; p.z -= this.datum_params[2]; } else if (this.datum_type == Proj4js.common.PJD_7PARAM) { var Dx_BF =this.datum_params[0]; var Dy_BF =this.datum_params[1]; var Dz_BF =this.datum_params[2]; var Rx_BF =this.datum_params[3]; var Ry_BF =this.datum_params[4]; var Rz_BF =this.datum_params[5]; var M_BF =this.datum_params[6]; var x_tmp = (p.x - Dx_BF) / M_BF; var y_tmp = (p.y - Dy_BF) / M_BF; var z_tmp = (p.z - Dz_BF) / M_BF; //if( x[io] == HUGE_VAL ) // continue; p.x = x_tmp + Rz_BF*y_tmp - Ry_BF*z_tmp; p.y = -Rz_BF*x_tmp + y_tmp + Rx_BF*z_tmp; p.z = Ry_BF*x_tmp - Rx_BF*y_tmp + z_tmp; } //cs_geocentric_from_wgs84() } }); /** point object, nothing fancy, just allows values to be passed back and forth by reference rather than by value. Other point classes may be used as long as they have x and y properties, which will get modified in the transform method. */ Proj4js.Point = Proj4js.Class({ /** * Constructor: Proj4js.Point * * Parameters: * - x {float} or {Array} either the first coordinates component or * the full coordinates * - y {float} the second component * - z {float} the third component, optional. */ initialize : function(x,y,z) { if (typeof x == 'object') { this.x = x[0]; this.y = x[1]; this.z = x[2] || 0.0; } else if (typeof x == 'string' && typeof y == 'undefined') { var coords = x.split(','); this.x = parseFloat(coords[0]); this.y = parseFloat(coords[1]); this.z = parseFloat(coords[2]) || 0.0; } else { this.x = x; this.y = y; this.z = z || 0.0; } }, /** * APIMethod: clone * Build a copy of a Proj4js.Point object. * * Return: * {Proj4js}.Point the cloned point. */ clone : function() { return new Proj4js.Point(this.x, this.y, this.z); }, /** * APIMethod: toString * Return a readable string version of the point * * Return: * {String} String representation of Proj4js.Point object. * (ex. "x=5,y=42") */ toString : function() { return ("x=" + this.x + ",y=" + this.y); }, /** * APIMethod: toShortString * Return a short string version of the point. * * Return: * {String} Shortened String representation of Proj4js.Point object. * (ex. "5, 42") */ toShortString : function() { return (this.x + ", " + this.y); } }); Proj4js.PrimeMeridian = { "greenwich": 0.0, //"0dE", "lisbon": -9.131906111111, //"9d07'54.862\"W", "paris": 2.337229166667, //"2d20'14.025\"E", "bogota": -74.080916666667, //"74d04'51.3\"W", "madrid": -3.687938888889, //"3d41'16.58\"W", "rome": 12.452333333333, //"12d27'8.4\"E", "bern": 7.439583333333, //"7d26'22.5\"E", "jakarta": 106.807719444444, //"106d48'27.79\"E", "ferro": -17.666666666667, //"17d40'W", "brussels": 4.367975, //"4d22'4.71\"E", "stockholm": 18.058277777778, //"18d3'29.8\"E", "athens": 23.7163375, //"23d42'58.815\"E", "oslo": 10.722916666667 //"10d43'22.5\"E" }; Proj4js.Ellipsoid = { "MERIT": {a:6378137.0, rf:298.257, ellipseName:"MERIT 1983"}, "SGS85": {a:6378136.0, rf:298.257, ellipseName:"Soviet Geodetic System 85"}, "GRS80": {a:6378137.0, rf:298.257222101, ellipseName:"GRS 1980(IUGG, 1980)"}, "IAU76": {a:6378140.0, rf:298.257, ellipseName:"IAU 1976"}, "airy": {a:6377563.396, b:6356256.910, ellipseName:"Airy 1830"}, "APL4.": {a:6378137, rf:298.25, ellipseName:"Appl. Physics. 1965"}, "NWL9D": {a:6378145.0, rf:298.25, ellipseName:"Naval Weapons Lab., 1965"}, "mod_airy": {a:6377340.189, b:6356034.446, ellipseName:"Modified Airy"}, "andrae": {a:6377104.43, rf:300.0, ellipseName:"Andrae 1876 (Den., Iclnd.)"}, "aust_SA": {a:6378160.0, rf:298.25, ellipseName:"Australian Natl & S. Amer. 1969"}, "GRS67": {a:6378160.0, rf:298.2471674270, ellipseName:"GRS 67(IUGG 1967)"}, "bessel": {a:6377397.155, rf:299.1528128, ellipseName:"Bessel 1841"}, "bess_nam": {a:6377483.865, rf:299.1528128, ellipseName:"Bessel 1841 (Namibia)"}, "clrk66": {a:6378206.4, b:6356583.8, ellipseName:"Clarke 1866"}, "clrk80": {a:6378249.145, rf:293.4663, ellipseName:"Clarke 1880 mod."}, "CPM": {a:6375738.7, rf:334.29, ellipseName:"Comm. des Poids et Mesures 1799"}, "delmbr": {a:6376428.0, rf:311.5, ellipseName:"Delambre 1810 (Belgium)"}, "engelis": {a:6378136.05, rf:298.2566, ellipseName:"Engelis 1985"}, "evrst30": {a:6377276.345, rf:300.8017, ellipseName:"Everest 1830"}, "evrst48": {a:6377304.063, rf:300.8017, ellipseName:"Everest 1948"}, "evrst56": {a:6377301.243, rf:300.8017, ellipseName:"Everest 1956"}, "evrst69": {a:6377295.664, rf:300.8017, ellipseName:"Everest 1969"}, "evrstSS": {a:6377298.556, rf:300.8017, ellipseName:"Everest (Sabah & Sarawak)"}, "fschr60": {a:6378166.0, rf:298.3, ellipseName:"Fischer (Mercury Datum) 1960"}, "fschr60m": {a:6378155.0, rf:298.3, ellipseName:"Fischer 1960"}, "fschr68": {a:6378150.0, rf:298.3, ellipseName:"Fischer 1968"}, "helmert": {a:6378200.0, rf:298.3, ellipseName:"Helmert 1906"}, "hough": {a:6378270.0, rf:297.0, ellipseName:"Hough"}, "intl": {a:6378388.0, rf:297.0, ellipseName:"International 1909 (Hayford)"}, "kaula": {a:6378163.0, rf:298.24, ellipseName:"Kaula 1961"}, "lerch": {a:6378139.0, rf:298.257, ellipseName:"Lerch 1979"}, "mprts": {a:6397300.0, rf:191.0, ellipseName:"Maupertius 1738"}, "new_intl": {a:6378157.5, b:6356772.2, ellipseName:"New International 1967"}, "plessis": {a:6376523.0, rf:6355863.0, ellipseName:"Plessis 1817 (France)"}, "krass": {a:6378245.0, rf:298.3, ellipseName:"Krassovsky, 1942"}, "SEasia": {a:6378155.0, b:6356773.3205, ellipseName:"Southeast Asia"}, "walbeck": {a:6376896.0, b:6355834.8467, ellipseName:"Walbeck"}, "WGS60": {a:6378165.0, rf:298.3, ellipseName:"WGS 60"}, "WGS66": {a:6378145.0, rf:298.25, ellipseName:"WGS 66"}, "WGS72": {a:6378135.0, rf:298.26, ellipseName:"WGS 72"}, "WGS84": {a:6378137.0, rf:298.257223563, ellipseName:"WGS 84"}, "sphere": {a:6370997.0, b:6370997.0, ellipseName:"Normal Sphere (r=6370997)"} }; Proj4js.Datum = { "WGS84": {towgs84: "0,0,0", ellipse: "WGS84", datumName: "WGS84"}, "GGRS87": {towgs84: "-199.87,74.79,246.62", ellipse: "GRS80", datumName: "Greek_Geodetic_Reference_System_1987"}, "NAD83": {towgs84: "0,0,0", ellipse: "GRS80", datumName: "North_American_Datum_1983"}, "NAD27": {nadgrids: "@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat", ellipse: "clrk66", datumName: "North_American_Datum_1927"}, "potsdam": {towgs84: "606.0,23.0,413.0", ellipse: "bessel", datumName: "Potsdam Rauenberg 1950 DHDN"}, "carthage": {towgs84: "-263.0,6.0,431.0", ellipse: "clark80", datumName: "Carthage 1934 Tunisia"}, "hermannskogel": {towgs84: "653.0,-212.0,449.0", ellipse: "bessel", datumName: "Hermannskogel"}, "ire65": {towgs84: "482.530,-130.596,564.557,-1.042,-0.214,-0.631,8.15", ellipse: "mod_airy", datumName: "Ireland 1965"}, "nzgd49": {towgs84: "59.47,-5.04,187.44,0.47,-0.1,1.024,-4.5993", ellipse: "intl", datumName: "New Zealand Geodetic Datum 1949"}, "OSGB36": {towgs84: "446.448,-125.157,542.060,0.1502,0.2470,0.8421,-20.4894", ellipse: "airy", datumName: "Airy 1830"} }; Proj4js.WGS84 = new Proj4js.Proj('WGS84'); Proj4js.Datum['OSB36'] = Proj4js.Datum['OSGB36']; //as returned from spatialreference.org //lookup table to go from the projection name in WKT to the Proj4js projection name //build this out as required Proj4js.wktProjections = { "Lambert Tangential Conformal Conic Projection": "lcc", "Mercator": "merc", "Popular Visualisation Pseudo Mercator": "merc", "Mercator_1SP": "merc", "Transverse_Mercator": "tmerc", "Transverse Mercator": "tmerc", "Lambert Azimuthal Equal Area": "laea", "Universal Transverse Mercator System": "utm" }; Proj4js.defs['EPSG:3857'] = Proj4js.defs['EPSG:3785']; /* ====================================================================== projCode/aea.js ====================================================================== */ /******************************************************************************* NAME ALBERS CONICAL EQUAL AREA PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Albers Conical Equal Area projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan, Feb, 1992 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ Proj4js.Proj.aea = { init : function() { if (Math.abs(this.lat1 + this.lat2) < Proj4js.common.EPSLN) { Proj4js.reportError("aeaInitEqualLatitudes"); return; } this.temp = this.b / this.a; this.es = 1.0 - Math.pow(this.temp,2); this.e3 = Math.sqrt(this.es); this.sin_po=Math.sin(this.lat1); this.cos_po=Math.cos(this.lat1); this.t1=this.sin_po; this.con = this.sin_po; this.ms1 = Proj4js.common.msfnz(this.e3,this.sin_po,this.cos_po); this.qs1 = Proj4js.common.qsfnz(this.e3,this.sin_po,this.cos_po); this.sin_po=Math.sin(this.lat2); this.cos_po=Math.cos(this.lat2); this.t2=this.sin_po; this.ms2 = Proj4js.common.msfnz(this.e3,this.sin_po,this.cos_po); this.qs2 = Proj4js.common.qsfnz(this.e3,this.sin_po,this.cos_po); this.sin_po=Math.sin(this.lat0); this.cos_po=Math.cos(this.lat0); this.t3=this.sin_po; this.qs0 = Proj4js.common.qsfnz(this.e3,this.sin_po,this.cos_po); if (Math.abs(this.lat1 - this.lat2) > Proj4js.common.EPSLN) { this.ns0 = (this.ms1 * this.ms1 - this.ms2 *this.ms2)/ (this.qs2 - this.qs1); } else { this.ns0 = this.con; } this.c = this.ms1 * this.ms1 + this.ns0 * this.qs1; this.rh = this.a * Math.sqrt(this.c - this.ns0 * this.qs0)/this.ns0; }, /* Albers Conical Equal Area forward equations--mapping lat,long to x,y -------------------------------------------------------------------*/ forward: function(p){ var lon=p.x; var lat=p.y; this.sin_phi=Math.sin(lat); this.cos_phi=Math.cos(lat); var qs = Proj4js.common.qsfnz(this.e3,this.sin_phi,this.cos_phi); var rh1 =this.a * Math.sqrt(this.c - this.ns0 * qs)/this.ns0; var theta = this.ns0 * Proj4js.common.adjust_lon(lon - this.long0); var x = rh1 * Math.sin(theta) + this.x0; var y = this.rh - rh1 * Math.cos(theta) + this.y0; p.x = x; p.y = y; return p; }, inverse: function(p) { var rh1,qs,con,theta,lon,lat; p.x -= this.x0; p.y = this.rh - p.y + this.y0; if (this.ns0 >= 0) { rh1 = Math.sqrt(p.x *p.x + p.y * p.y); con = 1.0; } else { rh1 = -Math.sqrt(p.x * p.x + p.y *p.y); con = -1.0; } theta = 0.0; if (rh1 != 0.0) { theta = Math.atan2(con * p.x, con * p.y); } con = rh1 * this.ns0 / this.a; qs = (this.c - con * con) / this.ns0; if (this.e3 >= 1e-10) { con = 1 - .5 * (1.0 -this.es) * Math.log((1.0 - this.e3) / (1.0 + this.e3))/this.e3; if (Math.abs(Math.abs(con) - Math.abs(qs)) > .0000000001 ) { lat = this.phi1z(this.e3,qs); } else { if (qs >= 0) { lat = .5 * Proj4js.common.PI; } else { lat = -.5 * Proj4js.common.PI; } } } else { lat = this.phi1z(this.e3,qs); } lon = Proj4js.common.adjust_lon(theta/this.ns0 + this.long0); p.x = lon; p.y = lat; return p; }, /* Function to compute phi1, the latitude for the inverse of the Albers Conical Equal-Area projection. -------------------------------------------*/ phi1z: function (eccent,qs) { var sinphi, cosphi, con, com, dphi; var phi = Proj4js.common.asinz(.5 * qs); if (eccent < Proj4js.common.EPSLN) return phi; var eccnts = eccent * eccent; for (var i = 1; i <= 25; i++) { sinphi = Math.sin(phi); cosphi = Math.cos(phi); con = eccent * sinphi; com = 1.0 - con * con; dphi = .5 * com * com / cosphi * (qs / (1.0 - eccnts) - sinphi / com + .5 / eccent * Math.log((1.0 - con) / (1.0 + con))); phi = phi + dphi; if (Math.abs(dphi) <= 1e-7) return phi; } Proj4js.reportError("aea:phi1z:Convergence error"); return null; } }; /* ====================================================================== projCode/sterea.js ====================================================================== */ Proj4js.Proj.sterea = { dependsOn : 'gauss', init : function() { Proj4js.Proj['gauss'].init.apply(this); if (!this.rc) { Proj4js.reportError("sterea:init:E_ERROR_0"); return; } this.sinc0 = Math.sin(this.phic0); this.cosc0 = Math.cos(this.phic0); this.R2 = 2.0 * this.rc; if (!this.title) this.title = "Oblique Stereographic Alternative"; }, forward : function(p) { var sinc, cosc, cosl, k; p.x = Proj4js.common.adjust_lon(p.x-this.long0); /* adjust del longitude */ Proj4js.Proj['gauss'].forward.apply(this, [p]); sinc = Math.sin(p.y); cosc = Math.cos(p.y); cosl = Math.cos(p.x); k = this.k0 * this.R2 / (1.0 + this.sinc0 * sinc + this.cosc0 * cosc * cosl); p.x = k * cosc * Math.sin(p.x); p.y = k * (this.cosc0 * sinc - this.sinc0 * cosc * cosl); p.x = this.a * p.x + this.x0; p.y = this.a * p.y + this.y0; return p; }, inverse : function(p) { var sinc, cosc, lon, lat, rho; p.x = (p.x - this.x0) / this.a; /* descale and de-offset */ p.y = (p.y - this.y0) / this.a; p.x /= this.k0; p.y /= this.k0; if ( (rho = Math.sqrt(p.x*p.x + p.y*p.y)) ) { var c = 2.0 * Math.atan2(rho, this.R2); sinc = Math.sin(c); cosc = Math.cos(c); lat = Math.asin(cosc * this.sinc0 + p.y * sinc * this.cosc0 / rho); lon = Math.atan2(p.x * sinc, rho * this.cosc0 * cosc - p.y * this.sinc0 * sinc); } else { lat = this.phic0; lon = 0.; } p.x = lon; p.y = lat; Proj4js.Proj['gauss'].inverse.apply(this,[p]); p.x = Proj4js.common.adjust_lon(p.x + this.long0); /* adjust longitude to CM */ return p; } }; /* ====================================================================== projCode/poly.js ====================================================================== */ /* Function to compute, phi4, the latitude for the inverse of the Polyconic projection. ------------------------------------------------------------*/ function phi4z (eccent,e0,e1,e2,e3,a,b,c,phi) { var sinphi, sin2ph, tanphi, ml, mlp, con1, con2, con3, dphi, i; phi = a; for (i = 1; i <= 15; i++) { sinphi = Math.sin(phi); tanphi = Math.tan(phi); c = tanphi * Math.sqrt (1.0 - eccent * sinphi * sinphi); sin2ph = Math.sin (2.0 * phi); /* ml = e0 * *phi - e1 * sin2ph + e2 * sin (4.0 * *phi); mlp = e0 - 2.0 * e1 * cos (2.0 * *phi) + 4.0 * e2 * cos (4.0 * *phi); */ ml = e0 * phi - e1 * sin2ph + e2 * Math.sin (4.0 * phi) - e3 * Math.sin (6.0 * phi); mlp = e0 - 2.0 * e1 * Math.cos (2.0 * phi) + 4.0 * e2 * Math.cos (4.0 * phi) - 6.0 * e3 * Math.cos (6.0 * phi); con1 = 2.0 * ml + c * (ml * ml + b) - 2.0 * a * (c * ml + 1.0); con2 = eccent * sin2ph * (ml * ml + b - 2.0 * a * ml) / (2.0 *c); con3 = 2.0 * (a - ml) * (c * mlp - 2.0 / sin2ph) - 2.0 * mlp; dphi = con1 / (con2 + con3); phi += dphi; if (Math.abs(dphi) <= .0000000001 ) return(phi); } Proj4js.reportError("phi4z: No convergence"); return null; } /* Function to compute the constant e4 from the input of the eccentricity of the spheroid, x. This constant is used in the Polar Stereographic projection. --------------------------------------------------------------------*/ function e4fn(x) { var con, com; con = 1.0 + x; com = 1.0 - x; return (Math.sqrt((Math.pow(con,con))*(Math.pow(com,com)))); } /******************************************************************************* NAME POLYCONIC PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Polyconic projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan Mar, 1993 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ Proj4js.Proj.poly = { /* Initialize the POLYCONIC projection ----------------------------------*/ init: function() { var temp; /* temporary variable */ if (this.lat0 == 0) this.lat0 = 90;//this.lat0 ca /* Place parameters in static storage for common use -------------------------------------------------*/ this.temp = this.b / this.a; this.es = 1.0 - Math.pow(this.temp,2);// devait etre dans tmerc.js mais n y est pas donc je commente sinon retour de valeurs nulles this.e = Math.sqrt(this.es); this.e0 = Proj4js.common.e0fn(this.es); this.e1 = Proj4js.common.e1fn(this.es); this.e2 = Proj4js.common.e2fn(this.es); this.e3 = Proj4js.common.e3fn(this.es); this.ml0 = Proj4js.common.mlfn(this.e0, this.e1,this.e2, this.e3, this.lat0);//si que des zeros le calcul ne se fait pas //if (!this.ml0) {this.ml0=0;} }, /* Polyconic forward equations--mapping lat,long to x,y ---------------------------------------------------*/ forward: function(p) { var sinphi, cosphi; /* sin and cos value */ var al; /* temporary values */ var c; /* temporary values */ var con, ml; /* cone constant, small m */ var ms; /* small m */ var x,y; var lon=p.x; var lat=p.y; con = Proj4js.common.adjust_lon(lon - this.long0); if (Math.abs(lat) <= .0000001) { x = this.x0 + this.a * con; y = this.y0 - this.a * this.ml0; } else { sinphi = Math.sin(lat); cosphi = Math.cos(lat); ml = Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, lat); ms = Proj4js.common.msfnz(this.e,sinphi,cosphi); con = sinphi; x = this.x0 + this.a * ms * Math.sin(con)/sinphi; y = this.y0 + this.a * (ml - this.ml0 + ms * (1.0 - Math.cos(con))/sinphi); } p.x=x; p.y=y; return p; }, /* Inverse equations -----------------*/ inverse: function(p) { var sin_phi, cos_phi; /* sin and cos value */ var al; /* temporary values */ var b; /* temporary values */ var c; /* temporary values */ var con, ml; /* cone constant, small m */ var iflg; /* error flag */ var lon,lat; p.x -= this.x0; p.y -= this.y0; al = this.ml0 + p.y/this.a; iflg = 0; if (Math.abs(al) <= .0000001) { lon = p.x/this.a + this.long0; lat = 0.0; } else { b = al * al + (p.x/this.a) * (p.x/this.a); iflg = phi4z(this.es,this.e0,this.e1,this.e2,this.e3,this.al,b,c,lat); if (iflg != 1) return(iflg); lon = Proj4js.common.adjust_lon((Proj4js.common.asinz(p.x * c / this.a) / Math.sin(lat)) + this.long0); } p.x=lon; p.y=lat; return p; } }; /* ====================================================================== projCode/equi.js ====================================================================== */ /******************************************************************************* NAME EQUIRECTANGULAR PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Equirectangular projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan Mar, 1993 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ Proj4js.Proj.equi = { init: function() { if(!this.x0) this.x0=0; if(!this.y0) this.y0=0; if(!this.lat0) this.lat0=0; if(!this.long0) this.long0=0; ///this.t2; }, /* Equirectangular forward equations--mapping lat,long to x,y ---------------------------------------------------------*/ forward: function(p) { var lon=p.x; var lat=p.y; var dlon = Proj4js.common.adjust_lon(lon - this.long0); var x = this.x0 +this. a * dlon *Math.cos(this.lat0); var y = this.y0 + this.a * lat; this.t1=x; this.t2=Math.cos(this.lat0); p.x=x; p.y=y; return p; }, //equiFwd() /* Equirectangular inverse equations--mapping x,y to lat/long ---------------------------------------------------------*/ inverse: function(p) { p.x -= this.x0; p.y -= this.y0; var lat = p.y /this. a; if ( Math.abs(lat) > Proj4js.common.HALF_PI) { Proj4js.reportError("equi:Inv:DataError"); } var lon = Proj4js.common.adjust_lon(this.long0 + p.x / (this.a * Math.cos(this.lat0))); p.x=lon; p.y=lat; }//equiInv() }; /* ====================================================================== projCode/merc.js ====================================================================== */ /******************************************************************************* NAME MERCATOR PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Mercator projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- D. Steinwand, EROS Nov, 1991 T. Mittan Mar, 1993 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ //static double r_major = a; /* major axis */ //static double r_minor = b; /* minor axis */ //static double lon_center = long0; /* Center longitude (projection center) */ //static double lat_origin = lat0; /* center latitude */ //static double e,es; /* eccentricity constants */ //static double m1; /* small value m */ //static double false_northing = y0; /* y offset in meters */ //static double false_easting = x0; /* x offset in meters */ //scale_fact = k0 Proj4js.Proj.merc = { init : function() { //?this.temp = this.r_minor / this.r_major; //this.temp = this.b / this.a; //this.es = 1.0 - Math.sqrt(this.temp); //this.e = Math.sqrt( this.es ); //?this.m1 = Math.cos(this.lat_origin) / (Math.sqrt( 1.0 - this.es * Math.sin(this.lat_origin) * Math.sin(this.lat_origin))); //this.m1 = Math.cos(0.0) / (Math.sqrt( 1.0 - this.es * Math.sin(0.0) * Math.sin(0.0))); if (this.lat_ts) { if (this.sphere) { this.k0 = Math.cos(this.lat_ts); } else { this.k0 = Proj4js.common.msfnz(this.es, Math.sin(this.lat_ts), Math.cos(this.lat_ts)); } } }, /* Mercator forward equations--mapping lat,long to x,y --------------------------------------------------*/ forward : function(p) { //alert("ll2m coords : "+coords); var lon = p.x; var lat = p.y; // convert to radians if ( lat*Proj4js.common.R2D > 90.0 && lat*Proj4js.common.R2D < -90.0 && lon*Proj4js.common.R2D > 180.0 && lon*Proj4js.common.R2D < -180.0) { Proj4js.reportError("merc:forward: llInputOutOfRange: "+ lon +" : " + lat); return null; } var x,y; if(Math.abs( Math.abs(lat) - Proj4js.common.HALF_PI) <= Proj4js.common.EPSLN) { Proj4js.reportError("merc:forward: ll2mAtPoles"); return null; } else { if (this.sphere) { x = this.x0 + this.a * this.k0 * Proj4js.common.adjust_lon(lon - this.long0); y = this.y0 + this.a * this.k0 * Math.log(Math.tan(Proj4js.common.FORTPI + 0.5*lat)); } else { var sinphi = Math.sin(lat); var ts = Proj4js.common.tsfnz(this.e,lat,sinphi); x = this.x0 + this.a * this.k0 * Proj4js.common.adjust_lon(lon - this.long0); y = this.y0 - this.a * this.k0 * Math.log(ts); } p.x = x; p.y = y; return p; } }, /* Mercator inverse equations--mapping x,y to lat/long --------------------------------------------------*/ inverse : function(p) { var x = p.x - this.x0; var y = p.y - this.y0; var lon,lat; if (this.sphere) { lat = Proj4js.common.HALF_PI - 2.0 * Math.atan(Math.exp(-y / this.a * this.k0)); } else { var ts = Math.exp(-y / (this.a * this.k0)); lat = Proj4js.common.phi2z(this.e,ts); if(lat == -9999) { Proj4js.reportError("merc:inverse: lat = -9999"); return null; } } lon = Proj4js.common.adjust_lon(this.long0+ x / (this.a * this.k0)); p.x = lon; p.y = lat; return p; } }; /* ====================================================================== projCode/utm.js ====================================================================== */ /******************************************************************************* NAME TRANSVERSE MERCATOR PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Transverse Mercator projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ /** Initialize Transverse Mercator projection */ Proj4js.Proj.utm = { dependsOn : 'tmerc', init : function() { if (!this.zone) { Proj4js.reportError("utm:init: zone must be specified for UTM"); return; } this.lat0 = 0.0; this.long0 = ((6 * Math.abs(this.zone)) - 183) * Proj4js.common.D2R; this.x0 = 500000.0; this.y0 = this.utmSouth ? 10000000.0 : 0.0; this.k0 = 0.9996; Proj4js.Proj['tmerc'].init.apply(this); this.forward = Proj4js.Proj['tmerc'].forward; this.inverse = Proj4js.Proj['tmerc'].inverse; } }; /* ====================================================================== projCode/eqdc.js ====================================================================== */ /******************************************************************************* NAME EQUIDISTANT CONIC PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Equidistant Conic projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan Mar, 1993 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ /* Variables common to all subroutines in this code file -----------------------------------------------------*/ Proj4js.Proj.eqdc = { /* Initialize the Equidistant Conic projection ------------------------------------------*/ init: function() { /* Place parameters in static storage for common use -------------------------------------------------*/ if(!this.mode) this.mode=0;//chosen default mode this.temp = this.b / this.a; this.es = 1.0 - Math.pow(this.temp,2); this.e = Math.sqrt(this.es); this.e0 = Proj4js.common.e0fn(this.es); this.e1 = Proj4js.common.e1fn(this.es); this.e2 = Proj4js.common.e2fn(this.es); this.e3 = Proj4js.common.e3fn(this.es); this.sinphi=Math.sin(this.lat1); this.cosphi=Math.cos(this.lat1); this.ms1 = Proj4js.common.msfnz(this.e,this.sinphi,this.cosphi); this.ml1 = Proj4js.common.mlfn(this.e0, this.e1, this.e2,this.e3, this.lat1); /* format B ---------*/ if (this.mode != 0) { if (Math.abs(this.lat1 + this.lat2) < Proj4js.common.EPSLN) { Proj4js.reportError("eqdc:Init:EqualLatitudes"); //return(81); } this.sinphi=Math.sin(this.lat2); this.cosphi=Math.cos(this.lat2); this.ms2 = Proj4js.common.msfnz(this.e,this.sinphi,this.cosphi); this.ml2 = Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, this.lat2); if (Math.abs(this.lat1 - this.lat2) >= Proj4js.common.EPSLN) { this.ns = (this.ms1 - this.ms2) / (this.ml2 - this.ml1); } else { this.ns = this.sinphi; } } else { this.ns = this.sinphi; } this.g = this.ml1 + this.ms1/this.ns; this.ml0 = Proj4js.common.mlfn(this.e0, this.e1,this. e2, this.e3, this.lat0); this.rh = this.a * (this.g - this.ml0); }, /* Equidistant Conic forward equations--mapping lat,long to x,y -----------------------------------------------------------*/ forward: function(p) { var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ var ml = Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, lat); var rh1 = this.a * (this.g - ml); var theta = this.ns * Proj4js.common.adjust_lon(lon - this.long0); var x = this.x0 + rh1 * Math.sin(theta); var y = this.y0 + this.rh - rh1 * Math.cos(theta); p.x=x; p.y=y; return p; }, /* Inverse equations -----------------*/ inverse: function(p) { p.x -= this.x0; p.y = this.rh - p.y + this.y0; var con, rh1; if (this.ns >= 0) { rh1 = Math.sqrt(p.x *p.x + p.y * p.y); con = 1.0; } else { rh1 = -Math.sqrt(p.x *p. x +p. y * p.y); con = -1.0; } var theta = 0.0; if (rh1 != 0.0) theta = Math.atan2(con *p.x, con *p.y); var ml = this.g - rh1 /this.a; var lat = this.phi3z(ml,this.e0,this.e1,this.e2,this.e3); var lon = Proj4js.common.adjust_lon(this.long0 + theta / this.ns); p.x=lon; p.y=lat; return p; }, /* Function to compute latitude, phi3, for the inverse of the Equidistant Conic projection. -----------------------------------------------------------------*/ phi3z: function(ml,e0,e1,e2,e3) { var phi; var dphi; phi = ml; for (var i = 0; i < 15; i++) { dphi = (ml + e1 * Math.sin(2.0 * phi) - e2 * Math.sin(4.0 * phi) + e3 * Math.sin(6.0 * phi))/ e0 - phi; phi += dphi; if (Math.abs(dphi) <= .0000000001) { return phi; } } Proj4js.reportError("PHI3Z-CONV:Latitude failed to converge after 15 iterations"); return null; } }; /* ====================================================================== projCode/tmerc.js ====================================================================== */ /******************************************************************************* NAME TRANSVERSE MERCATOR PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Transverse Mercator projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ /** Initialize Transverse Mercator projection */ Proj4js.Proj.tmerc = { init : function() { this.e0 = Proj4js.common.e0fn(this.es); this.e1 = Proj4js.common.e1fn(this.es); this.e2 = Proj4js.common.e2fn(this.es); this.e3 = Proj4js.common.e3fn(this.es); this.ml0 = this.a * Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, this.lat0); }, /** Transverse Mercator Forward - long/lat to x/y long/lat in radians */ forward : function(p) { var lon = p.x; var lat = p.y; var delta_lon = Proj4js.common.adjust_lon(lon - this.long0); // Delta longitude var con; // cone constant var x, y; var sin_phi=Math.sin(lat); var cos_phi=Math.cos(lat); if (this.sphere) { /* spherical form */ var b = cos_phi * Math.sin(delta_lon); if ((Math.abs(Math.abs(b) - 1.0)) < .0000000001) { Proj4js.reportError("tmerc:forward: Point projects into infinity"); return(93); } else { x = .5 * this.a * this.k0 * Math.log((1.0 + b)/(1.0 - b)); con = Math.acos(cos_phi * Math.cos(delta_lon)/Math.sqrt(1.0 - b*b)); if (lat < 0) con = - con; y = this.a * this.k0 * (con - this.lat0); } } else { var al = cos_phi * delta_lon; var als = Math.pow(al,2); var c = this.ep2 * Math.pow(cos_phi,2); var tq = Math.tan(lat); var t = Math.pow(tq,2); con = 1.0 - this.es * Math.pow(sin_phi,2); var n = this.a / Math.sqrt(con); var ml = this.a * Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, lat); x = this.k0 * n * al * (1.0 + als / 6.0 * (1.0 - t + c + als / 20.0 * (5.0 - 18.0 * t + Math.pow(t,2) + 72.0 * c - 58.0 * this.ep2))) + this.x0; y = this.k0 * (ml - this.ml0 + n * tq * (als * (0.5 + als / 24.0 * (5.0 - t + 9.0 * c + 4.0 * Math.pow(c,2) + als / 30.0 * (61.0 - 58.0 * t + Math.pow(t,2) + 600.0 * c - 330.0 * this.ep2))))) + this.y0; } p.x = x; p.y = y; return p; }, // tmercFwd() /** Transverse Mercator Inverse - x/y to long/lat */ inverse : function(p) { var con, phi; /* temporary angles */ var delta_phi; /* difference between longitudes */ var i; var max_iter = 6; /* maximun number of iterations */ var lat, lon; if (this.sphere) { /* spherical form */ var f = Math.exp(p.x/(this.a * this.k0)); var g = .5 * (f - 1/f); var temp = this.lat0 + p.y/(this.a * this.k0); var h = Math.cos(temp); con = Math.sqrt((1.0 - h * h)/(1.0 + g * g)); lat = Proj4js.common.asinz(con); if (temp < 0) lat = -lat; if ((g == 0) && (h == 0)) { lon = this.long0; } else { lon = Proj4js.common.adjust_lon(Math.atan2(g,h) + this.long0); } } else { // ellipsoidal form var x = p.x - this.x0; var y = p.y - this.y0; con = (this.ml0 + y / this.k0) / this.a; phi = con; for (i=0;true;i++) { delta_phi=((con + this.e1 * Math.sin(2.0*phi) - this.e2 * Math.sin(4.0*phi) + this.e3 * Math.sin(6.0*phi)) / this.e0) - phi; phi += delta_phi; if (Math.abs(delta_phi) <= Proj4js.common.EPSLN) break; if (i >= max_iter) { Proj4js.reportError("tmerc:inverse: Latitude failed to converge"); return(95); } } // for() if (Math.abs(phi) < Proj4js.common.HALF_PI) { // sincos(phi, &sin_phi, &cos_phi); var sin_phi=Math.sin(phi); var cos_phi=Math.cos(phi); var tan_phi = Math.tan(phi); var c = this.ep2 * Math.pow(cos_phi,2); var cs = Math.pow(c,2); var t = Math.pow(tan_phi,2); var ts = Math.pow(t,2); con = 1.0 - this.es * Math.pow(sin_phi,2); var n = this.a / Math.sqrt(con); var r = n * (1.0 - this.es) / con; var d = x / (n * this.k0); var ds = Math.pow(d,2); lat = phi - (n * tan_phi * ds / r) * (0.5 - ds / 24.0 * (5.0 + 3.0 * t + 10.0 * c - 4.0 * cs - 9.0 * this.ep2 - ds / 30.0 * (61.0 + 90.0 * t + 298.0 * c + 45.0 * ts - 252.0 * this.ep2 - 3.0 * cs))); lon = Proj4js.common.adjust_lon(this.long0 + (d * (1.0 - ds / 6.0 * (1.0 + 2.0 * t + c - ds / 20.0 * (5.0 - 2.0 * c + 28.0 * t - 3.0 * cs + 8.0 * this.ep2 + 24.0 * ts))) / cos_phi)); } else { lat = Proj4js.common.HALF_PI * Proj4js.common.sign(y); lon = this.long0; } } p.x = lon; p.y = lat; return p; } // tmercInv() }; /* ====================================================================== defs/GOOGLE.js ====================================================================== */ Proj4js.defs["GOOGLE"]="+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +no_defs"; Proj4js.defs["EPSG:900913"]=Proj4js.defs["GOOGLE"]; /* ====================================================================== projCode/gstmerc.js ====================================================================== */ Proj4js.Proj.gstmerc = { init : function() { // array of: a, b, lon0, lat0, k0, x0, y0 var temp= this.b / this.a; this.e= Math.sqrt(1.0 - temp*temp); this.lc= this.long0; this.rs= Math.sqrt(1.0+this.e*this.e*Math.pow(Math.cos(this.lat0),4.0)/(1.0-this.e*this.e)); var sinz= Math.sin(this.lat0); var pc= Math.asin(sinz/this.rs); var sinzpc= Math.sin(pc); this.cp= Proj4js.common.latiso(0.0,pc,sinzpc)-this.rs*Proj4js.common.latiso(this.e,this.lat0,sinz); this.n2= this.k0*this.a*Math.sqrt(1.0-this.e*this.e)/(1.0-this.e*this.e*sinz*sinz); this.xs= this.x0; this.ys= this.y0-this.n2*pc; if (!this.title) this.title = "Gauss Schreiber transverse mercator"; }, // forward equations--mapping lat,long to x,y // ----------------------------------------------------------------- forward : function(p) { var lon= p.x; var lat= p.y; var L= this.rs*(lon-this.lc); var Ls= this.cp+(this.rs*Proj4js.common.latiso(this.e,lat,Math.sin(lat))); var lat1= Math.asin(Math.sin(L)/Proj4js.common.cosh(Ls)); var Ls1= Proj4js.common.latiso(0.0,lat1,Math.sin(lat1)); p.x= this.xs+(this.n2*Ls1); p.y= this.ys+(this.n2*Math.atan(Proj4js.common.sinh(Ls)/Math.cos(L))); return p; }, // inverse equations--mapping x,y to lat/long // ----------------------------------------------------------------- inverse : function(p) { var x= p.x; var y= p.y; var L= Math.atan(Proj4js.common.sinh((x-this.xs)/this.n2)/Math.cos((y-this.ys)/this.n2)); var lat1= Math.asin(Math.sin((y-this.ys)/this.n2)/Proj4js.common.cosh((x-this.xs)/this.n2)); var LC= Proj4js.common.latiso(0.0,lat1,Math.sin(lat1)); p.x= this.lc+L/this.rs; p.y= Proj4js.common.invlatiso(this.e,(LC-this.cp)/this.rs); return p; } }; /* ====================================================================== projCode/ortho.js ====================================================================== */ /******************************************************************************* NAME ORTHOGRAPHIC PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Orthographic projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan Mar, 1993 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ Proj4js.Proj.ortho = { /* Initialize the Orthographic projection -------------------------------------*/ init: function(def) { //double temp; /* temporary variable */ /* Place parameters in static storage for common use -------------------------------------------------*/; this.sin_p14=Math.sin(this.lat0); this.cos_p14=Math.cos(this.lat0); }, /* Orthographic forward equations--mapping lat,long to x,y ---------------------------------------------------*/ forward: function(p) { var sinphi, cosphi; /* sin and cos value */ var dlon; /* delta longitude value */ var coslon; /* cos of longitude */ var ksp; /* scale factor */ var g; var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ dlon = Proj4js.common.adjust_lon(lon - this.long0); sinphi=Math.sin(lat); cosphi=Math.cos(lat); coslon = Math.cos(dlon); g = this.sin_p14 * sinphi + this.cos_p14 * cosphi * coslon; ksp = 1.0; if ((g > 0) || (Math.abs(g) <= Proj4js.common.EPSLN)) { var x = this.a * ksp * cosphi * Math.sin(dlon); var y = this.y0 + this.a * ksp * (this.cos_p14 * sinphi - this.sin_p14 * cosphi * coslon); } else { Proj4js.reportError("orthoFwdPointError"); } p.x=x; p.y=y; return p; }, inverse: function(p) { var rh; /* height above ellipsoid */ var z; /* angle */ var sinz,cosz; /* sin of z and cos of z */ var temp; var con; var lon , lat; /* Inverse equations -----------------*/ p.x -= this.x0; p.y -= this.y0; rh = Math.sqrt(p.x * p.x + p.y * p.y); if (rh > this.a + .0000001) { Proj4js.reportError("orthoInvDataError"); } z = Proj4js.common.asinz(rh / this.a); sinz=Math.sin(z); cosz=Math.cos(z); lon = this.long0; if (Math.abs(rh) <= Proj4js.common.EPSLN) { lat = this.lat0; } lat = Proj4js.common.asinz(cosz * this.sin_p14 + (p.y * sinz * this.cos_p14)/rh); con = Math.abs(this.lat0) - Proj4js.common.HALF_PI; if (Math.abs(con) <= Proj4js.common.EPSLN) { if (this.lat0 >= 0) { lon = Proj4js.common.adjust_lon(this.long0 + Math.atan2(p.x, -p.y)); } else { lon = Proj4js.common.adjust_lon(this.long0 -Math.atan2(-p.x, p.y)); } } con = cosz - this.sin_p14 * Math.sin(lat); p.x=lon; p.y=lat; return p; } }; /* ====================================================================== projCode/krovak.js ====================================================================== */ /** NOTES: According to EPSG the full Krovak projection method should have the following parameters. Within PROJ.4 the azimuth, and pseudo standard parallel are hardcoded in the algorithm and can't be altered from outside. The others all have defaults to match the common usage with Krovak projection. lat_0 = latitude of centre of the projection lon_0 = longitude of centre of the projection ** = azimuth (true) of the centre line passing through the centre of the projection ** = latitude of pseudo standard parallel k = scale factor on the pseudo standard parallel x_0 = False Easting of the centre of the projection at the apex of the cone y_0 = False Northing of the centre of the projection at the apex of the cone **/ Proj4js.Proj.krovak = { init: function() { /* we want Bessel as fixed ellipsoid */ this.a = 6377397.155; this.es = 0.006674372230614; this.e = Math.sqrt(this.es); /* if latitude of projection center is not set, use 49d30'N */ if (!this.lat0) { this.lat0 = 0.863937979737193; } if (!this.long0) { this.long0 = 0.7417649320975901 - 0.308341501185665; } /* if scale not set default to 0.9999 */ if (!this.k0) { this.k0 = 0.9999; } this.s45 = 0.785398163397448; /* 45� */ this.s90 = 2 * this.s45; this.fi0 = this.lat0; /* Latitude of projection centre 49� 30' */ /* Ellipsoid Bessel 1841 a = 6377397.155m 1/f = 299.1528128, e2=0.006674372230614; */ this.e2 = this.es; /* 0.006674372230614; */ this.e = Math.sqrt(this.e2); this.alfa = Math.sqrt(1. + (this.e2 * Math.pow(Math.cos(this.fi0), 4)) / (1. - this.e2)); this.uq = 1.04216856380474; /* DU(2, 59, 42, 42.69689) */ this.u0 = Math.asin(Math.sin(this.fi0) / this.alfa); this.g = Math.pow( (1. + this.e * Math.sin(this.fi0)) / (1. - this.e * Math.sin(this.fi0)) , this.alfa * this.e / 2. ); this.k = Math.tan( this.u0 / 2. + this.s45) / Math.pow (Math.tan(this.fi0 / 2. + this.s45) , this.alfa) * this.g; this.k1 = this.k0; this.n0 = this.a * Math.sqrt(1. - this.e2) / (1. - this.e2 * Math.pow(Math.sin(this.fi0), 2)); this.s0 = 1.37008346281555; /* Latitude of pseudo standard parallel 78� 30'00" N */ this.n = Math.sin(this.s0); this.ro0 = this.k1 * this.n0 / Math.tan(this.s0); this.ad = this.s90 - this.uq; }, /* ellipsoid */ /* calculate xy from lat/lon */ /* Constants, identical to inverse transform function */ forward: function(p) { var gfi, u, deltav, s, d, eps, ro; var lon = p.x; var lat = p.y; var delta_lon = Proj4js.common.adjust_lon(lon - this.long0); // Delta longitude /* Transformation */ gfi = Math.pow ( ((1. + this.e * Math.sin(lat)) / (1. - this.e * Math.sin(lat))) , (this.alfa * this.e / 2.)); u= 2. * (Math.atan(this.k * Math.pow( Math.tan(lat / 2. + this.s45), this.alfa) / gfi)-this.s45); deltav = - delta_lon * this.alfa; s = Math.asin(Math.cos(this.ad) * Math.sin(u) + Math.sin(this.ad) * Math.cos(u) * Math.cos(deltav)); d = Math.asin(Math.cos(u) * Math.sin(deltav) / Math.cos(s)); eps = this.n * d; ro = this.ro0 * Math.pow(Math.tan(this.s0 / 2. + this.s45) , this.n) / Math.pow(Math.tan(s / 2. + this.s45) , this.n); /* x and y are reverted! */ //p.y = ro * Math.cos(eps) / a; //p.x = ro * Math.sin(eps) / a; p.y = ro * Math.cos(eps) / 1.0; p.x = ro * Math.sin(eps) / 1.0; if(this.czech) { p.y *= -1.0; p.x *= -1.0; } return (p); }, /* calculate lat/lon from xy */ inverse: function(p) { /* Constants, identisch wie in der Umkehrfunktion */ var u, deltav, s, d, eps, ro, fi1; var ok; /* Transformation */ /* revert y, x*/ var tmp = p.x; p.x=p.y; p.y=tmp; if(this.czech) { p.y *= -1.0; p.x *= -1.0; } ro = Math.sqrt(p.x * p.x + p.y * p.y); eps = Math.atan2(p.y, p.x); d = eps / Math.sin(this.s0); s = 2. * (Math.atan( Math.pow(this.ro0 / ro, 1. / this.n) * Math.tan(this.s0 / 2. + this.s45)) - this.s45); u = Math.asin(Math.cos(this.ad) * Math.sin(s) - Math.sin(this.ad) * Math.cos(s) * Math.cos(d)); deltav = Math.asin(Math.cos(s) * Math.sin(d) / Math.cos(u)); p.x = this.long0 - deltav / this.alfa; /* ITERATION FOR lat */ fi1 = u; ok = 0; var iter = 0; do { p.y = 2. * ( Math.atan( Math.pow( this.k, -1. / this.alfa) * Math.pow( Math.tan(u / 2. + this.s45) , 1. / this.alfa) * Math.pow( (1. + this.e * Math.sin(fi1)) / (1. - this.e * Math.sin(fi1)) , this.e / 2.) ) - this.s45); if (Math.abs(fi1 - p.y) < 0.0000000001) ok=1; fi1 = p.y; iter += 1; } while (ok==0 && iter < 15); if (iter >= 15) { Proj4js.reportError("PHI3Z-CONV:Latitude failed to converge after 15 iterations"); //console.log('iter:', iter); return null; } return (p); } }; /* ====================================================================== projCode/somerc.js ====================================================================== */ /******************************************************************************* NAME SWISS OBLIQUE MERCATOR PURPOSE: Swiss projection. WARNING: X and Y are inverted (weird) in the swiss coordinate system. Not here, since we want X to be horizontal and Y vertical. ALGORITHM REFERENCES 1. "Formules et constantes pour le Calcul pour la projection cylindrique conforme à axe oblique et pour la transformation entre des systèmes de référence". http://www.swisstopo.admin.ch/internet/swisstopo/fr/home/topics/survey/sys/refsys/switzerland.parsysrelated1.31216.downloadList.77004.DownloadFile.tmp/swissprojectionfr.pdf *******************************************************************************/ Proj4js.Proj.somerc = { init: function() { var phy0 = this.lat0; this.lambda0 = this.long0; var sinPhy0 = Math.sin(phy0); var semiMajorAxis = this.a; var invF = this.rf; var flattening = 1 / invF; var e2 = 2 * flattening - Math.pow(flattening, 2); var e = this.e = Math.sqrt(e2); this.R = this.k0 * semiMajorAxis * Math.sqrt(1 - e2) / (1 - e2 * Math.pow(sinPhy0, 2.0)); this.alpha = Math.sqrt(1 + e2 / (1 - e2) * Math.pow(Math.cos(phy0), 4.0)); this.b0 = Math.asin(sinPhy0 / this.alpha); this.K = Math.log(Math.tan(Math.PI / 4.0 + this.b0 / 2.0)) - this.alpha * Math.log(Math.tan(Math.PI / 4.0 + phy0 / 2.0)) + this.alpha * e / 2 * Math.log((1 + e * sinPhy0) / (1 - e * sinPhy0)); }, forward: function(p) { var Sa1 = Math.log(Math.tan(Math.PI / 4.0 - p.y / 2.0)); var Sa2 = this.e / 2.0 * Math.log((1 + this.e * Math.sin(p.y)) / (1 - this.e * Math.sin(p.y))); var S = -this.alpha * (Sa1 + Sa2) + this.K; // spheric latitude var b = 2.0 * (Math.atan(Math.exp(S)) - Math.PI / 4.0); // spheric longitude var I = this.alpha * (p.x - this.lambda0); // psoeudo equatorial rotation var rotI = Math.atan(Math.sin(I) / (Math.sin(this.b0) * Math.tan(b) + Math.cos(this.b0) * Math.cos(I))); var rotB = Math.asin(Math.cos(this.b0) * Math.sin(b) - Math.sin(this.b0) * Math.cos(b) * Math.cos(I)); p.y = this.R / 2.0 * Math.log((1 + Math.sin(rotB)) / (1 - Math.sin(rotB))) + this.y0; p.x = this.R * rotI + this.x0; return p; }, inverse: function(p) { var Y = p.x - this.x0; var X = p.y - this.y0; var rotI = Y / this.R; var rotB = 2 * (Math.atan(Math.exp(X / this.R)) - Math.PI / 4.0); var b = Math.asin(Math.cos(this.b0) * Math.sin(rotB) + Math.sin(this.b0) * Math.cos(rotB) * Math.cos(rotI)); var I = Math.atan(Math.sin(rotI) / (Math.cos(this.b0) * Math.cos(rotI) - Math.sin(this.b0) * Math.tan(rotB))); var lambda = this.lambda0 + I / this.alpha; var S = 0.0; var phy = b; var prevPhy = -1000.0; var iteration = 0; while (Math.abs(phy - prevPhy) > 0.0000001) { if (++iteration > 20) { Proj4js.reportError("omercFwdInfinity"); return; } //S = Math.log(Math.tan(Math.PI / 4.0 + phy / 2.0)); S = 1.0 / this.alpha * (Math.log(Math.tan(Math.PI / 4.0 + b / 2.0)) - this.K) + this.e * Math.log(Math.tan(Math.PI / 4.0 + Math.asin(this.e * Math.sin(phy)) / 2.0)); prevPhy = phy; phy = 2.0 * Math.atan(Math.exp(S)) - Math.PI / 2.0; } p.x = lambda; p.y = phy; return p; } }; /* ====================================================================== projCode/stere.js ====================================================================== */ // Initialize the Stereographic projection Proj4js.Proj.stere = { ssfn_: function(phit, sinphi, eccen) { sinphi *= eccen; return (Math.tan (.5 * (Proj4js.common.HALF_PI + phit)) * Math.pow((1. - sinphi) / (1. + sinphi), .5 * eccen)); }, TOL: 1.e-8, NITER: 8, CONV: 1.e-10, S_POLE: 0, N_POLE: 1, OBLIQ: 2, EQUIT: 3, init: function() { this.phits = this.lat_ts ? this.lat_ts : Proj4js.common.HALF_PI; var t = Math.abs(this.lat0); if ((Math.abs(t) - Proj4js.common.HALF_PI) < Proj4js.common.EPSLN) { this.mode = this.lat0 < 0. ? this.S_POLE : this.N_POLE; } else { this.mode = t > Proj4js.common.EPSLN ? this.OBLIQ : this.EQUIT; } this.phits = Math.abs(this.phits); if (this.es) { var X; switch (this.mode) { case this.N_POLE: case this.S_POLE: if (Math.abs(this.phits - Proj4js.common.HALF_PI) < Proj4js.common.EPSLN) { this.akm1 = 2. * this.k0 / Math.sqrt(Math.pow(1+this.e,1+this.e)*Math.pow(1-this.e,1-this.e)); } else { t = Math.sin(this.phits); this.akm1 = Math.cos(this.phits) / Proj4js.common.tsfnz(this.e, this.phits, t); t *= this.e; this.akm1 /= Math.sqrt(1. - t * t); } break; case this.EQUIT: this.akm1 = 2. * this.k0; break; case this.OBLIQ: t = Math.sin(this.lat0); X = 2. * Math.atan(this.ssfn_(this.lat0, t, this.e)) - Proj4js.common.HALF_PI; t *= this.e; this.akm1 = 2. * this.k0 * Math.cos(this.lat0) / Math.sqrt(1. - t * t); this.sinX1 = Math.sin(X); this.cosX1 = Math.cos(X); break; } } else { switch (this.mode) { case this.OBLIQ: this.sinph0 = Math.sin(this.lat0); this.cosph0 = Math.cos(this.lat0); case this.EQUIT: this.akm1 = 2. * this.k0; break; case this.S_POLE: case this.N_POLE: this.akm1 = Math.abs(this.phits - Proj4js.common.HALF_PI) >= Proj4js.common.EPSLN ? Math.cos(this.phits) / Math.tan(Proj4js.common.FORTPI - .5 * this.phits) : 2. * this.k0 ; break; } } }, // Stereographic forward equations--mapping lat,long to x,y forward: function(p) { var lon = p.x; lon = Proj4js.common.adjust_lon(lon - this.long0); var lat = p.y; var x, y; if (this.sphere) { var sinphi, cosphi, coslam, sinlam; sinphi = Math.sin(lat); cosphi = Math.cos(lat); coslam = Math.cos(lon); sinlam = Math.sin(lon); switch (this.mode) { case this.EQUIT: y = 1. + cosphi * coslam; if (y <= Proj4js.common.EPSLN) { Proj4js.reportError("stere:forward:Equit"); } y = this.akm1 / y; x = y * cosphi * sinlam; y *= sinphi; break; case this.OBLIQ: y = 1. + this.sinph0 * sinphi + this.cosph0 * cosphi * coslam; if (y <= Proj4js.common.EPSLN) { Proj4js.reportError("stere:forward:Obliq"); } y = this.akm1 / y; x = y * cosphi * sinlam; y *= this.cosph0 * sinphi - this.sinph0 * cosphi * coslam; break; case this.N_POLE: coslam = -coslam; lat = -lat; //Note no break here so it conitnues through S_POLE case this.S_POLE: if (Math.abs(lat - Proj4js.common.HALF_PI) < this.TOL) { Proj4js.reportError("stere:forward:S_POLE"); } y = this.akm1 * Math.tan(Proj4js.common.FORTPI + .5 * lat); x = sinlam * y; y *= coslam; break; } } else { coslam = Math.cos(lon); sinlam = Math.sin(lon); sinphi = Math.sin(lat); var sinX, cosX; if (this.mode == this.OBLIQ || this.mode == this.EQUIT) { var Xt = 2. * Math.atan(this.ssfn_(lat, sinphi, this.e)); sinX = Math.sin(Xt - Proj4js.common.HALF_PI); cosX = Math.cos(Xt); } switch (this.mode) { case this.OBLIQ: var A = this.akm1 / (this.cosX1 * (1. + this.sinX1 * sinX + this.cosX1 * cosX * coslam)); y = A * (this.cosX1 * sinX - this.sinX1 * cosX * coslam); x = A * cosX; break; case this.EQUIT: var A = 2. * this.akm1 / (1. + cosX * coslam); y = A * sinX; x = A * cosX; break; case this.S_POLE: lat = -lat; coslam = - coslam; sinphi = -sinphi; case this.N_POLE: x = this.akm1 * Proj4js.common.tsfnz(this.e, lat, sinphi); y = - x * coslam; break; } x = x * sinlam; } p.x = x*this.a + this.x0; p.y = y*this.a + this.y0; return p; }, //* Stereographic inverse equations--mapping x,y to lat/long inverse: function(p) { var x = (p.x - this.x0)/this.a; /* descale and de-offset */ var y = (p.y - this.y0)/this.a; var lon, lat; var cosphi, sinphi, tp=0.0, phi_l=0.0, rho, halfe=0.0, pi2=0.0; var i; if (this.sphere) { var c, rh, sinc, cosc; rh = Math.sqrt(x*x + y*y); c = 2. * Math.atan(rh / this.akm1); sinc = Math.sin(c); cosc = Math.cos(c); lon = 0.; switch (this.mode) { case this.EQUIT: if (Math.abs(rh) <= Proj4js.common.EPSLN) { lat = 0.; } else { lat = Math.asin(y * sinc / rh); } if (cosc != 0. || x != 0.) lon = Math.atan2(x * sinc, cosc * rh); break; case this.OBLIQ: if (Math.abs(rh) <= Proj4js.common.EPSLN) { lat = this.phi0; } else { lat = Math.asin(cosc * this.sinph0 + y * sinc * this.cosph0 / rh); } c = cosc - this.sinph0 * Math.sin(lat); if (c != 0. || x != 0.) { lon = Math.atan2(x * sinc * this.cosph0, c * rh); } break; case this.N_POLE: y = -y; case this.S_POLE: if (Math.abs(rh) <= Proj4js.common.EPSLN) { lat = this.phi0; } else { lat = Math.asin(this.mode == this.S_POLE ? -cosc : cosc); } lon = (x == 0. && y == 0.) ? 0. : Math.atan2(x, y); break; } p.x = Proj4js.common.adjust_lon(lon + this.long0); p.y = lat; } else { rho = Math.sqrt(x*x + y*y); switch (this.mode) { case this.OBLIQ: case this.EQUIT: tp = 2. * Math.atan2(rho * this.cosX1 , this.akm1); cosphi = Math.cos(tp); sinphi = Math.sin(tp); if( rho == 0.0 ) { phi_l = Math.asin(cosphi * this.sinX1); } else { phi_l = Math.asin(cosphi * this.sinX1 + (y * sinphi * this.cosX1 / rho)); } tp = Math.tan(.5 * (Proj4js.common.HALF_PI + phi_l)); x *= sinphi; y = rho * this.cosX1 * cosphi - y * this.sinX1* sinphi; pi2 = Proj4js.common.HALF_PI; halfe = .5 * this.e; break; case this.N_POLE: y = -y; case this.S_POLE: tp = - rho / this.akm1; phi_l = Proj4js.common.HALF_PI - 2. * Math.atan(tp); pi2 = -Proj4js.common.HALF_PI; halfe = -.5 * this.e; break; } for (i = this.NITER; i--; phi_l = lat) { //check this sinphi = this.e * Math.sin(phi_l); lat = 2. * Math.atan(tp * Math.pow((1.+sinphi)/(1.-sinphi), halfe)) - pi2; if (Math.abs(phi_l - lat) < this.CONV) { if (this.mode == this.S_POLE) lat = -lat; lon = (x == 0. && y == 0.) ? 0. : Math.atan2(x, y); p.x = Proj4js.common.adjust_lon(lon + this.long0); p.y = lat; return p; } } } } }; /* ====================================================================== projCode/nzmg.js ====================================================================== */ /******************************************************************************* NAME NEW ZEALAND MAP GRID PURPOSE: Transforms input longitude and latitude to Easting and Northing for the New Zealand Map Grid projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. ALGORITHM REFERENCES 1. Department of Land and Survey Technical Circular 1973/32 http://www.linz.govt.nz/docs/miscellaneous/nz-map-definition.pdf 2. OSG Technical Report 4.1 http://www.linz.govt.nz/docs/miscellaneous/nzmg.pdf IMPLEMENTATION NOTES The two references use different symbols for the calculated values. This implementation uses the variable names similar to the symbols in reference [1]. The alogrithm uses different units for delta latitude and delta longitude. The delta latitude is assumed to be in units of seconds of arc x 10^-5. The delta longitude is the usual radians. Look out for these conversions. The algorithm is described using complex arithmetic. There were three options: * find and use a Javascript library for complex arithmetic * write my own complex library * expand the complex arithmetic by hand to simple arithmetic This implementation has expanded the complex multiplication operations into parallel simple arithmetic operations for the real and imaginary parts. The imaginary part is way over to the right of the display; this probably violates every coding standard in the world, but, to me, it makes it much more obvious what is going on. The following complex operations are used: - addition - multiplication - division - complex number raised to integer power - summation A summary of complex arithmetic operations: (from http://en.wikipedia.org/wiki/Complex_arithmetic) addition: (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i multiplication: (a + bi) x (c + di) = (ac - bd) + (bc + ad)i division: (a + bi) / (c + di) = [(ac + bd)/(cc + dd)] + [(bc - ad)/(cc + dd)]i The algorithm needs to calculate summations of simple and complex numbers. This is implemented using a for-loop, pre-loading the summed value to zero. The algorithm needs to calculate theta^2, theta^3, etc while doing a summation. There are three possible implementations: - use Math.pow in the summation loop - except for complex numbers - precalculate the values before running the loop - calculate theta^n = theta^(n-1) * theta during the loop This implementation uses the third option for both real and complex arithmetic. For example psi_n = 1; sum = 0; for (n = 1; n <=6; n++) { psi_n1 = psi_n * psi; // calculate psi^(n+1) psi_n = psi_n1; sum = sum + A[n] * psi_n; } TEST VECTORS NZMG E, N: 2487100.638 6751049.719 metres NZGD49 long, lat: 172.739194 -34.444066 degrees NZMG E, N: 2486533.395 6077263.661 metres NZGD49 long, lat: 172.723106 -40.512409 degrees NZMG E, N: 2216746.425 5388508.765 metres NZGD49 long, lat: 169.172062 -46.651295 degrees Note that these test vectors convert from NZMG metres to lat/long referenced to NZGD49, not the more usual WGS84. The difference is about 70m N/S and about 10m E/W. These test vectors are provided in reference [1]. Many more test vectors are available in http://www.linz.govt.nz/docs/topography/topographicdata/placenamesdatabase/nznamesmar08.zip which is a catalog of names on the 260-series maps. EPSG CODES NZMG EPSG:27200 NZGD49 EPSG:4272 http://spatialreference.org/ defines these as Proj4js.defs["EPSG:4272"] = "+proj=longlat +ellps=intl +datum=nzgd49 +no_defs "; Proj4js.defs["EPSG:27200"] = "+proj=nzmg +lat_0=-41 +lon_0=173 +x_0=2510000 +y_0=6023150 +ellps=intl +datum=nzgd49 +units=m +no_defs "; LICENSE Copyright: Stephen Irons 2008 Released under terms of the LGPL as per: http://www.gnu.org/copyleft/lesser.html *******************************************************************************/ /** Initialize New Zealand Map Grip projection */ Proj4js.Proj.nzmg = { /** * iterations: Number of iterations to refine inverse transform. * 0 -> km accuracy * 1 -> m accuracy -- suitable for most mapping applications * 2 -> mm accuracy */ iterations: 1, init : function() { this.A = new Array(); this.A[1] = +0.6399175073; this.A[2] = -0.1358797613; this.A[3] = +0.063294409; this.A[4] = -0.02526853; this.A[5] = +0.0117879; this.A[6] = -0.0055161; this.A[7] = +0.0026906; this.A[8] = -0.001333; this.A[9] = +0.00067; this.A[10] = -0.00034; this.B_re = new Array(); this.B_im = new Array(); this.B_re[1] = +0.7557853228; this.B_im[1] = 0.0; this.B_re[2] = +0.249204646; this.B_im[2] = +0.003371507; this.B_re[3] = -0.001541739; this.B_im[3] = +0.041058560; this.B_re[4] = -0.10162907; this.B_im[4] = +0.01727609; this.B_re[5] = -0.26623489; this.B_im[5] = -0.36249218; this.B_re[6] = -0.6870983; this.B_im[6] = -1.1651967; this.C_re = new Array(); this.C_im = new Array(); this.C_re[1] = +1.3231270439; this.C_im[1] = 0.0; this.C_re[2] = -0.577245789; this.C_im[2] = -0.007809598; this.C_re[3] = +0.508307513; this.C_im[3] = -0.112208952; this.C_re[4] = -0.15094762; this.C_im[4] = +0.18200602; this.C_re[5] = +1.01418179; this.C_im[5] = +1.64497696; this.C_re[6] = +1.9660549; this.C_im[6] = +2.5127645; this.D = new Array(); this.D[1] = +1.5627014243; this.D[2] = +0.5185406398; this.D[3] = -0.03333098; this.D[4] = -0.1052906; this.D[5] = -0.0368594; this.D[6] = +0.007317; this.D[7] = +0.01220; this.D[8] = +0.00394; this.D[9] = -0.0013; }, /** New Zealand Map Grid Forward - long/lat to x/y long/lat in radians */ forward : function(p) { var lon = p.x; var lat = p.y; var delta_lat = lat - this.lat0; var delta_lon = lon - this.long0; // 1. Calculate d_phi and d_psi ... // and d_lambda // For this algorithm, delta_latitude is in seconds of arc x 10-5, so we need to scale to those units. Longitude is radians. var d_phi = delta_lat / Proj4js.common.SEC_TO_RAD * 1E-5; var d_lambda = delta_lon; var d_phi_n = 1; // d_phi^0 var d_psi = 0; for (var n = 1; n <= 10; n++) { d_phi_n = d_phi_n * d_phi; d_psi = d_psi + this.A[n] * d_phi_n; } // 2. Calculate theta var th_re = d_psi; var th_im = d_lambda; // 3. Calculate z var th_n_re = 1; var th_n_im = 0; // theta^0 var th_n_re1; var th_n_im1; var z_re = 0; var z_im = 0; for (var n = 1; n <= 6; n++) { th_n_re1 = th_n_re*th_re - th_n_im*th_im; th_n_im1 = th_n_im*th_re + th_n_re*th_im; th_n_re = th_n_re1; th_n_im = th_n_im1; z_re = z_re + this.B_re[n]*th_n_re - this.B_im[n]*th_n_im; z_im = z_im + this.B_im[n]*th_n_re + this.B_re[n]*th_n_im; } // 4. Calculate easting and northing p.x = (z_im * this.a) + this.x0; p.y = (z_re * this.a) + this.y0; return p; }, /** New Zealand Map Grid Inverse - x/y to long/lat */ inverse : function(p) { var x = p.x; var y = p.y; var delta_x = x - this.x0; var delta_y = y - this.y0; // 1. Calculate z var z_re = delta_y / this.a; var z_im = delta_x / this.a; // 2a. Calculate theta - first approximation gives km accuracy var z_n_re = 1; var z_n_im = 0; // z^0 var z_n_re1; var z_n_im1; var th_re = 0; var th_im = 0; for (var n = 1; n <= 6; n++) { z_n_re1 = z_n_re*z_re - z_n_im*z_im; z_n_im1 = z_n_im*z_re + z_n_re*z_im; z_n_re = z_n_re1; z_n_im = z_n_im1; th_re = th_re + this.C_re[n]*z_n_re - this.C_im[n]*z_n_im; th_im = th_im + this.C_im[n]*z_n_re + this.C_re[n]*z_n_im; } // 2b. Iterate to refine the accuracy of the calculation // 0 iterations gives km accuracy // 1 iteration gives m accuracy -- good enough for most mapping applications // 2 iterations bives mm accuracy for (var i = 0; i < this.iterations; i++) { var th_n_re = th_re; var th_n_im = th_im; var th_n_re1; var th_n_im1; var num_re = z_re; var num_im = z_im; for (var n = 2; n <= 6; n++) { th_n_re1 = th_n_re*th_re - th_n_im*th_im; th_n_im1 = th_n_im*th_re + th_n_re*th_im; th_n_re = th_n_re1; th_n_im = th_n_im1; num_re = num_re + (n-1)*(this.B_re[n]*th_n_re - this.B_im[n]*th_n_im); num_im = num_im + (n-1)*(this.B_im[n]*th_n_re + this.B_re[n]*th_n_im); } th_n_re = 1; th_n_im = 0; var den_re = this.B_re[1]; var den_im = this.B_im[1]; for (var n = 2; n <= 6; n++) { th_n_re1 = th_n_re*th_re - th_n_im*th_im; th_n_im1 = th_n_im*th_re + th_n_re*th_im; th_n_re = th_n_re1; th_n_im = th_n_im1; den_re = den_re + n * (this.B_re[n]*th_n_re - this.B_im[n]*th_n_im); den_im = den_im + n * (this.B_im[n]*th_n_re + this.B_re[n]*th_n_im); } // Complex division var den2 = den_re*den_re + den_im*den_im; th_re = (num_re*den_re + num_im*den_im) / den2; th_im = (num_im*den_re - num_re*den_im) / den2; } // 3. Calculate d_phi ... // and d_lambda var d_psi = th_re; var d_lambda = th_im; var d_psi_n = 1; // d_psi^0 var d_phi = 0; for (var n = 1; n <= 9; n++) { d_psi_n = d_psi_n * d_psi; d_phi = d_phi + this.D[n] * d_psi_n; } // 4. Calculate latitude and longitude // d_phi is calcuated in second of arc * 10^-5, so we need to scale back to radians. d_lambda is in radians. var lat = this.lat0 + (d_phi * Proj4js.common.SEC_TO_RAD * 1E5); var lon = this.long0 + d_lambda; p.x = lon; p.y = lat; return p; } }; /* ====================================================================== projCode/mill.js ====================================================================== */ /******************************************************************************* NAME MILLER CYLINDRICAL PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Miller Cylindrical projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan March, 1993 This function was adapted from the Lambert Azimuthal Equal Area projection code (FORTRAN) in the General Cartographic Transformation Package software which is available from the U.S. Geological Survey National Mapping Division. ALGORITHM REFERENCES 1. "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder, The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355. 2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 3. "Software Documentation for GCTP General Cartographic Transformation Package", U.S. Geological Survey National Mapping Division, May 1982. *******************************************************************************/ Proj4js.Proj.mill = { /* Initialize the Miller Cylindrical projection -------------------------------------------*/ init: function() { //no-op }, /* Miller Cylindrical forward equations--mapping lat,long to x,y ------------------------------------------------------------*/ forward: function(p) { var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ var dlon = Proj4js.common.adjust_lon(lon -this.long0); var x = this.x0 + this.a * dlon; var y = this.y0 + this.a * Math.log(Math.tan((Proj4js.common.PI / 4.0) + (lat / 2.5))) * 1.25; p.x=x; p.y=y; return p; },//millFwd() /* Miller Cylindrical inverse equations--mapping x,y to lat/long ------------------------------------------------------------*/ inverse: function(p) { p.x -= this.x0; p.y -= this.y0; var lon = Proj4js.common.adjust_lon(this.long0 + p.x /this.a); var lat = 2.5 * (Math.atan(Math.exp(0.8*p.y/this.a)) - Proj4js.common.PI / 4.0); p.x=lon; p.y=lat; return p; }//millInv() }; /* ====================================================================== projCode/gnom.js ====================================================================== */ /***************************************************************************** NAME GNOMONIC PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Gnomonic Projection. Implementation based on the existing sterea and ortho implementations. PROGRAMMER DATE ---------- ---- Richard Marsden November 2009 ALGORITHM REFERENCES 1. Snyder, John P., "Flattening the Earth - Two Thousand Years of Map Projections", University of Chicago Press 1993 2. Wolfram Mathworld "Gnomonic Projection" http://mathworld.wolfram.com/GnomonicProjection.html Accessed: 12th November 2009 ******************************************************************************/ Proj4js.Proj.gnom = { /* Initialize the Gnomonic projection -------------------------------------*/ init: function(def) { /* Place parameters in static storage for common use -------------------------------------------------*/ this.sin_p14=Math.sin(this.lat0); this.cos_p14=Math.cos(this.lat0); // Approximation for projecting points to the horizon (infinity) this.infinity_dist = 1000 * this.a; this.rc = 1; }, /* Gnomonic forward equations--mapping lat,long to x,y ---------------------------------------------------*/ forward: function(p) { var sinphi, cosphi; /* sin and cos value */ var dlon; /* delta longitude value */ var coslon; /* cos of longitude */ var ksp; /* scale factor */ var g; var x, y; var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ dlon = Proj4js.common.adjust_lon(lon - this.long0); sinphi=Math.sin(lat); cosphi=Math.cos(lat); coslon = Math.cos(dlon); g = this.sin_p14 * sinphi + this.cos_p14 * cosphi * coslon; ksp = 1.0; if ((g > 0) || (Math.abs(g) <= Proj4js.common.EPSLN)) { x = this.x0 + this.a * ksp * cosphi * Math.sin(dlon) / g; y = this.y0 + this.a * ksp * (this.cos_p14 * sinphi - this.sin_p14 * cosphi * coslon) / g; } else { Proj4js.reportError("orthoFwdPointError"); // Point is in the opposing hemisphere and is unprojectable // We still need to return a reasonable point, so we project // to infinity, on a bearing // equivalent to the northern hemisphere equivalent // This is a reasonable approximation for short shapes and lines that // straddle the horizon. x = this.x0 + this.infinity_dist * cosphi * Math.sin(dlon); y = this.y0 + this.infinity_dist * (this.cos_p14 * sinphi - this.sin_p14 * cosphi * coslon); } p.x=x; p.y=y; return p; }, inverse: function(p) { var rh; /* Rho */ var z; /* angle */ var sinc, cosc; var c; var lon , lat; /* Inverse equations -----------------*/ p.x = (p.x - this.x0) / this.a; p.y = (p.y - this.y0) / this.a; p.x /= this.k0; p.y /= this.k0; if ( (rh = Math.sqrt(p.x * p.x + p.y * p.y)) ) { c = Math.atan2(rh, this.rc); sinc = Math.sin(c); cosc = Math.cos(c); lat = Proj4js.common.asinz(cosc*this.sin_p14 + (p.y*sinc*this.cos_p14) / rh); lon = Math.atan2(p.x*sinc, rh*this.cos_p14*cosc - p.y*this.sin_p14*sinc); lon = Proj4js.common.adjust_lon(this.long0+lon); } else { lat = this.phic0; lon = 0.0; } p.x=lon; p.y=lat; return p; } }; /* ====================================================================== projCode/sinu.js ====================================================================== */ /******************************************************************************* NAME SINUSOIDAL PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Sinusoidal projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- D. Steinwand, EROS May, 1991 This function was adapted from the Sinusoidal projection code (FORTRAN) in the General Cartographic Transformation Package software which is available from the U.S. Geological Survey National Mapping Division. ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. "Software Documentation for GCTP General Cartographic Transformation Package", U.S. Geological Survey National Mapping Division, May 1982. *******************************************************************************/ Proj4js.Proj.sinu = { /* Initialize the Sinusoidal projection ------------------------------------*/ init: function() { /* Place parameters in static storage for common use -------------------------------------------------*/ if (!this.sphere) { this.en = Proj4js.common.pj_enfn(this.es); } else { this.n = 1.; this.m = 0.; this.es = 0; this.C_y = Math.sqrt((this.m + 1.) / this.n); this.C_x = this.C_y/(this.m + 1.); } }, /* Sinusoidal forward equations--mapping lat,long to x,y -----------------------------------------------------*/ forward: function(p) { var x,y,delta_lon; var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ lon = Proj4js.common.adjust_lon(lon - this.long0); if (this.sphere) { if (!this.m) { lat = this.n != 1. ? Math.asin(this.n * Math.sin(lat)): lat; } else { var k = this.n * Math.sin(lat); for (var i = Proj4js.common.MAX_ITER; i ; --i) { var V = (this.m * lat + Math.sin(lat) - k) / (this.m + Math.cos(lat)); lat -= V; if (Math.abs(V) < Proj4js.common.EPSLN) break; } } x = this.a * this.C_x * lon * (this.m + Math.cos(lat)); y = this.a * this.C_y * lat; } else { var s = Math.sin(lat); var c = Math.cos(lat); y = this.a * Proj4js.common.pj_mlfn(lat, s, c, this.en); x = this.a * lon * c / Math.sqrt(1. - this.es * s * s); } p.x=x; p.y=y; return p; }, inverse: function(p) { var lat,temp,lon; /* Inverse equations -----------------*/ p.x -= this.x0; p.y -= this.y0; lat = p.y / this.a; if (this.sphere) { p.y /= this.C_y; lat = this.m ? Math.asin((this.m * p.y + Math.sin(p.y)) / this.n) : ( this.n != 1. ? Math.asin(Math.sin(p.y) / this.n) : p.y ); lon = p.x / (this.C_x * (this.m + Math.cos(p.y))); } else { lat = Proj4js.common.pj_inv_mlfn(p.y/this.a, this.es, this.en) var s = Math.abs(lat); if (s < Proj4js.common.HALF_PI) { s = Math.sin(lat); temp = this.long0 + p.x * Math.sqrt(1. - this.es * s * s) /(this.a * Math.cos(lat)); //temp = this.long0 + p.x / (this.a * Math.cos(lat)); lon = Proj4js.common.adjust_lon(temp); } else if ((s - Proj4js.common.EPSLN) < Proj4js.common.HALF_PI) { lon = this.long0; } } p.x=lon; p.y=lat; return p; } }; /* ====================================================================== projCode/vandg.js ====================================================================== */ /******************************************************************************* NAME VAN DER GRINTEN PURPOSE: Transforms input Easting and Northing to longitude and latitude for the Van der Grinten projection. The Easting and Northing must be in meters. The longitude and latitude values will be returned in radians. PROGRAMMER DATE ---------- ---- T. Mittan March, 1993 This function was adapted from the Van Der Grinten projection code (FORTRAN) in the General Cartographic Transformation Package software which is available from the U.S. Geological Survey National Mapping Division. ALGORITHM REFERENCES 1. "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder, The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355. 2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 3. "Software Documentation for GCTP General Cartographic Transformation Package", U.S. Geological Survey National Mapping Division, May 1982. *******************************************************************************/ Proj4js.Proj.vandg = { /* Initialize the Van Der Grinten projection ----------------------------------------*/ init: function() { this.R = 6370997.0; //Radius of earth }, forward: function(p) { var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ var dlon = Proj4js.common.adjust_lon(lon - this.long0); var x,y; if (Math.abs(lat) <= Proj4js.common.EPSLN) { x = this.x0 + this.R * dlon; y = this.y0; } var theta = Proj4js.common.asinz(2.0 * Math.abs(lat / Proj4js.common.PI)); if ((Math.abs(dlon) <= Proj4js.common.EPSLN) || (Math.abs(Math.abs(lat) - Proj4js.common.HALF_PI) <= Proj4js.common.EPSLN)) { x = this.x0; if (lat >= 0) { y = this.y0 + Proj4js.common.PI * this.R * Math.tan(.5 * theta); } else { y = this.y0 + Proj4js.common.PI * this.R * - Math.tan(.5 * theta); } // return(OK); } var al = .5 * Math.abs((Proj4js.common.PI / dlon) - (dlon / Proj4js.common.PI)); var asq = al * al; var sinth = Math.sin(theta); var costh = Math.cos(theta); var g = costh / (sinth + costh - 1.0); var gsq = g * g; var m = g * (2.0 / sinth - 1.0); var msq = m * m; var con = Proj4js.common.PI * this.R * (al * (g - msq) + Math.sqrt(asq * (g - msq) * (g - msq) - (msq + asq) * (gsq - msq))) / (msq + asq); if (dlon < 0) { con = -con; } x = this.x0 + con; con = Math.abs(con / (Proj4js.common.PI * this.R)); if (lat >= 0) { y = this.y0 + Proj4js.common.PI * this.R * Math.sqrt(1.0 - con * con - 2.0 * al * con); } else { y = this.y0 - Proj4js.common.PI * this.R * Math.sqrt(1.0 - con * con - 2.0 * al * con); } p.x = x; p.y = y; return p; }, /* Van Der Grinten inverse equations--mapping x,y to lat/long ---------------------------------------------------------*/ inverse: function(p) { var lon, lat; var xx,yy,xys,c1,c2,c3; var al,asq; var a1; var m1; var con; var th1; var d; /* inverse equations -----------------*/ p.x -= this.x0; p.y -= this.y0; con = Proj4js.common.PI * this.R; xx = p.x / con; yy =p.y / con; xys = xx * xx + yy * yy; c1 = -Math.abs(yy) * (1.0 + xys); c2 = c1 - 2.0 * yy * yy + xx * xx; c3 = -2.0 * c1 + 1.0 + 2.0 * yy * yy + xys * xys; d = yy * yy / c3 + (2.0 * c2 * c2 * c2 / c3 / c3 / c3 - 9.0 * c1 * c2 / c3 /c3) / 27.0; a1 = (c1 - c2 * c2 / 3.0 / c3) / c3; m1 = 2.0 * Math.sqrt( -a1 / 3.0); con = ((3.0 * d) / a1) / m1; if (Math.abs(con) > 1.0) { if (con >= 0.0) { con = 1.0; } else { con = -1.0; } } th1 = Math.acos(con) / 3.0; if (p.y >= 0) { lat = (-m1 *Math.cos(th1 + Proj4js.common.PI / 3.0) - c2 / 3.0 / c3) * Proj4js.common.PI; } else { lat = -(-m1 * Math.cos(th1 + Proj4js.common.PI / 3.0) - c2 / 3.0 / c3) * Proj4js.common.PI; } if (Math.abs(xx) < Proj4js.common.EPSLN) { lon = this.long0; } lon = Proj4js.common.adjust_lon(this.long0 + Proj4js.common.PI * (xys - 1.0 + Math.sqrt(1.0 + 2.0 * (xx * xx - yy * yy) + xys * xys)) / 2.0 / xx); p.x=lon; p.y=lat; return p; } }; /* ====================================================================== projCode/cea.js ====================================================================== */ /******************************************************************************* NAME LAMBERT CYLINDRICAL EQUAL AREA PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Lambert Cylindrical Equal Area projection. This class of projection includes the Behrmann and Gall-Peters Projections. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- R. Marsden August 2009 Winwaed Software Tech LLC, http://www.winwaed.com This function was adapted from the Miller Cylindrical Projection in the Proj4JS library. Note: This implementation assumes a Spherical Earth. The (commented) code has been included for the ellipsoidal forward transform, but derivation of the ellispoidal inverse transform is beyond me. Note that most of the Proj4JS implementations do NOT currently support ellipsoidal figures. Therefore this is not seen as a problem - especially this lack of support is explicitly stated here. ALGORITHM REFERENCES 1. "Cartographic Projection Procedures for the UNIX Environment - A User's Manual" by Gerald I. Evenden, USGS Open File Report 90-284 and Release 4 Interim Reports (2003) 2. Snyder, John P., "Flattening the Earth - Two Thousand Years of Map Projections", Univ. Chicago Press, 1993 *******************************************************************************/ Proj4js.Proj.cea = { /* Initialize the Cylindrical Equal Area projection -------------------------------------------*/ init: function() { //no-op }, /* Cylindrical Equal Area forward equations--mapping lat,long to x,y ------------------------------------------------------------*/ forward: function(p) { var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ var dlon = Proj4js.common.adjust_lon(lon -this.long0); var x = this.x0 + this.a * dlon * Math.cos(this.lat_ts); var y = this.y0 + this.a * Math.sin(lat) / Math.cos(this.lat_ts); /* Elliptical Forward Transform Not implemented due to a lack of a matchign inverse function { var Sin_Lat = Math.sin(lat); var Rn = this.a * (Math.sqrt(1.0e0 - this.es * Sin_Lat * Sin_Lat )); x = this.x0 + this.a * dlon * Math.cos(this.lat_ts); y = this.y0 + Rn * Math.sin(lat) / Math.cos(this.lat_ts); } */ p.x=x; p.y=y; return p; },//ceaFwd() /* Cylindrical Equal Area inverse equations--mapping x,y to lat/long ------------------------------------------------------------*/ inverse: function(p) { p.x -= this.x0; p.y -= this.y0; var lon = Proj4js.common.adjust_lon( this.long0 + (p.x / this.a) / Math.cos(this.lat_ts) ); var lat = Math.asin( (p.y/this.a) * Math.cos(this.lat_ts) ); p.x=lon; p.y=lat; return p; }//ceaInv() }; /* ====================================================================== projCode/eqc.js ====================================================================== */ /* similar to equi.js FIXME proj4 uses eqc */ Proj4js.Proj.eqc = { init : function() { if(!this.x0) this.x0=0; if(!this.y0) this.y0=0; if(!this.lat0) this.lat0=0; if(!this.long0) this.long0=0; if(!this.lat_ts) this.lat_ts=0; if (!this.title) this.title = "Equidistant Cylindrical (Plate Carre)"; this.rc= Math.cos(this.lat_ts); }, // forward equations--mapping lat,long to x,y // ----------------------------------------------------------------- forward : function(p) { var lon= p.x; var lat= p.y; var dlon = Proj4js.common.adjust_lon(lon - this.long0); var dlat = Proj4js.common.adjust_lat(lat - this.lat0 ); p.x= this.x0 + (this.a*dlon*this.rc); p.y= this.y0 + (this.a*dlat ); return p; }, // inverse equations--mapping x,y to lat/long // ----------------------------------------------------------------- inverse : function(p) { var x= p.x; var y= p.y; p.x= Proj4js.common.adjust_lon(this.long0 + ((x - this.x0)/(this.a*this.rc))); p.y= Proj4js.common.adjust_lat(this.lat0 + ((y - this.y0)/(this.a ))); return p; } }; /* ====================================================================== projCode/cass.js ====================================================================== */ /******************************************************************************* NAME CASSINI PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Cassini projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. Ported from PROJ.4. ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government *******************************************************************************/ //Proj4js.defs["EPSG:28191"] = "+proj=cass +lat_0=31.73409694444445 +lon_0=35.21208055555556 +x_0=170251.555 +y_0=126867.909 +a=6378300.789 +b=6356566.435 +towgs84=-275.722,94.7824,340.894,-8.001,-4.42,-11.821,1 +units=m +no_defs"; // Initialize the Cassini projection // ----------------------------------------------------------------- Proj4js.Proj.cass = { init : function() { if (!this.sphere) { this.en = Proj4js.common.pj_enfn(this.es) this.m0 = Proj4js.common.pj_mlfn(this.lat0, Math.sin(this.lat0), Math.cos(this.lat0), this.en); } }, C1: .16666666666666666666, C2: .00833333333333333333, C3: .04166666666666666666, C4: .33333333333333333333, C5: .06666666666666666666, /* Cassini forward equations--mapping lat,long to x,y -----------------------------------------------------------------------*/ forward: function(p) { /* Forward equations -----------------*/ var x,y; var lam=p.x; var phi=p.y; lam = Proj4js.common.adjust_lon(lam - this.long0); if (this.sphere) { x = Math.asin(Math.cos(phi) * Math.sin(lam)); y = Math.atan2(Math.tan(phi) , Math.cos(lam)) - this.phi0; } else { //ellipsoid this.n = Math.sin(phi); this.c = Math.cos(phi); y = Proj4js.common.pj_mlfn(phi, this.n, this.c, this.en); this.n = 1./Math.sqrt(1. - this.es * this.n * this.n); this.tn = Math.tan(phi); this.t = this.tn * this.tn; this.a1 = lam * this.c; this.c *= this.es * this.c / (1 - this.es); this.a2 = this.a1 * this.a1; x = this.n * this.a1 * (1. - this.a2 * this.t * (this.C1 - (8. - this.t + 8. * this.c) * this.a2 * this.C2)); y -= this.m0 - this.n * this.tn * this.a2 * (.5 + (5. - this.t + 6. * this.c) * this.a2 * this.C3); } p.x = this.a*x + this.x0; p.y = this.a*y + this.y0; return p; },//cassFwd() /* Inverse equations -----------------*/ inverse: function(p) { p.x -= this.x0; p.y -= this.y0; var x = p.x/this.a; var y = p.y/this.a; var phi, lam; if (this.sphere) { this.dd = y + this.lat0; phi = Math.asin(Math.sin(this.dd) * Math.cos(x)); lam = Math.atan2(Math.tan(x), Math.cos(this.dd)); } else { /* ellipsoid */ var ph1 = Proj4js.common.pj_inv_mlfn(this.m0 + y, this.es, this.en); this.tn = Math.tan(ph1); this.t = this.tn * this.tn; this.n = Math.sin(ph1); this.r = 1. / (1. - this.es * this.n * this.n); this.n = Math.sqrt(this.r); this.r *= (1. - this.es) * this.n; this.dd = x / this.n; this.d2 = this.dd * this.dd; phi = ph1 - (this.n * this.tn / this.r) * this.d2 * (.5 - (1. + 3. * this.t) * this.d2 * this.C3); lam = this.dd * (1. + this.t * this.d2 * (-this.C4 + (1. + 3. * this.t) * this.d2 * this.C5)) / Math.cos(ph1); } p.x = Proj4js.common.adjust_lon(this.long0+lam); p.y = phi; return p; }//cassInv() } /* ====================================================================== projCode/gauss.js ====================================================================== */ Proj4js.Proj.gauss = { init : function() { var sphi = Math.sin(this.lat0); var cphi = Math.cos(this.lat0); cphi *= cphi; this.rc = Math.sqrt(1.0 - this.es) / (1.0 - this.es * sphi * sphi); this.C = Math.sqrt(1.0 + this.es * cphi * cphi / (1.0 - this.es)); this.phic0 = Math.asin(sphi / this.C); this.ratexp = 0.5 * this.C * this.e; this.K = Math.tan(0.5 * this.phic0 + Proj4js.common.FORTPI) / (Math.pow(Math.tan(0.5*this.lat0 + Proj4js.common.FORTPI), this.C) * Proj4js.common.srat(this.e*sphi, this.ratexp)); }, forward : function(p) { var lon = p.x; var lat = p.y; p.y = 2.0 * Math.atan( this.K * Math.pow(Math.tan(0.5 * lat + Proj4js.common.FORTPI), this.C) * Proj4js.common.srat(this.e * Math.sin(lat), this.ratexp) ) - Proj4js.common.HALF_PI; p.x = this.C * lon; return p; }, inverse : function(p) { var DEL_TOL = 1e-14; var lon = p.x / this.C; var lat = p.y; var num = Math.pow(Math.tan(0.5 * lat + Proj4js.common.FORTPI)/this.K, 1./this.C); for (var i = Proj4js.common.MAX_ITER; i>0; --i) { lat = 2.0 * Math.atan(num * Proj4js.common.srat(this.e * Math.sin(p.y), -0.5 * this.e)) - Proj4js.common.HALF_PI; if (Math.abs(lat - p.y) < DEL_TOL) break; p.y = lat; } /* convergence failed */ if (!i) { Proj4js.reportError("gauss:inverse:convergence failed"); return null; } p.x = lon; p.y = lat; return p; } }; /* ====================================================================== projCode/omerc.js ====================================================================== */ /******************************************************************************* NAME OBLIQUE MERCATOR (HOTINE) PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Oblique Mercator projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- T. Mittan Mar, 1993 ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. *******************************************************************************/ Proj4js.Proj.omerc = { /* Initialize the Oblique Mercator projection ------------------------------------------*/ init: function() { if (!this.mode) this.mode=0; if (!this.lon1) {this.lon1=0;this.mode=1;} if (!this.lon2) this.lon2=0; if (!this.lat2) this.lat2=0; /* Place parameters in static storage for common use -------------------------------------------------*/ var temp = this.b/ this.a; var es = 1.0 - Math.pow(temp,2); var e = Math.sqrt(es); this.sin_p20=Math.sin(this.lat0); this.cos_p20=Math.cos(this.lat0); this.con = 1.0 - this.es * this.sin_p20 * this.sin_p20; this.com = Math.sqrt(1.0 - es); this.bl = Math.sqrt(1.0 + this.es * Math.pow(this.cos_p20,4.0)/(1.0 - es)); this.al = this.a * this.bl * this.k0 * this.com / this.con; if (Math.abs(this.lat0) < Proj4js.common.EPSLN) { this.ts = 1.0; this.d = 1.0; this.el = 1.0; } else { this.ts = Proj4js.common.tsfnz(this.e,this.lat0,this.sin_p20); this.con = Math.sqrt(this.con); this.d = this.bl * this.com / (this.cos_p20 * this.con); if ((this.d * this.d - 1.0) > 0.0) { if (this.lat0 >= 0.0) { this.f = this.d + Math.sqrt(this.d * this.d - 1.0); } else { this.f = this.d - Math.sqrt(this.d * this.d - 1.0); } } else { this.f = this.d; } this.el = this.f * Math.pow(this.ts,this.bl); } //this.longc=52.60353916666667; if (this.mode != 0) { this.g = .5 * (this.f - 1.0/this.f); this.gama = Proj4js.common.asinz(Math.sin(this.alpha) / this.d); this.longc= this.longc - Proj4js.common.asinz(this.g * Math.tan(this.gama))/this.bl; /* Report parameters common to format B -------------------------------------*/ //genrpt(azimuth * R2D,"Azimuth of Central Line: "); //cenlon(lon_origin); // cenlat(lat_origin); this.con = Math.abs(this.lat0); if ((this.con > Proj4js.common.EPSLN) && (Math.abs(this.con - Proj4js.common.HALF_PI) > Proj4js.common.EPSLN)) { this.singam=Math.sin(this.gama); this.cosgam=Math.cos(this.gama); this.sinaz=Math.sin(this.alpha); this.cosaz=Math.cos(this.alpha); if (this.lat0>= 0) { this.u = (this.al / this.bl) * Math.atan(Math.sqrt(this.d*this.d - 1.0)/this.cosaz); } else { this.u = -(this.al / this.bl) *Math.atan(Math.sqrt(this.d*this.d - 1.0)/this.cosaz); } } else { Proj4js.reportError("omerc:Init:DataError"); } } else { this.sinphi =Math. sin(this.at1); this.ts1 = Proj4js.common.tsfnz(this.e,this.lat1,this.sinphi); this.sinphi = Math.sin(this.lat2); this.ts2 = Proj4js.common.tsfnz(this.e,this.lat2,this.sinphi); this.h = Math.pow(this.ts1,this.bl); this.l = Math.pow(this.ts2,this.bl); this.f = this.el/this.h; this.g = .5 * (this.f - 1.0/this.f); this.j = (this.el * this.el - this.l * this.h)/(this.el * this.el + this.l * this.h); this.p = (this.l - this.h) / (this.l + this.h); this.dlon = this.lon1 - this.lon2; if (this.dlon < -Proj4js.common.PI) this.lon2 = this.lon2 - 2.0 * Proj4js.common.PI; if (this.dlon > Proj4js.common.PI) this.lon2 = this.lon2 + 2.0 * Proj4js.common.PI; this.dlon = this.lon1 - this.lon2; this.longc = .5 * (this.lon1 + this.lon2) -Math.atan(this.j * Math.tan(.5 * this.bl * this.dlon)/this.p)/this.bl; this.dlon = Proj4js.common.adjust_lon(this.lon1 - this.longc); this.gama = Math.atan(Math.sin(this.bl * this.dlon)/this.g); this.alpha = Proj4js.common.asinz(this.d * Math.sin(this.gama)); /* Report parameters common to format A -------------------------------------*/ if (Math.abs(this.lat1 - this.lat2) <= Proj4js.common.EPSLN) { Proj4js.reportError("omercInitDataError"); //return(202); } else { this.con = Math.abs(this.lat1); } if ((this.con <= Proj4js.common.EPSLN) || (Math.abs(this.con - Proj4js.common.HALF_PI) <= Proj4js.common.EPSLN)) { Proj4js.reportError("omercInitDataError"); //return(202); } else { if (Math.abs(Math.abs(this.lat0) - Proj4js.common.HALF_PI) <= Proj4js.common.EPSLN) { Proj4js.reportError("omercInitDataError"); //return(202); } } this.singam=Math.sin(this.gam); this.cosgam=Math.cos(this.gam); this.sinaz=Math.sin(this.alpha); this.cosaz=Math.cos(this.alpha); if (this.lat0 >= 0) { this.u = (this.al/this.bl) * Math.atan(Math.sqrt(this.d * this.d - 1.0)/this.cosaz); } else { this.u = -(this.al/this.bl) * Math.atan(Math.sqrt(this.d * this.d - 1.0)/this.cosaz); } } }, /* Oblique Mercator forward equations--mapping lat,long to x,y ----------------------------------------------------------*/ forward: function(p) { var theta; /* angle */ var sin_phi, cos_phi;/* sin and cos value */ var b; /* temporary values */ var c, t, tq; /* temporary values */ var con, n, ml; /* cone constant, small m */ var q,us,vl; var ul,vs; var s; var dlon; var ts1; var lon=p.x; var lat=p.y; /* Forward equations -----------------*/ sin_phi = Math.sin(lat); dlon = Proj4js.common.adjust_lon(lon - this.longc); vl = Math.sin(this.bl * dlon); if (Math.abs(Math.abs(lat) - Proj4js.common.HALF_PI) > Proj4js.common.EPSLN) { ts1 = Proj4js.common.tsfnz(this.e,lat,sin_phi); q = this.el / (Math.pow(ts1,this.bl)); s = .5 * (q - 1.0 / q); t = .5 * (q + 1.0/ q); ul = (s * this.singam - vl * this.cosgam) / t; con = Math.cos(this.bl * dlon); if (Math.abs(con) < .0000001) { us = this.al * this.bl * dlon; } else { us = this.al * Math.atan((s * this.cosgam + vl * this.singam) / con)/this.bl; if (con < 0) us = us + Proj4js.common.PI * this.al / this.bl; } } else { if (lat >= 0) { ul = this.singam; } else { ul = -this.singam; } us = this.al * lat / this.bl; } if (Math.abs(Math.abs(ul) - 1.0) <= Proj4js.common.EPSLN) { //alert("Point projects into infinity","omer-for"); Proj4js.reportError("omercFwdInfinity"); //return(205); } vs = .5 * this.al * Math.log((1.0 - ul)/(1.0 + ul)) / this.bl; us = us - this.u; var x = this.x0 + vs * this.cosaz + us * this.sinaz; var y = this.y0 + us * this.cosaz - vs * this.sinaz; p.x=x; p.y=y; return p; }, inverse: function(p) { var delta_lon; /* Delta longitude (Given longitude - center */ var theta; /* angle */ var delta_theta; /* adjusted longitude */ var sin_phi, cos_phi;/* sin and cos value */ var b; /* temporary values */ var c, t, tq; /* temporary values */ var con, n, ml; /* cone constant, small m */ var vs,us,q,s,ts1; var vl,ul,bs; var lon, lat; var flag; /* Inverse equations -----------------*/ p.x -= this.x0; p.y -= this.y0; flag = 0; vs = p.x * this.cosaz - p.y * this.sinaz; us = p.y * this.cosaz + p.x * this.sinaz; us = us + this.u; q = Math.exp(-this.bl * vs / this.al); s = .5 * (q - 1.0/q); t = .5 * (q + 1.0/q); vl = Math.sin(this.bl * us / this.al); ul = (vl * this.cosgam + s * this.singam)/t; if (Math.abs(Math.abs(ul) - 1.0) <= Proj4js.common.EPSLN) { lon = this.longc; if (ul >= 0.0) { lat = Proj4js.common.HALF_PI; } else { lat = -Proj4js.common.HALF_PI; } } else { con = 1.0 / this.bl; ts1 =Math.pow((this.el / Math.sqrt((1.0 + ul) / (1.0 - ul))),con); lat = Proj4js.common.phi2z(this.e,ts1); //if (flag != 0) //return(flag); //~ con = Math.cos(this.bl * us /al); theta = this.longc - Math.atan2((s * this.cosgam - vl * this.singam) , con)/this.bl; lon = Proj4js.common.adjust_lon(theta); } p.x=lon; p.y=lat; return p; } }; /* ====================================================================== projCode/lcc.js ====================================================================== */ /******************************************************************************* NAME LAMBERT CONFORMAL CONIC PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Lambert Conformal Conic projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. ALGORITHM REFERENCES 1. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government *******************************************************************************/ //<2104> +proj=lcc +lat_1=10.16666666666667 +lat_0=10.16666666666667 +lon_0=-71.60561777777777 +k_0=1 +x0=-17044 +x0=-23139.97 +ellps=intl +units=m +no_defs no_defs // Initialize the Lambert Conformal conic projection // ----------------------------------------------------------------- //Proj4js.Proj.lcc = Class.create(); Proj4js.Proj.lcc = { init : function() { // array of: r_maj,r_min,lat1,lat2,c_lon,c_lat,false_east,false_north //double c_lat; /* center latitude */ //double c_lon; /* center longitude */ //double lat1; /* first standard parallel */ //double lat2; /* second standard parallel */ //double r_maj; /* major axis */ //double r_min; /* minor axis */ //double false_east; /* x offset in meters */ //double false_north; /* y offset in meters */ if (!this.lat2){this.lat2=this.lat0;}//if lat2 is not defined if (!this.k0) this.k0 = 1.0; // Standard Parallels cannot be equal and on opposite sides of the equator if (Math.abs(this.lat1+this.lat2) < Proj4js.common.EPSLN) { Proj4js.reportError("lcc:init: Equal Latitudes"); return; } var temp = this.b / this.a; this.e = Math.sqrt(1.0 - temp*temp); var sin1 = Math.sin(this.lat1); var cos1 = Math.cos(this.lat1); var ms1 = Proj4js.common.msfnz(this.e, sin1, cos1); var ts1 = Proj4js.common.tsfnz(this.e, this.lat1, sin1); var sin2 = Math.sin(this.lat2); var cos2 = Math.cos(this.lat2); var ms2 = Proj4js.common.msfnz(this.e, sin2, cos2); var ts2 = Proj4js.common.tsfnz(this.e, this.lat2, sin2); var ts0 = Proj4js.common.tsfnz(this.e, this.lat0, Math.sin(this.lat0)); if (Math.abs(this.lat1 - this.lat2) > Proj4js.common.EPSLN) { this.ns = Math.log(ms1/ms2)/Math.log(ts1/ts2); } else { this.ns = sin1; } this.f0 = ms1 / (this.ns * Math.pow(ts1, this.ns)); this.rh = this.a * this.f0 * Math.pow(ts0, this.ns); if (!this.title) this.title = "Lambert Conformal Conic"; }, // Lambert Conformal conic forward equations--mapping lat,long to x,y // ----------------------------------------------------------------- forward : function(p) { var lon = p.x; var lat = p.y; // convert to radians if ( lat <= 90.0 && lat >= -90.0 && lon <= 180.0 && lon >= -180.0) { //lon = lon * Proj4js.common.D2R; //lat = lat * Proj4js.common.D2R; } else { Proj4js.reportError("lcc:forward: llInputOutOfRange: "+ lon +" : " + lat); return null; } var con = Math.abs( Math.abs(lat) - Proj4js.common.HALF_PI); var ts, rh1; if (con > Proj4js.common.EPSLN) { ts = Proj4js.common.tsfnz(this.e, lat, Math.sin(lat) ); rh1 = this.a * this.f0 * Math.pow(ts, this.ns); } else { con = lat * this.ns; if (con <= 0) { Proj4js.reportError("lcc:forward: No Projection"); return null; } rh1 = 0; } var theta = this.ns * Proj4js.common.adjust_lon(lon - this.long0); p.x = this.k0 * (rh1 * Math.sin(theta)) + this.x0; p.y = this.k0 * (this.rh - rh1 * Math.cos(theta)) + this.y0; return p; }, // Lambert Conformal Conic inverse equations--mapping x,y to lat/long // ----------------------------------------------------------------- inverse : function(p) { var rh1, con, ts; var lat, lon; var x = (p.x - this.x0)/this.k0; var y = (this.rh - (p.y - this.y0)/this.k0); if (this.ns > 0) { rh1 = Math.sqrt (x * x + y * y); con = 1.0; } else { rh1 = -Math.sqrt (x * x + y * y); con = -1.0; } var theta = 0.0; if (rh1 != 0) { theta = Math.atan2((con * x),(con * y)); } if ((rh1 != 0) || (this.ns > 0.0)) { con = 1.0/this.ns; ts = Math.pow((rh1/(this.a * this.f0)), con); lat = Proj4js.common.phi2z(this.e, ts); if (lat == -9999) return null; } else { lat = -Proj4js.common.HALF_PI; } lon = Proj4js.common.adjust_lon(theta/this.ns + this.long0); p.x = lon; p.y = lat; return p; } }; /* ====================================================================== projCode/laea.js ====================================================================== */ /******************************************************************************* NAME LAMBERT AZIMUTHAL EQUAL-AREA PURPOSE: Transforms input longitude and latitude to Easting and Northing for the Lambert Azimuthal Equal-Area projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- D. Steinwand, EROS March, 1991 This function was adapted from the Lambert Azimuthal Equal Area projection code (FORTRAN) in the General Cartographic Transformation Package software which is available from the U.S. Geological Survey National Mapping Division. ALGORITHM REFERENCES 1. "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder, The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355. 2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. 3. "Software Documentation for GCTP General Cartographic Transformation Package", U.S. Geological Survey National Mapping Division, May 1982. *******************************************************************************/ Proj4js.Proj.laea = { S_POLE: 1, N_POLE: 2, EQUIT: 3, OBLIQ: 4, /* Initialize the Lambert Azimuthal Equal Area projection ------------------------------------------------------*/ init: function() { var t = Math.abs(this.lat0); if (Math.abs(t - Proj4js.common.HALF_PI) < Proj4js.common.EPSLN) { this.mode = this.lat0 < 0. ? this.S_POLE : this.N_POLE; } else if (Math.abs(t) < Proj4js.common.EPSLN) { this.mode = this.EQUIT; } else { this.mode = this.OBLIQ; } if (this.es > 0) { var sinphi; this.qp = Proj4js.common.qsfnz(this.e, 1.0); this.mmf = .5 / (1. - this.es); this.apa = this.authset(this.es); switch (this.mode) { case this.N_POLE: case this.S_POLE: this.dd = 1.; break; case this.EQUIT: this.rq = Math.sqrt(.5 * this.qp); this.dd = 1. / this.rq; this.xmf = 1.; this.ymf = .5 * this.qp; break; case this.OBLIQ: this.rq = Math.sqrt(.5 * this.qp); sinphi = Math.sin(this.lat0); this.sinb1 = Proj4js.common.qsfnz(this.e, sinphi) / this.qp; this.cosb1 = Math.sqrt(1. - this.sinb1 * this.sinb1); this.dd = Math.cos(this.lat0) / (Math.sqrt(1. - this.es * sinphi * sinphi) * this.rq * this.cosb1); this.ymf = (this.xmf = this.rq) / this.dd; this.xmf *= this.dd; break; } } else { if (this.mode == this.OBLIQ) { this.sinph0 = Math.sin(this.lat0); this.cosph0 = Math.cos(this.lat0); } } }, /* Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y -----------------------------------------------------------------------*/ forward: function(p) { /* Forward equations -----------------*/ var x,y; var lam=p.x; var phi=p.y; lam = Proj4js.common.adjust_lon(lam - this.long0); if (this.sphere) { var coslam, cosphi, sinphi; sinphi = Math.sin(phi); cosphi = Math.cos(phi); coslam = Math.cos(lam); switch (this.mode) { case this.OBLIQ: case this.EQUIT: y = (this.mode == this.EQUIT) ? 1. + cosphi * coslam : 1. + this.sinph0 * sinphi + this.cosph0 * cosphi * coslam; if (y <= Proj4js.common.EPSLN) { Proj4js.reportError("laea:fwd:y less than eps"); return null; } y = Math.sqrt(2. / y); x = y * cosphi * Math.sin(lam); y *= (this.mode == this.EQUIT) ? sinphi : this.cosph0 * sinphi - this.sinph0 * cosphi * coslam; break; case this.N_POLE: coslam = -coslam; case this.S_POLE: if (Math.abs(phi + this.phi0) < Proj4js.common.EPSLN) { Proj4js.reportError("laea:fwd:phi < eps"); return null; } y = Proj4js.common.FORTPI - phi * .5; y = 2. * ((this.mode == this.S_POLE) ? Math.cos(y) : Math.sin(y)); x = y * Math.sin(lam); y *= coslam; break; } } else { var coslam, sinlam, sinphi, q, sinb=0.0, cosb=0.0, b=0.0; coslam = Math.cos(lam); sinlam = Math.sin(lam); sinphi = Math.sin(phi); q = Proj4js.common.qsfnz(this.e, sinphi); if (this.mode == this.OBLIQ || this.mode == this.EQUIT) { sinb = q / this.qp; cosb = Math.sqrt(1. - sinb * sinb); } switch (this.mode) { case this.OBLIQ: b = 1. + this.sinb1 * sinb + this.cosb1 * cosb * coslam; break; case this.EQUIT: b = 1. + cosb * coslam; break; case this.N_POLE: b = Proj4js.common.HALF_PI + phi; q = this.qp - q; break; case this.S_POLE: b = phi - Proj4js.common.HALF_PI; q = this.qp + q; break; } if (Math.abs(b) < Proj4js.common.EPSLN) { Proj4js.reportError("laea:fwd:b < eps"); return null; } switch (this.mode) { case this.OBLIQ: case this.EQUIT: b = Math.sqrt(2. / b); if (this.mode == this.OBLIQ) { y = this.ymf * b * (this.cosb1 * sinb - this.sinb1 * cosb * coslam); } else { y = (b = Math.sqrt(2. / (1. + cosb * coslam))) * sinb * this.ymf; } x = this.xmf * b * cosb * sinlam; break; case this.N_POLE: case this.S_POLE: if (q >= 0.) { x = (b = Math.sqrt(q)) * sinlam; y = coslam * ((this.mode == this.S_POLE) ? b : -b); } else { x = y = 0.; } break; } } //v 1.0 /* var sin_lat=Math.sin(lat); var cos_lat=Math.cos(lat); var sin_delta_lon=Math.sin(delta_lon); var cos_delta_lon=Math.cos(delta_lon); var g =this.sin_lat_o * sin_lat +this.cos_lat_o * cos_lat * cos_delta_lon; if (g == -1.0) { Proj4js.reportError("laea:fwd:Point projects to a circle of radius "+ 2.0 * R); return null; } var ksp = this.a * Math.sqrt(2.0 / (1.0 + g)); var x = ksp * cos_lat * sin_delta_lon + this.x0; var y = ksp * (this.cos_lat_o * sin_lat - this.sin_lat_o * cos_lat * cos_delta_lon) + this.y0; */ p.x = this.a*x + this.x0; p.y = this.a*y + this.y0; return p; },//lamazFwd() /* Inverse equations -----------------*/ inverse: function(p) { p.x -= this.x0; p.y -= this.y0; var x = p.x/this.a; var y = p.y/this.a; var lam, phi; if (this.sphere) { var cosz=0.0, rh, sinz=0.0; rh = Math.sqrt(x*x + y*y); phi = rh * .5; if (phi > 1.) { Proj4js.reportError("laea:Inv:DataError"); return null; } phi = 2. * Math.asin(phi); if (this.mode == this.OBLIQ || this.mode == this.EQUIT) { sinz = Math.sin(phi); cosz = Math.cos(phi); } switch (this.mode) { case this.EQUIT: phi = (Math.abs(rh) <= Proj4js.common.EPSLN) ? 0. : Math.asin(y * sinz / rh); x *= sinz; y = cosz * rh; break; case this.OBLIQ: phi = (Math.abs(rh) <= Proj4js.common.EPSLN) ? this.phi0 : Math.asin(cosz * this.sinph0 + y * sinz * this.cosph0 / rh); x *= sinz * this.cosph0; y = (cosz - Math.sin(phi) * this.sinph0) * rh; break; case this.N_POLE: y = -y; phi = Proj4js.common.HALF_PI - phi; break; case this.S_POLE: phi -= Proj4js.common.HALF_PI; break; } lam = (y == 0. && (this.mode == this.EQUIT || this.mode == this.OBLIQ)) ? 0. : Math.atan2(x, y); } else { var cCe, sCe, q, rho, ab=0.0; switch (this.mode) { case this.EQUIT: case this.OBLIQ: x /= this.dd; y *= this.dd; rho = Math.sqrt(x*x + y*y); if (rho < Proj4js.common.EPSLN) { p.x = 0.; p.y = this.phi0; return p; } sCe = 2. * Math.asin(.5 * rho / this.rq); cCe = Math.cos(sCe); x *= (sCe = Math.sin(sCe)); if (this.mode == this.OBLIQ) { ab = cCe * this.sinb1 + y * sCe * this.cosb1 / rho q = this.qp * ab; y = rho * this.cosb1 * cCe - y * this.sinb1 * sCe; } else { ab = y * sCe / rho; q = this.qp * ab; y = rho * cCe; } break; case this.N_POLE: y = -y; case this.S_POLE: q = (x * x + y * y); if (!q ) { p.x = 0.; p.y = this.phi0; return p; } /* q = this.qp - q; */ ab = 1. - q / this.qp; if (this.mode == this.S_POLE) { ab = - ab; } break; } lam = Math.atan2(x, y); phi = this.authlat(Math.asin(ab), this.apa); } /* var Rh = Math.Math.sqrt(p.x *p.x +p.y * p.y); var temp = Rh / (2.0 * this.a); if (temp > 1) { Proj4js.reportError("laea:Inv:DataError"); return null; } var z = 2.0 * Proj4js.common.asinz(temp); var sin_z=Math.sin(z); var cos_z=Math.cos(z); var lon =this.long0; if (Math.abs(Rh) > Proj4js.common.EPSLN) { var lat = Proj4js.common.asinz(this.sin_lat_o * cos_z +this. cos_lat_o * sin_z *p.y / Rh); var temp =Math.abs(this.lat0) - Proj4js.common.HALF_PI; if (Math.abs(temp) > Proj4js.common.EPSLN) { temp = cos_z -this.sin_lat_o * Math.sin(lat); if(temp!=0.0) lon=Proj4js.common.adjust_lon(this.long0+Math.atan2(p.x*sin_z*this.cos_lat_o,temp*Rh)); } else if (this.lat0 < 0.0) { lon = Proj4js.common.adjust_lon(this.long0 - Math.atan2(-p.x,p.y)); } else { lon = Proj4js.common.adjust_lon(this.long0 + Math.atan2(p.x, -p.y)); } } else { lat = this.lat0; } */ //return(OK); p.x = Proj4js.common.adjust_lon(this.long0+lam); p.y = phi; return p; },//lamazInv() /* determine latitude from authalic latitude */ P00: .33333333333333333333, P01: .17222222222222222222, P02: .10257936507936507936, P10: .06388888888888888888, P11: .06640211640211640211, P20: .01641501294219154443, authset: function(es) { var t; var APA = new Array(); APA[0] = es * this.P00; t = es * es; APA[0] += t * this.P01; APA[1] = t * this.P10; t *= es; APA[0] += t * this.P02; APA[1] += t * this.P11; APA[2] = t * this.P20; return APA; }, authlat: function(beta, APA) { var t = beta+beta; return(beta + APA[0] * Math.sin(t) + APA[1] * Math.sin(t+t) + APA[2] * Math.sin(t+t+t)); } }; /* ====================================================================== projCode/aeqd.js ====================================================================== */ Proj4js.Proj.aeqd = { init : function() { this.sin_p12=Math.sin(this.lat0); this.cos_p12=Math.cos(this.lat0); }, forward: function(p) { var lon=p.x; var lat=p.y; var ksp; var sinphi=Math.sin(p.y); var cosphi=Math.cos(p.y); var dlon = Proj4js.common.adjust_lon(lon - this.long0); var coslon = Math.cos(dlon); var g = this.sin_p12 * sinphi + this.cos_p12 * cosphi * coslon; if (Math.abs(Math.abs(g) - 1.0) < Proj4js.common.EPSLN) { ksp = 1.0; if (g < 0.0) { Proj4js.reportError("aeqd:Fwd:PointError"); return; } } else { var z = Math.acos(g); ksp = z/Math.sin(z); } p.x = this.x0 + this.a * ksp * cosphi * Math.sin(dlon); p.y = this.y0 + this.a * ksp * (this.cos_p12 * sinphi - this.sin_p12 * cosphi * coslon); return p; }, inverse: function(p){ p.x -= this.x0; p.y -= this.y0; var rh = Math.sqrt(p.x * p.x + p.y *p.y); if (rh > (2.0 * Proj4js.common.HALF_PI * this.a)) { Proj4js.reportError("aeqdInvDataError"); return; } var z = rh / this.a; var sinz=Math.sin(z); var cosz=Math.cos(z); var lon = this.long0; var lat; if (Math.abs(rh) <= Proj4js.common.EPSLN) { lat = this.lat0; } else { lat = Proj4js.common.asinz(cosz * this.sin_p12 + (p.y * sinz * this.cos_p12) / rh); var con = Math.abs(this.lat0) - Proj4js.common.HALF_PI; if (Math.abs(con) <= Proj4js.common.EPSLN) { if (this.lat0 >= 0.0) { lon = Proj4js.common.adjust_lon(this.long0 + Math.atan2(p.x , -p.y)); } else { lon = Proj4js.common.adjust_lon(this.long0 - Math.atan2(-p.x , p.y)); } } else { con = cosz - this.sin_p12 * Math.sin(lat); if ((Math.abs(con) < Proj4js.common.EPSLN) && (Math.abs(p.x) < Proj4js.common.EPSLN)) { //no-op, just keep the lon value as is } else { var temp = Math.atan2((p.x * sinz * this.cos_p12), (con * rh)); lon = Proj4js.common.adjust_lon(this.long0 + Math.atan2((p.x * sinz * this.cos_p12), (con * rh))); } } } p.x = lon; p.y = lat; return p; } }; /* ====================================================================== projCode/moll.js ====================================================================== */ /******************************************************************************* NAME MOLLWEIDE PURPOSE: Transforms input longitude and latitude to Easting and Northing for the MOllweide projection. The longitude and latitude must be in radians. The Easting and Northing values will be returned in meters. PROGRAMMER DATE ---------- ---- D. Steinwand, EROS May, 1991; Updated Sept, 1992; Updated Feb, 1993 S. Nelson, EDC Jun, 2993; Made corrections in precision and number of iterations. ALGORITHM REFERENCES 1. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections", U.S. Geological Survey Professional Paper 1453 , United State Government Printing Office, Washington D.C., 1989. 2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United State Government Printing Office, Washington D.C., 1987. *******************************************************************************/ Proj4js.Proj.moll = { /* Initialize the Mollweide projection ------------------------------------*/ init: function(){ //no-op }, /* Mollweide forward equations--mapping lat,long to x,y ----------------------------------------------------*/ forward: function(p) { /* Forward equations -----------------*/ var lon=p.x; var lat=p.y; var delta_lon = Proj4js.common.adjust_lon(lon - this.long0); var theta = lat; var con = Proj4js.common.PI * Math.sin(lat); /* Iterate using the Newton-Raphson method to find theta -----------------------------------------------------*/ for (var i=0;true;i++) { var delta_theta = -(theta + Math.sin(theta) - con)/ (1.0 + Math.cos(theta)); theta += delta_theta; if (Math.abs(delta_theta) < Proj4js.common.EPSLN) break; if (i >= 50) { Proj4js.reportError("moll:Fwd:IterationError"); //return(241); } } theta /= 2.0; /* If the latitude is 90 deg, force the x coordinate to be "0 + false easting" this is done here because of precision problems with "cos(theta)" --------------------------------------------------------------------------*/ if (Proj4js.common.PI/2 - Math.abs(lat) < Proj4js.common.EPSLN) delta_lon =0; var x = 0.900316316158 * this.a * delta_lon * Math.cos(theta) + this.x0; var y = 1.4142135623731 * this.a * Math.sin(theta) + this.y0; p.x=x; p.y=y; return p; }, inverse: function(p){ var theta; var arg; /* Inverse equations -----------------*/ p.x-= this.x0; //~ p.y -= this.y0; var arg = p.y / (1.4142135623731 * this.a); /* Because of division by zero problems, 'arg' can not be 1.0. Therefore a number very close to one is used instead. -------------------------------------------------------------------*/ if(Math.abs(arg) > 0.999999999999) arg=0.999999999999; var theta =Math.asin(arg); var lon = Proj4js.common.adjust_lon(this.long0 + (p.x / (0.900316316158 * this.a * Math.cos(theta)))); if(lon < (-Proj4js.common.PI)) lon= -Proj4js.common.PI; if(lon > Proj4js.common.PI) lon= Proj4js.common.PI; arg = (2.0 * theta + Math.sin(2.0 * theta)) / Proj4js.common.PI; if(Math.abs(arg) > 1.0)arg=1.0; var lat = Math.asin(arg); //return(OK); p.x=lon; p.y=lat; return p; } };