/*******************************************************************************
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NAME MOLLWEIDE
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PURPOSE: Transforms input longitude and latitude to Easting and
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Northing for the MOllweide projection. The
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longitude and latitude must be in radians. The Easting
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and Northing values will be returned in meters.
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PROGRAMMER DATE
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---------- ----
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D. Steinwand, EROS May, 1991; Updated Sept, 1992; Updated Feb, 1993
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S. Nelson, EDC Jun, 2993; Made corrections in precision and
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number of iterations.
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ALGORITHM REFERENCES
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1. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections",
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U.S. Geological Survey Professional Paper 1453 , United State Government
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Printing Office, Washington D.C., 1989.
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2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological
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Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United
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State Government Printing Office, Washington D.C., 1987.
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*******************************************************************************/
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Proj4js.Proj.moll = {
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/* Initialize the Mollweide projection
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------------------------------------*/
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init: function(){
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//no-op
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},
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/* Mollweide forward equations--mapping lat,long to x,y
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----------------------------------------------------*/
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forward: function(p) {
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/* Forward equations
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-----------------*/
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var lon=p.x;
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var lat=p.y;
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var delta_lon = Proj4js.common.adjust_lon(lon - this.long0);
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var theta = lat;
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var con = Proj4js.common.PI * Math.sin(lat);
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/* Iterate using the Newton-Raphson method to find theta
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-----------------------------------------------------*/
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for (var i=0;true;i++) {
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var delta_theta = -(theta + Math.sin(theta) - con)/ (1.0 + Math.cos(theta));
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theta += delta_theta;
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if (Math.abs(delta_theta) < Proj4js.common.EPSLN) break;
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if (i >= 50) {
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Proj4js.reportError("moll:Fwd:IterationError");
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//return(241);
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}
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}
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theta /= 2.0;
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/* If the latitude is 90 deg, force the x coordinate to be "0 + false easting"
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this is done here because of precision problems with "cos(theta)"
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--------------------------------------------------------------------------*/
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if (Proj4js.common.PI/2 - Math.abs(lat) < Proj4js.common.EPSLN) delta_lon =0;
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var x = 0.900316316158 * this.a * delta_lon * Math.cos(theta) + this.x0;
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var y = 1.4142135623731 * this.a * Math.sin(theta) + this.y0;
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p.x=x;
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p.y=y;
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return p;
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},
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inverse: function(p){
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var theta;
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var arg;
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/* Inverse equations
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-----------------*/
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p.x-= this.x0;
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//~ p.y -= this.y0;
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var arg = p.y / (1.4142135623731 * this.a);
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/* Because of division by zero problems, 'arg' can not be 1.0. Therefore
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a number very close to one is used instead.
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-------------------------------------------------------------------*/
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if(Math.abs(arg) > 0.999999999999) arg=0.999999999999;
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var theta =Math.asin(arg);
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var lon = Proj4js.common.adjust_lon(this.long0 + (p.x / (0.900316316158 * this.a * Math.cos(theta))));
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if(lon < (-Proj4js.common.PI)) lon= -Proj4js.common.PI;
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if(lon > Proj4js.common.PI) lon= Proj4js.common.PI;
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arg = (2.0 * theta + Math.sin(2.0 * theta)) / Proj4js.common.PI;
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if(Math.abs(arg) > 1.0)arg=1.0;
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var lat = Math.asin(arg);
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//return(OK);
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p.x=lon;
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p.y=lat;
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return p;
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}
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};
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