moll.js
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/*******************************************************************************
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;
}
};