/*!\file Xy2llx.cpp
 */

#include "./Xy2llx.h"
#include "../../shared/shared.h"
#include "../../include/include.h"
#include "../../toolkits/toolkits.h"
#include "../../EnumDefinitions/EnumDefinitions.h"

int Xy2llx(double* lat, double* lon,
		   double* x, double* y, int ncoord,
		   int sgn){

/*  This is a cpp conversion of the following:
%XY2LL - converts xy to lat long
%
%   Converts Polar  Stereographic (X,Y) coordinates for the polar regions to
%   latitude and longitude Stereographic (X,Y) coordinates for the polar
%   regions.
%   Author: Michael P. Schodlok, December 2003 (map2xy.m)
%
%   Usage:
%      [lat,lon] = xy2ll(x,y,sgn);
%      [lat,lon] = xy2ll(x,y,sgn,central_meridian,standard_parallel);
%
%      - sgn = Sign of latitude +1 : north latitude (default is mer=45 lat=70)
%                               -1 : south latitude (default is mer=0  lat=71)
*/

	double  delta,slat;
	bool    flag=false;

	/*  Get central_meridian and standard_parallel depending on hemisphere  */
	if      (sgn ==  1) {
		delta = 45;
		slat = 70;
		_printf_(flag,"Warning: expecting coordinates in polar stereographic (Std Latitude: 70N Meridian: 45)");
	}
	else if (sgn == -1) {
		delta = 0;
		slat = 71;
		_printf_(flag,"Warning: expecting coordinates in polar stereographic (Std Latitude: 71S Meridian: 0)");
	}
	else
		_error_("Sign should be either +1 or -1");

	return(Xy2llx(lat,lon,
				  x,y,ncoord,
				  sgn,delta,slat));
}

int Xy2llx(double* lat, double* lon,
		   double* x, double* y, int ncoord,
		   int sgn, double central_meridian, double standard_parallel){

/*  This is a cpp conversion of the following:
%XY2LL - converts xy to lat long
%
%   Converts Polar  Stereographic (X,Y) coordinates for the polar regions to
%   latitude and longitude Stereographic (X,Y) coordinates for the polar
%   regions.
%   Author: Michael P. Schodlok, December 2003 (map2xy.m)
%
%   Usage:
%      [lat,lon] = xy2ll(x,y,sgn);
%      [lat,lon] = xy2ll(x,y,sgn,central_meridian,standard_parallel);
%
%      - sgn = Sign of latitude +1 : north latitude (default is mer=45 lat=70)
%                               -1 : south latitude (default is mer=0  lat=71)
*/

	int     i;
	double  delta,slat;
	double  cde,re,ex2,ex,pi;
	double  sl,rho,cm,T,chi;

	if      ((sgn !=  1) && (sgn != -1))
		_error_("Sign should be either +1 or -1");

	delta = central_meridian;
	slat  = standard_parallel;

	/*  Conversion constant from degrees to radians  */
	cde  = 57.29577951;
	/*  Radius of the earth in meters  */
	re   = 6378.273*pow(10.,3.);
	/*  Eccentricity of the Hughes ellipsoid squared  */
	ex2   = .006693883;
	/*  Eccentricity of the Hughes ellipsoid  */
	ex    =  sqrt(ex2);
	/*  pi is not defined in cpp  */
	pi   = 4.*atan(1.);

	/*  loop over all the coordinate pairs  */

	for (i=0; i<ncoord; i++) {
		sl  = slat*pi/180.;
		cm = cos(sl) / sqrt(1.0 - ex2 * (pow(sin(sl),2.)));
		rho = sqrt(pow(x[i],2.) + pow(y[i],2.));
		T = tan((pi / 4.0) - (sl / 2.0)) / pow(((1.0 - ex * sin(sl)) / (1.0 + ex * sin(sl))),(ex / 2.0));

		if  (fabs(slat-90.) < 1.e-5)
			T = rho * sqrt(pow((1. + ex),(1. + ex)) * pow((1. - ex),(1. - ex))) / 2. / re;
		else
			T = rho * T / (re * cm);

		chi = (pi / 2.0) - 2.0 * atan(T);
		lat[i] = chi + ((ex2 / 2.0) + (5.0 * pow(ex2,2.0) / 24.0) + (pow(ex2,3.0) / 12.0)) *
			   sin(2.0 * chi) + ((7.0 * pow(ex2,2.0) / 48.0) + (29.0 * pow(ex2,3.0) / 240.0)) *
			   sin(4.0 * chi) + (7.0 * pow(ex2,3.0) / 120.0) * sin(6.0 * chi) ;

		lat[i] = (double)sgn * lat[i];
		lon[i] = atan2((double)sgn * x[i],-(double)sgn * y[i]);
		lon[i] = (double)sgn * lon[i];

		if (rho <= 0.1) {
			lat[i] = 90. * (double)sgn;
			lon[i] = 0.0;
		}

		lon[i] = lon[i] * 180. / pi;
		lat[i] = lat[i] * 180. / pi;
		lon[i] = lon[i] - delta; 
	}

	return(0);
}