/*******************************************************************************
NAME                            POLAR STEREOGRAPHIC 

PURPOSE:	Transforms input Easting and Northing to longitude and
		latitude for the Polar Stereographic projection.  The
		Easting and Northing must be in meters.  The longitude
		and latitude values will be returned in radians.

PROGRAMMER              DATE
----------              ----
T. Mittan		2-26-93

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.
*******************************************************************************/
#include "gctpc/cproj.h"
#include "gctpc/report.h"

/* Variables common to all subroutines in this code file
  -----------------------------------------------------*/
  static double r_major;                /* major axis                   */
  static double r_minor;                /* minor axis                   */
  static double e;                      /* eccentricity                 */
  static double e4;                     /* e4 calculated from eccentricity*/
  static double center_lon;             /* center longitude             */
  static double center_lat;             /* center latitude              */
  static double fac;                    /* sign variable                */
  static double ind;                    /* flag variable                */
  static double mcs;			/* small value m		*/
  static double tcs;			/* small value t		*/
  static double false_northing;		/* y offset in meters		*/
  static double false_easting;		/* x offset in meters		*/

/* Initialize the Polar Stereographic projection
  --------------------------------------------*/
long
psinvint(double r_maj, double r_min, double c_lon, double c_lat, double false_east, double false_north)

             				/* center longitude		*/
             				/* center latitude		*/
             				/* major axis			*/
             				/* minor axis			*/
                  			/* x offset in meters		*/
                   			/* y offset in meters		*/

{
double temp;				/* temporary variable		*/
double con1;				/* temporary angle		*/
double sinphi;				/* sin value			*/
double cosphi;				/* cos value			*/
double es;                     /* eccentricity squared         */
double e4fn(double x);				/* function to compute e4	*/
double msfnz(double eccent, double sinphi, double cosphi);				/* function to compute small m	*/
double tsfnz(double eccent, double phi, double sinphi);				/* function to compute small t	*/

r_major = r_maj;
r_minor = r_min;
false_easting = false_east;
false_northing = false_north;
temp = r_minor / r_major;
es = 1.0 - SQUARE(temp);
e = sqrt(es);
e4 = e4fn(e);
center_lon = c_lon;
center_lat = c_lat;

if (c_lat < 0)
   fac = -1.0;
else
   fac = 1.0;
ind = 0;
if (fabs(fabs(c_lat) - HALF_PI) > EPSLN)
   {
   ind = 1;
   con1 = fac * center_lat; 
   sincos(con1,&sinphi,&cosphi);
   mcs = msfnz(e,sinphi,cosphi);
   tcs = tsfnz(e,con1,sinphi);
   }
/* Report parameters to the user
  -----------------------------*/
ptitle("POLAR STEREOGRAPHIC");
radius2(r_major, r_minor);
cenlon(center_lon);
offsetp(false_east,false_north);

return(OK);
}

/* Polar Stereographic inverse equations--mapping x,y to lat/long
  --------------------------------------------------------------*/
long
psinv(double x, double y, double *lon, double *lat)
         			/* (O) X projection coordinate 	*/
         			/* (O) Y projection coordinate 	*/
            			/* (I) Longitude 		*/
            			/* (I) Latitude 		*/

{
double rh;			/* height above ellipsiod	*/
double ts;			/* small value t		*/
double phi2z(double eccent, double ts, long int *flag);			/* function to compute phi	*/
double adjust_lon(double x);		/* function to adjust longitude	*/
double temp;			/* temporary variable		*/
long   flag;			/* error flag			*/

flag = 0;
x = (x - false_easting) * fac;
y = (y - false_northing) *fac;
rh = sqrt(x * x + y * y);
if (ind != 0)
  ts = rh * tcs/(r_major * mcs);
else
  ts = rh * e4 / (r_major * 2.0);
*lat = fac * phi2z(e,ts,&flag);
if (flag != 0)
   return(flag);
if (rh == 0)
   *lon = fac * center_lon;
else
   {
   temp = atan2(x, -y);
   *lon = adjust_lon(fac *temp + center_lon);
   }

return(OK);
}