/*******************************************************************************
NAME                       OBLIQUE MERCATOR (HOTINE)

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

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

/* Variables common to all subroutines in this code file
  -----------------------------------------------------*/
static double azimuth;
static double r_major;		/* major axis 				*/
static double r_minor;		/* minor axis 				*/
static double scale_factor;	/* scale factor				*/
static double lon_origin;	/* center longitude			*/
static double lat_origin;	/* center latitude			*/
static double e,es;		/* eccentricity constants		*/
static double false_northing;	/* y offset in meters			*/
static double false_easting;	/* x offset in meters			*/
static double sin_p20,cos_p20;	/* sin and cos values			*/
static double bl;
static double al;
static double ts;
static double d;
static double el,u;
static double singam,cosgam;
static double sinaz,cosaz;


/* Initialize the Oblique Mercator  projection
  ------------------------------------------*/
long
omerinvint(double r_maj, double r_min, double scale_fact, double azimuth, double lon_orig, double lat_orig, double false_east, double false_north, double lon1, double lat1, double lon2, double lat2, long int mode) 

             			/* major axis			*/
             			/* minor axis			*/
                  		/* scale factor			*/
               			/* azimuth east of north	*/
                		/* longitude of origin		*/
                		/* center latitude		*/
                  		/* x offset in meters		*/
                   		/* y offset in meters		*/
            			/* fist point to define central line	*/
            			/* fist point to define central line	*/
            			/* second point to define central line	*/
            			/* second point to define central line	*/
            			/* which format type A or B	*/
{
double temp;			/* temporary variable		*/
double adjust_lon(double x);
double asinz(double con);
double con,com;
double tsfnz(double eccent, double phi, double sinphi);			/* function to compute t	*/
double h,l,ts1,ts2;
double j,p,dlon;
double f,g,gama;
double sinphi,cosphi;

/* Place parameters in static storage for common use
  -------------------------------------------------*/
r_major = r_maj;
r_minor = r_min;
scale_factor = scale_fact;
lat_origin = lat_orig;
false_northing = false_north;
false_easting = false_east;

temp = r_minor / r_major;
es = 1.0 - SQUARE(temp);
e = sqrt(es);

sincos(lat_origin,&sin_p20,&cos_p20);
con = 1.0 - es * sin_p20 * sin_p20;
com = sqrt(1.0 - es);
bl = sqrt(1.0 + es * pow(cos_p20,4.0)/(1.0 - es));
al = r_major * bl * scale_factor * com / con;
if (fabs(lat_origin) < EPSLN)
   {
   ts = 1.0;
   d = 1.0;
   el = 1.0;
   }
else
   {
   ts = tsfnz(e,lat_origin,sin_p20);
   con = sqrt(con);
   d = bl * com / (cos_p20 * con);
   if ((d * d - 1.0) > 0.0)
      {
      if (lat_origin >= 0.0)
         f = d + sqrt(d * d - 1.0);
      else
         f = d - sqrt(d * d - 1.0);
      }
   else
      f = d;
   el = f * pow(ts,bl);
   }

/* Report parameters to the user that are the same for both formats
  ---------------------------------------------------------------*/
ptitle("OBLIQUE MERCATOR (HOTINE)"); 
radius2(r_major, r_minor);
genrpt(scale_factor,"Scale Factor at C. Meridian:    ");
offsetp(false_easting,false_northing);

if (mode != 0)
   {
   g = .5 * (f - 1.0/f);
   gama = asinz(sin(azimuth) / d);
   lon_origin = lon_orig - asinz(g * tan(gama))/bl;

   /* Report parameters common to format B
   -------------------------------------*/
   genrpt(azimuth * R2D,"Azimuth of Central Line:    ");
   cenlon(lon_origin);
   cenlat(lat_origin);
   
   con = fabs(lat_origin);
   if ((con > EPSLN) && (fabs(con - HALF_PI) > EPSLN))
      {
      sincos(gama,&singam,&cosgam);
      sincos(azimuth,&sinaz,&cosaz);
      if (lat_origin >= 0)
         u =  (al / bl) * atan(sqrt(d*d - 1.0)/cosaz);
      else
         u =  -(al / bl) * atan(sqrt(d*d - 1.0)/cosaz);
      }
   else
      {
      p_error("Input data error","omer-init");
      return(201);
      }
   }
else
   {
   sinphi = sin(lat1);
   ts1 = tsfnz(e,lat1,sinphi);
   sinphi = sin(lat2);
   ts2 = tsfnz(e,lat2,sinphi);
   h = pow(ts1,bl);
   l = pow(ts2,bl);
   f = el/h;
   g = .5 * (f - 1.0/f);
   j = (el * el - l * h)/(el * el + l * h);
   p = (l - h) / (l + h);
   dlon = lon1 - lon2;
   if (dlon < -PI)
      lon2 = lon2 - 2.0 * PI;
   if (dlon > PI)
      lon2 = lon2 + 2.0 * PI;
   dlon = lon1 - lon2;
   lon_origin = .5 * (lon1 + lon2) - atan(j * tan(.5 * bl * dlon)/p)/bl;
   dlon  = adjust_lon(lon1 - lon_origin);
   gama = atan(sin(bl * dlon)/g);
   azimuth = asinz(d * sin(gama));
   
   /* Report parameters common to format A
   -------------------------------------*/
   genrpt(lon1 * R2D,"Longitude of First Point:     ");
   genrpt(lat1 * R2D,"Latitude of First Point:      ");
   genrpt(lon2 * R2D,"Longitude of Second Point:    ");
   genrpt(lat2 * R2D,"Latitude of Second Point:     ");
   
   if (fabs(lat1 - lat2) <= EPSLN)
      {
      p_error("Input data error","omer-init");
      return(202);
      }
   else
      con = fabs(lat1);
   if ((con <= EPSLN) || (fabs(con - HALF_PI) <= EPSLN))
      {
      p_error("Input data error","omer-init");
      return(202);
      }
   else 
   if (fabs(fabs(lat_origin) - HALF_PI) <= EPSLN)
      {
      p_error("Input data error","omer-init");
      return(202);
      }
      
   sincos(gama,&singam,&cosgam);
   sincos(azimuth,&sinaz,&cosaz);
   if (lat_origin >= 0)
      u =  (al/bl) * atan(sqrt(d * d - 1.0)/cosaz);
   else
      u = -(al/bl) * atan(sqrt(d * d - 1.0)/cosaz);
   }
return(OK);
}


/* Oblique Mercator inverse equations--mapping x,y to lat/long
  ----------------------------------------------------------*/
long
omerinv(double x, double y, double *lon, double *lat)
         			/* (O) X projection coordinate 	*/
         			/* (O) Y projection coordinate 	*/
            			/* (I) Longitude 		*/
            			/* (I) Latitude 		*/
{
double adjust_lon(double x);	/* Function to adjust longitude to -180 - 180 	*/
double delta_lon;	/* Delta longitude (Given longitude - center 	*/
double theta;		/* angle					*/
double delta_theta;	/* adjusted longitude				*/
double sin_phi, cos_phi;/* sin and cos value				*/
double b;		/* temporary values				*/
double c, t, tq;	/* temporary values				*/
double con, n, ml;	/* cone constant, small m			*/
double vs,us,q,s,ts1;
double vl,ul,bs;
double phi2z(double eccent, double ts, long int *flag);
double dlon;
long   flag;

/* Inverse equations
  -----------------*/
x -= false_easting;
y -= false_northing;
flag = 0;
vs = x * cosaz - y * sinaz;
us = y * cosaz + x * sinaz;
us = us + u;
q = exp(-bl * vs / al);
s = .5 * (q - 1.0/q);
t = .5 * (q + 1.0/q);
vl = sin(bl * us / al);
ul = (vl * cosgam + s * singam)/t;
if (fabs(fabs(ul) - 1.0) <= EPSLN)
   {
   *lon = lon_origin;
   if (ul >= 0.0)
      *lat = HALF_PI;
   else
      *lat = -HALF_PI;
   }
else
   {
   con = 1.0 / bl;
   ts1 = pow((el / sqrt((1.0 + ul) / (1.0 - ul))),con);
   *lat = phi2z(e,ts1,&flag);
   if (flag != 0)
      return(flag);
   con = cos(bl * us /al);
   theta = lon_origin - atan2((s * cosgam - vl * singam) , con)/bl;
   *lon = adjust_lon(theta);
   }
return(OK);
}