/*******************************************************************************
NAME                            ROBINSON 

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

PROGRAMMER              DATE            REASON
----------              ----            ------
T. Mittan		March, 1993	Converted from FORTRAN to C.
S. Nelson		Nov, 1993	Changed number of iterations from 20
					to 75.  This seemed to give a valid
					Latitude with less fatal errors.

This function was adapted from the Robinson projection code (FORTRAN)
in the General Cartographic Transformation Package software which is
available from the U.S. Geological Survey National Mapping Division.
 
ALGORITHM REFERENCES

1.  "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
    The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.

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.

3.  "Software Documentation for GCTP General Cartographic Transformation
    Package", U.S. Geological Survey National Mapping Division, May 1982.
*******************************************************************************/
#include "cproj.h"

/* Variables common to all subroutines in this code file
  -----------------------------------------------------*/
static double lon_center;	/* Center longitude (projection center) */
static double R;		/* Radius of the earth (sphere)	 	*/
static double false_easting;	/* x offset in meters			*/
static double false_northing;	/* y offset in meters			*/
static double pr[21];
static double xlr[21];

/* Initialize the ROBINSON projection
  ---------------------------------*/
long robinvint(double r, double center_long, double false_east,
        double false_north) {
//long robinvint(r, center_long,false_east,false_north) 
//
//double r; 			/* (I) Radius of the earth (sphere) 	*/
//double center_long;		/* (I) Center longitude 		*/
//double false_east;		/* x offset in meters			*/
//double false_north;		/* y offset in meters			*/
//{
long i;

/* Place parameters in static storage for common use
  -------------------------------------------------*/
R = r;
lon_center = center_long;
false_easting = false_east;
false_northing = false_north;

         pr[1]= -0.062; 
         xlr[1]=0.9986; 
         pr[2]=0.0; 
         xlr[2]=1.0; 
         pr[3]=0.062; 
         xlr[3]=0.9986;
         pr[4]=0.124;   
         xlr[4]=0.9954;  
         pr[5]=0.186;
         xlr[5]=0.99; 
         pr[6]=0.248;  
         xlr[6]=0.9822; 
         pr[7]=0.31;     
         xlr[7]=0.973;    
         pr[8]=0.372;      
         xlr[8]=0.96;
         pr[9]=0.434; 
         xlr[9]=0.9427;
         pr[10]=0.4958;
         xlr[10]=0.9216;
         pr[11]=0.5571;  
         xlr[11]=0.8962;  
         pr[12]=0.6176;
         xlr[12]=0.8679;
         pr[13]=0.6769; 
         xlr[13]=0.835;  
         pr[14]=0.7346;
         xlr[14]=0.7986;
         pr[15]=0.7903;  
         xlr[15]=0.7597;  
         pr[16]=0.8435;
         xlr[16]=0.7186;
         pr[17]=0.8936; 
         xlr[17]=0.6732; 
         pr[18]=0.9394; 
         xlr[18]=0.6213;
         pr[19]=0.9761;  
         xlr[19]=0.5722;  
         pr[20]=1.0;  
         xlr[20]=0.5322;

         for (i = 0; i < 21; i++)
            xlr[i] *= 0.9858;   

/* Report parameters to the user
  -----------------------------*/
ptitle("ROBINSON"); 
radius(r);
cenlon(center_long);
offsetp(false_easting,false_northing);
return(OK);
}

/* Robinson inverse equations--mapping x,y to lat/long
  ------------------------------------------------------------*/
long robinv(double x, double y, double *lon, double *lat) {
//long robinv(x, y, lon, lat)
//double x;			/* (O) X projection coordinate */
//double y;			/* (O) Y projection coordinate */
//double *lon;			/* (I) Longitude */
//double *lat;			/* (I) Latitude */
//
//{
double yy;
double p2;
double u,v,t,c;
double phid;
double y1;
long ip1;
long i;


/* Inverse equations
  -----------------*/
x -= false_easting;
y -= false_northing;

yy = 2.0 * y / PI / R;
phid = yy * 90.0;
p2 = fabs(phid / 5.0);
ip1 = (long) (p2 - EPSLN);
if (ip1 == 0)
   ip1 = 1;

/* Stirling's interpolation formula as used in forward transformation is 
   reversed for first estimation of LAT. from rectangular coordinates. LAT.
   is then adjusted by iteration until use of forward series provides correct 
   value of Y within tolerance.
---------------------------------------------------------------------------*/
for (i = 0;;)
   {
   u = pr[ip1 + 3] - pr[ip1 + 1];
   v = pr[ip1 + 3] - 2.0 * pr[ip1 + 2] + pr[ip1 + 1];
   t = 2.0 * (fabs(yy) - pr[ip1 + 2]) / u;
   c = v / u;
   p2 = t * (1.0 - c * t * (1.0 - 2.0 * c * t));

   if ((p2 >= 0.0) || (ip1 == 1))
      {
      if (y >= 0)
         phid = (p2 + (double) ip1 ) * 5.0;
      else
         phid = -(p2 + (double) ip1 ) * 5.0;
      
      do
        {
        p2 = fabs(phid / 5.0);
        ip1 = (long) (p2 - EPSLN);
        p2 -= (double) ip1;
 
        if (y >= 0)
           y1 = R * (pr[ip1 +2] + p2 *(pr[ip1 + 3] - pr[ip1 +1]) / 2.0 + p2 
                  * p2 * (pr[ip1 + 3] - 2.0 * pr[ip1 + 2] + pr[ip1 + 1])/2.0) 
                  * PI / 2.0; 
        else
           y1 = -R * (pr[ip1 +2] + p2 *(pr[ip1 + 3] - pr[ip1 +1]) / 2.0 + p2 
                   * p2 * (pr[ip1 + 3] - 2.0 * pr[ip1 + 2] + pr[ip1 + 1])/2.0) 
                   * PI / 2.0; 
        phid += -180.0 * (y1 - y) / PI / R;
        i++;
        if (i > 75)
           {
           p_error("Too many iterations in inverse","robinv-conv");
           return(234);
           }
        }
      while (fabs(y1 - y) > .00001);
      break;
      }
   else
      {
      ip1 -= 1;
      if (ip1 < 0)
           {
           p_error("Too many iterations in inverse","robinv-conv");
           return(234);
           }
      }
   }
*lat  = phid * .01745329252;

/* calculate  LONG. using final LAT. with transposed forward Stirling's 
   interpolation formula.
---------------------------------------------------------------------*/
*lon = lon_center + x / R / (xlr[ip1 + 2] + p2 * (xlr[ip1 + 3] - xlr[ip1 + 1])
                      / 2.0 + p2 * p2 * (xlr[ip1 + 3] - 2.0 * xlr[ip1 + 2] + 
                      xlr[ip1 + 1]) / 2.0);
*lon = adjust_lon(*lon);

return(OK);
}
