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/*******************************************************************************
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(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(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 temp;
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);
}
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