proj_robinv.c

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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 "proj_cproj.h"
#include <stdint.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
  ---------------------------------*/
int 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           */
{
    int32_t 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;
 
    return (OK);
}
 
/* Robinson inverse equations--mapping x,y to lat/long
  ------------------------------------------------------------*/
int 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 adjust_lon();
    double yy;
    double p2;
    double u, v, t, c;
    double phid;
    double y1;
    int32_t ip1;
    int32_t 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 = (int32_t) (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 = (int32_t) (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);
    if ((*lon < (-PI)) || (*lon > PI))
        return -1;
    /*
     *lon = adjust_lon(*lon);
     */
    return (OK);
}