imolwfor.c

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/*******************************************************************************
NAME                        INTERRUPTED MOLLWEIDE
 
PURPOSE:        Transforms input longitude and latitude to Easting and
                Northing for the Interrupted Mollweide projection.  The
                longitude and latitude must be in radians.  The Easting
                and Northing values will be returned in meters.
 
ALGORITHM REFERENCES
 
1.  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.
 
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.
*******************************************************************************/
#include "oli_cproj.h"
#include "oli_local.h"
 
/* Variables common to all subroutines in this code file
  -----------------------------------------------------*/
static double R;        /* Radius of the earth (sphere) */
static double lon_center[6];    /* Central meridians, one for each region */
static double feast[6];     /* False easting, one for each region */
 
/* Initialize the Interrupted Mollweide projection
  --------------------------------------------*/
long imolwforint
(
    double r            /* (I) Radius of the earth (sphere) */
)
{
/* Place parameters in static storage for common use
  -------------------------------------------------*/
R = r;
 
/* Initialize central meridians for each of the 6 regions
  ------------------------------------------------------*/
lon_center[0] = 1.0471975512;       /*   60.0 degrees */
lon_center[1] = -2.96705972839;     /* -170.0 degrees */
lon_center[2] = -0.523598776;       /*  -30.0 degrees */
lon_center[3] =  1.57079632679;     /*   90.0 degrees */
lon_center[4] = -2.44346095279;     /* -140.0 degrees */
lon_center[5] = -0.34906585;        /*  -20.0 degrees */
 
/* Initialize false eastings for each of the 6 regions
  ---------------------------------------------------*/
feast[0] = R * -2.19988776387;
feast[1] = R * -0.15713484;
feast[2] = R * 2.04275292359;
feast[3] = R * -1.72848324304;
feast[4] = R * 0.31426968;
feast[5] = R * 2.19988776387;
 
/* Report parameters to the user
  -----------------------------*/
gctp_print_title("INTERRUPTED MOLLWEIDE EQUAL-AREA"); 
gctp_print_radius(r);
return(OK);
}

/* Interrupted Mollweide forward equations--mapping lat,long to x,y
  -------------------------------------------------------------*/
long imolwfor
(
    double lon,         /* (I) Longitude */
    double lat,         /* (I) Latitude */
    double *x,          /* (O) X projection coordinate */
    double *y           /* (O) Y projection coordinate */
)
{
double delta_lon;   /* Delta longitude (Given longitude - center */
double theta;
double delta_theta;
double con;
long i;
long region;
 
/* Forward equations
  -----------------*/
/* Note:  PI has been adjusted so that the correct region will be assigned
   when lon = 180 deg.
   ----------------------------------------------------------------------*/
if (lat >= 0.0)
   {
   if (lon >= 0.34906585 && lon < 1.91986217719) region = 0; 
   else if 
     ((lon >= 1.919862177 && lon <= (PI + 1.0E-14)) ||
                 (lon >= (-PI - 1.0E-14) && lon < -1.745329252))
        region=1; 
   else region = 2;
   }
else
   {
   if (lon >= 0.34906585 && lon < 2.44346095279) region = 3; 
   else if 
     ((lon >= 2.44346095279 && lon <= (PI +1.0E-14)) ||
                (lon >= (-PI - 1.0E-14) && lon<-1.2217304764))
        region=4; 
   else region = 5;
   }
 
delta_lon = adjust_lon(lon - lon_center[region]);
theta = lat;
con = PI * sin(lat);
 
/* Iterate using the Newton-Raphson method to find theta
  -----------------------------------------------------*/
for (i=0;;i++)
      {
      delta_theta = -(theta + sin(theta) - con) / (1.0 + cos(theta));
      theta += delta_theta;
      if (fabs(delta_theta) < EPSLN) break;
      if (i >= 50)
          GCTP_PRINT_ERROR("Iteration failed to converge");
      }
theta /= 2.0;
 
/* If the latitude is 90 deg, force the x coordinate to be "0 + false easting"
   this is done here because of percision problems with "cos(theta)"
   --------------------------------------------------------------------------*/
if (PI / 2 - fabs(lat) < EPSLN)
   delta_lon = 0;
*x = feast[region] + 0.900316316158 * R * delta_lon * cos(theta);
*y = R * 1.4142135623731 * sin(theta);
return(OK);
}