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albers.c

/* RSB #include <u.h>
#include <libc.h> */
#include "map.h"

/* For Albers formulas see Deetz and Adams "Elements of Map Projection", */
/* USGS Special Publication No. 68, GPO 1921 */

static double r0sq, r1sq, d2, n, den, sinb1, sinb2;
static struct coord plat1, plat2;
static southpole;

static double num(double s)
{
      if(d2==0)
            return(1);
      s = d2*s*s;
      return(1+s*(2./3+s*(3./5+s*(4./7+s*5./9))));
}

/* Albers projection for a spheroid, good only when N pole is fixed */

static int
Xspalbers(struct place *place, double *x, double *y)
{
      double r = sqrt(r0sq-2*(1-d2)*place->nlat.s*num(place->nlat.s)/n);
      double t = n*place->wlon.l;
      *y = r*cos(t);
      *x = -r*sin(t);
      if(!southpole)
            *y = -*y;
      else
            *x = -*x;
      return(1);
}

/* lat1, lat2: std parallels; e2: squared eccentricity */

static proj albinit(double lat1, double lat2, double e2)
{
      double r1;
      double t;
      for(;;) {
            if(lat1 < -90)
                  lat1 = -180 - lat1;
            if(lat2 > 90)
                  lat2 = 180 - lat2;
            if(lat1 <= lat2)
                  break;
            t = lat1; lat1 = lat2; lat2 = t;
      }
      if(lat2-lat1 < 1) {
            if(lat1 > 89)
                  return(azequalarea());
            return(0);
      }
      if(fabs(lat2+lat1) < 1)
            return(cylequalarea(lat1));
      d2 = e2;
      den = num(1.);
      deg2rad(lat1,&plat1);
      deg2rad(lat2,&plat2);
      sinb1 = plat1.s*num(plat1.s)/den;
      sinb2 = plat2.s*num(plat2.s)/den;
      n = (plat1.c*plat1.c/(1-e2*plat1.s*plat1.s) -
          plat2.c*plat2.c/(1-e2*plat2.s*plat2.s)) /
          (2*(1-e2)*den*(sinb2-sinb1));
      r1 = plat1.c/(n*sqrt(1-e2*plat1.s*plat1.s));
      r1sq = r1*r1;
      r0sq = r1sq + 2*(1-e2)*den*sinb1/n;
      southpole = lat1<0 && plat2.c>plat1.c;
      return(Xspalbers);
}

proj
sp_albers(double lat1, double lat2)
{
      return(albinit(lat1,lat2,EC2));
}

proj
albers(double lat1, double lat2)
{
      return(albinit(lat1,lat2,0.));
}

static double scale = 1;
static double twist = 0;

void
albscale(double x, double y, double lat, double lon)
{
      struct place place;
      double alat, alon, x1,y1;
      scale = 1;
      twist = 0;
      invalb(x,y,&alat,&alon);
      twist = lon - alon;
      deg2rad(lat,&place.nlat);
      deg2rad(lon,&place.wlon);
      Xspalbers(&place,&x1,&y1);
      scale = sqrt((x1*x1+y1*y1)/(x*x+y*y));
}

void
invalb(double x, double y, double *lat, double *lon)
{
      int i;
      double sinb_den, sinp;
      x *= scale;
      y *= scale;
      *lon = atan2(-x,fabs(y))/(RAD*n) + twist;
      sinb_den = (r0sq - x*x - y*y)*n/(2*(1-d2));
      sinp = sinb_den;
      for(i=0; i<5; i++)
            sinp = sinb_den/num(sinp);
      *lat = asin(sinp)/RAD;
}

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