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#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 int 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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