ref: 8a4a2dea70aa77475a50968f4c5bd6cdab5d2fb1
dir: /sys/src/cmd/map/libmap/lune.c/
#include <u.h>
#include <libc.h>
#include "map.h"
int Xstereographic(struct place *place, double *x, double *y);
static struct place eastpole;
static struct place westpole;
static double eastx, easty;
static double westx, westy;
static double scale;
static double pwr;
/* conformal map w = ((1+z)^A - (1-z)^A)/((1+z)^A + (1-z)^A),
where A<1, maps unit circle onto a convex lune with x= +-1
mapping to vertices of angle A*PI at w = +-1 */
/* there are cuts from E and W poles to S pole,
in absence of a cut routine, error is returned for
points outside a polar cap through E and W poles */
static Xlune(struct place *place, double *x, double *y)
{
double stereox, stereoy;
double z1x, z1y, z2x, z2y;
double w1x, w1y, w2x, w2y;
double numx, numy, denx, deny;
if(place->nlat.l < eastpole.nlat.l-FUZZ)
return -1;
Xstereographic(place, &stereox, &stereoy);
stereox *= scale;
stereoy *= scale;
z1x = 1 + stereox;
z1y = stereoy;
z2x = 1 - stereox;
z2y = -stereoy;
cpow(z1x,z1y,&w1x,&w1y,pwr);
cpow(z2x,z2y,&w2x,&w2y,pwr);
numx = w1x - w2x;
numy = w1y - w2y;
denx = w1x + w2x;
deny = w1y + w2y;
cdiv(numx, numy, denx, deny, x, y);
return 1;
}
proj
lune(double lat, double theta)
{
deg2rad(lat, &eastpole.nlat);
deg2rad(-90.,&eastpole.wlon);
deg2rad(lat, &westpole.nlat);
deg2rad(90. ,&westpole.wlon);
Xstereographic(&eastpole, &eastx, &easty);
Xstereographic(&westpole, &westx, &westy);
if(fabs(easty)>FUZZ || fabs(westy)>FUZZ ||
fabs(eastx+westx)>FUZZ)
abort();
scale = 1/eastx;
pwr = theta/180;
return Xlune;
}