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#include <u.h>
#include <libc.h>
#include "map.h"
#define BIG 1.e15
#define HFUZZ .0001
static double hcut[3] ;
static double kr[3] = { .5, -1., .5 };
static double ki[3] = { -1., 0., 1. }; /*to multiply by sqrt(3)/2*/
static double cr[3];
static double ci[3];
static struct place hem;
static struct coord twist;
static double rootroot3, hkc;
static double w2;
static double rootk;
static void
reflect(int i, double wr, double wi, double *x, double *y)
{
double pr,pi,l;
pr = cr[i]-wr;
pi = ci[i]-wi;
l = 2*(kr[i]*pr + ki[i]*pi);
*x = wr + l*kr[i];
*y = wi + l*ki[i];
}
static int
Xhex(struct place *place, double *x, double *y)
{
int ns;
int i;
double zr,zi;
double sr,si,tr,ti,ur,ui,vr,vi,yr,yi;
struct place p;
copyplace(place,&p);
ns = place->nlat.l >= 0;
if(!ns) {
p.nlat.l = -p.nlat.l;
p.nlat.s = -p.nlat.s;
}
if(p.nlat.l<HFUZZ) {
for(i=0;i<3;i++)
if(fabs(reduce(p.wlon.l-hcut[i]))<HFUZZ) {
if(i==2) {
*x = 2*cr[0] - cr[1];
*y = 0;
} else {
*x = cr[1];
*y = 2*ci[2*i];
}
return(1);
}
p.nlat.l = HFUZZ;
sincos(&p.nlat);
}
norm(&p,&hem,&twist);
Xstereographic(&p,&zr,&zi);
zr /= 2;
zi /= 2;
cdiv(1-zr,-zi,1+zr,zi,&sr,&si);
csq(sr,si,&tr,&ti);
ccubrt(1+3*tr,3*ti,&ur,&ui);
csqrt(ur-1,ui,&vr,&vi);
cdiv(rootroot3+vr,vi,rootroot3-vr,-vi,&yr,&yi);
yr /= rootk;
yi /= rootk;
elco2(fabs(yr),yi,hkc,1.,1.,x,y);
if(yr < 0)
*x = w2 - *x;
if(!ns) reflect(hcut[0]>place->wlon.l?0:
hcut[1]>=place->wlon.l?1:
2,*x,*y,x,y);
return(1);
}
proj
hex(void)
{
int i;
double t;
double root3;
double c,d;
struct place p;
hcut[2] = PI;
hcut[1] = hcut[2]/3;
hcut[0] = -hcut[1];
root3 = sqrt(3.);
rootroot3 = sqrt(root3);
t = 15 -8*root3;
hkc = t*(1-sqrt(1-1/(t*t)));
elco2(BIG,0.,hkc,1.,1.,&w2,&t);
w2 *= 2;
rootk = sqrt(hkc);
latlon(90.,90.,&hem);
latlon(90.,0.,&p);
Xhex(&p,&c,&t);
latlon(0.,0.,&p);
Xhex(&p,&d,&t);
for(i=0;i<3;i++) {
ki[i] *= root3/2;
cr[i] = c + (c-d)*kr[i];
ci[i] = (c-d)*ki[i];
}
deg2rad(0.,&twist);
return(Xhex);
}
int
hexcut(struct place *g, struct place *og, double *cutlon)
{
int t,i;
if(g->nlat.l>=-HFUZZ&&og->nlat.l>=-HFUZZ)
return(1);
for(i=0;i<3;i++) {
t = ckcut(g,og,*cutlon=hcut[i]);
if(t!=1) return(t);
}
return(1);
}
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