1 #include <u.h>
2 #include <libc.h>
3 #include "map.h"
4
5 #define BIG 1.e15
6 #define HFUZZ .0001
7
8 static double hcut[3] ;
9 static double kr[3] = { .5, -1., .5 };
10 static double ki[3] = { -1., 0., 1. }; /*to multiply by sqrt(3)/2*/
11 static double cr[3];
12 static double ci[3];
13 static struct place hem;
14 static struct coord twist;
15 static double rootroot3, hkc;
16 static double w2;
17 static double rootk;
18
19 static void
reflect(int i,double wr,double wi,double * x,double * y)20 reflect(int i, double wr, double wi, double *x, double *y)
21 {
22 double pr,pi,l;
23 pr = cr[i]-wr;
24 pi = ci[i]-wi;
25 l = 2*(kr[i]*pr + ki[i]*pi);
26 *x = wr + l*kr[i];
27 *y = wi + l*ki[i];
28 }
29
30 static int
Xhex(struct place * place,double * x,double * y)31 Xhex(struct place *place, double *x, double *y)
32 {
33 int ns;
34 register i;
35 double zr,zi;
36 double sr,si,tr,ti,ur,ui,vr,vi,yr,yi;
37 struct place p;
38 copyplace(place,&p);
39 ns = place->nlat.l >= 0;
40 if(!ns) {
41 p.nlat.l = -p.nlat.l;
42 p.nlat.s = -p.nlat.s;
43 }
44 if(p.nlat.l<HFUZZ) {
45 for(i=0;i<3;i++)
46 if(fabs(reduce(p.wlon.l-hcut[i]))<HFUZZ) {
47 if(i==2) {
48 *x = 2*cr[0] - cr[1];
49 *y = 0;
50 } else {
51 *x = cr[1];
52 *y = 2*ci[2*i];
53 }
54 return(1);
55 }
56 p.nlat.l = HFUZZ;
57 sincos(&p.nlat);
58 }
59 norm(&p,&hem,&twist);
60 Xstereographic(&p,&zr,&zi);
61 zr /= 2;
62 zi /= 2;
63 cdiv(1-zr,-zi,1+zr,zi,&sr,&si);
64 csq(sr,si,&tr,&ti);
65 ccubrt(1+3*tr,3*ti,&ur,&ui);
66 csqrt(ur-1,ui,&vr,&vi);
67 cdiv(rootroot3+vr,vi,rootroot3-vr,-vi,&yr,&yi);
68 yr /= rootk;
69 yi /= rootk;
70 elco2(fabs(yr),yi,hkc,1.,1.,x,y);
71 if(yr < 0)
72 *x = w2 - *x;
73 if(!ns) reflect(hcut[0]>place->wlon.l?0:
74 hcut[1]>=place->wlon.l?1:
75 2,*x,*y,x,y);
76 return(1);
77 }
78
79 proj
hex(void)80 hex(void)
81 {
82 register i;
83 double t;
84 double root3;
85 double c,d;
86 struct place p;
87 hcut[2] = PI;
88 hcut[1] = hcut[2]/3;
89 hcut[0] = -hcut[1];
90 root3 = sqrt(3.);
91 rootroot3 = sqrt(root3);
92 t = 15 -8*root3;
93 hkc = t*(1-sqrt(1-1/(t*t)));
94 elco2(BIG,0.,hkc,1.,1.,&w2,&t);
95 w2 *= 2;
96 rootk = sqrt(hkc);
97 latlon(90.,90.,&hem);
98 latlon(90.,0.,&p);
99 Xhex(&p,&c,&t);
100 latlon(0.,0.,&p);
101 Xhex(&p,&d,&t);
102 for(i=0;i<3;i++) {
103 ki[i] *= root3/2;
104 cr[i] = c + (c-d)*kr[i];
105 ci[i] = (c-d)*ki[i];
106 }
107 deg2rad(0.,&twist);
108 return(Xhex);
109 }
110
111 int
hexcut(struct place * g,struct place * og,double * cutlon)112 hexcut(struct place *g, struct place *og, double *cutlon)
113 {
114 int t,i;
115 if(g->nlat.l>=-HFUZZ&&og->nlat.l>=-HFUZZ)
116 return(1);
117 for(i=0;i<3;i++) {
118 t = ckcut(g,og,*cutlon=hcut[i]);
119 if(t!=1) return(t);
120 }
121 return(1);
122 }
123