1 #include <u.h>
2 #include <libc.h>
3 #include "map.h"
4
5 int Xstereographic(struct place *place, double *x, double *y);
6
7 static struct place eastpole;
8 static struct place westpole;
9 static double eastx, easty;
10 static double westx, westy;
11 static double scale;
12 static double pwr;
13
14 /* conformal map w = ((1+z)^A - (1-z)^A)/((1+z)^A + (1-z)^A),
15 where A<1, maps unit circle onto a convex lune with x= +-1
16 mapping to vertices of angle A*PI at w = +-1 */
17
18 /* there are cuts from E and W poles to S pole,
19 in absence of a cut routine, error is returned for
20 points outside a polar cap through E and W poles */
21
Xlune(struct place * place,double * x,double * y)22 static Xlune(struct place *place, double *x, double *y)
23 {
24 double stereox, stereoy;
25 double z1x, z1y, z2x, z2y;
26 double w1x, w1y, w2x, w2y;
27 double numx, numy, denx, deny;
28 if(place->nlat.l < eastpole.nlat.l-FUZZ)
29 return -1;
30 Xstereographic(place, &stereox, &stereoy);
31 stereox *= scale;
32 stereoy *= scale;
33 z1x = 1 + stereox;
34 z1y = stereoy;
35 z2x = 1 - stereox;
36 z2y = -stereoy;
37 cpow(z1x,z1y,&w1x,&w1y,pwr);
38 cpow(z2x,z2y,&w2x,&w2y,pwr);
39 numx = w1x - w2x;
40 numy = w1y - w2y;
41 denx = w1x + w2x;
42 deny = w1y + w2y;
43 cdiv(numx, numy, denx, deny, x, y);
44 return 1;
45 }
46
47 proj
lune(double lat,double theta)48 lune(double lat, double theta)
49 {
50 deg2rad(lat, &eastpole.nlat);
51 deg2rad(-90.,&eastpole.wlon);
52 deg2rad(lat, &westpole.nlat);
53 deg2rad(90. ,&westpole.wlon);
54 Xstereographic(&eastpole, &eastx, &easty);
55 Xstereographic(&westpole, &westx, &westy);
56 if(fabs(easty)>FUZZ || fabs(westy)>FUZZ ||
57 fabs(eastx+westx)>FUZZ)
58 abort();
59 scale = 1/eastx;
60 pwr = theta/180;
61 return Xlune;
62 }
63