1 #include <u.h>
2 #include <libc.h>
3 #include "map.h"
4 
5 /* For Albers formulas see Deetz and Adams "Elements of Map Projection", */
6 /* USGS Special Publication No. 68, GPO 1921 */
7 
8 static double r0sq, r1sq, d2, n, den, sinb1, sinb2;
9 static struct coord plat1, plat2;
10 static int southpole;
11 
12 static double num(double s)
13 {
14 	if(d2==0)
15 		return(1);
16 	s = d2*s*s;
17 	return(1+s*(2./3+s*(3./5+s*(4./7+s*5./9))));
18 }
19 
20 /* Albers projection for a spheroid, good only when N pole is fixed */
21 
22 static int
23 Xspalbers(struct place *place, double *x, double *y)
24 {
25 	double r = sqrt(r0sq-2*(1-d2)*place->nlat.s*num(place->nlat.s)/n);
26 	double t = n*place->wlon.l;
27 	*y = r*cos(t);
28 	*x = -r*sin(t);
29 	if(!southpole)
30 		*y = -*y;
31 	else
32 		*x = -*x;
33 	return(1);
34 }
35 
36 /* lat1, lat2: std parallels; e2: squared eccentricity */
37 
38 static proj albinit(double lat1, double lat2, double e2)
39 {
40 	double r1;
41 	double t;
42 	for(;;) {
43 		if(lat1 < -90)
44 			lat1 = -180 - lat1;
45 		if(lat2 > 90)
46 			lat2 = 180 - lat2;
47 		if(lat1 <= lat2)
48 			break;
49 		t = lat1; lat1 = lat2; lat2 = t;
50 	}
51 	if(lat2-lat1 < 1) {
52 		if(lat1 > 89)
53 			return(azequalarea());
54 		return(0);
55 	}
56 	if(fabs(lat2+lat1) < 1)
57 		return(cylequalarea(lat1));
58 	d2 = e2;
59 	den = num(1.);
60 	deg2rad(lat1,&plat1);
61 	deg2rad(lat2,&plat2);
62 	sinb1 = plat1.s*num(plat1.s)/den;
63 	sinb2 = plat2.s*num(plat2.s)/den;
64 	n = (plat1.c*plat1.c/(1-e2*plat1.s*plat1.s) -
65 	    plat2.c*plat2.c/(1-e2*plat2.s*plat2.s)) /
66 	    (2*(1-e2)*den*(sinb2-sinb1));
67 	r1 = plat1.c/(n*sqrt(1-e2*plat1.s*plat1.s));
68 	r1sq = r1*r1;
69 	r0sq = r1sq + 2*(1-e2)*den*sinb1/n;
70 	southpole = lat1<0 && plat2.c>plat1.c;
71 	return(Xspalbers);
72 }
73 
74 proj
75 sp_albers(double lat1, double lat2)
76 {
77 	return(albinit(lat1,lat2,EC2));
78 }
79 
80 proj
81 albers(double lat1, double lat2)
82 {
83 	return(albinit(lat1,lat2,0.));
84 }
85 
86 static double scale = 1;
87 static double twist = 0;
88 
89 void
90 albscale(double x, double y, double lat, double lon)
91 {
92 	struct place place;
93 	double alat, alon, x1,y1;
94 	scale = 1;
95 	twist = 0;
96 	invalb(x,y,&alat,&alon);
97 	twist = lon - alon;
98 	deg2rad(lat,&place.nlat);
99 	deg2rad(lon,&place.wlon);
100 	Xspalbers(&place,&x1,&y1);
101 	scale = sqrt((x1*x1+y1*y1)/(x*x+y*y));
102 }
103 
104 void
105 invalb(double x, double y, double *lat, double *lon)
106 {
107 	int i;
108 	double sinb_den, sinp;
109 	x *= scale;
110 	y *= scale;
111 	*lon = atan2(-x,fabs(y))/(RAD*n) + twist;
112 	sinb_den = (r0sq - x*x - y*y)*n/(2*(1-d2));
113 	sinp = sinb_den;
114 	for(i=0; i<5; i++)
115 		sinp = sinb_den/num(sinp);
116 	*lat = asin(sinp)/RAD;
117 }