blob: 56e3e9f591b5b0c84633cd4db0da07f6b66835aa [file] [log] [blame]
 #include #include #include "map.h" /* For Albers formulas see Deetz and Adams "Elements of Map Projection", */ /* USGS Special Publication No. 68, GPO 1921 */ static double r0sq, r1sq, d2, n, den, sinb1, sinb2; static struct coord plat1, plat2; static int southpole; static double num(double s) { if(d2==0) return(1); s = d2*s*s; return(1+s*(2./3+s*(3./5+s*(4./7+s*5./9)))); } /* Albers projection for a spheroid, good only when N pole is fixed */ static int Xspalbers(struct place *place, double *x, double *y) { double r = sqrt(r0sq-2*(1-d2)*place->nlat.s*num(place->nlat.s)/n); double t = n*place->wlon.l; *y = r*cos(t); *x = -r*sin(t); if(!southpole) *y = -*y; else *x = -*x; return(1); } /* lat1, lat2: std parallels; e2: squared eccentricity */ static proj albinit(double lat1, double lat2, double e2) { double r1; double t; for(;;) { if(lat1 < -90) lat1 = -180 - lat1; if(lat2 > 90) lat2 = 180 - lat2; if(lat1 <= lat2) break; t = lat1; lat1 = lat2; lat2 = t; } if(lat2-lat1 < 1) { if(lat1 > 89) return(azequalarea()); return(0); } if(fabs(lat2+lat1) < 1) return(cylequalarea(lat1)); d2 = e2; den = num(1.); deg2rad(lat1,&plat1); deg2rad(lat2,&plat2); sinb1 = plat1.s*num(plat1.s)/den; sinb2 = plat2.s*num(plat2.s)/den; n = (plat1.c*plat1.c/(1-e2*plat1.s*plat1.s) - plat2.c*plat2.c/(1-e2*plat2.s*plat2.s)) / (2*(1-e2)*den*(sinb2-sinb1)); r1 = plat1.c/(n*sqrt(1-e2*plat1.s*plat1.s)); r1sq = r1*r1; r0sq = r1sq + 2*(1-e2)*den*sinb1/n; southpole = lat1<0 && plat2.c>plat1.c; return(Xspalbers); } proj sp_albers(double lat1, double lat2) { return(albinit(lat1,lat2,EC2)); } proj albers(double lat1, double lat2) { return(albinit(lat1,lat2,0.)); } static double scale = 1; static double twist = 0; void albscale(double x, double y, double lat, double lon) { struct place place; double alat, alon, x1,y1; scale = 1; twist = 0; invalb(x,y,&alat,&alon); twist = lon - alon; deg2rad(lat,&place.nlat); deg2rad(lon,&place.wlon); Xspalbers(&place,&x1,&y1); scale = sqrt((x1*x1+y1*y1)/(x*x+y*y)); } void invalb(double x, double y, double *lat, double *lon) { int i; double sinb_den, sinp; x *= scale; y *= scale; *lon = atan2(-x,fabs(y))/(RAD*n) + twist; sinb_den = (r0sq - x*x - y*y)*n/(2*(1-d2)); sinp = sinb_den; for(i=0; i<5; i++) sinp = sinb_den/num(sinp); *lat = asin(sinp)/RAD; }