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Annotation of researchv8dc/cmd/map/libmap/albers.c, revision 1.1.1.1

1.1       root        1: #include "map.h"
                      2: 
                      3: /* For Albers formulas see Deetz and Adams "Elements of Map Projection", */
                      4: /* USGS Special Publication No. 68, GPO 1921 */
                      5: 
                      6: static float r0sq, r1sq, d2, n, den, sinb1, sinb2;
                      7: static struct place plat1, plat2;
                      8: static southpole;
                      9: 
                     10: static float num(s)
                     11: float s;
                     12: {
                     13:        if(d2==0)
                     14:                return(1);
                     15:        s = d2*s*s;
                     16:        return(1+s*(2./3+s*(3./5+s*(4./7+s*5./9))));
                     17: }
                     18: 
                     19: /* Albers projection for a spheroid, good only when N pole is fixed */
                     20: 
                     21: static int
                     22: Xspalbers(place,x,y)
                     23: struct place *place;
                     24: float *x, *y;
                     25: {
                     26:        float r = sqrt(r0sq-2*(1-d2)*place->nlat.s*num(place->nlat.s)/n);
                     27:        float t = n*place->wlon.l;
                     28:        *y = r*cos(t);
                     29:        if(!southpole)
                     30:                *y = -*y;
                     31:        *x = -r*sin(t);
                     32:        return(1);
                     33: }
                     34: 
                     35: /* lat1, lat2: std parallels; e2: squared eccentricity */
                     36: 
                     37: int (*albinit(lat1,lat2,e2))()
                     38: float lat1,lat2,e2;
                     39: {
                     40:        float r1,r2;
                     41:        extern (*azequalarea())();
                     42:        extern (*cylequalarea())();
                     43:        float t;
                     44:        for(;;) {
                     45:                if(lat1 < -90)
                     46:                        lat1 = -180 - lat1;
                     47:                if(lat2 > 90)
                     48:                        lat2 = 180 - lat2;
                     49:                if(lat1 <= lat2)
                     50:                        break;
                     51:                t = lat1; lat1 = lat2; lat2 = t;
                     52:        }
                     53:        if(lat2-lat1 < 1) {
                     54:                if(lat1 > 89)
                     55:                        return(azequalarea());
                     56:                return(0);
                     57:        }
                     58:        if(fabs(lat2+lat1) < 1)
                     59:                return(cylequalarea(lat1));
                     60:        d2 = e2;
                     61:        den = num(1.);
                     62:        deg2rad(lat1,&plat1);
                     63:        deg2rad(lat2,&plat2);
                     64:        sinb1 = plat1.nlat.s*num(plat1.nlat.s)/den;
                     65:        sinb2 = plat2.nlat.s*num(plat2.nlat.s)/den;
                     66:        n = (plat1.nlat.c*plat1.nlat.c/(1-e2*plat1.nlat.s*plat1.nlat.s) -
                     67:            plat2.nlat.c*plat2.nlat.c/(1-e2*plat2.nlat.s*plat2.nlat.s)) /
                     68:            (2*(1-e2)*den*(sinb2-sinb1));
                     69:        r1 = plat1.nlat.c/(n*sqrt(1-e2*plat1.nlat.s*plat1.nlat.s));
                     70:        r2 = plat2.nlat.c/(n*sqrt(2-e2*plat2.nlat.s*plat2.nlat.s));
                     71:        r1sq = r1*r1;
                     72:        r0sq = r1sq + 2*(1-e2)*den*sinb1/n;
                     73:        southpole = lat1<0 && plat2.nlat.c>plat1.nlat.c;
                     74:        return(Xspalbers);
                     75: }
                     76: 
                     77: int (*sp_albers(lat1,lat2))()
                     78: float lat1, lat2;
                     79: {
                     80:        return(albinit(lat1,lat2,EC2));
                     81: }
                     82: 
                     83: int (*albers(lat1,lat2))()
                     84: float lat1,lat2;
                     85: {
                     86:        return(albinit(lat1,lat2,0.));
                     87: }
                     88: 
                     89: static float scale = 1;
                     90: static float twist = 0;
                     91: 
                     92: albscale(x,y,lat,lon)
                     93: float x,y,lat,lon;
                     94: {
                     95:        struct place place;
                     96:        float alat, alon, x1,y1;
                     97:        scale = 1;
                     98:        twist = 0;
                     99:        invalb(x,y,&alat,&alon);
                    100:        twist = lon - alon;
                    101:        deg2rad(lat,&place.nlat);
                    102:        deg2rad(lon,&place.wlon);
                    103:        Xspalbers(&place,&x1,&y1);
                    104:        scale = sqrt((x1*x1+y1*y1)/(x*x+y*y));
                    105: }
                    106: 
                    107: invalb(x,y,lat,lon)
                    108: float x,y,*lat,*lon;
                    109: {
                    110:        int i;
                    111:        float sinb_den, sinp;
                    112:        x *= scale;
                    113:        y *= scale;
                    114:        *lon = atan2(-x,fabs(y))/(RAD*n) + twist;
                    115:        sinb_den = (r0sq - x*x - y*y)*n/(2*(1-d2));
                    116:        sinp = sinb_den;
                    117:        for(i=0; i<5; i++)
                    118:                sinp = sinb_den/num(sinp);
                    119:        *lat = asin(sinp)/RAD;
                    120: }

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