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Annotation of researchv10no/cmd/map/libmap/albers.c, revision 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 double r0sq, r1sq, d2, n, den, sinb1, sinb2;
        !             7: static struct coord plat1, plat2;
        !             8: static southpole;
        !             9: 
        !            10: static double num(double s)
        !            11: {
        !            12:        if(d2==0)
        !            13:                return(1);
        !            14:        s = d2*s*s;
        !            15:        return(1+s*(2./3+s*(3./5+s*(4./7+s*5./9))));
        !            16: }
        !            17: 
        !            18: /* Albers projection for a spheroid, good only when N pole is fixed */
        !            19: 
        !            20: static int
        !            21: Xspalbers(struct place *place, double *x, double *y)
        !            22: {
        !            23:        double r = sqrt(r0sq-2*(1-d2)*place->nlat.s*num(place->nlat.s)/n);
        !            24:        double t = n*place->wlon.l;
        !            25:        *y = r*cos(t);
        !            26:        *x = -r*sin(t);
        !            27:        if(!southpole)
        !            28:                *y = -*y;
        !            29:        else
        !            30:                *x = -*x;
        !            31:        return(1);
        !            32: }
        !            33: 
        !            34: /* lat1, lat2: std parallels; e2: squared eccentricity */
        !            35: 
        !            36: static proj albinit(double lat1, double lat2, double e2)
        !            37: {
        !            38:        double r1,r2;
        !            39:        double t;
        !            40:        for(;;) {
        !            41:                if(lat1 < -90)
        !            42:                        lat1 = -180 - lat1;
        !            43:                if(lat2 > 90)
        !            44:                        lat2 = 180 - lat2;
        !            45:                if(lat1 <= lat2)
        !            46:                        break;
        !            47:                t = lat1; lat1 = lat2; lat2 = t;
        !            48:        }
        !            49:        if(lat2-lat1 < 1) {
        !            50:                if(lat1 > 89)
        !            51:                        return(azequalarea());
        !            52:                return(0);
        !            53:        }
        !            54:        if(fabs(lat2+lat1) < 1)
        !            55:                return(cylequalarea(lat1));
        !            56:        d2 = e2;
        !            57:        den = num(1.);
        !            58:        deg2rad(lat1,&plat1);
        !            59:        deg2rad(lat2,&plat2);
        !            60:        sinb1 = plat1.s*num(plat1.s)/den;
        !            61:        sinb2 = plat2.s*num(plat2.s)/den;
        !            62:        n = (plat1.c*plat1.c/(1-e2*plat1.s*plat1.s) -
        !            63:            plat2.c*plat2.c/(1-e2*plat2.s*plat2.s)) /
        !            64:            (2*(1-e2)*den*(sinb2-sinb1));
        !            65:        r1 = plat1.c/(n*sqrt(1-e2*plat1.s*plat1.s));
        !            66:        r2 = plat2.c/(n*sqrt(2-e2*plat2.s*plat2.s));
        !            67:        r1sq = r1*r1;
        !            68:        r0sq = r1sq + 2*(1-e2)*den*sinb1/n;
        !            69:        southpole = lat1<0 && plat2.c>plat1.c;
        !            70:        return(Xspalbers);
        !            71: }
        !            72: 
        !            73: proj
        !            74: sp_albers(double lat1, double lat2)
        !            75: {
        !            76:        return(albinit(lat1,lat2,EC2));
        !            77: }
        !            78: 
        !            79: proj
        !            80: albers(double lat1, double lat2)
        !            81: {
        !            82:        return(albinit(lat1,lat2,0.));
        !            83: }
        !            84: 
        !            85: static double scale = 1;
        !            86: static double twist = 0;
        !            87: 
        !            88: void
        !            89: albscale(double x, double y, double lat, double lon)
        !            90: {
        !            91:        struct place place;
        !            92:        double alat, alon, x1,y1;
        !            93:        scale = 1;
        !            94:        twist = 0;
        !            95:        invalb(x,y,&alat,&alon);
        !            96:        twist = lon - alon;
        !            97:        deg2rad(lat,&place.nlat);
        !            98:        deg2rad(lon,&place.wlon);
        !            99:        Xspalbers(&place,&x1,&y1);
        !           100:        scale = sqrt((x1*x1+y1*y1)/(x*x+y*y));
        !           101: }
        !           102: 
        !           103: void
        !           104: invalb(double x, double y, double *lat, double *lon)
        !           105: {
        !           106:        int i;
        !           107:        double sinb_den, sinp;
        !           108:        x *= scale;
        !           109:        y *= scale;
        !           110:        *lon = atan2(-x,fabs(y))/(RAD*n) + twist;
        !           111:        sinb_den = (r0sq - x*x - y*y)*n/(2*(1-d2));
        !           112:        sinp = sinb_den;
        !           113:        for(i=0; i<5; i++)
        !           114:                sinp = sinb_den/num(sinp);
        !           115:        *lat = asin(sinp)/RAD;
        !           116: }

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