gps_conversions.h

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/* Taken from utexas-art-ros-pkg:art_vehicle/applanix */

/*
 * Conversions between coordinate systems.
 *
 * Includes LatLong<->UTM.
 */

#ifndef _UTM_H
#define _UTM_H

#include <cmath>
#include <cstdio>
#include <cstdlib>

namespace UTM
{

const double RADIANS_PER_DEGREE = M_PI/180.0;
const double DEGREES_PER_RADIAN = 180.0/M_PI;

// WGS84 Parameters
const double WGS84_A = 6378137.0;               // major axis
const double WGS84_B = 6356752.31424518;        // minor axis
const double WGS84_F = 0.0033528107;            // ellipsoid flattening
const double WGS84_E = 0.0818191908;            // first eccentricity
const double WGS84_EP = 0.0820944379;           // second eccentricity

// UTM Parameters
const double UTM_K0 = 0.9996;                   // scale factor
const double UTM_FE = 500000.0;                 // false easting
const double UTM_FN_N = 0.0;                    // false northing on north hemisphere
const double UTM_FN_S = 10000000.0;             // false northing on south hemisphere
const double UTM_E2 = (WGS84_E*WGS84_E);        // e^2
const double UTM_E4 = (UTM_E2*UTM_E2);          // e^4
const double UTM_E6 = (UTM_E4*UTM_E2);          // e^6
const double UTM_EP2 = (UTM_E2/(1-UTM_E2));     // e'^2

static inline void UTM(double lat, double lon, double *x, double *y)
{
        // constants
        const static double m0 = (1 - UTM_E2/4 - 3*UTM_E4/64 - 5*UTM_E6/256);
        const static double m1 = -(3*UTM_E2/8 + 3*UTM_E4/32 + 45*UTM_E6/1024);
        const static double m2 = (15*UTM_E4/256 + 45*UTM_E6/1024);
        const static double m3 = -(35*UTM_E6/3072);

        // compute the central meridian
        int cm = ((lon >= 0.0)
                        ? ((int)lon - ((int)lon)%6 + 3)
                        : ((int)lon - ((int)lon)%6 - 3));

        // convert degrees into radians
        double rlat = lat * RADIANS_PER_DEGREE;
        double rlon = lon * RADIANS_PER_DEGREE;
        double rlon0 = cm * RADIANS_PER_DEGREE;

        // compute trigonometric functions
        double slat = sin(rlat);
        double clat = cos(rlat);
        double tlat = tan(rlat);

        // decide the false northing at origin
        double fn = (lat > 0) ? UTM_FN_N : UTM_FN_S;

        double T = tlat * tlat;
        double C = UTM_EP2 * clat * clat;
        double A = (rlon - rlon0) * clat;
        double M = WGS84_A * (m0*rlat + m1*sin(2*rlat)
                        + m2*sin(4*rlat) + m3*sin(6*rlat));
        double V = WGS84_A / sqrt(1 - UTM_E2*slat*slat);

        // compute the easting-northing coordinates
        *x = UTM_FE + UTM_K0 * V * (A + (1-T+C)*pow(A,3)/6
                        + (5-18*T+T*T+72*C-58*UTM_EP2)*pow(A,5)/120);
        *y = fn + UTM_K0 * (M + V * tlat * (A*A/2
                                + (5-T+9*C+4*C*C)*pow(A,4)/24
                                + ((61-58*T+T*T+600*C-330*UTM_EP2)
                                        * pow(A,6)/720)));

        return;
}


static inline char UTMLetterDesignator(double Lat)
{
        char LetterDesignator;

        if     ((84 >= Lat) && (Lat >= 72))  LetterDesignator = 'X';
        else if ((72 > Lat) && (Lat >= 64))  LetterDesignator = 'W';
        else if ((64 > Lat) && (Lat >= 56))  LetterDesignator = 'V';
        else if ((56 > Lat) && (Lat >= 48))  LetterDesignator = 'U';
        else if ((48 > Lat) && (Lat >= 40))  LetterDesignator = 'T';
        else if ((40 > Lat) && (Lat >= 32))  LetterDesignator = 'S';
        else if ((32 > Lat) && (Lat >= 24))  LetterDesignator = 'R';
        else if ((24 > Lat) && (Lat >= 16))  LetterDesignator = 'Q';
        else if ((16 > Lat) && (Lat >= 8))   LetterDesignator = 'P';
        else if (( 8 > Lat) && (Lat >= 0))   LetterDesignator = 'N';
        else if (( 0 > Lat) && (Lat >= -8))  LetterDesignator = 'M';
        else if ((-8 > Lat) && (Lat >= -16)) LetterDesignator = 'L';
        else if((-16 > Lat) && (Lat >= -24)) LetterDesignator = 'K';
        else if((-24 > Lat) && (Lat >= -32)) LetterDesignator = 'J';
        else if((-32 > Lat) && (Lat >= -40)) LetterDesignator = 'H';
        else if((-40 > Lat) && (Lat >= -48)) LetterDesignator = 'G';
        else if((-48 > Lat) && (Lat >= -56)) LetterDesignator = 'F';
        else if((-56 > Lat) && (Lat >= -64)) LetterDesignator = 'E';
        else if((-64 > Lat) && (Lat >= -72)) LetterDesignator = 'D';
        else if((-72 > Lat) && (Lat >= -80)) LetterDesignator = 'C';
        // 'Z' is an error flag, the Latitude is outside the UTM limits
        else LetterDesignator = 'Z';
        return LetterDesignator;
}

static inline void LLtoUTM(const double Lat, const double Long,
                double &UTMNorthing, double &UTMEasting,
                char* UTMZone)
{
        double a = WGS84_A;
        double eccSquared = UTM_E2;
        double k0 = UTM_K0;

        double LongOrigin;
        double eccPrimeSquared;
        double N, T, C, A, M;

        //Make sure the longitude is between -180.00 .. 179.9
        double LongTemp = (Long+180)-int((Long+180)/360)*360-180;

        double LatRad = Lat*RADIANS_PER_DEGREE;
        double LongRad = LongTemp*RADIANS_PER_DEGREE;
        double LongOriginRad;
        int    ZoneNumber;

        ZoneNumber = int((LongTemp + 180)/6) + 1;

        if( Lat >= 56.0 && Lat < 64.0 && LongTemp >= 3.0 && LongTemp < 12.0 )
                ZoneNumber = 32;

        // Special zones for Svalbard
        if( Lat >= 72.0 && Lat < 84.0 )
        {
                if(      LongTemp >= 0.0  && LongTemp <  9.0 ) ZoneNumber = 31;
                else if( LongTemp >= 9.0  && LongTemp < 21.0 ) ZoneNumber = 33;
                else if( LongTemp >= 21.0 && LongTemp < 33.0 ) ZoneNumber = 35;
                else if( LongTemp >= 33.0 && LongTemp < 42.0 ) ZoneNumber = 37;
        }
        // +3 puts origin in middle of zone
        LongOrigin = (ZoneNumber - 1)*6 - 180 + 3;
        LongOriginRad = LongOrigin * RADIANS_PER_DEGREE;

        //compute the UTM Zone from the latitude and longitude
        snprintf(UTMZone, 4, "%d%c", ZoneNumber, UTMLetterDesignator(Lat));

        eccPrimeSquared = (eccSquared)/(1-eccSquared);

        N = a/sqrt(1-eccSquared*sin(LatRad)*sin(LatRad));
        T = tan(LatRad)*tan(LatRad);
        C = eccPrimeSquared*cos(LatRad)*cos(LatRad);
        A = cos(LatRad)*(LongRad-LongOriginRad);

        M = a*((1       - eccSquared/4          - 3*eccSquared*eccSquared/64    - 5*eccSquared*eccSquared*eccSquared/256)*LatRad
                        - (3*eccSquared/8       + 3*eccSquared*eccSquared/32    + 45*eccSquared*eccSquared*eccSquared/1024)*sin(2*LatRad)
                        + (15*eccSquared*eccSquared/256 + 45*eccSquared*eccSquared*eccSquared/1024)*sin(4*LatRad)
                        - (35*eccSquared*eccSquared*eccSquared/3072)*sin(6*LatRad));

        UTMEasting = (double)(k0*N*(A+(1-T+C)*A*A*A/6
                                + (5-18*T+T*T+72*C-58*eccPrimeSquared)*A*A*A*A*A/120)
                        + 500000.0);

        UTMNorthing = (double)(k0*(M+N*tan(LatRad)*(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24
                                        + (61-58*T+T*T+600*C-330*eccPrimeSquared)*A*A*A*A*A*A/720)));
        if(Lat < 0)
                UTMNorthing += 10000000.0; //10000000 meter offset for southern hemisphere
}

static inline void LLtoUTM(const double Lat, const double Long,
                double &UTMNorthing, double &UTMEasting,
                std::string &UTMZone) {
        char zone_buf[] = {0, 0, 0, 0};

        LLtoUTM(Lat, Long, UTMNorthing, UTMEasting, zone_buf);

        UTMZone = zone_buf;
}


static inline void UTMtoLL(const double UTMNorthing, const double UTMEasting,
                const char* UTMZone, double& Lat,  double& Long )
{
        double k0 = UTM_K0;
        double a = WGS84_A;
        double eccSquared = UTM_E2;
        double eccPrimeSquared;
        double e1 = (1-sqrt(1-eccSquared))/(1+sqrt(1-eccSquared));
        double N1, T1, C1, R1, D, M;
        double LongOrigin;
        double mu, phi1, phi1Rad;
        double x, y;
        int ZoneNumber;
        char* ZoneLetter;
        int NorthernHemisphere; //1 for northern hemispher, 0 for southern

        x = UTMEasting - 500000.0; //remove 500,000 meter offset for longitude
        y = UTMNorthing;

        ZoneNumber = strtoul(UTMZone, &ZoneLetter, 10);
        if((*ZoneLetter - 'N') >= 0)
                NorthernHemisphere = 1;//point is in northern hemisphere
        else
        {
                NorthernHemisphere = 0;//point is in southern hemisphere
                y -= 10000000.0;//remove 10,000,000 meter offset used for southern hemisphere
        }

        LongOrigin = (ZoneNumber - 1)*6 - 180 + 3;  //+3 puts origin in middle of zone

        eccPrimeSquared = (eccSquared)/(1-eccSquared);

        M = y / k0;
        mu = M/(a*(1-eccSquared/4-3*eccSquared*eccSquared/64-5*eccSquared*eccSquared*eccSquared/256));

        phi1Rad = mu    + (3*e1/2-27*e1*e1*e1/32)*sin(2*mu)
                + (21*e1*e1/16-55*e1*e1*e1*e1/32)*sin(4*mu)
                +(151*e1*e1*e1/96)*sin(6*mu);
        phi1 = phi1Rad*DEGREES_PER_RADIAN;

        N1 = a/sqrt(1-eccSquared*sin(phi1Rad)*sin(phi1Rad));
        T1 = tan(phi1Rad)*tan(phi1Rad);
        C1 = eccPrimeSquared*cos(phi1Rad)*cos(phi1Rad);
        R1 = a*(1-eccSquared)/pow(1-eccSquared*sin(phi1Rad)*sin(phi1Rad), 1.5);
        D = x/(N1*k0);

        Lat = phi1Rad - (N1*tan(phi1Rad)/R1)*(D*D/2-(5+3*T1+10*C1-4*C1*C1-9*eccPrimeSquared)*D*D*D*D/24
                        +(61+90*T1+298*C1+45*T1*T1-252*eccPrimeSquared-3*C1*C1)*D*D*D*D*D*D/720);
        Lat = Lat * DEGREES_PER_RADIAN;

        Long = (D-(1+2*T1+C1)*D*D*D/6+(5-2*C1+28*T1-3*C1*C1+8*eccPrimeSquared+24*T1*T1)
                        *D*D*D*D*D/120)/cos(phi1Rad);
        Long = LongOrigin + Long * DEGREES_PER_RADIAN;
}

static inline void UTMtoLL(const double UTMNorthing, const double UTMEasting,
                std::string UTMZone, double& Lat, double& Long) {
        UTMtoLL(UTMNorthing, UTMEasting, UTMZone.c_str(), Lat, Long);
}

}; // end namespace UTM

#endif // _UTM_H