UTM.h

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/* -*- mode: C++ -*-
 *
 *  Conversions between Latitude/Longitude and UTM
 *              (Universal Transverse Mercator) coordinates.
 *
 *  License: Modified BSD Software License Agreement
 *
 *  $Id: UTM.h 1876 2011-11-26 23:48:08Z jack.oquin $
 */

#ifndef _UTM_H
#define _UTM_H

#include <cmath>
#include <stdio.h>
#include <stdlib.h>

#include <art/conversions.h>

namespace UTM
{
  // Grid granularity for rounding UTM coordinates to generate MapXY.
  const double grid_size = 100000.0;    // 100 km grid

// WGS84 Parameters
#define WGS84_A         6378137.0               // major axis
#define WGS84_B         6356752.31424518        // minor axis
#define WGS84_F         0.0033528107            // ellipsoid flattening
#define WGS84_E         0.0818191908            // first eccentricity
#define WGS84_EP        0.0820944379            // second eccentricity

// UTM Parameters
#define UTM_K0          0.9996                  // scale factor
#define UTM_FE          500000.0                // false easting
#define UTM_FN_N        0.0           // false northing, northern hemisphere
#define UTM_FN_S        10000000.0    // false northing, southern hemisphere
#define UTM_E2          (WGS84_E*WGS84_E)       // e^2
#define UTM_E4          (UTM_E2*UTM_E2)         // e^4
#define UTM_E6          (UTM_E4*UTM_E2)         // e^6
#define 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
        sprintf(UTMZone, "%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)
          {
            //10000000 meter offset for southern hemisphere
            UTMNorthing += 10000000.0;
          }
}

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, phi1Rad;
        double x, y;
        int ZoneNumber;
        char* ZoneLetter;

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

        ZoneNumber = strtoul(UTMZone, &ZoneLetter, 10);
        if((*ZoneLetter - 'N') < 0)
          {
            //remove 10,000,000 meter offset used for southern hemisphere
            y -= 10000000.0;
          }

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

        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;

}
} // end namespace UTM

#endif // _UTM_H