navsat_conversions.h

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/*
* Copyright (C) 2010 Austin Robot Technology, and others
* All rights reserved.
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* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
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* be used to endorse or promote products derived from this
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*
* This file contains code from multiple files in the original
* source. The originals can be found here:
*
* https://github.com/austin-robot/utexas-art-ros-pkg/blob/afd147a1eb944fc3dbd138574c39699813f797bf/stacks/art_vehicle/art_common/include/art/UTM.h
* https://github.com/austin-robot/utexas-art-ros-pkg/blob/afd147a1eb944fc3dbd138574c39699813f797bf/stacks/art_vehicle/art_common/include/art/conversions.h
*/

#ifndef ROBOT_LOCALIZATION_NAVSAT_CONVERSIONS_H
#define ROBOT_LOCALIZATION_NAVSAT_CONVERSIONS_H

#include <cmath>
#include <string>

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

namespace RobotLocalization
{
namespace NavsatConversions
{

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

// 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
  static const double m0 = (1 - UTM_E2/4 - 3*UTM_E4/64 - 5*UTM_E6/256);
  static const double m1 = -(3*UTM_E2/8 + 3*UTM_E4/32 + 45*UTM_E6/1024);
  static const double m2 = (15*UTM_E4/256 + 45*UTM_E6/1024);
  static const double m3 = -(35*UTM_E6/3072);

  // compute the central meridian
  int cm = ((lon >= 0.0)
    ? (static_cast<int>(lon) - (static_cast<int>(lon)) % 6 + 3)
    : (static_cast<int>(lon) - (static_cast<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,
                           std::string &UTMZone, double &gamma)
{
  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)-static_cast<int>((Long+180)/360)*360-180;

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

  ZoneNumber = static_cast<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
  char zone_buf[] = {0, 0, 0, 0};
  snprintf(zone_buf, sizeof(zone_buf), "%d%c", ZoneNumber, UTMLetterDesignator(Lat));
  UTMZone = std::string(zone_buf);

  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 = static_cast<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 = static_cast<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)));

  gamma = atan(tan(LongRad-LongOriginRad)*sin(LatRad)) * DEGREES_PER_RADIAN;

  if (Lat < 0)
          {
            // 10000000 meter offset for southern hemisphere
            UTMNorthing += 10000000.0;
          }
}

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

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

  gamma = atan(tanh(x/(k0*a))*tan(y/(k0*a))) * DEGREES_PER_RADIAN;
}

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

}  // namespace NavsatConversions
}  // namespace RobotLocalization

#endif  // ROBOT_LOCALIZATION_NAVSAT_CONVERSIONS_H