tranmerc.c

/***************************************************************************/
/* RSC IDENTIFIER: TRANSVERSE MERCATOR
 *
 * ABSTRACT
 *
 *    This component provides conversions between Geodetic coordinates 
 *    (latitude and longitude) and Transverse Mercator projection coordinates
 *    (easting and northing).
 *
 * ERROR HANDLING
 *
 *    This component checks parameters for valid values.  If an invalid value
 *    is found the error code is combined with the current error code using 
 *    the bitwise or.  This combining allows multiple error codes to be
 *    returned. The possible error codes are:
 *
 *       TRANMERC_NO_ERROR           : No errors occurred in function
 *       TRANMERC_LAT_ERROR          : Latitude outside of valid range
 *                                      (-90 to 90 degrees)
 *       TRANMERC_LON_ERROR          : Longitude outside of valid range
 *                                      (-180 to 360 degrees, and within
 *                                        +/-90 of Central Meridian)
 *       TRANMERC_EASTING_ERROR      : Easting outside of valid range
 *                                      (depending on ellipsoid and
 *                                       projection parameters)
 *       TRANMERC_NORTHING_ERROR     : Northing outside of valid range
 *                                      (depending on ellipsoid and
 *                                       projection parameters)
 *       TRANMERC_ORIGIN_LAT_ERROR   : Origin latitude outside of valid range
 *                                      (-90 to 90 degrees)
 *       TRANMERC_CENT_MER_ERROR     : Central meridian outside of valid range
 *                                      (-180 to 360 degrees)
 *       TRANMERC_A_ERROR            : Semi-major axis less than or equal to zero
 *       TRANMERC_INV_F_ERROR        : Inverse flattening outside of valid range
 *								  	                  (250 to 350)
 *       TRANMERC_SCALE_FACTOR_ERROR : Scale factor outside of valid
 *                                     range (0.3 to 3.0)
 *		 TM_LON_WARNING              : Distortion will result if longitude is more
 *                                       than 9 degrees from the Central Meridian
 *
 * REUSE NOTES
 *
 *    TRANSVERSE MERCATOR is intended for reuse by any application that 
 *    performs a Transverse Mercator projection or its inverse.
 *    
 * REFERENCES
 *
 *    Further information on TRANSVERSE MERCATOR can be found in the 
 *    Reuse Manual.
 *
 *    TRANSVERSE MERCATOR originated from :  
 *                      U.S. Army Topographic Engineering Center
 *                      Geospatial Information Division
 *                      7701 Telegraph Road
 *                      Alexandria, VA  22310-3864
 *
 * LICENSES
 *
 *    None apply to this component.
 *
 * RESTRICTIONS
 *
 *    TRANSVERSE MERCATOR has no restrictions.
 *
 * ENVIRONMENT
 *
 *    TRANSVERSE MERCATOR was tested and certified in the following 
 *    environments:
 *
 *    1. Solaris 2.5 with GCC, version 2.8.1
 *    2. Windows 95 with MS Visual C++, version 6
 *
 * MODIFICATIONS
 *
 *    Date              Description
 *    ----              -----------
 *    10-02-97          Original Code
 *    03-02-97          Re-engineered Code
 *
 */


/***************************************************************************/
/*
 *                               INCLUDES
 */

#include <math.h>
#include "tranmerc.h"

/*
 *    math.h      - Standard C math library
 *    tranmerc.h  - Is for prototype error checking
 */


/***************************************************************************/
/*                               DEFINES 
 *
 */

#define PI              3.14159265358979323e0   /* PI     */
#define PI_OVER_2         (PI/2.0e0)            /* PI over 2 */
#define MAX_LAT         ((PI * 89.99)/180.0)    /* 89.99 degrees in radians */
#define MAX_DELTA_LONG  ((PI * 90)/180.0)       /* 90 degrees in radians */
#define MIN_SCALE_FACTOR  0.3
#define MAX_SCALE_FACTOR  3.0

#define SPHTMD(Latitude) ((double) (TranMerc_ap * Latitude \
      - TranMerc_bp * sin(2.e0 * Latitude) + TranMerc_cp * sin(4.e0 * Latitude) \
      - TranMerc_dp * sin(6.e0 * Latitude) + TranMerc_ep * sin(8.e0 * Latitude) ) )

#define SPHSN(Latitude) ((double) (TranMerc_a / sqrt( 1.e0 - TranMerc_es * \
      pow(sin(Latitude), 2))))

#define SPHSR(Latitude) ((double) (TranMerc_a * (1.e0 - TranMerc_es) / \
    pow(DENOM(Latitude), 3)))

#define DENOM(Latitude) ((double) (sqrt(1.e0 - TranMerc_es * pow(sin(Latitude),2))))


/**************************************************************************/
/*                               GLOBAL DECLARATIONS
 *
 */

/* Ellipsoid Parameters, default to WGS 84  */
static double TranMerc_a = 6378137.0;              /* Semi-major axis of ellipsoid in meters */
static double TranMerc_f = 1 / 298.257223563;      /* Flattening of ellipsoid  */
static double TranMerc_es = 0.0066943799901413800; /* Eccentricity (0.08181919084262188000) squared */
static double TranMerc_ebs = 0.0067394967565869;   /* Second Eccentricity squared */

/* Transverse_Mercator projection Parameters */
static double TranMerc_Origin_Lat = 0.0;           /* Latitude of origin in radians */
static double TranMerc_Origin_Long = 0.0;          /* Longitude of origin in radians */
static double TranMerc_False_Northing = 0.0;       /* False northing in meters */
static double TranMerc_False_Easting = 0.0;        /* False easting in meters */
static double TranMerc_Scale_Factor = 1.0;         /* Scale factor  */

/* Isometeric to geodetic latitude parameters, default to WGS 84 */
static double TranMerc_ap = 6367449.1458008;
static double TranMerc_bp = 16038.508696861;
static double TranMerc_cp = 16.832613334334;
static double TranMerc_dp = 0.021984404273757;
static double TranMerc_ep = 3.1148371319283e-005;

/* Maximum variance for easting and northing values for WGS 84. */
static double TranMerc_Delta_Easting = 40000000.0;
static double TranMerc_Delta_Northing = 40000000.0;

/* These state variables are for optimization purposes. The only function
 * that should modify them is Set_Tranverse_Mercator_Parameters.         */


/************************************************************************/
/*                              FUNCTIONS     
 *
 */


long Set_Transverse_Mercator_Parameters(double a,
                                        double f,
                                        double Origin_Latitude,
                                        double Central_Meridian,
                                        double False_Easting,
                                        double False_Northing,
                                        double Scale_Factor)

{ /* BEGIN Set_Tranverse_Mercator_Parameters */
  /*
   * The function Set_Tranverse_Mercator_Parameters receives the ellipsoid
   * parameters and Tranverse Mercator projection parameters as inputs, and
   * sets the corresponding state variables. If any errors occur, the error
   * code(s) are returned by the function, otherwise TRANMERC_NO_ERROR is
   * returned.
   *
   *    a                 : Semi-major axis of ellipsoid, in meters    (input)
   *    f                 : Flattening of ellipsoid						         (input)
   *    Origin_Latitude   : Latitude in radians at the origin of the   (input)
   *                         projection
   *    Central_Meridian  : Longitude in radians at the center of the  (input)
   *                         projection
   *    False_Easting     : Easting/X at the center of the projection  (input)
   *    False_Northing    : Northing/Y at the center of the projection (input)
   *    Scale_Factor      : Projection scale factor                    (input) 
   */

  double tn;        /* True Meridianal distance constant  */
  double tn2;
  double tn3;
  double tn4;
  double tn5;
  double dummy_northing;
  double TranMerc_b; /* Semi-minor axis of ellipsoid, in meters */
  double inv_f = 1 / f;
  long Error_Code = TRANMERC_NO_ERROR;

  if (a <= 0.0)
  { /* Semi-major axis must be greater than zero */
    Error_Code |= TRANMERC_A_ERROR;
  }
  if ((inv_f < 250) || (inv_f > 350))
  { /* Inverse flattening must be between 250 and 350 */
    Error_Code |= TRANMERC_INV_F_ERROR;
  }
  if ((Origin_Latitude < -PI_OVER_2) || (Origin_Latitude > PI_OVER_2))
  { /* origin latitude out of range */
    Error_Code |= TRANMERC_ORIGIN_LAT_ERROR;
  }
  if ((Central_Meridian < -PI) || (Central_Meridian > (2*PI)))
  { /* origin longitude out of range */
    Error_Code |= TRANMERC_CENT_MER_ERROR;
  }
  if ((Scale_Factor < MIN_SCALE_FACTOR) || (Scale_Factor > MAX_SCALE_FACTOR))
  {
    Error_Code |= TRANMERC_SCALE_FACTOR_ERROR;
  }
  if (!Error_Code)
  { /* no errors */
    TranMerc_a = a;
    TranMerc_f = f;
    TranMerc_Origin_Lat = Origin_Latitude;
    if (Central_Meridian > PI)
      Central_Meridian -= (2*PI);
    TranMerc_Origin_Long = Central_Meridian;
    TranMerc_False_Northing = False_Northing;
    TranMerc_False_Easting = False_Easting; 
    TranMerc_Scale_Factor = Scale_Factor;

    /* Eccentricity Squared */
    TranMerc_es = 2 * TranMerc_f - TranMerc_f * TranMerc_f;
    /* Second Eccentricity Squared */
    TranMerc_ebs = (1 / (1 - TranMerc_es)) - 1;

    TranMerc_b = TranMerc_a * (1 - TranMerc_f);    
    /*True meridianal constants  */
    tn = (TranMerc_a - TranMerc_b) / (TranMerc_a + TranMerc_b);
    tn2 = tn * tn;
    tn3 = tn2 * tn;
    tn4 = tn3 * tn;
    tn5 = tn4 * tn;

    TranMerc_ap = TranMerc_a * (1.e0 - tn + 5.e0 * (tn2 - tn3)/4.e0
                                + 81.e0 * (tn4 - tn5)/64.e0 );
    TranMerc_bp = 3.e0 * TranMerc_a * (tn - tn2 + 7.e0 * (tn3 - tn4)
                                       /8.e0 + 55.e0 * tn5/64.e0 )/2.e0;
    TranMerc_cp = 15.e0 * TranMerc_a * (tn2 - tn3 + 3.e0 * (tn4 - tn5 )/4.e0) /16.0;
    TranMerc_dp = 35.e0 * TranMerc_a * (tn3 - tn4 + 11.e0 * tn5 / 16.e0) / 48.e0;
    TranMerc_ep = 315.e0 * TranMerc_a * (tn4 - tn5) / 512.e0;
    Convert_Geodetic_To_Transverse_Mercator(MAX_LAT,
                                            MAX_DELTA_LONG + Central_Meridian,
                                            &TranMerc_Delta_Easting,
                                            &TranMerc_Delta_Northing);
    Convert_Geodetic_To_Transverse_Mercator(0,
                                            MAX_DELTA_LONG + Central_Meridian,
                                            &TranMerc_Delta_Easting,
                                            &dummy_northing);
    TranMerc_Delta_Northing++;
    TranMerc_Delta_Easting++;

  } /* END OF if(!Error_Code) */
  return (Error_Code);
}  /* END of Set_Transverse_Mercator_Parameters  */


void Get_Transverse_Mercator_Parameters(double *a,
                                        double *f,
                                        double *Origin_Latitude,
                                        double *Central_Meridian,
                                        double *False_Easting,
                                        double *False_Northing,
                                        double *Scale_Factor)

{ /* BEGIN Get_Tranverse_Mercator_Parameters  */
  /*
   * The function Get_Transverse_Mercator_Parameters returns the current
   * ellipsoid and Transverse Mercator projection parameters.
   *
   *    a                 : Semi-major axis of ellipsoid, in meters    (output)
   *    f                 : Flattening of ellipsoid						         (output)
   *    Origin_Latitude   : Latitude in radians at the origin of the   (output)
   *                         projection
   *    Central_Meridian  : Longitude in radians at the center of the  (output)
   *                         projection
   *    False_Easting     : Easting/X at the center of the projection  (output)
   *    False_Northing    : Northing/Y at the center of the projection (output)
   *    Scale_Factor      : Projection scale factor                    (output) 
   */

  *a = TranMerc_a;
  *f = TranMerc_f;
  *Origin_Latitude = TranMerc_Origin_Lat;
  *Central_Meridian = TranMerc_Origin_Long;
  *False_Easting = TranMerc_False_Easting;
  *False_Northing = TranMerc_False_Northing;
  *Scale_Factor = TranMerc_Scale_Factor;
  return;
} /* END OF Get_Tranverse_Mercator_Parameters */



long Convert_Geodetic_To_Transverse_Mercator (double Latitude,
                                              double Longitude,
                                              double *Easting,
                                              double *Northing)

{      /* BEGIN Convert_Geodetic_To_Transverse_Mercator */

  /*
   * The function Convert_Geodetic_To_Transverse_Mercator converts geodetic
   * (latitude and longitude) coordinates to Transverse Mercator projection
   * (easting and northing) coordinates, according to the current ellipsoid
   * and Transverse Mercator projection coordinates.  If any errors occur, the
   * error code(s) are returned by the function, otherwise TRANMERC_NO_ERROR is
   * returned.
   *
   *    Latitude      : Latitude in radians                         (input)
   *    Longitude     : Longitude in radians                        (input)
   *    Easting       : Easting/X in meters                         (output)
   *    Northing      : Northing/Y in meters                        (output)
   */

  double c;       /* Cosine of latitude                          */
  double c2;
  double c3;
  double c5;
  double c7;
  double dlam;    /* Delta longitude - Difference in Longitude       */
  double eta;     /* constant - TranMerc_ebs *c *c                   */
  double eta2;
  double eta3;
  double eta4;
  double s;       /* Sine of latitude                        */
  double sn;      /* Radius of curvature in the prime vertical       */
  double t;       /* Tangent of latitude                             */
  double tan2;
  double tan3;
  double tan4;
  double tan5;
  double tan6;
  double t1;      /* Term in coordinate conversion formula - GP to Y */
  double t2;      /* Term in coordinate conversion formula - GP to Y */
  double t3;      /* Term in coordinate conversion formula - GP to Y */
  double t4;      /* Term in coordinate conversion formula - GP to Y */
  double t5;      /* Term in coordinate conversion formula - GP to Y */
  double t6;      /* Term in coordinate conversion formula - GP to Y */
  double t7;      /* Term in coordinate conversion formula - GP to Y */
  double t8;      /* Term in coordinate conversion formula - GP to Y */
  double t9;      /* Term in coordinate conversion formula - GP to Y */
  double tmd;     /* True Meridional distance                        */
  double tmdo;    /* True Meridional distance for latitude of origin */
  long    Error_Code = TRANMERC_NO_ERROR;
  double temp_Origin;
  double temp_Long;

  if ((Latitude < -MAX_LAT) || (Latitude > MAX_LAT))
  {  /* Latitude out of range */
    Error_Code|= TRANMERC_LAT_ERROR;
  }
  if (Longitude > PI)
    Longitude -= (2 * PI);
  if ((Longitude < (TranMerc_Origin_Long - MAX_DELTA_LONG))
      || (Longitude > (TranMerc_Origin_Long + MAX_DELTA_LONG)))
  {
    if (Longitude < 0)
      temp_Long = Longitude + 2 * PI;
    else
      temp_Long = Longitude;
    if (TranMerc_Origin_Long < 0)
      temp_Origin = TranMerc_Origin_Long + 2 * PI;
    else
      temp_Origin = TranMerc_Origin_Long;
    if ((temp_Long < (temp_Origin - MAX_DELTA_LONG))
        || (temp_Long > (temp_Origin + MAX_DELTA_LONG)))
      Error_Code|= TRANMERC_LON_ERROR;
  }
  if (!Error_Code)
  { /* no errors */

    /* 
     *  Delta Longitude
     */
    dlam = Longitude - TranMerc_Origin_Long;

    if (fabs(dlam) > (9.0 * PI / 180))
    { /* Distortion will result if Longitude is more than 9 degrees from the Central Meridian */
      Error_Code |= TRANMERC_LON_WARNING;
    }

    if (dlam > PI)
      dlam -= (2 * PI);
    if (dlam < -PI)
      dlam += (2 * PI);
    if (fabs(dlam) < 2.e-10)
      dlam = 0.0;

    s = sin(Latitude);
    c = cos(Latitude);
    c2 = c * c;
    c3 = c2 * c;
    c5 = c3 * c2;
    c7 = c5 * c2;
    t = tan (Latitude);
    tan2 = t * t;
    tan3 = tan2 * t;
    tan4 = tan3 * t;
    tan5 = tan4 * t;
    tan6 = tan5 * t;
    eta = TranMerc_ebs * c2;
    eta2 = eta * eta;
    eta3 = eta2 * eta;
    eta4 = eta3 * eta;

    /* radius of curvature in prime vertical */
    sn = SPHSN(Latitude);

    /* True Meridianal Distances */
    tmd = SPHTMD(Latitude);

    /*  Origin  */
    tmdo = SPHTMD (TranMerc_Origin_Lat);

    /* northing */
    t1 = (tmd - tmdo) * TranMerc_Scale_Factor;
    t2 = sn * s * c * TranMerc_Scale_Factor/ 2.e0;
    t3 = sn * s * c3 * TranMerc_Scale_Factor * (5.e0 - tan2 + 9.e0 * eta 
                                                + 4.e0 * eta2) /24.e0; 

    t4 = sn * s * c5 * TranMerc_Scale_Factor * (61.e0 - 58.e0 * tan2
                                                + tan4 + 270.e0 * eta - 330.e0 * tan2 * eta + 445.e0 * eta2
                                                + 324.e0 * eta3 -680.e0 * tan2 * eta2 + 88.e0 * eta4 
                                                -600.e0 * tan2 * eta3 - 192.e0 * tan2 * eta4) / 720.e0;

    t5 = sn * s * c7 * TranMerc_Scale_Factor * (1385.e0 - 3111.e0 * 
                                                tan2 + 543.e0 * tan4 - tan6) / 40320.e0;

    *Northing = TranMerc_False_Northing + t1 + pow(dlam,2.e0) * t2
                + pow(dlam,4.e0) * t3 + pow(dlam,6.e0) * t4
                + pow(dlam,8.e0) * t5; 

    /* Easting */
    t6 = sn * c * TranMerc_Scale_Factor;
    t7 = sn * c3 * TranMerc_Scale_Factor * (1.e0 - tan2 + eta ) /6.e0;
    t8 = sn * c5 * TranMerc_Scale_Factor * (5.e0 - 18.e0 * tan2 + tan4
                                            + 14.e0 * eta - 58.e0 * tan2 * eta + 13.e0 * eta2 + 4.e0 * eta3 
                                            - 64.e0 * tan2 * eta2 - 24.e0 * tan2 * eta3 )/ 120.e0;
    t9 = sn * c7 * TranMerc_Scale_Factor * ( 61.e0 - 479.e0 * tan2
                                             + 179.e0 * tan4 - tan6 ) /5040.e0;

    *Easting = TranMerc_False_Easting + dlam * t6 + pow(dlam,3.e0) * t7 
               + pow(dlam,5.e0) * t8 + pow(dlam,7.e0) * t9;
  }
  return (Error_Code);
} /* END OF Convert_Geodetic_To_Transverse_Mercator */


long Convert_Transverse_Mercator_To_Geodetic (
                                             double Easting,
                                             double Northing,
                                             double *Latitude,
                                             double *Longitude)
{      /* BEGIN Convert_Transverse_Mercator_To_Geodetic */

  /*
   * The function Convert_Transverse_Mercator_To_Geodetic converts Transverse
   * Mercator projection (easting and northing) coordinates to geodetic
   * (latitude and longitude) coordinates, according to the current ellipsoid
   * and Transverse Mercator projection parameters.  If any errors occur, the
   * error code(s) are returned by the function, otherwise TRANMERC_NO_ERROR is
   * returned.
   *
   *    Easting       : Easting/X in meters                         (input)
   *    Northing      : Northing/Y in meters                        (input)
   *    Latitude      : Latitude in radians                         (output)
   *    Longitude     : Longitude in radians                        (output)
   */

  double c;       /* Cosine of latitude                          */
  double de;      /* Delta easting - Difference in Easting (Easting-Fe)    */
  double dlam;    /* Delta longitude - Difference in Longitude       */
  double eta;     /* constant - TranMerc_ebs *c *c                   */
  double eta2;
  double eta3;
  double eta4;
  double ftphi;   /* Footpoint latitude                              */
  int    i;       /* Loop iterator                   */
  //double s;       /* Sine of latitude                        */
  double sn;      /* Radius of curvature in the prime vertical       */
  double sr;      /* Radius of curvature in the meridian             */
  double t;       /* Tangent of latitude                             */
  double tan2;
  double tan4;
  double t10;     /* Term in coordinate conversion formula - GP to Y */
  double t11;     /* Term in coordinate conversion formula - GP to Y */
  double t12;     /* Term in coordinate conversion formula - GP to Y */
  double t13;     /* Term in coordinate conversion formula - GP to Y */
  double t14;     /* Term in coordinate conversion formula - GP to Y */
  double t15;     /* Term in coordinate conversion formula - GP to Y */
  double t16;     /* Term in coordinate conversion formula - GP to Y */
  double t17;     /* Term in coordinate conversion formula - GP to Y */
  double tmd;     /* True Meridional distance                        */
  double tmdo;    /* True Meridional distance for latitude of origin */
  long Error_Code = TRANMERC_NO_ERROR;

  if ((Easting < (TranMerc_False_Easting - TranMerc_Delta_Easting))
      ||(Easting > (TranMerc_False_Easting + TranMerc_Delta_Easting)))
  { /* Easting out of range  */
    Error_Code |= TRANMERC_EASTING_ERROR;
  }
  if ((Northing < (TranMerc_False_Northing - TranMerc_Delta_Northing))
      || (Northing > (TranMerc_False_Northing + TranMerc_Delta_Northing)))
  { /* Northing out of range */
    Error_Code |= TRANMERC_NORTHING_ERROR;
  }

  if (!Error_Code)
  {
    /* True Meridional Distances for latitude of origin */
    tmdo = SPHTMD(TranMerc_Origin_Lat);

    /*  Origin  */
    tmd = tmdo +  (Northing - TranMerc_False_Northing) / TranMerc_Scale_Factor; 

    /* First Estimate */
    sr = SPHSR(0.e0);
    ftphi = tmd/sr;

    for (i = 0; i < 5 ; i++)
    {
      t10 = SPHTMD (ftphi);
      sr = SPHSR(ftphi);
      ftphi = ftphi + (tmd - t10) / sr;
    }

    /* Radius of Curvature in the meridian */
    sr = SPHSR(ftphi);

    /* Radius of Curvature in the meridian */
    sn = SPHSN(ftphi);

    /* Sine Cosine terms */
    //s = sin(ftphi);
    c = cos(ftphi);

    /* Tangent Value  */
    t = tan(ftphi);
    tan2 = t * t;
    tan4 = tan2 * tan2;
    eta = TranMerc_ebs * pow(c,2);
    eta2 = eta * eta;
    eta3 = eta2 * eta;
    eta4 = eta3 * eta;
    de = Easting - TranMerc_False_Easting;
    if (fabs(de) < 0.0001)
      de = 0.0;

    /* Latitude */
    t10 = t / (2.e0 * sr * sn * pow(TranMerc_Scale_Factor, 2));
    t11 = t * (5.e0  + 3.e0 * tan2 + eta - 4.e0 * pow(eta,2)
               - 9.e0 * tan2 * eta) / (24.e0 * sr * pow(sn,3) 
                                       * pow(TranMerc_Scale_Factor,4));
    t12 = t * (61.e0 + 90.e0 * tan2 + 46.e0 * eta + 45.E0 * tan4
               - 252.e0 * tan2 * eta  - 3.e0 * eta2 + 100.e0 
               * eta3 - 66.e0 * tan2 * eta2 - 90.e0 * tan4
               * eta + 88.e0 * eta4 + 225.e0 * tan4 * eta2
               + 84.e0 * tan2* eta3 - 192.e0 * tan2 * eta4)
          / ( 720.e0 * sr * pow(sn,5) * pow(TranMerc_Scale_Factor, 6) );
    t13 = t * ( 1385.e0 + 3633.e0 * tan2 + 4095.e0 * tan4 + 1575.e0 
                * pow(t,6))/ (40320.e0 * sr * pow(sn,7) * pow(TranMerc_Scale_Factor,8));
    *Latitude = ftphi - pow(de,2) * t10 + pow(de,4) * t11 - pow(de,6) * t12 
                + pow(de,8) * t13;

    t14 = 1.e0 / (sn * c * TranMerc_Scale_Factor);

    t15 = (1.e0 + 2.e0 * tan2 + eta) / (6.e0 * pow(sn,3) * c * 
                                        pow(TranMerc_Scale_Factor,3));

    t16 = (5.e0 + 6.e0 * eta + 28.e0 * tan2 - 3.e0 * eta2
           + 8.e0 * tan2 * eta + 24.e0 * tan4 - 4.e0 
           * eta3 + 4.e0 * tan2 * eta2 + 24.e0 
           * tan2 * eta3) / (120.e0 * pow(sn,5) * c  
                             * pow(TranMerc_Scale_Factor,5));

    t17 = (61.e0 +  662.e0 * tan2 + 1320.e0 * tan4 + 720.e0 
           * pow(t,6)) / (5040.e0 * pow(sn,7) * c 
                          * pow(TranMerc_Scale_Factor,7));

    /* Difference in Longitude */
    dlam = de * t14 - pow(de,3) * t15 + pow(de,5) * t16 - pow(de,7) * t17;

    /* Longitude */
    (*Longitude) = TranMerc_Origin_Long + dlam;

    if((fabs)(*Latitude) > (90.0 * PI / 180.0))
      Error_Code |= TRANMERC_NORTHING_ERROR;

    if((*Longitude) > (PI))
    {
      *Longitude -= (2 * PI);
      if((fabs)(*Longitude) > PI)
        Error_Code |= TRANMERC_EASTING_ERROR;
    }
    else if((*Longitude) < (-PI))
    {
      *Longitude += (2 * PI);
      if((fabs)(*Longitude) > PI)
        Error_Code |= TRANMERC_EASTING_ERROR;
    }

    if (fabs(dlam) > (9.0 * PI / 180) * cos(*Latitude))
    { /* Distortion will result if Longitude is more than 9 degrees from the Central Meridian at the equator */
      /* and decreases to 0 degrees at the poles */
      /* As you move towards the poles, distortion will become more significant */
      Error_Code |= TRANMERC_LON_WARNING;
    }
  }
  return (Error_Code);
} /* END OF Convert_Transverse_Mercator_To_Geodetic */