/***************************************************************************/
/* 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 */