/***************************************************************************/
/* RSC IDENTIFIER: POLAR STEREOGRAPHIC
*
*
* ABSTRACT
*
* This component provides conversions between geodetic (latitude and
* longitude) coordinates and Polar Stereographic (easting and northing)
* coordinates.
*
* 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:
*
* POLAR_NO_ERROR : No errors occurred in function
* POLAR_LAT_ERROR : Latitude outside of valid range
* (-90 to 90 degrees)
* POLAR_LON_ERROR : Longitude outside of valid range
* (-180 to 360 degrees)
* POLAR_ORIGIN_LAT_ERROR : Latitude of true scale outside of valid
* range (-90 to 90 degrees)
* POLAR_ORIGIN_LON_ERROR : Longitude down from pole outside of valid
* range (-180 to 360 degrees)
* POLAR_EASTING_ERROR : Easting outside of valid range,
* depending on ellipsoid and
* projection parameters
* POLAR_NORTHING_ERROR : Northing outside of valid range,
* depending on ellipsoid and
* projection parameters
* POLAR_RADIUS_ERROR : Coordinates too far from pole,
* depending on ellipsoid and
* projection parameters
* POLAR_A_ERROR : Semi-major axis less than or equal to zero
* POLAR_INV_F_ERROR : Inverse flattening outside of valid range
* (250 to 350)
*
*
* REUSE NOTES
*
* POLAR STEREOGRAPHIC is intended for reuse by any application that
* performs a Polar Stereographic projection.
*
*
* REFERENCES
*
* Further information on POLAR STEREOGRAPHIC can be found in the
* Reuse Manual.
*
*
* POLAR STEREOGRAPHIC 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
*
* POLAR STEREOGRAPHIC has no restrictions.
*
*
* ENVIRONMENT
*
* POLAR STEREOGRAPHIC was tested and certified in the following
* environments:
*
* 1. Solaris 2.5 with GCC, version 2.8.1
* 2. Window 95 with MS Visual C++, version 6
*
*
* MODIFICATIONS
*
* Date Description
* ---- -----------
* 06-11-95 Original Code
* 03-01-97 Original Code
*
*
*/
/************************************************************************/
/*
* INCLUDES
*/
#include <math.h>
#include "polarst.h"
/*
* math.h - Standard C math library
* polarst.h - Is for prototype error checking
*/
/************************************************************************/
/* DEFINES
*
*/
#define PI 3.14159265358979323e0 /* PI */
#define PI_OVER_2 (PI / 2.0)
#define TWO_PI (2.0 * PI)
#define POLAR_POW(EsSin) pow((1.0 - EsSin) / (1.0 + EsSin), es_OVER_2)
/************************************************************************/
/* GLOBAL DECLARATIONS
*
*/
const double PI_Over_4 = (PI / 4.0);
/* Ellipsoid Parameters, default to WGS 84 */
static double Polar_a = 6378137.0; /* Semi-major axis of ellipsoid in meters */
static double Polar_f = 1 / 298.257223563; /* Flattening of ellipsoid */
static double es = 0.08181919084262188000; /* Eccentricity of ellipsoid */
static double es_OVER_2 = .040909595421311; /* es / 2.0 */
static double Southern_Hemisphere = 0; /* Flag variable */
static double tc = 1.0;
static double e4 = 1.0033565552493;
static double Polar_a_mc = 6378137.0; /* Polar_a * mc */
static double two_Polar_a = 12756274.0; /* 2.0 * Polar_a */
/* Polar Stereographic projection Parameters */
static double Polar_Origin_Lat = ((PI * 90) / 180); /* Latitude of origin in radians */
static double Polar_Origin_Long = 0.0; /* Longitude of origin in radians */
static double Polar_False_Easting = 0.0; /* False easting in meters */
static double Polar_False_Northing = 0.0; /* False northing in meters */
/* Maximum variance for easting and northing values for WGS 84. */
static double Polar_Delta_Easting = 12713601.0;
static double Polar_Delta_Northing = 12713601.0;
/* These state variables are for optimization purposes. The only function
* that should modify them is Set_Polar_Stereographic_Parameters.
*/
/************************************************************************/
/* FUNCTIONS
*
*/
long Set_Polar_Stereographic_Parameters (double a,
double f,
double Latitude_of_True_Scale,
double Longitude_Down_from_Pole,
double False_Easting,
double False_Northing)
{ /* BEGIN Set_Polar_Stereographic_Parameters */
/*
* The function Set_Polar_Stereographic_Parameters receives the ellipsoid
* parameters and Polar Stereograpic projection parameters as inputs, and
* sets the corresponding state variables. If any errors occur, error
* code(s) are returned by the function, otherwise POLAR_NO_ERROR is returned.
*
* a : Semi-major axis of ellipsoid, in meters (input)
* f : Flattening of ellipsoid (input)
* Latitude_of_True_Scale : Latitude of true scale, in radians (input)
* Longitude_Down_from_Pole : Longitude down from pole, in radians (input)
* False_Easting : Easting (X) at center of projection, in meters (input)
* False_Northing : Northing (Y) at center of projection, in meters (input)
*/
double es2;
double slat, clat;
double essin;
double one_PLUS_es, one_MINUS_es;
double pow_es;
double temp, temp_northing = 0;
double inv_f = 1 / f;
double mc;
// const double epsilon = 1.0e-2;
long Error_Code = POLAR_NO_ERROR;
if (a <= 0.0)
{ /* Semi-major axis must be greater than zero */
Error_Code |= POLAR_A_ERROR;
}
if ((inv_f < 250) || (inv_f > 350))
{ /* Inverse flattening must be between 250 and 350 */
Error_Code |= POLAR_INV_F_ERROR;
}
if ((Latitude_of_True_Scale < -PI_OVER_2) || (Latitude_of_True_Scale > PI_OVER_2))
{ /* Origin Latitude out of range */
Error_Code |= POLAR_ORIGIN_LAT_ERROR;
}
if ((Longitude_Down_from_Pole < -PI) || (Longitude_Down_from_Pole > TWO_PI))
{ /* Origin Longitude out of range */
Error_Code |= POLAR_ORIGIN_LON_ERROR;
}
if (!Error_Code)
{ /* no errors */
Polar_a = a;
two_Polar_a = 2.0 * Polar_a;
Polar_f = f;
if (Longitude_Down_from_Pole > PI)
Longitude_Down_from_Pole -= TWO_PI;
if (Latitude_of_True_Scale < 0)
{
Southern_Hemisphere = 1;
Polar_Origin_Lat = -Latitude_of_True_Scale;
Polar_Origin_Long = -Longitude_Down_from_Pole;
}
else
{
Southern_Hemisphere = 0;
Polar_Origin_Lat = Latitude_of_True_Scale;
Polar_Origin_Long = Longitude_Down_from_Pole;
}
Polar_False_Easting = False_Easting;
Polar_False_Northing = False_Northing;
es2 = 2 * Polar_f - Polar_f * Polar_f;
es = sqrt(es2);
es_OVER_2 = es / 2.0;
if (fabs(fabs(Polar_Origin_Lat) - PI_OVER_2) > 1.0e-10)
{
slat = sin(Polar_Origin_Lat);
essin = es * slat;
pow_es = POLAR_POW(essin);
clat = cos(Polar_Origin_Lat);
mc = clat / sqrt(1.0 - essin * essin);
Polar_a_mc = Polar_a * mc;
tc = tan(PI_Over_4 - Polar_Origin_Lat / 2.0) / pow_es;
}
else
{
one_PLUS_es = 1.0 + es;
one_MINUS_es = 1.0 - es;
e4 = sqrt(pow(one_PLUS_es, one_PLUS_es) * pow(one_MINUS_es, one_MINUS_es));
}
/* Calculate Radius */
Convert_Geodetic_To_Polar_Stereographic(0, Longitude_Down_from_Pole,
&temp, &temp_northing);
Polar_Delta_Northing = temp_northing;
if(Polar_False_Northing)
Polar_Delta_Northing -= Polar_False_Northing;
if (Polar_Delta_Northing < 0)
Polar_Delta_Northing = -Polar_Delta_Northing;
Polar_Delta_Northing *= 1.01;
Polar_Delta_Easting = Polar_Delta_Northing;
/* Polar_Delta_Easting = temp_northing;
if(Polar_False_Easting)
Polar_Delta_Easting -= Polar_False_Easting;
if (Polar_Delta_Easting < 0)
Polar_Delta_Easting = -Polar_Delta_Easting;
Polar_Delta_Easting *= 1.01;*/
}
return (Error_Code);
} /* END OF Set_Polar_Stereographic_Parameters */
void Get_Polar_Stereographic_Parameters (double *a,
double *f,
double *Latitude_of_True_Scale,
double *Longitude_Down_from_Pole,
double *False_Easting,
double *False_Northing)
{ /* BEGIN Get_Polar_Stereographic_Parameters */
/*
* The function Get_Polar_Stereographic_Parameters returns the current
* ellipsoid parameters and Polar projection parameters.
*
* a : Semi-major axis of ellipsoid, in meters (output)
* f : Flattening of ellipsoid (output)
* Latitude_of_True_Scale : Latitude of true scale, in radians (output)
* Longitude_Down_from_Pole : Longitude down from pole, in radians (output)
* False_Easting : Easting (X) at center of projection, in meters (output)
* False_Northing : Northing (Y) at center of projection, in meters (output)
*/
*a = Polar_a;
*f = Polar_f;
*Latitude_of_True_Scale = Polar_Origin_Lat;
*Longitude_Down_from_Pole = Polar_Origin_Long;
*False_Easting = Polar_False_Easting;
*False_Northing = Polar_False_Northing;
return;
} /* END OF Get_Polar_Stereographic_Parameters */
long Convert_Geodetic_To_Polar_Stereographic (double Latitude,
double Longitude,
double *Easting,
double *Northing)
{ /* BEGIN Convert_Geodetic_To_Polar_Stereographic */
/*
* The function Convert_Geodetic_To_Polar_Stereographic converts geodetic
* coordinates (latitude and longitude) to Polar Stereographic coordinates
* (easting and northing), according to the current ellipsoid
* and Polar Stereographic projection parameters. If any errors occur, error
* code(s) are returned by the function, otherwise POLAR_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 dlam;
double slat;
double essin;
double t;
double rho;
double pow_es;
long Error_Code = POLAR_NO_ERROR;
if ((Latitude < -PI_OVER_2) || (Latitude > PI_OVER_2))
{ /* Latitude out of range */
Error_Code |= POLAR_LAT_ERROR;
}
if ((Latitude < 0) && (Southern_Hemisphere == 0))
{ /* Latitude and Origin Latitude in different hemispheres */
Error_Code |= POLAR_LAT_ERROR;
}
if ((Latitude > 0) && (Southern_Hemisphere == 1))
{ /* Latitude and Origin Latitude in different hemispheres */
Error_Code |= POLAR_LAT_ERROR;
}
if ((Longitude < -PI) || (Longitude > TWO_PI))
{ /* Longitude out of range */
Error_Code |= POLAR_LON_ERROR;
}
if (!Error_Code)
{ /* no errors */
if (fabs(fabs(Latitude) - PI_OVER_2) < 1.0e-10)
{
*Easting = Polar_False_Easting;
*Northing = Polar_False_Northing;
}
else
{
if (Southern_Hemisphere != 0)
{
Longitude *= -1.0;
Latitude *= -1.0;
}
dlam = Longitude - Polar_Origin_Long;
if (dlam > PI)
{
dlam -= TWO_PI;
}
if (dlam < -PI)
{
dlam += TWO_PI;
}
slat = sin(Latitude);
essin = es * slat;
pow_es = POLAR_POW(essin);
t = tan(PI_Over_4 - Latitude / 2.0) / pow_es;
if (fabs(fabs(Polar_Origin_Lat) - PI_OVER_2) > 1.0e-10)
rho = Polar_a_mc * t / tc;
else
rho = two_Polar_a * t / e4;
if (Southern_Hemisphere != 0)
{
*Easting = -(rho * sin(dlam) - Polar_False_Easting);
// *Easting *= -1.0;
*Northing = rho * cos(dlam) + Polar_False_Northing;
}
else
{
*Easting = rho * sin(dlam) + Polar_False_Easting;
*Northing = -rho * cos(dlam) + Polar_False_Northing;
}
}
}
return (Error_Code);
} /* END OF Convert_Geodetic_To_Polar_Stereographic */
long Convert_Polar_Stereographic_To_Geodetic (double Easting,
double Northing,
double *Latitude,
double *Longitude)
{ /* BEGIN Convert_Polar_Stereographic_To_Geodetic */
/*
* The function Convert_Polar_Stereographic_To_Geodetic converts Polar
* Stereographic coordinates (easting and northing) to geodetic
* coordinates (latitude and longitude) according to the current ellipsoid
* and Polar Stereographic projection Parameters. If any errors occur, the
* code(s) are returned by the function, otherwise POLAR_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 dy = 0, dx = 0;
double rho = 0;
double t;
double PHI, sin_PHI;
double tempPHI = 0.0;
double essin;
double pow_es;
double delta_radius;
long Error_Code = POLAR_NO_ERROR;
double min_easting = Polar_False_Easting - Polar_Delta_Easting;
double max_easting = Polar_False_Easting + Polar_Delta_Easting;
double min_northing = Polar_False_Northing - Polar_Delta_Northing;
double max_northing = Polar_False_Northing + Polar_Delta_Northing;
if (Easting > max_easting || Easting < min_easting)
{ /* Easting out of range */
Error_Code |= POLAR_EASTING_ERROR;
}
if (Northing > max_northing || Northing < min_northing)
{ /* Northing out of range */
Error_Code |= POLAR_NORTHING_ERROR;
}
if (!Error_Code)
{
dy = Northing - Polar_False_Northing;
dx = Easting - Polar_False_Easting;
/* Radius of point with origin of false easting, false northing */
rho = sqrt(dx * dx + dy * dy);
delta_radius = sqrt(Polar_Delta_Easting * Polar_Delta_Easting + Polar_Delta_Northing * Polar_Delta_Northing);
if(rho > delta_radius)
{ /* Point is outside of projection area */
Error_Code |= POLAR_RADIUS_ERROR;
}
if (!Error_Code)
{ /* no errors */
if ((dy == 0.0) && (dx == 0.0))
{
*Latitude = PI_OVER_2;
*Longitude = Polar_Origin_Long;
}
else
{
if (Southern_Hemisphere != 0)
{
dy *= -1.0;
dx *= -1.0;
}
if (fabs(fabs(Polar_Origin_Lat) - PI_OVER_2) > 1.0e-10)
t = rho * tc / (Polar_a_mc);
else
t = rho * e4 / (two_Polar_a);
PHI = PI_OVER_2 - 2.0 * atan(t);
while (fabs(PHI - tempPHI) > 1.0e-10)
{
tempPHI = PHI;
sin_PHI = sin(PHI);
essin = es * sin_PHI;
pow_es = POLAR_POW(essin);
PHI = PI_OVER_2 - 2.0 * atan(t * pow_es);
}
*Latitude = PHI;
*Longitude = Polar_Origin_Long + atan2(dx, -dy);
if (*Longitude > PI)
*Longitude -= TWO_PI;
else if (*Longitude < -PI)
*Longitude += TWO_PI;
if (*Latitude > PI_OVER_2) /* force distorted values to 90, -90 degrees */
*Latitude = PI_OVER_2;
else if (*Latitude < -PI_OVER_2)
*Latitude = -PI_OVER_2;
if (*Longitude > PI) /* force distorted values to 180, -180 degrees */
*Longitude = PI;
else if (*Longitude < -PI)
*Longitude = -PI;
}
if (Southern_Hemisphere != 0)
{
*Latitude *= -1.0;
*Longitude *= -1.0;
}
}
}
return (Error_Code);
} /* END OF Convert_Polar_Stereographic_To_Geodetic */