/***************************************************************************/ /* 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 #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 */