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/***************************************************************************/
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/* RSC IDENTIFIER: ECKERT4
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* This component provides conversions between Geodetic coordinates
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* (latitude and longitude in radians) and Eckert IV projection coordinates
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* (easting and northing in meters). This projection employs a spherical
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* Earth model. The spherical radius used is the radius of the sphere
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* having the same area as the ellipsoid.
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* This component checks parameters for valid values. If an invalid value
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* is found, the error code is combined with the current error code using
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* the bitwise or. This combining allows multiple error codes to be
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* returned. The possible error codes are:
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* ECK4_NO_ERROR : No errors occurred in function
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* ECK4_LAT_ERROR : Latitude outside of valid range
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* ECK4_LON_ERROR : Longitude outside of valid range
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* (-180 to 360 degrees)
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* ECK4_EASTING_ERROR : Easting outside of valid range
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* (False_Easting +/- ~17,000,000 m,
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* depending on ellipsoid parameters)
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* ECK4_NORTHING_ERROR : Northing outside of valid range
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* (False_Northing +/- 0 to 8,000,000 m,
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* depending on ellipsoid parameters)
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* ECK4_CENT_MER_ERROR : Central_Meridian outside of valid range
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* (-180 to 360 degrees)
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* ECK4_A_ERROR : Semi-major axis less than or equal to zero
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* ECK4_INV_F_ERROR : Inverse flattening outside of valid range
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* ECKERT4 is intended for reuse by any application that performs a
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* Eckert IV projection or its inverse.
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* Further information on ECKERT4 can be found in the Reuse Manual.
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* ECKERT4 originated from : U.S. Army Topographic Engineering Center
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* Geospatial Information Division
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* Alexandria, VA 22310-3864
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* None apply to this component.
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* ECKERT4 has no restrictions.
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* ECKERT4 was tested and certified in the following environments:
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* 1. Solaris 2.5 with GCC 2.8.1
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* 2. MS Windows 95 with MS Visual C++ 6
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* 04/16/99 Original Code
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/***************************************************************************/
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* math.h - Standard C math library
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* eckert4.h - Is for prototype error checking.
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/***************************************************************************/
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#define PI 3.14159265358979323e0 /* PI */
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#define PI_OVER_2 ( PI / 2.0)
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#define TWO_PI (2.0 * PI)
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#define NUM(Theta, SinTheta, CosTheta) (Theta + SinTheta * CosTheta + 2.0 * SinTheta)
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/***************************************************************************/
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const double two_PLUS_PI_OVER_2 = (2.0 + PI / 2.0);
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/* Ellipsoid Parameters, default to WGS 84 */
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static double Eck4_a = 6378137.0; /* Semi-major axis of ellipsoid in meters */
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static double Eck4_f = 1 / 298.257223563; /* Flattening of ellipsoid */
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static double es2 = 0.0066943799901413800; /* Eccentricity (0.08181919084262188000) squared */
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static double es4 = 4.4814723452405e-005; /* es2 * es2 */
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static double es6 = 3.0000678794350e-007; /* es4 * es2 */
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static double Ra0 = 2690082.6043273; /* 0.4222382 * Sperical Radius (6371007.1810824) */
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static double Ra1 = 8451143.5741087; /* 1.3265004 * Sperical Radius (6371007.1810824) */
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/* Eckert4 projection Parameters */
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static double Eck4_Origin_Long = 0.0; /* Longitude of origin in radians */
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static double Eck4_False_Easting = 0.0;
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static double Eck4_False_Northing = 0.0;
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static double Eck4_Delta_Northing = 8451144.0;
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static double Eck4_Max_Easting = 16902288.0;
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static double Eck4_Min_Easting = -16902288.0;
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* These state variables are for optimization purposes. The only function
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* that should modify them is Set_Eckert IV_Parameters.
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/***************************************************************************/
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long Set_Eckert4_Parameters(double a,
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double Central_Meridian,
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double False_Easting,
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double False_Northing)
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{ /* Begin Set_Eckert4_Parameters */
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* The function Set_Eckert4_Parameters receives the ellipsoid parameters and
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* projection parameters as inputs, and sets the corresponding state
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* variables. If any errors occur, the error code(s) are returned by the
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* function, otherwise ECK4_NO_ERROR is returned.
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* a : Semi-major axis of ellipsoid, in meters (input)
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* f : Flattening of ellipsoid (input)
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* Central_Meridian : Longitude in radians at the center of (input)
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* False_Easting : A coordinate value in meters assigned to the
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* central meridian of the projection. (input)
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* False_Northing : A coordinate value in meters assigned to the
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* origin latitude of the projection (input)
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double Ra; /* Spherical radius */
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double inv_f = 1 / f;
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long Error_Code = ECK4_NO_ERROR;
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{ /* Semi-major axis must be greater than zero */
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Error_Code |= ECK4_A_ERROR;
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if ((inv_f < 250) || (inv_f > 350))
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{ /* Inverse flattening must be between 250 and 350 */
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Error_Code |= ECK4_INV_F_ERROR;
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if ((Central_Meridian < -PI) || (Central_Meridian > TWO_PI))
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{ /* origin longitude out of range */
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Error_Code |= ECK4_CENT_MER_ERROR;
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es2 = 2 * Eck4_f - Eck4_f * Eck4_f;
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/* spherical radius */
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Ra = Eck4_a * (1.0 - es2 / 6.0 - 17.0 * es4 / 360.0 - 67.0 * es6 / 3024.0);
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Ra0 = 0.4222382 * Ra;
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Ra1 = 1.3265004 * Ra;
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if (Central_Meridian > PI)
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Central_Meridian -= TWO_PI;
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Eck4_Origin_Long = Central_Meridian;
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Eck4_False_Easting = False_Easting;
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Eck4_False_Northing = False_Northing;
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if (Eck4_Origin_Long > 0)
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Eck4_Max_Easting = 16808386.0;
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Eck4_Min_Easting = -16902288.0;
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else if (Eck4_Origin_Long < 0)
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Eck4_Max_Easting = 16902288.0;
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Eck4_Min_Easting = -16808386.0;
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Eck4_Max_Easting = 16902288.0;
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Eck4_Min_Easting = -16902288.0;
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} /* End if(!Error_Code) */
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} /* End Set_Eckert4_Parameters */
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void Get_Eckert4_Parameters(double *a,
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double *Central_Meridian,
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double *False_Easting,
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double *False_Northing)
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{ /* Begin Get_Eckert4_Parameters */
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* The function Get_Eckert4_Parameters returns the current ellipsoid
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* parameters and Eckert IV projection parameters.
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* a : Semi-major axis of ellipsoid, in meters (output)
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* f : Flattening of ellipsoid (output)
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* Central_Meridian : Longitude in radians at the center of (output)
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* False_Easting : A coordinate value in meters assigned to the
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* central meridian of the projection. (output)
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* False_Northing : A coordinate value in meters assigned to the
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* origin latitude of the projection (output)
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*Central_Meridian = Eck4_Origin_Long;
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*False_Easting = Eck4_False_Easting;
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*False_Northing = Eck4_False_Northing;
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} /* End Get_Eckert4_Parameters */
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long Convert_Geodetic_To_Eckert4 (double Latitude,
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{ /* Begin Convert_Geodetic_To_Eckert4 */
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* The function Convert_Geodetic_To_Eckert4 converts geodetic (latitude and
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* longitude) coordinates to Eckert IV projection (easting and northing)
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* coordinates, according to the current ellipsoid, spherical radius and
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* Eckert IV projection parameters.
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* If any errors occur, the error code(s) are returned by the
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* function, otherwise ECK4_NO_ERROR is returned.
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* Latitude : Latitude (phi) in radians (input)
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* Longitude : Longitude (lambda) in radians (input)
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* Easting : Easting (X) in meters (output)
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* Northing : Northing (Y) in meters (output)
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double slat = sin(Latitude);
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double sin_theta, cos_theta;
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double dlam; /* Longitude - Central Meridan */
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double theta = Latitude / 2.0;
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double delta_theta = 1.0;
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double dt_tolerance = 4.85e-10; /* approximately 1/1000th of
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an arc second or 1/10th meter */
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long Error_Code = ECK4_NO_ERROR;
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if ((Latitude < -PI_OVER_2) || (Latitude > PI_OVER_2))
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{ /* Latitude out of range */
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Error_Code |= ECK4_LAT_ERROR;
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if ((Longitude < -PI) || (Longitude > TWO_PI))
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{ /* Longitude out of range */
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Error_Code|= ECK4_LON_ERROR;
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dlam = Longitude - Eck4_Origin_Long;
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while (fabs(delta_theta) > dt_tolerance)
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sin_theta = sin(theta);
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cos_theta = cos(theta);
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num = NUM(theta, sin_theta, cos_theta);
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delta_theta = -(num - two_PLUS_PI_OVER_2 * slat) /
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(2.0 * cos_theta * (1.0 + cos_theta));
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theta += delta_theta;
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*Easting = Ra0 * dlam * (1.0 + cos(theta)) + Eck4_False_Easting;
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*Northing = Ra1 * sin(theta) + Eck4_False_Northing;
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} /* End Convert_Geodetic_To_Eckert4 */
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long Convert_Eckert4_To_Geodetic(double Easting,
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{ /* Begin Convert_Eckert4_To_Geodetic */
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* The function Convert_Eckert4_To_Geodetic converts Eckert IV projection
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* (easting and northing) coordinates to geodetic (latitude and longitude)
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* coordinates, according to the current ellipsoid, spherical radius and
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* Eckert IV projection coordinates.
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* If any errors occur, the error code(s) are returned by the
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* function, otherwise ECK4_NO_ERROR is returned.
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* Easting : Easting (X) in meters (input)
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* Northing : Northing (Y) in meters (input)
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* Latitude : Latitude (phi) in radians (output)
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* Longitude : Longitude (lambda) in radians (output)
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double sin_theta, cos_theta;
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long Error_Code = ECK4_NO_ERROR;
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if ((Easting < (Eck4_False_Easting + Eck4_Min_Easting))
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|| (Easting > (Eck4_False_Easting + Eck4_Max_Easting)))
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{ /* Easting out of range */
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Error_Code |= ECK4_EASTING_ERROR;
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if ((Northing < (Eck4_False_Northing - Eck4_Delta_Northing))
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|| (Northing > (Eck4_False_Northing + Eck4_Delta_Northing)))
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{ /* Northing out of range */
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Error_Code |= ECK4_NORTHING_ERROR;
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dy = Northing - Eck4_False_Northing;
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dx = Easting - Eck4_False_Easting;
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sin_theta = sin(theta);
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cos_theta = cos(theta);
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num = NUM(theta, sin_theta, cos_theta);
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*Latitude = asin(num / two_PLUS_PI_OVER_2);
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*Longitude = Eck4_Origin_Long + dx / (Ra0 * (1 + cos_theta));
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if (*Latitude > PI_OVER_2) /* force distorted values to 90, -90 degrees */
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*Latitude = PI_OVER_2;
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else if (*Latitude < -PI_OVER_2)
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*Latitude = -PI_OVER_2;
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*Longitude -= TWO_PI;
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if (*Longitude < -PI)
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*Longitude += TWO_PI;
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if (*Longitude > PI) /* force distorted values to 180, -180 degrees */
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else if (*Longitude < -PI)
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} /* End Convert_Eckert4_To_Geodetic */
added
removed
dt_cc/eckert4/eckert4.c
