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/***************************************************************************/
/* RSC IDENTIFIER: CASSINI
*
* ABSTRACT
*
* This component provides conversions between Geodetic coordinates
* (latitude and longitude in radians) and Cassini projection coordinates
* (easting and northing in meters).
*
* 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:
*
* CASS_NO_ERROR : No errors occurred in function
* CASS_LAT_ERROR : Latitude outside of valid range
* (-90 to 90 degrees)
* CASS_LON_ERROR : Longitude outside of valid range
* (-180 to 360 degrees)
* CASS_EASTING_ERROR : Easting outside of valid range
* (False_Easting +/- ~20,000,000 m,
* depending on ellipsoid parameters
* and Origin_Latitude)
* CASS_NORTHING_ERROR : Northing outside of valid range
* (False_Northing +/- ~57,000,000 m,
* depending on ellipsoid parameters
* and Origin_Latitude)
* CASS_ORIGIN_LAT_ERROR : Origin latitude outside of valid range
* (-90 to 90 degrees)
* CASS_CENT_MER_ERROR : Central meridian outside of valid range
* (-180 to 360 degrees)
* CASS_A_ERROR : Semi-major axis less than or equal to zero
* CASS_INV_F_ERROR : Inverse flattening outside of valid range
* (250 to 350)
* CASS_LON_WARNING : Distortion will result if longitude is more
* than 4 degrees from the Central Meridian
*
* REUSE NOTES
*
* CASSINI is intended for reuse by any application that performs a
* Cassini projection or its inverse.
*
* REFERENCES
*
* Further information on CASSINI can be found in the Reuse Manual.
*
* CASSINI 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
*
* CASSINI has no restrictions.
*
* ENVIRONMENT
*
* CASSINI was tested and certified in the following environments:
*
* 1. Solaris 2.5 with GCC 2.8.1
* 2. MS Windows 95 with MS Visual C++ 6
*
* MODIFICATIONS
*
* Date Description
* ---- -----------
* 04/16/99 Original Code
*
*/
/***************************************************************************/
/*
* INCLUDES
*/
#include <math.h>
#include "cassini.h"
/*
* math.h - Standard C math library
* cassini.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 CASS_M(c0lat, c1s2lat, c2s4lat, c3s6lat) (Cass_a*(c0lat-c1s2lat+c2s4lat-c3s6lat))
#define CASS_RD(sinlat) (sqrt(1.0 - es2 * (sinlat * sinlat)))
#define CASS_COEFF_TIMES_SIN(coeff, x, latit) (coeff * (sin (x * latit)))
#define FLOAT_EQ(x,v,epsilon) (((v - epsilon) < x) && (x < (v + epsilon)))
#define THIRTY_ONE (31.0 * PI / 180) /* 31 degrees in radians */
/***************************************************************************/
/*
* GLOBALS
*/
/* Ellipsoid Parameters, default to WGS 84 */
static double Cass_a = 6378137.0; /* Semi-major axis of ellipsoid in meters */
static double Cass_f = 1 / 298.257223563; /* Flattening of ellipsoid */
static double es2 = 0.0066943799901413800; /* Eccentricity (0.08181919084262188000) squared */
static double es4 =4.4814723452405e-005; /* es2 * es2 */
static double es6 = 3.0000678794350e-007; /* es4 * es2 */
static double M0 = 0.0;
static double c0 = .99832429845280; /* 1 - es2 / 4.0 - 3.0 * es4 / 64.0 - 5.0 * es6 / 256.0 */
static double c1 = .0025146070605187; /* 3.0 * es2 / 8.0 + 3.0 * es4 / 32.0 + 45.0 * es6 / 1024.0 */
static double c2 = 2.6390465943377e-006; /* 15.0 * es4 / 256.0 + 45.0 * es6 / 1024.0 */
static double c3 = 3.4180460865959e-009; /* 35.0 * es6 / 3072.0 */
static double One_Minus_es2 = .99330562000986; /* 1.0 - es2 */
static double a0 = .0025188265843907; /* 3.0 * e1 / 2.0 - 27.0 * e3 / 32.0 */
static double a1 = 3.7009490356205e-006; /* 21.0 * e2 / 16.0 - 55.0 * e4 / 32.0 */
static double a2 = 7.4478137675038e-009; /* 151.0 * e3 / 96.0 */
static double a3 = 1.7035993238596e-011; /* 1097.0 * e4 /512.0 */
/* Cassini projection Parameters */
static double Cass_Origin_Lat = 0.0; /* Latitude of origin in radians */
static double Cass_Origin_Long = 0.0; /* Longitude of origin in radians */
static double Cass_False_Northing = 0.0; /* False northing in meters */
static double Cass_False_Easting = 0.0; /* False easting in meters */
/* Maximum variance for easting and northing values for WGS 84.
*/
static double Cass_Min_Easting = -20037508.4;
static double Cass_Max_Easting = 20037508.4;
static double Cass_Min_Northing = -56575846.0;
static double Cass_Max_Northing = 56575846.0;
/*
* These state variables are for optimization purposes. The only function
* that should modify them is Set_Cassini_Parameters.
*/
/***************************************************************************/
/*
* FUNCTIONS
*/
long Set_Cassini_Parameters(double a,
double f,
double Origin_Latitude,
double Central_Meridian,
double False_Easting,
double False_Northing)
{ /* Begin Set_Cassini_Parameters */
/*
* The function Set_Cassini_Parameters receives the ellipsoid parameters and
* Cassini projection parameters as inputs, and sets the corresponding state
* variables. If any errors occur, the error code(s) are returned by the
* function, otherwise CASS_NO_ERROR is returned.
*
* a : Semi-major axis of ellipsoid, in meters (input)
* f : Flattening of ellipsoid (input)
* Origin_Latitude : Latitude in radians at which the (input)
* point scale factor is 1.0
* Central_Meridian : Longitude in radians at the center of (input)
* the projection
* False_Easting : A coordinate value in meters assigned to the
* central meridian of the projection. (input)
* False_Northing : A coordinate value in meters assigned to the
* origin latitude of the projection (input)
*/
double j,three_es4;
double x, e1, e2, e3, e4;
double lat, sin2lat, sin4lat, sin6lat;
double temp;
double inv_f = 1 / f;
long Error_Code = CASS_NO_ERROR;
if (a <= 0.0)
{ /* Semi-major axis must be greater than zero */
Error_Code |= CASS_A_ERROR;
}
if ((inv_f < 250) || (inv_f > 350))
{ /* Inverse flattening must be between 250 and 350 */
Error_Code |= CASS_INV_F_ERROR;
}
if ((Origin_Latitude < -PI_OVER_2) || (Origin_Latitude > PI_OVER_2))
{ /* origin latitude out of range */
Error_Code |= CASS_ORIGIN_LAT_ERROR;
}
if ((Central_Meridian < -PI) || (Central_Meridian > TWO_PI))
{ /* origin longitude out of range */
Error_Code |= CASS_CENT_MER_ERROR;
}
if (!Error_Code)
{ /* no errors */
Cass_a = a;
Cass_f = f;
Cass_Origin_Lat = Origin_Latitude;
if (Central_Meridian > PI)
Central_Meridian -= TWO_PI;
Cass_Origin_Long = Central_Meridian;
Cass_False_Northing = False_Northing;
Cass_False_Easting = False_Easting;
es2 = 2 * Cass_f - Cass_f * Cass_f;
es4 = es2 * es2;
es6 = es4 * es2;
j = 45.0 * es6 / 1024.0;
three_es4 = 3.0 * es4;
c0 = 1 - es2 / 4.0 - three_es4 / 64.0 - 5.0 * es6 / 256.0;
c1 = 3.0 * es2 /8.0 + three_es4 / 32.0 + j;
c2 = 15.0 * es4 / 256.0 + j;
c3 = 35.0 * es6 / 3072.0;
lat = c0 * Cass_Origin_Lat;
sin2lat = CASS_COEFF_TIMES_SIN(c1, 2.0, Cass_Origin_Lat);
sin4lat = CASS_COEFF_TIMES_SIN(c2, 4.0, Cass_Origin_Lat);
sin6lat = CASS_COEFF_TIMES_SIN(c3, 6.0, Cass_Origin_Lat);
M0 = CASS_M(lat, sin2lat, sin4lat, sin6lat);
One_Minus_es2 = 1.0 - es2;
x = sqrt (One_Minus_es2);
e1 = (1 - x) / (1 + x);
e2 = e1 * e1;
e3 = e2 * e1;
e4 = e3 * e1;
a0 = 3.0 * e1 / 2.0 - 27.0 * e3 / 32.0;
a1 = 21.0 * e2 / 16.0 - 55.0 * e4 / 32.0;
a2 = 151.0 * e3 / 96.0;
a3 = 1097.0 * e4 /512.0;
if (Cass_Origin_Long > 0)
{
Convert_Geodetic_To_Cassini(THIRTY_ONE, Cass_Origin_Long - PI, &temp, &Cass_Max_Northing);
Convert_Geodetic_To_Cassini(-THIRTY_ONE, Cass_Origin_Long - PI, &temp, &Cass_Min_Northing);
Cass_Max_Easting = 19926188.9;
Cass_Min_Easting = -20037508.4;
}
else if (Cass_Origin_Long < 0)
{
Convert_Geodetic_To_Cassini(THIRTY_ONE, PI + Cass_Origin_Long, &temp, &Cass_Max_Northing);
Convert_Geodetic_To_Cassini(-THIRTY_ONE, PI + Cass_Origin_Long, &temp, &Cass_Min_Northing);
Cass_Max_Easting = 20037508.4;
Cass_Min_Easting = -19926188.9;
}
else
{
Convert_Geodetic_To_Cassini(THIRTY_ONE, PI, &temp, &Cass_Max_Northing);
Convert_Geodetic_To_Cassini(-THIRTY_ONE, PI , &temp, &Cass_Min_Northing);
Cass_Max_Easting = 20037508.4;
Cass_Min_Easting = -20037508.4;
}
if(Cass_False_Northing)
{
Cass_Min_Northing -= Cass_False_Northing;
Cass_Max_Northing -= Cass_False_Northing;
}
} /* End if(!Error_Code) */
return (Error_Code);
} /* End Set_Cassini_Parameters */
void Get_Cassini_Parameters(double *a,
double *f,
double *Origin_Latitude,
double *Central_Meridian,
double *False_Easting,
double *False_Northing)
{ /* Begin Get_Cassini_Parameters */
/*
* The function Get_Cassini_Parameters returns the current ellipsoid
* parameters, Cassini projection parameters.
*
* a : Semi-major axis of ellipsoid, in meters (output)
* f : Flattening of ellipsoid (output)
* Origin_Latitude : Latitude in radians at which the (output)
* point scale factor is 1.0
* Central_Meridian : Longitude in radians at the center of (output)
* the projection
* False_Easting : A coordinate value in meters assigned to the
* central meridian of the projection. (output)
* False_Northing : A coordinate value in meters assigned to the
* origin latitude of the projection (output)
*/
*a = Cass_a;
*f = Cass_f;
*Origin_Latitude = Cass_Origin_Lat;
*Central_Meridian = Cass_Origin_Long;
*False_Easting = Cass_False_Easting;
*False_Northing = Cass_False_Northing;
return;
} /* End Get_Cassini_Parameters */
long Convert_Geodetic_To_Cassini (double Latitude,
double Longitude,
double *Easting,
double *Northing)
{ /* Begin Convert_Geodetic_To_Cassini */
/*
* The function Convert_Geodetic_To_Cassini converts geodetic (latitude and
* longitude) coordinates to Cassini projection (easting and northing)
* coordinates, according to the current ellipsoid and Cassini projection
* parameters. If any errors occur, the error code(s) are returned by the
* function, otherwise CASS_NO_ERROR is returned.
*
* Latitude : Latitude (phi) in radians (input)
* Longitude : Longitude (lambda) in radians (input)
* Easting : Easting (X) in meters (output)
* Northing : Northing (Y) in meters (output)
*/
double lat, sin2lat, sin4lat, sin6lat;
double RD;
double tlat = tan(Latitude);
double clat = cos(Latitude);
double slat = sin(Latitude);
double dlam; /* Longitude - Central Meridan */
double NN;
double TT;
double AA, A2, A3, A4, A5;
double CC;
double MM;
long Error_Code = CASS_NO_ERROR;
if ((Latitude < -PI_OVER_2) || (Latitude > PI_OVER_2))
{ /* Latitude out of range */
Error_Code |= CASS_LAT_ERROR;
}
if ((Longitude < -PI) || (Longitude > TWO_PI))
{ /* Longitude out of range */
Error_Code |= CASS_LON_ERROR;
}
if (!Error_Code)
{ /* no errors */
dlam = Longitude - Cass_Origin_Long;
if (fabs(dlam) > (4.0 * PI / 180))
{ /* Distortion will result if Longitude is more than 4 degrees from the Central Meridian */
Error_Code |= CASS_LON_WARNING;
}
if (dlam > PI)
{
dlam -= TWO_PI;
}
if (dlam < -PI)
{
dlam += TWO_PI;
}
RD = CASS_RD(slat);
NN = Cass_a / RD;
TT = tlat * tlat;
AA = dlam * clat;
A2 = AA * AA;
A3 = AA * A2;
A4 = AA * A3;
A5 = AA * A4;
CC = es2 * clat * clat / One_Minus_es2;
lat = c0 * Latitude;
sin2lat = CASS_COEFF_TIMES_SIN(c1, 2.0, Latitude);
sin4lat = CASS_COEFF_TIMES_SIN(c2, 4.0, Latitude);
sin6lat = CASS_COEFF_TIMES_SIN(c3, 6.0, Latitude);
MM = CASS_M(lat, sin2lat, sin4lat, sin6lat);
*Easting = NN * (AA - (TT * A3 / 6.0) - (8.0 - TT + 8.0 * CC) *
(TT * A5 / 120.0)) + Cass_False_Easting;
*Northing = MM - M0 + NN * tlat * ((A2 / 2.0) + (5.0 - TT +
6.0 * CC) * A4 / 24.0) + Cass_False_Northing;
}
return (Error_Code);
} /* End Convert_Geodetic_To_Cassini */
long Convert_Cassini_To_Geodetic(double Easting,
double Northing,
double *Latitude,
double *Longitude)
{ /* Begin Convert_Cassini_To_Geodetic */
/*
* The function Convert_Cassini_To_Geodetic converts Cassini projection
* (easting and northing) coordinates to geodetic (latitude and longitude)
* coordinates, according to the current ellipsoid and Cassini projection
* coordinates. If any errors occur, the error code(s) are returned by the
* function, otherwise CASS_NO_ERROR is returned.
*
* Easting : Easting (X) in meters (input)
* Northing : Northing (Y) in meters (input)
* Latitude : Latitude (phi) in radians (output)
* Longitude : Longitude (lambda) in radians (output)
*/
double dx; /* Delta easting - Difference in easting (easting-FE) */
double dy; /* Delta northing - Difference in northing (northing-FN) */
double mu1;
double sin2mu, sin4mu, sin6mu, sin8mu;
double M1;
double phi1;
double tanphi1, sinphi1, cosphi1;
double T1, T;
double N1;
double RD, R1;
double DD, D2, D3, D4, D5;
const double epsilon = 1.0e-1;
long Error_Code = CASS_NO_ERROR;
if ((Easting < (Cass_False_Easting + Cass_Min_Easting))
|| (Easting > (Cass_False_Easting + Cass_Max_Easting)))
{ /* Easting out of range */
Error_Code |= CASS_EASTING_ERROR;
}
if ((Northing < (Cass_False_Northing + Cass_Min_Northing - epsilon))
|| (Northing > (Cass_False_Northing + Cass_Max_Northing + epsilon)))
{ /* Northing out of range */
Error_Code |= CASS_NORTHING_ERROR;
}
if (!Error_Code)
{ /* no errors */
dy = Northing - Cass_False_Northing;
dx = Easting - Cass_False_Easting;
M1 = M0 + dy;
mu1 = M1 / (Cass_a * c0);
sin2mu = CASS_COEFF_TIMES_SIN(a0, 2.0, mu1);
sin4mu = CASS_COEFF_TIMES_SIN(a1, 4.0, mu1);
sin6mu = CASS_COEFF_TIMES_SIN(a2, 6.0, mu1);
sin8mu = CASS_COEFF_TIMES_SIN(a3, 8.0, mu1);
phi1 = mu1 + sin2mu + sin4mu + sin6mu + sin8mu;
if (FLOAT_EQ(phi1,PI_OVER_2,.00001))
{
*Latitude = PI_OVER_2;
*Longitude = Cass_Origin_Long;
}
else if (FLOAT_EQ(phi1,-PI_OVER_2,.00001))
{
*Latitude = -PI_OVER_2;
*Longitude = Cass_Origin_Long;
}
else
{
tanphi1 = tan(phi1);
sinphi1 = sin(phi1);
cosphi1 = cos(phi1);
T1 = tanphi1 * tanphi1;
RD = CASS_RD(sinphi1);
N1 = Cass_a / RD;
R1 = N1 * One_Minus_es2 / (RD * RD);
DD = dx / N1;
D2 = DD * DD;
D3 = D2 * DD;
D4 = D3 * DD;
D5 = D4 * DD;
T = (1.0 + 3.0 * T1);
*Latitude = phi1 - (N1 * tanphi1 / R1) * (D2 / 2.0 - T * D4 / 24.0);
*Longitude = Cass_Origin_Long + (DD - T1 * D3 / 3.0 + T * T1 * D5 / 15.0) / cosphi1;
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)
*Longitude -= TWO_PI;
if (*Longitude < -PI)
*Longitude += TWO_PI;
if (*Longitude > PI) /* force distorted values to 180, -180 degrees */
*Longitude = PI;
else if (*Longitude < -PI)
*Longitude = -PI;
}
if (fabs(*Longitude - Cass_Origin_Long) > (4.0 * PI / 180))
{ /* Distortion will result if Longitude is more than 4 degrees from the Central Meridian */
Error_Code |= CASS_LON_WARNING;
}
}
return (Error_Code);
} /* End Convert_Cassini_To_Geodetic */
|