/***************************************************************************/
/* RSC IDENTIFIER: GEOCENTRIC
*
* ABSTRACT
*
* This component provides conversions between Geodetic coordinates (latitude,
* longitude in radians and height in meters) and Geocentric coordinates
* (X, Y, Z) 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:
*
* GEOCENT_NO_ERROR : No errors occurred in function
* GEOCENT_LAT_ERROR : Latitude out of valid range
* (-90 to 90 degrees)
* GEOCENT_LON_ERROR : Longitude out of valid range
* (-180 to 360 degrees)
* GEOCENT_A_ERROR : Semi-major axis lessthan or equal to zero
* GEOCENT_B_ERROR : Semi-minor axis lessthan or equal to zero
* GEOCENT_A_LESS_B_ERROR : Semi-major axis less than semi-minor axis
*
*
* REUSE NOTES
*
* GEOCENTRIC is intended for reuse by any application that performs
* coordinate conversions between geodetic coordinates and geocentric
* coordinates.
*
*
* REFERENCES
*
* An Improved Algorithm for Geocentric to Geodetic Coordinate Conversion,
* Ralph Toms, February 1996 UCRL-JC-123138.
*
* Further information on GEOCENTRIC can be found in the Reuse Manual.
*
* GEOCENTRIC 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
*
* GEOCENTRIC has no restrictions.
*
* ENVIRONMENT
*
* GEOCENTRIC 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
* ---- -----------
* 25-02-97 Original Code
*
* $Log$
* Revision 1.1 2005/02/01 22:08:43 jdh2358
* Initial revision
*
* Revision 1.5 2004/10/25 15:34:36 fwarmerdam
* make names of geodetic funcs from geotrans unique
*
* Revision 1.4 2004/05/03 16:28:01 warmerda
* Apply iterative solution to geocentric_to_geodetic as suggestion from
* Lothar Gorling.
* http://bugzilla.remotesensing.org/show_bug.cgi?id=563
*
* Revision 1.3 2002/01/08 15:04:08 warmerda
* The latitude clamping fix from September in Convert_Geodetic_To_Geocentric
* was botched. Fixed up now.
*
*/
/***************************************************************************/
/*
* INCLUDES
*/
#include <math.h>
#include "geocent.h"
/*
* math.h - is needed for calls to sin, cos, tan and sqrt.
* geocent.h - is needed for Error codes and prototype error checking.
*/
/***************************************************************************/
/*
* DEFINES
*/
#define PI 3.14159265358979323e0
#define PI_OVER_2 (PI / 2.0e0)
#define FALSE 0
#define TRUE 1
#define COS_67P5 0.38268343236508977 /* cosine of 67.5 degrees */
#define AD_C 1.0026000 /* Toms region 1 constant */
/***************************************************************************/
/*
* GLOBAL DECLARATIONS
*/
/* Ellipsoid parameters, default to WGS 84 */
double Geocent_a = 6378137.0; /* Semi-major axis of ellipsoid in meters */
double Geocent_b = 6356752.3142; /* Semi-minor axis of ellipsoid */
double Geocent_a2 = 40680631590769.0; /* Square of semi-major axis */
double Geocent_b2 = 40408299984087.05; /* Square of semi-minor axis */
double Geocent_e2 = 0.0066943799901413800; /* Eccentricity squared */
double Geocent_ep2 = 0.00673949675658690300; /* 2nd eccentricity squared */
/*
* These state variables are for optimization purposes. The only function
* that should modify them is Set_Geocentric_Parameters.
*/
/***************************************************************************/
/*
* FUNCTIONS
*/
long pj_Set_Geocentric_Parameters (double a, double b)
{ /* BEGIN Set_Geocentric_Parameters */
/*
* The function Set_Geocentric_Parameters receives the ellipsoid parameters
* as inputs and sets the corresponding state variables.
*
* a : Semi-major axis, in meters. (input)
* b : Semi-minor axis, in meters. (input)
*/
long Error_Code = GEOCENT_NO_ERROR;
if (a <= 0.0)
Error_Code |= GEOCENT_A_ERROR;
if (b <= 0.0)
Error_Code |= GEOCENT_B_ERROR;
if (a < b)
Error_Code |= GEOCENT_A_LESS_B_ERROR;
if (!Error_Code)
{
Geocent_a = a;
Geocent_b = b;
Geocent_a2 = a * a;
Geocent_b2 = b * b;
Geocent_e2 = (Geocent_a2 - Geocent_b2) / Geocent_a2;
Geocent_ep2 = (Geocent_a2 - Geocent_b2) / Geocent_b2;
}
return (Error_Code);
} /* END OF Set_Geocentric_Parameters */
void pj_Get_Geocentric_Parameters (double *a,
double *b)
{ /* BEGIN Get_Geocentric_Parameters */
/*
* The function Get_Geocentric_Parameters returns the ellipsoid parameters
* to be used in geocentric coordinate conversions.
*
* a : Semi-major axis, in meters. (output)
* b : Semi-minor axis, in meters. (output)
*/
*a = Geocent_a;
*b = Geocent_b;
} /* END OF Get_Geocentric_Parameters */
long pj_Convert_Geodetic_To_Geocentric (double Latitude,
double Longitude,
double Height,
double *X,
double *Y,
double *Z)
{ /* BEGIN Convert_Geodetic_To_Geocentric */
/*
* The function Convert_Geodetic_To_Geocentric converts geodetic coordinates
* (latitude, longitude, and height) to geocentric coordinates (X, Y, Z),
* according to the current ellipsoid parameters.
*
* Latitude : Geodetic latitude in radians (input)
* Longitude : Geodetic longitude in radians (input)
* Height : Geodetic height, in meters (input)
* X : Calculated Geocentric X coordinate, in meters (output)
* Y : Calculated Geocentric Y coordinate, in meters (output)
* Z : Calculated Geocentric Z coordinate, in meters (output)
*
*/
long Error_Code = GEOCENT_NO_ERROR;
double Rn; /* Earth radius at location */
double Sin_Lat; /* sin(Latitude) */
double Sin2_Lat; /* Square of sin(Latitude) */
double Cos_Lat; /* cos(Latitude) */
/*
** Don't blow up if Latitude is just a little out of the value
** range as it may just be a rounding issue. Also removed longitude
** test, it should be wrapped by cos() and sin(). NFW for PROJ.4, Sep/2001.
*/
if( Latitude < -PI_OVER_2 && Latitude > -1.001 * PI_OVER_2 )
Latitude = -PI_OVER_2;
else if( Latitude > PI_OVER_2 && Latitude < 1.001 * PI_OVER_2 )
Latitude = PI_OVER_2;
else if ((Latitude < -PI_OVER_2) || (Latitude > PI_OVER_2))
{ /* Latitude out of range */
Error_Code |= GEOCENT_LAT_ERROR;
}
if (!Error_Code)
{ /* no errors */
if (Longitude > PI)
Longitude -= (2*PI);
Sin_Lat = sin(Latitude);
Cos_Lat = cos(Latitude);
Sin2_Lat = Sin_Lat * Sin_Lat;
Rn = Geocent_a / (sqrt(1.0e0 - Geocent_e2 * Sin2_Lat));
*X = (Rn + Height) * Cos_Lat * cos(Longitude);
*Y = (Rn + Height) * Cos_Lat * sin(Longitude);
*Z = ((Rn * (1 - Geocent_e2)) + Height) * Sin_Lat;
}
return (Error_Code);
} /* END OF Convert_Geodetic_To_Geocentric */
/*
* The function Convert_Geocentric_To_Geodetic converts geocentric
* coordinates (X, Y, Z) to geodetic coordinates (latitude, longitude,
* and height), according to the current ellipsoid parameters.
*
* X : Geocentric X coordinate, in meters. (input)
* Y : Geocentric Y coordinate, in meters. (input)
* Z : Geocentric Z coordinate, in meters. (input)
* Latitude : Calculated latitude value in radians. (output)
* Longitude : Calculated longitude value in radians. (output)
* Height : Calculated height value, in meters. (output)
*/
#define USE_ITERATIVE_METHOD
void pj_Convert_Geocentric_To_Geodetic (double X,
double Y,
double Z,
double *Latitude,
double *Longitude,
double *Height)
{ /* BEGIN Convert_Geocentric_To_Geodetic */
#if !defined(USE_ITERATIVE_METHOD)
/*
* The method used here is derived from 'An Improved Algorithm for
* Geocentric to Geodetic Coordinate Conversion', by Ralph Toms, Feb 1996
*/
/* Note: Variable names follow the notation used in Toms, Feb 1996 */
double W; /* distance from Z axis */
double W2; /* square of distance from Z axis */
double T0; /* initial estimate of vertical component */
double T1; /* corrected estimate of vertical component */
double S0; /* initial estimate of horizontal component */
double S1; /* corrected estimate of horizontal component */
double Sin_B0; /* sin(B0), B0 is estimate of Bowring aux variable */
double Sin3_B0; /* cube of sin(B0) */
double Cos_B0; /* cos(B0) */
double Sin_p1; /* sin(phi1), phi1 is estimated latitude */
double Cos_p1; /* cos(phi1) */
double Rn; /* Earth radius at location */
double Sum; /* numerator of cos(phi1) */
int At_Pole; /* indicates location is in polar region */
At_Pole = FALSE;
if (X != 0.0)
{
*Longitude = atan2(Y,X);
}
else
{
if (Y > 0)
{
*Longitude = PI_OVER_2;
}
else if (Y < 0)
{
*Longitude = -PI_OVER_2;
}
else
{
At_Pole = TRUE;
*Longitude = 0.0;
if (Z > 0.0)
{ /* north pole */
*Latitude = PI_OVER_2;
}
else if (Z < 0.0)
{ /* south pole */
*Latitude = -PI_OVER_2;
}
else
{ /* center of earth */
*Latitude = PI_OVER_2;
*Height = -Geocent_b;
return;
}
}
}
W2 = X*X + Y*Y;
W = sqrt(W2);
T0 = Z * AD_C;
S0 = sqrt(T0 * T0 + W2);
Sin_B0 = T0 / S0;
Cos_B0 = W / S0;
Sin3_B0 = Sin_B0 * Sin_B0 * Sin_B0;
T1 = Z + Geocent_b * Geocent_ep2 * Sin3_B0;
Sum = W - Geocent_a * Geocent_e2 * Cos_B0 * Cos_B0 * Cos_B0;
S1 = sqrt(T1*T1 + Sum * Sum);
Sin_p1 = T1 / S1;
Cos_p1 = Sum / S1;
Rn = Geocent_a / sqrt(1.0 - Geocent_e2 * Sin_p1 * Sin_p1);
if (Cos_p1 >= COS_67P5)
{
*Height = W / Cos_p1 - Rn;
}
else if (Cos_p1 <= -COS_67P5)
{
*Height = W / -Cos_p1 - Rn;
}
else
{
*Height = Z / Sin_p1 + Rn * (Geocent_e2 - 1.0);
}
if (At_Pole == FALSE)
{
*Latitude = atan(Sin_p1 / Cos_p1);
}
#else /* defined(USE_ITERATIVE_METHOD) */
/*
* Reference...
* ============
* Wenzel, H.-G.(1985): Hochauflösende Kugelfunktionsmodelle für
* das Gravitationspotential der Erde. Wiss. Arb. Univ. Hannover
* Nr. 137, p. 130-131.
* Programmed by GGA- Leibniz-Institue of Applied Geophysics
* Stilleweg 2
* D-30655 Hannover
* Federal Republic of Germany
* Internet: www.gga-hannover.de
*
* Hannover, March 1999, April 2004.
* see also: comments in statements
* remarks:
* Mathematically exact and because of symmetry of rotation-ellipsoid,
* each point (X,Y,Z) has at least two solutions (Latitude1,Longitude1,Height1) and
* (Latitude2,Longitude2,Height2). Is point=(0.,0.,Z) (P=0.), so you get even
* four solutions, every two symmetrical to the semi-minor axis.
* Here Height1 and Height2 have at least a difference in order of
* radius of curvature (e.g. (0,0,b)=> (90.,0.,0.) or (-90.,0.,-2b);
* (a+100.)*(sqrt(2.)/2.,sqrt(2.)/2.,0.) => (0.,45.,100.) or
* (0.,225.,-(2a+100.))).
* The algorithm always computes (Latitude,Longitude) with smallest |Height|.
* For normal computations, that means |Height|<10000.m, algorithm normally
* converges after to 2-3 steps!!!
* But if |Height| has the amount of length of ellipsoid's axis
* (e.g. -6300000.m), algorithm needs about 15 steps.
*/
/* local defintions and variables */
/* end-criterium of loop, accuracy of sin(Latitude) */
#define genau 1.E-12
#define genau2 (genau*genau)
#define maxiter 30
double P; /* distance between semi-minor axis and location */
double RR; /* distance between center and location */
double CT; /* sin of geocentric latitude */
double ST; /* cos of geocentric latitude */
double RX;
double RK;
double RN; /* Earth radius at location */
double CPHI0; /* cos of start or old geodetic latitude in iterations */
double SPHI0; /* sin of start or old geodetic latitude in iterations */
double CPHI; /* cos of searched geodetic latitude */
double SPHI; /* sin of searched geodetic latitude */
double SDPHI; /* end-criterium: addition-theorem of sin(Latitude(iter)-Latitude(iter-1)) */
int At_Pole; /* indicates location is in polar region */
int iter; /* # of continous iteration, max. 30 is always enough (s.a.) */
At_Pole = FALSE;
P = sqrt(X*X+Y*Y);
RR = sqrt(X*X+Y*Y+Z*Z);
/* special cases for latitude and longitude */
if (P/Geocent_a < genau) {
/* special case, if P=0. (X=0., Y=0.) */
At_Pole = TRUE;
*Longitude = 0.;
/* if (X,Y,Z)=(0.,0.,0.) then Height becomes semi-minor axis
* of ellipsoid (=center of mass), Latitude becomes PI/2 */
if (RR/Geocent_a < genau) {
*Latitude = PI_OVER_2;
*Height = -Geocent_b;
return ;
}
}
else {
/* ellipsoidal (geodetic) longitude
* interval: -PI < Longitude <= +PI */
*Longitude=atan2(Y,X);
}
/* --------------------------------------------------------------
* Following iterative algorithm was developped by
* "Institut für Erdmessung", University of Hannover, July 1988.
* Internet: www.ife.uni-hannover.de
* Iterative computation of CPHI,SPHI and Height.
* Iteration of CPHI and SPHI to 10**-12 radian resp.
* 2*10**-7 arcsec.
* --------------------------------------------------------------
*/
CT = Z/RR;
ST = P/RR;
RX = 1.0/sqrt(1.0-Geocent_e2*(2.0-Geocent_e2)*ST*ST);
CPHI0 = ST*(1.0-Geocent_e2)*RX;
SPHI0 = CT*RX;
iter = 0;
/* loop to find sin(Latitude) resp. Latitude
* until |sin(Latitude(iter)-Latitude(iter-1))| < genau */
do
{
iter++;
RN = Geocent_a/sqrt(1.0-Geocent_e2*SPHI0*SPHI0);
/* ellipsoidal (geodetic) height */
*Height = P*CPHI0+Z*SPHI0-RN*(1.0-Geocent_e2*SPHI0*SPHI0);
RK = Geocent_e2*RN/(RN+*Height);
RX = 1.0/sqrt(1.0-RK*(2.0-RK)*ST*ST);
CPHI = ST*(1.0-RK)*RX;
SPHI = CT*RX;
SDPHI = SPHI*CPHI0-CPHI*SPHI0;
CPHI0 = CPHI;
SPHI0 = SPHI;
}
while (SDPHI*SDPHI > genau2 && iter < maxiter);
/* ellipsoidal (geodetic) latitude */
*Latitude=atan(SPHI/fabs(CPHI));
return;
#endif /* defined(USE_ITERATIVE_METHOD) */
} /* END OF Convert_Geocentric_To_Geodetic */
