path: root/src/3rdparty/proj/geocent.c

/***************************************************************************/
/* 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
 *
 */


/***************************************************************************/
/*
 *                               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 */


/***************************************************************************/
/*
 *                              FUNCTIONS     
 */


long pj_Set_Geocentric_Parameters (GeocentricInfo *gi, 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)
    {
        gi->Geocent_a = a;
        gi->Geocent_b = b;
        gi->Geocent_a2 = a * a;
        gi->Geocent_b2 = b * b;
        gi->Geocent_e2 = (gi->Geocent_a2 - gi->Geocent_b2) / gi->Geocent_a2;
        gi->Geocent_ep2 = (gi->Geocent_a2 - gi->Geocent_b2) / gi->Geocent_b2;
    }
    return (Error_Code);
} /* END OF Set_Geocentric_Parameters */


void pj_Get_Geocentric_Parameters (GeocentricInfo *gi,
                                   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 = gi->Geocent_a;
    *b = gi->Geocent_b;
} /* END OF Get_Geocentric_Parameters */


long pj_Convert_Geodetic_To_Geocentric (GeocentricInfo *gi,
                                        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 = gi->Geocent_a / (sqrt(1.0e0 - gi->Geocent_e2 * Sin2_Lat));
    *X = (Rn + Height) * Cos_Lat * cos(Longitude);
    *Y = (Rn + Height) * Cos_Lat * sin(Longitude);
    *Z = ((Rn * (1 - gi->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 (GeocentricInfo *gi,
                                        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 + gi->Geocent_b * gi->Geocent_ep2 * Sin3_B0;
    Sum = W - gi->Geocent_a * gi->Geocent_e2 * Cos_B0 * Cos_B0 * Cos_B0;
    S1 = sqrt(T1*T1 + Sum * Sum);
    Sin_p1 = T1 / S1;
    Cos_p1 = Sum / S1;
    Rn = gi->Geocent_a / sqrt(1.0 - gi->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 * (gi->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/gi->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/gi->Geocent_a < genau) {
            *Latitude = PI_OVER_2;
            *Height   = -gi->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-gi->Geocent_e2*(2.0-gi->Geocent_e2)*ST*ST);
    CPHI0 = ST*(1.0-gi->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 = gi->Geocent_a/sqrt(1.0-gi->Geocent_e2*SPHI0*SPHI0);

/*  ellipsoidal (geodetic) height */
        *Height = P*CPHI0+Z*SPHI0-RN*(1.0-gi->Geocent_e2*SPHI0*SPHI0);

        RK = gi->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 */