gc2gde.c

#include "erfa.h"
#include "erfam.h"

int eraGc2gde ( double a, double f, double xyz[3],
                double *elong, double *phi, double *height )
/*
**  - - - - - - - - - -
**   e r a G c 2 g d e
**  - - - - - - - - - -
**
**  Transform geocentric coordinates to geodetic for a reference
**  ellipsoid of specified form.
**
**  Given:
**     a       double     equatorial radius (Notes 2,4)
**     f       double     flattening (Note 3)
**     xyz     double[3]  geocentric vector (Note 4)
**
**  Returned:
**     elong   double     longitude (radians, east +ve)
**     phi     double     latitude (geodetic, radians)
**     height  double     height above ellipsoid (geodetic, Note 4)
**
**  Returned (function value):
**             int        status:  0 = OK
**                                -1 = illegal f
**                                -2 = illegal a
**
**  Notes:
**
**  1) This function is based on the GCONV2H Fortran subroutine by
**     Toshio Fukushima (see reference).
**
**  2) The equatorial radius, a, can be in any units, but meters is
**     the conventional choice.
**
**  3) The flattening, f, is (for the Earth) a value around 0.00335,
**     i.e. around 1/298.
**
**  4) The equatorial radius, a, and the geocentric vector, xyz,
**     must be given in the same units, and determine the units of
**     the returned height, height.
**
**  5) If an error occurs (status < 0), elong, phi and height are
**     unchanged.
**
**  6) The inverse transformation is performed in the function
**     eraGd2gce.
**
**  7) The transformation for a standard ellipsoid (such as ERFA_WGS84) can
**     more conveniently be performed by calling eraGc2gd, which uses a
**     numerical code to identify the required A and F values.
**
**  Reference:
**
**     Fukushima, T., "Transformation from Cartesian to geodetic
**     coordinates accelerated by Halley's method", J.Geodesy (2006)
**     79: 689-693
**
**  This revision:  2021 May 11
**
**  Copyright (C) 2013-2023, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   double aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc,
                 c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1,
                 cc, s12, cc2;


/* ------------- */
/* Preliminaries */
/* ------------- */

/* Validate ellipsoid parameters. */
   if ( f < 0.0 || f >= 1.0 ) return -1;
   if ( a <= 0.0 ) return -2;

/* Functions of ellipsoid parameters (with further validation of f). */
   aeps2 = a*a * 1e-32;
   e2 = (2.0 - f) * f;
   e4t = e2*e2 * 1.5;
   ec2 = 1.0 - e2;
   if ( ec2 <= 0.0 ) return -1;
   ec = sqrt(ec2);
   b = a * ec;

/* Cartesian components. */
   x = xyz[0];
   y = xyz[1];
   z = xyz[2];

/* Distance from polar axis squared. */
   p2 = x*x + y*y;

/* Longitude. */
   *elong = p2 > 0.0 ? atan2(y, x) : 0.0;

/* Unsigned z-coordinate. */
   absz = fabs(z);

/* Proceed unless polar case. */
   if ( p2 > aeps2 ) {

   /* Distance from polar axis. */
      p = sqrt(p2);

   /* Normalization. */
      s0 = absz / a;
      pn = p / a;
      zc = ec * s0;

   /* Prepare Newton correction factors. */
      c0 = ec * pn;
      c02 = c0 * c0;
      c03 = c02 * c0;
      s02 = s0 * s0;
      s03 = s02 * s0;
      a02 = c02 + s02;
      a0 = sqrt(a02);
      a03 = a02 * a0;
      d0 = zc*a03 + e2*s03;
      f0 = pn*a03 - e2*c03;

   /* Prepare Halley correction factor. */
      b0 = e4t * s02 * c02 * pn * (a0 - ec);
      s1 = d0*f0 - b0*s0;
      cc = ec * (f0*f0 - b0*c0);

   /* Evaluate latitude and height. */
      *phi = atan(s1/cc);
      s12 = s1 * s1;
      cc2 = cc * cc;
      *height = (p*cc + absz*s1 - a * sqrt(ec2*s12 + cc2)) /
                                                        sqrt(s12 + cc2);
   } else {

   /* Exception: pole. */
      *phi = ERFA_DPI / 2.0;
      *height = absz - b;
   }

/* Restore sign of latitude. */
   if ( z < 0 ) *phi = -*phi;

/* OK status. */
   return 0;

/* Finished. */

}
/*----------------------------------------------------------------------
**  
**  
**  Copyright (C) 2013-2023, NumFOCUS Foundation.
**  All rights reserved.
**  
**  This library is derived, with permission, from the International
**  Astronomical Union's "Standards of Fundamental Astronomy" library,
**  available from http://www.iausofa.org.
**  
**  The ERFA version is intended to retain identical functionality to
**  the SOFA library, but made distinct through different function and
**  file names, as set out in the SOFA license conditions.  The SOFA
**  original has a role as a reference standard for the IAU and IERS,
**  and consequently redistribution is permitted only in its unaltered
**  state.  The ERFA version is not subject to this restriction and
**  therefore can be included in distributions which do not support the
**  concept of "read only" software.
**  
**  Although the intent is to replicate the SOFA API (other than
**  replacement of prefix names) and results (with the exception of
**  bugs;  any that are discovered will be fixed), SOFA is not
**  responsible for any errors found in this version of the library.
**  
**  If you wish to acknowledge the SOFA heritage, please acknowledge
**  that you are using a library derived from SOFA, rather than SOFA
**  itself.
**  
**  
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