Example #1
0
void palSubet ( double rc, double dc, double eq, double *rm, double *dm ) {
  double a[3];   /* The E-terms */
  double v[3];
  double f;
  int i;

  /* Note the preference for IAU routines */

  /* Retrieve the E-terms */
  palEtrms( eq, a );

  /* Spherical to Cartesian */
  iauS2c( rc, dc, v );

  /* Include the E-terms */
  f = 1.0 + iauPdp( v, a );
  for (i=0; i<3; i++) {
    v[i] = f*v[i] - a[i];
  }

  /* Cartesian to spherical */
  iauC2s( v, rm, dm );

  /* Bring RA into conventional range */
  *rm = iauAnp( *rm );

}
Example #2
0
void palAddet ( double rm, double dm, double eq, double *rc, double *dc ) {
  double a[3];   /* The E-terms */
  double v[3];
  int i;

  /* Note the preference for IAU routines */

  /* Retrieve the E-terms */
  palEtrms( eq, a );

  /* Spherical to Cartesian */
  iauS2c( rm, dm, v );

  /* Include the E-terms */
  for (i=0; i<3; i++) {
    v[i] += a[i];
  }

  /* Cartesian to spherical */
  iauC2s( v, rc, dc );

  /* Bring RA into conventional range */
  *rc = iauAnp( *rc );

}
Example #3
0
void palEqgal ( double dr, double dd, double *dl, double *db ) {

  double v1[3];
  double v2[3];

/*
*  L2,B2 system of galactic coordinates
*
*  P = 192.25       RA of galactic north pole (mean B1950.0)
*  Q =  62.6        inclination of galactic to mean B1950.0 equator
*  R =  33          longitude of ascending node
*
*  P,Q,R are degrees
*
*  Equatorial to galactic rotation matrix (J2000.0), obtained by
*  applying the standard FK4 to FK5 transformation, for zero proper
*  motion in FK5, to the columns of the B1950 equatorial to
*  galactic rotation matrix:
*/
  double rmat[3][3] = {
    { -0.054875539726,-0.873437108010,-0.483834985808 },
    { +0.494109453312,-0.444829589425,+0.746982251810 },
    { -0.867666135858,-0.198076386122,+0.455983795705 }
  };

  /* Spherical to Cartesian */
  iauS2c( dr, dd, v1 );

  /* Equatorial to Galactic */
  iauRxp( rmat, v1, v2 );

  /* Cartesian to spherical */
  iauC2s( v2, dl, db );

  /* Express in conventional ranges */
  *dl = iauAnp( *dl );
  *db = iauAnpm( *db );

}
void iauHfk5z(double rh, double dh, double date1, double date2,
              double *r5, double *d5, double *dr5, double *dd5)
/*
**  - - - - - - - - -
**   i a u H f k 5 z
**  - - - - - - - - -
**
**  Transform a Hipparcos star position into FK5 J2000.0, assuming
**  zero Hipparcos proper motion.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards Of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     rh            double    Hipparcos RA (radians)
**     dh            double    Hipparcos Dec (radians)
**     date1,date2   double    TDB date (Note 1)
**
**  Returned (all FK5, equinox J2000.0, date date1+date2):
**     r5            double    RA (radians)
**     d5            double    Dec (radians)
**     dr5           double    FK5 RA proper motion (rad/year, Note 4)
**     dd5           double    Dec proper motion (rad/year, Note 4)
**
**  Notes:
**
**  1) The TT date date1+date2 is a Julian Date, apportioned in any
**     convenient way between the two arguments.  For example,
**     JD(TT)=2450123.7 could be expressed in any of these ways,
**     among others:
**
**            date1          date2
**
**         2450123.7           0.0       (JD method)
**         2451545.0       -1421.3       (J2000 method)
**         2400000.5       50123.2       (MJD method)
**         2450123.5           0.2       (date & time method)
**
**     The JD method is the most natural and convenient to use in
**     cases where the loss of several decimal digits of resolution
**     is acceptable.  The J2000 method is best matched to the way
**     the argument is handled internally and will deliver the
**     optimum resolution.  The MJD method and the date & time methods
**     are both good compromises between resolution and convenience.
**
**  2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
**  3) The FK5 to Hipparcos transformation is modeled as a pure rotation
**     and spin;  zonal errors in the FK5 catalogue are not taken into
**     account.
**
**  4) It was the intention that Hipparcos should be a close
**     approximation to an inertial frame, so that distant objects have
**     zero proper motion;  such objects have (in general) non-zero
**     proper motion in FK5, and this function returns those fictitious
**     proper motions.
**
**  5) The position returned by this function is in the FK5 J2000.0
**     reference system but at date date1+date2.
**
**  6) See also iauFk52h, iauH2fk5, iauFk5zhz.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauFk5hip    FK5 to Hipparcos rotation and spin
**     iauRxp       product of r-matrix and p-vector
**     iauSxp       multiply p-vector by scalar
**     iauRxr       product of two r-matrices
**     iauTrxp      product of transpose of r-matrix and p-vector
**     iauPxp       vector product of two p-vectors
**     iauPv2s      pv-vector to spherical
**     iauAnp       normalize angle into range 0 to 2pi
**
**  Reference:
**
**     F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
**  This revision:  2013 June 18
**
**  SOFA release 2013-12-02
**
**  Copyright (C) 2013 IAU SOFA Board.  See notes at end.
*/
{
   double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3],
   rst[3][3], r5ht[3][3], pv5e[2][3], vv[3],
   w, r, v;


/* Time interval from fundamental epoch J2000.0 to given date (JY). */
   t = ((date1 - DJ00) + date2) / DJY;

/* Hipparcos barycentric position vector (normalized). */
   iauS2c(rh, dh, ph);

/* FK5 to Hipparcos orientation matrix and spin vector. */
   iauFk5hip(r5h, s5h);

/* Rotate the spin into the Hipparcos system. */
   iauRxp(r5h, s5h, sh);

/* Accumulated Hipparcos wrt FK5 spin over that interval. */
   iauSxp(t, s5h, vst);

/* Express the accumulated spin as a rotation matrix. */
   iauRv2m(vst, rst);

/* Rotation matrix:  accumulated spin, then FK5 to Hipparcos. */
   iauRxr(r5h, rst, r5ht);

/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
   iauTrxp(r5ht, ph, pv5e[0]);

/* Apply spin to the position giving a space motion. */
   iauPxp(sh, ph, vv);

/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
   iauTrxp(r5ht, vv, pv5e[1]);

/* FK5 position/velocity pv-vector to spherical. */
   iauPv2s(pv5e, &w, d5, &r, dr5, dd5, &v);
   *r5 = iauAnp(w);

   return;

/*----------------------------------------------------------------------
**
**  Copyright (C) 2013
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  [email protected]
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}
Example #5
0
void iauAticqn(double ri, double di, iauASTROM *astrom,
               int n, iauLDBODY b[], double *rc, double *dc)
/*
**  - - - - - - - - -
**   i a u A t i c q n
**  - - - - - - - - -
**
**  Quick CIRS to ICRS astrometric place transformation, given the star-
**  independent astrometry parameters plus a list of light-deflecting
**  bodies.
**
**  Use of this function is appropriate when efficiency is important and
**  where many star positions are all to be transformed for one date.
**  The star-independent astrometry parameters can be obtained by
**  calling one of the functions iauApci[13], iauApcg[13], iauApco[13]
**  or iauApcs[13].
*
*  If the only light-deflecting body to be taken into account is the
*  Sun, the iauAticq function can be used instead.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     ri,di  double      CIRS RA,Dec (radians)
**     astrom iauASTROM*  star-independent astrometry parameters:
**      pmt    double       PM time interval (SSB, Julian years)
**      eb     double[3]    SSB to observer (vector, au)
**      eh     double[3]    Sun to observer (unit vector)
**      em     double       distance from Sun to observer (au)
**      v      double[3]    barycentric observer velocity (vector, c)
**      bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
**      bpn    double[3][3] bias-precession-nutation matrix
**      along  double       longitude + s' (radians)
**      xpl    double       polar motion xp wrt local meridian (radians)
**      ypl    double       polar motion yp wrt local meridian (radians)
**      sphi   double       sine of geodetic latitude
**      cphi   double       cosine of geodetic latitude
**      diurab double       magnitude of diurnal aberration vector
**      eral   double       "local" Earth rotation angle (radians)
**      refa   double       refraction constant A (radians)
**      refb   double       refraction constant B (radians)
**      n     int           number of bodies (Note 3)
**      b     iauLDBODY[n] data for each of the n bodies (Notes 3,4):
**       bm    double       mass of the body (solar masses, Note 5)
**       dl    double       deflection limiter (Note 6)
**       pv    [2][3]       barycentric PV of the body (au, au/day)
**
**  Returned:
**     rc,dc  double     ICRS astrometric RA,Dec (radians)
**
**  Notes:
**
**  1) Iterative techniques are used for the aberration and light
**     deflection corrections so that the functions iauAticqn and
**     iauAtciqn are accurate inverses; even at the edge of the Sun's
**     disk the discrepancy is only about 1 nanoarcsecond.
**
**  2) If the only light-deflecting body to be taken into account is the
**     Sun, the iauAticq function can be used instead.
**
**  3) The struct b contains n entries, one for each body to be
**     considered.  If n = 0, no gravitational light deflection will be
**     applied, not even for the Sun.
**
**  4) The struct b should include an entry for the Sun as well as for
**     any planet or other body to be taken into account.  The entries
**     should be in the order in which the light passes the body.
**
**  5) In the entry in the b struct for body i, the mass parameter
**     b[i].bm can, as required, be adjusted in order to allow for such
**     effects as quadrupole field.
**
**  6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is
**     the angular separation (in radians) between star and body at
**     which limiting is applied.  As phi shrinks below the chosen
**     threshold, the deflection is artificially reduced, reaching zero
**     for phi = 0.   Example values suitable for a terrestrial
**     observer, together with masses, are as follows:
**
**        body i     b[i].bm        b[i].dl
**
**        Sun        1.0            6e-6
**        Jupiter    0.00095435     3e-9
**        Saturn     0.00028574     3e-10
**
**  7) For efficiency, validation of the contents of the b array is
**     omitted.  The supplied masses must be greater than zero, the
**     position and velocity vectors must be right, and the deflection
**     limiter greater than zero.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauTrxp      product of transpose of r-matrix and p-vector
**     iauZp        zero p-vector
**     iauAb        stellar aberration
**     iauLdn       light deflection by n bodies
**     iauC2s       p-vector to spherical
**     iauAnp       normalize angle into range +/- pi
**
**  This revision:   2013 October 9
**
**  SOFA release 2015-02-09
**
**  Copyright (C) 2015 IAU SOFA Board.  See notes at end.
*/
{
   int j, i;
   double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r,
          after[3];

/* CIRS RA,Dec to Cartesian. */
   iauS2c(ri, di, pi);

/* Bias-precession-nutation, giving GCRS proper direction. */
   iauTrxp(astrom->bpn, pi, ppr);

/* Aberration, giving GCRS natural direction. */
   iauZp(d);
   for (j = 0; j < 2; j++) {
      r2 = 0.0;
      for (i = 0; i < 3; i++) {
         w = ppr[i] - d[i];
         before[i] = w;
         r2 += w*w;
      }
      r = sqrt(r2);
      for (i = 0; i < 3; i++) {
         before[i] /= r;
      }
      iauAb(before, astrom->v, astrom->em, astrom->bm1, after);
      r2 = 0.0;
      for (i = 0; i < 3; i++) {
         d[i] = after[i] - before[i];
         w = ppr[i] - d[i];
         pnat[i] = w;
         r2 += w*w;
      }
      r = sqrt(r2);
      for (i = 0; i < 3; i++) {
         pnat[i] /= r;
      }
   }

/* Light deflection, giving BCRS coordinate direction. */
   iauZp(d);
   for (j = 0; j < 5; j++) {
      r2 = 0.0;
      for (i = 0; i < 3; i++) {
         w = pnat[i] - d[i];
         before[i] = w;
         r2 += w*w;
      }
      r = sqrt(r2);
      for (i = 0; i < 3; i++) {
         before[i] /= r;
      }
      iauLdn(n, b, astrom->eb, before, after);
      r2 = 0.0;
      for (i = 0; i < 3; i++) {
         d[i] = after[i] - before[i];
         w = pnat[i] - d[i];
         pco[i] = w;
         r2 += w*w;
      }
      r = sqrt(r2);
      for (i = 0; i < 3; i++) {
         pco[i] /= r;
      }
   }

/* ICRS astrometric RA,Dec. */
   iauC2s(pco, &w, dc);
   *rc = iauAnp(w);

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2015
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  [email protected]
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/

}
void iauS2p(double theta, double phi, double r, double p[3])
/*
**  - - - - - - -
**   i a u S 2 p
**  - - - - - - -
**
**  Convert spherical polar coordinates to p-vector.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards Of Fundamental Astronomy) software collection.
**
**  Status:  vector/matrix support function.
**
**  Given:
**     theta   double       longitude angle (radians)
**     phi     double       latitude angle (radians)
**     r       double       radial distance
**
**  Returned:
**     p       double[3]    Cartesian coordinates
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauSxp       multiply p-vector by scalar
**
**  This revision:  2013 June 18
**
**  SOFA release 2016-05-03
**
**  Copyright (C) 2016 IAU SOFA Board.  See notes at end.
*/
{
    double u[3];


    iauS2c(theta, phi, u);
    iauSxp(r, u, p);

    return;

    /*----------------------------------------------------------------------
    **
    **  Copyright (C) 2016
    **  Standards Of Fundamental Astronomy Board
    **  of the International Astronomical Union.
    **
    **  =====================
    **  SOFA Software License
    **  =====================
    **
    **  NOTICE TO USER:
    **
    **  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
    **  CONDITIONS WHICH APPLY TO ITS USE.
    **
    **  1. The Software is owned by the IAU SOFA Board ("SOFA").
    **
    **  2. Permission is granted to anyone to use the SOFA software for any
    **     purpose, including commercial applications, free of charge and
    **     without payment of royalties, subject to the conditions and
    **     restrictions listed below.
    **
    **  3. You (the user) may copy and distribute SOFA source code to others,
    **     and use and adapt its code and algorithms in your own software,
    **     on a world-wide, royalty-free basis.  That portion of your
    **     distribution that does not consist of intact and unchanged copies
    **     of SOFA source code files is a "derived work" that must comply
    **     with the following requirements:
    **
    **     a) Your work shall be marked or carry a statement that it
    **        (i) uses routines and computations derived by you from
    **        software provided by SOFA under license to you; and
    **        (ii) does not itself constitute software provided by and/or
    **        endorsed by SOFA.
    **
    **     b) The source code of your derived work must contain descriptions
    **        of how the derived work is based upon, contains and/or differs
    **        from the original SOFA software.
    **
    **     c) The names of all routines in your derived work shall not
    **        include the prefix "iau" or "sofa" or trivial modifications
    **        thereof such as changes of case.
    **
    **     d) The origin of the SOFA components of your derived work must
    **        not be misrepresented;  you must not claim that you wrote the
    **        original software, nor file a patent application for SOFA
    **        software or algorithms embedded in the SOFA software.
    **
    **     e) These requirements must be reproduced intact in any source
    **        distribution and shall apply to anyone to whom you have
    **        granted a further right to modify the source code of your
    **        derived work.
    **
    **     Note that, as originally distributed, the SOFA software is
    **     intended to be a definitive implementation of the IAU standards,
    **     and consequently third-party modifications are discouraged.  All
    **     variations, no matter how minor, must be explicitly marked as
    **     such, as explained above.
    **
    **  4. You shall not cause the SOFA software to be brought into
    **     disrepute, either by misuse, or use for inappropriate tasks, or
    **     by inappropriate modification.
    **
    **  5. The SOFA software is provided "as is" and SOFA makes no warranty
    **     as to its use or performance.   SOFA does not and cannot warrant
    **     the performance or results which the user may obtain by using the
    **     SOFA software.  SOFA makes no warranties, express or implied, as
    **     to non-infringement of third party rights, merchantability, or
    **     fitness for any particular purpose.  In no event will SOFA be
    **     liable to the user for any consequential, incidental, or special
    **     damages, including any lost profits or lost savings, even if a
    **     SOFA representative has been advised of such damages, or for any
    **     claim by any third party.
    **
    **  6. The provision of any version of the SOFA software under the terms
    **     and conditions specified herein does not imply that future
    **     versions will also be made available under the same terms and
    **     conditions.
    *
    **  In any published work or commercial product which uses the SOFA
    **  software directly, acknowledgement (see www.iausofa.org) is
    **  appreciated.
    **
    **  Correspondence concerning SOFA software should be addressed as
    **  follows:
    **
    **      By email:  [email protected]
    **      By post:   IAU SOFA Center
    **                 HM Nautical Almanac Office
    **                 UK Hydrographic Office
    **                 Admiralty Way, Taunton
    **                 Somerset, TA1 2DN
    **                 United Kingdom
    **
    **--------------------------------------------------------------------*/
}
void iauAtoiq(const char *type,
              double ob1, double ob2, iauASTROM *astrom,
              double *ri, double *di)
/*
**  - - - - - - - - -
**   i a u A t o i q
**  - - - - - - - - -
**
**  Quick observed place to CIRS, given the star-independent astrometry
**  parameters.
**
**  Use of this function is appropriate when efficiency is important and
**  where many star positions are all to be transformed for one date.
**  The star-independent astrometry parameters can be obtained by
**  calling iauApio[13] or iauApco[13].
**
**  Status:  support function.
**
**  Given:
**     type   char[]     type of coordinates: "R", "H" or "A" (Note 1)
**     ob1    double     observed Az, HA or RA (radians; Az is N=0,E=90)
**     ob2    double     observed ZD or Dec (radians)
**     astrom iauASTROM* star-independent astrometry parameters:
**      pmt    double       PM time interval (SSB, Julian years)
**      eb     double[3]    SSB to observer (vector, au)
**      eh     double[3]    Sun to observer (unit vector)
**      em     double       distance from Sun to observer (au)
**      v      double[3]    barycentric observer velocity (vector, c)
**      bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
**      bpn    double[3][3] bias-precession-nutation matrix
**      along  double       longitude + s' (radians)
**      xpl    double       polar motion xp wrt local meridian (radians)
**      ypl    double       polar motion yp wrt local meridian (radians)
**      sphi   double       sine of geodetic latitude
**      cphi   double       cosine of geodetic latitude
**      diurab double       magnitude of diurnal aberration vector
**      eral   double       "local" Earth rotation angle (radians)
**      refa   double       refraction constant A (radians)
**      refb   double       refraction constant B (radians)
**
**  Returned:
**     ri     double*    CIRS right ascension (CIO-based, radians)
**     di     double*    CIRS declination (radians)
**
**  Notes:
**
**  1) "Observed" Az,El means the position that would be seen by a
**     perfect geodetically aligned theodolite.  This is related to
**     the observed HA,Dec via the standard rotation, using the geodetic
**     latitude (corrected for polar motion), while the observed HA and
**     RA are related simply through the Earth rotation angle and the
**     site longitude.  "Observed" RA,Dec or HA,Dec thus means the
**     position that would be seen by a perfect equatorial with its
**     polar axis aligned to the Earth's axis of rotation.  By removing
**     from the observed place the effects of atmospheric refraction and
**     diurnal aberration, the CIRS RA,Dec is obtained.
**
**  2) Only the first character of the type argument is significant.
**     "R" or "r" indicates that ob1 and ob2 are the observed right
**     ascension and declination;  "H" or "h" indicates that they are
**     hour angle (west +ve) and declination;  anything else ("A" or
**     "a" is recommended) indicates that ob1 and ob2 are azimuth (north
**     zero, east 90 deg) and zenith distance.  (Zenith distance is used
**     rather than altitude in order to reflect the fact that no
**     allowance is made for depression of the horizon.)
**
**  3) The accuracy of the result is limited by the corrections for
**     refraction, which use a simple A*tan(z) + B*tan^3(z) model.
**     Providing the meteorological parameters are known accurately and
**     there are no gross local effects, the predicted observed
**     coordinates should be within 0.05 arcsec (optical) or 1 arcsec
**     (radio) for a zenith distance of less than 70 degrees, better
**     than 30 arcsec (optical or radio) at 85 degrees and better than
**     20 arcmin (optical) or 30 arcmin (radio) at the horizon.
**
**     Without refraction, the complementary functions iauAtioq and
**     iauAtoiq are self-consistent to better than 1 microarcsecond all
**     over the celestial sphere.  With refraction included, consistency
**     falls off at high zenith distances, but is still better than
**     0.05 arcsec at 85 degrees.
**
**  4) It is advisable to take great care with units, as even unlikely
**     values of the input parameters are accepted and processed in
**     accordance with the models used.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauC2s       p-vector to spherical
**     iauAnp       normalize angle into range 0 to 2pi
**
**  This revision:   2013 October 9
**
**  SOFA release 2013-12-02
**
**  Copyright (C) 2013 IAU SOFA Board.  See notes at end.
*/
{
   int c;
   double c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo, v[3],
          xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref,
          zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda,
          f, xhd, yhd, zhd, xpl, ypl, w, hma;


/* Coordinate type. */
   c = (int) type[0];

/* Coordinates. */
   c1 = ob1;
   c2 = ob2;

/* Sin, cos of latitude. */
   sphi = astrom->sphi;
   cphi = astrom->cphi;

/* Standardize coordinate type. */
   if ( c == 'r' || c == 'R' ) {
      c = 'R';
   } else if ( c == 'h' || c == 'H' ) {
      c = 'H';
   } else {
      c = 'A';
   }

/* If Az,ZD, convert to Cartesian (S=0,E=90). */
   if ( c == 'A' ) {
      ce = sin(c2);
      xaeo = - cos(c1) * ce;
      yaeo = sin(c1) * ce;
      zaeo = cos(c2);

   } else {

   /* If RA,Dec, convert to HA,Dec. */
      if ( c == 'R' ) c1 = astrom->eral - c1;

   /* To Cartesian -HA,Dec. */
      iauS2c ( -c1, c2, v );
      xmhdo = v[0];
      ymhdo = v[1];
      zmhdo = v[2];

   /* To Cartesian Az,El (S=0,E=90). */
      xaeo = sphi*xmhdo - cphi*zmhdo;
      yaeo = ymhdo;
      zaeo = cphi*xmhdo + sphi*zmhdo;
   }

/* Azimuth (S=0,E=90). */
   az = ( xaeo != 0.0 || yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0;

/* Sine of observed ZD, and observed ZD. */
   sz = sqrt ( xaeo*xaeo + yaeo*yaeo );
   zdo = atan2 ( sz, zaeo );

/*
** Refraction
** ----------
*/

/* Fast algorithm using two constant model. */
   refa = astrom->refa;
   refb = astrom->refb;
   tz = sz / zaeo;
   dref = ( refa + refb*tz*tz ) * tz;
   zdt = zdo + dref;

/* To Cartesian Az,ZD. */
   ce = sin(zdt);
   xaet = cos(az) * ce;
   yaet = sin(az) * ce;
   zaet = cos(zdt);

/* Cartesian Az,ZD to Cartesian -HA,Dec. */
   xmhda = sphi*xaet + cphi*zaet;
   ymhda = yaet;
   zmhda = - cphi*xaet + sphi*zaet;

/* Diurnal aberration. */
   f = ( 1.0 + astrom->diurab*ymhda );
   xhd = f * xmhda;
   yhd = f * ( ymhda - astrom->diurab );
   zhd = f * zmhda;

/* Polar motion. */
   xpl = astrom->xpl;
   ypl = astrom->ypl;
   w = xpl*xhd - ypl*yhd + zhd;
   v[0] = xhd - xpl*w;
   v[1] = yhd + ypl*w;
   v[2] = w - ( xpl*xpl + ypl*ypl ) * zhd;

/* To spherical -HA,Dec. */
   iauC2s(v, &hma, di);

/* Right ascension. */
   *ri = iauAnp(astrom->eral + hma);

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2013
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  [email protected]
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/

}
Example #8
0
void iauAtciqz(double rc, double dc, iauASTROM *astrom,
               double *ri, double *di)
/*
**  - - - - - - - - - -
**   i a u A t c i q z
**  - - - - - - - - - -
**
**  Quick ICRS to CIRS transformation, given precomputed star-
**  independent astrometry parameters, and assuming zero parallax and
**  proper motion.
**
**  Use of this function is appropriate when efficiency is important and
**  where many star positions are to be transformed for one date.  The
**  star-independent parameters can be obtained by calling one of the
**  functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
**
**  The corresponding function for the case of non-zero parallax and
**  proper motion is iauAtciq.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     rc,dc  double     ICRS astrometric RA,Dec (radians)
**     astrom iauASTROM* star-independent astrometry parameters:
**      pmt    double       PM time interval (SSB, Julian years)
**      eb     double[3]    SSB to observer (vector, au)
**      eh     double[3]    Sun to observer (unit vector)
**      em     double       distance from Sun to observer (au)
**      v      double[3]    barycentric observer velocity (vector, c)
**      bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
**      bpn    double[3][3] bias-precession-nutation matrix
**      along  double       longitude + s' (radians)
**      xpl    double       polar motion xp wrt local meridian (radians)
**      ypl    double       polar motion yp wrt local meridian (radians)
**      sphi   double       sine of geodetic latitude
**      cphi   double       cosine of geodetic latitude
**      diurab double       magnitude of diurnal aberration vector
**      eral   double       "local" Earth rotation angle (radians)
**      refa   double       refraction constant A (radians)
**      refb   double       refraction constant B (radians)
**
**  Returned:
**     ri,di  double     CIRS RA,Dec (radians)
**
**  Note:
**
**     All the vectors are with respect to BCRS axes.
**
**  References:
**
**     Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
**     the Astronomical Almanac, 3rd ed., University Science Books
**     (2013).
**
**     Klioner, Sergei A., "A practical relativistic model for micro-
**     arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauLdsun     light deflection due to Sun
**     iauAb        stellar aberration
**     iauRxp       product of r-matrix and p-vector
**     iauC2s       p-vector to spherical
**     iauAnp       normalize angle into range +/- pi
**
**  This revision:   2013 October 9
**
**  SOFA release 2015-02-09
**
**  Copyright (C) 2015 IAU SOFA Board.  See notes at end.
*/
{
   double pco[3], pnat[3], ppr[3], pi[3], w;

/* BCRS coordinate direction (unit vector). */
   iauS2c(rc, dc, pco);

/* Light deflection by the Sun, giving BCRS natural direction. */
   iauLdsun(pco, astrom->eh, astrom->em, pnat);

/* Aberration, giving GCRS proper direction. */
   iauAb(pnat, astrom->v, astrom->em, astrom->bm1, ppr);

/* Bias-precession-nutation, giving CIRS proper direction. */
   iauRxp(astrom->bpn, ppr, pi);

/* CIRS RA,Dec. */
   iauC2s(pi, &w, di);
   *ri = iauAnp(w);

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2015
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  [email protected]
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/

}
void iauLteqec(double epj, double dr, double dd, double *dl, double *db)
/*
**  - - - - - - - - - -
**   i a u L t e q e c
**  - - - - - - - - - -
**
**  Transformation from ICRS equatorial coordinates to ecliptic
**  coordinates (mean equinox and ecliptic of date) using a long-term
**  precession model.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     epj     double     Julian epoch (TT)
**     dr,dd   double     ICRS right ascension and declination (radians)
**
**  Returned:
**     dl,db   double     ecliptic longitude and latitude (radians)
**
**  1) No assumptions are made about whether the coordinates represent
**     starlight and embody astrometric effects such as parallax or
**     aberration.
**
**  2) The transformation is approximately that from mean J2000.0 right
**     ascension and declination to ecliptic longitude and latitude
**     (mean equinox and ecliptic of date), with only frame bias (always
**     less than 25 mas) to disturb this classical picture.
**
**  3) The Vondrak et al. (2011, 2012) 400 millennia precession model
**     agrees with the IAU 2006 precession at J2000.0 and stays within
**     100 microarcseconds during the 20th and 21st centuries.  It is
**     accurate to a few arcseconds throughout the historical period,
**     worsening to a few tenths of a degree at the end of the
**     +/- 200,000 year time span.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauLtecm     J2000.0 to ecliptic rotation matrix, long term
**     iauRxp       product of r-matrix and p-vector
**     iauC2s       unit vector to spherical coordinates
**     iauAnp       normalize angle into range 0 to 2pi
**     iauAnpm      normalize angle into range +/- pi
**
**  References:
**
**    Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
**    expressions, valid for long time intervals, Astron.Astrophys. 534,
**    A22
**
**    Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
**    expressions, valid for long time intervals (Corrigendum),
**    Astron.Astrophys. 541, C1
**
**  This revision:  2016 February 9
**
**  SOFA release 2016-05-03
**
**  Copyright (C) 2016 IAU SOFA Board.  See notes at end.
*/
{
   double rm[3][3], v1[3], v2[3], a, b;


/* Spherical to Cartesian. */
   iauS2c(dr, dd, v1);

/* Rotation matrix, ICRS equatorial to ecliptic. */
   iauLtecm(epj, rm);

/* The transformation from ICRS to ecliptic. */
   iauRxp(rm, v1, v2);

/* Cartesian to spherical. */
   iauC2s(v2, &a, &b);

/* Express in conventional ranges. */
   *dl = iauAnp(a);
   *db = iauAnpm(b);

/*----------------------------------------------------------------------
**
**  Copyright (C) 2016
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  [email protected]
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/

}
Example #10
0
void iauAtioq(double ri, double di, iauASTROM *astrom,
              double *aob, double *zob,
              double *hob, double *dob, double *rob)
/*
**  - - - - - - - - -
**   i a u A t i o q
**  - - - - - - - - -
**
**  Quick CIRS to observed place transformation.
**
**  Use of this function is appropriate when efficiency is important and
**  where many star positions are all to be transformed for one date.
**  The star-independent astrometry parameters can be obtained by
**  calling iauApio[13] or iauApco[13].
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  support function.
**
**  Given:
**     ri     double     CIRS right ascension
**     di     double     CIRS declination
**     astrom iauASTROM* star-independent astrometry parameters:
**      pmt    double       PM time interval (SSB, Julian years)
**      eb     double[3]    SSB to observer (vector, au)
**      eh     double[3]    Sun to observer (unit vector)
**      em     double       distance from Sun to observer (au)
**      v      double[3]    barycentric observer velocity (vector, c)
**      bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
**      bpn    double[3][3] bias-precession-nutation matrix
**      along  double       longitude + s' (radians)
**      xpl    double       polar motion xp wrt local meridian (radians)
**      ypl    double       polar motion yp wrt local meridian (radians)
**      sphi   double       sine of geodetic latitude
**      cphi   double       cosine of geodetic latitude
**      diurab double       magnitude of diurnal aberration vector
**      eral   double       "local" Earth rotation angle (radians)
**      refa   double       refraction constant A (radians)
**      refb   double       refraction constant B (radians)
**
**  Returned:
**     aob    double*    observed azimuth (radians: N=0,E=90)
**     zob    double*    observed zenith distance (radians)
**     hob    double*    observed hour angle (radians)
**     dob    double*    observed declination (radians)
**     rob    double*    observed right ascension (CIO-based, radians)
**
**  Notes:
**
**  1) This function returns zenith distance rather than altitude in
**     order to reflect the fact that no allowance is made for
**     depression of the horizon.
**
**  2) The accuracy of the result is limited by the corrections for
**     refraction, which use a simple A*tan(z) + B*tan^3(z) model.
**     Providing the meteorological parameters are known accurately and
**     there are no gross local effects, the predicted observed
**     coordinates should be within 0.05 arcsec (optical) or 1 arcsec
**     (radio) for a zenith distance of less than 70 degrees, better
**     than 30 arcsec (optical or radio) at 85 degrees and better
**     than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
**
**     Without refraction, the complementary functions iauAtioq and
**     iauAtoiq are self-consistent to better than 1 microarcsecond all
**     over the celestial sphere.  With refraction included, consistency
**     falls off at high zenith distances, but is still better than
**     0.05 arcsec at 85 degrees.
**
**  3) It is advisable to take great care with units, as even unlikely
**     values of the input parameters are accepted and processed in
**     accordance with the models used.
**
**  4) The CIRS RA,Dec is obtained from a star catalog mean place by
**     allowing for space motion, parallax, the Sun's gravitational lens
**     effect, annual aberration and precession-nutation.  For star
**     positions in the ICRS, these effects can be applied by means of
**     the iauAtci13 (etc.) functions.  Starting from classical "mean
**     place" systems, additional transformations will be needed first.
**
**  5) "Observed" Az,El means the position that would be seen by a
**     perfect geodetically aligned theodolite.  This is obtained from
**     the CIRS RA,Dec by allowing for Earth orientation and diurnal
**     aberration, rotating from equator to horizon coordinates, and
**     then adjusting for refraction.  The HA,Dec is obtained by
**     rotating back into equatorial coordinates, and is the position
**     that would be seen by a perfect equatorial with its polar axis
**     aligned to the Earth's axis of rotation.  Finally, the RA is
**     obtained by subtracting the HA from the local ERA.
**
**  6) The star-independent CIRS-to-observed-place parameters in ASTROM
**     may be computed with iauApio[13] or iauApco[13].  If nothing has
**     changed significantly except the time, iauAper[13] may be used to
**     perform the requisite adjustment to the astrom structure.
**
**  Called:
**     iauS2c       spherical coordinates to unit vector
**     iauC2s       p-vector to spherical
**     iauAnp       normalize angle into range 0 to 2pi
**
**  This revision:   2013 December 5
**
**  SOFA release 2015-02-09
**
**  Copyright (C) 2015 IAU SOFA Board.  See notes at end.
*/
{
/* Minimum cos(alt) and sin(alt) for refraction purposes */
   const double CELMIN = 1e-6;
   const double SELMIN = 0.05;

   double v[3], x, y, z, xhd, yhd, zhd, f, xhdt, yhdt, zhdt,
          xaet, yaet, zaet, azobs, r, tz, w, del, cosdel,
          xaeo, yaeo, zaeo, zdobs, hmobs, dcobs, raobs;

/*--------------------------------------------------------------------*/

/* CIRS RA,Dec to Cartesian -HA,Dec. */
   iauS2c(ri-astrom->eral, di, v);
   x = v[0];
   y = v[1];
   z = v[2];

/* Polar motion. */
   xhd = x + astrom->xpl*z;
   yhd = y - astrom->ypl*z;
   zhd = z - astrom->xpl*x + astrom->ypl*y;

/* Diurnal aberration. */
   f = ( 1.0 - astrom->diurab*yhd );
   xhdt = f * xhd;
   yhdt = f * ( yhd + astrom->diurab );
   zhdt = f * zhd;

/* Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). */
   xaet = astrom->sphi*xhdt - astrom->cphi*zhdt;
   yaet = yhdt;
   zaet = astrom->cphi*xhdt + astrom->sphi*zhdt;

/* Azimuth (N=0,E=90). */
   azobs = ( xaet != 0.0 || yaet != 0.0 ) ? atan2(yaet,-xaet) : 0.0;

/* ---------- */
/* Refraction */
/* ---------- */

/* Cosine and sine of altitude, with precautions. */
   r = sqrt(xaet*xaet + yaet*yaet);
   r = r > CELMIN ? r : CELMIN;
   z = zaet > SELMIN ? zaet : SELMIN;

/* A*tan(z)+B*tan^3(z) model, with Newton-Raphson correction. */
   tz = r/z;
   w = astrom->refb*tz*tz;
   del = ( astrom->refa + w ) * tz /
         ( 1.0 + ( astrom->refa + 3.0*w ) / ( z*z ) );

/* Apply the change, giving observed vector. */
   cosdel = 1.0 - del*del/2.0;
   f = cosdel - del*z/r;
   xaeo = xaet*f;
   yaeo = yaet*f;
   zaeo = cosdel*zaet + del*r;

/* Observed ZD. */
   zdobs = atan2(sqrt(xaeo*xaeo+yaeo*yaeo), zaeo);

/* Az/El vector to HA,Dec vector (both right-handed). */
   v[0] = astrom->sphi*xaeo + astrom->cphi*zaeo;
   v[1] = yaeo;
   v[2] = - astrom->cphi*xaeo + astrom->sphi*zaeo;

/* To spherical -HA,Dec. */
   iauC2s ( v, &hmobs, &dcobs );

/* Right ascension (with respect to CIO). */
   raobs = astrom->eral + hmobs;

/* Return the results. */
   *aob = iauAnp(azobs);
   *zob = zdobs;
   *hob = -hmobs;
   *dob = dcobs;
   *rob = iauAnp(raobs);

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2015
**  Standards Of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  [email protected]
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/

}