#include "sofa.h"

double iauPap(double a[3], double b[3])
/*
**  - - - - - - -
**   i a u P a p
**  - - - - - - -
**
**  Position-angle from two p-vectors.
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  vector/matrix support function.
**
**  Given:
**     a      double[3]  direction of reference point
**     b      double[3]  direction of point whose PA is required
**
**  Returned (function value):
**            double     position angle of b with respect to a (radians)
**
**  Notes:
**
**  1) The result is the position angle, in radians, of direction b with
**     respect to direction a.  It is in the range -pi to +pi.  The
**     sense is such that if b is a small distance "north" of a the
**     position angle is approximately zero, and if b is a small
**     distance "east" of a the position angle is approximately +pi/2.
**
**  2) The vectors a and b need not be of unit length.
**
**  3) Zero is returned if the two directions are the same or if either
**     vector is null.
**
**  4) If vector a is at a pole, the result is ill-defined.
**
**  Called:
**     iauPn        decompose p-vector into modulus and direction
**     iauPm        modulus of p-vector
**     iauPxp       vector product of two p-vectors
**     iauPmp       p-vector minus p-vector
**     iauPdp       scalar product of two p-vectors
**
**  This revision:  2021 May 11
**
**  SOFA release 2023-10-11
**
**  Copyright (C) 2023 IAU SOFA Board.  See notes at end.
*/
{
   double am, au[3], bm, st, ct, xa, ya, za, eta[3], xi[3], a2b[3], pa;


/* Modulus and direction of the a vector. */
   iauPn(a, &am, au);

/* Modulus of the b vector. */
   bm = iauPm(b);

/* Deal with the case of a null vector. */
   if ((am == 0.0) || (bm == 0.0)) {
      st = 0.0;
      ct = 1.0;
   } else {

   /* The "north" axis tangential from a (arbitrary length). */
      xa = a[0];
      ya = a[1];
      za = a[2];
      eta[0] = -xa * za;
      eta[1] = -ya * za;
      eta[2] =  xa*xa + ya*ya;

   /* The "east" axis tangential from a (same length). */
      iauPxp(eta, au, xi);

   /* The vector from a to b. */
      iauPmp(b, a, a2b);

   /* Resolve into components along the north and east axes. */
      st = iauPdp(a2b, xi);
      ct = iauPdp(a2b, eta);

   /* Deal with degenerate cases. */
      if ((st == 0.0) && (ct == 0.0)) ct = 1.0;
   }

/* Position angle. */
   pa = atan2(st, ct);

   return pa;

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2023
**  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:  sofa@ukho.gov.uk
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}
