#include "sofa.h"
void iauPb06(double date1, double date2,
double *bzeta, double *bz, double *btheta)
/*
** - - - - - - - -
** i a u P b 0 6
** - - - - - - - -
**
** This function forms three Euler angles which implement general
** precession from epoch J2000.0, using the IAU 2006 model. Frame
** bias (the offset between ICRS and mean J2000.0) is included.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** bzeta double 1st rotation: radians cw around z
** bz double 3rd rotation: radians cw around z
** btheta double 2nd rotation: radians ccw around y
**
** 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 traditional accumulated precession angles zeta_A, z_A,
** theta_A cannot be obtained in the usual way, namely through
** polynomial expressions, because of the frame bias. The latter
** means that two of the angles undergo rapid changes near this
** date. They are instead the results of decomposing the
** precession-bias matrix obtained by using the Fukushima-Williams
** method, which does not suffer from the problem. The
** decomposition returns values which can be used in the
** conventional formulation and which include frame bias.
**
** 3) The three angles are returned in the conventional order, which
** is not the same as the order of the corresponding Euler
** rotations. The precession-bias matrix is
** R_3(-z) x R_2(+theta) x R_3(-zeta).
**
** 4) Should zeta_A, z_A, theta_A angles be required that do not
** contain frame bias, they are available by calling the SOFA
** function iauP06e.
**
** Called:
** iauPmat06 PB matrix, IAU 2006
** iauRz rotate around Z-axis
**
** This revision: 2021 May 11
**
** SOFA release 2021-05-12
**
** Copyright (C) 2021 IAU SOFA Board. See notes at end.
*/
{
double r[3][3], y, x;
/* Precession matrix via Fukushima-Williams angles. */
iauPmat06(date1, date2, r);
/* Solve for z, choosing the +/- pi alternative. */
y = r[1][2];
x = -r[0][2];
if ( x < 0.0 ) {
y = -y;
x = -x;
}
*bz = ( x != 0.0 || y != 0.0 ) ? - atan2(y,x) : 0.0;
/* Derotate it out of the matrix. */
iauRz ( *bz, r );
/* Solve for the remaining two angles. */
y = r[0][2];
x = r[2][2];
*btheta = ( x != 0.0 || y != 0.0 ) ? - atan2(y,x) : 0.0;
y = -r[1][0];
x = r[1][1];
*bzeta = ( x != 0.0 || y != 0.0 ) ? - atan2(y,x) : 0.0;
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2021
** 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
**
**--------------------------------------------------------------------*/
}