#include "sofa.h"
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: 2020 December 7
**
** SOFA release 2021-05-12
**
** Copyright (C) 2021 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, sx, cx, sy, cy, 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. */
sx = sin(astrom->xpl);
cx = cos(astrom->xpl);
sy = sin(astrom->ypl);
cy = cos(astrom->ypl);
xhd = cx*x + sx*z;
yhd = sx*sy*x + cy*y - cx*sy*z;
zhd = -sx*cy*x + sy*y + cx*cy*z;
/* 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) 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
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**
** 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
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** 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
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** United Kingdom
**
**--------------------------------------------------------------------*/
}