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sph.h
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/*============================================================================
WCSLIB 8.4 - an implementation of the FITS WCS standard.
Copyright (C) 1995-2024, Mark Calabretta
This file is part of WCSLIB.
WCSLIB is free software: you can redistribute it and/or modify it under the
terms of the GNU Lesser General Public License as published by the Free
Software Foundation, either version 3 of the License, or (at your option)
any later version.
WCSLIB is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
more details.
You should have received a copy of the GNU Lesser General Public License
along with WCSLIB. If not, see http://www.gnu.org/licenses.
Author: Mark Calabretta, Australia Telescope National Facility, CSIRO.
http://www.atnf.csiro.au/people/Mark.Calabretta
$Id: sph.h,v 8.4 2024/10/28 13:56:16 mcalabre Exp $
*=============================================================================
*
* WCSLIB 8.4 - C routines that implement the FITS World Coordinate System
* (WCS) standard. Refer to the README file provided with WCSLIB for an
* overview of the library.
*
*
* Summary of the sph routines
* ---------------------------
* Routines in this suite implement the spherical coordinate transformations
* defined by the FITS World Coordinate System (WCS) standard
*
= "Representations of world coordinates in FITS",
= Greisen, E.W., & Calabretta, M.R. 2002, A&A, 395, 1061 (WCS Paper I)
=
= "Representations of celestial coordinates in FITS",
= Calabretta, M.R., & Greisen, E.W. 2002, A&A, 395, 1077 (WCS Paper II)
*
* The transformations are implemented via separate functions, sphx2s() and
* sphs2x(), for the spherical rotation in each direction.
*
* A utility function, sphdpa(), computes the angular distances and position
* angles from a given point on the sky to a number of other points. sphpad()
* does the complementary operation - computes the coordinates of points offset
* by the given angular distances and position angles from a given point on the
* sky.
*
*
* sphx2s() - Rotation in the pixel-to-world direction
* ---------------------------------------------------
* sphx2s() transforms native coordinates of a projection to celestial
* coordinates.
*
* Given:
* eul const double[5]
* Euler angles for the transformation:
* 0: Celestial longitude of the native pole [deg].
* 1: Celestial colatitude of the native pole, or
* native colatitude of the celestial pole [deg].
* 2: Native longitude of the celestial pole [deg].
* 3: cos(eul[1])
* 4: sin(eul[1])
*
* nphi,
* ntheta int Vector lengths.
*
* spt,sxy int Vector strides.
*
* phi,theta const double[]
* Longitude and latitude in the native coordinate
* system of the projection [deg].
*
* Returned:
* lng,lat double[] Celestial longitude and latitude [deg]. These may
* refer to the same storage as phi and theta
* respectively.
*
* Function return value:
* int Status return value:
* 0: Success.
*
*
* sphs2x() - Rotation in the world-to-pixel direction
* ---------------------------------------------------
* sphs2x() transforms celestial coordinates to the native coordinates of a
* projection.
*
* Given:
* eul const double[5]
* Euler angles for the transformation:
* 0: Celestial longitude of the native pole [deg].
* 1: Celestial colatitude of the native pole, or
* native colatitude of the celestial pole [deg].
* 2: Native longitude of the celestial pole [deg].
* 3: cos(eul[1])
* 4: sin(eul[1])
*
* nlng,nlat int Vector lengths.
*
* sll,spt int Vector strides.
*
* lng,lat const double[]
* Celestial longitude and latitude [deg].
*
* Returned:
* phi,theta double[] Longitude and latitude in the native coordinate system
* of the projection [deg]. These may refer to the same
* storage as lng and lat respectively.
*
* Function return value:
* int Status return value:
* 0: Success.
*
*
* sphdpa() - Compute angular distance and position angle
* ------------------------------------------------------
* sphdpa() computes the angular distance and generalized position angle (see
* notes) from a "reference" point to a number of "field" points on the sphere.
* The points must be specified consistently in any spherical coordinate
* system.
*
* sphdpa() is complementary to sphpad().
*
* Given:
* nfield int The number of field points.
*
* lng0,lat0 double Spherical coordinates of the reference point [deg].
*
* lng,lat const double[]
* Spherical coordinates of the field points [deg].
*
* Returned:
* dist,pa double[] Angular distances and position angles [deg]. These
* may refer to the same storage as lng and lat
* respectively.
*
* Function return value:
* int Status return value:
* 0: Success.
*
* Notes:
* 1. sphdpa() uses sphs2x() to rotate coordinates so that the reference
* point is at the north pole of the new system with the north pole of the
* old system at zero longitude in the new. The Euler angles required by
* sphs2x() for this rotation are
*
= eul[0] = lng0;
= eul[1] = 90.0 - lat0;
= eul[2] = 0.0;
*
* The angular distance and generalized position angle are readily
* obtained from the longitude and latitude of the field point in the new
* system. This applies even if the reference point is at one of the
* poles, in which case the "position angle" returned is as would be
* computed for a reference point at (lng0,+90-epsilon) or
* (lng0,-90+epsilon), in the limit as epsilon goes to zero.
*
* It is evident that the coordinate system in which the two points are
* expressed is irrelevant to the determination of the angular separation
* between the points. However, this is not true of the generalized
* position angle.
*
* The generalized position angle is here defined as the angle of
* intersection of the great circle containing the reference and field
* points with that containing the reference point and the pole. It has
* its normal meaning when the the reference and field points are
* specified in equatorial coordinates (right ascension and declination).
*
* Interchanging the reference and field points changes the position angle
* in a non-intuitive way (because the sum of the angles of a spherical
* triangle normally exceeds 180 degrees).
*
* The position angle is undefined if the reference and field points are
* coincident or antipodal. This may be detected by checking for a
* distance of 0 or 180 degrees (within rounding tolerance). sphdpa()
* will return an arbitrary position angle in such circumstances.
*
*
* sphpad() - Compute field points offset from a given point
* ---------------------------------------------------------
* sphpad() computes the coordinates of a set of points that are offset by the
* specified angular distances and position angles from a given "reference"
* point on the sky. The distances and position angles must be specified
* consistently in any spherical coordinate system.
*
* sphpad() is complementary to sphdpa().
*
* Given:
* nfield int The number of field points.
*
* lng0,lat0 double Spherical coordinates of the reference point [deg].
*
* dist,pa const double[]
* Angular distances and position angles [deg].
*
* Returned:
* lng,lat double[] Spherical coordinates of the field points [deg].
* These may refer to the same storage as dist and pa
* respectively.
*
* Function return value:
* int Status return value:
* 0: Success.
*
* Notes:
* 1: sphpad() is implemented analogously to sphdpa() although using sphx2s()
* for the inverse transformation. In particular, when the reference
* point is at one of the poles, "position angle" is interpreted as though
* the reference point was at (lng0,+90-epsilon) or (lng0,-90+epsilon), in
* the limit as epsilon goes to zero.
*
* Applying sphpad() with the distances and position angles computed by
* sphdpa() should return the original field points.
*
*===========================================================================*/
#ifndef WCSLIB_SPH
#define WCSLIB_SPH
#ifdef __cplusplus
extern "C" {
#endif
int sphx2s(const double eul[5], int nphi, int ntheta, int spt, int sxy,
const double phi[], const double theta[],
double lng[], double lat[]);
int sphs2x(const double eul[5], int nlng, int nlat, int sll , int spt,
const double lng[], const double lat[],
double phi[], double theta[]);
int sphdpa(int nfield, double lng0, double lat0,
const double lng[], const double lat[],
double dist[], double pa[]);
int sphpad(int nfield, double lng0, double lat0,
const double dist[], const double pa[],
double lng[], double lat[]);
#ifdef __cplusplus
}
#endif
#endif // WCSLIB_SPH
sphs2x
int sphs2x(const double eul[5], int nlng, int nlat, int sll, int spt, const double lng[], const double lat[], double phi[], double theta[])
Rotation in the world-to-pixel direction.
sphpad
int sphpad(int nfield, double lng0, double lat0, const double dist[], const double pa[], double lng[], double lat[])
Compute field points offset from a given point.
sphx2s
int sphx2s(const double eul[5], int nphi, int ntheta, int spt, int sxy, const double phi[], const double theta[], double lng[], double lat[])
Rotation in the pixel-to-world direction.
sphdpa
int sphdpa(int nfield, double lng0, double lat0, const double lng[], const double lat[], double dist[], double pa[])
Compute angular distance and position angle.