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cel.h
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/*============================================================================
WCSLIB 8.9 - an implementation of the FITS WCS standard.
Copyright (C) 1995-2026, 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/computing/software/wcs
$Id: cel.h,v 8.9 2026/06/18 13:00:03 mcalabre Exp $
*=============================================================================
*
* WCSLIB 8.9 - 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 cel routines
* ---------------------------
* Routines in this suite implement the part of the FITS World Coordinate
* System (WCS) standard that deals with celestial coordinates, as described in
*
= "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)
*
* These routines define methods to be used for computing celestial world
* coordinates from intermediate world coordinates (a linear transformation
* of image pixel coordinates), and vice versa. They are based on the celprm
* struct which contains all information needed for the computations. This
* struct contains some elements that must be set by the user, and others that
* are maintained by these routines, somewhat like a C++ class but with no
* encapsulation.
*
* Routine celini() is provided to initialize the celprm struct with default
* values, celfree() reclaims any memory that may have been allocated to store
* an error message, celsize() computes its total size including allocated
* memory, celenq() returns information about the state of the struct, and
* celprt() prints its contents.
*
* celperr() prints the error message(s), if any, stored in a celprm struct and
* the prjprm struct that it contains.
*
* A setup routine, celset(), computes intermediate values in the celprm struct
* from parameters in it that were supplied by the user. The struct always
* needs to be set up by celset() but it need not be called explicitly - refer
* to the explanation of celprm::flag.
*
* celx2s() and cels2x() implement the WCS celestial coordinate
* transformations. In fact, they are high level driver routines for the lower
* level spherical coordinate rotation and projection routines described in
* sph.h and prj.h.
*
*
* celini() - Default constructor for the celprm struct
* ----------------------------------------------------
* celini() sets all members of a celprm struct to default values. It should
* be used to initialize every celprm struct.
*
* PLEASE NOTE: If the celprm struct has already been initialized, then before
* reinitializing, it celfree() should be used to free any memory that may have
* been allocated to store an error message. A memory leak may otherwise
* result.
*
* Returned:
* cel struct celprm*
* Celestial transformation parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
*
*
* celfree() - Destructor for the celprm struct
* --------------------------------------------
* celfree() frees any memory that may have been allocated to store an error
* message in the celprm struct.
*
* Given and returned:
* cel struct celprm*
* Celestial transformation parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
*
*
* celsize() - Compute the size of a celprm struct
* -----------------------------------------------
* celsize() computes the full size of a celprm struct, including allocated
* memory.
*
* Given:
* cel const struct celprm*
* Celestial transformation parameters.
*
* If NULL, the base size of the struct and the allocated
* size are both set to zero.
*
* Returned:
* sizes int[2] The first element is the base size of the struct as
* returned by sizeof(struct celprm). The second element
* is the total allocated size, in bytes. This figure
* includes memory allocated for the constituent struct,
* celprm::err.
*
* It is not an error for the struct not to have been set
* up via celset().
*
* Function return value:
* int Status return value:
* 0: Success.
*
*
* celenq() - enquire about the state of a celprm struct
* -----------------------------------------------------
* celenq() may be used to obtain information about the state of a celprm
* struct. The function returns a true/false answer for the enquiry asked.
*
* Given:
* cel const struct celprm*
* Celestial transformation parameters.
*
* enquiry int Enquiry according to the following parameters:
* CELENQ_SET: the struct has been set up by celset().
* CELENQ_BYP: the struct is in bypass mode (see
* celset()).
*
* Function return value:
* int Enquiry result:
* 0: No.
* 1: Yes.
*
*
* celprt() - Print routine for the celprm struct
* ----------------------------------------------
* celprt() prints the contents of a celprm struct using wcsprintf(). Mainly
* intended for diagnostic purposes.
*
* Given:
* cel const struct celprm*
* Celestial transformation parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
*
*
* celperr() - Print error messages from a celprm struct
* -----------------------------------------------------
* celperr() prints the error message(s), if any, stored in a celprm struct and
* the prjprm struct that it contains. If there are no errors then nothing is
* printed. It uses wcserr_prt(), q.v.
*
* Given:
* cel const struct celprm*
* Coordinate transformation parameters.
*
* prefix const char *
* If non-NULL, each output line will be prefixed with
* this string.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
*
*
* celset() - Setup routine for the celprm struct
* ----------------------------------------------
* celset() sets up a celprm struct according to information supplied within
* it.
*
* Note that this routine need not be called directly; it will be invoked by
* celx2s() and cels2x() if celprm::flag is anything other than a predefined
* magic value.
* celset() normally operates regardless of the value of celprm::flag; i.e.
* even if a struct was previously set up it will be reset unconditionally.
* However, a celprm struct may be put into "bypass" mode by invoking celset()
* initially with celprm::flag == 1 (rather than 0). celset() will return
* immediately if invoked on a struct in that state. To take a struct out of
* bypass mode, simply reset celprm::flag to zero. See also celenq().
*
* Given and returned:
* cel struct celprm*
* Celestial transformation parameters.
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
* 2: Invalid projection parameters.
* 3: Invalid coordinate transformation parameters.
* 4: Ill-conditioned coordinate transformation
* parameters.
*
* For returns > 1, a detailed error message is set in
* celprm::err if enabled, see wcserr_enable().
*
*
* celx2s() - Pixel-to-world celestial transformation
* --------------------------------------------------
* celx2s() transforms (x,y) coordinates in the plane of projection to
* celestial coordinates (lng,lat).
*
* Given and returned:
* cel struct celprm*
* Celestial transformation parameters.
*
* Given:
* nx,ny int Vector lengths.
*
* sxy,sll int Vector strides.
*
* x,y const double[]
* Projected coordinates in pseudo "degrees".
*
* Returned:
* phi,theta double[] Longitude and latitude (phi,theta) in the native
* coordinate system of the projection [deg].
*
* lng,lat double[] Celestial longitude and latitude (lng,lat) of the
* projected point [deg].
*
* stat int[] Status return value for each vector element:
* 0: Success.
* 1: Invalid value of (x,y).
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
* 2: Invalid projection parameters.
* 3: Invalid coordinate transformation parameters.
* 4: Ill-conditioned coordinate transformation
* parameters.
* 5: One or more of the (x,y) coordinates were
* invalid, as indicated by the stat vector.
*
* For returns > 1, a detailed error message is set in
* celprm::err if enabled, see wcserr_enable().
*
*
* cels2x() - World-to-pixel celestial transformation
* --------------------------------------------------
* cels2x() transforms celestial coordinates (lng,lat) to (x,y) coordinates in
* the plane of projection.
*
* Given and returned:
* cel struct celprm*
* Celestial transformation parameters.
*
* Given:
* nlng,nlat int Vector lengths.
*
* sll,sxy int Vector strides.
*
* lng,lat const double[]
* Celestial longitude and latitude (lng,lat) of the
* projected point [deg].
*
* Returned:
* phi,theta double[] Longitude and latitude (phi,theta) in the native
* coordinate system of the projection [deg].
*
* x,y double[] Projected coordinates in pseudo "degrees".
*
* stat int[] Status return value for each vector element:
* 0: Success.
* 1: Invalid value of (lng,lat).
*
* Function return value:
* int Status return value:
* 0: Success.
* 1: Null celprm pointer passed.
* 2: Invalid projection parameters.
* 3: Invalid coordinate transformation parameters.
* 4: Ill-conditioned coordinate transformation
* parameters.
* 6: One or more of the (lng,lat) coordinates were
* invalid, as indicated by the stat vector.
*
* For returns > 1, a detailed error message is set in
* celprm::err if enabled, see wcserr_enable().
*
*
* celprm struct - Celestial transformation parameters
* ---------------------------------------------------
* The celprm struct contains information required to transform celestial
* coordinates. It consists of certain members that must be set by the user
* ("given") and others that are set by the WCSLIB routines ("returned"). Some
* of the latter are supplied for informational purposes and others are for
* internal use only.
*
* Returned celprm struct members must not be modified by the user.
*
* int flag
* (Given and returned) This flag must be set to zero (or 1, see celset())
* whenever any of the following celprm struct members are set or changed:
*
* - celprm::offset,
* - celprm::phi0,
* - celprm::theta0,
* - celprm::ref[4],
* - celprm::prj:
* - prjprm::code,
* - prjprm::r0,
* - prjprm::pv[],
* - prjprm::phi0,
* - prjprm::theta0.
*
* This signals the initialization routine, celset(), to recompute the
* returned members of the celprm struct. celset() will reset flag to
* indicate that this has been done.
*
* int offset
* (Given) If true (non-zero), an offset will be applied to (x,y) to
* force (x,y) = (0,0) at the fiducial point, (phi_0,theta_0).
* Default is 0 (false).
*
* double phi0
* (Given) The native longitude, phi_0 [deg], and ...
*
* double theta0
* (Given) ... the native latitude, theta_0 [deg], of the fiducial point,
* i.e. the point whose celestial coordinates are given in
* celprm::ref[1:2]. If undefined (set to a magic value by prjini()) the
* initialization routine, celset(), will set this to a projection-specific
* default.
*
* double ref[4]
* (Given) The first pair of values should be set to the celestial
* longitude and latitude of the fiducial point [deg] - typically right
* ascension and declination. These are given by the CRVALia keywords in
* FITS.
*
* (Given and returned) The second pair of values are the native longitude,
* phi_p [deg], and latitude, theta_p [deg], of the celestial pole (the
* latter is the same as the celestial latitude of the native pole,
* delta_p) and these are given by the FITS keywords LONPOLEa and LATPOLEa
* (or by PVi_2a and PVi_3a attached to the longitude axis which take
* precedence if defined).
*
* LONPOLEa defaults to phi_0 (see above) if the celestial latitude of the
* fiducial point of the projection is greater than or equal to the native
* latitude, otherwise phi_0 + 180 [deg]. (This is the condition for the
* celestial latitude to increase in the same direction as the native
* latitude at the fiducial point.) ref[2] may be set to UNDEFINED (from
* wcsmath.h) or 999.0 to indicate that the correct default should be
* substituted.
*
* theta_p, the native latitude of the celestial pole (or equally the
* celestial latitude of the native pole, delta_p) is often determined
* uniquely by CRVALia and LONPOLEa in which case LATPOLEa is ignored.
* However, in some circumstances there are two valid solutions for theta_p
* and LATPOLEa is used to choose between them. LATPOLEa is set in ref[3]
* and the solution closest to this value is used to reset ref[3]. It is
* therefore legitimate, for example, to set ref[3] to +90.0 to choose the
* more northerly solution - the default if the LATPOLEa keyword is omitted
* from the FITS header. For the special case where the fiducial point of
* the projection is at native latitude zero, its celestial latitude is
* zero, and LONPOLEa = +/- 90.0 then the celestial latitude of the native
* pole is not determined by the first three reference values and LATPOLEa
* specifies it completely.
*
* The returned value, celprm::latpreq, specifies how LATPOLEa was actually
* used.
*
* struct prjprm prj
* (Given and returned) Projection parameters described in the prologue to
* prj.h.
*
* double euler[5]
* (Returned) Euler angles and associated intermediaries derived from the
* coordinate reference values. The first three values are the Z-, X-, and
* Z'-Euler angles [deg], and the remaining two are the cosine and sine of
* the X-Euler angle.
*
* int latpreq
* (Returned) For informational purposes, this indicates how the LATPOLEa
* keyword was used
* - 0: Not required, theta_p (== delta_p) was determined uniquely by the
* CRVALia and LONPOLEa keywords.
* - 1: Required to select between two valid solutions of theta_p.
* - 2: theta_p was specified solely by LATPOLEa.
*
* int isolat
* (Returned) True if the spherical rotation preserves the magnitude of the
* latitude, which occurs iff the axes of the native and celestial
* coordinates are coincident. It signals an opportunity to cache
* intermediate calculations common to all elements in a vector
* computation.
*
* struct wcserr *err
* (Returned) If enabled, when an error status is returned, this struct
* contains detailed information about the error, see wcserr_enable().
*
* void *padding
* (An unused variable inserted for alignment purposes only.)
*
*
* Global variable: const char *cel_errmsg[] - Status return messages
* ------------------------------------------------------------------
* Status messages to match the status value returned from each function.
*
*===========================================================================*/
#ifndef WCSLIB_CEL
#define WCSLIB_CEL
#include "prj.h"
#ifdef __cplusplus
extern "C" {
#endif
enum celenq_enum {
CELENQ_SET = 2, // celprm struct has been set up.
CELENQ_BYP = 4, // celprm struct is in bypass mode.
};
extern const char *cel_errmsg[];
enum cel_errmsg_enum {
CELERR_SUCCESS = 0, // Success.
CELERR_NULL_POINTER = 1, // Null celprm pointer passed.
CELERR_BAD_PARAM = 2, // Invalid projection parameters.
CELERR_BAD_COORD_TRANS = 3, // Invalid coordinate transformation
// parameters.
CELERR_ILL_COORD_TRANS = 4, // Ill-conditioned coordinated transformation
// parameters.
CELERR_BAD_PIX = 5, // One or more of the (x,y) coordinates were
// invalid.
CELERR_BAD_WORLD = 6 // One or more of the (lng,lat) coordinates
// were invalid.
};
struct celprm {
// Initialization flag (see the prologue above).
//--------------------------------------------------------------------------
int flag; // Set to zero to force initialization.
// Parameters to be provided (see the prologue above).
//--------------------------------------------------------------------------
int offset; // Force (x,y) = (0,0) at (phi_0,theta_0).
double phi0, theta0; // Native coordinates of fiducial point.
double ref[4]; // Celestial coordinates of fiducial
// point and native coordinates of
// celestial pole.
struct prjprm prj; // Projection parameters (see prj.h).
// Information derived from the parameters supplied.
//--------------------------------------------------------------------------
double euler[5]; // Euler angles and functions thereof.
int latpreq; // LATPOLEa requirement.
int isolat; // True if |latitude| is preserved.
// Error messaging, if enabled.
//--------------------------------------------------------------------------
struct wcserr *err; // Error handling, if enabled.
//--------------------------------------------------------------------------
// Private - the remainder are for internal use.
//--------------------------------------------------------------------------
void *padding; // (Dummy inserted for alignment purposes.)
};
// Size of the celprm struct in int units, used by the Fortran wrappers.
#define CELLEN (sizeof(struct celprm)/sizeof(int))
int celini(struct celprm *cel);
int celfree(struct celprm *cel);
int celsize(const struct celprm *cel, int sizes[2]);
int celenq(const struct celprm *cel, int enquiry);
int celprt(const struct celprm *cel);
int celperr(const struct celprm *cel, const char *prefix);
int celset(struct celprm *cel);
int celx2s(struct celprm *cel, int nx, int ny, int sxy, int sll,
const double x[], const double y[],
double phi[], double theta[], double lng[], double lat[],
int stat[]);
int cels2x(struct celprm *cel, int nlng, int nlat, int sll, int sxy,
const double lng[], const double lat[],
double phi[], double theta[], double x[], double y[],
int stat[]);
// Deprecated.
#define celini_errmsg cel_errmsg
#define celprt_errmsg cel_errmsg
#define celset_errmsg cel_errmsg
#define celx2s_errmsg cel_errmsg
#define cels2x_errmsg cel_errmsg
#ifdef __cplusplus
}
#endif
#endif // WCSLIB_CEL
celini
int celini(struct celprm *cel)
Default constructor for the celprm struct.
celx2s
int celx2s(struct celprm *cel, int nx, int ny, int sxy, int sll, const double x[], const double y[], double phi[], double theta[], double lng[], double lat[], int stat[])
Pixel-to-world celestial transformation.
celenq
int celenq(const struct celprm *cel, int enquiry)
enquire about the state of a celprm struct.
cel_errmsg
const char * cel_errmsg[]
Status return messages.
celfree
int celfree(struct celprm *cel)
Destructor for the celprm struct.
cels2x
int cels2x(struct celprm *cel, int nlng, int nlat, int sll, int sxy, const double lng[], const double lat[], double phi[], double theta[], double x[], double y[], int stat[])
World-to-pixel celestial transformation.
celperr
int celperr(const struct celprm *cel, const char *prefix)
Print error messages from a celprm struct.
celsize
int celsize(const struct celprm *cel, int sizes[2])
Compute the size of a celprm struct.
celenq_enum
celenq_enum
Definition cel.h:435
CELENQ_SET
@ CELENQ_SET
Definition cel.h:436
CELENQ_BYP
@ CELENQ_BYP
Definition cel.h:437
celset
int celset(struct celprm *cel)
Setup routine for the celprm struct.
cel_errmsg_enum
cel_errmsg_enum
Definition cel.h:442
CELERR_BAD_PARAM
@ CELERR_BAD_PARAM
Definition cel.h:445
CELERR_BAD_COORD_TRANS
@ CELERR_BAD_COORD_TRANS
Definition cel.h:446
CELERR_BAD_PIX
@ CELERR_BAD_PIX
Definition cel.h:450
CELERR_SUCCESS
@ CELERR_SUCCESS
Definition cel.h:443
CELERR_NULL_POINTER
@ CELERR_NULL_POINTER
Definition cel.h:444
CELERR_BAD_WORLD
@ CELERR_BAD_WORLD
Definition cel.h:452
CELERR_ILL_COORD_TRANS
@ CELERR_ILL_COORD_TRANS
Definition cel.h:448
celprt
int celprt(const struct celprm *cel)
Print routine for the celprm struct.
prj.h
celprm
Celestial transformation parameters.
Definition cel.h:456
celprm::theta0
double theta0
Definition cel.h:464
celprm::padding
void * padding
Definition cel.h:484
celprm::flag
int flag
Definition cel.h:459
celprm::ref
double ref[4]
Definition cel.h:465
celprm::err
struct wcserr * err
Definition cel.h:479
celprm::offset
int offset
Definition cel.h:463
celprm::latpreq
int latpreq
Definition cel.h:474
celprm::isolat
int isolat
Definition cel.h:475
celprm::phi0
double phi0
Definition cel.h:464
celprm::prj
struct prjprm prj
Definition cel.h:469
celprm::euler
double euler[5]
Definition cel.h:473
prjprm
Projection parameters.
Definition prj.h:730
wcserr
Error message handling.
Definition wcserr.h:243