GNU Astronomy Utilities

12.3.13 World Coordinate System (wcs.h)

The FITS standard defines the world coordinate system (WCS) as a mechanism to associate physical values to positions within a dataset. For example, it can be used to convert pixel coordinates in an image to celestial coordinates like the right ascension and declination. The functions in this section are mainly just wrappers over CFITSIO, WCSLIB and GSL library functions to help in common applications.

[Tread safety] Since WCSLIB version 5.18 (released in January 2018), most WCSLIB functions are thread safe255. Gnuastro has high-level functions to easily spin-off threads and speed up your programs. For a fully working example see Library demo - multi-threaded operation. However you still need to be cautious in the following scenarios below.

The full set of functions and global constants that are defined by Gnuastro’s gnuastro/wcs.h are described below.


Gnuastro identifiers of the various WCS distortion conventions, for more, see Calabretta et al. (2004, preprint)256. Among these, SIP is a prior distortion, the rest other are sequent distortions. TPD is a superset of all these, hence it has both prior and sequeal distortion coefficients. More information is given in the documentation of dis.h, from the WCSLIB manual257.

Global integer: GAL_WCS_COORDSYS_EQB1950
Global integer: GAL_WCS_COORDSYS_EQJ2000
Global integer: GAL_WCS_COORDSYS_ECB1950
Global integer: GAL_WCS_COORDSYS_ECJ2000

Recognized WCS coordinate systems in Gnuastro. EQ and EC stand for the EQuatorial and ECliptic coordinate systems. In the equatorial and ecliptic coordinates, B1950 stands for the Besselian 1950 epoch and J2000 stands for the Julian 2000 epoch.


Identifiers of the linear transformation matrix: either in the PCi_j or the CDi_j formalism. For more, see the description of --wcslinearmatrix in Input/Output options.


Limit of rounding for floating point errors.

struct wcsprm *
gal_wcs_create (double *crpix, double *crval, double *cdelt, double *pc, char **cunit, char **ctype, size_t ndim, int linearmatrix)

Given all the most common standard components of the WCS standard, construct a struct wcsprm, initialize and set it for future processing. See the FITS WCS standard for more on these keywords. All the arrays must have ndim elements with them except for pc which should have ndim*ndim elements (a square matrix). Also, cunit and ctype are arrays of strings. If GAL_WCS_LINEAR_MATRIX_CD is passed to linearmatrix then the output WCS structure will have a CD matrix (even though you have given a PC and CDELT matrix as input to this function). Otherwise, the output will have a PC and CDELT matrix (which is the recommended format by WCSLIB).

#include <stdio.h>
#include <stdlib.h>
#include <gnuastro/wcs.h>

  int status;
  size_t ndim=2;
  struct wcsprm *wcs;
  double crpix[]={50, 50};
  double pc[]={-1, 0, 0, 1};
  double cdelt[]={0.4, 0.4};
  double crval[]={178.23, 36.98};
  char   *cunit[]={"deg", "deg"};
  char   *ctype[]={"RA---TAN", "DEC--TAN"};
  int linearmatrix = GAL_WCS_LINEAR_MATRIX_PC;

  /* Allocate and fill the 'wcsprm' structure. */
  wcs=gal_wcs_create(crpix, crval, cdelt, pc, cunit,
		     ctype, ndim, linearmatrix);
  printf("WCS structure created.\n");

  /*... Add any operation with the WCS structure here ...*/

  /* Free the WCS structure. */
  printf("WCS structure freed.\n");

  /* Return successfully. */
  return EXIT_SUCCESS;
struct wcsprm *
gal_wcs_read_fitsptr (fitsfile *fptr, int linearmatrix, size_t hstartwcs, size_t hendwcs, int *nwcs)

Return the WCSLIB wcsprm structure that is read from the CFITSIO fptr pointer to an opened FITS file. With older WCSLIB versions (in particular below version 5.18) this function may not be thread-safe.

Also put the number of coordinate representations found into the space that nwcs points to. To read the WCS structure directly from a filename, see gal_wcs_read below. After processing has finished, you should free the WCS structure that this function returns with gal_wcs_free.

The linearmatrix argument takes one of three values: 0, GAL_WCS_LINEAR_MATRIX_PC and GAL_WCS_LINEAR_MATRIX_CD. It will determine the format of the WCS when it is later written to file with gal_wcs_write or gal_wcs_write_in_fitsptr (which is called by gal_fits_img_write) So if you do not want to write the WCS into a file later, just give it a value of 0. For more on the difference between these modes, see the description of --wcslinearmatrix in Input/Output options.

If you do not want to search the full FITS header for WCS-related FITS keywords (for example, due to conflicting keywords), but only a specific range of the header keywords you can use the hstartwcs and hendwcs arguments to specify the keyword number range (counting from zero). If hendwcs is larger than hstartwcs, then only keywords in the given range will be checked. Hence, to ignore this feature (and search the full FITS header), give both these arguments the same value.

If the WCS information could not be read from the FITS file, this function will return a NULL pointer and put a zero in nwcs. A WCSLIB error message will also be printed in stderr if there was an error.

This function is just a wrapper over WCSLIB’s wcspih function which is not thread-safe. Therefore, be sure to not call this function simultaneously (over multiple threads).

struct wcsprm *
gal_wcs_read (char *filename, char *hdu, int linearmatrix, size_t hstartwcs, size_t hendwcs, int *nwcs)

[Not thread-safe] Return the WCSLIB structure that is read from the HDU/extension hdu of the file filename. Also put the number of coordinate representations found into the space that nwcs points to. Please see gal_wcs_read_fitsptr for more.

After processing has finished, you should free the WCS structure that this function returns with gal_wcs_free.

gal_wcs_free (struct wcsprm *wcs)

Free the contents and the space that wcs points to. WCSLIB’s wcsfree function only frees the contents of the wcsprm structure, not the actual pointer. However, Gnuastro’s wcsprm creation and reading functions allocate the structure also. This higher-level function therefore simplifies the processing. A complete working example is given in the description of gal_wcs_create.

char *
gal_wcs_dimension_name (struct wcsprm *wcs, size_t dimension)

Return an allocated string array (that should be freed later) containing the first part of the CTYPEi FITS keyword (which contains the dimension name in the FITS standard). For example, if CTYPE1 is RA---TAN, the string that function returns will be RA. Recall that the second component of CTYPEi contains the type of projection.

char *
gal_wcs_write_wcsstr (struct wcsprm *wcs, int *nkeyrec)

Return an allocated string which contains the respective FITS keywords for the given WCS structure into it. The number of keywords is written in the space pointed by nkeyrec. Each FITS keyword is 80 characters wide (according to the FITS standard), and the next one is placed immediately after it, so the full string has 80*nkeyrec bytes. The output of this function can later be written into an opened FITS file using gal_fits_key_write_wcsstr (see FITS header keywords).

gal_wcs_write (struct wcsprm *wcs, char *filename, char *extname, gal_fits_list_key_t *headers, char *program_string)

Write the given WCS structure into the second extension of an empty FITS header. The first/primary extension will be empty like the default format of all Gnuastro outputs. When extname!=NULL it will be used as the FITS extension name. Any set of extra headers can also be written through the headers list and if program_string!=NULL it will be used in a commented keyword title just above the written version information.

gal_wcs_write_in_fitsptr (fitsfile *fptr, struct wcsprm *wcs)

Convert the input wcs structure (keeping the WCS programmatically) into FITS keywords and write them into the given FITS file pointer. This is a relatively low-level function which assumes the FITS file has already been opened with CFITSIO. If you just want to write the WCS into an empty file, you can use gal_wcs_write (which internally calls this function after creating the FITS file and later closes it safely).

struct wcsprm *
gal_wcs_copy (struct wcsprm *wcs)

Return a fully allocated (independent) copy of wcs.

gal_wcs_remove_dimension (struct wcsprm *wcs, size_t fitsdim)

Remove the given FITS dimension from the given wcs structure.

gal_wcs_on_tile (gal_data_t *tile)

Create a WCSLIB wcsprm structure for tile using WCS parameters of the tile’s allocated block dataset, see Tessellation library (tile.h) for the definition of tiles. If tile already has a WCS structure, this function will not do anything.

In many cases, tiles are created for internal/low-level processing. Hence for performance reasons, when creating the tiles they do not have any WCS structure. When needed, this function can be used to add a WCS structure to each tile tile by copying the WCS structure of its block and correcting the reference point’s coordinates within the tile.

double *
gal_wcs_warp_matrix (struct wcsprm *wcs)

Return the Warping matrix of the given WCS structure as an array of double precision floating points. This will be the final matrix, irrespective of the type of storage in the WCS structure. Recall that the FITS standard has several methods to store the matrix. The output is an allocated square matrix with each side equal to the number of dimensions.

gal_wcs_clean_small_errors (struct wcsprm *wcs)

Errors can make small differences between the pixel-scale elements (CDELT) and can also lead to extremely small values in the PC matrix. With this function, such errors will be “cleaned” as follows: 1) if the maximum difference between the CDELT elements is smaller than the reference error, it will be set to the mean value. When the FITS keyword CRDER (optional) is defined it will be used as a reference, if not the default value is GAL_WCS_FLTERROR. 2) If any of the PC elements differ from 0, 1 or -1 by less than GAL_WCS_FLTERROR, they will be rounded to the respective value.

gal_wcs_decompose_pc_cdelt (struct wcsprm *wcs)

Decompose the PCi_j and CDELTi elements of wcs. According to the FITS standard, in the PCi_j WCS formalism, the rotation matrix elements \(m_{ij}\) are encoded in the PCi_j keywords and the scale factors are encoded in the CDELTi keywords. There is also another formalism (the CDi_j formalism) which merges the two into one matrix.

However, WCSLIB’s internal operations are apparently done in the PCi_j formalism. So its outputs are also all in that format by default. When the input is a CDi_j, WCSLIB will still read the matrix directly into the PCi_j matrix and the CDELTi values are set to 1 (one). This function is designed to correct such issues: after it is finished, the CDELTi values in wcs will correspond to the pixel scale, and the PCi_j will correction show the rotation.

gal_wcs_to_cd (struct wcsprm *wcs)

Make sure that the WCS structure’s PCi_j and CDi_j keywords have the same value and that the CDELTi keywords have a value of 1.0. Also, set the wcs->altlin=2 (for the CDi_j formalism). With these changes gal_wcs_write_in_fitsptr (and thus gal_wcs_write and gal_fits_img_write and its derivatives) will have an output file in the format of CDi_j.

gal_wcs_coordsys_from_string (char *coordsys)

Convert the given string to Gnuastro’s integer-based WCS coordinate system identifier (one of the GAL_WCS_COORDSYS_*, listed above). The expected strings can be seen in the description of the --wcscoordsys option of the Fits program, see Keyword inspection and manipulation.

gal_wcs_coordsys_identify (struct wcsprm *wcs)

Read the given WCS structure and return its coordinate system as one of Gnuastro’s WCS coordinate system identifiers (the macros GAL_WCS_COORDSYS_*, listed above).

struct wcsprm *
gal_wcs_coordsys_convert (struct wcsprm *inwcs, int coordsysid)

Return a newly allocated WCS structure with the coordsysid coordinate system identifier. The Gnuastro WCS distortion identifiers are defined in the GAL_WCS_COORDSYS_* macros mentioned above. Since the returned dataset is newly allocated, if you do not need the original dataset after this, use the WCSLIB library function wcsfree to free the input, for example, wcsfree(inwcs).

gal_wcs_distortion_from_string (char *distortion)

Convert the given string (assumed to be a FITS-standard, string-based distortion identifier) to a Gnuastro’s integer-based distortion identifier (one of the GAL_WCS_DISTORTION_* macros defined above). The sting-based distortion identifiers have three characters and are all in capital letters.

gal_wcs_distortion_to_string (int distortion)

Convert the given Gnuastro integer-based distortion identifier (one of the GAL_WCS_DISTORTION_* macros defined above) to the string-based distortion identifier) of the FITS standard. The sting-based distortion identifiers have three characters and are all in capital letters.

gal_wcs_distortion_identify (struct wcsprm *wcs)

Returns the Gnuastro identifier for the distortion of the input WCS structure. The returned value is one of the GAL_WCS_DISTORTION_* macros defined above. When the input pointer to a structure is NULL, or it does not contain a distortion, the returned value will be GAL_WCS_DISTORTION_INVALID.

struct wcsprm *
gal_wcs_distortion_convert(struct wcsprm *inwcs, int outdisptype, size_t *fitsize)

Return a newly allocated WCS structure, where the distortion is implemented in a different standard, identified by the identifier outdisptype. The Gnuastro WCS distortion identifiers are defined in the GAL_WCS_DISTORTION_* macros mentioned above.

The available conversions in this function will grow. Currently it only supports converting TPV to SIP and vice versa, following the recipe of Shupe et al. (2012)258. Please get in touch with us if you need other types of conversions.

For some conversions, direct analytical conversions do not exist. It is thus necessary to model and fit the two types. In such cases, it is also necessary to specify the fitsize array that is the size of the array along each C-ordered dimension, so you can simply pass the dsize element of your gal_data_t dataset, see Generic data container (gal_data_t). Currently this is only necessary when converting TPV to SIP. For other conversions you may simply pass a NULL pointer.

For example, if you want to convert the TPV coefficients of your input image.fits to SIP coefficients, you can use the following functions (which are also available as a command-line operation in Fits).

int nwcs;
gal_data_t *data=gal_fits_img_read("image.fits", "1", -1, 1);
inwcs=gal_wcs_read("image.fits", "1", 0, 0, 0, &nwcs);
data->wcs=gal_wcs_distortion_convert(inwcs, GAL_WCS_DISTORTION_TPV,
gal_fits_img_write(data, "tpv.fits", NULL, NULL);
gal_wcs_angular_distance_deg (double r1, double d1, double r2, double d2)

Return the angular distance (in degrees) between a point located at (r1, d1) to (r2, d2). All input coordinates are in degrees. The distance (along a great circle) on a sphere between two points is calculated with the equation below.


However, since the pixel scales are usually very small numbers, this function will not use that direct formula. It will be use the Haversine formula which is better considering floating point errors:

$${\sin^2(d)\over 2}=\sin^2\left( {d_1-d_2\over 2} \right)+\cos(d_1)\cos(d_2)\sin^2\left( {r_1-r_2\over 2} \right)$$

gal_wcs_box_vertices_from_center (double ra_center, double dec_center, double ra_delta, double dec_delta, double *out)

Calculate the vertices of a rectangular box given the central RA and Dec and delta of each. The vertice coordinates are written in the space that out points to (assuming it has space for eight doubles).

Given the spherical nature of the coordinate system, the vertice lengths can’t be calculated with a simple addition/subtraction. For the declination, a simple addition/subtraction is enough. Also, on the equator (where the RA is defined), a simple addition/subtraction along the RA is fine. However, at other declinations, the new RA after a shift needs special treatment, such that close to the poles, a shift of 1 degree can correspond to a new RA that is much more distant than the original RA. Assuming a point at Right Ascension (RA) and Declination of \(\alpha\) and \(\delta\), a shift of \(R\) degrees along the positive RA direction corresponds to a right ascension of \(\alpha+\frac{R}{\cos(\delta)}\). For more, see the description of box-vertices-on-sphere in Box shape operators.

The 8 coordinates of the 4 vertices of the box are written in the order below. Where “bottom” corresponds to a lower declination and “top” to higher declination, “left” corresponds to a larger RA and “right” corresponds to lower RA.

out[0]: bottom-left  RA
out[1]: bottom-left  Dec
out[2]: bottom-right RA
out[3]: bottom-right Dec
out[4]: top-right    RA
out[5]: top-right    Dec
out[6]: top-left     RA
out[7]: top-left     Dec
double *
gal_wcs_pixel_scale (struct wcsprm *wcs)

Return the pixel scale for each dimension of wcs in degrees. The output is an allocated array of double precision floating point type with one element for each dimension. If it is not successful, this function will return NULL.

gal_wcs_pixel_area_arcsec2 (struct wcsprm *wcs)

Return the pixel area of wcs in arc-second squared. This only works when the input dataset has at least two dimensions and the units of the first two dimensions (CUNIT keywords) are deg (for degrees). In other cases, this function will return a NaN.

gal_wcs_coverage (char *filename, char *hdu, size_t *ondim, double **ocenter, double **owidth, double **omin, double **omax)

Find the sky coverage of the image HDU (hdu) within filename. The number of dimensions is written into ndim, and space for the various output arrays is internally allocated and filled with the respective values. Therefore you need to free them afterwards.

Currently this function only supports images that are less than 180 degrees in width (which is usually the case!). This requirement has been necessary to account for images that cross the RA=0 hour circle on the sky. Please get in touch with us at if you have an image that is larger than 180 degrees so we try to find a solution based on need.

gal_data_t *
gal_wcs_world_to_img (gal_data_t *coords, struct wcsprm *wcs, int inplace)

Convert the linked list of world coordinates in coords to a linked list of image coordinates given the input WCS structure. coords must be a linked list of data structures of float64 (‘double’) type, seeLinked lists (list.h) and List of gal_data_t. The top (first popped/read) node of the linked list must be the first WCS coordinate (RA in an image usually) etc. Similarly, the top node of the output will be the first image coordinate (in the FITS standard). In case WCSLIB fails to convert any of the coordinates (for example, the RA of one coordinate is given as 400!), the respective element in the output will be written as NaN.

If inplace is zero, then the output will be a newly allocated list and the input list will be untouched. However, if inplace is non-zero, the output values will be written into the input’s already allocated array and the returned pointer will be the same pointer to coords (in other words, you can ignore the returned value). Note that in the latter case, only the values will be changed, things like units or name (if present) will be untouched.

gal_data_t *
gal_wcs_img_to_world (gal_data_t *coords, struct wcsprm *wcs, int inplace)

Convert the linked list of image coordinates in coords to a linked list of world coordinates given the input WCS structure. See the description of gal_wcs_world_to_img for more details.






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