## GNU Astronomy Utilities

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#### 10.3.13 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.

Function:
struct wcsprm *
gal_wcs_read_fitsptr (fitsfile *fptr, size_t hstartwcs, size_t hendwcs, int *nwcs)

[Not thread-safe] Return the WCSLIB wcsprm structure that is read from the CFITSIO fptr pointer to an opened FITS file. 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 can free the returned structure with WCSLIB’s wcsvfree keyword:

status = wcsvfree(&nwcs,&wcs);


If you don’t 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 couldn’t 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).

Function:
struct wcsprm *
gal_wcs_read (char *filename, char *hdu, 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.

Function:
struct wcsprm *
gal_wcs_copy (struct wcsprm *wcs)

Return a fully allocated (independent) copy of wcs.

Function:
void
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 won’t do anything.

In many cases, tiles are created for internal/low-level processing. Hence for performance reasons, when creating the tiles they don’t 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.

Function:
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.

Function:
void
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.

Function:
double
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.

$$\cos(d)=\sin(d_1)\sin(d_2)+\cos(d_1)\cos(d_2)\cos(r_1-r_2)$$

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

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

Function:
double *
gal_wcs_pixel_scale (struct wcsprm *wcs)

Return the pixel scale for each dimension of wcs in degrees. The output is an array of double precision floating point type with one element for each dimension.

Function:
double
gal_wcs_pixel_area_arcsec2 (struct wcsprm *wcs)

Return the pixel area of wcs in arcsecond squared. If the input WCS structure is not two dimensional and the units (CUNIT keywords) are not deg (for degrees), then this function will return a NaN.

Function:
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) and etc. Similarly, the top node of the output will be the first image coordinate (in the FITS standard).

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.

Function:
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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