# Fitting a WCS to input pixels & sky positions¶

Suppose we have an image where we have centroid positions for a number of sources, and we have matched these positions to an external catalog to obtain (RA, Dec). If this data is missing or has inaccurate WCS information, it is useful to fit or re-fit a GWCS object with this matched list of coordinate pairs to be able to transform between pixel and sky.

This example shows how to use the `wcs_from_points` tool to fit a WCS to a matched set of pixel and sky positions. Along with arrays of the (x,y) pixel position in the image and the matched sky coordinates, the fiducial point for the projection must be supplied as a `SkyCoord` object. Additionally, the projection type must be specified from the available projections in `projcodes`.

Geometric distortion can also be fit to the input coordinates - the distortion type (2D polynomial, chebyshev, legendre) and the degree can be supplied to fit this component of the model.

The following example will show how to fit a WCS, including a 4th degree 2D polynomial, to a set of input pixel positions of sources in an image and their corresponding positions on the sky obtained from a catalog.

Import the wcs_from_points function,

```>>> from gwcs.wcstools import wcs_from_points
```

along with some useful general imports.

```>>> from astropy.coordinates import SkyCoord
>>> from astropy.io import ascii
>>> import astropy.units as u
>>> import numpy as np
```

A collection of 20 matched coordinate pairs in x, y, RA, and Dec will be used to fit the WCS information. The function requires tuples of arrays for x & y, and a `SkyCoord` object for sky coordinates.

```>>> xy = (np.array([2810.156, 2810.156,  650.236, 1820.927, 3425.779, 2750.369,
...                 212.422, 1146.91 ,   27.055, 2100.888,  648.149,   22.212,
...                 2003.314,  727.098,  248.91 ,  409.998, 1986.931,  128.925,
...                 1106.654, 1502.67 ]),
...       np.array([1670.347, 1670.347,  360.325,  165.663,  900.922,  700.148,
...                 1416.235, 1372.364,  398.823,  580.316,  317.952,  733.984,
...                 339.024,  234.29 , 1241.608,  293.545, 1794.522, 1365.706,
...                 583.135,   25.306]))
>>> ra, dec = (np.array([246.75001315, 246.75001315, 246.72033646, 246.72303144,
...                    246.74164072, 246.73540614, 246.73379121, 246.73761455,
...                    246.7179495 , 246.73051123, 246.71970072, 246.7228646 ,
...                    246.72647213, 246.7188386 , 246.7314031 , 246.71821002,
...                    246.74785534, 246.73265223, 246.72579817, 246.71943263]),
...          np.array([43.48690547,  43.48690547,  43.46792989,  43.48075238,
...                    43.49560501,  43.48903538,  43.46045875,  43.47030776,
...                    43.46132376,  43.48252763,  43.46802566,  43.46035331,
...                    43.48218262,  43.46908299,  43.46131665,  43.46560591,
...                    43.47791234,  43.45973025,  43.47208325,  43.47779988]))
>>> radec = SkyCoord(ra, dec, unit=(u.deg, u.deg))
```

We can now choose the reference point on the sky for the projection. This can either be an `SkyCoord` object, or the string ‘center’ to use the geometric center of input points. In this example, we will specify exact coordinates for the fiducial.

```>>> proj_point = SkyCoord(246.7368408, 43.480712949, frame = 'icrs', unit = (u.deg,u.deg))
```

We can now call the function that returns a GWCS object corresponding to the best fit parameters that relate the input pixels and sky coordinates with a TAN projection centered at the reference point we specified, with a distortion model (degree 4 polynomial). This function will return a GWCS object that can be used to transform between coordinate frames.

```>>> gwcs_obj = wcs_from_points(xy, radec, proj_point)
```

This GWCS object contains parameters for a TAN projection, rotation, scale, skew and a polynomial fit to x and y that represent the best-fit to the input coordinates. With WCS information associated with the data now, we can easily work in both pixel and sky space, and transform between frames.

The GWCS object, which by default when called executes for forward transformation, can be used to convert coordinates from pixel to world.

```>>> gwcs_obj(36.235,642.215)
(246.72158004206716, 43.46075091731673)
```
Or equivalently
```>>> gwcs_obj.forward_transform(36.235,642.215)
(246.72158004206716, 43.46075091731673)
```