# Geometry Utilities¶

Pyresample provides convenience functions for constructing area definitions. This includes functions for loading `AreaDefinition` from on-disk files, and netCDF/CF files. Some of these utility functions are described below.

The main utility function for creating `AreaDefinition` objects is the `create_area_def()` function. This function will take whatever information can be provided to describe a geographic region and create a valid `AreaDefinition` object if possible. If it can’t make a fully specified `AreaDefinition` then it will provide a `DynamicAreaDefinition` instead. The function can handle unit conversions and will perform the coordinate calculations necessary to get an area’s `shape` and `area_extent`.

The `create_area_def` function has the following required arguments:

• area_id: ID of area

• projection: Projection parameters as a dictionary or string of PROJ parameters.

and optional arguments:

• description: Human-readable description. If not provided, defaults to area_id

• proj_id: ID of projection (deprecated)

• units: Units that provided arguments should be interpreted as. This can be one of ‘deg’, ‘degrees’, ‘meters’, ‘metres’, and any parameter supported by the cs2cs -lu command. Units are determined in the following priority:

1. units expressed with each variable through a DataArray’s attrs attribute.

2. units passed to `units`

3. units used in `projection`

4. meters

• shape: Number of pixels in the y and x direction following row-column format (height, width)

• area_extent: Area extent as a tuple (lower_left_x, lower_left_y, upper_right_x, upper_right_y)

• upper_left_extent: x and y coordinates of the upper left corner of the upper left pixel (x, y)

• center: x and y coordinate of the center of projection (x, y)

• resolution: Size of pixels in the x and y direction (dx, dy)

• radius: Length from the center to the left/right and top/bottom outer edges (dx, dy)

```>>> from pyresample import create_area_def
>>> area_id = 'ease_sh'
>>> proj_dict = {'proj': 'laea', 'lat_0': -90, 'lon_0': 0, 'a': 6371228.0, 'units': 'm'}
>>> center = (0, 0)
>>> resolution = (25067.525, 25067.525)
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

Note

Projection (CRS) information is stored internally using the pyproj library’s `CRS` object. To meet certain standards for representing CRS information, pyproj may rename parameters or use completely different parameters from what you provide.

The `create_area_def` function accepts some parameters in multiple forms to make it as easy as possible. For example, the resolution and radius keyword arguments can be specified with one value if `dx == dy`:

```>>> proj_string = '+proj=laea +lat_0=-90 +lon_0=0 +a=6371228.0 +units=m'
>>> area_def = create_area_def(area_id, proj_string, center=center,
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

You can also specify parameters in degrees even if the projection space is defined in meters. For example the below code creates an area in the mercator projection with radius and resolution defined in degrees.

```>>> proj_dict = {'proj': 'merc', 'lon_0': 0, 'no_defs': None, 'proj': 'merc', 'R': 6371228, 'k': 1, 'units': 'm'}
>>> area_def = create_area_def(area_id, proj_dict, center=(0, 0),
...                              resolution=(0.22542960090875294, 0.22542901929487608),
...                              units='degrees', description='Antarctic EASE grid')
>>> print(area_def)
Area ID: ease_sh
Description: Antarctic EASE grid
Projection: {'R': '6371228', 'k': '1', 'lon_0': '0', 'no_defs': 'None', 'proj': 'merc', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

The area definition corresponding to a given lat-lon grid (defined by area extent and resolution) can be obtained as follows:

```>>> area_def = create_area_def('my_area',
...                            {'proj': 'longlat', 'datum': 'WGS84'},
...                            area_extent=[-180, -90, 180, 90],
...                            resolution=1,
...                            units='degrees',
...                            description='Global 1x1 degree lat-lon grid')
>>> print(area_def)
Area ID: my_area
Description: Global 1x1 degree lat-lon grid
Projection: {'datum': 'WGS84', 'no_defs': 'None', 'proj': 'longlat', 'type': 'crs'}
Number of columns: 360
Number of rows: 180
Area extent: (-180.0, -90.0, 180.0, 90.0)
```

If only one of area_extent or shape can be computed from the information provided by the user, a `DynamicAreaDefinition` object is returned:

```>>> area_def = create_area_def(area_id, proj_string, radius=radius, resolution=resolution)
>>> print(type(area_def))
```

Note

radius and resolution are distances, NOT coordinates. When expressed as angles, they represent the degrees of longitude/latitude away from the center that they should span. Hence in these cases center or area_extent must be provided.

There are four class methods available on the `AreaDefinition` class utilizing `create_area_def()` providing a simpler interface to the functionality described in the previous section. Hence each argument used below is the same as the `create_area_def` arguments described above and can be used in the same way (i.e. units). The following functions require area_id and projection along with a few other arguments:

### from_extent¶

`from_extent()`

```>>> from pyresample.geometry import AreaDefinition
>>> area_id = 'ease_sh'
>>> proj_string = '+proj=laea +lat_0=-90 +lon_0=0 +a=6371228.0 +units=m'
>>> area_extent = (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
>>> shape = (425, 425)
>>> area_def = AreaDefinition.from_extent(area_id, proj_string, shape, area_extent)
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

### from_circle¶

`from_circle()`

```>>> proj_dict = {'proj': 'laea', 'lat_0': -90, 'lon_0': 0, 'a': 6371228.0, 'units': 'm'}
>>> center = (0, 0)
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```
```>>> resolution = 25067.525
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

### from_area_of_interest¶

`from_area_of_interest()`

```>>> area_def = AreaDefinition.from_area_of_interest(area_id, proj_dict, shape, center, resolution)
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

### from_ul_corner¶

`from_ul_corner()`

```>>> upper_left_extent = (-5326849.0625, 5326849.0625)
>>> area_def = AreaDefinition.from_ul_corner(area_id, proj_string, shape, upper_left_extent, resolution)
>>> print(area_def)
Area ID: ease_sh
Description: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

The `load_area()` function can be used to parse area definitions from a configuration file by giving it the area file name and regions you wish to load. `load_area()` takes advantage of `create_area_def()` and hence allows for the same arguments in the on-disk file. Pyresample uses the YAML file format to store on-disk area definitions. Below is an example YAML configuration file showing the various ways an area might be specified.

```boundary:
area_id: ease_sh
description: Example of making an area definition using shape and area_extent
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
shape: [425, 425]
area_extent: [-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625]

boundary_2:
description: Another example of making an area definition using shape and area_extent
units: degrees
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
shape:
height: 425
width: 425
area_extent:
lower_left_xy: [-135.0, -17.516001139327766]
upper_right_xy: [45.0, -17.516001139327766]

corner:
description: Example of making an area definition using shape, upper_left_extent, and resolution
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
shape: [425, 425]
upper_left_extent: [-5326849.0625, 5326849.0625]
resolution: 25067.525

corner_2:
area_id: ease_sh
description: Another example of making an area definition using shape, upper_left_extent, and resolution
units:  degrees
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
shape: [425, 425]
upper_left_extent:
x: -45.0
y: -17.516001139327766
resolution:
dx: 25067.525
dy: 25067.525
units: meters

circle:
description: Example of making an area definition using center, resolution, and radius
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
center: [0, 0]
resolution: [25067.525, 25067.525]

circle_2:
area_id: ease_sh
description: Another example of making an area definition using center, resolution, and radius
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
center:
x: 0
y: -90
units: degrees
shape:
width: 425
height: 425
dx: 49.4217406986
dy: 49.4217406986
units: degrees

area_of_interest:
description: Example of making an area definition using shape, center, and resolution
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
shape: [425, 425]
center: [0, 0]
resolution: [25067.525, 25067.525]

area_of_interest_2:
area_id: ease_sh
description: Another example of making an area definition using shape, center, and resolution
projection:
proj: laea
lat_0: -90
lon_0: 0
a: 6371228.0
units: m
shape: [425, 425]
center:
center: [0, -90]
units: deg
resolution:
resolution: 0.22542974631297721
units: deg

epsg:
area_id: ease_sh
description: Example of making an area definition using EPSG codes
projection:
init: EPSG:3410
shape: [425, 425]
area_extent: [-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625]
```

Note

The lower_left_xy and upper_right_xy items give the coordinates of the outer edges of the corner pixels on the x and y axis respectively. When the projection coordinates are longitudes and latitudes, it is expected to provide the extent in longitude, latitude order.

Note

When using pyproj 2.0+, please use the new `'EPSG: XXXX'` syntax as the old `'init: EPSG:XXXX'` is no longer supported.

If we assume the YAML content is stored in an `areas.yaml` file, we can read a single `AreaDefinition` named `corner` by doing:

```>>> from pyresample import load_area
>>> import yaml
>>> print(area_def)
Area ID: corner
Description: Example of making an area definition using shape, upper_left_extent, and resolution
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

Several area definitions can be read at once using the region names as a series of arguments:

```>>> corner, boundary = load_area('areas.yaml', 'corner', 'boundary')
>>> print(boundary)
Area ID: ease_sh
Description: Example of making an area definition using shape and area_extent
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

For backwards compatibility, we still support the legacy area file format. Assuming the file areas.cfg exists with the following content

```REGION: ease_sh {
NAME:           Antarctic EASE grid
PCS_ID:         ease_sh
PCS_DEF:        proj=laea, lat_0=-90, lon_0=0, a=6371228.0, units=m
XSIZE:          425
YSIZE:          425
AREA_EXTENT:    (-5326849.0625,-5326849.0625,5326849.0625,5326849.0625)
};

REGION: ease_nh {
NAME:           Arctic EASE grid
PCS_ID:         ease_nh
PCS_DEF:        proj=laea, lat_0=90, lon_0=0, a=6371228.0, units=m
XSIZE:          425
YSIZE:          425
AREA_EXTENT:    (-5326849.0625,-5326849.0625,5326849.0625,5326849.0625)
};
```

An area definition dict can be read using

```>>> from pyresample import load_area
>>> print(area)
Area ID: ease_nh
Description: Arctic EASE grid
Projection ID: ease_nh
Projection: {'R': '6371228', 'lat_0': '90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

Note: In the configuration file REGION maps to area_id and PCS_ID maps to proj_id.

Several area definitions can be read at once using the region names in an argument list:

```>>> nh_def, sh_def = load_area('areas.cfg', 'ease_nh', 'ease_sh')
>>> print(sh_def)
Area ID: ease_sh
Description: Antarctic EASE grid
Projection ID: ease_sh
Projection: {'R': '6371228', 'lat_0': '-90', 'lon_0': '0', 'no_defs': 'None', 'proj': 'laea', 'type': 'crs', 'units': 'm', 'x_0': '0', 'y_0': '0'}
Number of columns: 425
Number of rows: 425
Area extent: (-5326849.0625, -5326849.0625, 5326849.0625, 5326849.0625)
```

## Writing to disk¶

To write an area definition to a yaml file to disk use the `dump()` function of the `AreaDefinition`.

`AreaDefinition` objects can be loaded from netCDF CF files with function `load_cf_area()`.

```>>> from pyresample.utils import load_cf_area
```

The `load_cf_area()` routine offers three call forms:

• Load the `AreaDefinition` from a specific CF grid_mapping object: with all three of `variable=`, `x=`, and `y=` ;

• Load the `AreaDefinition` sustaining a CF variable: only `variable=` ;

• Find and load the valid `AreaDefinition` in a CF file: no parameter ;

Consider the following netCDF/CF file:

```netcdf cf_nh10km {
dimensions:
xc = 760 ;
yc = 1120 ;
variables:
int Polar_Stereographic_Grid ;
Polar_Stereographic_Grid:grid_mapping_name = "polar_stereographic" ;
Polar_Stereographic_Grid:false_easting = 0. ;
Polar_Stereographic_Grid:false_northing = 0. ;
Polar_Stereographic_Grid:semi_major_axis = 6378273. ;
Polar_Stereographic_Grid:semi_minor_axis = 6356889.44891 ;
Polar_Stereographic_Grid:straight_vertical_longitude_from_pole = -45. ;
Polar_Stereographic_Grid:latitude_of_projection_origin = 90. ;
Polar_Stereographic_Grid:standard_parallel = 70. ;
double xc(xc) ;
xc:axis = "X" ;
xc:units = "km" ;
xc:long_name = "x coordinate in Cartesian system" ;
xc:standard_name = "projection_x_coordinate" ;
double yc(yc) ;
yc:axis = "Y" ;
yc:units = "km" ;
yc:long_name = "y coordinate in Cartesian system" ;
yc:standard_name = "projection_y_coordinate" ;
float lat(yc, xc) ;
lat:long_name = "latitude coordinate" ;
lat:standard_name = "latitude" ;
lat:units = "degrees_north" ;
float lon(yc, xc) ;
lon:long_name = "longitude coordinate" ;
lon:standard_name = "longitude" ;
lon:units = "degrees_east" ;
short ice_conc(yc, xc) ;
ice_conc:_FillValue = -999s ;
ice_conc:grid_mapping = "Polar_Stereographic_Grid" ;
ice_conc:coordinates = "lat lon" ;
ice_conc:standard_name = "sea_ice_area_fraction" ;
ice_conc:units = "%" ;
ice_conc:scale_factor = 0.01f ;
ice_conc:valid_min = 0 ;
ice_conc:valid_max = 10000 ;
// global attributes:
:Conventions = "CF-1.7"

}
```

The three call forms are:

1st call form:

```>>> area_def, cf_info = load_cf_area('/path/to/cf_nh10km.nc', variable='Polar_Stereographic_Grid', x='xc', y='yc')
```

This will directly create the AreaDefinition `area_def` from the content of the grid_mapping variable ‘Polar_Stereographic_Grid’, and the area extent from the ‘xc’ and ‘yc’.

2nd call form:

```>>> area_def, cf_info = load_cf_area('/path/to/cf_nh10km.nc', variable='ice_conc')
```

This will search which grid_mapping, x and y axes sustain the ‘ice_conc’ variable, and create the `AreaDefinition` from this information.

3rd call form:

```>>> area_def, cf_info = load_cf_area('/path/to/cf_nh10km.nc')
```

This will look through the whole netCDF/CF file, and guess all information needed to load a `AreaDefinition` object.

Note

The CF convention allows that a single file defines several different grid_mappings. At present, the 3rd call form of `load_cf_area()` will raise a `ValueError` exception when this happens.

If you have several grid_mappings in your CF file, be specific which one you want to access with the 1st or 2nd call form.

Although a recommended practice, it cannot be trusted that the ‘y’ and ‘x’ axes are in the last two dimensions of a CF variable. This is because the CF convention does not impose the order of the dimensions of a variable. `load_cf_area()` will effectively look for the variables holding the x and y coordinates of the Earth mapping projection, not based on the order of the dimensions of the CF variable.

Not all relevant information can be stored in the `AreaDefinition` object. For example, it can be useful to know what were the names of the variables holding the coordinate variables (‘xc’ and ‘yc’ in the example above), or that the latitude and longitude associated to the grid_mapping are stored in variables ‘lat’ and ‘lon’. Such information can be useful for writing additional variables to the CF file, or to create a new file that looks similar to the one we just read.

This information is in a second return value `cf_info`:

```>>> area_def, cf_info = load_cf_area('/path/to/cf_nh10km.nc', with_cf_info=True)
```

The `cf_info` is a `dict()` holding additional information about the way the grid_mapping information was coded in the CF file. It may not contain the same amount of information in all three call forms. For example, the 1st call form does not allow to find the name of the latitude or longitude variables, since the 1st call form only gives access to the grid_mapping variable and its coordinate axes.

## Converting Coordinates¶

The `AreaDefinition` have a few handy coordinate conversion methods available:

We also have two methods returning integers for array indices:

These two raise a `ValueError` if the scalar input coordinates are oustide the extent of the area.