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# Working with Angles

The angular components of the various coordinate objects are represented by objects of the |Angle| class. While most likely to be encountered in the context of coordinate objects, |Angle| objects can also be used on their own wherever a representation of an angle is needed.

## Creation

The creation of an |Angle| object is quite flexible and supports a wide variety of input object types and formats. The type of the input angle(s) can be array, scalar, tuple, string, `Quantity` or another |Angle|. This is best illustrated with a number of examples of valid ways to create an |Angle|.

### Examples

There are a number of ways to create an |Angle|:

    >>> import numpy as np
    >>> from astropy import units as u
    >>> from astropy.coordinates import Angle

    >>> Angle('10.2345d')              # String with 'd' abbreviation for degrees
    <Angle 10.2345 deg>
    >>> Angle(['10.2345d', '-20d'])    # Array of strings
    <Angle [ 10.2345, -20.    ] deg>
    >>> Angle('1:2:30.43 degrees')     # Sexagesimal degrees
    <Angle 1.04178611 deg>
    >>> Angle('1 2 0 hours')           # Sexagesimal hours
    <Angle 1.03333333 hourangle>
    >>> Angle(np.arange(1., 8.), unit=u.deg)  # Numpy array from 1..7 in degrees
    <Angle [1., 2., 3., 4., 5., 6., 7.] deg>
    >>> Angle('1°2′3″')               # Unicode degree, arcmin and arcsec symbols
    <Angle 1.03416667 deg>
    >>> Angle('1°2′3″N')               # Unicode degree, arcmin, arcsec symbols and direction
    <Angle 1.03416667 deg>
    >>> Angle('1d2m3.4s')              # Degree, arcmin, arcsec.
    <Angle 1.03427778 deg>
    >>> Angle('1d2m3.4sS')              # Degree, arcmin, arcsec, direction.
    <Angle -1.03427778 deg>
    >>> Angle('-1h2m3s')               # Hour, minute, second
    <Angle -1.03416667 hourangle>
    >>> Angle('-1h2m3sW')               # Hour, minute, second, direction
    <Angle 1.03416667 hourangle>
    >>> Angle(10.2345 * u.deg)         # From a Quantity object in degrees
    <Angle 10.2345 deg>
    >>> Angle(Angle(10.2345 * u.deg))  # From another Angle object
    <Angle 10.2345 deg>

## Representation

The |Angle| object also supports a variety of ways of representing the value of the angle, both as a floating point number and as a string.

### Examples

There are many ways to represent the value of an |Angle|:

    >>> a = Angle(1, u.radian)
    >>> a
    <Angle 1. rad>
    >>> a.radian
    np.float64(1.0)
    >>> a.degree
    np.float64(57.29577951308232)
    >>> a.hour
    np.float64(3.8197186342054885)
    >>> a.hms
    hms_tuple(h=np.float64(3.0), m=np.float64(49.0), s=np.float64(10.987083139758766))
    >>> a.dms
    dms_tuple(d=np.float64(57.0), m=np.float64(17.0), s=np.float64(44.806247096362313))
    >>> a.signed_dms
    signed_dms_tuple(sign=np.float64(1.0), d=np.float64(57.0), m=np.float64(17.0), s=np.float64(44.806247096362313))
    >>> (-a).dms
    dms_tuple(d=np.float64(-57.0), m=np.float64(-17.0), s=np.float64(-44.806247096362313))
    >>> (-a).signed_dms
    signed_dms_tuple(sign=np.float64(-1.0), d=np.float64(57.0), m=np.float64(17.0), s=np.float64(44.806247096362313))
    >>> a.arcminute
    np.float64(3437.7467707849396)
    >>> f"{a}"
    '1.0 rad'
    >>> f"{a:latex}"
    np.str_('$1\\;\\mathrm{rad}$')
    >>> f"{a.to(u.deg):latex}"
    np.str_('$57^\\circ17{}^\\prime44.8062471{}^{\\prime\\prime}$')
    >>> a.to_string()
    np.str_('1 rad')
    >>> a.to_string(unit=u.degree)
    np.str_('57d17m44.8062471s')
    >>> a.to_string(unit=u.degree, sep=':')
    np.str_('57:17:44.8062471')
    >>> a.to_string(unit=u.degree, sep=('deg', 'm', 's'))
    np.str_('57deg17m44.8062471s')
    >>> a.to_string(unit=u.hour)
    np.str_('3h49m10.98708314s')
    >>> a.to_string(unit=u.hour, decimal=True)
    np.str_('3.81972')

## Usage

Angles will also behave correctly for appropriate arithmetic operations.

### Example

To use |Angle| objects in arithmetic operations:

    >>> a = Angle(1.0, u.radian)
    >>> a + 0.5 * u.radian + 2 * a
    <Angle 3.5 rad>
    >>> np.sin(a / 2)
    <Quantity 0.47942554>
    >>> a == a
    array(True, dtype=bool)
    >>> a == (a + a)
    array(False, dtype=bool)

|Angle| objects can also be used for creating coordinate objects.

### Example

To create a coordinate object using an |Angle|:

    >>> from astropy.coordinates import ICRS
    >>> ICRS(Angle(1, u.deg), Angle(0.5, u.deg))
    <ICRS Coordinate: (ra, dec) in deg
        (1., 0.5)>

## Wrapping and Bounds

There are two utility methods for working with angles that should have bounds. The `wrap_at()` method allows taking an angle or angles and wrapping to be within a single 360 degree slice. The `is_within_bounds()` method returns a boolean indicating whether an angle or angles is within the specified bounds.

Note

While creating |Angle| instances from arrays with integral data types is technically possible (for example with `dtype=int`), it is very limited in functionality and in particular wrapping is not supported for such objects.

## Longitude and Latitude Objects

|Longitude| and |Latitude| are two specialized subclasses of the |Angle| class that are used for all of the spherical coordinate classes. |Longitude| is used to represent values like right ascension, Galactic longitude, and azimuth (for Equatorial, Galactic, and Alt-Az coordinates, respectively). |Latitude| is used for declination, Galactic latitude, and elevation.

### Longitude

A |Longitude| object is distinguished from a pure |Angle| by virtue of a `wrap_angle` property. The `wrap_angle` specifies that all angle values represented by the object will be in the range:

    wrap_angle - 360 * u.deg <= angle(s) < wrap_angle

The default `wrap_angle` is 360 deg. Setting `'wrap_angle=180 * u.deg'` would instead result in values between -180 and +180 deg. Setting the `wrap_angle` attribute of an existing `Longitude` object will result in re-wrapping the angle values in-place. For example:

    >>> from astropy.coordinates import Longitude
    >>> a = Longitude([-20, 150, 350, 360] * u.deg)
    >>> a.degree
    array([340., 150., 350.,   0.])
    >>> a.wrap_angle = 180 * u.deg
    >>> a.degree
    array([-20., 150., -10.,   0.])

### Latitude

A Latitude object is distinguished from a pure |Angle| by virtue of being bounded so that:

    -90.0 * u.deg <= angle(s) <= +90.0 * u.deg

Any attempt to set a value outside of that range will result in a `ValueError`.

## Generating Angle Values

Astropy provides utility functions for generating angular or spherical positions, either with random sampling or with a grid of values. These functions all return `BaseRepresentation` subclass instances, which can be passed directly into coordinate frame classes or |SkyCoord| to create random or gridded coordinate objects.

### With Random Sampling

These functions both use standard, random spherical point picking to generate angular positions that are uniformly distributed on the surface of the unit sphere. To retrieve angular values only, use `uniform_spherical_random_surface`. For example, to generate 4 random angular positions:

    >>> from astropy.coordinates import uniform_spherical_random_surface
    >>> pts = uniform_spherical_random_surface(size=4)
    >>> pts
    <UnitSphericalRepresentation (lon, lat) in rad
        [(0.52561028, 0.38712031), (0.29900285, 0.52776066),
         (0.98199282, 0.34247723), (2.15260367, 1.01499232)]>

To generate three-dimensional positions uniformly within a spherical volume set by a maximum radius, instead use the `uniform_spherical_random_volume` function. For example, to generate 4 random 3D positions:

    >>> from astropy.coordinates import uniform_spherical_random_volume
    >>> pts_3d = uniform_spherical_random_volume(size=4)
    >>> pts_3d
    <SphericalRepresentation (lon, lat, distance) in (rad, rad, )
        [(4.98504602, -0.74247419, 0.39752416),
         (5.53281607,  0.89425191, 0.7391255 ),
         (0.88100456,  0.21080555, 0.5531785 ),
         (6.00879324,  0.61547168, 0.61746148)]>

By default, the distance values returned are uniformly distributed within the unit sphere (i.e., the distance values are dimensionless). To instead generate random points within a sphere of a given dimensional radius, for example, 1 parsec, pass in a |Quantity| object with the `max_radius` argument:

    >>> import astropy.units as u
    >>> pts_3d = uniform_spherical_random_volume(size=4, max_radius=2*u.pc)
    >>> pts_3d
    <SphericalRepresentation (lon, lat, distance) in (rad, rad, pc)
        [(3.36590297, -0.23085809, 1.47210093),
         (6.14591179,  0.06840621, 0.9325143 ),
         (2.19194797,  0.55099774, 1.19294064),
         (5.25689272, -1.17703409, 1.63773358)]>

### On a Grid

No grid or lattice of points on the sphere can produce equal spacing between all grid points, but many approximate algorithms exist for generating angular grids with nearly even spacing (for example, see this page).

One simple and popular method in this context is the golden spiral method, which is available in `astropy.coordinates` through the utility function `golden_spiral_grid`. This function accepts a single argument, `size`, which specifies the number of points to generate in the grid:

    >>> from astropy.coordinates import golden_spiral_grid
    >>> golden_pts = golden_spiral_grid(size=32)
    >>> golden_pts
    <UnitSphericalRepresentation (lon, lat) in rad
        [(1.94161104,  1.32014066), (5.82483312,  1.1343273 ),
         (3.42486989,  1.004232  ), (1.02490666,  0.89666582),
         (4.90812873,  0.80200278), (2.5081655 ,  0.71583806),
         (0.10820227,  0.63571129), (3.99142435,  0.56007531),
         (1.59146112,  0.48787515), (5.4746832 ,  0.41834639),
         (3.07471997,  0.35090734), (0.67475674,  0.28509644),
         (4.55797882,  0.22053326), (2.15801559,  0.15689287),
         (6.04123767,  0.09388788), (3.64127444,  0.03125509),
         (1.24131121, -0.03125509), (5.12453328, -0.09388788),
         (2.72457005, -0.15689287), (0.32460682, -0.22053326),
         (4.2078289 , -0.28509644), (1.80786567, -0.35090734),
         (5.69108775, -0.41834639), (3.29112452, -0.48787515),
         (0.89116129, -0.56007531), (4.77438337, -0.63571129),
         (2.37442014, -0.71583806), (6.25764222, -0.80200278),
         (3.85767899, -0.89666582), (1.45771576, -1.004232  ),
         (5.34093783, -1.1343273 ), (2.9409746 , -1.32014066)]>

### Comparing Spherical Point Generation Methods

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