testbed/astropy__astropy/docs/coordinates/angles.rst

.. include:: references.txt

.. _working_with_angles:

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.

.. _angle-creation:

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, `~astropy.units.Quantity` or another
|Angle|. This is best illustrated with a number of examples of valid 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  # doctest: +FLOAT_CMP
    <Angle 10.2345 deg>
    >>> Angle(['10.2345d', '-20d'])    # Array of strings  # doctest: +FLOAT_CMP
    <Angle [ 10.2345, -20.    ] deg>
    >>> Angle('1:2:30.43 degrees')     # Sexagesimal degrees  # doctest: +FLOAT_CMP
    <Angle 1.04178611 deg>
    >>> Angle('1 2 0 hours')           # Sexagesimal hours  # doctest: +FLOAT_CMP
    <Angle 1.03333333 hourangle>
    >>> Angle(np.arange(1., 8.), unit=u.deg)  # Numpy array from 1..7 in degrees  # doctest: +FLOAT_CMP
    <Angle [1., 2., 3., 4., 5., 6., 7.] deg>
    >>> Angle('1°2′3″')               # Unicode degree, arcmin and arcsec symbols  # doctest: +FLOAT_CMP
    <Angle 1.03416667 deg>
    >>> Angle('1d2m3.4s')              # Degree, arcmin, arcsec.  # doctest: +FLOAT_CMP
    <Angle 1.03427778 deg>
    >>> Angle('-1h2m3s')               # Hour, minute, second  # doctest: +FLOAT_CMP
    <Angle -1.03416667 hourangle>
    >>> Angle((-1, 2, 3), unit=u.deg)  # (degree, arcmin, arcsec)  # doctest: +FLOAT_CMP
    <Angle -1.03416667 deg>
    >>> Angle(10.2345 * u.deg)         # From a Quantity object in degrees  # doctest: +FLOAT_CMP
    <Angle 10.2345 deg>
    >>> Angle(Angle(10.2345 * u.deg))  # From another Angle object  # doctest: +FLOAT_CMP
    <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::

    >>> a = Angle(1, u.radian)
    >>> a  # doctest: +FLOAT_CMP
    <Angle 1. rad>
    >>> a.radian
    1.0
    >>> a.degree  # doctest: +FLOAT_CMP
    57.29577951308232
    >>> a.hour  # doctest: +FLOAT_CMP
    3.8197186342054885
    >>> a.hms  # doctest: +FLOAT_CMP
    hms_tuple(h=3.0, m=49.0, s=10.987083139758766)
    >>> a.dms  # doctest: +FLOAT_CMP
    dms_tuple(d=57.0, m=17.0, s=44.806247096362313)
    >>> a.signed_dms  # doctest: +FLOAT_CMP
    signed_dms_tuple(sign=1.0, d=57.0, m=17.0, s=44.806247096362313)
    >>> (-a).dms  # doctest: +FLOAT_CMP
    dms_tuple(d=-57.0, m=-17.0, s=-44.806247096362313)
    >>> (-a).signed_dms  # doctest: +FLOAT_CMP
    signed_dms_tuple(sign=-1.0, d=57.0, m=17.0, s=44.806247096362313)
    >>> a.arcminute  # doctest: +FLOAT_CMP
    3437.7467707849396
    >>> a.to_string()
    '1rad'
    >>> a.to_string(unit=u.degree)
    '57d17m44.8062s'
    >>> a.to_string(unit=u.degree, sep=':')
    '57:17:44.8062'
    >>> a.to_string(unit=u.degree, sep=('deg', 'm', 's'))
    '57deg17m44.8062s'
    >>> a.to_string(unit=u.hour)
    '3h49m10.9871s'
    >>> a.to_string(unit=u.hour, decimal=True)
    '3.81972'


Usage
=====

Angles will also behave correctly for appropriate arithmetic operations::

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

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

    >>> from astropy.coordinates import ICRS
    >>> ICRS(Angle(1, u.deg), Angle(0.5, u.deg))  # doctest: +FLOAT_CMP
    <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 :meth:`~astropy.coordinates.Angle.wrap_at` method allows taking an angle or
angles and wrapping to be within a single 360 degree slice. The
:meth:`~astropy.coordinates.Angle.is_within_bounds` method returns a
boolean indicating whether an angle or angles is within the specified bounds.


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  # doctest: +FLOAT_CMP
    array([340., 150., 350.,   0.])
    >>> a.wrap_angle = 180 * u.deg
    >>> a.degree  # doctest: +FLOAT_CMP
    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`.