| .. 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`. |
|
|
