angles 2.0

The Angles module defines several classes for representing angles, and positions on a sphere. It also has several functions for performing common operations on angles, such as unit conversion, normalization, creating string representations and others.

The position of M100 reported by SIMBAD is “12 22 54.899 +15 49 20.57”. We can easily parse these coordinates as follows:

>>> from __future__ import print_function
>>> from angles import AngularPosition

>>> a = AngularPosition.from_hd("12 22 54.899 +15 49 20.57")
>>> a.alpha
3.24157813039
>>> a.delta
0.276152636198

>>> print(a.alpha)
+12HH 22MM 54.899SS
>>> print(a.delta)
+15DD 49MM 20.570SS

>>> a.alpha.hms.hms
(1, 12, 22, 54.899)
>>> a.delta.dms.dms
(1, 15, 49, 20.57)
>>> a.alpha.dms.dms
(1, 185, 43, 43.485)
>>> a.delta.hms.hms
(1, 1, 3, 17.371)

>>> a.alpha.r, a.alpha.d, a.alpha.h, a.alpha.arcs
(3.2415781303913653, 185.72874583333328, 12.381916388888886, 668623.4849999998)
>>> a.delta.r, a.delta.d, a.delta.h, a.delta.arcs
(0.27615263619797403, 15.822380555555556, 1.0548253703703705, 56960.57)

$ pip install angles

$ easy_install angles

>>> import math
>>> from angles import r2d, r2arcs, h2r, h2d, d2arcs

>>> r2d(math.pi)
180.0
>>> r2arcs(math.pi)
648000.0
>>> h2r(12.0)
3.141592653589793
>>> h2d(12.0)
180.0
>>> d2arcs(1.0)
3600.0

>>> from angles import normalize

>>> normalize(-180, -180, 180)
-180.0
>>> normalize(180, -180, 180)
-180.0
>>> normalize(180, -180, 180, b=True)
180.0
>>> normalize(181,-180,180)
-179.0
>>> normalize(181, -180, 180, b=True)
179.0
>>> normalize(-180,0,360)
180.0
>>> normalize(36,0,24)
12.0
>>> normalize(368.5,-180,180)
8.5
>>> normalize(-100, -90, 90)
80.0
>>> normalize(-100, -90, 90, b=True)
-80.0
>>> normalize(100, -90, 90, b=True)
80.0
>>> normalize(181, -90, 90, b=True)
-1.0
>>> normalize(270, -90, 90, b=True)
-90.0
>>> normalize(271, -90, 90, b=True)
-89.0

>>> from angles import normalize_sphere

>>> normalize_sphere(180, 91)
(0.0, 89.0000000000001)

>>> normalize_sphere(180, -91)
(0.0, -89.0000000000001)

>>> normalize_sphere(0, 91)
(180.0, 89.0000000000001)

>>> normalize_sphere(0, -91)
(180.0, -89.0000000000001)

>>> normalize_sphere(120, 280)
(119.99999999999999, -80.00000000000003)

>>> normalize_sphere(375, 45)  # 25 hours ,45 degrees
(14.999999999999966, 44.99999999999999)

>>> normalize_sphere(-375, -45)
(345.00000000000006, -44.99999999999999)

>>> from angles import deci2sexa

>>> deci2sexa(-11.2345678)
(-1, 11, 14, 4.444)
>>> deci2sexa(-11.2345678, pre=5)
(-1, 11, 14, 4.44408)
>>> deci2sexa(-11.2345678, pre=4)
(-1, 11, 14, 4.4441)
>>> deci2sexa(-11.2345678, pre=4, trunc=True)
(-1, 11, 14, 4.444)

>>> deci2sexa(-11.2345678, pre=1)
(-1, 11, 14, 4.4)
>>> deci2sexa(-11.2345678, pre=0)
(-1, 11, 14, 4.0)
>>> deci2sexa(-11.2345678, pre=-1)
(-1, 11, 14, 0.0)

>>> x = 23+59/60.0+59.99999/3600.0

>>> deci2sexa(x, pre=3, lower=0, upper=24)
(1, 24, 0, 0.0)
>>> deci2sexa(x, pre=3, lower=0, upper=24, upper_trim=True)
(1, 0, 0, 0.0)

>>> deci2sexa(x, pre=5, lower=0, upper=24, upper_trim=True)
(1, 23, 59, 59.99999)

>>> from angles import fmt_angle

>>> fmt_angle(12.348978659, pre=4, trunc=True)
'+12 20 56.3231'
>>> fmt_angle(12.348978659, pre=5)
'+12 20 56.32317'
>>> fmt_angle(12.348978659, s1='HH ', s2='MM ', s3='SS', pre=5)
'+12HH 20MM 56.32317SS'

>>> x = 23+59/60.0+59.99999/3600.0
>>> fmt_angle(x)
'+24 00 00.000'
>>> fmt_angle(x, lower=0, upper=24, upper_trim=True)
'+00 00 00.000'
>>> fmt_angle(x, pre=5)
'+23 59 59.99999'
>>> fmt_angle(-x, lower=0, upper=24, upper_trim=True)
'+00 00 00.000'
>>> fmt_angle(-x)
'-24 00 00.000'

>>> from angles import phmsdms

>>> phmsdms("12") == {
... 'parts': [12.0, None, None],
... 'sign': 1,
... 'units': 'degrees',
... 'vals': [12.0, 0.0, 0.0]
... }
True

>>> phmsdms("12h") == {
... 'parts': [12.0, None, None],
... 'sign': 1,
... 'units': 'hours',
... 'vals': [12.0, 0.0, 0.0]
... }
True

>>> phmsdms("12d13m14.56") == {
... 'parts': [12.0, 13.0, 14.56],
... 'sign': 1,
... 'units': 'degrees',
... 'vals': [12.0, 13.0, 14.56]
... }
True

>>> phmsdms("12d14.56ss") == {
... 'parts': [12.0, None, 14.56],
... 'sign': 1,
... 'units': 'degrees',
... 'vals': [12.0, 0.0, 14.56]
... }
True

>>> phmsdms("14.56ss") == {
... 'parts': [None, None, 14.56],
... 'sign': 1,
... 'units': 'degrees',
... 'vals': [0.0, 0.0, 14.56]
... }
True

>>> phmsdms("12h13m12.4s") == {
... 'parts': [12.0, 13.0, 12.4],
... 'sign': 1,
... 'units': 'hours',
... 'vals': [12.0, 13.0, 12.4]
... }
True

>>> phmsdms("12:13:12.4s") == {
... 'parts': [12.0, 13.0, 12.4],
... 'sign': 1,
... 'units': 'degrees',
...  'vals': [12.0, 13.0, 12.4]
... }
True

>>> from angles import pposition

>>> ra, de = pposition("12 22 54.899 +15 49 20.57")
>>> ra
12.38191638888889
>>> de
15.822380555555556

>>> pposition("12 22 54.899 +15 49 20.57", details=True)  # doctest: +SKIP
{'y': 15.822380555555556,
 'x': 12.38191638888889,
 'numvals': 6,
 'raw_x': {
    'vals': [12.0, 22.0, 54.899],
    'units': 'degrees',
    'parts': [12.0, 22.0, 54.899],
    'sign': 1
  },
 'raw_y': {
    'vals': [15.0, 49.0, 20.57],
    'units': 'degrees',
    'parts': [15.0, 49.0, 20.57],
    'sign': 1
  }
}

>>> from angles import r2d, d2r, sep

>>> r2d(sep(0, 0, 0, d2r(90.0)))
90.0
>>> r2d(sep(0, d2r(45.0), 0, d2r(90.0)))
45.00000000000001
>>> r2d(sep(0, d2r(-45.0), 0, d2r(90.0)))
135.0

>>> r2d(sep(0, d2r(-90.0), 0, d2r(90.0)))
180.0
>>> r2d(sep(d2r(45.0), d2r(-90.0), d2r(45.0), d2r(90.0)))
180.0
>>> r2d(sep(0, 0, d2r(90.0), 0))
90.0

>>> r2d(sep(0, d2r(45.0), d2r(90.0), d2r(45.0)))
60.00000000000001
>>> import math
>>> 90.0 * math.cos(d2r(45.0))  # Distance along latitude circle.
63.63961030678928

>>> from angles import bear, r2d, d2r
>>> bear(0, 0, 0, -d2r(90.0))
3.141592653589793
>>> bear(0, -d2r(90.0), 0, 0)
0.0
>>> bear(0, -d2r(45.0), 0, 0)
0.0
>>> bear(0, -d2r(89.678), 0, 0)
0.0

>>> r2d(bear(d2r(45.0), d2r(45.0), d2r(46.0), d2r(45.0)))
89.64644212193384

>>> r2d(bear(d2r(45.0), d2r(45.0), d2r(44.0), d2r(45.0)))
-89.64644212193421

>>> from __future__ import print_function
>>> from angles import Angle

>>> a = Angle(sg="12h34m16.592849219")
>>> a.r, a.d, a.h, a.arcs  # doctest: +NORMALIZE_WHITESPACE
(3.291152306055805, 188.56913687174583, 12.571275791449722, 678848.892738285)

>>> a.hms.sign, a.hms.hh, a.hms.mm, a.hms.ss
(1, 12, 34, 16.593)
>>> a.hms.hms
(1, 12, 34, 16.593)
>>> a.h
12.571275791449722

>>> a.dms.sign, a.dms.dd, a.dms.mm, a.dms.ss
(1, 188, 34, 8.893)
>>> a.dms.dms
(1, 188, 34, 8.893)
>>> a.d
188.56913687174583

>>> print(a.ounit)
hours
>>> print(a)
+12 34 16.593
>>> a.pre, a.trunc
(3, False)
>>> a.pre = 4
>>> print(a)
+12 34 16.5928
>>> a.pre = 3
>>> a.trunc = True
>>> print(a)
+12 34 16.592

>>> a.ounit = "degrees"
>>> print(a)
+188 34 08.892
>>> a.ounit = "radians"
>>> print(a)  # doctest: +SKIP
3.29115230606

>>> a.ounit = "degrees"
>>> a.s1 = "DD "
>>> a.s2 = "MM "
>>> a.s3 = "SS"
>>> print(a)
+188DD 34MM 08.892SS

>>> a = Angle(r=10)
>>> a.d, a.h, a.r, a.arcs, a.ounit  # doctest: +NORMALIZE_WHITESPACE
(572.9577951308232, 38.197186342054884, 10, 2062648.0624709637, 'radians')

>>> a.d = 10
>>> a.d, a.h, a.r, a.arcs, a.ounit  # doctest: +NORMALIZE_WHITESPACE
(10.0, 0.6666666666666666, 0.17453292519943295, 36000.0, 'radians')

>>> a.dms.mm = 60
>>> a.d, a.h, a.r, a.arcs, a.ounit  # doctest: +NORMALIZE_WHITESPACE
(11.0, 0.7333333333333333, 0.19198621771937624, 39600.0, 'radians')

>>> a.dms.dms = (1, 12, 10, 5.234)
>>> a.d, a.h, a.r, a.arcs, a.ounit  # doctest: +NORMALIZE_WHITESPACE
(12.168120555555557, 0.8112080370370371, 0.21237376747404604,
43805.234000000004, 'radians')

>>> a.hms.hms = (1, 1, 1, 1)
>>> a.d, a.h, a.r, a.arcs, a.ounit  # doctest: +NORMALIZE_WHITESPACE
(15.254166666666668, 1.0169444444444444, 0.2662354329813017,
54915.00000000001, 'radians')

>>> print(a)  # doctest: +SKIP
0.266235432981
>>> a.ounit = 'hours'
>>> print(a)
+01 01 01.000
>>> a.ounit = 'degrees'
>>> print(a)
+15 15 15.000

>>> from __future__ import print_function
>>> from angles import AlphaAngle

>>> a = AlphaAngle(d=180.5)
>>> print(a)
+12HH 02MM 00.000SS
>>> a = AlphaAngle(h=12.0)
>>> print(a)
+12HH 00MM 00.000SS
>>> a = AlphaAngle(h=-12.0)

>>> a = AlphaAngle("12h14m23.4s")
>>> print(a)
+12HH 14MM 23.400SS
>>> a.r, a.d, a.h, a.arcs
(3.204380873430289, 183.5975, 12.239833333333333, 660951.0)

>>> a = AlphaAngle(h=12.54678345)
>>> a.hms.hms
(1, 12, 32, 48.42)
>>> a.hms.sign, a.hms.hh, a.hms.mm, a.hms.ss
(1, 12, 32, 48.42)
>>> print(a)
+12HH 32MM 48.420SS
>>> a.pre = 5
>>> a.hms.hms
(1, 12, 32, 48.42042)
>>> print(a)
+12HH 32MM 48.42042SS

>>> a.s1 = " : "
>>> a.s2 = " : "
>>> a.s3 = ""
>>> print(a)
+12 : 32 : 48.42042

>>> a.pre = 3
>>> a.dms.dms
(1, 188, 12, 6.306)

>>> a = AlphaAngle(h=25.0)
>>> print(a)
+01HH 00MM 00.000SS
>>> a = AlphaAngle(h=-1.0)
>>> print(a)
+23HH 00MM 00.000SS

>>> a.hms.hh = 23
>>> a.hms.mm = 59
>>> a.hms.ss = 59.99999
>>> a.hms.hms
(1, 0, 0, 0.0)
>>> print(a)
+00HH 00MM 00.000SS
>>> a.pre = 5
>>> a.hms.hms
(1, 23, 59, 59.99999)
>>> print(a)
+23HH 59MM 59.99999SS

>>> from __future__ import print_function
>>> from angles import DeltaAngle

>>> a = DeltaAngle(d=-45.0)
>>> print(a)
-45DD 00MM 00.000SS
>>> a = DeltaAngle(d=180.0)
>>> print(a)
+00DD 00MM 00.000SS
>>> a = DeltaAngle(h=12.0)
>>> print(a)
+00DD 00MM 00.000SS
>>> a = DeltaAngle(sg="91d")
>>> print(a)
+89DD 00MM 00.000SS

>>> a = DeltaAngle("12d23m14.2s")
>>> print(a)
+12DD 23MM 14.200SS
>>> a.r, a.d, a.h, a.arcs
(0.2161987825813487, 12.387277777777777, 0.8258185185185185, 44594.2)

>>> a = DeltaAngle(d=12.1987546)
>>> a.dms.dms
(1, 12, 11, 55.517)
>>> a.pre = 5
>>> a.dms.dms
(1, 12, 11, 55.51656)
>>> a.dms.dd, a.dms.mm, a.dms.ss
(12, 11, 55.51656)
>>> a.pre = 0
>>> a.dms.dms
(1, 12, 11, 56.0)

>>> a = DeltaAngle(d=12.3459876)
>>> a.s1 = " : "
>>> a.s2 = " : "
>>> a.s3 = ""
>>> print(a)
+12 : 20 : 45.555

>>> a = DeltaAngle(d=-91.0)
>>> print(a)
-89DD 00MM 00.000SS
>>> a = DeltaAngle(d=91.0)
>>> print(a)
+89DD 00MM 00.000SS

>>> a.dms.sign = 1
>>> a.dms.dd = 89
>>> a.dms.mm = 59
>>> a.dms.ss = 59.9999
>>> a.pre = 3
>>> print(a)
+90DD 00MM 00.000SS
>>> a.pre = 5
>>> print(a)
+89DD 59MM 59.99990SS

>>> a.dms.dms = (1, 0, 0, 0.0)
>>> a.dms.dd = 89
>>> a.dms.mm = 60
>>> a.dms.ss = 60
>>> a.pre = 3
>>> print(a)
+89DD 59MM 00.000SS

>>> from __future__ import print_function
 >>> from angles import AngularPosition, r2d

 >>> a = AngularPosition.from_hd("12 22 54.899 +15 49 20.57")
 >>> print(a)
 +12HH 22MM 54.899SS +15DD 49MM 20.570SS
 >>> a = AngularPosition.from_hd("12dd 22 54.899 +15 49 20.57")
 >>> print(a)
 +00HH 49MM 31.660SS +15DD 49MM 20.570SS
 >>> a = AngularPosition.from_hd("12d 22 54.899 +15 49 20.57")
 >>> print(a)
 +00HH 49MM 31.660SS +15DD 49MM 20.570SS

 >>> a = AngularPosition(alpha=165, delta=-91)  # alpha should flip by 180 degrees
 >>> round(a.alpha.d , 12), round(a.delta.d, 12)
 (345.0, -89.0)

 >>> a.delta.d = -91 # alpha should now do another 180 flip and come back to 165
 >>> round(a.alpha.d, 12), round(a.delta.d, 12)
 (165.0, -89.0)

 >>> a.delta.d = 89  # there should be no change in normalized angles
 >>> round(a.alpha.d, 12), round(a.delta.d, 12)
 (165.0, 89.0)

 >>> a.alpha.d = -180  # alpha should normalize to 180 delta shouldn't change
 >>> round(a.alpha.d, 12), round(a.delta.d, 12)
 (180.0, 89.0)

 >>> pos1 = AngularPosition(alpha=12.0, delta=90.0)
 >>> pos2 = AngularPosition(alpha=12.0, delta=0.0)
 >>> r2d(pos2.bear(pos1))
 0.0
 >>> r2d(pos1.bear(pos2))
 0.0
 >>> r2d(pos1.sep(pos2))
 90.0
 >>> pos1.alpha.h = 0.0
 >>> pos2.alpha.h = 0.0
 >>> r2d(pos1.sep(pos2))
 90.0
 >>> r2d(pos2.bear(pos1))
 0.0
 >>> r2d(pos1.bear(pos2))
 0.0