angles 2.0

Angles模块定义了多个类，用于表示角度和球面上的位置。它还包括几个函数，用于执行对角度的常见操作，例如单位转换、归一化、创建字符串表示等。

SIMBAD报告M100的位置为“12 22 54.899 +15 49 20.57”。我们可以轻松地将这些坐标解析如下

>>> 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