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# angles 1.1

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## Classes for representing angles, and positions on a unit sphere

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

Examples

Some examples are given below. For more information see http://oneau.wordpress.com/angles/.

Unit conversion:

>>> import math
>>> angles.r2d(math.pi)
180.0
>>> angles.r2arcs(math.pi)
648000.0
>>> angles.h2r(12.0)
3.1415926535897931
>>> angles.h2d(12.0)
180.0
>>> angles.d2arcs(1.0)
3600.0

Normalizing angles:

>>> normalize(-270,-180,180)
90.0
>>> import math
>>> math.degrees(normalize(-2*math.pi,-math.pi,math.pi))
0.0
>>> 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

Sexagesimal representation:

>>> x = 23+59/60.0+59.99999/3600.0
>>> deci2sexa(x, pre=3, lower=0, upper=24, upper_trim=True)
(1, 0, 0, 0.0)
>>> deci2sexa(x, pre=3, lower=0, upper=24, upper_trim=False)
(1, 24, 0, 0.0)
>>> deci2sexa(x, pre=5, lower=0, upper=24, upper_trim=True)
(1, 23, 59, 59.99999)

Formatting angles:

>>> 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 '

Parsing sexagesimal strings:

>>> phmsdms("12d14.56ss")

{'parts': [12.0, None, 14.56],
'sign': 1,
'units': 'degrees',
'vals': [12.0, 0.0, 14.56]}
>>> phmsdms("14.56ss")

{'parts': [None, None, 14.56],
'sign': 1,
'units': 'degrees',
'vals': [0.0, 0.0, 14.56]}

>>> phmsdms("12h13m12.4s")

{'parts': [12.0, 13.0, 12.4],
'sign': 1,
'units': 'hours',
'vals': [12.0, 13.0, 12.4]}

Separation angle along a great circle, using vectors:

>>> 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

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

Bearing between two points, using vectors:

>>> angles.bear(0, 0, 0, -angles.d2r(90.0))
3.141592653589793
>>> angles.bear(0, -angles.d2r(90.0), 0, 0)
0.0
>>> angles.bear(0, -angles.d2r(45.0), 0, 0)
0.0
>>> angles.bear(0, -angles.d2r(89.678), 0, 0)
0.0

>>> r2d(bear(angles.d2r(45.0), angles.d2r(45.0),
angles.d2r(60.0), angles.d2r(45.0)))
84.68152816060062

Angle class:

>>> a = Angle(sg="12h34m16.592849219")
>>> print a.r, a.d, a.h, a.arcs
3.29115230606 188.569136872 12.5712757914 678848.892738
>>> print a.ounit
hours
>>> print a
+12 34 16.593
>>> print 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 08.8927
>>> a.ounit = "radians"
>>> print a
3.29115230606

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

Class for longitudinal angles:

>>> 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.hms
(1, 12, 0, 0.0)
>>> a = AlphaAngle(h=12.54678345)
>>> a.hms
(1, 12, 32, 48.42)
>>> a.sign, a.hh, a.mm, a.ss
(1, 12, 32, 48.42)
>>> print a
+12HH 32MM 48.420SS
>>> a.pre = 5
>>> a.hms
(1, 12, 32, 48.42042)
>>> print a
+12HH 32MM 48.42042SS

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

Class for latitudinal angles:

>>> a = DeltaAngle(d=-45.0)
>>> print a
-45DD 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
>>> print a.r, a.d, a.h, a.arcs
0.216198782581 12.3872777778 0.825818518519 44594.2

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

>>> a.dd = 89
>>> a.mm = 59
>>> a.ss = 59.9999
>>> print a
+90DD 00MM 00.000SS
>>> a.pre = 5
>>> print a
+89DD 59MM 59.99990SS
>>> a.dd = 89
>>> a.mm = 60
>>> a.ss = 60
>>> print a
+89DD 59MM 00.000SS

Class for points on a unit sphere:

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

>>> pos2.delta.d = -90
>>> angles.r2d(pos1.bear(pos2))
0.0
>>> angles.r2d(pos1.sep(pos2))
180.0

Installation

Use pip or easy_install:

pip install angles

or,

easy_install angles

Details

This module provides three classes for representing angles: Angle, AlphaAngle and DeltaAngle, and one class for representing a point on a unit sphere, AngularPosition.

Angle is for representing generic angles. AlphaAngle is for representing longitudinal angles such as geographic longitude, right ascension and others. DeltaAngle is for representing latitudinal angles such as geographic latitude, declination and others.

An angle object can be initialized with value in various units, it can normalize its value into an appropriate range. The value can be retrieved in various units, using appropriately named attributes.

Sexagesimal representation of an angle can be obtained through appropriate attributes of the angle object. The number of decimal places in the final part of a sexagesimal representation, and whether rounding or truncation is used to produce these many decimal places, can be customized.

An angle object can provide string representation of itself. The delimiters used in the string representation can be customized. The string representation is based on the sexagesimal value and hence it also reflects the precision and truncation settings.

The AngularPosition class can be used for representing points on a sphere. It uses an AlphaAngle instance for storing the longitudinal angle, and a DeltaAngle instance for storing the latitudinal angle. It can calcuate the separation and bearing, also called position angle, to another point on the sphere. The results for separation and bearing agree with those from the SLALIB (pyslalib) library (see the function _test_with_slalib()).

The separation and bearing calculations do not use spherical trignometry. They involve Cartesian vectors, and objects of the class CartesianVector are used for these calculations.

Almost all the methods of the classes call functions for performing calculations. If needed these functions can be used directly.

Functions include those for converting angles between different units, parsing sexagesimal strings, creating string representations of angles, converting angles between various units, normalizing angles into a given range, finding separation and bearing bewteen two points and others. Normalization of angles can be performed in two different ways. One method normalizes angles in the manner that longitudinal angles are normalized i.e., [0, 360.0) or [0, 2π) or [0, 24.0). The other method normalizes angles in the manner that latitudinal angles are normalized i.e., [-90, 90] or [-π/2, π/2].

See docstrings of classes and functions for documentation and examples. Also see http://oneau.wordpress.com/angles/.

Requirements:

### TAGS:

unit sphere | sphere angles | sphere position | unit | sphere | position

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