将任意角度转换为区间 [ -pi, pi ]

Question

How to convert the value of one arbitrary angle x , in radians, from the interval ]-infinite, infinite[ to the equivalent angle in the interval [-pi, pi] ?

Examples of such a conversion, in degrees:

• 45 deg => 45 deg
• 180 deg => 180 deg
• 181 deg => -179 deg
• -200 deg => 160 deg
• 380 deg => 20 deg

Answer 1

If you have access to at least version 3.7 of Python, then the math module has a function math.remainder that does exactly what you want in a single function call. Just use math.remainder(my_angle, 2*math.pi) (or for fun, use math.tau instead of 2 * math.pi ).

Example:

>>> from math import remainder, tau
>>> math.remainder(2.7, tau)
2.7
>>> math.remainder(3.7, tau)  # note wraparound to 3.7 - 2*pi
-2.583185307179586
>>> math.remainder(1000.0, tau)
0.9735361584457891

Answer 2

One possible way:

import numpy as np

np.arctan2(np.sin(x), np.cos(x))  # converts x to [-np.pi, np.pi]

...and:

np.arctan2(np.sin(x), np.cos(x)) + np.pi  # converts x to [0, 2*np.pi]