Python单元测试：测试两个角度是否几乎相等

Question

I want to test a function that outputs a heading in degrees, which is a number in the interval [0, 360). Since the result is a floating-point number, comparing the actual result against the expected with unittest.assertEqual() does not work. unittest.assertAlmostEqual() is better since it provides a tolerance. This approach works for heading that are not close to 0 degrees.

Question: What is the correct way to test for headings whose expected value is 0 degrees? assertAlmostEquals() would only include angles that are slightly larger than 0 degrees, but would miss those that are slightly smaller than 0, ie 360 degrees...

Answer 1

You can use the squared Euclidian distance between two points on the unit circle and the law of cosines to get the absolute difference between two angles:

from math import sin, cos, acos
from unittest import assertAlmostEqual        

def assertAlmostEqualAngles(x, y, **kwargs):
    c2 = (sin(x)-sin(y))**2 + (cos(x)-cos(y))**2
    angle_diff = acos((2.0 - c2)/2.0) # a = b = 1
    assertAlmostEqual(angle_diff, 0.0, **kwargs)

This works with radians. If the angle is in degrees, you must do a conversion:

from math import sin, cos, acos, radians, degrees
from unittest import assertAlmostEqual        

def assertAlmostEqualAngles(x, y, **kwargs):
    x,y = radians(x),radians(y)
    c2 = (sin(x)-sin(y))**2 + (cos(x)-cos(y))**2
    angle_diff = degrees(acos((2.0 - c2)/2.0))
    assertAlmostEqual(angle_diff, 0.0, **kwargs)

Answer 2

I encountered the same situation, and found a much, much simpler solution, by taking advantage of modulo computation:

In [20]: def d(a, b):
    ...:     c = (b - a) % 360
    ...:     if c > 180:
    ...:         c -= 360
    ...:     return c
    ...:

In [21]: d(1, 3)
Out[21]: 2

In [22]: d(1, 358)
Out[22]: -3