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Functions for working with angles
import math
def average_angles(angles):
"""Average (mean) of angles
Return the average of an input sequence of angles. The result is between
``0`` and ``2 * math.pi``.
If the average is not defined (e.g. ``average_angles([0, math.pi]))``,
a ``ValueError`` is raised.
"""
x = sum(math.cos(a) for a in angles)
y = sum(math.sin(a) for a in angles)
if x == 0 and y == 0:
raise ValueError(
"The angle average of the inputs is undefined: %r" % angles)
# To get outputs from -pi to +pi, delete everything but math.atan2() here.
return math.fmod(math.atan2(y, x) + 2 * math.pi, 2 * math.pi)
def subtract_angles(lhs, rhs):
"""Return the signed difference between angles lhs and rhs
Return ``(lhs - rhs)``, the value will be within ``[-math.pi, math.pi)``.
Both ``lhs`` and ``rhs`` may either be zero-based (within
``[0, 2*math.pi]``), or ``-pi``-based (within ``[-math.pi, math.pi]``).
"""
return math.fmod((lhs - rhs) + math.pi * 3, 2 * math.pi) - math.pi
def is_close(lhs, rhs):
return abs(lhs - rhs) < 1E-5
def test_average_angles():
assert is_close(average_angles([-math.pi/4, +math.pi/4]), 0)
assert is_close(average_angles([-math.pi/4, +math.pi*3/8]), math.pi/16)
assert is_close(average_angles([-math.pi*3/8, +math.pi/4]), math.pi*31/16)
assert is_close(average_angles([math.pi*7/4, +math.pi/4]), 0)
assert is_close(average_angles([math.pi*7/4, +math.pi*3/8]), math.pi/16)
assert is_close(average_angles([math.pi*13/8, +math.pi/4]), math.pi*31/16)
def test_subtract_angles():
assert is_close(subtract_angles(0, math.pi/2), -math.pi/2)
assert is_close(subtract_angles(math.pi/2, 0), +math.pi/2)
assert is_close(subtract_angles(0, math.pi*3/2), +math.pi/2)
assert is_close(subtract_angles(math.pi*3/2, 0), -math.pi/2)
assert is_close(subtract_angles(math.pi, math.pi/8), +math.pi * 7/8)
assert is_close(subtract_angles(math.pi, math.pi*15/8), -math.pi * 7/8)
assert is_close(subtract_angles(math.pi*9/8, math.pi/8), -math.pi)
assert is_close(subtract_angles(math.pi*9/8, math.pi*15/8), -math.pi * 6/8)
def test_subtract_angles_bradphelan():
# Cf. https://gist.github.com/bradphelan/7fe21ad8ebfcb43696b8
assert is_close(subtract_angles(0.1, 0.2), -0.1)
assert is_close(subtract_angles(0.1, 0.2+math.pi*2), -0.1)
assert is_close(subtract_angles(0.1, 0.2-math.pi*2), -0.1)
assert is_close(subtract_angles(0.1+math.pi*2, 0.2), -0.1)
assert is_close(subtract_angles(0.1-math.pi*2, 0.2), -0.1)
assert is_close(subtract_angles(0.2, 0.1), 0.1)
assert is_close(subtract_angles(0.2, 0.1-math.pi*2), 0.1)
assert is_close(subtract_angles(0.2, 0.1+math.pi*2), 0.1)
assert is_close(subtract_angles(0.2+math.pi*2, 0.1), 0.1)
assert is_close(subtract_angles(0.2-math.pi*2, 0.1), 0.1)
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