计算地球上两个坐标之间的距离 [英] Calculate distance between two coordinates on a globe
问题描述
我得到两个坐标对,它们的形式为 90°0′0″ N 0°0′0″ E
作为字符串,并希望计算这些点之间的距离一个半径为R = 6371km的球体。
I get two coordinate pairs in the form 90°0′0″N 0°0′0″E
as string and want to calculate the distance between those points on a sphere with radius R=6371km.
我在互联网上发现了两个公式此处, haversine和余弦的球形定律,但它们似乎无效。对于应返回 2 * pi * R / 4
的90°角,haversine操作正确,但余弦失败并返回0。具有更多随机坐标的其他点返回false
I found two formulas on the internet here, the "haversine" and the "spherical law of cosines", but they don't seem to work. For a 90° angle which should return 2*pi*R / 4
, the haversine operates correct but the cosines fail and return 0. A different point with more random coordinates returns false values with both algorithms: the haversine is too high and the cosines are too low.
我的实现是错误的还是选择了错误的算法?
Is my implementation wrong or did I chose an incorrect algorithm?
我应该如何进行这些计算(坐标对与地球表面上的距离)?
How should I make these calculations (coordinate pairs to distance on globe surface) instead?
(是的,我知道我我还没有检查N / S和E / W,但测试的坐标都在东北半球。)
(And yes, I know that I'm not checking for N/S and E/W yet, but the tested coordinates are all in the north-eastern hemisphere.)
这是我的Python 3代码:
Here's my Python 3 code:
import math, re
R = 6371
PAT = r'(\d+)°(\d+)′(\d+)″([NSEW])'
def distance(first, second):
def coords_to_rads(s):
return [math.radians(int(d) +int(m)/60 +int(s)/3600) \
for d, m, s, nswe in re.findall(PAT, s)]
y1, x1 = coords_to_rads(first)
y2, x2 = coords_to_rads(second)
dx = x1 - x2
dy = y1 - y2
print("coord string:", first, "|", second)
print("coord radians:", y1, x1, "|", y2, x2)
print("x/y-distances:", dy, dx)
a = math.sin(dx/2)**2 + math.cos(x1) * math.cos(x2) * math.sin(dy/2)**2
c = 2 * math.atan2(math.sqrt(a), math.sqrt(1-a))
haversine = R * c
law_of_cosines = math.acos( math.sin(x1) * math.sin(x2) + \
math.cos(x1) * math.cos(x2) ) * R
print("HS:", round(haversine, 2), "LOC:", round(law_of_cosines, 2))
return haversine
#return law_of_cosines
if __name__ == '__main__':
def test(result, correct):
print("result: ", result)
print("correct:", correct)
test(distance("90°0′0″N 0°0′0″E", "0°0′0″N, 0°0′0″E"), 10007.5)
test(distance("51°28′48″N 0°0′0″E", "46°12′0″N, 6°9′0″E"), 739.2)
test(distance("90°0′0″N 0°0′0″E", "90°0′0″S, 0°0′0″W"), 20015.1)
test(distance("33°51′31″S, 151°12′51″E", "40°46′22″N 73°59′3″W"), 15990.2)
这是一些输出:
coord string: 90°0′0″N 0°0′0″E | 0°0′0″N, 0°0′0″E
coord radians: 1.5707963267948966 0.0 | 0.0 0.0
x/y-distances: 1.5707963267948966 0.0
HS: 10007.54 LOC: 0.0
result: 10007.543398010286
correct: 10007.5
coord string: 51°28′48″N 0°0′0″E | 46°12′0″N, 6°9′0″E
coord radians: 0.8984954989266809 0.0 | 0.8063421144213803 0.10733774899765128
x/y-distances: 0.09215338450530064 -0.10733774899765128
HS: 900.57 LOC: 683.85
result: 900.5669567853056
correct: 739.2
推荐答案
您似乎混淆了 x
和<$在计算 a
时得出c $ c> y 。您应该采用纬度( y
)的余弦,而不是经度( x
)的余弦。
It looks like you mixed up x
and y
in your calculation of a
. You're supposed to take the cosine of latitude (y
), not longitude (x
).
我是通过将您的距离
更改为 angular_distance
来发现这一点的(即, t乘以 R
)并添加一些其他测试:
I discovered this by changing your distance
to angular_distance
(i.e. don't multiply by R
) and adding some additional tests:
test(angular_distance("90°0′0″N 0°0′0″E", "89°0′0″N, 0°0′0″E"), math.radians(1))
test(angular_distance("90°0′0″N 0°0′0″E", "80°0′0″N, 0°0′0″E"), math.radians(10))
test(angular_distance("90°0′0″N 0°0′0″E", "50°0′0″N, 0°0′0″E"), math.radians(40))
test(angular_distance("90°0′0″N 0°0′0″E", "50°0′0″N, 20°0′0″E"), math.radians(40))
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