如何使用python比较大圆距与两个球体点的欧几里得距离? [英] How to compare great circle distance with euclidean distance of two sphere points using python?

问题描述

我正在尝试检查您用欧几里德距离而不是大圆距离(gcd)计算地球上两点的距离时引入的误差.我有两个要点，分别是它们的纬度和经度. 我将python geopy框架用于大圆距离.这是gcd的代码:

I am trying to check the error that is introduced when you compute the distance of two points on earth with the euclidean distance instead of using the great circle distance (gcd). I have two points that are defined by their lattitude and longtitude. I used the python geopy framework for the great circle distance. Here the code for the gcd:

def measure(self, a, b):
        a, b = Point(a), Point(b)

        lat1, lng1 = radians(degrees=a.latitude), radians(degrees=a.longitude)
        lat2, lng2 = radians(degrees=b.latitude), radians(degrees=b.longitude)

        sin_lat1, cos_lat1 = sin(lat1), cos(lat1)
        sin_lat2, cos_lat2 = sin(lat2), cos(lat2)

        delta_lng = lng2 - lng1
        cos_delta_lng, sin_delta_lng = cos(delta_lng), sin(delta_lng)

        d = atan2(sqrt((cos_lat2 * sin_delta_lng) ** 2 +
                       (cos_lat1 * sin_lat2 -
                        sin_lat1 * cos_lat2 * cos_delta_lng) ** 2),
                  sin_lat1 * sin_lat2 + cos_lat1 * cos_lat2 * cos_delta_lng)

        return self.RADIUS * d

所以还是两点:

p1 = [39.8616，-75.0748]，p2 = [-7.30933,112.76]

p1=[39.8616,-75.0748], p2=[-7.30933,112.76]

gcd = 78.8433004543197 klm

使用geopy的great_circle(p1,p2).kilometers函数

然后我使用以下公式将这两个点转换为笛卡尔坐标:

I then transformed these two points in cartesian coordinates using this formula:

  def spherical_to_cartesian(r,la,lo):
       x=r*np.sin(90-la)*np.cos(lo)
       y=r*np.sin(90-la)*np.sin(lo)
       z=r*np.cos(90-la)
       return (x,y,z)

其中r=6372.795，这将导致以下笛卡尔坐标

where r=6372.795, which results in the following cartesians coordinates

p1=[ -765.81579368,  -256.69640558,  6321.40405587], 
p2=[480.8302149,-168.64726394,-6352.39140142]

然后通过键入:np.linalg.norm(p2-p1)我得到了1103.4963114787836作为其欧几里得范数，与来自gcd的〜78klm相比，这似乎并不合理.我是说错了吗?

Then by typing: np.linalg.norm(p2-p1) i am getting 1103.4963114787836 as their euclidean norm which doesn't seem reasonable compared with ~78klm from the gcd. Am i inffering sth wrong?

推荐答案

Python在math软件包中包含两个函数；弧度将度转换为弧度，度将弧度转换为度.

Python includes two functions in the math package; radians converts degrees to radians, and degrees converts radians to degrees.

sin()方法以弧度返回x的正弦.

The method sin() returns the sine of x, in radians.

import math
def spherical_to_cartesian(r,la,lo):
   rlo = math.radians(lo)
   rla = math.radians(90-la)
   x=r*np.sin(rla)*np.cos(rlo)
   y=r*np.sin(rla)*np.sin(rlo)
   z=r*np.cos(rla)
   return (x,y,z)

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