136

问题

我想知道如何获得2 个 GPS 点之间的距离和方位。我研究了haversine公式。有人告诉我，我也可以使用相同的数据找到方位。

编辑

一切正常，但轴承还不能正常工作。轴承输出负值，但应在 0 - 360 度之间。设定的数据应该是水平方向的96.02166666666666 ，并且是：

Start point: 53.32055555555556 , -1.7297222222222221   
Bearing:  96.02166666666666  
Distance: 2 km  
Destination point: 53.31861111111111, -1.6997222222222223  
Final bearing: 96.04555555555555

这是我的新代码：

from math import *

Aaltitude = 2000
Oppsite  = 20000

lat1 = 53.32055555555556
lat2 = 53.31861111111111
lon1 = -1.7297222222222221
lon2 = -1.6997222222222223

lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])

dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
c = 2 * atan2(sqrt(a), sqrt(1-a))
Base = 6371 * c


Bearing =atan2(cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(lon2-lon1), sin(lon2-lon1)*cos(lat2)) 

Bearing = degrees(Bearing)
print ""
print ""
print "--------------------"
print "Horizontal Distance:"
print Base
print "--------------------"
print "Bearing:"
print Bearing
print "--------------------"


Base2 = Base * 1000
distance = Base * 2 + Oppsite * 2 / 2
Caltitude = Oppsite - Aaltitude

a = Oppsite/Base
b = atan(a)
c = degrees(b)

distance = distance / 1000

print "The degree of vertical angle is:"
print c
print "--------------------"
print "The distance between the Balloon GPS and the Antenna GPS is:"
print distance
print "--------------------"
4

10 回答 10

291

这是一个 Python 版本：

from math import radians, cos, sin, asin, sqrt

def haversine(lon1, lat1, lon2, lat2):
    """
    Calculate the great circle distance in kilometers between two points 
    on the earth (specified in decimal degrees)
    """
    # convert decimal degrees to radians 
    lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])

    # haversine formula 
    dlon = lon2 - lon1 
    dlat = lat2 - lat1 
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * asin(sqrt(a)) 
    r = 6371 # Radius of earth in kilometers. Use 3956 for miles. Determines return value units.
    return c * r
于 2011-02-06T13:47:08.280 回答
17

这些答案中的大多数都是“四舍五入”地球的半径。如果您将这些与其他距离计算器（例如 geopy）进行检查，这些功能将被关闭。

这很好用：

from math import radians, cos, sin, asin, sqrt

def haversine(lat1, lon1, lat2, lon2):

      R = 3959.87433 # this is in miles.  For Earth radius in kilometers use 6372.8 km

      dLat = radians(lat2 - lat1)
      dLon = radians(lon2 - lon1)
      lat1 = radians(lat1)
      lat2 = radians(lat2)

      a = sin(dLat/2)**2 + cos(lat1)*cos(lat2)*sin(dLon/2)**2
      c = 2*asin(sqrt(a))

      return R * c

# Usage
lon1 = -103.548851
lat1 = 32.0004311
lon2 = -103.6041946
lat2 = 33.374939

print(haversine(lat1, lon1, lat2, lon2))
于 2017-07-30T03:00:40.223 回答
11

还有一个矢量化实现，它允许使用 4 个 numpy 数组而不是坐标的标量值：

def distance(s_lat, s_lng, e_lat, e_lng):

   # approximate radius of earth in km
   R = 6373.0

   s_lat = s_lat*np.pi/180.0                      
   s_lng = np.deg2rad(s_lng)     
   e_lat = np.deg2rad(e_lat)                       
   e_lng = np.deg2rad(e_lng)  

   d = np.sin((e_lat - s_lat)/2)**2 + np.cos(s_lat)*np.cos(e_lat) * np.sin((e_lng - s_lng)/2)**2

   return 2 * R * np.arcsin(np.sqrt(d))
于 2018-08-07T08:22:34.730 回答
8

你可以试试 hasrsine 包： https ://pypi.org/project/haversine/

示例代码：

from haversine import haversine
haversine((45.7597, 4.8422),(48.8567, 2.3508), unit='mi')
243.71209416020253
于 2015-06-23T18:58:47.350 回答
5

方位计算不正确，您需要将输入交换到 atan2。

    bearing = atan2(sin(long2-long1)*cos(lat2), cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(long2-long1))
    bearing = degrees(bearing)
    bearing = (bearing + 360) % 360

这将为您提供正确的方位。

于 2015-04-30T03:03:04.040 回答
4

这是@Michael Dunn 给出的Haversine 公式的一个numpy 向量化实现，比大向量提高了10-50 倍。

from numpy import radians, cos, sin, arcsin, sqrt

def haversine(lon1, lat1, lon2, lat2):
    """
    Calculate the great circle distance between two points 
    on the earth (specified in decimal degrees)
    """

    #Convert decimal degrees to Radians:
    lon1 = np.radians(lon1.values)
    lat1 = np.radians(lat1.values)
    lon2 = np.radians(lon2.values)
    lat2 = np.radians(lat2.values)

    #Implementing Haversine Formula: 
    dlon = np.subtract(lon2, lon1)
    dlat = np.subtract(lat2, lat1)

    a = np.add(np.power(np.sin(np.divide(dlat, 2)), 2),  
                          np.multiply(np.cos(lat1), 
                                      np.multiply(np.cos(lat2), 
                                                  np.power(np.sin(np.divide(dlon, 2)), 2))))
    c = np.multiply(2, np.arcsin(np.sqrt(a)))
    r = 6371

    return c*r
于 2018-07-19T21:20:34.607 回答
2

您可以通过添加 360° 来解决负方位问题。不幸的是，这可能导致正向轴承的轴承大于 360°。这是模运算符的一个很好的候选者，所以总而言之，您应该添加该行

Bearing = (Bearing + 360) % 360

在你的方法结束时。

于 2013-08-30T20:42:30.780 回答
1

默认情况下，atan2 中的 Y 是第一个参数。这是文档。您需要切换输入以获得正确的方位角。

bearing = atan2(sin(lon2-lon1)*cos(lat2), cos(lat1)*sin(lat2)in(lat1)*cos(lat2)*cos(lon2-lon1))
bearing = degrees(bearing)
bearing = (bearing + 360) % 360
于 2016-01-07T20:04:19.610 回答
1

请参阅此链接：https ://gis.stackexchange.com/questions/84885/whats-the-difference-between-vincenty-and-great-circle-distance-calculations

这实际上提供了两种获取距离的方法。他们是Haversine 和Vincentys。根据我的研究，我知道 Vincentys 是相对准确的。也可以使用 import 语句来实现。

于 2017-03-05T06:24:31.447 回答
0

这里有两个计算距离和方位的函数，它们基于之前消息中的代码和https://gist.github.com/jeromer/2005586（为清楚起见，为这两个函数添加了 lat、lon 格式的地理点的元组类型）。我测试了这两个功能，它们似乎工作正常。

#coding:UTF-8
from math import radians, cos, sin, asin, sqrt, atan2, degrees

def haversine(pointA, pointB):

    if (type(pointA) != tuple) or (type(pointB) != tuple):
        raise TypeError("Only tuples are supported as arguments")

    lat1 = pointA[0]
    lon1 = pointA[1]

    lat2 = pointB[0]
    lon2 = pointB[1]

    # convert decimal degrees to radians 
    lat1, lon1, lat2, lon2 = map(radians, [lat1, lon1, lat2, lon2]) 

    # haversine formula 
    dlon = lon2 - lon1 
    dlat = lat2 - lat1 
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * asin(sqrt(a)) 
    r = 6371 # Radius of earth in kilometers. Use 3956 for miles
    return c * r


def initial_bearing(pointA, pointB):

    if (type(pointA) != tuple) or (type(pointB) != tuple):
        raise TypeError("Only tuples are supported as arguments")

    lat1 = radians(pointA[0])
    lat2 = radians(pointB[0])

    diffLong = radians(pointB[1] - pointA[1])

    x = sin(diffLong) * cos(lat2)
    y = cos(lat1) * sin(lat2) - (sin(lat1)
            * cos(lat2) * cos(diffLong))

    initial_bearing = atan2(x, y)

    # Now we have the initial bearing but math.atan2 return values
    # from -180° to + 180° which is not what we want for a compass bearing
    # The solution is to normalize the initial bearing as shown below
    initial_bearing = degrees(initial_bearing)
    compass_bearing = (initial_bearing + 360) % 360

    return compass_bearing

pA = (46.2038,6.1530)
pB = (46.449, 30.690)

print haversine(pA, pB)

print initial_bearing(pA, pB)
于 2017-05-14T05:39:59.230 回答