如何计算由经纬度指定的两点之间的距离?

为了澄清,我想用千米来表示距离;这些点使用WGS84系统,我想了解可用方法的相对准确性。


当前回答

下面是Erlang实现

lat_lng({Lat1, Lon1}=_Point1, {Lat2, Lon2}=_Point2) ->
  P = math:pi() / 180,
  R = 6371, % Radius of Earth in KM
  A = 0.5 - math:cos((Lat2 - Lat1) * P) / 2 +
    math:cos(Lat1 * P) * math:cos(Lat2 * P) * (1 - math:cos((Lon2 - Lon1) * P))/2,
  R * 2 * math:asin(math:sqrt(A)).

其他回答

正如指出的那样,精确的计算应该考虑到地球不是一个完美的球体。以下是这里提供的各种算法的一些比较:

geoDistance(50,5,58,3)
Haversine: 899 km
Maymenn: 833 km
Keerthana: 897 km
google.maps.geometry.spherical.computeDistanceBetween(): 900 km

geoDistance(50,5,-58,-3)
Haversine: 12030 km
Maymenn: 11135 km
Keerthana: 10310 km
google.maps.geometry.spherical.computeDistanceBetween(): 12044 km

geoDistance(.05,.005,.058,.003)
Haversine: 0.9169 km
Maymenn: 0.851723 km
Keerthana: 0.917964 km
google.maps.geometry.spherical.computeDistanceBetween(): 0.917964 km

geoDistance(.05,80,.058,80.3)
Haversine: 33.37 km
Maymenn: 33.34 km
Keerthana: 33.40767 km
google.maps.geometry.spherical.computeDistanceBetween(): 33.40770 km

在小范围内,Keerthana的算法似乎与谷歌Maps的算法一致。谷歌Maps似乎没有遵循任何简单的算法,这表明它可能是这里最准确的方法。

不管怎样,这里是Keerthana算法的Javascript实现:

function geoDistance(lat1, lng1, lat2, lng2){
    const a = 6378.137; // equitorial radius in km
    const b = 6356.752; // polar radius in km

    var sq = x => (x*x);
    var sqr = x => Math.sqrt(x);
    var cos = x => Math.cos(x);
    var sin = x => Math.sin(x);
    var radius = lat => sqr((sq(a*a*cos(lat))+sq(b*b*sin(lat)))/(sq(a*cos(lat))+sq(b*sin(lat))));

    lat1 = lat1 * Math.PI / 180;
    lng1 = lng1 * Math.PI / 180;
    lat2 = lat2 * Math.PI / 180;
    lng2 = lng2 * Math.PI / 180;

    var R1 = radius(lat1);
    var x1 = R1*cos(lat1)*cos(lng1);
    var y1 = R1*cos(lat1)*sin(lng1);
    var z1 = R1*sin(lat1);

    var R2 = radius(lat2);
    var x2 = R2*cos(lat2)*cos(lng2);
    var y2 = R2*cos(lat2)*sin(lng2);
    var z2 = R2*sin(lat2);

    return sqr(sq(x1-x2)+sq(y1-y2)+sq(z1-z2));
}

你也可以使用像geolib这样的模块:

安装方法:

$ npm install geolib

使用方法:

import { getDistance } from 'geolib'

const distance = getDistance(
    { latitude: 51.5103, longitude: 7.49347 },
    { latitude: "51° 31' N", longitude: "7° 28' E" }
)

console.log(distance)

文档: https://www.npmjs.com/package/geolib

仅限飞镖:

import 'dart:math' show cos, sqrt, asin;

double calculateDistance(LatLng l1, LatLng l2) {
  const p = 0.017453292519943295;
  final a = 0.5 -
      cos((l2.latitude - l1.latitude) * p) / 2 +
      cos(l1.latitude * p) *
          cos(l2.latitude * p) *
          (1 - cos((l2.longitude - l1.longitude) * p)) /
          2;
  return 12742 * asin(sqrt(a));
}

这个链接可能对你有帮助,因为它详细介绍了使用哈弗辛公式来计算距离。

摘录:

这个脚本计算两点之间的大圆距离 也就是说,在地球表面上的最短距离-使用 “半正矢”公式。

function getDistanceFromLatLonInKm(lat1,lon1,lat2,lon2) {
  var R = 6371; // Radius of the earth in km
  var dLat = deg2rad(lat2-lat1);  // deg2rad below
  var dLon = deg2rad(lon2-lon1); 
  var a = 
    Math.sin(dLat/2) * Math.sin(dLat/2) +
    Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * 
    Math.sin(dLon/2) * Math.sin(dLon/2)
    ; 
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
  var d = R * c; // Distance in km
  return d;
}

function deg2rad(deg) {
  return deg * (Math.PI/180)
}

Java实现在根据哈弗辛公式

double calculateDistance(double latPoint1, double lngPoint1, 
                         double latPoint2, double lngPoint2) {
    if(latPoint1 == latPoint2 && lngPoint1 == lngPoint2) {
        return 0d;
    }

    final double EARTH_RADIUS = 6371.0; //km value;

    //converting to radians
    latPoint1 = Math.toRadians(latPoint1);
    lngPoint1 = Math.toRadians(lngPoint1);
    latPoint2 = Math.toRadians(latPoint2);
    lngPoint2 = Math.toRadians(lngPoint2);

    double distance = Math.pow(Math.sin((latPoint2 - latPoint1) / 2.0), 2) 
            + Math.cos(latPoint1) * Math.cos(latPoint2)
            * Math.pow(Math.sin((lngPoint2 - lngPoint1) / 2.0), 2);
    distance = 2.0 * EARTH_RADIUS * Math.asin(Math.sqrt(distance));

    return distance; //km value
}