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

在其他答案中,r中的实现是缺失的。

用地质圈包中的distm函数计算两点之间的距离非常简单:

distm(p1, p2, fun = distHaversine)

地点:

p1 = longitude/latitude for point(s)
p2 = longitude/latitude for point(s)
# type of distance calculation
fun = distCosine / distHaversine / distVincentySphere / distVincentyEllipsoid 

由于地球不是完美的球形,所以椭球体的文森提公式可能是计算距离的最佳方法。因此,在地质圈包中,您可以使用:

distm(p1, p2, fun = distVincentyEllipsoid)

当然,你不一定要使用geosphere包,你也可以用一个函数来计算以R为基底的距离:

hav.dist <- function(long1, lat1, long2, lat2) {
  R <- 6371
  diff.long <- (long2 - long1)
  diff.lat <- (lat2 - lat1)
  a <- sin(diff.lat/2)^2 + cos(lat1) * cos(lat2) * sin(diff.long/2)^2
  b <- 2 * asin(pmin(1, sqrt(a))) 
  d = R * b
  return(d)
}

其他回答

这是一个简单的PHP函数,它将给出一个非常合理的近似值(误差小于+/-1%)。

<?php
function distance($lat1, $lon1, $lat2, $lon2) {

    $pi80 = M_PI / 180;
    $lat1 *= $pi80;
    $lon1 *= $pi80;
    $lat2 *= $pi80;
    $lon2 *= $pi80;

    $r = 6372.797; // mean radius of Earth in km
    $dlat = $lat2 - $lat1;
    $dlon = $lon2 - $lon1;
    $a = sin($dlat / 2) * sin($dlat / 2) + cos($lat1) * cos($lat2) * sin($dlon / 2) * sin($dlon / 2);
    $c = 2 * atan2(sqrt($a), sqrt(1 - $a));
    $km = $r * $c;

    //echo '<br/>'.$km;
    return $km;
}
?>

如前所述;地球不是一个球体。它就像马克·麦奎尔决定用来练习的一个很旧很旧的棒球——到处都是凹痕和凸起。简单的计算(像这样)把它当作一个球体。

不同的方法或多或少的精确取决于你在这个不规则的卵形上的位置以及你的点之间的距离(它们越近,绝对误差范围就越小)。你的期望越精确,计算就越复杂。

更多信息:维基百科地理距离

下面是Haversine公式的typescript实现

static getDistanceFromLatLonInKm(lat1: number, lon1: number, lat2: number, lon2: number): number {
    var deg2Rad = deg => {
        return deg * Math.PI / 180;
    }

    var r = 6371; // Radius of the earth in km
    var dLat = deg2Rad(lat2 - lat1);   
    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;
}

下面是移植到Java的已接受的答案实现,以备任何人需要。

package com.project529.garage.util;


/**
 * Mean radius.
 */
private static double EARTH_RADIUS = 6371;

/**
 * Returns the distance between two sets of latitudes and longitudes in meters.
 * <p/>
 * Based from the following JavaScript SO answer:
 * http://stackoverflow.com/questions/27928/calculate-distance-between-two-latitude-longitude-points-haversine-formula,
 * which is based on https://en.wikipedia.org/wiki/Haversine_formula (error rate: ~0.55%).
 */
public double getDistanceBetween(double lat1, double lon1, double lat2, double lon2) {
    double dLat = toRadians(lat2 - lat1);
    double dLon = toRadians(lon2 - lon1);

    double a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
            Math.cos(toRadians(lat1)) * Math.cos(toRadians(lat2)) *
                    Math.sin(dLon / 2) * Math.sin(dLon / 2);
    double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
    double d = EARTH_RADIUS * c;

    return d;
}

public double toRadians(double degrees) {
    return degrees * (Math.PI / 180);
}

下面是SQL实现,以km为单位计算距离,

SELECT UserId, ( 3959 * acos( cos( radians( your latitude here ) ) * cos( radians(latitude) ) * 
cos( radians(longitude) - radians( your longitude here ) ) + sin( radians( your latitude here ) ) * 
sin( radians(latitude) ) ) ) AS distance FROM user HAVING
distance < 5  ORDER BY distance LIMIT 0 , 5;

要获得通过编程语言实现的更多细节,您可以浏览这里给出的php脚本

对于那些寻找基于WGS-84和GRS-80标准的Excel公式的人:

=ACOS(COS(RADIANS(90-Lat1))*COS(RADIANS(90-Lat2))+SIN(RADIANS(90-Lat1))*SIN(RADIANS(90-Lat2))*COS(RADIANS(Long1-Long2)))*6371