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

这个脚本[在PHP中]计算两点之间的距离。

public static function getDistanceOfTwoPoints($source, $dest, $unit='K') {
        $lat1 = $source[0];
        $lon1 = $source[1];
        $lat2 = $dest[0];
        $lon2 = $dest[1];

        $theta = $lon1 - $lon2;
        $dist = sin(deg2rad($lat1)) * sin(deg2rad($lat2)) +  cos(deg2rad($lat1)) * cos(deg2rad($lat2)) * cos(deg2rad($theta));
        $dist = acos($dist);
        $dist = rad2deg($dist);
        $miles = $dist * 60 * 1.1515;
        $unit = strtoupper($unit);

        if ($unit == "K") {
            return ($miles * 1.609344);
        }
        else if ($unit == "M")
        {
            return ($miles * 1.609344 * 1000);
        }
        else if ($unit == "N") {
            return ($miles * 0.8684);
        } 
        else {
            return $miles;
        }
    }

其他回答

这是一个简单的javascript函数,从这个链接可能是有用的。不知何故相关,但我们使用谷歌地球javascript插件而不是地图

function getApproximateDistanceUnits(point1, point2) {

    var xs = 0;
    var ys = 0;

    xs = point2.getX() - point1.getX();
    xs = xs * xs;

    ys = point2.getY() - point1.getY();
    ys = ys * ys;

    return Math.sqrt(xs + ys);
}

单位不是距离,而是相对于坐标的比率。还有其他相关的计算,你可以在这里代替getApproximateDistanceUnits函数链接

然后我使用这个函数来查看经纬度是否在半径内

function isMapPlacemarkInRadius(point1, point2, radi) {
    if (point1 && point2) {
        return getApproximateDistanceUnits(point1, point2) <= radi;
    } else {
        return 0;
    }
}

点可以定义为

 $$.getPoint = function(lati, longi) {
        var location = {
            x: 0,
            y: 0,
            getX: function() { return location.x; },
            getY: function() { return location.y; }
        };
        location.x = lati;
        location.y = longi;

        return location;
    };

然后你可以做你的事情,看看一个点是否在一个半径范围内,比如:

 //put it on the map if within the range of a specified radi assuming 100,000,000 units
        var iconpoint = Map.getPoint(pp.latitude, pp.longitude);
        var centerpoint = Map.getPoint(Settings.CenterLatitude, Settings.CenterLongitude);

        //approx ~200 units to show only half of the globe from the default center radius
        if (isMapPlacemarkInRadius(centerpoint, iconpoint, 120)) {
            addPlacemark(pp.latitude, pp.longitude, pp.name);
        }
        else {
            otherSidePlacemarks.push({
                latitude: pp.latitude,
                longitude: pp.longitude,
                name: pp.name
            });

        }

哈弗辛公式在大多数情况下都是很好的公式,其他答案已经包含了它所以我就不占用空间了。但重要的是要注意,无论使用什么公式(是的,不仅仅是一个)。因为可能的精度范围很大,以及所需的计算时间。公式的选择需要更多的思考,而不是简单的无脑答案。

这个帖子来自nasa的一个人,是我在讨论这些选项时发现的最好的一个

http://www.cs.nyu.edu/visual/home/proj/tiger/gisfaq.html

例如,如果您只是在100英里半径内按距离对行进行排序。地平公式比哈弗辛公式快得多。

HalfPi = 1.5707963;
R = 3956; /* the radius gives you the measurement unit*/

a = HalfPi - latoriginrad;
b = HalfPi - latdestrad;
u = a * a + b * b;
v = - 2 * a * b * cos(longdestrad - longoriginrad);
c = sqrt(abs(u + v));
return R * c;

注意这里只有一个余弦和一个平方根。在哈弗辛公式中有9个。

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postgres SQL中的一个示例(以公里为单位,为英里版本,将1.609344替换为0.8684版本)

CREATE OR REPLACE FUNCTION public.geodistance(alat float, alng float, blat  

float, blng  float)
  RETURNS float AS
$BODY$
DECLARE
    v_distance float;
BEGIN

    v_distance = asin( sqrt(
            sin(radians(blat-alat)/2)^2 
                + (
                    (sin(radians(blng-alng)/2)^2) *
                    cos(radians(alat)) *
                    cos(radians(blat))
                )
          )
        ) * cast('7926.3352' as float) * cast('1.609344' as float) ;


    RETURN v_distance;
END 
$BODY$
language plpgsql VOLATILE SECURITY DEFINER;
alter function geodistance(alat float, alng float, blat float, blng float)
owner to postgres;

FSharp版本,使用里程:

let radialDistanceHaversine location1 location2 : float = 
                let degreeToRadian degrees = degrees * System.Math.PI / 180.0
                let earthRadius = 3959.0
                let deltaLat = location2.Latitude - location1.Latitude |> degreeToRadian
                let deltaLong = location2.Longitude - location1.Longitude |> degreeToRadian
                let a =
                    (deltaLat / 2.0 |> sin) ** 2.0
                    + (location1.Latitude |> degreeToRadian |> cos)
                    * (location2.Latitude |> degreeToRadian |> cos)
                    * (deltaLong / 2.0 |> sin) ** 2.0
                atan2 (a |> sqrt) (1.0 - a |> sqrt)
                * 2.0
                * earthRadius