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。
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VB的实现。NET,这个实现将根据您传递的Enum值以KM或Miles为单位给您结果。
Public Enum DistanceType
Miles
KiloMeters
End Enum
Public Structure Position
Public Latitude As Double
Public Longitude As Double
End Structure
Public Class Haversine
Public Function Distance(Pos1 As Position,
Pos2 As Position,
DistType As DistanceType) As Double
Dim R As Double = If((DistType = DistanceType.Miles), 3960, 6371)
Dim dLat As Double = Me.toRadian(Pos2.Latitude - Pos1.Latitude)
Dim dLon As Double = Me.toRadian(Pos2.Longitude - Pos1.Longitude)
Dim a As Double = Math.Sin(dLat / 2) * Math.Sin(dLat / 2) + Math.Cos(Me.toRadian(Pos1.Latitude)) * Math.Cos(Me.toRadian(Pos2.Latitude)) * Math.Sin(dLon / 2) * Math.Sin(dLon / 2)
Dim c As Double = 2 * Math.Asin(Math.Min(1, Math.Sqrt(a)))
Dim result As Double = R * c
Return result
End Function
Private Function toRadian(val As Double) As Double
Return (Math.PI / 180) * val
End Function
End Class
其他回答
你可以用Haversine公式计算它,它是:
a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)
c = 2 ⋅ atan2( √a, √(1−a) )
d = R ⋅ c
下面给出了一个计算两点之间距离的例子
假设我要计算从新德里到伦敦的距离,那么我该如何使用这个公式:
New delhi co-ordinates= 28.7041° N, 77.1025° E
London co-ordinates= 51.5074° N, 0.1278° W
var R = 6371e3; // metres
var φ1 = 28.7041.toRadians();
var φ2 = 51.5074.toRadians();
var Δφ = (51.5074-28.7041).toRadians();
var Δλ = (0.1278-77.1025).toRadians();
var a = Math.sin(Δφ/2) * Math.sin(Δφ/2) +
Math.cos(φ1) * Math.cos(φ2) *
Math.sin(Δλ/2) * Math.sin(Δλ/2);
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
var d = R * c; // metres
d = d/1000; // km
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
});
}
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);
}
下面是一个c#实现:
static class DistanceAlgorithm
{
const double PIx = 3.141592653589793;
const double RADIUS = 6378.16;
/// <summary>
/// Convert degrees to Radians
/// </summary>
/// <param name="x">Degrees</param>
/// <returns>The equivalent in radians</returns>
public static double Radians(double x)
{
return x * PIx / 180;
}
/// <summary>
/// Calculate the distance between two places.
/// </summary>
/// <param name="lon1"></param>
/// <param name="lat1"></param>
/// <param name="lon2"></param>
/// <param name="lat2"></param>
/// <returns></returns>
public static double DistanceBetweenPlaces(
double lon1,
double lat1,
double lon2,
double lat2)
{
double dlon = Radians(lon2 - lon1);
double dlat = Radians(lat2 - lat1);
double a = (Math.Sin(dlat / 2) * Math.Sin(dlat / 2)) + Math.Cos(Radians(lat1)) * Math.Cos(Radians(lat2)) * (Math.Sin(dlon / 2) * Math.Sin(dlon / 2));
double angle = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1 - a));
return angle * RADIUS;
}
}
你可以使用CLLocationDistance中的构建来计算这个:
CLLocation *location1 = [[CLLocation alloc] initWithLatitude:latitude1 longitude:longitude1];
CLLocation *location2 = [[CLLocation alloc] initWithLatitude:latitude2 longitude:longitude2];
[self distanceInMetersFromLocation:location1 toLocation:location2]
- (int)distanceInMetersFromLocation:(CLLocation*)location1 toLocation:(CLLocation*)location2 {
CLLocationDistance distanceInMeters = [location1 distanceFromLocation:location2];
return distanceInMeters;
}
在你的例子中,如果你想要公里,只要除以1000。