靠谱的根据经纬度计算两点之间距离的方法

网上找的中文的例子都不靠谱，还得是英文网站好用。

网址： https://www.movable-type.co.uk/scripts/latlong.html

 

Haversine formula

Using Chrome on a middling Core i5 PC, a distance calcula­tion takes around 2 – 5 micro­seconds (hence around 200,000 – 500,000 per second). Little to no benefit is obtained by factoring out common terms; probably the JIT compiler optimises them out.

 

formula：

a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)

c = 2 ⋅ atan2( √a, √(1−a) )

d = R ⋅ c

 

 

where

φ is latitude, λ is longitude, R is earth’s radius (mean radius = 6,371km); note that angles need to be in radians to pass to trig functions!

 

 

Javascript:

var R =6371e3;// metresvarφ1= lat1.toRadians();

varφ2= lat2.toRadians();varΔφ=(lat2-lat1).toRadians();

varΔλ=(lon2-lon1).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;
 

 

 

 

Spherical Law of Cosines

the simple spherical law of cosinesformula (cos c = cos a cos b + sin a sin b cos C) gives well-condi­tioned results down to distances as small as a few metres on the earth’s surface

 

formula: 

d = acos( sin φ1 ⋅ sin φ2 + cos φ1 ⋅ cos φ2 ⋅ cos Δλ ) ⋅ R

 

Javascript:

 

varφ1= lat1.toRadians(),φ2= lat2.toRadians(),Δλ=(lon2-lon1).toRadians(), R =6371e3;// gives d in metres
var d =Math.acos(Math.sin(φ1)*Math.sin(φ2)+Math.cos(φ1)*Math.cos(φ2)*Math.cos(Δλ))* R;
 

 

 

Equirectangular approximation

If performance is an issue and accuracy less important, for small distances Pythagoras’ theorem can be used on an equi­rectangular projec­tion:*

 

Formula	x = Δλ ⋅ cos φm
	y = Δφ
	d = R ⋅ √x² + y²
JavaScript:	var x =(λ2-λ1)*Math.cos((φ1+φ2)/2); var y =(φ2-φ1); var d =Math.sqrt(x*x + y*y)* R;

 λ2就是lon2

 λ1就是lon1

 

角度和弧度换算的原理：

网址： https://tianyelina.iteye.com/blog/756031

Javascript实现（根据原理自己实现也很容易）： 

网址： https://www.w3resource.com/javascript-exercises/javascript-math-exercise-33.php