JavaScript calculates the distance between two places by longitude and latitude.

How does JavaScript calculate the distance between two places? I believe there are many ways to achieve this, the next article will introduce you to JavaScript through latitude and longitude to calculate the distance between the two places.

Recently work needs, online search under the latitude and longitude to calculate the distance between the two methods, found that either the geometric method, draw, make a bunch of auxiliary lines, and then prove reasoning, or apart directly set formula. This article introduces an easy-to-understand way to find this distance.

Ideas

The earth is an irregular ellipsoid, for simplicity we calculate as a sphere.
The shortest distance between the two sides of a sphere is the length of the counterclockwise of a great circle.

Ideas are as follows:

Arc length ← Chord length (two point distance) ← Two point coordinate (Cartesian coordinates) ← Latitude and longitude

Calculation

1. Coordinate conversion

Set

The radius of the earth is $R $

The center of gravity to E 0°n 0° is connected to the x-axis

The center of gravity to E 90°n 0° is connected to the Y axis.

Center of gravity to E 0°n 90° to Z-axis

The surface of the earth is a little $A $, longitude $e $, latitude is $n $, Unit is radians

The coordinates of the $A $ are expressed as:

$ $x = r \cdot cos (n) \cdot cos (e) \\y = r \cdot cos (n) \cdot sin (e) \\z = R \cdot sin (n) $$

Code

Const R = 6371const {cos, sin, PI} = Mathlet GetPoint = (e, n) + = {    //first convert angle to radians    e *= pi/180    n *= pi/180
  
   reutrn {        x:r*cos (n) *cos (e),        Y:r*cos (n) *sin (e),        z:r*sin (n)    }}
  

2. Calculate two-point distance according to coordinates

This is too simple to skip

3. Arc length based on chord length

This can draw a diagram to help understand:

Now known chord length $c $, radius $R $, required arc $r $ length
This is simple, just to find out the size of the $∠\alpha$:

$$\alpha = \arcsin (c/2/r) \\r = 2\alpha \cdot r$$

Code

const {ASIN} = mathconst R = 6371R = ASIN (C/2/R) *2*r

Final code

/** * Gets the distance between the two latitude and longitude * @param {Number} e1 point 1 east longitude, unit: angle, if it is West, negative * @param {number} n1 point 1    Latitude, Unit: angle, if South latitude is negative * @param {number} e2 * @param {number} n2 */function getdistance (E1, N1, E2, N2) {Const R = 6371         const {sin, cos, ASIN, PI, hypot} = Math/** Get the coordinates of points based on latitude and longitude */Let GetPoint = (e, n) + = {e *= pi/180 n *= pi/180//Here r* is removed, equivalent to the unit circle on the distance of two points, and finally will then enlarge the distance R times return {x:cos (n) *cos (e), Y:cos (n) *sin (e), Z:sin (N)}} Let A = GetPoint (e1, n1) Let B = GetPoint (e2, n2) Let C = Hypot (a.x-b.x, A.Y-B.Y, A.z-b . z) Let R = Asin (C/2) *2*r return R}