Calculate area of a polygon using longitude and latitude using javascript

Question

The approach I've been working on is implementing a sinusoidal projection to get x,y coordinates and then use a function to calculate the area of an irregular polygon in a plane. Below is the code I've been working on (the points variable is an array of Cesium Cartesian points that is defined elsewhere in the program).

https://stackoverflow.com/a/4682656/7924630 This was a very useful answer that helped me work on this

function polygonArea(X, Y, numPoints) {
  let area = 0;         // Accumulates area in the loop
  let j = numPoints-1;  // The last vertex is the 'previous' one to the first

  for (i=0; i<numPoints; i++) {
    area = area +  (X[j]+X[i]) * (Y[j]-Y[i]);
    j = i;  //j is previous vertex to i
  }
  return area/2;
}


let xpoints = [];
let ypoints = [];
let lat_dist = (6371009 * Math.PI) / 180;
var i;
for (i = 0; i < points.length; i++) {
    let cartoPoint = Cesium.Cartographic.fromCartesian(points[i]);
    let lng = cartoPoint.longitude;
    let lat = cartoPoint.latitude;
    xpoints[i] = lng * lat_dist * Math.cos(lat);
    ypoints[i] = lat * lat_dist;
};
surfaceArea = polygonArea(xpoints, ypoints, xpoints.length);

For some reason this is returning really small values for the area and I can't understand why. For example, I tested this on a rectangle area. The area should be approximately 45m², but it's returning 0.0137m². I've tried following other implementations of this, but haven't been able to find anything useful for native Javascript.

Formula and code looks right. Check real values of coordinates lat and lon. Also consider possibility of precision loss in float arithmetics (small difference of two large values `(Y[j]-Y[i])` — MBo, Dec 04 '18 at 03:01
Small addition (don't influence on area magnitude, only corrects sign if needed): `return Math.abs(area/2);` — MBo, Dec 04 '18 at 03:54
I thought that might be the case @MBo, but even on larger scales the formula still returns tiny values. — thornton, Dec 04 '18 at 04:02
log `lng and lat` into console/file. For area 45m^2 I expect values like `40.0001-40.0000` for 10 m difference by latitude (111111m=1 degree, 0.0001 degree = 10 m) — MBo, Dec 04 '18 at 04:06
I solved it using a different implementation. In case anyone wants help with this, here is the article that gave me the idea for my implementation: http://mathforum.org/library/drmath/view/73894.html — thornton, Dec 04 '18 at 04:57
@MBo The difference between lng/lat points that I was testing on was approximately 0.000001 for lng and lat. I guess there was probably an issue somewhere there. They were just the points provided by Cesium when clicking on a position on the globe. — thornton, Dec 04 '18 at 05:02
Link describes [shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula) that you have used (note - for Earth it gives approximation nad might fail at equator and 0th meridian) . So I was right about coordinates discrepance. 10^-6 degree is 0.1m, perhaps Cesium gives not degrees. — MBo, Dec 04 '18 at 05:13

score 1 · Answer 1 · answered Dec 04 '18 at 05:26

You are using shoelace formula for polygon area, here it gives approximation for spherical polygon. Add Math/abs in the end to get result independently on traversal direction and beware of coordinate sign change at equator and 0th meridian.

But calculations are incorrect due to this issue:

Cesium.Cartographic.fromCartesian function returns result coordinates in radians

while you treat them as degrees (quick check: 45/(57*57)=0.0138).

So it is enough to make correction:

 let lat_dist = 6371009;

score 1 · Answer 2 · answered Apr 12 '22 at 19:23

You can use Spherical Geometry Library This library ports a small but useful subset of classes from the Google Maps Javascript API

How to use

Install library

npm install spherical-geometry-js

include library in your code

import { computeArea ,LatLng} from 'spherical-geometry-js/src/index';

import computeArea ,LatLng

import { computeArea ,LatLng} from 'spherical-geometry-js/src/index';

Compute the area by passing coordinate array

  getArea(){
     var coords = [
        { lat: 12.963340185241163, lng: 77.59504217857734 },
        { lat: 12.963959666837907, lng: 77.5952513908759 },
        { lat: 12.96387994460954, lng: 77.59548340195072 },
        { lat: 12.963263076659977, lng: 77.59528357738415 }
     ];

     //convert coords to latlng
     var latLngs = coords.map(function(coord) { 
        return new LatLng(coord.lat, coord.lng);
     });


    return computeArea(latLngs)  //return the area 

   }

Calculate area of a polygon using longitude and latitude using javascript

2 Answers2