Polygon area calculation using Latitude and Longitude generated from Cartesian space and a world file

Question

Given a series of GPS coordinate pairs, I need to calculate the area of a polygon (n-gon). This is relatively small (not larger than 50,000 sqft). The geocodes are created by applying an affine transform with data from a world file.

I have tried to use a two step approach by doing converting the geocodes to cartesian coordinates:

double xPos = (lon-lonAnchor)*( Math.toRadians( 6378137 ) )*Math.cos( latAnchor );
double yPos = (lat-latAnchor)*( Math.toRadians( 6378137 ) );

then I use a cross product calculation to determine the area.

The issue is that the results are a bit off in accuracy (around 1%). Is there anything I can look into to improve this?

Thanks.

Answer 1

I checked on internet for various polygon area formulas(or code) but did not find any one good or easy to implement.

Now I have written the code snippet to calculate area of a polygon drawn on earth surface. The polygon can have n vertices with each vertex has having its own latitude longitude.

Few Important Points

1. The array input to this function will have "n + 1" elements. The last element will have same values as that of first one.
2. I have written very basic C# code, so that guys can also adapt it in other language.
3. 6378137 is the value of earth radius in metres.

4. The output area will have unit of square metres

   private static double CalculatePolygonArea(IList<MapPoint> coordinates)
   {
       double area = 0;
   
       if (coordinates.Count > 2)
       {
           for (var i = 0; i < coordinates.Count - 1; i++)
           {
               MapPoint p1 = coordinates[i];
               MapPoint p2 = coordinates[i + 1];
               area += ConvertToRadian(p2.Longitude - p1.Longitude) * (2 + Math.Sin(ConvertToRadian(p1.Latitude)) + Math.Sin(ConvertToRadian(p2.Latitude)));
           }
   
           area = area * 6378137 * 6378137 / 2;
       }
   
       return Math.Abs(area);
   }
   
   private static double ConvertToRadian(double input)
   {
       return input * Math.PI / 180;
   }
   

Answer 2

I am modifying a Google Map so that a user can calculate the area of a polygon by clicking the vertices. It wasn't giving correct areas until I made sure the Math.cos(latAnchor) was in radians first

So:

double xPos = (lon-lonAnchor)*( Math.toRadians( 6378137 ) )*Math.cos( latAnchor );

became:

double xPos = (lon-lonAnchor)*( 6378137*PI/180 ) )*Math.cos( latAnchor*PI/180 );

where lon, lonAnchor and latAnchor are in degrees. Works like a charm now.