Calculating Distance between two Latitude and Long

Question

I'm calculating the distance between two GeoCoordinates. I'm testing my app against 3-4 other apps. When I'm calculating distance, I tend to get an average of 3.3 miles for my calculation whereas other apps are getting 3.5 miles. It's a big difference for the calculation I'm trying to perform. Are there any good class libraries out there for calculating distance? I'm calculating it like this in C#:

public static double Calculate(double sLatitude,double sLongitude, double eLatitude, 
                               double eLongitude)
{
    var radiansOverDegrees = (Math.PI / 180.0);

    var sLatitudeRadians = sLatitude * radiansOverDegrees;
    var sLongitudeRadians = sLongitude * radiansOverDegrees;
    var eLatitudeRadians = eLatitude * radiansOverDegrees;
    var eLongitudeRadians = eLongitude * radiansOverDegrees;

    var dLongitude = eLongitudeRadians - sLongitudeRadians;
    var dLatitude = eLatitudeRadians - sLatitudeRadians;

    var result1 = Math.Pow(Math.Sin(dLatitude / 2.0), 2.0) + 
                  Math.Cos(sLatitudeRadians) * Math.Cos(eLatitudeRadians) * 
                  Math.Pow(Math.Sin(dLongitude / 2.0), 2.0);

    // Using 3956 as the number of miles around the earth
    var result2 = 3956.0 * 2.0 * 
                  Math.Atan2(Math.Sqrt(result1), Math.Sqrt(1.0 - result1));

    return result2;
}

What could I be doing wrong? Should I calculate it in km first and then convert to miles?

Answer 1

The GeoCoordinate class (.NET Framework 4 and higher) already has GetDistanceTo method.

var sCoord = new GeoCoordinate(sLatitude, sLongitude);
var eCoord = new GeoCoordinate(eLatitude, eLongitude);

return sCoord.GetDistanceTo(eCoord);

The distance is in meters.

You need to reference System.Device.

Answer 2

You can use this function :

Source : https://www.geodatasource.com/developers/c-sharp

private double distance(double lat1, double lon1, double lat2, double lon2, char unit) {
  if ((lat1 == lat2) && (lon1 == lon2)) {
    return 0;
  }
  else {
    double theta = lon1 - lon2;
    double dist = Math.Sin(deg2rad(lat1)) * Math.Sin(deg2rad(lat2)) + Math.Cos(deg2rad(lat1)) * Math.Cos(deg2rad(lat2)) * Math.Cos(deg2rad(theta));
    dist = Math.Acos(dist);
    dist = rad2deg(dist);
    dist = dist * 60 * 1.1515;
    if (unit == 'K') {
      dist = dist * 1.609344;
    } else if (unit == 'N') {
      dist = dist * 0.8684;
    }
    return (dist);
  }
}

//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
//::  This function converts decimal degrees to radians             :::
//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
private double deg2rad(double deg) {
  return (deg * Math.PI / 180.0);
}

//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
//::  This function converts radians to decimal degrees             :::
//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
private double rad2deg(double rad) {
  return (rad / Math.PI * 180.0);
}

Console.WriteLine(distance(32.9697, -96.80322, 29.46786, -98.53506, "M"));
Console.WriteLine(distance(32.9697, -96.80322, 29.46786, -98.53506, "K"));
Console.WriteLine(distance(32.9697, -96.80322, 29.46786, -98.53506, "N"));

Answer 3

GetDistance is the best solution, but in many cases we can't use this Method (e.g. Universal App)

• Pseudocode of the Algorithm to calculate the distance between to coorindates:

  public static double DistanceTo(double lat1, double lon1, double lat2, double lon2, char unit = 'K')
  {
      double rlat1 = Math.PI*lat1/180;
      double rlat2 = Math.PI*lat2/180;
      double theta = lon1 - lon2;
      double rtheta = Math.PI*theta/180;
      double dist =
          Math.Sin(rlat1)*Math.Sin(rlat2) + Math.Cos(rlat1)*
          Math.Cos(rlat2)*Math.Cos(rtheta);
      dist = Math.Acos(dist);
      dist = dist*180/Math.PI;
      dist = dist*60*1.1515;
  
      switch (unit)
      {
          case 'K': //Kilometers -> default
              return dist*1.609344;
          case 'N': //Nautical Miles 
              return dist*0.8684;
          case 'M': //Miles
              return dist;
      }
  
      return dist;
  }
  

• Real World C# Implementation, which makes use of an Extension Methods

  Usage:

  var distance = new Coordinates(48.672309, 15.695585)
                  .DistanceTo(
                      new Coordinates(48.237867, 16.389477),
                      UnitOfLength.Kilometers
                  );
  

  Implementation:

  public class Coordinates
  {
      public double Latitude { get; private set; }
      public double Longitude { get; private set; }
  
      public Coordinates(double latitude, double longitude)
      {
          Latitude = latitude;
          Longitude = longitude;
      }
  }
  public static class CoordinatesDistanceExtensions
  {
      public static double DistanceTo(this Coordinates baseCoordinates, Coordinates targetCoordinates)
      {
          return DistanceTo(baseCoordinates, targetCoordinates, UnitOfLength.Kilometers);
      }
  
      public static double DistanceTo(this Coordinates baseCoordinates, Coordinates targetCoordinates, UnitOfLength unitOfLength)
      {
          var baseRad = Math.PI * baseCoordinates.Latitude / 180;
          var targetRad = Math.PI * targetCoordinates.Latitude/ 180;
          var theta = baseCoordinates.Longitude - targetCoordinates.Longitude;
          var thetaRad = Math.PI * theta / 180;
  
          double dist =
              Math.Sin(baseRad) * Math.Sin(targetRad) + Math.Cos(baseRad) *
              Math.Cos(targetRad) * Math.Cos(thetaRad);
          dist = Math.Acos(dist);
  
          dist = dist * 180 / Math.PI;
          dist = dist * 60 * 1.1515;
  
          return unitOfLength.ConvertFromMiles(dist);
      }
  }
  
  public class UnitOfLength
  {
      public static UnitOfLength Kilometers = new UnitOfLength(1.609344);
      public static UnitOfLength NauticalMiles = new UnitOfLength(0.8684);
      public static UnitOfLength Miles = new UnitOfLength(1);
  
      private readonly double _fromMilesFactor;
  
      private UnitOfLength(double fromMilesFactor)
      {
          _fromMilesFactor = fromMilesFactor;
      }
  
      public double ConvertFromMiles(double input)
      {
          return input*_fromMilesFactor;
      }
  } 
  

Answer 4

Here is the JavaScript version guys and gals

function distanceTo(lat1, lon1, lat2, lon2, unit) {
      var rlat1 = Math.PI * lat1/180
      var rlat2 = Math.PI * lat2/180
      var rlon1 = Math.PI * lon1/180
      var rlon2 = Math.PI * lon2/180
      var theta = lon1-lon2
      var rtheta = Math.PI * theta/180
      var dist = Math.sin(rlat1) * Math.sin(rlat2) + Math.cos(rlat1) * Math.cos(rlat2) * Math.cos(rtheta);
      dist = Math.acos(dist)
      dist = dist * 180/Math.PI
      dist = dist * 60 * 1.1515
      if (unit=="K") { dist = dist * 1.609344 }
      if (unit=="N") { dist = dist * 0.8684 }
      return dist
}

Answer 5

And here, for those still not satisfied, the original code from .NET-Frameworks GeoCoordinate class, refactored into a standalone method:

public double GetDistance(double longitude, double latitude, double otherLongitude, double otherLatitude)
{
    var d1 = latitude * (Math.PI / 180.0);
    var num1 = longitude * (Math.PI / 180.0);
    var d2 = otherLatitude * (Math.PI / 180.0);
    var num2 = otherLongitude * (Math.PI / 180.0) - num1;
    var d3 = Math.Pow(Math.Sin((d2 - d1) / 2.0), 2.0) + Math.Cos(d1) * Math.Cos(d2) * Math.Pow(Math.Sin(num2 / 2.0), 2.0);

    return 6376500.0 * (2.0 * Math.Atan2(Math.Sqrt(d3), Math.Sqrt(1.0 - d3)));
}

Answer 6

Earth mean radius = 6,371km = 3958.76 miles

Rather than use var I suggest you use double, just to be explicit.