Calculate distance and bearing between two positions in C#

Published 04 Feb 2011

I am currently working on a GPS-based web application, that lets a mobile device post its position to the app, which then replies with nearby items of interest.

Despite extensive Googling, I was not able to find a nice C# implementation that lets me determine the distance between the user’s coordinate and the coordinates of the various database items…until I found this one.

Although wowi’s implementation (thank you SO much for publishing it btw) is good, it uses a biiiig class and one enum. Being a solid kind of guy (oh yeah), I felt like breaking it up into smaller parts and introduce some of interfaces as well.

Step 1 - Break the code up into smaller classes

I first extracted the angle/radian conversion logic into a tiny AngleConverter class (since this logic never changes, it could be a static util class as well):

public class AngleConverter
{
   public double ConvertDegreesToRadians(double angle)
   {
      return Math.PI * angle / 180.0;
   }	

   public double ConvertRadiansToDegrees(double angle)
   {
      return 180.0 * angle / Math.PI;
   }
}

I also created a DistanceConverter class as well (could also be static, since the implementation should never change):

public class DistanceConverter
{
   public double ConvertMilesToKilometers(double miles)
   {
      return miles * 1.609344;
   }	

   public double ConvertKilometersToMiles(double kilometers)
   {
      return kilometers * 0.621371192;
   }
}

Next, I extracted the DistanceType enum into a separate file…

public enum DistanceType
{
   Miles = 0,
   Kilometers = 1
}

and created a simple Position data class (could also be struct), that only has a Latitude and a Longitude property, but no other functionality:

public class Position
{
   public Position(double latitude, double longitude)
   {
      Latitude = latitude;
      Longitude = longitude;
   }
 
   public double Latitude { get; set; }
   public double Longitude { get; set; }
}

Step 2 - Define interfaces

With all these small classes, the previously big class only contains calculation methods, which now can use Position instead of a latitude/longitude tuple.

Before adjusting the class, let’s define interfaces that it should implement (to make it possible to switch out any implementation later, if needed):

public interface IBearingCalculator
{
   double CalculateBearing(Position position1, Position position2);
}

public interface IDistanceCalculator
{
   double CalculateDistance(Position position1, Position position2, DistanceType distanceType1);
}

public interface IRhumbBearingCalculator
{
   double CalculateRhumbBearing(Position position1, Position position2);
}

public interface IRhumbDistanceCalculator
{
   double CalculateRhumbDistance(Position position1, Position position2, DistanceType distanceType);
}

Step 3 - Implement the interfaces

With all these small bits and pieces in place, the class can be set to implement the interfaces as such:

public class PositionHandler : IBearingCalculator, IDistanceCalculator, IRhumbBearingCalculator, IRhumbDistanceCalculator
{
   private readonly AngleConverter angleConverter;

   public PositionHandler()
   {
      angleConverter = new AngleConverter();
   }

   public static double EarthRadiusInKilometers { get { return 6367.0; } }
   public static double EarthRadiusInMiles { get { return 3956.0; } }

   public double CalculateBearing(Position position1, Position position2)
   {
      var lat1 = angleConverter.ConvertDegreesToRadians(position1.Latitude);
      var lat2 = angleConverter.ConvertDegreesToRadians(position2.Latitude);
      var long1 = angleConverter.ConvertDegreesToRadians(position2.Longitude);
      var long2 = angleConverter.ConvertDegreesToRadians(position1.Longitude);
      var dLon = long1 - long2;

      var y = Math.Sin(dLon) * Math.Cos(lat2);
      var x = Math.Cos(lat1) * Math.Sin(lat2) - Math.Sin(lat1) * Math.Cos(lat2) * Math.Cos(dLon);
      var brng = Math.Atan2(y, x);

      return (angleConverter.ConvertRadiansToDegrees(brng) + 360) % 360;
   }

   public double CalculateDistance(Position position1, Position position2, DistanceType distanceType)
   {
      var R = (distanceType == DistanceType.Miles) ? EarthRadiusInMiles : EarthRadiusInKilometers;
      var dLat = angleConverter.ConvertDegreesToRadians(position2.Latitude) - angleConverter.ConvertDegreesToRadians(position1.Latitude);
      var dLon = angleConverter.ConvertDegreesToRadians(position2.Longitude) - angleConverter.ConvertDegreesToRadians(position1.Longitude);
      var a = Math.Sin(dLat / 2) * Math.Sin(dLat / 2) + Math.Cos(angleConverter.ConvertDegreesToRadians(position1.Latitude)) * Math.Cos(angleConverter.ConvertDegreesToRadians(position2.Latitude)) * Math.Sin(dLon / 2) * Math.Sin(dLon / 2);
      var c = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1 - a));
      var distance = c * R;

      return Math.Round(distance, 2);
   }

   public double CalculateRhumbBearing(Position position1, Position position2)
   {
      var lat1 = angleConverter.ConvertDegreesToRadians(position1.Latitude);
      var lat2 = angleConverter.ConvertDegreesToRadians(position2.Latitude);
      var dLon = angleConverter.ConvertDegreesToRadians(position2.Longitude - position1.Longitude);

      var dPhi = Math.Log(Math.Tan(lat2 / 2 + Math.PI / 4) / Math.Tan(lat1 / 2 + Math.PI / 4));
      if (Math.Abs(dLon) > Math.PI) dLon = (dLon > 0) ? -(2 * Math.PI - dLon) : (2 * Math.PI + dLon);
      var brng = Math.Atan2(dLon, dPhi);

      return (angleConverter.ConvertRadiansToDegrees(brng) + 360) % 360;
   }

   public double CalculateRhumbDistance(Position position1, Position position2, DistanceType distanceType)
   {
      var R = (distanceType == DistanceType.Miles) ? EarthRadiusInMiles : EarthRadiusInKilometers;
      var lat1 = angleConverter.ConvertDegreesToRadians(position1.Latitude);
      var lat2 = angleConverter.ConvertDegreesToRadians(position2.Latitude);
      var dLat = angleConverter.ConvertDegreesToRadians(position2.Latitude - position1.Latitude);
      var dLon = angleConverter.ConvertDegreesToRadians(Math.Abs(position2.Longitude - position1.Longitude));

      var dPhi = Math.Log(Math.Tan(lat2 / 2 + Math.PI / 4) / Math.Tan(lat1 / 2 + Math.PI / 4));
      var q = Math.Cos(lat1);
      if (dPhi != 0) q = dLat / dPhi;  // E-W line gives dPhi=0
      // if dLon over 180° take shorter rhumb across 180° meridian:
      if (dLon > Math.PI) dLon = 2 * Math.PI - dLon;
      var dist = Math.Sqrt(dLat * dLat + q * q * dLon * dLon) * R;

      return dist;
   }
}

That’s it!

Once again, a big thanks to wowi, who posted the original implementation. If you like this implementation, you owe it all to wowi :)