// The method iIsInside has four parameters of type Position.
   // The first three are those for the vertices of the triangle.
   // The last parameter is for the point.
   // It returns true if and only if the point is inside the triangle.
   private static boolean iIsInside(final Position pPosition1,
                                    final Position pPosition2,
                                    final Position pPosition3,
                                    final Position pPoint)
   {
      final double x1 = pPosition1.getLongitude().getDistance(); 
      final double y1 = pPosition1.getLatitude().getDistance(); 
      final double x2 = pPosition2.getLongitude().getDistance(); 
      final double y2 = pPosition2.getLatitude().getDistance();
      final double x3 = pPosition3.getLongitude().getDistance();
      final double y3 = pPosition3.getLatitude().getDistance();
      final double x0 =     pPoint.getLongitude().getDistance();
      final double y0 =     pPoint.getLatitude().getDistance();
      // thanks to Horst Kraemer for the clever stuff from here on
      final double  d = (x2-x1)*(y3-y1) - (y2-y1)*(x3-x1);
      final double  a = (x0-x1)*(y3-y1) - (y0-y1)*(x3-x1);
      final double  b = (x2-x1)*(y0-y1) - (y2-y1)*(x0-x1);
      if (d==0)
      {
         return true;
      }
      return 0<=a/d && 0<=b/d && a/d+b/d<=1;
   }