}
  

//Computes the ellipsoidal distance from the equator to a point at a given latitude.
//phi - Latitude of the point, in radians.
//sm_a - Ellipsoid model major axis.
//sm_b - Ellipsoid model minor axis.

//Returns: The ellipsoidal distance of the point from the equator, in meters.

  function ArcLengthOfMeridian (phi)
  {
   var alpha, beta, gamma, delta, epsilon, n;
   var result;

 //Precalculate n
   n = (sm_a - sm_b) / (sm_a + sm_b);
 
 //Precalculate alpha
   alpha = ((sm_a + sm_b) / 2.0) * (1.0 + (Math.pow (n, 2.0) / 4.0) + (Math.pow (n, 4.0) / 64.0));

 //Precalculate beta
   beta = (-3.0 * n / 2.0) + (9.0 * Math.pow (n, 3.0) / 16.0) + (-3.0 * Math.pow (n, 5.0) / 32.0);

 //Precalculate gamma
   gamma = (15.0 * Math.pow (n, 2.0) / 16.0) + (-15.0 * Math.pow (n, 4.0) / 32.0);
    
 //Precalculate delta
   delta = (-35.0 * Math.pow (n, 3.0) / 48.0) + (105.0 * Math.pow (n, 5.0) / 256.0);
    
 //Precalculate epsilon
   epsilon = (315.0 * Math.pow (n, 4.0) / 512.0);
    
 //Now calculate the sum of the series and return
   result = alpha * (phi + (beta * Math.sin (2.0 * phi)) + (gamma * Math.sin (4.0 * phi)) + (delta * Math.sin (6.0 * phi)) + (epsilon * Math.sin (8.0 * phi)));

   return result;
  }  
  
//Determines the central meridian for the given UTM zone.
//Inputs:zone - An integer value designating the UTM zone, range [1,60].

//Returns:The central meridian for the given UTM zone, in radians, or zero
//        if the UTM zone parameter is outside the range [1,60].
//        Range of the central meridian is the radian equivalent of [-177,+177].

  function UTMCentralMeridian(zone)
  {
   var cmeridian;
   cmeridian = DegToRad (-183.0 + (zone * 6.0));
   
   return cmeridian;
  }   
  
  
  function getDD(x,y,lon,lat)
  {
   var latlon = new Array(2);
   var zone,southhemi;

   var zone = Math.floor ((lon + 180.0) / 6) + 1;
   
   if (lat < 0)
    southhemi = true;
   else
    southhemi = false;

   UTMXYToLatLon (x, y, zone, southhemi, latlon);

   latlon[0] = RadToDeg (latlon[0]);
   latlon[1] = RadToDeg (latlon[1]);
    
   return latlon;
  }   
  

//Converts x and y coordinates in the Universal Transverse Mercator
//projection to a latitude/longitude pair.

//Inputs:
//x - The easting of the point, in meters.
//y - The northing of the point, in meters.
//zone - The UTM zone in which the point lies.
//southhemi - True if the point is in the southern hemisphere;
//            false otherwise.

//Outputs:latlon - A 2-element array containing the latitude and longitude of the point, in radians.

//Returns:The function does not return a value.

  function UTMXYToLatLon (x, y, zone, southhemi, latlon)
  {
   var cmeridian;
        	
   x -= 500000.0;
   x /= UTMScaleFactor;
        	
 //If in southern hemisphere, adjust y accordingly. */
   if (southhemi)
    y -= 10000000.0;
        		
   y /= UTMScaleFactor;
        
   cmeridian = UTMCentralMeridian (zone);
   MapXYToLatLon (x, y, cmeridian, latlon);
        	
   return;
  }
  
  
//Converts x and y coordinates in the Transverse Mercator projection to
//a latitude/longitude pair.  Note that Transverse Mercator is not
//the same as UTM; a scale factor is required to convert between them.

//Inputs:
//x - The easting of the point, in meters.
//y - The northing of the point, in meters.
//lambda0 - Longitude of the central meridian to be used, in radians.

//Outputs:philambda - A 2-element containing the latitude and longitude in radians.

//Returns:The function does not return a value.

//Remarks:
///The local variables Nf, nuf2, tf, and tf2 serve the same purpose as
//N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
//to the footpoint latitude phif.

//x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and to optimize computations.

  function MapXYToLatLon (x, y, lambda0, philambda)
  {
   var phif, Nf, Nfpow, nuf2, ep2, tf, tf2, tf4, cf;
   var x1frac, x2frac, x3frac, x4frac, x5frac, x6frac, x7frac, x8frac;
   var x2poly, x3poly, x4poly, x5poly, x6poly, x7poly, x8poly;
    	
 //Get the value of phif, the footpoint latitude
 //---------------------------------------------
   phif = FootpointLatitude (y);
   	
 //Precalculate ep2
 //----------------
   ep2 = (Math.pow (sm_a, 2.0) - Math.pow (sm_b, 2.0)) / Math.pow (sm_b, 2.0);
   	
 //Precalculate cos (phif)
 //-----------------------
   cf = Math.cos (phif);
   	
 //Precalculate nuf2
 //-----------------
   nuf2 = ep2 * Math.pow (cf, 2.0);
   	
 //Precalculate Nf and initialize Nfpow
 //------------------------------------
   Nf = Math.pow (sm_a, 2.0) / (sm_b * Math.sqrt (1 + nuf2));
   Nfpow = Nf;
   	
 //Precalculate tf
 //---------------
   tf = Math.tan (phif);
   tf2 = tf * tf;
   tf4 = tf2 * tf2;
   
 //Precalculate fractional coefficients for x**n in the equations
 //below to simplify the expressions for latitude and longitude
 //------------------------------------------------------------
   x1frac = 1.0 / (Nfpow * cf);
 
 //now equals Nf**2)
 //-----------------  
   Nfpow *= Nf;
   x2frac = tf / (2.0 * Nfpow);
 
 //now equals Nf**3)  
 //-----------------
   Nfpow *= Nf;
   x3frac = 1.0 / (6.0 * Nfpow * cf);
 
 //now equals Nf**4)
 //-----------------  
   Nfpow *= Nf;
   x4frac = tf / (24.0 * Nfpow);
 
 //now equals Nf**5)
 //-----------------  
   Nfpow *= Nf;
   x5frac = 1.0 / (120.0 * Nfpow * cf);
 
 //now equals Nf**6)
 //-----------------  
   Nfpow *= Nf;
   x6frac = tf / (720.0 * Nfpow);
 
 //now equals Nf**7)
 //-----------------  
   Nfpow *= Nf;
   x7frac = 1.0 / (5040.0 * Nfpow * cf);
 
 //now equals Nf**8)  
 //-----------------
   Nfpow *= Nf;
   x8frac = tf / (40320.0 * Nfpow);
   
 //Precalculate polynomial coefficients for x**n.
 //x**1 does not have a polynomial coefficient
 //-------------------------------------------
   x2poly = -1.0 - nuf2;
   
   x3poly = -1.0 - 2 * tf2 - nuf2;
   
   x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 *nuf2) - 9.0 * tf2 * (nuf2 * nuf2);
   
   x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
   
   x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2;
         
   x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
         
   x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
         	
 //Calculate latitude
 //------------------
   philambda[0] = phif + x2frac * x2poly * (x * x)
               	+ x4frac * x4poly * Math.pow (x, 4.0)
               	+ x6frac * x6poly * Math.pow (x, 6.0)
         	      + x8frac * x8poly * Math.pow (x, 8.0);
         	
 //Calculate longitude
 //-------------------
   philambda[1] = lambda0 + x1frac * x
               	+ x3frac * x3poly * Math.pow (x, 3.0)
               	+ x5frac * x5poly * Math.pow (x, 5.0)
         	      + x7frac * x7poly * Math.pow (x, 7.0);
         	
   return;
  }  

//Computes the footpoint latitude for use in converting transverse
//Mercator coordinates to ellipsoidal coordinates.

//Inputs:y - The UTM northing coordinate, in meters.

//Returns:The footpoint latitude, in radians.

  function FootpointLatitude(y)
  {
   var y_, alpha_, beta_, gamma_, delta_, epsilon_, n;
   var result;
        
 //Precalculate n
 //--------------
   n = (sm_a - sm_b) / (sm_a + sm_b);
 	
 //Precalculate alpha_
 //-------------------
   alpha_ = ((sm_a + sm_b) / 2.0) * (1 + (Math.pow (n, 2.0) / 4) + (Math.pow (n, 4.0) / 64));
 
 //Precalculate y_
 //---------------
   y_ = y / alpha_;
 
 //Precalculate beta_
 //------------------
   beta_ = (3.0 * n / 2.0) + (-27.0 * Math.pow (n, 3.0) / 32.0) + (269.0 * Math.pow (n, 5.0) / 512.0);
 
 //Precalculate gamma_
 //-------------------
   gamma_ = (21.0 * Math.pow (n, 2.0) / 16.0) + (-55.0 * Math.pow (n, 4.0) / 32.0);
 	
 //Precalculate delta_
 //-------------------
   delta_ = (151.0 * Math.pow (n, 3.0) / 96.0) + (-417.0 * Math.pow (n, 5.0) / 128.0);
 	
 //Precalculate epsilon_
 //---------------------
   epsilon_ = (1097.0 * Math.pow (n, 4.0) / 512.0);
 	
 //Now calculate the sum of the series
 //-----------------------------------
   result = y_ + (beta_ * Math.sin (2.0 * y_))
          + (gamma_ * Math.sin (4.0 * y_))
          + (delta_ * Math.sin (6.0 * y_))
          + (epsilon_ * Math.sin (8.0 * y_));
 
   return result;
  }