path: root/src/js/OpenLayers.Projection.OrdnanceSurvey.js

/**
 * OpenLayers OSGB Grid Projection Transformations
 *
 * Conversion to OpenLayers by Thomas Wood (grand.edgemaster@gmail.com)
 *
 * this program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 * 
 * this program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 * 
 * --------------------------------------------------------------------------- 
 *
 * PLEASE DO NOT HOTLINK THIS, save this onto your own server
 *  - I cannot guarantee this file will remain here forever.
 *
 * ---------------------------------------------------------------------------
 * 
 * Credits:
 * Based from the geotools js library by Paul Dixon
 * GeoTools javascript coordinate transformations
 * http://files.dixo.net/geotools.html
 *
 * Portions of this file copyright (c)2005 Paul Dixon (paul@elphin.com)
 *
 * The algorithm used by the script for WGS84-OSGB36 conversions is derived 
 * from an OSGB spreadsheet (www.gps.gov.uk) with permission. This has been
 * adapted into Perl by Ian Harris, and into PHP by Barry Hunter. Conversion
 * accuracy is in the order of 7m for 90% of Great Britain, and should be 
 * be similar to the conversion made by a typical GPSr
 *
 */
 
OpenLayers.Projection.OS = {

    /**
     * Method: projectForwardBritish
     * Given an object with x and y properties in EPSG:4326, modify the x,y
     * properties on the object to be the OSGB36 (transverse mercator)
     * projected coordinates.
     *
     * Parameters:
     * point - {Object} An object with x and y properties. 
     * 
     * Returns:
     * {Object} The point, with the x and y properties transformed to spherical
     * mercator.
     */
    projectForwardBritish: function(point) {
        var x1 = OpenLayers.Projection.OS.Lat_Long_H_to_X(point.y,point.x,0,6378137.00,6356752.313);
        var y1 = OpenLayers.Projection.OS.Lat_Long_H_to_Y(point.y,point.x,0,6378137.00,6356752.313);
        var z1 = OpenLayers.Projection.OS.Lat_H_to_Z     (point.y,        0,6378137.00,6356752.313);

        var x2 = OpenLayers.Projection.OS.Helmert_X(x1,y1,z1,-446.448,-0.2470,-0.8421,20.4894);
        var y2 = OpenLayers.Projection.OS.Helmert_Y(x1,y1,z1, 125.157,-0.1502,-0.8421,20.4894);
        var z2 = OpenLayers.Projection.OS.Helmert_Z(x1,y1,z1,-542.060,-0.1502,-0.2470,20.4894);

        var lat2 = OpenLayers.Projection.OS.XYZ_to_Lat (x2,y2,z2,6377563.396,6356256.910);
        var lon2 = OpenLayers.Projection.OS.XYZ_to_Long(x2,y2);

        point.x = OpenLayers.Projection.OS.Lat_Long_to_East (lat2,lon2,6377563.396,6356256.910,400000,0.999601272,49.00000,-2.00000);
        point.y = OpenLayers.Projection.OS.Lat_Long_to_North(lat2,lon2,6377563.396,6356256.910,400000,-100000,0.999601272,49.00000,-2.00000);

        return point;
    },
    
    /**
     * Method: projectInverseBritish
     * Given an object with x and y properties in OSGB36 (transverse mercator),
     * modify the x,y properties on the object to be the unprojected coordinates.
     *
     * Parameters:
     * point - {Object} An object with x and y properties. 
     * 
     * Returns:
     * {Object} The point, with the x and y properties transformed from
     * OSGB36 to unprojected coordinates..
     */
    projectInverseBritish: function(point) {
        var lat1 = OpenLayers.Projection.OS.E_N_to_Lat (point.x,point.y,6377563.396,6356256.910,400000,-100000,0.999601272,49.00000,-2.00000);
        var lon1 = OpenLayers.Projection.OS.E_N_to_Long(point.x,point.y,6377563.396,6356256.910,400000,-100000,0.999601272,49.00000,-2.00000);

        var x1 = OpenLayers.Projection.OS.Lat_Long_H_to_X(lat1,lon1,0,6377563.396,6356256.910);
        var y1 = OpenLayers.Projection.OS.Lat_Long_H_to_Y(lat1,lon1,0,6377563.396,6356256.910);
        var z1 = OpenLayers.Projection.OS.Lat_H_to_Z     (lat1,     0,6377563.396,6356256.910);

        var x2 = OpenLayers.Projection.OS.Helmert_X(x1,y1,z1,446.448 ,0.2470,0.8421,-20.4894);
        var y2 = OpenLayers.Projection.OS.Helmert_Y(x1,y1,z1,-125.157,0.1502,0.8421,-20.4894);
        var z2 = OpenLayers.Projection.OS.Helmert_Z(x1,y1,z1,542.060 ,0.1502,0.2470,-20.4894);

        var lat = OpenLayers.Projection.OS.XYZ_to_Lat(x2,y2,z2,6378137.000,6356752.313);
        var lon = OpenLayers.Projection.OS.XYZ_to_Long(x2,y2);        
        
        point.x = lon;
        point.y = lat;
        return point;
    },
  
    goog2osgb: function(point) {
        return OpenLayers.Projection.OS.projectForwardBritish(OpenLayers.Layer.SphericalMercator.projectInverse(point));
    },
  
    osgb2goog: function(point) {
        return OpenLayers.Layer.SphericalMercator.projectForward(OpenLayers.Projection.OS.projectInverseBritish(point));
    },
    
    /*****
     * Mathematical functions
     *****/
    E_N_to_Lat: function(East, North, a, b, e0, n0, f0, PHI0, LAM0) {
      //Un-project Transverse Mercator eastings and northings back to latitude.
      //eastings (East) and northings (North) in meters; _
      //ellipsoid axis dimensions (a & b) in meters; _
      //eastings (e0) and northings (n0) of false origin in meters; _
      //central meridian scale factor (f0) and _
      //latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.

      //Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI0 = PHI0 * (Pi / 180);
        var RadLAM0 = LAM0 * (Pi / 180);

      //Compute af0, bf0, e squared (e2), n and Et
        var af0 = a * f0;
        var bf0 = b * f0;
        var e2 = (Math.pow(af0,2) - Math.pow(bf0,2)) / Math.pow(af0,2);
        var n = (af0 - bf0) / (af0 + bf0);
        var Et = East - e0;

      //Compute initial value for latitude (PHI) in radians
        var PHId = OpenLayers.Projection.OS.InitialLat(North, n0, af0, RadPHI0, n, bf0);
        
      //Compute nu, rho and eta2 using value for PHId
        var nu = af0 / (Math.sqrt(1 - (e2 * ( Math.pow(Math.sin(PHId),2)))));
        var rho = (nu * (1 - e2)) / (1 - (e2 * Math.pow(Math.sin(PHId),2)));
        var eta2 = (nu / rho) - 1;
        
      //Compute Latitude
        var VII = (Math.tan(PHId)) / (2 * rho * nu);
        var VIII = ((Math.tan(PHId)) / (24 * rho * Math.pow(nu,3))) * (5 + (3 * (Math.pow(Math.tan(PHId),2))) + eta2 - (9 * eta2 * (Math.pow(Math.tan(PHId),2))));
        var IX = ((Math.tan(PHId)) / (720 * rho * Math.pow(nu,5))) * (61 + (90 * ((Math.tan(PHId)) ^ 2)) + (45 * (Math.pow(Math.tan(PHId),4))));
        
        var E_N_to_Lat = (180 / Pi) * (PHId - (Math.pow(Et,2) * VII) + (Math.pow(Et,4) * VIII) - ((Et ^ 6) * IX));
  
        return (E_N_to_Lat);
    },

    E_N_to_Long: function(East, North, a, b, e0, n0, f0, PHI0, LAM0) {
      //Un-project Transverse Mercator eastings and northings back to longitude.
      //eastings (East) and northings (North) in meters; _
      //ellipsoid axis dimensions (a & b) in meters; _
      //eastings (e0) and northings (n0) of false origin in meters; _
      //central meridian scale factor (f0) and _
      //latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.

      //Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI0 = PHI0 * (Pi / 180);
        var RadLAM0 = LAM0 * (Pi / 180);

      //Compute af0, bf0, e squared (e2), n and Et
        var af0 = a * f0;
        var bf0 = b * f0;
        var e2 = (Math.pow(af0,2) - Math.pow(bf0,2)) / Math.pow(af0,2);
        var n = (af0 - bf0) / (af0 + bf0);
        var Et = East - e0;

      //Compute initial value for latitude (PHI) in radians
        var PHId = OpenLayers.Projection.OS.InitialLat(North, n0, af0, RadPHI0, n, bf0);
        
      //Compute nu, rho and eta2 using value for PHId
         var nu = af0 / (Math.sqrt(1 - (e2 * (Math.pow(Math.sin(PHId),2)))));
        var rho = (nu * (1 - e2)) / (1 - (e2 * Math.pow(Math.sin(PHId),2)));
        var eta2 = (nu / rho) - 1;

      //Compute Longitude
        var X = (Math.pow(Math.cos(PHId),-1)) / nu;
        var XI = ((Math.pow(Math.cos(PHId),-1)) / (6 * Math.pow(nu,3))) * ((nu / rho) + (2 * (Math.pow(Math.tan(PHId),2))));
        var XII = ((Math.pow(Math.cos(PHId),-1)) / (120 * Math.pow(nu,5))) * (5 + (28 * (Math.pow(Math.tan(PHId),2))) + (24 * (Math.pow(Math.tan(PHId),4))));
        var XIIA = ((Math.pow(Math.cos(PHId),-1)) / (5040 * Math.pow(nu,7))) * (61 + (662 * (Math.pow(Math.tan(PHId),2))) + (1320 * (Math.pow(Math.tan(PHId),4))) + (720 * (Math.pow(Math.tan(PHId),6))));

        var E_N_to_Long = (180 / Pi) * (RadLAM0 + (Et * X) - (Math.pow(Et,3) * XI) + (Math.pow(Et,5) * XII) - (Math.pow(Et,7) * XIIA));
  
      return E_N_to_Long;
    },

    InitialLat: function(North, n0, afo, PHI0, n, bfo) {
      //Compute initial value for Latitude (PHI) IN RADIANS.
      //northing of point (North) and northing of false origin (n0) in meters; _
      //semi major axis multiplied by central meridian scale factor (af0) in meters; _
      //latitude of false origin (PHI0) IN RADIANS; _
      //n (computed from a, b and f0) and _
      //ellipsoid semi major axis multiplied by central meridian scale factor (bf0) in meters.

      //First PHI value (PHI1)
         var PHI1 = ((North - n0) / afo) + PHI0;
        
      //Calculate M
        var M = OpenLayers.Projection.OS.Marc(bfo, n, PHI0, PHI1);
        
      //Calculate new PHI value (PHI2)
        var PHI2 = ((North - n0 - M) / afo) + PHI1;
        
      //Iterate to get final value for InitialLat
      while (Math.abs(North - n0 - M) > 0.00001) 
      {
            PHI2 = ((North - n0 - M) / afo) + PHI1;
            M = OpenLayers.Projection.OS.Marc(bfo, n, PHI0, PHI2);
            PHI1 = PHI2;
      }    
        return PHI2;
    },

    Lat_Long_H_to_X: function(PHI, LAM, H, a, b) {
      // Convert geodetic coords lat (PHI), long (LAM) and height (H) to cartesian X coordinate.
      // Input: - _
      //    Latitude (PHI)& Longitude (LAM) both in decimal degrees; _
      //  Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.

      // Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI = PHI * (Pi / 180);
        var RadLAM = LAM * (Pi / 180);

      // Compute eccentricity squared and nu
        var e2 = (Math.pow(a,2) - Math.pow(b,2)) / Math.pow(a,2);
        var V = a / (Math.sqrt(1 - (e2 * (  Math.pow(Math.sin(RadPHI),2)))));

      // Compute X
        return (V + H) * (Math.cos(RadPHI)) * (Math.cos(RadLAM));
    },


    Lat_Long_H_to_Y: function(PHI, LAM, H, a, b) {
      // Convert geodetic coords lat (PHI), long (LAM) and height (H) to cartesian Y coordinate.
      // Input: - _
      // Latitude (PHI)& Longitude (LAM) both in decimal degrees; _
      // Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.

      // Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI = PHI * (Pi / 180);
        var RadLAM = LAM * (Pi / 180);

      // Compute eccentricity squared and nu
        var e2 = (Math.pow(a,2) - Math.pow(b,2)) / Math.pow(a,2);
        var V = a / (Math.sqrt(1 - (e2 * (  Math.pow(Math.sin(RadPHI),2))) ));

      // Compute Y
        return (V + H) * (Math.cos(RadPHI)) * (Math.sin(RadLAM));
    },


    Lat_H_to_Z: function(PHI, H, a, b) {
      // Convert geodetic coord components latitude (PHI) and height (H) to cartesian Z coordinate.
      // Input: - _
      //    Latitude (PHI) decimal degrees; _
      // Ellipsoidal height (H) and ellipsoid axis dimensions (a & b) all in meters.

      // Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI = PHI * (Pi / 180);

      // Compute eccentricity squared and nu
        var e2 = (Math.pow(a,2) - Math.pow(b,2)) / Math.pow(a,2);
        var V = a / (Math.sqrt(1 - (e2 * (  Math.pow(Math.sin(RadPHI),2)) )));

      // Compute X
        return ((V * (1 - e2)) + H) * (Math.sin(RadPHI));
    },


    Helmert_X: function(X,Y,Z,DX,Y_Rot,Z_Rot,s)  {

      // (X, Y, Z, DX, Y_Rot, Z_Rot, s)
      // Computed Helmert transformed X coordinate.
      // Input: - _
      //    cartesian XYZ coords (X,Y,Z), X translation (DX) all in meters ; _
      // Y and Z rotations in seconds of arc (Y_Rot, Z_Rot) and scale in ppm (s).

      // Convert rotations to radians and ppm scale to a factor
      var Pi = 3.14159265358979;
      var sfactor = s * 0.000001;

      var RadY_Rot = (Y_Rot / 3600) * (Pi / 180);

      var RadZ_Rot = (Z_Rot / 3600) * (Pi / 180);

      //Compute transformed X coord
        return  (X + (X * sfactor) - (Y * RadZ_Rot) + (Z * RadY_Rot) + DX);
    },


    Helmert_Y: function(X,Y,Z,DY,X_Rot,Z_Rot,s) {
      // Computed Helmert transformed Y coordinate.
      // Input: - _
      //    cartesian XYZ coords (X,Y,Z), Y translation (DY) all in meters ; _
      //  X and Z rotations in seconds of arc (X_Rot, Z_Rot) and scale in ppm (s).

      // Convert rotations to radians and ppm scale to a factor
      var Pi = 3.14159265358979;
      var sfactor = s * 0.000001;
      var RadX_Rot = (X_Rot / 3600) * (Pi / 180);
      var RadZ_Rot = (Z_Rot / 3600) * (Pi / 180);

      // Compute transformed Y coord
      return (X * RadZ_Rot) + Y + (Y * sfactor) - (Z * RadX_Rot) + DY;
    },



    Helmert_Z: function(X, Y, Z, DZ, X_Rot, Y_Rot, s) {
      // Computed Helmert transformed Z coordinate.
      // Input: - _
      //    cartesian XYZ coords (X,Y,Z), Z translation (DZ) all in meters ; _
      // X and Y rotations in seconds of arc (X_Rot, Y_Rot) and scale in ppm (s).
      // 
      // Convert rotations to radians and ppm scale to a factor
      var Pi = 3.14159265358979;
      var sfactor = s * 0.000001;
      var RadX_Rot = (X_Rot / 3600) * (Pi / 180);
      var RadY_Rot = (Y_Rot / 3600) * (Pi / 180);

      // Compute transformed Z coord
      return (-1 * X * RadY_Rot) + (Y * RadX_Rot) + Z + (Z * sfactor) + DZ;
    } ,

    XYZ_to_Lat: function(X, Y, Z, a, b)  {
      // Convert XYZ to Latitude (PHI) in Dec Degrees.
      // Input: - _
      // XYZ cartesian coords (X,Y,Z) and ellipsoid axis dimensions (a & b), all in meters.

      // this FUNCTION REQUIRES THE "Iterate_XYZ_to_Lat" FUNCTION
      // this FUNCTION IS CALLED BY THE "XYZ_to_H" FUNCTION

        var RootXYSqr = Math.sqrt(Math.pow(X,2) + Math.pow(Y,2));
        var e2 = (Math.pow(a,2) - Math.pow(b,2)) / Math.pow(a,2);
        var PHI1 = Math.atan2(Z , (RootXYSqr * (1 - e2)) );
        
        var PHI = OpenLayers.Projection.OS.Iterate_XYZ_to_Lat(a, e2, PHI1, Z, RootXYSqr);
        
        var Pi = 3.14159265358979;
        
        return PHI * (180 / Pi);
    },


    Iterate_XYZ_to_Lat: function(a, e2, PHI1, Z, RootXYSqr) {
      // Iteratively computes Latitude (PHI).
      // Input: - _
      //    ellipsoid semi major axis (a) in meters; _
      //    eta squared (e2); _
      //    estimated value for latitude (PHI1) in radians; _
      //    cartesian Z coordinate (Z) in meters; _
      // RootXYSqr computed from X & Y in meters.

      // this FUNCTION IS CALLED BY THE "XYZ_to_PHI" FUNCTION
      // this FUNCTION IS ALSO USED ON IT'S OWN IN THE _
      // "Projection and Transformation Calculations.xls" SPREADSHEET


        var V = a / (Math.sqrt(1 - (e2 * Math.pow(Math.sin(PHI1),2))));
        var PHI2 = Math.atan2((Z + (e2 * V * (Math.sin(PHI1)))) , RootXYSqr);
        
        while (Math.abs(PHI1 - PHI2) > 0.000000001) {
            PHI1 = PHI2;
            V = a / (Math.sqrt(1 - (e2 * Math.pow(Math.sin(PHI1),2))));
            PHI2 = Math.atan2((Z + (e2 * V * (Math.sin(PHI1)))) , RootXYSqr);
        }

        return PHI2;
    },


    XYZ_to_Long: function (X, Y) {
      // Convert XYZ to Longitude (LAM) in Dec Degrees.
      // Input: - _
      // X and Y cartesian coords in meters.

        var Pi = 3.14159265358979;
        return Math.atan2(Y , X) * (180 / Pi);
    },

    Marc: function (bf0, n, PHI0, PHI) {
      //Compute meridional arc.
      //Input: - _
      // ellipsoid semi major axis multiplied by central meridian scale factor (bf0) in meters; _
      // n (computed from a, b and f0); _
      // lat of false origin (PHI0) and initial or final latitude of point (PHI) IN RADIANS.

      //this FUNCTION IS CALLED BY THE - _
      // "Lat_Long_to_North" and "InitialLat" FUNCTIONS
      // this FUNCTION IS ALSO USED ON IT'S OWN IN THE "Projection and Transformation Calculations.xls" SPREADSHEET

        return bf0 * (((1 + n + ((5 / 4) * Math.pow(n,2)) + ((5 / 4) * Math.pow(n,3))) * (PHI - PHI0)) - (((3 * n) + (3 * Math.pow(n,2)) + ((21 / 8) * Math.pow(n,3))) * (Math.sin(PHI - PHI0)) * (Math.cos(PHI + PHI0))) + ((((15 / 8
      ) * Math.pow(n,2)) + ((15 / 8) * Math.pow(n,3))) * (Math.sin(2 * (PHI - PHI0))) * (Math.cos(2 * (PHI + PHI0)))) - (((35 / 24) * Math.pow(n,3)) * (Math.sin(3 * (PHI - PHI0))) * (Math.cos(3 * (PHI + PHI0)))));
    },

    Lat_Long_to_East: function (PHI, LAM, a, b, e0, f0, PHI0, LAM0) {
      //Project Latitude and longitude to Transverse Mercator eastings.
      //Input: - _
      //    Latitude (PHI) and Longitude (LAM) in decimal degrees; _
      //    ellipsoid axis dimensions (a & b) in meters; _
      //    eastings of false origin (e0) in meters; _
      //    central meridian scale factor (f0); _
      // latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.

      // Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI = PHI * (Pi / 180);
        var RadLAM = LAM * (Pi / 180);
        var RadPHI0 = PHI0 * (Pi / 180);
        var RadLAM0 = LAM0 * (Pi / 180);

        var af0 = a * f0;
        var bf0 = b * f0;
        var e2 = (Math.pow(af0,2) - Math.pow(bf0,2)) / Math.pow(af0,2);
        var n = (af0 - bf0) / (af0 + bf0);
        var nu = af0 / (Math.sqrt(1 - (e2 * Math.pow(Math.sin(RadPHI),2) )));
        var rho = (nu * (1 - e2)) / (1 - (e2 * Math.pow(Math.sin(RadPHI),2) ));
        var eta2 = (nu / rho) - 1;
        var p = RadLAM - RadLAM0;
        
        var IV = nu * (Math.cos(RadPHI));
        var V = (nu / 6) * ( Math.pow(Math.cos(RadPHI),3)) * ((nu / rho) - (Math.pow(Math.tan(RadPHI),2)));
        var VI = (nu / 120) * (Math.pow(Math.cos(RadPHI),5)) * (5 - (18 * (Math.pow(Math.tan(RadPHI),2))) + (Math.pow(Math.tan(RadPHI),4)) + (14 * eta2) - (58 * (Math.pow(Math.tan(RadPHI),2)) * eta2));
        
        return e0 + (p * IV) + (Math.pow(p,3) * V) + (Math.pow(p,5) * VI);
    },

    Lat_Long_to_North: function (PHI, LAM, a, b, e0, n0, f0, PHI0, LAM0) {
      // Project Latitude and longitude to Transverse Mercator northings
      // Input: - _
      // Latitude (PHI) and Longitude (LAM) in decimal degrees; _
      // ellipsoid axis dimensions (a & b) in meters; _
      // eastings (e0) and northings (n0) of false origin in meters; _
      // central meridian scale factor (f0); _
      // latitude (PHI0) and longitude (LAM0) of false origin in decimal degrees.

      // REQUIRES THE "Marc" FUNCTION

      // Convert angle measures to radians
        var Pi = 3.14159265358979;
        var RadPHI = PHI * (Pi / 180);
        var RadLAM = LAM * (Pi / 180);
        var RadPHI0 = PHI0 * (Pi / 180);
        var RadLAM0 = LAM0 * (Pi / 180);
        
        var af0 = a * f0;
        var bf0 = b * f0;
        var e2 = (Math.pow(af0,2) - Math.pow(bf0,2)) / Math.pow(af0,2);
        var n = (af0 - bf0) / (af0 + bf0);
        var nu = af0 / (Math.sqrt(1 - (e2 * Math.pow(Math.sin(RadPHI),2))));
        var rho = (nu * (1 - e2)) / (1 - (e2 * Math.pow(Math.sin(RadPHI),2)));
        var eta2 = (nu / rho) - 1;
        var p = RadLAM - RadLAM0;
        var M = OpenLayers.Projection.OS.Marc(bf0, n, RadPHI0, RadPHI);
        
        var I = M + n0;
        var II = (nu / 2) * (Math.sin(RadPHI)) * (Math.cos(RadPHI));
        var III = ((nu / 24) * (Math.sin(RadPHI)) * (Math.pow(Math.cos(RadPHI),3))) * (5 - (Math.pow(Math.tan(RadPHI),2)) + (9 * eta2));
        var IIIA = ((nu / 720) * (Math.sin(RadPHI)) * (Math.pow(Math.cos(RadPHI),5))) * (61 - (58 * (Math.pow(Math.tan(RadPHI),2))) + (Math.pow(Math.tan(RadPHI),4)));
        
        return I + (Math.pow(p,2) * II) + (Math.pow(p,4) * III) + (Math.pow(p,6) * IIIA);
    }

};

/**
 * Note: Two transforms declared
 * Transforms from EPSG:4326 to EPSG:27700 and from EPSG:27700 to EPSG:4326
 *     are set by this class.
 */
OpenLayers.Projection.addTransform("EPSG:4326", "EPSG:27700",
    OpenLayers.Projection.OS.projectForwardBritish);
OpenLayers.Projection.addTransform("EPSG:27700", "EPSG:4326",
    OpenLayers.Projection.OS.projectInverseBritish);
OpenLayers.Projection.addTransform("EPSG:900913", "EPSG:27700",
    OpenLayers.Projection.OS.goog2osgb);
OpenLayers.Projection.addTransform("EPSG:27700", "EPSG:900913",
    OpenLayers.Projection.OS.osgb2goog);