/*
 * convert geodesic co-ordinates to OS grid reference
 */
function LatLongToOSGrid(p) {
  var lat = p.lat.toRad(), lon = p.lon.toRad();
  
  var a = 6377563.396, b = 6356256.910;          // Airy 1830 major & minor semi-axes
  var F0 = 0.9996012717;                         // NatGrid scale factor on central meridian
  var lat0 = (49).toRad(), lon0 = (-2).toRad();  // NatGrid true origin
  var N0 = -100000, E0 = 400000;                 // northing & easting of true origin, metres
  var e2 = 1 - (b*b)/(a*a);                      // eccentricity squared
  var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n;

  var cosLat = Math.cos(lat), sinLat = Math.sin(lat);
  var nu = a*F0/Math.sqrt(1-e2*sinLat*sinLat);              // transverse radius of curvature
  var rho = a*F0*(1-e2)/Math.pow(1-e2*sinLat*sinLat, 1.5);  // meridional radius of curvature
  var eta2 = nu/rho-1;

  var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (lat-lat0);
  var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(lat-lat0) * Math.cos(lat+lat0);
  var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(lat-lat0)) * Math.cos(2*(lat+lat0));
  var Md = (35/24)*n3 * Math.sin(3*(lat-lat0)) * Math.cos(3*(lat+lat0));
  var M = b * F0 * (Ma - Mb + Mc - Md);              // meridional arc

  var cos3lat = cosLat*cosLat*cosLat;
  var cos5lat = cos3lat*cosLat*cosLat;
  var tan2lat = Math.tan(lat)*Math.tan(lat);
  var tan4lat = tan2lat*tan2lat;

  var I = M + N0;
  var II = (nu/2)*sinLat*cosLat;
  var III = (nu/24)*sinLat*cos3lat*(5-tan2lat+9*eta2);
  var IIIA = (nu/720)*sinLat*cos5lat*(61-58*tan2lat+tan4lat);
  var IV = nu*cosLat;
  var V = (nu/6)*cos3lat*(nu/rho-tan2lat);
  var VI = (nu/120) * cos5lat * (5 - 18*tan2lat + tan4lat + 14*eta2 - 58*tan2lat*eta2);

  var dLon = lon-lon0;
  var dLon2 = dLon*dLon, dLon3 = dLon2*dLon, dLon4 = dLon3*dLon, dLon5 = dLon4*dLon, dLon6 = dLon5*dLon;

  var N = I + II*dLon2 + III*dLon4 + IIIA*dLon6;
  var E = E0 + IV*dLon + V*dLon3 + VI*dLon5;

  return gridrefNumToLet(E, N, 8);
}


/*
 * convert OS grid reference to geodesic co-ordinates
 */
function OSGridToLatLong(gridRef,wibble) {
  var gr = gridrefLetToNum(gridRef);
  var E = gr[0], N = gr[1];

  var a = 6377563.396, b = 6356256.910;              // Airy 1830 major & minor semi-axes
  var F0 = 0.9996012717;                             // NatGrid scale factor on central meridian
  var lat0 = 49*Math.PI/180, lon0 = -2*Math.PI/180;  // NatGrid true origin
  var N0 = -100000, E0 = 400000;                     // northing & easting of true origin, metres
  var e2 = 1 - (b*b)/(a*a);                          // eccentricity squared
  var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n;

  var lat=lat0, M=0;
  do {
    lat = (N-N0-M)/(a*F0) + lat;

    var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (lat-lat0);
    var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(lat-lat0) * Math.cos(lat+lat0);
    var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(lat-lat0)) * Math.cos(2*(lat+lat0));
    var Md = (35/24)*n3 * Math.sin(3*(lat-lat0)) * Math.cos(3*(lat+lat0));
    M = b * F0 * (Ma - Mb + Mc - Md);                // meridional arc

  } while (N-N0-M >= 0.0001);  // ie until < 0.01mm

  var cosLat = Math.cos(lat), sinLat = Math.sin(lat);
  var nu = a*F0/Math.sqrt(1-e2*sinLat*sinLat);              // transverse radius of curvature
  var rho = a*F0*(1-e2)/Math.pow(1-e2*sinLat*sinLat, 1.5);  // meridional radius of curvature
  var eta2 = nu/rho-1;

  var tanLat = Math.tan(lat);
  var tan2lat = tanLat*tanLat, tan4lat = tan2lat*tan2lat, tan6lat = tan4lat*tan2lat;
  var secLat = 1/cosLat;
  var nu3 = nu*nu*nu, nu5 = nu3*nu*nu, nu7 = nu5*nu*nu;
  var VII = tanLat/(2*rho*nu);
  var VIII = tanLat/(24*rho*nu3)*(5+3*tan2lat+eta2-9*tan2lat*eta2);
  var IX = tanLat/(720*rho*nu5)*(61+90*tan2lat+45*tan4lat);
  var X = secLat/nu;
  var XI = secLat/(6*nu3)*(nu/rho+2*tan2lat);
  var XII = secLat/(120*nu5)*(5+28*tan2lat+24*tan4lat);
  var XIIA = secLat/(5040*nu7)*(61+662*tan2lat+1320*tan4lat+720*tan6lat);

  var dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2;
  lat = lat - VII*dE2 + VIII*dE4 - IX*dE6;
  var lon = lon0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7;

  var rout;
  if (wibble==0){rout=lat.toDeg();}
  if (wibble==1){rout=lon.toDeg();}
 
  return rout;
}

Number.prototype.toDeg = function() {  // convert radians to degrees (signed)
  return this * 180 / Math.PI;
}



function gridrefLetToNum(gridref) {
  // get numeric values of letter references, mapping A->0, B->1, C->2, etc:
  var l1 = gridref.toUpperCase().charCodeAt(0) - 'A'.charCodeAt(0);
  var l2 = gridref.toUpperCase().charCodeAt(1) - 'A'.charCodeAt(0);
  // shuffle down letters after 'I' since 'I' is not used in grid:
  if (l1 > 7) l1--;
  if (l2 > 7) l2--;

  // convert grid letters into 100km-square indexes from false origin (grid square SV):
  var e = ((l1-2)%5)*5 + (l2%5);
  var n = (19-Math.floor(l1/5)*5) - Math.floor(l2/5);

  // skip grid letters to get numeric part of ref, stripping any spaces:
  gridref = gridref.slice(2).replace(/ /g,'');

  // append numeric part of references to grid index:
  e += gridref.slice(0, gridref.length/2);
  n += gridref.slice(gridref.length/2);

  // normalise to 1m grid, rounding up to centre of grid square:
  switch (gridref.length) {
    case 6: e += '50'; n += '50'; break;
    case 8: e += '5'; n += '5'; break;
    // 10-digit refs are already 1m
  }

  return [e, n];
}



/*
 * convert numeric grid reference (in metres) to standard-form grid ref
 */
function gridrefNumToLet(e, n, digits) {
  // get the 100km-grid indices
  var e100k = Math.floor(e/100000), n100k = Math.floor(n/100000);
  
  if (e100k<0 || e100k>6 || n100k<0 || n100k>12) return '';

  // translate those into numeric equivalents of the grid letters
  var l1 = (19-n100k) - (19-n100k)%5 + Math.floor((e100k+10)/5);
  var l2 = (19-n100k)*5%25 + e100k%5;

  // compensate for skipped 'I' and build grid letter-pairs
  if (l1 > 7) l1++;
  if (l2 > 7) l2++;
  var letPair = String.fromCharCode(l1+'A'.charCodeAt(0), l2+'A'.charCodeAt(0));

  // strip 100km-grid indices from easting & northing, and reduce precision
  e = Math.floor((e%100000)/Math.pow(10,5-digits/2));
  n = Math.floor((n%100000)/Math.pow(10,5-digits/2));

  var gridRef = letPair + e.padLZ(digits/2) + n.padLZ(digits/2);

  return gridRef;
}


/*
 * pad a number with sufficient leading zeros to make it w chars wide
 */
Number.prototype.padLZ = function(w) {
  var n = this.toString();
  for (var i=0; i<w-n.length; i++) n = '0' + n;
  return n;
}