/**
* Convert a latitude and longitude to easting and northing using a Transverse Mercator projection
* Formula for transformation is taken from OS document
* "A Guide to Coordinate Systems in Great Britain"
*
* @param float $scale scale factor on central meridian
* @param float $originEasting easting of true origin
* @param float $originNorthing northing of true origin
* @param float $originLat latitude of true origin
* @param float $originLong longitude of true origin
* @return array
*/
public function toTransverseMercatorEastingNorthing($scale, $originEasting, $originNorthing, $originLat, $originLong)
{
$originLat = deg2rad($originLat);
$originLong = deg2rad($originLong);
$lat = deg2rad($this->lat);
$sinLat = sin($lat);
$cosLat = cos($lat);
$tanLat = tan($lat);
$tanLatSq = pow($tanLat, 2);
$long = deg2rad($this->lng);
$n = ($this->refEll->getMaj() - $this->refEll->getMin()) / ($this->refEll->getMaj() + $this->refEll->getMin());
$nSq = pow($n, 2);
$nCu = pow($n, 3);
$v = $this->refEll->getMaj() * $scale * pow(1 - $this->refEll->getEcc() * pow($sinLat, 2), -0.5);
$p = $this->refEll->getMaj() * $scale * (1 - $this->refEll->getEcc()) * pow(1 - $this->refEll->getEcc() * pow($sinLat, 2), -1.5);
$hSq = $v / $p - 1;
$latPlusOrigin = $lat + $originLat;
$latMinusOrigin = $lat - $originLat;
$longMinusOrigin = $long - $originLong;
$M = $this->refEll->getMin() * $scale * ((1 + $n + 1.25 * ($nSq + $nCu)) * $latMinusOrigin - (3 * ($n + $nSq) + 2.625 * $nCu) * sin($latMinusOrigin) * cos($latPlusOrigin) + 1.875 * ($nSq + $nCu) * sin(2 * $latMinusOrigin) * cos(2 * $latPlusOrigin) - 35 / 24 * $nCu * sin(3 * $latMinusOrigin) * cos(3 * $latPlusOrigin));
$I = $M + $originNorthing;
$II = $v / 2 * $sinLat * $cosLat;
$III = $v / 24 * $sinLat * pow($cosLat, 3) * (5 - $tanLatSq + 9 * $hSq);
$IIIA = $v / 720 * $sinLat * pow($cosLat, 5) * (61 - 58 * $tanLatSq + pow($tanLatSq, 2));
$IV = $v * $cosLat;
$V = $v / 6 * pow($cosLat, 3) * ($v / $p - $tanLatSq);
$VI = $v / 120 * pow($cosLat, 5) * (5 - 18 * $tanLatSq + pow($tanLatSq, 2) + 14 * $hSq - 58 * $tanLatSq * $hSq);
$E = $originEasting + $IV * $longMinusOrigin + $V * pow($longMinusOrigin, 3) + $VI * pow($longMinusOrigin, 5);
$N = $I + $II * pow($longMinusOrigin, 2) + $III * pow($longMinusOrigin, 4) + $IIIA * pow($longMinusOrigin, 6);
return array('E' => $E, 'N' => $N);
}
/**
* Convert these coordinates into a latitude, longitude
* Formula for transformation is taken from OS document
* "A Guide to Coordinate Systems in Great Britain"
*
* @return LatLng
*/
public function toLatitudeLongitude()
{
$lambda = rad2deg(atan2($this->y, $this->x));
$p = sqrt(pow($this->x, 2) + pow($this->y, 2));
$phi = atan($this->z / ($p * (1 - $this->refEll->getEcc())));
do {
$phi1 = $phi;
$v = $this->refEll->getMaj() / sqrt(1 - $this->refEll->getEcc() * pow(sin($phi), 2));
$phi = atan(($this->z + $this->refEll->getEcc() * $v * sin($phi)) / $p);
} while (abs($phi - $phi1) >= 1.0E-5);
$h = $p / cos($phi) - $v;
$phi = rad2deg($phi);
return new LatLng($phi, $lambda, $h, $this->refEll);
}
