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File: gPoint.php
Role: Class source
Content type: text/plain
Description: The GeoPoint Class
Class: gPoint
Convert geographic coordinates between projections
Author: By
Last change: Updated the rev number in file header
Date: 6 years ago
Size: 25,852 bytes
 

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<?php
/*------------------------------------------------------------------------------
** File:		gPoint.php
** Description:	PHP class to convert Latitude & Longitude coordinates into
**				UTM & Lambert Conic Conformal Northing/Easting coordinates. 
** Version:		1.3
** Author:		Brenor Brophy
** Email:		brenor dot brophy at gmail dot com
** Homepage:	brenorbrophy.com 
**------------------------------------------------------------------------------
** COPYRIGHT (c) 2005, 2006, 2007, 2008 BRENOR BROPHY
**
** The source code included in this package 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. This license can be
** read at:
**
** http://www.opensource.org/licenses/gpl-license.php
**
** 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. 
**------------------------------------------------------------------------------
**
** Code for datum and UTM conversion was converted from C++ code written by
** Chuck Gantz (chuck dot gantz at globalstar dot com) from
** http://www.gpsy.com/gpsinfo/geotoutm/ This URL has many other references to
** useful information concerning conversion of coordinates.
**
** Rev History
** -----------------------------------------------------------------------------
** 1.0	08/25/2005	Initial Release
** 1.1	05/15/2006	Added software license language to header comments
**					Fixed an error in the convertTMtoLL() method. The latitude
**					calculation had a bunch of variables without $ symbols.
**					Fixed an error in convertLLtoTM() method, The $this-> was
**					missing in front of a couple of variables. Thanks to Bob
**					Robins of Maryland for catching the bugs.
** 1.2	05/18/2007	Added default of NULL to $LongOrigin arguement in convertTMtoLL()
**					and convertLLtoTM() to eliminate warning messages when the
**					methods are called without a value for $LongOrigin.
** 1.3	02/21/2008	Fixed a bug in the distanceFrom method, where the input parameters
**					were not being converted to radians prior to calculating the
**					distance. Thanks to Enrico Benco for finding pointing it out.
*/
define ("meter2nm", (1/1852));
define ("nm2meter", 1852);

/*------------------------------------------------------------------------------
** class gPoint		... for Geographic Point
**
** This class encapsulates the methods for representing a geographic point on the
** earth in three different coordinate systema. Lat/Long, UTM and Lambert Conic
** Conformal.
*/
class gPoint
{
/* Reference ellipsoids derived from Peter H. Dana's website- 
** http://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html
** email: pdana@pdana.com, web page: www.pdana.com
**
** Source:
** Defense Mapping Agency. 1987b. DMA Technical Report: Supplement to Department
** of Defense World Geodetic System 1984 Technical Report. Part I and II.
** Washington, DC: Defense Mapping Agency
*/
	var $ellipsoid = array(//Ellipsoid name, Equatorial Radius, square of eccentricity	
	"Airy"					=>array (6377563, 0.00667054),
	"Australian National"	=>array	(6378160, 0.006694542),
	"Bessel 1841"			=>array	(6377397, 0.006674372),
	"Bessel 1841 Nambia"	=>array	(6377484, 0.006674372),
	"Clarke 1866"			=>array	(6378206, 0.006768658),
	"Clarke 1880"			=>array	(6378249, 0.006803511),
	"Everest"				=>array	(6377276, 0.006637847),
	"Fischer 1960 Mercury"	=>array (6378166, 0.006693422),
	"Fischer 1968"			=>array (6378150, 0.006693422),
	"GRS 1967"				=>array	(6378160, 0.006694605),
	"GRS 1980"				=>array	(6378137, 0.00669438),
	"Helmert 1906"			=>array	(6378200, 0.006693422),
	"Hough"					=>array	(6378270, 0.00672267),
	"International"			=>array	(6378388, 0.00672267),
	"Krassovsky"			=>array	(6378245, 0.006693422),
	"Modified Airy"			=>array	(6377340, 0.00667054),
	"Modified Everest"		=>array	(6377304, 0.006637847),
	"Modified Fischer 1960"	=>array	(6378155, 0.006693422),
	"South American 1969"	=>array	(6378160, 0.006694542),
	"WGS 60"				=>array (6378165, 0.006693422),
	"WGS 66"				=>array (6378145, 0.006694542),
	"WGS 72"				=>array (6378135, 0.006694318),
	"WGS 84"				=>array (6378137, 0.00669438));

	// Properties
	var $a;										// Equatorial Radius
	var	$e2;									// Square of eccentricity
	var	$datum;									// Selected datum
	var	$Xp, $Yp;								// X,Y pixel location
	var $lat, $long;							// Latitude & Longitude of the point
	var $utmNorthing, $utmEasting, $utmZone;	// UTM Coordinates of the point
	var	$lccNorthing, $lccEasting;				// Lambert coordinates of the point
	var $falseNorthing, $falseEasting;			// Origin coordinates for Lambert Projection
	var $latOfOrigin;							// For Lambert Projection
	var $longOfOrigin;							// For Lambert Projection
	var $firstStdParallel;						// For lambert Projection
	var $secondStdParallel;						// For lambert Projection

	// constructor
	function gPoint($datum='WGS 84')			// Default datum is WGS 84
	{
		$this->a = $this->ellipsoid[$datum][0];		// Set datum Equatorial Radius
		$this->e2 = $this->ellipsoid[$datum][1];	// Set datum Square of eccentricity
		$this->datum = $datum;						// Save the datum
	}
	//
	// Set/Get X & Y pixel of the point (used if it is being drawn on an image)
	//
	function setXY($x, $y)
	{
		$this->Xp = $x; $this->Yp = $y;
	}
	function Xp() { return $this->Xp; }
	function Yp() { return $this->Yp; }
	//
	// Set/Get/Output Longitude & Latitude of the point
	//
	function setLongLat($long, $lat)
	{
		$this->long = $long; $this->lat = $lat;
	}
	function Lat() { return $this->lat; }
	function Long() { return $this->long; }
	function printLatLong() { printf("Latitude: %1.5f Longitude: %1.5f",$this->lat, $this->long); }
	//
	// Set/Get/Output Universal Transverse Mercator Coordinates
	//
	function setUTM($easting, $northing, $zone='')	// Zone is optional
	{
		$this->utmNorthing = $northing;
		$this->utmEasting = $easting;
		$this->utmZone = $zone;
	}
	function N() { return $this->utmNorthing; }
	function E() { return $this->utmEasting; }
	function Z() { return $this->utmZone; }
	function printUTM() { print( "Northing: ".(int)$this->utmNorthing.", Easting: ".(int)$this->utmEasting.", Zone: ".$this->utmZone); }
	//
	// Set/Get/Output Lambert Conic Conformal Coordinates
	//
	function setLambert($easting, $northing)
	{
		$this->lccNorthing = $northing;
		$this->lccEasting = $easting;
	}
	function lccN() { return $this->lccNorthing; }
	function lccE() { return $this->lccEasting; }
	function printLambert() { print( "Northing: ".(int)$this->lccNorthing.", Easting: ".(int)$this->lccEasting); }

//------------------------------------------------------------------------------
//
// Convert Longitude/Latitude to UTM
//
// Equations from USGS Bulletin 1532 
// East Longitudes are positive, West longitudes are negative. 
// North latitudes are positive, South latitudes are negative
// Lat and Long are in decimal degrees
// Written by Chuck Gantz- chuck dot gantz at globalstar dot com, converted to PHP by
// Brenor Brophy, brenor dot brophy at gmail dot com
//
// UTM coordinates are useful when dealing with paper maps. Basically the
// map will can cover a single UTM zone which is 6 degrees on longitude.
// So you really don't care about an object crossing two zones. You just get a
// second map of the other zone. However, if you happen to live in a place that
// straddles two zones (For example the Santa Babara area in CA straddles zone 10
// and zone 11) Then it can become a real pain having to have two maps all the time.
// So relatively small parts of the world (like say California) create their own
// version of UTM coordinates that are adjusted to conver the whole area of interest
// on a single map. These are called state grids. The projection system is the
// usually same as UTM (i.e. Transverse Mercator), but the central meridian
// aka Longitude of Origin is selected to suit the logitude of the area being
// mapped (like being moved to the central meridian of the area) and the grid
// may cover more than the 6 degrees of lingitude found on a UTM map. Areas
// that are wide rather than long - think Montana as an example. May still
// have to have a couple of maps to cover the whole state because TM projection
// looses accuracy as you move further away from the Longitude of Origin, 15 degrees
// is usually the limit.
//
// Now, in the case where we want to generate electronic maps that may be
// placed pretty much anywhere on the globe we really don't to deal with the
// issue of UTM zones in our coordinate system. We would really just like a
// grid that is fully contigious over the area of the map we are drawing. Similiar
// to the state grid, but local to the area we are interested in. I call this
// Local Transverse Mercator and I have modified the function below to also
// make this conversion. If you pass a Longitude value to the function as $LongOrigin
// then that is the Longitude of Origin that will be used for the projection.
// Easting coordinates will be returned (in meters) relative to that line of
// longitude - So an Easting coordinate for a point located East of the longitude
// of origin will be a positive value in meters, an Easting coordinate for a point
// West of the longitude of Origin will have a negative value in meters. Northings
// will always be returned in meters from the equator same as the UTM system. The
// UTMZone value will be valid for Long/Lat given - thought it is not meaningful
// in the context of Local TM. If a NULL value is passed for $LongOrigin
// then the standard UTM coordinates are calculated.
//
	function convertLLtoTM($LongOrigin = NULL)
	{
		$k0 = 0.9996;
		$falseEasting = 0.0;

		//Make sure the longitude is between -180.00 .. 179.9
		$LongTemp = ($this->long+180)-(integer)(($this->long+180)/360)*360-180; // -180.00 .. 179.9;
		$LatRad = deg2rad($this->lat);
		$LongRad = deg2rad($LongTemp);

		if (!$LongOrigin)
		{ // Do a standard UTM conversion - so findout what zone the point is in
			$ZoneNumber = (integer)(($LongTemp + 180)/6) + 1;
			// Special zone for South Norway
			if( $this->lat >= 56.0 && $this->lat < 64.0 && $LongTemp >= 3.0 && $LongTemp < 12.0 ) // Fixed 1.1
				$ZoneNumber = 32;
			// Special zones for Svalbard
			if( $this->lat >= 72.0 && $this->lat < 84.0 ) 
			{
				if(      $LongTemp >= 0.0  && $LongTemp <  9.0 ) $ZoneNumber = 31;
				else if( $LongTemp >= 9.0  && $LongTemp < 21.0 ) $ZoneNumber = 33;
				else if( $LongTemp >= 21.0 && $LongTemp < 33.0 ) $ZoneNumber = 35;
				else if( $LongTemp >= 33.0 && $LongTemp < 42.0 ) $ZoneNumber = 37;
			}
			$LongOrigin = ($ZoneNumber - 1)*6 - 180 + 3;  //+3 puts origin in middle of zone
			//compute the UTM Zone from the latitude and longitude
			$this->utmZone = sprintf("%d%s", $ZoneNumber, $this->UTMLetterDesignator());
			// We also need to set the false Easting value adjust the UTM easting coordinate
			$falseEasting = 500000.0;
		}
		$LongOriginRad = deg2rad($LongOrigin);

		$eccPrimeSquared = ($this->e2)/(1-$this->e2);

		$N = $this->a/sqrt(1-$this->e2*sin($LatRad)*sin($LatRad));
		$T = tan($LatRad)*tan($LatRad);
		$C = $eccPrimeSquared*cos($LatRad)*cos($LatRad);
		$A = cos($LatRad)*($LongRad-$LongOriginRad);

		$M = $this->a*((1	- $this->e2/4		- 3*$this->e2*$this->e2/64	- 5*$this->e2*$this->e2*$this->e2/256)*$LatRad 
							- (3*$this->e2/8	+ 3*$this->e2*$this->e2/32	+ 45*$this->e2*$this->e2*$this->e2/1024)*sin(2*$LatRad)
												+ (15*$this->e2*$this->e2/256 + 45*$this->e2*$this->e2*$this->e2/1024)*sin(4*$LatRad) 
												- (35*$this->e2*$this->e2*$this->e2/3072)*sin(6*$LatRad));
	
		$this->utmEasting = ($k0*$N*($A+(1-$T+$C)*$A*$A*$A/6
						+ (5-18*$T+$T*$T+72*$C-58*$eccPrimeSquared)*$A*$A*$A*$A*$A/120)
						+ $falseEasting);

		$this->utmNorthing = ($k0*($M+$N*tan($LatRad)*($A*$A/2+(5-$T+9*$C+4*$C*$C)*$A*$A*$A*$A/24
					 + (61-58*$T+$T*$T+600*$C-330*$eccPrimeSquared)*$A*$A*$A*$A*$A*$A/720)));
		if($this->lat < 0)
			$this->utmNorthing += 10000000.0; //10000000 meter offset for southern hemisphere
	}
//
// This routine determines the correct UTM letter designator for the given latitude
// returns 'Z' if latitude is outside the UTM limits of 84N to 80S
// Written by Chuck Gantz- chuck dot gantz at globalstar dot com, converted to PHP by
// Brenor Brophy, brenor dot brophy at gmail dot com
//
	function UTMLetterDesignator()
	{	
		if((84 >= $this->lat) && ($this->lat >= 72)) $LetterDesignator = 'X';
		else if((72 > $this->lat) && ($this->lat >= 64)) $LetterDesignator = 'W';
		else if((64 > $this->lat) && ($this->lat >= 56)) $LetterDesignator = 'V';
		else if((56 > $this->lat) && ($this->lat >= 48)) $LetterDesignator = 'U';
		else if((48 > $this->lat) && ($this->lat >= 40)) $LetterDesignator = 'T';
		else if((40 > $this->lat) && ($this->lat >= 32)) $LetterDesignator = 'S';
		else if((32 > $this->lat) && ($this->lat >= 24)) $LetterDesignator = 'R';
		else if((24 > $this->lat) && ($this->lat >= 16)) $LetterDesignator = 'Q';
		else if((16 > $this->lat) && ($this->lat >= 8)) $LetterDesignator = 'P';
		else if(( 8 > $this->lat) && ($this->lat >= 0)) $LetterDesignator = 'N';
		else if(( 0 > $this->lat) && ($this->lat >= -8)) $LetterDesignator = 'M';
		else if((-8 > $this->lat) && ($this->lat >= -16)) $LetterDesignator = 'L';
		else if((-16 > $this->lat) && ($this->lat >= -24)) $LetterDesignator = 'K';
		else if((-24 > $this->lat) && ($this->lat >= -32)) $LetterDesignator = 'J';
		else if((-32 > $this->lat) && ($this->lat >= -40)) $LetterDesignator = 'H';
		else if((-40 > $this->lat) && ($this->lat >= -48)) $LetterDesignator = 'G';
		else if((-48 > $this->lat) && ($this->lat >= -56)) $LetterDesignator = 'F';
		else if((-56 > $this->lat) && ($this->lat >= -64)) $LetterDesignator = 'E';
		else if((-64 > $this->lat) && ($this->lat >= -72)) $LetterDesignator = 'D';
		else if((-72 > $this->lat) && ($this->lat >= -80)) $LetterDesignator = 'C';
		else $LetterDesignator = 'Z'; //This is here as an error flag to show that the Latitude is outside the UTM limits

		return($LetterDesignator);
	}

//------------------------------------------------------------------------------
//
// Convert UTM to Longitude/Latitude
//
// Equations from USGS Bulletin 1532 
// East Longitudes are positive, West longitudes are negative. 
// North latitudes are positive, South latitudes are negative
// Lat and Long are in decimal degrees. 
// Written by Chuck Gantz- chuck dot gantz at globalstar dot com, converted to PHP by
// Brenor Brophy, brenor dot brophy at gmail dot com
//
// If a value is passed for $LongOrigin then the function assumes that
// a Local (to the Longitude of Origin passed in) Transverse Mercator
// coordinates is to be converted - not a UTM coordinate. This is the
// complementary function to the previous one. The function cannot
// tell if a set of Northing/Easting coordinates are in the North
// or South hemesphere - they just give distance from the equator not
// direction - so only northern hemesphere lat/long coordinates are returned.
// If you live south of the equator there is a note later in the code
// explaining how to have it just return southern hemesphere lat/longs.
//
	function convertTMtoLL($LongOrigin = NULL)
	{
		$k0 = 0.9996;
		$e1 = (1-sqrt(1-$this->e2))/(1+sqrt(1-$this->e2));
		$falseEasting = 0.0;
		$y = $this->utmNorthing;

		if (!$LongOrigin)
		{ // It is a UTM coordinate we want to convert
			sscanf($this->utmZone,"%d%s",$ZoneNumber,$ZoneLetter);
			if($ZoneLetter >= 'N')
				$NorthernHemisphere = 1;//point is in northern hemisphere
			else
			{
				$NorthernHemisphere = 0;//point is in southern hemisphere
				$y -= 10000000.0;//remove 10,000,000 meter offset used for southern hemisphere
			}
			$LongOrigin = ($ZoneNumber - 1)*6 - 180 + 3;  //+3 puts origin in middle of zone
			$falseEasting = 500000.0;
		}

//		$y -= 10000000.0;	// Uncomment line to make LOCAL coordinates return southern hemesphere Lat/Long
		$x = $this->utmEasting - $falseEasting; //remove 500,000 meter offset for longitude

		$eccPrimeSquared = ($this->e2)/(1-$this->e2);

		$M = $y / $k0;
		$mu = $M/($this->a*(1-$this->e2/4-3*$this->e2*$this->e2/64-5*$this->e2*$this->e2*$this->e2/256));

		$phi1Rad = $mu	+ (3*$e1/2-27*$e1*$e1*$e1/32)*sin(2*$mu) 
					+ (21*$e1*$e1/16-55*$e1*$e1*$e1*$e1/32)*sin(4*$mu)
					+(151*$e1*$e1*$e1/96)*sin(6*$mu);
		$phi1 = rad2deg($phi1Rad);

		$N1 = $this->a/sqrt(1-$this->e2*sin($phi1Rad)*sin($phi1Rad));
		$T1 = tan($phi1Rad)*tan($phi1Rad);
		$C1 = $eccPrimeSquared*cos($phi1Rad)*cos($phi1Rad);
		$R1 = $this->a*(1-$this->e2)/pow(1-$this->e2*sin($phi1Rad)*sin($phi1Rad), 1.5);
		$D = $x/($N1*$k0);

		$tlat = $phi1Rad - ($N1*tan($phi1Rad)/$R1)*($D*$D/2-(5+3*$T1+10*$C1-4*$C1*$C1-9*$eccPrimeSquared)*$D*$D*$D*$D/24
						+(61+90*$T1+298*$C1+45*$T1*$T1-252*$eccPrimeSquared-3*$C1*$C1)*$D*$D*$D*$D*$D*$D/720); // fixed in 1.1
		$this->lat = rad2deg($tlat);

		$tlong = ($D-(1+2*$T1+$C1)*$D*$D*$D/6+(5-2*$C1+28*$T1-3*$C1*$C1+8*$eccPrimeSquared+24*$T1*$T1)
						*$D*$D*$D*$D*$D/120)/cos($phi1Rad);
		$this->long = $LongOrigin + rad2deg($tlong);
	}

//------------------------------------------------------------------------------
// Configure a Lambert Conic Conformal Projection
//
// falseEasting & falseNorthing are just an offset in meters added to the final
// coordinate calculated.
//
// longOfOrigin & LatOfOrigin are the "center" latitiude and longitude of the
// area being projected. All coordinates will be calculated in meters relative
// to this point on the earth.
//
// firstStdParallel & secondStdParallel are the two lines of longitude (that
// is they run east-west) that define where the "cone" intersects the earth.
// Simply put they should bracket the area being projected. 
//
// google is your friend to find out more
//
	function configLambertProjection ($falseEasting, $falseNorthing,
									  $longOfOrigin, $latOfOrigin,
									  $firstStdParallel, $secondStdParallel)
	{
		$this->falseEasting = $falseEasting;
		$this->falseNorthing = $falseNorthing;
		$this->longOfOrigin = $longOfOrigin;
		$this->latOfOrigin = $latOfOrigin;
		$this->firstStdParallel = $firstStdParallel;
		$this->secondStdParallel = $secondStdParallel;
	}

//------------------------------------------------------------------------------
//
// Convert Longitude/Latitude to Lambert Conic Easting/Northing
//
// This routine will convert a Latitude/Longitude coordinate to an Northing/
// Easting coordinate on a Lambert Conic Projection. The configLambertProjection()
// function should have been called prior to this one to setup the specific
// parameters for the projection. The Northing/Easting parameters calculated are
// in meters (because the datum used is in meters) and are relative to the
// falseNorthing/falseEasting coordinate. Which in turn is relative to the
// Lat/Long of origin The formula were obtained from URL:
// http://www.ihsenergy.com/epsg/guid7_2.html.
// Code was written by Brenor Brophy, brenor dot brophy at gmail dot com
//
	function convertLLtoLCC()
	{
		$e = sqrt($this->e2);

		$phi 	= deg2rad($this->lat);						// Latitude to convert
		$phi1	= deg2rad($this->firstStdParallel);			// Latitude of 1st std parallel
		$phi2	= deg2rad($this->secondStdParallel);		// Latitude of 2nd std parallel
		$lamda	= deg2rad($this->long);						// Lonitude to convert
		$phio	= deg2rad($this->latOfOrigin);				// Latitude of  Origin
		$lamdao	= deg2rad($this->longOfOrigin);				// Longitude of  Origin

		$m1 = cos($phi1) / sqrt(( 1 - $this->e2*sin($phi1)*sin($phi1)));
		$m2 = cos($phi2) / sqrt(( 1 - $this->e2*sin($phi2)*sin($phi2)));
		$t1 = tan((pi()/4)-($phi1/2)) / pow(( ( 1 - $e*sin($phi1) ) / ( 1 + $e*sin($phi1) )),$e/2);
		$t2 = tan((pi()/4)-($phi2/2)) / pow(( ( 1 - $e*sin($phi2) ) / ( 1 + $e*sin($phi2) )),$e/2);
		$to = tan((pi()/4)-($phio/2)) / pow(( ( 1 - $e*sin($phio) ) / ( 1 + $e*sin($phio) )),$e/2);
		$t  = tan((pi()/4)-($phi /2)) / pow(( ( 1 - $e*sin($phi ) ) / ( 1 + $e*sin($phi ) )),$e/2);
		$n	= (log($m1)-log($m2)) / (log($t1)-log($t2));
		$F	= $m1/($n*pow($t1,$n));
		$rf	= $this->a*$F*pow($to,$n);
		$r	= $this->a*$F*pow($t,$n);
		$theta = $n*($lamda - $lamdao);

		$this->lccEasting = $this->falseEasting + $r*sin($theta);
		$this->lccNorthing = $this->falseNorthing + $rf - $r*cos($theta);
	}
//------------------------------------------------------------------------------
//
// Convert Easting/Northing on a Lambert Conic projection to Longitude/Latitude
//
// This routine will convert a Lambert Northing/Easting coordinate to an
// Latitude/Longitude coordinate.  The configLambertProjection() function should
// have been called prior to this one to setup the specific parameters for the
// projection. The Northing/Easting parameters are in meters (because the datum
// used is in meters) and are relative to the falseNorthing/falseEasting
// coordinate. Which in turn is relative to the Lat/Long of origin The formula
// were obtained from URL http://www.ihsenergy.com/epsg/guid7_2.html. Code
// was written by Brenor Brophy, brenor dot brophy at gmail dot com
//
	function convertLCCtoLL()
	{
		$e = sqrt($this->e2);

		$phi1	= deg2rad($this->firstStdParallel);			// Latitude of 1st std parallel
		$phi2	= deg2rad($this->secondStdParallel);		// Latitude of 2nd std parallel
		$phio	= deg2rad($this->latOfOrigin);				// Latitude of  Origin
		$lamdao	= deg2rad($this->longOfOrigin);				// Longitude of  Origin
		$E		= $this->lccEasting;
		$N		= $this->lccNorthing;
		$Ef		= $this->falseEasting;
		$Nf		= $this->falseNorthing;

		$m1 = cos($phi1) / sqrt(( 1 - $this->e2*sin($phi1)*sin($phi1)));
		$m2 = cos($phi2) / sqrt(( 1 - $this->e2*sin($phi2)*sin($phi2)));
		$t1 = tan((pi()/4)-($phi1/2)) / pow(( ( 1 - $e*sin($phi1) ) / ( 1 + $e*sin($phi1) )),$e/2);
		$t2 = tan((pi()/4)-($phi2/2)) / pow(( ( 1 - $e*sin($phi2) ) / ( 1 + $e*sin($phi2) )),$e/2);
		$to = tan((pi()/4)-($phio/2)) / pow(( ( 1 - $e*sin($phio) ) / ( 1 + $e*sin($phio) )),$e/2);
		$n	= (log($m1)-log($m2)) / (log($t1)-log($t2));
		$F	= $m1/($n*pow($t1,$n));
		$rf	= $this->a*$F*pow($to,$n);
		$r_	= sqrt( pow(($E-$Ef),2) + pow(($rf-($N-$Nf)),2) );
		$t_	= pow($r_/($this->a*$F),(1/$n));
		$theta_ = atan(($E-$Ef)/($rf-($N-$Nf)));

		$lamda	= $theta_/$n + $lamdao;
		$phi0	= (pi()/2) - 2*atan($t_);
		$phi1	= (pi()/2) - 2*atan($t_*pow(((1-$e*sin($phi0))/(1+$e*sin($phi0))),$e/2));
		$phi2	= (pi()/2) - 2*atan($t_*pow(((1-$e*sin($phi1))/(1+$e*sin($phi1))),$e/2));
		$phi	= (pi()/2) - 2*atan($t_*pow(((1-$e*sin($phi2))/(1+$e*sin($phi2))),$e/2));
		
		$this->lat 	= rad2deg($phi);
		$this->long = rad2deg($lamda);
	}

//------------------------------------------------------------------------------
// This is a useful function that returns the Great Circle distance from the
// gPoint to another Long/Lat coordinate
//
// Result is returned as meters
//
	function distanceFrom($lon1, $lat1)
	{ 
		$lon1 = deg2rad($lon1); $lat1 = deg2rad($lat1); // Added in 1.3
		$lon2 = deg2rad($this->Long()); $lat2 = deg2rad($this->Lat());
 
		$theta = $lon2 - $lon1;
		$dist = acos(sin($lat1) * sin($lat2) + cos($lat1) * cos($lat2) * cos($theta));

//		Alternative formula supposed to be more accurate for short distances
//		$dist = 2*asin(sqrt( pow(sin(($lat1-$lat2)/2),2) + cos($lat1)*cos($lat2)*pow(sin(($lon1-$lon2)/2),2)));
		return ( $dist * 6366710 ); // from http://williams.best.vwh.net/avform.htm#GCF
	}

//------------------------------------------------------------------------------
// This function also calculates the distance between two points. In this case
// it just uses Pythagoras's theorm using TM coordinates.
//
	function distanceFromTM(&$pt)
	{ 
		$E1 = $pt->E(); 	$N1 = $pt->N();
		$E2 = $this->E(); 	$N2 = $this->N();
 
		$dist = sqrt(pow(($E1-$E2),2)+pow(($N1-$N2),2));
		return $dist; 
	}

//------------------------------------------------------------------------------
// This function geo-references a geoPoint to a given map. This means that it
// calculates the x,y pixel coordinate that coresponds to the Lat/Long value of
// the geoPoint. The calculation is done using the Transverse Mercator(TM)
// coordinates of the gPoint with respect to the TM coordinates of the center
// point of the map. So this only makes sense if you are using Local TM
// projection.
//
// $rX & $rY are the pixel coordinates that corespond to the Northing/Easting
// ($rE/$rN) coordinate it is to this coordinate that the point will be
// geo-referenced. The $LongOrigin is needed to make sure the Easting/Northing
// coordinates of the point are correctly converted.
//
	function gRef($rX, $rY, $rE, $rN, $Scale, $LongOrigin)
	{
		$this->convertLLtoTM($LongOrigin);
		$x = (($this->E() - $rE) / $Scale)		// The easting in meters times the scale to get pixels
												// is relative to the center of the image so adjust to
			+ ($rX);							// the left coordinate.
		$y = $rY -  							// Adjust to bottom coordinate.
			(($rN - $this->N()) / $Scale);		// The northing in meters
												// relative to the equator. Subtract center point northing
												// to get relative to image center and convert meters to pixels
		$this->setXY((int)$x,(int)$y);			// Save the geo-referenced result.
	}
} // end of class gPoint

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