Subversion Repositories eFlore/Projets.eflore-projets

<?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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