Coordinates.php

<?php
        /**
	 * Coordinates.php
	 * An utility for converting HK80 to WGS84 coordinates
	 *
	 * Copyright (C) 2010, 2013 Kelvin Wong
	 * Licensed under the MIT License (http://opensource.org/licenses/MIT)
	 * 
	 * Note: For the glossaries and conventions for coordinates convertion, please refer to
	 * the website of Geodetic Survey of Hong Kong.
	 * 
	 * References:
	 * - http://www.geodetic.gov.hk/smo/gsi/programs/en/GSS/grid/grid_index.htm
	 * - http://www.geodetic.gov.hk/smo/gsi/data/parameter/7P_ITRF96_HK80_V1.pdf
	 * - http://www.geodetic.gov.hk/data/parameter/SchematicDiagram.pdf
	 */
	class Coordinates {
		// Reference ellipsoid of HK80 (based on International 1910 / Transverse Mercator)
		static $a  = 6378388;            // Semi-major axis
		static $f =  0.0033670033670034; // Flattening
		static $e2 = 0.0067226700223333; // First eccentricity (e^2 = 2f - f^2)
		static $m0 = 1;                  // Scale factor along central meridian
		
		// Reference point of HK80 (Patridge Hill Trigonometric Station)
		static $lat0 = 0.38942018399288; // deg2rad( 22d 18' 43.68" N)
		static $lng0 = 1.99279173737270; // deg2rad(114d 10' 42.80" E)
		static $N0 = 819069.80;
		static $E0 = 836694.05;
		
		/**
		 * doBisectIter
		 * @desc find the root of $f($x) = 0 by bisection method
		 * @param  f        the function to be evaluated
		 * @param  x1       the starting value
		 * @param  x2       the ending value
		 * @param  epsilon  precision
		 * @return the root got by the iteration
		 */
		static function doBisectIter($f, $x1, $x2, $epsilon = 0.00000001) {
			$y1 = $f($x1);
			$y2 = $f($x2);
			
			// Ensure the signs are opposite
			if ($y1 * $y2 > 0)
				return false;
			// Ensure the y1 must be the smaller side
			if ($y1 > 0)
				return call_user_func(array('self', __FUNCTION__), $f, $x2, $x1, $epsilon);
			
			$x = ($x1 + $x2) / 2;
			$y = $f($x);
			
			if (abs($y) <= $epsilon)
				return $x;
			
			return call_user_func(array('self', __FUNCTION__), $f, ($y<0)?($x):($x1), ($y>0)?($x):($x2), $epsilon);
		}
		
		/**
		 * getMeridianDist
		 * @param   lat latitude
		 * @return  meridian distance
		 */
		static function getMeridianDist($lat) {
			$a  = self::$a;
			$e2 = self::$e2;
			
			$A0 = 1 - $e2 / 4 - 3 * $e2 * $e2 / 64;
			$A2 = 3 * ($e2 + $e2 * $e2 / 4) / 8;
			$A4 = 15 * $e2 * $e2 / 256;
			return $a * ($A0 * $lat - $A2 * sin(2*$lat) - $A4 * sin(4*$lat));
		}
		
		/**
		 * convertHK80GridToCartesian
		 * @param   hk1980 grid reference in HK80, in terms of n and e
		 * @return  corresponding Cartesian co-ordinates
		 */
		static function convertHK80GridToCartesian($hk1980) {
			$N = $hk1980['n'];
			$E = $hk1980['e'];
			
			// Constants
			$a  = self::$a;
			$e2 = self::$e2;
			$N0 = self::$N0;
			$E0 = self::$E0;
			$m0 = self::$m0;
			$lat0 = self::$lat0;
			$lng0 = self::$lng0;
			
			// Calculate dN and dE
			$dN = $N - $N0;
			$dE = $E - $E0;
			
			// Calculate meridian distance
			$M0 = self::getMeridianDist($lat0);
			$M = ($dN + $M0) / $m0;
			
			// Step 1: HK80 Grid => HK80 Geographic Co-ordinates
			// Newtonian iteration to get the latitude reference evaluated, given meridian distance
			$latP = self::doBisectIter(
					create_function('$x', 'return '.$M.' - Coordinates::getMeridianDist($x);'),
				-10000, 10000);
			
			// By the latitude reference, the v (radius of curvature in prime vertical),
			// p (that in meridian) and phi (isometric latitude) at point P are evaluated
			$vP = $a / pow(1 - $e2 * pow(sin($latP), 2), 0.5);
			$pP = $a * (1 - $e2) / pow(1 - $e2 * pow(sin($latP), 2), 1.5);
			$phiP = $vP / $pP;
			
			// The latitude/longitude (at HK1980) is evaluated by the radius of curvature
			$lat = $latP - tan($latP) * pow($dE/$m0, 2) / (2*$pP*$vP);
			$lng = $lng0 + $dE / ($m0*$vP * cos($latP)) - (pow($dE, 3) / (6 * pow($m0*$vP, 3) * cos($latP)))*($phiP + 2 * pow(tan($latP), 2));
			
			// Step 2: HK80 Geographic => WGS84 Geographic Co-ordinates
			// This is the lazy and fast way, suitable for general usage
			// This uses a rule of thumb to convert coordinate from HK80 to WGS84 directly
			// TODO: Implement the proper way :P
			return array(
				'lat' => rad2deg($lat) - 5.5/3600,
				'lng' => rad2deg($lng) + 8.8/3600
			);
		}
	};
?>

LICENSE.txt

Copyright (c) 2010, 2013 Kelvin Wong

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