TransverseMercator::getScaleFactor()

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by Doug

created 2017-09-04 14:23 UTC

↳ Parent: TransverseMercator

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<?php
/**
 * PHPCoord
 * @package PHPCoord
 * @author Jonathan Stott
 * @author Doug Wright
 */
namespace PHPCoord;

/**
 * Abstract class representing a Tranverse Mercator Projection
 * @author Doug Wright
 * @package PHPCoord
 */
abstract class TransverseMercator
{

    /**
     * X
     * @var float
     */
    protected $x;

    /**
     * Y
     * @var float
     */
    protected $y;

    /**
     * h
     * @var float
     */
    protected $h;

    /**
     * Reference ellipsoid used in this datum
     * @var RefEll
     */
    protected $refEll;

    /**
     * Cartesian constructor.
     * @param float $x
     * @param float $y
     * @param float $h
     * @param RefEll $refEll
     */
    public function __construct($x, $y, $h, RefEll $refEll)
    {
        $this->setX($x);
        $this->setY($y);
        $this->setH($h);
        $this->setRefEll($refEll);
    }

    /**
     * String version of coordinate.
     * @return string
     */
    public function __toString()
    {
        return "({$this->x}, {$this->y}, {$this->h})";
    }

    /**
     * @return float
     */
    public function getX()
    {
        return $this->x;
    }

    /**
     * @param float $x
     */
    public function setX($x)
    {
        $this->x = $x;
    }

    /**
     * @return float
     */
    public function getY()
    {
        return $this->y;
    }

    /**
     * @param float $y
     */
    public function setY($y)
    {
        $this->y = $y;
    }

    /**
     * @return float
     */
    public function getH()
    {
        return $this->h;
    }

    /**
     * @param float $h
     */
    public function setH($h)
    {
        $this->h = $h;
    }

    /**
     * @return RefEll
     */
    public function getRefEll()
    {
        return $this->refEll;
    }

    /**
     * @param RefEll $refEll
     */
    public function setRefEll(RefEll $refEll)
    {
        $this->refEll = $refEll;
    }


    /**
     * Reference ellipsoid used by this projection
     * @return RefEll
     */
    abstract public function getReferenceEllipsoid();

    /**
     * Scale factor at central meridian
     * @return float
     */
    abstract public function getScaleFactor();

    /**
     * Northing of true origin
     * @return float
     */
    abstract public function getOriginNorthing();

    /**
     * Easting of true origin
     * @return float
     */
    abstract public function getOriginEasting();

    /**
     * Latitude of true origin
     * @return float
     */
    abstract public function getOriginLatitude();

    /**
     * Longitude of true origin
     * @return float
     */
    abstract public function getOriginLongitude();

    /**
     * Convert this grid reference into a latitude and longitude
     * Formula for transformation is taken from OS document
     * "A Guide to Coordinate Systems in Great Britain"
     *
     * @param float $N map coordinate (northing) of point to convert
     * @param float $E map coordinate (easting) of point to convert
     * @param float $N0 map coordinate (northing) of true origin
     * @param float $E0 map coordinate (easting) of true origin
     * @param float $phi0 map coordinate (latitude) of true origin
     * @param float $lambda0 map coordinate (longitude) of true origin and central meridian
     * @return LatLng
     */
    public function convertToLatitudeLongitude($N, $E, $N0, $E0, $phi0, $lambda0)
    {

        $phi0 = deg2rad($phi0);
        $lambda0 = deg2rad($lambda0);

        $refEll = $this->getReferenceEllipsoid();
        $F0 = $this->getScaleFactor();

        $a = $refEll->getMaj();
        $b = $refEll->getMin();
        $eSquared = $refEll->getEcc();
        $n = ($a - $b) / ($a + $b);
        $phiPrime = (($N - $N0) / ($a * $F0)) + $phi0;

        do {
            $M =
                ($b * $F0)
                * (((1 + $n + ((5 / 4) * $n * $n) + ((5 / 4) * $n * $n * $n))
                        * ($phiPrime - $phi0))
                    - (((3 * $n) + (3 * $n * $n) + ((21 / 8) * $n * $n * $n))
                        * sin($phiPrime - $phi0)
                        * cos($phiPrime + $phi0))
                    + ((((15 / 8) * $n * $n) + ((15 / 8) * $n * $n * $n))
                        * sin(2 * ($phiPrime - $phi0))
                        * cos(2 * ($phiPrime + $phi0)))
                    - (((35 / 24) * $n * $n * $n)
                        * sin(3 * ($phiPrime - $phi0))
                        * cos(3 * ($phiPrime + $phi0))));
            $phiPrime += ($N - $N0 - $M) / ($a * $F0);
        } while (($N - $N0 - $M) >= 0.00001);
        $v = $a * $F0 * pow(1 - $eSquared * pow(sin($phiPrime), 2), -0.5);
        $rho =
            $a
            * $F0
            * (1 - $eSquared)
            * pow(1 - $eSquared * pow(sin($phiPrime), 2), -1.5);
        $etaSquared = ($v / $rho) - 1;
        $VII = tan($phiPrime) / (2 * $rho * $v);
        $VIII =
            (tan($phiPrime) / (24 * $rho * pow($v, 3)))
            * (5
                + (3 * pow(tan($phiPrime), 2))
                + $etaSquared
                - (9 * pow(tan($phiPrime), 2) * $etaSquared));
        $IX =
            (tan($phiPrime) / (720 * $rho * pow($v, 5)))
            * (61
                + (90 * pow(tan($phiPrime), 2))
                + (45 * pow(tan($phiPrime), 2) * pow(tan($phiPrime), 2)));
        $X = (1 / cos($phiPrime)) / $v;
        $XI =
            ((1 / cos($phiPrime)) / (6 * $v * $v * $v))
            * (($v / $rho) + (2 * pow(tan($phiPrime), 2)));
        $XII =
            ((1 / cos($phiPrime)) / (120 * pow($v, 5)))
            * (5
                + (28 * pow(tan($phiPrime), 2))
                + (24 * pow(tan($phiPrime), 4)));
        $XIIA =
            ((1 / cos($phiPrime)) / (5040 * pow($v, 7)))
            * (61
                + (662 * pow(tan($phiPrime), 2))
                + (1320 * pow(tan($phiPrime), 4))
                + (720
                    * pow(tan($phiPrime), 6)));
        $phi =
            $phiPrime
            - ($VII * pow($E - $E0, 2))
            + ($VIII * pow($E - $E0, 4))
            - ($IX * pow($E - $E0, 6));
        $lambda =
            $lambda0
            + ($X * ($E - $E0))
            - ($XI * pow($E - $E0, 3))
            + ($XII * pow($E - $E0, 5))
            - ($XIIA * pow($E - $E0, 7));

        return new LatLng(rad2deg($phi), rad2deg($lambda), 0, $refEll);
    }

    /**
     * Calculate the surface distance between this object and the one
     * passed in as a parameter.
     *
     * @param self $to object to measure the distance to

     * @return float

     */
    public function distance(self $to) {

        if ($this->refEll != $to->refEll) {
            throw new \RuntimeException('Source and destination co-ordinates are not using the same ellipsoid');
        }

        //Because this is a 2D grid, we can use simple Pythagoras
        $distanceX = $to->getX()-$this->getX();
        $distanceY = $to->getY()-$this->getY();

        return pow(pow($distanceX, 2) + pow($distanceY, 2), 0.5);

    }
}


1		<?php
2		/**
3		* PHPCoord
4		* @package PHPCoord
5		* @author Jonathan Stott
6		* @author Doug Wright
7		*/
8		namespace PHPCoord;
9
10		/**
11		* Abstract class representing a Tranverse Mercator Projection
12		* @author Doug Wright
13		* @package PHPCoord
14		*/
15		abstract class TransverseMercator
16		{
17
18		/**
19		* X
20		* @var float
21		*/
22		protected $x;
23
24		/**
25		* Y
26		* @var float
27		*/
28		protected $y;
29
30		/**
31		* h
32		* @var float
33		*/
34		protected $h;
35
36		/**
37		* Reference ellipsoid used in this datum
38		* @var RefEll
39		*/
40		protected $refEll;
41
42		/**
43		* Cartesian constructor.
44		* @param float $x
45		* @param float $y
46		* @param float $h
47		* @param RefEll $refEll
48		*/
49	30	public function __construct($x, $y, $h, RefEll $refEll)
50		{
51	30	$this->setX($x);
52	30	$this->setY($y);
53	30	$this->setH($h);
54	30	$this->setRefEll($refEll);
55		}
56
57		/**
58		* String version of coordinate.
59		* @return string
60		*/
61		public function __toString()
62		{
63		return "({$this->x}, {$this->y}, {$this->h})";
64		}
65
66		/**
67		* @return float
68		*/
69	2	public function getX()
70		{
71	2	return $this->x;
72		}
73
74		/**
75		* @param float $x
76		*/
77	30	public function setX($x)
78		{
79	30	$this->x = $x;
80		}
81
82		/**
83		* @return float
84		*/
85	2	public function getY()
86		{
87	2	return $this->y;
88		}
89
90		/**
91		* @param float $y
92		*/
93	30	public function setY($y)
94		{
95	30	$this->y = $y;
96		}
97
98		/**
99		* @return float
100		*/
101	1	public function getH()
102		{
103	1	return $this->h;
104		}
105
106		/**
107		* @param float $h
108		*/
109	30	public function setH($h)
110		{
111	30	$this->h = $h;
112		}
113
114		/**
115		* @return RefEll
116		*/
117	1	public function getRefEll()
118		{
119	1	return $this->refEll;
120		}
121
122		/**
123		* @param RefEll $refEll
124		*/
125	30	public function setRefEll(RefEll $refEll)
126		{
127	30	$this->refEll = $refEll;
128		}
129
130
131		/**
132		* Reference ellipsoid used by this projection
133		* @return RefEll
134		*/
135		abstract public function getReferenceEllipsoid();
136
137		/**
138		* Scale factor at central meridian
139		* @return float
140		*/
141		abstract public function getScaleFactor();
142
143		/**
144		* Northing of true origin
145		* @return float
146		*/
147		abstract public function getOriginNorthing();
148
149		/**
150		* Easting of true origin
151		* @return float
152		*/
153		abstract public function getOriginEasting();
154
155		/**
156		* Latitude of true origin
157		* @return float
158		*/
159		abstract public function getOriginLatitude();
160
161		/**
162		* Longitude of true origin
163		* @return float
164		*/
165		abstract public function getOriginLongitude();
166
167		/**
168		* Convert this grid reference into a latitude and longitude
169		* Formula for transformation is taken from OS document
170		* "A Guide to Coordinate Systems in Great Britain"
171		*
172		* @param float $N map coordinate (northing) of point to convert
173		* @param float $E map coordinate (easting) of point to convert
174		* @param float $N0 map coordinate (northing) of true origin
175		* @param float $E0 map coordinate (easting) of true origin
176		* @param float $phi0 map coordinate (latitude) of true origin
177		* @param float $lambda0 map coordinate (longitude) of true origin and central meridian
178		* @return LatLng
179		*/
180	7	public function convertToLatitudeLongitude($N, $E, $N0, $E0, $phi0, $lambda0)
181		{
182
183	7	$phi0 = deg2rad($phi0);
184	7	$lambda0 = deg2rad($lambda0);
185
186	7	$refEll = $this->getReferenceEllipsoid();
187	7	$F0 = $this->getScaleFactor();
188
189	7	$a = $refEll->getMaj();
190	7	$b = $refEll->getMin();
191	7	$eSquared = $refEll->getEcc();
192	7	$n = ($a - $b) / ($a + $b);
193	7	$phiPrime = (($N - $N0) / ($a * $F0)) + $phi0;
194
195		do {
196		$M =
197	7	($b * $F0)
198	7	* (((1 + $n + ((5 / 4) * $n * $n) + ((5 / 4) * $n * $n * $n))
199	7	* ($phiPrime - $phi0))
200	7	- (((3 * $n) + (3 * $n * $n) + ((21 / 8) * $n * $n * $n))
201	7	* sin($phiPrime - $phi0)
202	7	* cos($phiPrime + $phi0))
203	7	+ ((((15 / 8) * $n * $n) + ((15 / 8) * $n * $n * $n))
204	7	* sin(2 * ($phiPrime - $phi0))
205	7	* cos(2 * ($phiPrime + $phi0)))
206	7	- (((35 / 24) * $n * $n * $n)
207	7	* sin(3 * ($phiPrime - $phi0))
208	7	* cos(3 * ($phiPrime + $phi0))));
209	7	$phiPrime += ($N - $N0 - $M) / ($a * $F0);
210	7	} while (($N - $N0 - $M) >= 0.00001);
211	7	$v = $a * $F0 * pow(1 - $eSquared * pow(sin($phiPrime), 2), -0.5);
212		$rho =
213		$a
214	7	* $F0
215	7	* (1 - $eSquared)
216	7	* pow(1 - $eSquared * pow(sin($phiPrime), 2), -1.5);
217	7	$etaSquared = ($v / $rho) - 1;
218	7	$VII = tan($phiPrime) / (2 * $rho * $v);
219		$VIII =
220	7	(tan($phiPrime) / (24 * $rho * pow($v, 3)))
221		* (5
222	7	+ (3 * pow(tan($phiPrime), 2))
223	7	+ $etaSquared
224	7	- (9 * pow(tan($phiPrime), 2) * $etaSquared));
225		$IX =
226	7	(tan($phiPrime) / (720 * $rho * pow($v, 5)))
227		* (61
228	7	+ (90 * pow(tan($phiPrime), 2))
229	7	+ (45 * pow(tan($phiPrime), 2) * pow(tan($phiPrime), 2)));
230	7	$X = (1 / cos($phiPrime)) / $v;
231		$XI =
232	7	((1 / cos($phiPrime)) / (6 * $v * $v * $v))
233	7	* (($v / $rho) + (2 * pow(tan($phiPrime), 2)));
234		$XII =
235	7	((1 / cos($phiPrime)) / (120 * pow($v, 5)))
236		* (5
237	7	+ (28 * pow(tan($phiPrime), 2))
238	7	+ (24 * pow(tan($phiPrime), 4)));
239		$XIIA =
240	7	((1 / cos($phiPrime)) / (5040 * pow($v, 7)))
241		* (61
242	7	+ (662 * pow(tan($phiPrime), 2))
243	7	+ (1320 * pow(tan($phiPrime), 4))
244		+ (720
245	7	* pow(tan($phiPrime), 6)));
246		$phi =
247		$phiPrime
248	7	- ($VII * pow($E - $E0, 2))
249	7	+ ($VIII * pow($E - $E0, 4))
250	7	- ($IX * pow($E - $E0, 6));
251		$lambda =
252		$lambda0
253	7	+ ($X * ($E - $E0))
254	7	- ($XI * pow($E - $E0, 3))
255	7	+ ($XII * pow($E - $E0, 5))
256	7	- ($XIIA * pow($E - $E0, 7));
257
258	7	return new LatLng(rad2deg($phi), rad2deg($lambda), 0, $refEll);
259		}
260
261		/**
262		* Calculate the surface distance between this object and the one
263		* passed in as a parameter.
264		*
265		* @param self $to object to measure the distance to
		0 ignored issues – show Documentation introduced 2017-01-22 19:24 UTC by Report Bug Copy Issue Report Should the type for parameter `$to` not be `\self`? This check looks for `@param` annotations where the type inferred by our type inference engine differs from the declared type. It makes a suggestion as to what type it considers more descriptive. Most often this is a case of a parameter that can be null in addition to its declared types. Loading history...
266		* @return float
		0 ignored issues – show Documentation introduced 2017-01-22 19:24 UTC by Report Bug Copy Issue Report Should the return type not be `integer\|double`? This check compares the return type specified in the `@return` annotation of a function or method doc comment with the types returned by the function and raises an issue if they mismatch. Loading history...
267		*/
268	1	public function distance(self $to) {
269
270	1	if ($this->refEll != $to->refEll) {
271		throw new \RuntimeException('Source and destination co-ordinates are not using the same ellipsoid');
272		}
273
274		//Because this is a 2D grid, we can use simple Pythagoras
275	1	$distanceX = $to->getX()-$this->getX();
276	1	$distanceY = $to->getY()-$this->getY();
277
278	1	return pow(pow($distanceX, 2) + pow($distanceY, 2), 0.5);
279
280		}
281		}
282

dvdoug / PHPCoord

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TransverseMercator::getScaleFactor()

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