|
1
|
|
|
<?php |
|
2
|
|
|
|
|
3
|
|
|
/** |
|
4
|
|
|
* PHPCoord. |
|
5
|
|
|
* |
|
6
|
|
|
* @author Doug Wright |
|
7
|
|
|
*/ |
|
8
|
|
|
declare(strict_types=1); |
|
9
|
|
|
|
|
10
|
|
|
namespace PHPCoord\Point; |
|
11
|
|
|
|
|
12
|
|
|
use DateTime; |
|
13
|
|
|
use DateTimeImmutable; |
|
14
|
|
|
use DateTimeInterface; |
|
15
|
|
|
use PHPCoord\CoordinateOperation\AutoConversion; |
|
16
|
|
|
use PHPCoord\CoordinateOperation\ComplexNumber; |
|
17
|
|
|
use PHPCoord\CoordinateOperation\ConvertiblePoint; |
|
18
|
|
|
use PHPCoord\CoordinateOperation\OSTNOSGM15Grid; |
|
19
|
|
|
use PHPCoord\CoordinateReferenceSystem\Compound; |
|
20
|
|
|
use PHPCoord\CoordinateReferenceSystem\Geocentric; |
|
21
|
|
|
use PHPCoord\CoordinateReferenceSystem\Geographic2D; |
|
22
|
|
|
use PHPCoord\CoordinateReferenceSystem\Geographic3D; |
|
23
|
|
|
use PHPCoord\CoordinateReferenceSystem\Projected; |
|
24
|
|
|
use PHPCoord\CoordinateReferenceSystem\Vertical; |
|
25
|
|
|
use PHPCoord\CoordinateSystem\Axis; |
|
26
|
|
|
use PHPCoord\CoordinateSystem\Cartesian; |
|
27
|
|
|
use PHPCoord\Exception\InvalidAxesException; |
|
28
|
|
|
use PHPCoord\Exception\InvalidCoordinateReferenceSystemException; |
|
29
|
|
|
use PHPCoord\Exception\UnknownAxisException; |
|
30
|
|
|
use PHPCoord\UnitOfMeasure\Angle\Angle; |
|
31
|
|
|
use PHPCoord\UnitOfMeasure\Angle\ArcSecond; |
|
32
|
|
|
use PHPCoord\UnitOfMeasure\Angle\Degree; |
|
33
|
|
|
use PHPCoord\UnitOfMeasure\Angle\Radian; |
|
34
|
|
|
use PHPCoord\UnitOfMeasure\Length\Length; |
|
35
|
|
|
use PHPCoord\UnitOfMeasure\Length\Metre; |
|
36
|
|
|
use PHPCoord\UnitOfMeasure\Scale\Coefficient; |
|
37
|
|
|
use PHPCoord\UnitOfMeasure\Scale\Scale; |
|
38
|
|
|
use PHPCoord\UnitOfMeasure\Scale\Unity; |
|
39
|
|
|
|
|
40
|
|
|
use function abs; |
|
41
|
|
|
use function asinh; |
|
42
|
|
|
use function atan; |
|
43
|
|
|
use function atan2; |
|
44
|
|
|
use function atanh; |
|
45
|
|
|
use function cos; |
|
46
|
|
|
use function cosh; |
|
47
|
|
|
use function count; |
|
48
|
|
|
use function hypot; |
|
49
|
|
|
use function implode; |
|
50
|
|
|
use function is_nan; |
|
51
|
|
|
use function log; |
|
52
|
|
|
use function max; |
|
53
|
|
|
use function sin; |
|
54
|
|
|
use function sinh; |
|
55
|
|
|
use function sqrt; |
|
56
|
|
|
use function substr; |
|
57
|
|
|
use function tan; |
|
58
|
|
|
use function tanh; |
|
59
|
|
|
use function assert; |
|
60
|
|
|
|
|
61
|
|
|
use const M_E; |
|
62
|
|
|
use const M_PI; |
|
63
|
|
|
use const M_PI_2; |
|
64
|
|
|
|
|
65
|
|
|
/** |
|
66
|
|
|
* Coordinate representing a point on a map projection. |
|
67
|
|
|
*/ |
|
68
|
|
|
class ProjectedPoint extends Point implements ConvertiblePoint |
|
69
|
|
|
{ |
|
70
|
|
|
use AutoConversion { |
|
71
|
|
|
convert as protected autoConvert; |
|
72
|
|
|
} |
|
73
|
|
|
|
|
74
|
|
|
/** |
|
75
|
|
|
* Easting. |
|
76
|
|
|
*/ |
|
77
|
|
|
protected Length $easting; |
|
78
|
|
|
|
|
79
|
|
|
/** |
|
80
|
|
|
* Northing. |
|
81
|
|
|
*/ |
|
82
|
|
|
protected Length $northing; |
|
83
|
|
|
|
|
84
|
|
|
/** |
|
85
|
|
|
* Westing. |
|
86
|
|
|
*/ |
|
87
|
|
|
protected Length $westing; |
|
88
|
|
|
|
|
89
|
|
|
/** |
|
90
|
|
|
* Southing. |
|
91
|
|
|
*/ |
|
92
|
|
|
protected Length $southing; |
|
93
|
|
|
|
|
94
|
|
|
/** |
|
95
|
|
|
* Height. |
|
96
|
|
|
*/ |
|
97
|
|
|
protected ?Length $height; |
|
98
|
|
|
|
|
99
|
|
|
/** |
|
100
|
|
|
* Coordinate reference system. |
|
101
|
|
|
*/ |
|
102
|
|
|
protected Projected $crs; |
|
103
|
|
|
|
|
104
|
|
|
/** |
|
105
|
|
|
* Coordinate epoch (date for which the specified coordinates represented this point). |
|
106
|
|
|
*/ |
|
107
|
|
|
protected ?DateTimeImmutable $epoch; |
|
108
|
1441 |
|
|
|
109
|
|
|
protected function __construct(Projected $crs, ?Length $easting, ?Length $northing, ?Length $westing, ?Length $southing, ?DateTimeInterface $epoch, ?Length $height) |
|
110
|
1441 |
|
{ |
|
111
|
|
|
if (count($crs->getCoordinateSystem()->getAxes()) === 2 && $height !== null) { |
|
112
|
|
|
throw new InvalidCoordinateReferenceSystemException('A 2D projected point must not include a height'); |
|
113
|
|
|
} |
|
114
|
1441 |
|
|
|
115
|
|
|
if (count($crs->getCoordinateSystem()->getAxes()) === 3 && $height === null) { |
|
116
|
|
|
throw new InvalidCoordinateReferenceSystemException('A 3D projected point must include a height, none given'); |
|
117
|
|
|
} |
|
118
|
1441 |
|
|
|
119
|
1441 |
|
$this->crs = $crs; |
|
120
|
|
|
$cs = $this->crs->getCoordinateSystem(); |
|
121
|
1441 |
|
|
|
122
|
1441 |
|
$eastingAxis = $cs->hasAxisByName(Axis::EASTING) ? $cs->getAxisByName(Axis::EASTING) : null; |
|
123
|
1441 |
|
$westingAxis = $cs->hasAxisByName(Axis::WESTING) ? $cs->getAxisByName(Axis::WESTING) : null; |
|
124
|
1441 |
|
$northingAxis = $cs->hasAxisByName(Axis::NORTHING) ? $cs->getAxisByName(Axis::NORTHING) : null; |
|
125
|
|
|
$southingAxis = $cs->hasAxisByName(Axis::SOUTHING) ? $cs->getAxisByName(Axis::SOUTHING) : null; |
|
126
|
1441 |
|
|
|
127
|
1315 |
|
if ($easting && $eastingAxis) { |
|
128
|
1315 |
|
$this->easting = $easting::convert($easting, $eastingAxis->getUnitOfMeasureId()); |
|
129
|
126 |
|
$this->westing = $this->easting->multiply(-1); |
|
130
|
117 |
|
} elseif ($westing && $westingAxis) { |
|
131
|
117 |
|
$this->westing = $westing::convert($westing, $westingAxis->getUnitOfMeasureId()); |
|
132
|
|
|
$this->easting = $this->westing->multiply(-1); |
|
133
|
9 |
|
} else { |
|
134
|
|
|
throw new InvalidAxesException($crs->getCoordinateSystem()->getAxes()); |
|
135
|
|
|
} |
|
136
|
1432 |
|
|
|
137
|
1342 |
|
if ($northing && $northingAxis) { |
|
138
|
1342 |
|
$this->northing = $northing::convert($northing, $northingAxis->getUnitOfMeasureId()); |
|
139
|
90 |
|
$this->southing = $this->northing->multiply(-1); |
|
140
|
81 |
|
} elseif ($southing && $southingAxis) { |
|
141
|
81 |
|
$this->southing = $southing::convert($southing, $southingAxis->getUnitOfMeasureId()); |
|
142
|
|
|
$this->northing = $this->southing->multiply(-1); |
|
143
|
9 |
|
} else { |
|
144
|
|
|
throw new InvalidAxesException($crs->getCoordinateSystem()->getAxes()); |
|
145
|
|
|
} |
|
146
|
1423 |
|
|
|
147
|
36 |
|
if ($epoch instanceof DateTime) { |
|
148
|
|
|
$epoch = DateTimeImmutable::createFromMutable($epoch); |
|
149
|
1423 |
|
} |
|
150
|
|
|
$this->epoch = $epoch; |
|
151
|
1423 |
|
|
|
152
|
|
|
$this->height = $height; |
|
153
|
|
|
} |
|
154
|
1198 |
|
|
|
155
|
|
|
public static function create(Projected $crs, ?Length $easting, ?Length $northing, ?Length $westing, ?Length $southing, ?DateTimeInterface $epoch = null, ?Length $height = null): self |
|
156
|
1198 |
|
{ |
|
157
|
1198 |
|
return match ($crs->getSRID()) { |
|
158
|
1144 |
|
Projected::EPSG_OSGB36_BRITISH_NATIONAL_GRID => new BritishNationalGridPoint($easting, $northing, $epoch), |
|
|
|
|
|
|
159
|
1108 |
|
Projected::EPSG_TM75_IRISH_GRID => new IrishGridPoint($easting, $northing, $epoch), |
|
|
|
|
|
|
160
|
1198 |
|
Projected::EPSG_IRENET95_IRISH_TRANSVERSE_MERCATOR => new IrishTransverseMercatorPoint($easting, $northing, $epoch), |
|
|
|
|
|
|
161
|
1198 |
|
default => new self($crs, $easting, $northing, $westing, $southing, $epoch, $height), |
|
162
|
|
|
}; |
|
163
|
|
|
} |
|
164
|
532 |
|
|
|
165
|
|
|
public static function createFromEastingNorthing(Projected $crs, Length $easting, Length $northing, ?DateTimeInterface $epoch = null, ?Length $height = null): self |
|
166
|
532 |
|
{ |
|
167
|
|
|
return static::create($crs, $easting, $northing, null, null, $epoch, $height); |
|
168
|
|
|
} |
|
169
|
27 |
|
|
|
170
|
|
|
public static function createFromWestingNorthing(Projected $crs, Length $westing, Length $northing, ?DateTimeInterface $epoch = null, ?Length $height = null): self |
|
171
|
27 |
|
{ |
|
172
|
|
|
return static::create($crs, null, $northing, $westing, null, $epoch, $height); |
|
173
|
|
|
} |
|
174
|
54 |
|
|
|
175
|
|
|
public static function createFromWestingSouthing(Projected $crs, Length $westing, Length $southing, ?DateTimeInterface $epoch = null, ?Length $height = null): self |
|
176
|
54 |
|
{ |
|
177
|
|
|
return static::create($crs, null, null, $westing, $southing, $epoch, $height); |
|
178
|
|
|
} |
|
179
|
640 |
|
|
|
180
|
|
|
public function getEasting(): Length |
|
181
|
640 |
|
{ |
|
182
|
|
|
return $this->easting; |
|
183
|
|
|
} |
|
184
|
658 |
|
|
|
185
|
|
|
public function getNorthing(): Length |
|
186
|
658 |
|
{ |
|
187
|
|
|
return $this->northing; |
|
188
|
|
|
} |
|
189
|
90 |
|
|
|
190
|
|
|
public function getWesting(): Length |
|
191
|
90 |
|
{ |
|
192
|
|
|
return $this->westing; |
|
193
|
|
|
} |
|
194
|
72 |
|
|
|
195
|
|
|
public function getSouthing(): Length |
|
196
|
72 |
|
{ |
|
197
|
|
|
return $this->southing; |
|
198
|
|
|
} |
|
199
|
9 |
|
|
|
200
|
|
|
public function getHeight(): ?Length |
|
201
|
9 |
|
{ |
|
202
|
|
|
return $this->height; |
|
203
|
|
|
} |
|
204
|
289 |
|
|
|
205
|
|
|
public function getCRS(): Projected |
|
206
|
289 |
|
{ |
|
207
|
|
|
return $this->crs; |
|
208
|
|
|
} |
|
209
|
27 |
|
|
|
210
|
|
|
public function getCoordinateEpoch(): ?DateTimeImmutable |
|
211
|
27 |
|
{ |
|
212
|
|
|
return $this->epoch; |
|
213
|
|
|
} |
|
214
|
|
|
|
|
215
|
|
|
/** |
|
216
|
|
|
* Calculate distance between two points. |
|
217
|
|
|
* Because this is a simple grid, we can use Pythagoras. |
|
218
|
63 |
|
*/ |
|
219
|
|
|
public function calculateDistance(Point $to): Length |
|
220
|
|
|
{ |
|
221
|
63 |
|
try { |
|
222
|
63 |
|
if ($to instanceof ConvertiblePoint) { |
|
223
|
|
|
$to = $to->convert($this->crs); |
|
224
|
|
|
} |
|
225
|
63 |
|
} finally { |
|
226
|
9 |
|
if ($to->getCRS()->getSRID() !== $this->crs->getSRID()) { |
|
227
|
|
|
throw new InvalidCoordinateReferenceSystemException('Can only calculate distances between two points in the same CRS'); |
|
228
|
|
|
} |
|
229
|
|
|
|
|
230
|
54 |
|
/** @var ProjectedPoint $to */ |
|
231
|
54 |
|
return new Metre( |
|
232
|
54 |
|
sqrt( |
|
233
|
54 |
|
($to->getEasting()->getValue() - $this->getEasting()->getValue()) ** 2 + |
|
234
|
54 |
|
($to->getNorthing()->getValue() - $this->getNorthing()->getValue()) ** 2 |
|
235
|
54 |
|
) |
|
236
|
|
|
); |
|
237
|
|
|
} |
|
238
|
|
|
} |
|
239
|
54 |
|
|
|
240
|
|
|
public function asGeographicPoint(): GeographicPoint |
|
241
|
54 |
|
{ |
|
242
|
54 |
|
$geographicPoint = $this->performOperation($this->crs->getDerivingConversion(), $this->crs->getBaseCRS(), true); |
|
243
|
|
|
assert($geographicPoint instanceof GeographicPoint); |
|
244
|
54 |
|
|
|
245
|
|
|
return $geographicPoint; |
|
246
|
|
|
} |
|
247
|
118 |
|
|
|
248
|
|
|
public function convert(Compound|Geocentric|Geographic2D|Geographic3D|Projected|Vertical $to, bool $ignoreBoundaryRestrictions = false): Point |
|
249
|
118 |
|
{ |
|
250
|
45 |
|
if ($to->getSRID() === $this->crs->getBaseCRS()->getSRID()) { |
|
251
|
|
|
return $this->performOperation($this->crs->getDerivingConversion(), $this->crs->getBaseCRS(), true); |
|
252
|
|
|
} |
|
253
|
100 |
|
|
|
254
|
|
|
return $this->autoConvert($to, $ignoreBoundaryRestrictions); |
|
255
|
|
|
} |
|
256
|
162 |
|
|
|
257
|
|
|
public function __toString(): string |
|
258
|
162 |
|
{ |
|
259
|
162 |
|
$values = []; |
|
260
|
162 |
|
foreach ($this->getCRS()->getCoordinateSystem()->getAxes() as $axis) { |
|
261
|
144 |
|
if ($axis->getName() === Axis::EASTING) { |
|
262
|
162 |
|
$values[] = $this->easting; |
|
263
|
153 |
|
} elseif ($axis->getName() === Axis::NORTHING) { |
|
264
|
18 |
|
$values[] = $this->northing; |
|
265
|
18 |
|
} elseif ($axis->getName() === Axis::WESTING) { |
|
266
|
9 |
|
$values[] = $this->westing; |
|
267
|
9 |
|
} elseif ($axis->getName() === Axis::SOUTHING) { |
|
268
|
|
|
$values[] = $this->southing; |
|
269
|
|
|
} elseif ($axis->getName() === Axis::ELLIPSOIDAL_HEIGHT) { |
|
270
|
|
|
$values[] = $this->height; |
|
271
|
|
|
} else { |
|
272
|
|
|
throw new UnknownAxisException(); // @codeCoverageIgnore |
|
273
|
|
|
} |
|
274
|
|
|
} |
|
275
|
162 |
|
|
|
276
|
|
|
return '(' . implode(', ', $values) . ')'; |
|
277
|
|
|
} |
|
278
|
|
|
|
|
279
|
|
|
/** |
|
280
|
|
|
* Affine parametric transformation. |
|
281
|
9 |
|
*/ |
|
282
|
|
|
public function affineParametricTransform( |
|
283
|
|
|
Projected $to, |
|
284
|
|
|
Length $A0, |
|
285
|
|
|
Coefficient $A1, |
|
286
|
|
|
Coefficient $A2, |
|
287
|
|
|
Length $B0, |
|
288
|
|
|
Coefficient $B1, |
|
289
|
|
|
Coefficient $B2, |
|
290
|
|
|
bool $inReverse |
|
291
|
9 |
|
): self { |
|
292
|
9 |
|
$xs = $this->easting->getValue(); // native unit to metre conversion already embedded in the scale factor |
|
293
|
|
|
$ys = $this->northing->getValue(); // native unit to metre conversion already embedded in the scale factor |
|
294
|
9 |
|
|
|
295
|
|
|
if ($inReverse) { |
|
296
|
|
|
$D = ($A1->getValue() * $B2->getValue()) - ($A2->getValue() * $B1->getValue()); |
|
297
|
|
|
$a0 = (($A2->getValue() * $B0->asMetres()->getValue()) - ($B2->getValue() * $A0->asMetres()->getValue())) / $D; |
|
298
|
|
|
$b0 = (($B1->getValue() * $A0->asMetres()->getValue()) - ($A1->getValue() * $B0->asMetres()->getValue())) / $D; |
|
299
|
|
|
$a1 = $B2->getValue() / $D; |
|
300
|
|
|
$a2 = -$A2->getValue() / $D; |
|
301
|
|
|
$b1 = -$B1->getValue() / $D; |
|
302
|
|
|
$b2 = $A1->getValue() / $D; |
|
303
|
9 |
|
} else { |
|
304
|
9 |
|
$a0 = $A0->asMetres()->getValue(); |
|
305
|
9 |
|
$a1 = $A1->getValue(); |
|
306
|
9 |
|
$a2 = $A2->getValue(); |
|
307
|
9 |
|
$b0 = $B0->asMetres()->getValue(); |
|
308
|
9 |
|
$b1 = $B1->getValue(); |
|
309
|
|
|
$b2 = $B2->getValue(); |
|
310
|
|
|
} |
|
311
|
9 |
|
|
|
312
|
9 |
|
$xt = $a0 + ($a1 * $xs) + ($a2 * $ys); |
|
313
|
|
|
$yt = $b0 + ($b1 * $xs) + ($b2 * $ys); |
|
314
|
9 |
|
|
|
315
|
|
|
return static::create($to, new Metre($xt), new Metre($yt), new Metre(-$xt), new Metre(-$yt), $this->epoch); |
|
316
|
|
|
} |
|
317
|
|
|
|
|
318
|
|
|
/** |
|
319
|
|
|
* Albers Equal Area. |
|
320
|
18 |
|
*/ |
|
321
|
|
|
public function albersEqualArea( |
|
322
|
|
|
Geographic2D|Geographic3D $to, |
|
323
|
|
|
Angle $latitudeOfFalseOrigin, |
|
324
|
|
|
Angle $longitudeOfFalseOrigin, |
|
325
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
326
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
327
|
|
|
Length $eastingAtFalseOrigin, |
|
328
|
|
|
Length $northingAtFalseOrigin |
|
329
|
18 |
|
): GeographicPoint { |
|
330
|
18 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
331
|
18 |
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtFalseOrigin->asMetres()->getValue(); |
|
332
|
18 |
|
$northing = $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue(); |
|
333
|
18 |
|
$phiOrigin = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
334
|
18 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
335
|
18 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
336
|
18 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
337
|
18 |
|
$e = $ellipsoid->getEccentricity(); |
|
338
|
18 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
339
|
18 |
|
$e4 = $e ** 4; |
|
340
|
|
|
$e6 = $e ** 6; |
|
341
|
18 |
|
|
|
342
|
18 |
|
$centralMeridianFirstParallel = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
343
|
|
|
$centralMeridianSecondParallel = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
344
|
18 |
|
|
|
345
|
18 |
|
$alphaOrigin = (1 - $e2) * (sin($phiOrigin) / (1 - $e2 * sin($phiOrigin) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($phiOrigin)) / (1 + $e * sin($phiOrigin)))); |
|
346
|
18 |
|
$alphaFirstParallel = (1 - $e2) * (sin($phi1) / (1 - $e2 * sin($phi1) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($phi1)) / (1 + $e * sin($phi1)))); |
|
347
|
|
|
$alphaSecondParallel = (1 - $e2) * (sin($phi2) / (1 - $e2 * sin($phi2) ** 2) - (1 / 2 / $e) * log((1 - $e * sin($phi2)) / (1 + $e * sin($phi2)))); |
|
348
|
18 |
|
|
|
349
|
18 |
|
$n = ($centralMeridianFirstParallel ** 2 - $centralMeridianSecondParallel ** 2) / ($alphaSecondParallel - $alphaFirstParallel); |
|
350
|
18 |
|
$C = $centralMeridianFirstParallel ** 2 + $n * $alphaFirstParallel; |
|
351
|
18 |
|
$rhoOrigin = $a * sqrt($C - $n * $alphaOrigin) / $n; |
|
352
|
18 |
|
$rhoPrime = hypot($easting, $rhoOrigin - $northing); |
|
353
|
18 |
|
$alphaPrime = ($C - $rhoPrime ** 2 * $n ** 2 / $a ** 2) / $n; |
|
354
|
18 |
|
$betaPrime = self::asin($alphaPrime / (1 - (1 - $e2) / 2 / $e * log((1 - $e) / (1 + $e)))); |
|
355
|
9 |
|
if ($n > 0) { |
|
356
|
|
|
$theta = atan2($easting, $rhoOrigin - $northing); |
|
357
|
9 |
|
} else { |
|
358
|
|
|
$theta = atan2(-$easting, $northing - $rhoOrigin); |
|
359
|
|
|
} |
|
360
|
18 |
|
|
|
361
|
18 |
|
$latitude = $betaPrime + (($e2 / 3 + 31 * $e4 / 180 + 517 * $e6 / 5040) * sin(2 * $betaPrime)) + ((23 * $e4 / 360 + 251 * $e6 / 3780) * sin(4 * $betaPrime)) + ((761 * $e6 / 45360) * sin(6 * $betaPrime)); |
|
362
|
|
|
$longitude = $longitudeOfFalseOrigin->asRadians()->getValue() + ($theta / $n); |
|
363
|
18 |
|
|
|
364
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
365
|
|
|
} |
|
366
|
|
|
|
|
367
|
|
|
/** |
|
368
|
|
|
* American Polyconic. |
|
369
|
9 |
|
*/ |
|
370
|
|
|
public function americanPolyconic( |
|
371
|
|
|
Geographic2D|Geographic3D $to, |
|
372
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
373
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
374
|
|
|
Length $falseEasting, |
|
375
|
|
|
Length $falseNorthing |
|
376
|
9 |
|
): GeographicPoint { |
|
377
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
378
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
379
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
380
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
381
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
382
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
383
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
384
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
385
|
9 |
|
$e4 = $e ** 4; |
|
386
|
|
|
$e6 = $e ** 6; |
|
387
|
9 |
|
|
|
388
|
9 |
|
$i = (1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256); |
|
389
|
9 |
|
$ii = (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024); |
|
390
|
9 |
|
$iii = (15 * $e4 / 256 + 45 * $e6 / 1024); |
|
391
|
|
|
$iv = (35 * $e6 / 3072); |
|
392
|
9 |
|
|
|
393
|
|
|
$MO = $a * ($i * $latitudeOrigin - $ii * sin(2 * $latitudeOrigin) + $iii * sin(4 * $latitudeOrigin) - $iv * sin(6 * $latitudeOrigin)); |
|
394
|
9 |
|
|
|
395
|
|
|
if ($MO === $northing) { |
|
396
|
|
|
$latitude = 0; |
|
397
|
|
|
$longitude = $longitudeOrigin + $easting / $a; |
|
398
|
9 |
|
} else { |
|
399
|
9 |
|
$A = ($MO + $northing) / $a; |
|
400
|
|
|
$B = $A ** 2 + $easting ** 2 / $a ** 2; |
|
401
|
9 |
|
|
|
402
|
9 |
|
$latitude = $A; |
|
403
|
|
|
$C = sqrt(1 - $e2 * sin($latitude) ** 2) * tan($latitude); |
|
404
|
9 |
|
do { |
|
405
|
9 |
|
$latitudeN = $latitude; |
|
406
|
9 |
|
$Ma = $i * $latitude - $ii * sin(2 * $latitude) + $iii * sin(4 * $latitude) - $iv * sin(6 * $latitude); |
|
407
|
9 |
|
$MnPrime = $i - 2 * $ii * cos(2 * $latitude) + 4 * $iii * cos(4 * $latitude) - 6 * $iv * cos(6 * $latitude); |
|
408
|
9 |
|
$latitude = $latitude - ($A * ($C * $Ma + 1) - $Ma - $C * ($Ma ** 2 + $B) / 2) / ($e2 * sin(2 * $latitude) * ($Ma ** 2 + $B - 2 * $A * $Ma) / 4 * $C + ($A - $Ma) * ($C * $MnPrime - (2 / sin(2 * $latitude))) - $MnPrime); |
|
409
|
9 |
|
$C = sqrt(1 - $e2 * sin($latitude) ** 2) * tan($latitude); |
|
410
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
411
|
9 |
|
|
|
412
|
|
|
$longitude = $longitudeOrigin + self::asin($easting * $C / $a) / sin($latitude); |
|
413
|
|
|
} |
|
414
|
9 |
|
|
|
415
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
416
|
|
|
} |
|
417
|
|
|
|
|
418
|
|
|
/** |
|
419
|
|
|
* Bonne. |
|
420
|
9 |
|
*/ |
|
421
|
|
|
public function bonne( |
|
422
|
|
|
Geographic2D|Geographic3D $to, |
|
423
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
424
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
425
|
|
|
Length $falseEasting, |
|
426
|
|
|
Length $falseNorthing |
|
427
|
9 |
|
): GeographicPoint { |
|
428
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
429
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
430
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
431
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
432
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
433
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
434
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
435
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
436
|
9 |
|
$e4 = $e ** 4; |
|
437
|
|
|
$e6 = $e ** 6; |
|
438
|
9 |
|
|
|
439
|
9 |
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
440
|
9 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
441
|
|
|
$rho = hypot($easting, $a * $mO / sin($latitudeOrigin) - $northing) * static::sign($latitudeOrigin); |
|
442
|
9 |
|
|
|
443
|
9 |
|
$M = $a * $mO / sin($latitudeOrigin) + $MO - $rho; |
|
444
|
9 |
|
$mu = $M / ($a * (1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256)); |
|
445
|
|
|
$e1 = (1 - sqrt(1 - $e2)) / (1 + sqrt(1 - $e2)); |
|
446
|
9 |
|
|
|
447
|
9 |
|
$latitude = $mu + ((3 * $e1 / 2) - (27 * $e1 ** 3 / 32)) * sin(2 * $mu) + ((21 * $e1 ** 2 / 16) - (55 * $e1 ** 4 / 32)) * sin(4 * $mu) + (151 * $e1 ** 3 / 96) * sin(6 * $mu) + (1097 * $e1 ** 4 / 512) * sin(8 * $mu); |
|
448
|
|
|
$m = cos($latitude) / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
449
|
9 |
|
|
|
450
|
|
|
if ($m === 0.0) { |
|
451
|
9 |
|
$longitude = $longitudeOrigin; // pole |
|
452
|
9 |
|
} elseif ($latitudeOrigin >= 0) { |
|
453
|
|
|
$longitude = $longitudeOrigin + $rho * atan2($easting, $a * $mO / sin($latitudeOrigin) - $northing) / $a / $m; |
|
454
|
|
|
} else { |
|
455
|
|
|
$longitude = $longitudeOrigin + $rho * atan2(-$easting, -($a * $mO / sin($latitudeOrigin) - $northing)) / $a / $m; |
|
456
|
|
|
} |
|
457
|
9 |
|
|
|
458
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
459
|
|
|
} |
|
460
|
|
|
|
|
461
|
|
|
/** |
|
462
|
|
|
* Bonne South Orientated. |
|
463
|
9 |
|
*/ |
|
464
|
|
|
public function bonneSouthOrientated( |
|
465
|
|
|
Geographic2D|Geographic3D $to, |
|
466
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
467
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
468
|
|
|
Length $falseEasting, |
|
469
|
|
|
Length $falseNorthing |
|
470
|
9 |
|
): GeographicPoint { |
|
471
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
472
|
9 |
|
$westing = $falseEasting->asMetres()->getValue() - $this->westing->asMetres()->getValue(); |
|
473
|
9 |
|
$southing = $falseNorthing->asMetres()->getValue() - $this->southing->asMetres()->getValue(); |
|
474
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
475
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
476
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
477
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
478
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
479
|
9 |
|
$e4 = $e ** 4; |
|
480
|
|
|
$e6 = $e ** 6; |
|
481
|
9 |
|
|
|
482
|
9 |
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
483
|
9 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
484
|
|
|
$rho = hypot($westing, $a * $mO / sin($latitudeOrigin) - $southing) * static::sign($latitudeOrigin); |
|
485
|
9 |
|
|
|
486
|
9 |
|
$M = $a * $mO / sin($latitudeOrigin) + $MO - $rho; |
|
487
|
9 |
|
$mu = $M / ($a * (1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256)); |
|
488
|
|
|
$e1 = (1 - sqrt(1 - $e2)) / (1 + sqrt(1 - $e2)); |
|
489
|
9 |
|
|
|
490
|
9 |
|
$latitude = $mu + ((3 * $e1 / 2) - (27 * $e1 ** 3 / 32)) * sin(2 * $mu) + ((21 * $e1 ** 2 / 16) - (55 * $e1 ** 4 / 32)) * sin(4 * $mu) + (151 * $e1 ** 3 / 96) * sin(6 * $mu) + (1097 * $e1 ** 4 / 512) * sin(8 * $mu); |
|
491
|
|
|
$m = cos($latitude) / sqrt(1 - $e2 * sin($latitude) ** 2); |
|
492
|
9 |
|
|
|
493
|
|
|
if ($m === 0.0) { |
|
494
|
9 |
|
$longitude = $longitudeOrigin; // pole |
|
495
|
9 |
|
} elseif ($latitudeOrigin >= 0) { |
|
496
|
|
|
$longitude = $longitudeOrigin + $rho * atan2($westing, $a * $mO / sin($latitudeOrigin) - $southing) / $a / $m; |
|
497
|
|
|
} else { |
|
498
|
|
|
$longitude = $longitudeOrigin + $rho * atan2(-$westing, -($a * $mO / sin($latitudeOrigin) - $southing)) / $a / $m; |
|
499
|
|
|
} |
|
500
|
9 |
|
|
|
501
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
502
|
|
|
} |
|
503
|
|
|
|
|
504
|
|
|
/** |
|
505
|
|
|
* Cartesian Grid Offsets |
|
506
|
|
|
* This transformation allows calculation of coordinates in the target system by adding the parameter value to the |
|
507
|
|
|
* coordinate values of the point in the source system. |
|
508
|
9 |
|
*/ |
|
509
|
|
|
public function offsets( |
|
510
|
|
|
Projected $to, |
|
511
|
|
|
Length $eastingOffset, |
|
512
|
|
|
Length $northingOffset |
|
513
|
9 |
|
): self { |
|
514
|
9 |
|
$easting = $this->easting->asMetres()->getValue() + $eastingOffset->asMetres()->getValue(); |
|
515
|
|
|
$northing = $this->northing->asMetres()->getValue() + $northingOffset->asMetres()->getValue(); |
|
516
|
9 |
|
|
|
517
|
|
|
return static::create($to, new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $this->epoch); |
|
518
|
|
|
} |
|
519
|
|
|
|
|
520
|
|
|
/** |
|
521
|
|
|
* Cassini-Soldner. |
|
522
|
9 |
|
*/ |
|
523
|
|
|
public function cassiniSoldner( |
|
524
|
|
|
Geographic2D|Geographic3D $to, |
|
525
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
526
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
527
|
|
|
Length $falseEasting, |
|
528
|
|
|
Length $falseNorthing |
|
529
|
9 |
|
): GeographicPoint { |
|
530
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
531
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
532
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
533
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
534
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
535
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
536
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
537
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
538
|
9 |
|
$e4 = $e ** 4; |
|
539
|
|
|
$e6 = $e ** 6; |
|
540
|
9 |
|
|
|
541
|
|
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
542
|
9 |
|
|
|
543
|
9 |
|
$e1 = (1 - sqrt(1 - $e2)) / (1 + sqrt(1 - $e2)); |
|
544
|
9 |
|
$M = $MO + $northing; |
|
545
|
9 |
|
$mu = $M / ($a * (1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256)); |
|
546
|
|
|
$latitudeCentralMeridian = $mu + (3 * $e1 / 2 - 27 * $e1 ** 3 / 32) * sin(2 * $mu) + (21 * $e1 ** 2 / 16 - 55 * $e1 ** 4 / 32) * sin(4 * $mu) + (151 * $e1 ** 3 / 96) * sin(6 * $mu) + (1097 * $e1 ** 4 / 512) * sin(8 * $mu); |
|
547
|
9 |
|
|
|
548
|
9 |
|
$nu = $a / sqrt(1 - $e2 * sin($latitudeCentralMeridian) ** 2); |
|
549
|
|
|
$rho = $a * (1 - $e2) / (1 - $e2 * sin($latitudeCentralMeridian) ** 2) ** 1.5; |
|
550
|
9 |
|
|
|
551
|
9 |
|
$T = tan($latitudeCentralMeridian) ** 2; |
|
552
|
|
|
$D = $easting / $nu; |
|
553
|
9 |
|
|
|
554
|
9 |
|
$latitude = $latitudeCentralMeridian - ($nu * tan($latitudeCentralMeridian) / $rho) * ($D ** 2 / 2 - (1 + 3 * $T) * $D ** 4 / 24); |
|
555
|
|
|
$longitude = $longitudeOrigin + ($D - $T * $D ** 3 / 3 + (1 + 3 * $T) * $T * $D ** 5 / 15) / cos($latitudeCentralMeridian); |
|
556
|
9 |
|
|
|
557
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
558
|
|
|
} |
|
559
|
|
|
|
|
560
|
|
|
/** |
|
561
|
|
|
* Hyperbolic Cassini-Soldner. |
|
562
|
9 |
|
*/ |
|
563
|
|
|
public function hyperbolicCassiniSoldner( |
|
564
|
|
|
Geographic2D|Geographic3D $to, |
|
565
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
566
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
567
|
|
|
Length $falseEasting, |
|
568
|
|
|
Length $falseNorthing |
|
569
|
9 |
|
): GeographicPoint { |
|
570
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
571
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
572
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
573
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
574
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
575
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
576
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
577
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
578
|
9 |
|
$e4 = $e ** 4; |
|
579
|
|
|
$e6 = $e ** 6; |
|
580
|
9 |
|
|
|
581
|
9 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
582
|
|
|
$e1 = (1 - sqrt(1 - $e2)) / (1 + sqrt(1 - $e2)); |
|
583
|
9 |
|
|
|
584
|
|
|
$latitude1 = $latitudeOrigin + $northing / 1567446; |
|
585
|
9 |
|
|
|
586
|
9 |
|
$nu = $a / sqrt(1 - $e2 * sin($latitude1) ** 2); |
|
587
|
|
|
$rho = $a * (1 - $e2) / (1 - $e2 * sin($latitude1) ** 2) ** 1.5; |
|
588
|
9 |
|
|
|
589
|
9 |
|
$qPrime = $northing ** 3 / (6 * $rho * $nu); |
|
590
|
9 |
|
$q = ($northing + $qPrime) ** 3 / (6 * $rho * $nu); |
|
591
|
|
|
$M = $MO + $northing + $q; |
|
592
|
9 |
|
|
|
593
|
9 |
|
$mu = $M / ($a * (1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256)); |
|
594
|
|
|
$latitudeCentralMeridian = $mu + (3 * $e1 / 2 - 27 * $e1 ** 3 / 32) * sin(2 * $mu) + (21 * $e1 ** 2 / 16 - 55 * $e1 ** 4 / 32) * sin(4 * $mu) + (151 * $e1 ** 3 / 96) * sin(6 * $mu) + (1097 * $e1 ** 4 / 512) * sin(8 * $mu); |
|
595
|
9 |
|
|
|
596
|
9 |
|
$T = tan($latitudeCentralMeridian) ** 2; |
|
597
|
|
|
$D = $easting / $nu; |
|
598
|
9 |
|
|
|
599
|
9 |
|
$latitude = $latitudeCentralMeridian - ($nu * tan($latitudeCentralMeridian) / $rho) * ($D ** 2 / 2 - (1 + 3 * $T) * $D ** 4 / 24); |
|
600
|
|
|
$longitude = $longitudeOrigin + ($D - $T * $D ** 3 / 3 + (1 + 3 * $T) * $T * $D ** 5 / 15) / cos($latitudeCentralMeridian); |
|
601
|
9 |
|
|
|
602
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
603
|
|
|
} |
|
604
|
|
|
|
|
605
|
|
|
/** |
|
606
|
|
|
* Colombia Urban. |
|
607
|
9 |
|
*/ |
|
608
|
|
|
public function columbiaUrban( |
|
609
|
|
|
Geographic2D|Geographic3D $to, |
|
610
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
611
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
612
|
|
|
Length $falseEasting, |
|
613
|
|
|
Length $falseNorthing, |
|
614
|
|
|
Length $projectionPlaneOriginHeight |
|
615
|
9 |
|
): GeographicPoint { |
|
616
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
617
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
618
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
619
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
620
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
621
|
9 |
|
$heightOrigin = $projectionPlaneOriginHeight->asMetres()->getValue(); |
|
622
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
623
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
624
|
9 |
|
|
|
625
|
|
|
$rhoOrigin = $a * (1 - $e2) / (1 - $e2 * sin($latitudeOrigin) ** 2) ** 1.5; |
|
626
|
9 |
|
|
|
627
|
|
|
$nuOrigin = $a / sqrt(1 - $e2 * (sin($latitudeOrigin) ** 2)); |
|
628
|
9 |
|
|
|
629
|
9 |
|
$B = tan($latitudeOrigin) / (2 * $rhoOrigin * $nuOrigin); |
|
630
|
9 |
|
$C = 1 + $heightOrigin / $a; |
|
631
|
|
|
$D = $rhoOrigin * (1 + $heightOrigin / ($a * (1 - $e2))); |
|
632
|
9 |
|
|
|
633
|
9 |
|
$latitude = $latitudeOrigin + ($northing / $D) - $B * ($easting / $C) ** 2; |
|
634
|
9 |
|
$nu = $a / sqrt(1 - $e2 * (sin($latitude) ** 2)); |
|
635
|
|
|
$longitude = $longitudeOrigin + $easting / ($C * $nu * cos($latitude)); |
|
636
|
9 |
|
|
|
637
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
638
|
|
|
} |
|
639
|
|
|
|
|
640
|
|
|
/** |
|
641
|
|
|
* Equal Earth. |
|
642
|
9 |
|
*/ |
|
643
|
|
|
public function equalEarth( |
|
644
|
|
|
Geographic2D|Geographic3D $to, |
|
645
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
646
|
|
|
Length $falseEasting, |
|
647
|
|
|
Length $falseNorthing |
|
648
|
9 |
|
): GeographicPoint { |
|
649
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
650
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
651
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
652
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
653
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
654
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
655
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
656
|
9 |
|
$e4 = $e ** 4; |
|
657
|
|
|
$e6 = $e ** 6; |
|
658
|
9 |
|
|
|
659
|
9 |
|
$qP = (1 - $e2) * ((1 / (1 - $e2)) - (1 / (2 * $e) * log((1 - $e) / (1 + $e)))); |
|
660
|
|
|
$Rq = $a * sqrt($qP / 2); |
|
661
|
9 |
|
|
|
662
|
|
|
$theta = $northing / $Rq; |
|
663
|
9 |
|
do { |
|
664
|
9 |
|
$thetaN = $theta; |
|
665
|
9 |
|
$correctionFactor = ($theta * (1.340264 - 0.081106 * $theta ** 2 + $theta ** 6 * (0.000893 + 0.003796 * $theta ** 2)) - $northing / $Rq) / (1.340264 - 0.243318 * $theta ** 2 + $theta ** 6 * (0.006251 + 0.034164 * $theta ** 2)); |
|
666
|
9 |
|
$theta -= $correctionFactor; |
|
667
|
|
|
} while (abs($theta - $thetaN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
668
|
9 |
|
|
|
669
|
|
|
$beta = self::asin(2 * sin($theta) / sqrt(3)); |
|
670
|
9 |
|
|
|
671
|
9 |
|
$latitude = $beta + (($e2 / 3 + 31 * $e4 / 180 + 517 * $e6 / 5040) * sin(2 * $beta)) + ((23 * $e4 / 360 + 251 * $e6 / 3780) * sin(4 * $beta)) + ((761 * $e6 / 45360) * sin(6 * $beta)); |
|
672
|
|
|
$longitude = $longitudeOrigin + sqrt(3) * $easting * (1.340264 - 0.243318 * $theta ** 2 + $theta ** 6 * (0.006251 + 0.034164 * $theta ** 2)) / (2 * $Rq * cos($theta)); |
|
673
|
9 |
|
|
|
674
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
675
|
|
|
} |
|
676
|
|
|
|
|
677
|
|
|
/** |
|
678
|
|
|
* Equidistant Cylindrical |
|
679
|
|
|
* See method code 1029 for spherical development. See also Pseudo Plate Carree, method code 9825. |
|
680
|
9 |
|
*/ |
|
681
|
|
|
public function equidistantCylindrical( |
|
682
|
|
|
Geographic2D|Geographic3D $to, |
|
683
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
684
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
685
|
|
|
Length $falseEasting, |
|
686
|
|
|
Length $falseNorthing |
|
687
|
9 |
|
): GeographicPoint { |
|
688
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
689
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
690
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
691
|
9 |
|
$latitudeFirstParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
692
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
693
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
694
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
695
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
696
|
9 |
|
$e4 = $e ** 4; |
|
697
|
9 |
|
$e6 = $e ** 6; |
|
698
|
9 |
|
$e8 = $e ** 8; |
|
699
|
9 |
|
$e10 = $e ** 10; |
|
700
|
9 |
|
$e12 = $e ** 12; |
|
701
|
|
|
$e14 = $e ** 14; |
|
702
|
9 |
|
|
|
703
|
9 |
|
$n = (1 - sqrt(1 - $e2)) / (1 + sqrt(1 - $e2)); |
|
704
|
9 |
|
$n2 = $n ** 2; |
|
705
|
9 |
|
$n3 = $n ** 3; |
|
706
|
9 |
|
$n4 = $n ** 4; |
|
707
|
9 |
|
$n5 = $n ** 5; |
|
708
|
9 |
|
$n6 = $n ** 6; |
|
709
|
9 |
|
$n7 = $n ** 7; |
|
710
|
|
|
$mu = $northing / ($a * (1 - 1 / 4 * $e2 - 3 / 64 * $e4 - 5 / 256 * $e6 - 175 / 16384 * $e8 - 441 / 65536 * $e10 - 4851 / 1048576 * $e12 - 14157 / 4194304 * $e14)); |
|
711
|
9 |
|
|
|
712
|
9 |
|
$latitude = $mu + (3 / 2 * $n - 27 / 32 * $n3 + 269 / 512 * $n5 - 6607 / 24576 * $n7) * sin(2 * $mu) |
|
713
|
9 |
|
+ (21 / 16 * $n2 - 55 / 32 * $n4 + 6759 / 4096 * $n6) * sin(4 * $mu) |
|
714
|
9 |
|
+ (151 / 96 * $n3 - 417 / 128 * $n5 + 87963 / 20480 * $n7) * sin(6 * $mu) |
|
715
|
9 |
|
+ (1097 / 512 * $n4 - 15543 / 2560 * $n6) * sin(8 * $mu) |
|
716
|
9 |
|
+ (8011 / 2560 * $n5 - 69119 / 6144 * $n7) * sin(10 * $mu) |
|
717
|
9 |
|
+ (293393 / 61440 * $n6) * sin(12 * $mu) |
|
718
|
|
|
+ (6845701 / 860160 * $n7) * sin(14 * $mu); |
|
719
|
9 |
|
|
|
720
|
|
|
$longitude = $longitudeOrigin + $easting * sqrt(1 - $e2 * sin($latitudeFirstParallel) ** 2) / ($a * cos($latitudeFirstParallel)); |
|
721
|
9 |
|
|
|
722
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
723
|
|
|
} |
|
724
|
|
|
|
|
725
|
|
|
/** |
|
726
|
|
|
* Guam Projection |
|
727
|
|
|
* Simplified form of Oblique Azimuthal Equidistant projection method. |
|
728
|
9 |
|
*/ |
|
729
|
|
|
public function guamProjection( |
|
730
|
|
|
Geographic2D|Geographic3D $to, |
|
731
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
732
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
733
|
|
|
Length $falseEasting, |
|
734
|
|
|
Length $falseNorthing |
|
735
|
9 |
|
): GeographicPoint { |
|
736
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
737
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
738
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
739
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
740
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
741
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
742
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
743
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
744
|
9 |
|
$e4 = $e ** 4; |
|
745
|
|
|
$e6 = $e ** 6; |
|
746
|
9 |
|
|
|
747
|
9 |
|
$MO = $a * ((1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256) * $latitudeOrigin - (3 * $e2 / 8 + 3 * $e4 / 32 + 45 * $e6 / 1024) * sin(2 * $latitudeOrigin) + (15 * $e4 / 256 + 45 * $e6 / 1024) * sin(4 * $latitudeOrigin) - (35 * $e6 / 3072) * sin(6 * $latitudeOrigin)); |
|
748
|
9 |
|
$e1 = (1 - sqrt(1 - $e2)) / (1 + sqrt(1 - $e2)); |
|
749
|
|
|
$i = (1 - $e2 / 4 - 3 * $e4 / 64 - 5 * $e6 / 256); |
|
750
|
9 |
|
|
|
751
|
|
|
$latitude = $latitudeOrigin; |
|
752
|
9 |
|
do { |
|
753
|
9 |
|
$latitudeN = $latitude; |
|
754
|
9 |
|
$M = $MO + $northing - ($easting ** 2 * tan($latitude) * sqrt(1 - $e2 * sin($latitude) ** 2) / (2 * $a)); |
|
755
|
9 |
|
$mu = $M / ($a * $i); |
|
756
|
9 |
|
$latitude = $mu + (3 * $e1 / 2 - 27 * $e1 ** 3 / 32) * sin(2 * $mu) + (21 * $e1 ** 2 / 16 - 55 * $e1 ** 4 / 32) * sin(4 * $mu) + (151 * $e1 ** 3 / 96) * sin(6 * $mu) + (1097 * $e1 ** 4 / 512) * sin(8 * $mu); |
|
757
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
758
|
9 |
|
|
|
759
|
|
|
$longitude = $longitudeOrigin + $easting * sqrt(1 - $e2 * sin($latitude) ** 2) / ($a * cos($latitude)); |
|
760
|
9 |
|
|
|
761
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
762
|
|
|
} |
|
763
|
|
|
|
|
764
|
|
|
/** |
|
765
|
|
|
* Krovak. |
|
766
|
36 |
|
*/ |
|
767
|
|
|
public function krovak( |
|
768
|
|
|
Geographic2D|Geographic3D $to, |
|
769
|
|
|
Angle $latitudeOfProjectionCentre, |
|
770
|
|
|
Angle $longitudeOfOrigin, |
|
771
|
|
|
Angle $coLatitudeOfConeAxis, |
|
772
|
|
|
Angle $latitudeOfPseudoStandardParallel, |
|
773
|
|
|
Scale $scaleFactorOnPseudoStandardParallel, |
|
774
|
|
|
Length $falseEasting, |
|
775
|
|
|
Length $falseNorthing |
|
776
|
36 |
|
): GeographicPoint { |
|
777
|
36 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
778
|
36 |
|
$longitudeOffset = $this->crs->getDatum()->getPrimeMeridian()->getGreenwichLongitude()->asRadians()->getValue() - $to->getDatum()->getPrimeMeridian()->getGreenwichLongitude()->asRadians()->getValue(); |
|
779
|
36 |
|
$westing = $this->westing->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
780
|
36 |
|
$southing = $this->southing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
781
|
36 |
|
$latitudeC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
782
|
36 |
|
$longitudeO = $longitudeOfOrigin->asRadians()->getValue(); |
|
783
|
36 |
|
$alphaC = $coLatitudeOfConeAxis->asRadians()->getValue(); |
|
784
|
36 |
|
$latitudeP = $latitudeOfPseudoStandardParallel->asRadians()->getValue(); |
|
785
|
36 |
|
$kP = $scaleFactorOnPseudoStandardParallel->asUnity()->getValue(); |
|
786
|
36 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
787
|
36 |
|
$e = $ellipsoid->getEccentricity(); |
|
788
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
789
|
36 |
|
|
|
790
|
36 |
|
$A = $a * sqrt(1 - $e2) / (1 - $e2 * sin($latitudeC) ** 2); |
|
791
|
36 |
|
$B = sqrt(1 + $e2 * cos($latitudeC) ** 4 / (1 - $e2)); |
|
792
|
36 |
|
$upsilonO = self::asin(sin($latitudeC) / $B); |
|
793
|
36 |
|
$tO = tan(M_PI / 4 + $upsilonO / 2) * ((1 + $e * sin($latitudeC)) / (1 - $e * sin($latitudeC))) ** ($e * $B / 2) / (tan(M_PI / 4 + $latitudeC / 2) ** $B); |
|
794
|
36 |
|
$n = sin($latitudeP); |
|
795
|
|
|
$rO = $kP * $A / tan($latitudeP); |
|
796
|
36 |
|
|
|
797
|
36 |
|
$r = hypot($southing, $westing) ?: 1; |
|
798
|
36 |
|
$theta = atan2($westing, $southing); |
|
799
|
36 |
|
$D = $theta / sin($latitudeP); |
|
800
|
36 |
|
$T = 2 * (atan(($rO / $r) ** (1 / $n) * tan(M_PI / 4 + $latitudeP / 2)) - M_PI / 4); |
|
801
|
36 |
|
$U = self::asin(cos($alphaC) * sin($T) - sin($alphaC) * cos($T) * cos($D)); |
|
802
|
|
|
$V = self::asin(cos($T) * sin($D) / cos($U)); |
|
803
|
36 |
|
|
|
804
|
|
|
$latitude = $U; |
|
805
|
36 |
|
do { |
|
806
|
36 |
|
$latitudeN = $latitude; |
|
807
|
36 |
|
$latitude = 2 * (atan($tO ** (-1 / $B) * tan($U / 2 + M_PI / 4) ** (1 / $B) * ((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2)) - M_PI / 4); |
|
808
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
809
|
36 |
|
|
|
810
|
|
|
$longitude = $longitudeO + $longitudeOffset - $V / $B; |
|
811
|
36 |
|
|
|
812
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
813
|
|
|
} |
|
814
|
|
|
|
|
815
|
|
|
/** |
|
816
|
|
|
* Krovak Modified |
|
817
|
|
|
* Incorporates a polynomial transformation which is defined to be exact and for practical purposes is considered |
|
818
|
|
|
* to be a map projection. |
|
819
|
18 |
|
*/ |
|
820
|
|
|
public function krovakModified( |
|
821
|
|
|
Geographic2D|Geographic3D $to, |
|
822
|
|
|
Angle $latitudeOfProjectionCentre, |
|
823
|
|
|
Angle $longitudeOfOrigin, |
|
824
|
|
|
Angle $coLatitudeOfConeAxis, |
|
825
|
|
|
Angle $latitudeOfPseudoStandardParallel, |
|
826
|
|
|
Scale $scaleFactorOnPseudoStandardParallel, |
|
827
|
|
|
Length $falseEasting, |
|
828
|
|
|
Length $falseNorthing, |
|
829
|
|
|
Length $ordinate1OfEvaluationPoint, |
|
830
|
|
|
Length $ordinate2OfEvaluationPoint, |
|
831
|
|
|
Coefficient $C1, |
|
832
|
|
|
Coefficient $C2, |
|
833
|
|
|
Coefficient $C3, |
|
834
|
|
|
Coefficient $C4, |
|
835
|
|
|
Coefficient $C5, |
|
836
|
|
|
Coefficient $C6, |
|
837
|
|
|
Coefficient $C7, |
|
838
|
|
|
Coefficient $C8, |
|
839
|
|
|
Coefficient $C9, |
|
840
|
|
|
Coefficient $C10 |
|
841
|
18 |
|
): GeographicPoint { |
|
842
|
18 |
|
$Xr = $this->getSouthing()->asMetres()->getValue() - $falseNorthing->asMetres()->getValue() - $ordinate1OfEvaluationPoint->asMetres()->getValue(); |
|
843
|
18 |
|
$Yr = $this->getWesting()->asMetres()->getValue() - $falseEasting->asMetres()->getValue() - $ordinate2OfEvaluationPoint->asMetres()->getValue(); |
|
844
|
18 |
|
$c1 = $C1->asUnity()->getValue(); |
|
845
|
18 |
|
$c2 = $C2->asUnity()->getValue(); |
|
846
|
18 |
|
$c3 = $C3->asUnity()->getValue(); |
|
847
|
18 |
|
$c4 = $C4->asUnity()->getValue(); |
|
848
|
18 |
|
$c5 = $C5->asUnity()->getValue(); |
|
849
|
18 |
|
$c6 = $C6->asUnity()->getValue(); |
|
850
|
18 |
|
$c7 = $C7->asUnity()->getValue(); |
|
851
|
18 |
|
$c8 = $C8->asUnity()->getValue(); |
|
852
|
18 |
|
$c9 = $C9->asUnity()->getValue(); |
|
853
|
|
|
$c10 = $C10->asUnity()->getValue(); |
|
854
|
18 |
|
|
|
855
|
18 |
|
$dX = $c1 + $c3 * $Xr - $c4 * $Yr - 2 * $c6 * $Xr * $Yr + $c5 * ($Xr ** 2 - $Yr ** 2) + $c7 * $Xr * ($Xr ** 2 - 3 * $Yr ** 2) - $c8 * $Yr * (3 * $Xr ** 2 - $Yr ** 2) + 4 * $c9 * $Xr * $Yr * ($Xr ** 2 - $Yr ** 2) + $c10 * ($Xr ** 4 + $Yr ** 4 - 6 * $Xr ** 2 * $Yr ** 2); |
|
856
|
|
|
$dY = $c2 + $c3 * $Yr + $c4 * $Xr + 2 * $c5 * $Xr * $Yr + $c6 * ($Xr ** 2 - $Yr ** 2) + $c8 * $Xr * ($Xr ** 2 - 3 * $Yr ** 2) + $c7 * $Yr * (3 * $Xr ** 2 - $Yr ** 2) - 4 * $c10 * $Xr * $Yr * ($Xr ** 2 - $Yr ** 2) + $c9 * ($Xr ** 4 + $Yr ** 4 - 6 * $Xr ** 2 * $Yr ** 2); |
|
857
|
18 |
|
|
|
858
|
18 |
|
$Xp = $this->getSouthing()->asMetres()->getValue() - $falseNorthing->asMetres()->getValue() + $dX; |
|
859
|
|
|
$Yp = $this->getWesting()->asMetres()->getValue() - $falseEasting->asMetres()->getValue() + $dY; |
|
860
|
18 |
|
|
|
861
|
|
|
$asKrovak = self::create($this->crs, new Metre(-$Yp), new Metre(-$Xp), new Metre($Yp), new Metre($Xp), $this->epoch); |
|
862
|
18 |
|
|
|
863
|
|
|
return $asKrovak->krovak($to, $latitudeOfProjectionCentre, $longitudeOfOrigin, $coLatitudeOfConeAxis, $latitudeOfPseudoStandardParallel, $scaleFactorOnPseudoStandardParallel, new Metre(0), new Metre(0)); |
|
864
|
|
|
} |
|
865
|
|
|
|
|
866
|
|
|
/** |
|
867
|
|
|
* Lambert Azimuthal Equal Area |
|
868
|
|
|
* This is the ellipsoidal form of the projection. |
|
869
|
9 |
|
*/ |
|
870
|
|
|
public function lambertAzimuthalEqualArea( |
|
871
|
|
|
Geographic2D|Geographic3D $to, |
|
872
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
873
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
874
|
|
|
Length $falseEasting, |
|
875
|
|
|
Length $falseNorthing |
|
876
|
9 |
|
): GeographicPoint { |
|
877
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
878
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
879
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
880
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
881
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
882
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
883
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
884
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
885
|
9 |
|
$e4 = $e ** 4; |
|
886
|
|
|
$e6 = $e ** 6; |
|
887
|
9 |
|
|
|
888
|
9 |
|
$qO = (1 - $e2) * ((sin($latitudeOrigin) / (1 - $e2 * sin($latitudeOrigin) ** 2)) - ((1 / (2 * $e)) * log((1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin))))); |
|
889
|
9 |
|
$qP = (1 - $e2) * ((1 / (1 - $e2)) - ((1 / (2 * $e)) * log((1 - $e) / (1 + $e)))); |
|
890
|
9 |
|
$betaO = self::asin($qO / $qP); |
|
891
|
9 |
|
$Rq = $a * sqrt($qP / 2); |
|
892
|
9 |
|
$D = $a * (cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2)) / ($Rq * cos($betaO)); |
|
893
|
9 |
|
$rho = hypot($easting / $D, $D * $northing) ?: 1; |
|
894
|
9 |
|
$C = 2 * self::asin($rho / (2 * $Rq)); |
|
895
|
|
|
$beta = self::asin(cos($C) * sin($betaO) + ($D * $northing * sin($C) * cos($betaO)) / $rho); |
|
896
|
9 |
|
|
|
897
|
9 |
|
$latitude = $beta + (($e2 / 3 + 31 * $e4 / 180 + 517 * $e6 / 5040) * sin(2 * $beta)) + ((23 * $e4 / 360 + 251 * $e6 / 3780) * sin(4 * $beta)) + ((761 * $e6 / 45360) * sin(6 * $beta)); |
|
898
|
|
|
$longitude = $longitudeOrigin + atan2($easting * sin($C), $D * $rho * cos($betaO) * cos($C) - $D ** 2 * $northing * sin($betaO) * sin($C)); |
|
899
|
9 |
|
|
|
900
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
901
|
|
|
} |
|
902
|
|
|
|
|
903
|
|
|
/** |
|
904
|
|
|
* Lambert Azimuthal Equal Area (Spherical) |
|
905
|
|
|
* This is the spherical form of the projection. See coordinate operation method Lambert Azimuthal Equal Area |
|
906
|
|
|
* (code 9820) for ellipsoidal form. Differences of several tens of metres result from comparison of the two |
|
907
|
|
|
* methods. |
|
908
|
9 |
|
*/ |
|
909
|
|
|
public function lambertAzimuthalEqualAreaSpherical( |
|
910
|
|
|
Geographic2D|Geographic3D $to, |
|
911
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
912
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
913
|
|
|
Length $falseEasting, |
|
914
|
|
|
Length $falseNorthing |
|
915
|
9 |
|
): GeographicPoint { |
|
916
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
917
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
918
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
919
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
920
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
921
|
|
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
922
|
9 |
|
|
|
923
|
9 |
|
$rho = hypot($easting, $northing) ?: 1; |
|
924
|
|
|
$c = 2 * self::asin($rho / (2 * $a)); |
|
925
|
9 |
|
|
|
926
|
|
|
$latitude = self::asin(cos($c) * sin($latitudeOrigin) + ($northing * sin($c) * cos($latitudeOrigin) / $rho)); |
|
927
|
9 |
|
|
|
928
|
|
|
if ($latitudeOrigin === 90.0) { |
|
|
|
|
|
|
929
|
9 |
|
$longitude = $longitudeOrigin + atan($easting / -$northing); |
|
930
|
|
|
} elseif ($latitudeOrigin === -90.0) { |
|
|
|
|
|
|
931
|
|
|
$longitude = $longitudeOrigin + atan($easting / $northing); |
|
932
|
9 |
|
} else { |
|
933
|
9 |
|
$longitudeDenominator = ($rho * cos($latitudeOrigin) * cos($c) - $northing * sin($latitudeOrigin) * sin($c)); |
|
934
|
9 |
|
$longitude = $longitudeOrigin + atan($easting * sin($c) / $longitudeDenominator); |
|
935
|
9 |
|
if ($longitudeDenominator < 0) { |
|
936
|
|
|
$longitude += M_PI; |
|
937
|
|
|
} |
|
938
|
|
|
} |
|
939
|
9 |
|
|
|
940
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
941
|
|
|
} |
|
942
|
|
|
|
|
943
|
|
|
/** |
|
944
|
|
|
* Lambert Conic Conformal (1SP). |
|
945
|
9 |
|
*/ |
|
946
|
|
|
public function lambertConicConformal1SP( |
|
947
|
|
|
Geographic2D|Geographic3D $to, |
|
948
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
949
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
950
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
951
|
|
|
Length $falseEasting, |
|
952
|
|
|
Length $falseNorthing |
|
953
|
9 |
|
): GeographicPoint { |
|
954
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
955
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
956
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
957
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
958
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
959
|
9 |
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
960
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
961
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
962
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
963
|
9 |
|
|
|
964
|
9 |
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
965
|
9 |
|
$tO = tan(M_PI / 4 - $latitudeOrigin / 2) / ((1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin))) ** ($e / 2); |
|
966
|
9 |
|
$n = sin($latitudeOrigin); |
|
967
|
9 |
|
$F = $mO / ($n * $tO ** $n); |
|
968
|
9 |
|
$rO = $a * $F * $tO ** $n * $scaleFactorOrigin; |
|
969
|
9 |
|
$r = hypot($easting, $rO - $northing); |
|
970
|
9 |
|
if ($n >= 0) { |
|
971
|
|
|
$theta = atan2($easting, $rO - $northing); |
|
972
|
|
|
} else { |
|
973
|
|
|
$r = -$r; |
|
974
|
|
|
$theta = atan2(-$easting, -($rO - $northing)); |
|
975
|
|
|
} |
|
976
|
9 |
|
|
|
977
|
|
|
$t = ($r / ($a * $scaleFactorOrigin * $F)) ** (1 / $n); |
|
978
|
9 |
|
|
|
979
|
|
|
$latitude = M_PI / (2 - 2 * atan($t)); |
|
980
|
9 |
|
do { |
|
981
|
9 |
|
$latitudeN = $latitude; |
|
982
|
9 |
|
$latitude = M_PI / 2 - 2 * atan($t * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
983
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
984
|
9 |
|
|
|
985
|
|
|
$longitude = $theta / $n + $longitudeOrigin; |
|
986
|
9 |
|
|
|
987
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
988
|
|
|
} |
|
989
|
|
|
|
|
990
|
|
|
/** |
|
991
|
|
|
* Lambert Conic Conformal (west orientated). |
|
992
|
|
|
*/ |
|
993
|
|
|
public function lambertConicConformalWestOrientated( |
|
994
|
|
|
Geographic2D|Geographic3D $to, |
|
995
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
996
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
997
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
998
|
|
|
Length $falseEasting, |
|
999
|
|
|
Length $falseNorthing |
|
1000
|
|
|
): GeographicPoint { |
|
1001
|
|
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1002
|
|
|
$westing = $falseEasting->asMetres()->getValue() - $this->westing->asMetres()->getValue(); |
|
1003
|
|
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1004
|
|
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1005
|
|
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1006
|
|
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1007
|
|
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1008
|
|
|
$e = $ellipsoid->getEccentricity(); |
|
1009
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1010
|
|
|
|
|
1011
|
|
|
$mO = cos($latitudeOrigin) / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
1012
|
|
|
$tO = tan(M_PI / 4 - $latitudeOrigin / 2) / ((1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin))) ** ($e / 2); |
|
1013
|
|
|
$n = sin($latitudeOrigin); |
|
1014
|
|
|
$F = $mO / ($n * $tO ** $n); |
|
1015
|
|
|
$rO = $a * $F * $tO ** $n ** $scaleFactorOrigin; |
|
1016
|
|
|
$r = hypot($westing, $rO - $northing); |
|
1017
|
|
|
if ($n >= 0) { |
|
1018
|
|
|
$theta = atan2($westing, $rO - $northing); |
|
1019
|
|
|
} else { |
|
1020
|
|
|
$r = -$r; |
|
1021
|
|
|
$theta = atan2(-$westing, -($rO - $northing)); |
|
1022
|
|
|
} |
|
1023
|
|
|
|
|
1024
|
|
|
$t = ($r / ($a * $scaleFactorOrigin * $F)) ** (1 / $n); |
|
1025
|
|
|
|
|
1026
|
|
|
$latitude = M_PI / (2 - 2 * atan($t)); |
|
1027
|
|
|
do { |
|
1028
|
|
|
$latitudeN = $latitude; |
|
1029
|
|
|
$latitude = M_PI / 2 - 2 * atan($t * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1030
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1031
|
|
|
|
|
1032
|
|
|
$longitude = $theta / $n + $longitudeOrigin; |
|
1033
|
|
|
|
|
1034
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1035
|
|
|
} |
|
1036
|
|
|
|
|
1037
|
|
|
/** |
|
1038
|
|
|
* Lambert Conic Conformal (1SP) Variant B. |
|
1039
|
|
|
*/ |
|
1040
|
|
|
public function lambertConicConformal1SPVariantB( |
|
1041
|
|
|
Geographic2D|Geographic3D $to, |
|
1042
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1043
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1044
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1045
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1046
|
|
|
Length $eastingAtFalseOrigin, |
|
1047
|
|
|
Length $northingAtFalseOrigin |
|
1048
|
|
|
): GeographicPoint { |
|
1049
|
|
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1050
|
|
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtFalseOrigin->asMetres()->getValue(); |
|
1051
|
|
|
$northing = $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue(); |
|
1052
|
|
|
$latitudeNaturalOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1053
|
|
|
$latitudeFalseOrigin = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1054
|
|
|
$longitudeFalseOrigin = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1055
|
|
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1056
|
|
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1057
|
|
|
$e = $ellipsoid->getEccentricity(); |
|
1058
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1059
|
|
|
|
|
1060
|
|
|
$mO = cos($latitudeNaturalOrigin) / sqrt(1 - $e2 * sin($latitudeNaturalOrigin) ** 2); |
|
1061
|
|
|
$tO = tan(M_PI / 4 - $latitudeNaturalOrigin / 2) / ((1 - $e * sin($latitudeNaturalOrigin)) / (1 + $e * sin($latitudeNaturalOrigin))) ** ($e / 2); |
|
1062
|
|
|
$tF = tan(M_PI / 4 - $latitudeFalseOrigin / 2) / ((1 - $e * sin($latitudeFalseOrigin)) / (1 + $e * sin($latitudeFalseOrigin))) ** ($e / 2); |
|
1063
|
|
|
$n = sin($latitudeNaturalOrigin); |
|
1064
|
|
|
$F = $mO / ($n * $tO ** $n); |
|
1065
|
|
|
$rF = $a * $F * $tF ** $n * $scaleFactorOrigin; |
|
1066
|
|
|
$r = hypot($easting, $rF - $northing); |
|
1067
|
|
|
if ($n >= 0) { |
|
1068
|
|
|
$theta = atan2($easting, $rF - $northing); |
|
1069
|
|
|
} else { |
|
1070
|
|
|
$r = -$r; |
|
1071
|
|
|
$theta = atan2(-$easting, -($rF - $northing)); |
|
1072
|
|
|
} |
|
1073
|
|
|
|
|
1074
|
|
|
$t = ($r / ($a * $scaleFactorOrigin * $F)) ** (1 / $n); |
|
1075
|
|
|
|
|
1076
|
|
|
$latitude = M_PI / (2 - 2 * atan($t)); |
|
1077
|
|
|
do { |
|
1078
|
|
|
$latitudeN = $latitude; |
|
1079
|
|
|
$latitude = M_PI / 2 - 2 * atan($t * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1080
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1081
|
|
|
|
|
1082
|
|
|
$longitude = $theta / $n + $longitudeFalseOrigin; |
|
1083
|
|
|
|
|
1084
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1085
|
|
|
} |
|
1086
|
|
|
|
|
1087
|
|
|
/** |
|
1088
|
|
|
* Lambert Conic Conformal (2SP). |
|
1089
|
19 |
|
*/ |
|
1090
|
|
|
public function lambertConicConformal2SP( |
|
1091
|
|
|
Geographic2D|Geographic3D $to, |
|
1092
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1093
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1094
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1095
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
1096
|
|
|
Length $eastingAtFalseOrigin, |
|
1097
|
|
|
Length $northingAtFalseOrigin |
|
1098
|
19 |
|
): GeographicPoint { |
|
1099
|
19 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1100
|
19 |
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtFalseOrigin->asMetres()->getValue(); |
|
1101
|
19 |
|
$northing = $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue(); |
|
1102
|
19 |
|
$lambdaOrigin = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1103
|
19 |
|
$phiF = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1104
|
19 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1105
|
19 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
1106
|
19 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1107
|
19 |
|
$e = $ellipsoid->getEccentricity(); |
|
1108
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1109
|
19 |
|
|
|
1110
|
19 |
|
$m1 = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
1111
|
19 |
|
$m2 = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
1112
|
19 |
|
$t1 = tan(M_PI / 4 - $phi1 / 2) / ((1 - $e * sin($phi1)) / (1 + $e * sin($phi1))) ** ($e / 2); |
|
1113
|
19 |
|
$t2 = tan(M_PI / 4 - $phi2 / 2) / ((1 - $e * sin($phi2)) / (1 + $e * sin($phi2))) ** ($e / 2); |
|
1114
|
19 |
|
$tF = tan(M_PI / 4 - $phiF / 2) / ((1 - $e * sin($phiF)) / (1 + $e * sin($phiF))) ** ($e / 2); |
|
1115
|
19 |
|
$n = (log($m1) - log($m2)) / (log($t1) - log($t2)); |
|
1116
|
19 |
|
$F = $m1 / ($n * $t1 ** $n); |
|
1117
|
19 |
|
$rF = $a * $F * $tF ** $n; |
|
1118
|
19 |
|
$r = hypot($easting, $rF - $northing) * static::sign($n); |
|
1119
|
19 |
|
$t = ($r / ($a * $F)) ** (1 / $n); |
|
1120
|
19 |
|
if ($n >= 0) { |
|
1121
|
|
|
$theta = atan2($easting, $rF - $northing); |
|
1122
|
|
|
} else { |
|
1123
|
|
|
$theta = atan2(-$easting, -($rF - $northing)); |
|
1124
|
|
|
} |
|
1125
|
19 |
|
|
|
1126
|
|
|
$latitude = M_PI / 2 - 2 * atan($t); |
|
1127
|
19 |
|
do { |
|
1128
|
19 |
|
$latitudeN = $latitude; |
|
1129
|
19 |
|
$latitude = M_PI / 2 - 2 * atan($t * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1130
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1131
|
19 |
|
|
|
1132
|
|
|
$longitude = $theta / $n + $lambdaOrigin; |
|
1133
|
19 |
|
|
|
1134
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1135
|
|
|
} |
|
1136
|
|
|
|
|
1137
|
|
|
/** |
|
1138
|
|
|
* Lambert Conic Conformal (2SP Michigan). |
|
1139
|
9 |
|
*/ |
|
1140
|
|
|
public function lambertConicConformal2SPMichigan( |
|
1141
|
|
|
Geographic2D|Geographic3D $to, |
|
1142
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1143
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1144
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1145
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
1146
|
|
|
Length $eastingAtFalseOrigin, |
|
1147
|
|
|
Length $northingAtFalseOrigin, |
|
1148
|
|
|
Scale $ellipsoidScalingFactor |
|
1149
|
9 |
|
): GeographicPoint { |
|
1150
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1151
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtFalseOrigin->asMetres()->getValue(); |
|
1152
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue(); |
|
1153
|
9 |
|
$lambdaOrigin = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1154
|
9 |
|
$phiF = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1155
|
9 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1156
|
9 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
1157
|
9 |
|
$K = $ellipsoidScalingFactor->asUnity()->getValue(); |
|
1158
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1159
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1160
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1161
|
9 |
|
|
|
1162
|
9 |
|
$m1 = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
1163
|
9 |
|
$m2 = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
1164
|
9 |
|
$t1 = tan(M_PI / 4 - $phi1 / 2) / ((1 - $e * sin($phi1)) / (1 + $e * sin($phi1))) ** ($e / 2); |
|
1165
|
9 |
|
$t2 = tan(M_PI / 4 - $phi2 / 2) / ((1 - $e * sin($phi2)) / (1 + $e * sin($phi2))) ** ($e / 2); |
|
1166
|
9 |
|
$tF = tan(M_PI / 4 - $phiF / 2) / ((1 - $e * sin($phiF)) / (1 + $e * sin($phiF))) ** ($e / 2); |
|
1167
|
9 |
|
$n = (log($m1) - log($m2)) / (log($t1) - log($t2)); |
|
1168
|
9 |
|
$F = $m1 / ($n * $t1 ** $n); |
|
1169
|
9 |
|
$rF = $a * $K * $F * $tF ** $n; |
|
1170
|
9 |
|
$r = sqrt($easting ** 2 + ($rF - $northing) ** 2) * static::sign($n); |
|
1171
|
9 |
|
$t = ($r / ($a * $K * $F)) ** (1 / $n); |
|
1172
|
9 |
|
if ($n >= 0) { |
|
1173
|
|
|
$theta = atan2($easting, $rF - $northing); |
|
1174
|
|
|
} else { |
|
1175
|
|
|
$theta = atan2(-$easting, -($rF - $northing)); |
|
1176
|
|
|
} |
|
1177
|
9 |
|
|
|
1178
|
|
|
$latitude = M_PI / 2 - 2 * atan($t); |
|
1179
|
9 |
|
do { |
|
1180
|
9 |
|
$latitudeN = $latitude; |
|
1181
|
9 |
|
$latitude = M_PI / 2 - 2 * atan($t * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1182
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1183
|
9 |
|
|
|
1184
|
|
|
$longitude = $theta / $n + $lambdaOrigin; |
|
1185
|
9 |
|
|
|
1186
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1187
|
|
|
} |
|
1188
|
|
|
|
|
1189
|
|
|
/** |
|
1190
|
|
|
* Lambert Conic Conformal (2SP Belgium) |
|
1191
|
|
|
* In 2000 this modification was replaced through use of the regular Lambert Conic Conformal (2SP) method [9802] |
|
1192
|
|
|
* with appropriately modified parameter values. |
|
1193
|
9 |
|
*/ |
|
1194
|
|
|
public function lambertConicConformal2SPBelgium( |
|
1195
|
|
|
Geographic2D|Geographic3D $to, |
|
1196
|
|
|
Angle $latitudeOfFalseOrigin, |
|
1197
|
|
|
Angle $longitudeOfFalseOrigin, |
|
1198
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1199
|
|
|
Angle $latitudeOf2ndStandardParallel, |
|
1200
|
|
|
Length $eastingAtFalseOrigin, |
|
1201
|
|
|
Length $northingAtFalseOrigin |
|
1202
|
9 |
|
): GeographicPoint { |
|
1203
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1204
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtFalseOrigin->asMetres()->getValue(); |
|
1205
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue(); |
|
1206
|
9 |
|
$lambdaOrigin = $longitudeOfFalseOrigin->asRadians()->getValue(); |
|
1207
|
9 |
|
$phiF = $latitudeOfFalseOrigin->asRadians()->getValue(); |
|
1208
|
9 |
|
$phi1 = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1209
|
9 |
|
$phi2 = $latitudeOf2ndStandardParallel->asRadians()->getValue(); |
|
1210
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1211
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1212
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1213
|
9 |
|
|
|
1214
|
9 |
|
$m1 = cos($phi1) / sqrt(1 - $e2 * sin($phi1) ** 2); |
|
1215
|
9 |
|
$m2 = cos($phi2) / sqrt(1 - $e2 * sin($phi2) ** 2); |
|
1216
|
9 |
|
$t1 = tan(M_PI / 4 - $phi1 / 2) / ((1 - $e * sin($phi1)) / (1 + $e * sin($phi1))) ** ($e / 2); |
|
1217
|
9 |
|
$t2 = tan(M_PI / 4 - $phi2 / 2) / ((1 - $e * sin($phi2)) / (1 + $e * sin($phi2))) ** ($e / 2); |
|
1218
|
9 |
|
$tF = tan(M_PI / 4 - $phiF / 2) / ((1 - $e * sin($phiF)) / (1 + $e * sin($phiF))) ** ($e / 2); |
|
1219
|
9 |
|
$n = (log($m1) - log($m2)) / (log($t1) - log($t2)); |
|
1220
|
9 |
|
$F = $m1 / ($n * $t1 ** $n); |
|
1221
|
9 |
|
$rF = $a * $F * $tF ** $n; |
|
1222
|
9 |
|
if (is_nan($rF)) { |
|
1223
|
|
|
$rF = 0; |
|
1224
|
9 |
|
} |
|
1225
|
9 |
|
$r = hypot($easting, $rF - $northing) * static::sign($n); |
|
1226
|
9 |
|
$t = ($r / ($a * $F)) ** (1 / $n); |
|
1227
|
9 |
|
if ($n >= 0) { |
|
1228
|
|
|
$theta = atan2($easting, $rF - $northing); |
|
1229
|
|
|
} else { |
|
1230
|
|
|
$theta = atan2(-$easting, -($rF - $northing)); |
|
1231
|
|
|
} |
|
1232
|
9 |
|
|
|
1233
|
|
|
$latitude = M_PI / 2 - 2 * atan($t); |
|
1234
|
9 |
|
do { |
|
1235
|
9 |
|
$latitudeN = $latitude; |
|
1236
|
9 |
|
$latitude = M_PI / 2 - 2 * atan($t * ((1 - $e * sin($latitude)) / (1 + $e * sin($latitude))) ** ($e / 2)); |
|
1237
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1238
|
9 |
|
|
|
1239
|
|
|
$longitude = ($theta + (new ArcSecond(29.2985))->asRadians()->getValue()) / $n + $lambdaOrigin; |
|
1240
|
9 |
|
|
|
1241
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1242
|
|
|
} |
|
1243
|
|
|
|
|
1244
|
|
|
/** |
|
1245
|
|
|
* Lambert Conic Near-Conformal |
|
1246
|
|
|
* The Lambert Near-Conformal projection is derived from the Lambert Conformal Conic projection by truncating the |
|
1247
|
|
|
* series expansion of the projection formulae. |
|
1248
|
9 |
|
*/ |
|
1249
|
|
|
public function lambertConicNearConformal( |
|
1250
|
|
|
Geographic2D|Geographic3D $to, |
|
1251
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1252
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1253
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1254
|
|
|
Length $falseEasting, |
|
1255
|
|
|
Length $falseNorthing |
|
1256
|
9 |
|
): GeographicPoint { |
|
1257
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1258
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1259
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1260
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1261
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1262
|
9 |
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1263
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1264
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1265
|
|
|
$f = $ellipsoid->getFlattening(); |
|
1266
|
9 |
|
|
|
1267
|
9 |
|
$n = $f / (2 - $f); |
|
1268
|
9 |
|
$rhoO = $a * (1 - $e2) / (1 - $e2 * sin($latitudeOrigin) ** 2) ** (3 / 2); |
|
1269
|
9 |
|
$nuO = $a / sqrt(1 - $e2 * (sin($latitudeOrigin) ** 2)); |
|
1270
|
9 |
|
$A = 1 / (6 * $rhoO * $nuO); |
|
1271
|
9 |
|
$APrime = $a * (1 - $n + 5 * ($n ** 2 - $n ** 3) / 4 + 81 * ($n ** 4 - $n ** 5) / 64); |
|
1272
|
9 |
|
$BPrime = 3 * $a * ($n - $n ** 2 + 7 * ($n ** 3 - $n ** 4) / 8 + 55 * $n ** 5 / 64) / 2; |
|
1273
|
9 |
|
$CPrime = 15 * $a * ($n ** 2 - $n ** 3 + 3 * ($n ** 4 - $n ** 5) / 4) / 16; |
|
1274
|
9 |
|
$DPrime = 35 * $a * ($n ** 3 - $n ** 4 + 11 * $n ** 5 / 16) / 48; |
|
1275
|
9 |
|
$EPrime = 315 * $a * ($n ** 4 - $n ** 5) / 512; |
|
1276
|
9 |
|
$rO = $scaleFactorOrigin * $nuO / tan($latitudeOrigin); |
|
1277
|
|
|
$sO = $APrime * $latitudeOrigin - $BPrime * sin(2 * $latitudeOrigin) + $CPrime * sin(4 * $latitudeOrigin) - $DPrime * sin(6 * $latitudeOrigin) + $EPrime * sin(8 * $latitudeOrigin); |
|
1278
|
9 |
|
|
|
1279
|
9 |
|
$theta = atan2($easting, $rO - $northing); |
|
1280
|
9 |
|
$r = hypot($easting, $rO - $northing) * static::sign($latitudeOrigin); |
|
1281
|
|
|
$M = $rO - $r; |
|
1282
|
9 |
|
|
|
1283
|
|
|
$m = $M; |
|
1284
|
9 |
|
do { |
|
1285
|
9 |
|
$mN = $m; |
|
1286
|
9 |
|
$m = $m - ($M - $scaleFactorOrigin * $m - $scaleFactorOrigin * $A * $m ** 3) / (-$scaleFactorOrigin - 3 * $scaleFactorOrigin * $A * $m ** 2); |
|
1287
|
|
|
} while (abs($m - $mN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1288
|
9 |
|
|
|
1289
|
|
|
$latitude = $latitudeOrigin + $m / $A; |
|
1290
|
9 |
|
do { |
|
1291
|
9 |
|
$latitudeN = $latitude; |
|
1292
|
9 |
|
$latitude = $latitude + ($m + $sO - ($APrime * $latitude - $BPrime * sin(2 * $latitude) + $CPrime * sin(4 * $latitude) - $DPrime * sin(6 * $latitude) + $EPrime * sin(8 * $latitude))) / $APrime; |
|
1293
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1294
|
9 |
|
|
|
1295
|
|
|
$longitude = $longitudeOrigin + $theta / sin($latitudeOrigin); |
|
1296
|
9 |
|
|
|
1297
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1298
|
|
|
} |
|
1299
|
|
|
|
|
1300
|
|
|
/** |
|
1301
|
|
|
* Lambert Cylindrical Equal Area |
|
1302
|
|
|
* This is the ellipsoidal form of the projection. |
|
1303
|
9 |
|
*/ |
|
1304
|
|
|
public function lambertCylindricalEqualArea( |
|
1305
|
|
|
Geographic2D|Geographic3D $to, |
|
1306
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1307
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1308
|
|
|
Length $falseEasting, |
|
1309
|
|
|
Length $falseNorthing |
|
1310
|
9 |
|
): GeographicPoint { |
|
1311
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1312
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1313
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1314
|
9 |
|
$latitudeFirstParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1315
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1316
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1317
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1318
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1319
|
9 |
|
$e4 = $e ** 4; |
|
1320
|
|
|
$e6 = $e ** 6; |
|
1321
|
9 |
|
|
|
1322
|
9 |
|
$k = cos($latitudeFirstParallel) / sqrt(1 - $e2 * sin($latitudeFirstParallel) ** 2); |
|
1323
|
9 |
|
$qP = (1 - $e2) * ((sin(M_PI_2) / (1 - $e2 * sin(M_PI_2) ** 2)) - (1 / (2 * $e)) * log((1 - $e * sin(M_PI_2)) / (1 + $e * sin(M_PI_2)))); |
|
1324
|
|
|
$beta = self::asin(2 * $northing * $k / ($a * $qP)); |
|
1325
|
9 |
|
|
|
1326
|
9 |
|
$latitude = $beta + (($e2 / 3 + 31 * $e4 / 180 + 517 * $e6 / 5040) * sin(2 * $beta)) + ((23 * $e4 / 360 + 251 * $e6 / 3780) * sin(4 * $beta)) + ((761 * $e6 / 45360) * sin(6 * $beta)); |
|
1327
|
|
|
$longitude = $longitudeOrigin + $easting / ($a * $k); |
|
1328
|
9 |
|
|
|
1329
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1330
|
|
|
} |
|
1331
|
|
|
|
|
1332
|
|
|
/** |
|
1333
|
|
|
* Lambert Cylindrical Equal Area |
|
1334
|
|
|
* This is the spherical form of the projection. |
|
1335
|
9 |
|
*/ |
|
1336
|
|
|
public function lambertCylindricalEqualAreaSpherical( |
|
1337
|
|
|
Geographic2D|Geographic3D $to, |
|
1338
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1339
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1340
|
|
|
Length $falseEasting, |
|
1341
|
|
|
Length $falseNorthing |
|
1342
|
9 |
|
): GeographicPoint { |
|
1343
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1344
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1345
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1346
|
9 |
|
$latitudeFirstParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1347
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1348
|
|
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1349
|
9 |
|
|
|
1350
|
9 |
|
$latitude = self::asin(($northing / $a) * cos($latitudeFirstParallel)); |
|
1351
|
|
|
$longitude = $longitudeOrigin + $easting / ($a * cos($latitudeFirstParallel)); |
|
1352
|
9 |
|
|
|
1353
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1354
|
|
|
} |
|
1355
|
|
|
|
|
1356
|
|
|
/** |
|
1357
|
|
|
* Modified Azimuthal Equidistant |
|
1358
|
|
|
* Modified form of Oblique Azimuthal Equidistant projection method developed for Polynesian islands. For the |
|
1359
|
|
|
* distances over which these projections are used (under 800km) this modification introduces no significant error. |
|
1360
|
9 |
|
*/ |
|
1361
|
|
|
public function modifiedAzimuthalEquidistant( |
|
1362
|
|
|
Geographic2D|Geographic3D $to, |
|
1363
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1364
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1365
|
|
|
Length $falseEasting, |
|
1366
|
|
|
Length $falseNorthing |
|
1367
|
9 |
|
): GeographicPoint { |
|
1368
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1369
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1370
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1371
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1372
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1373
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1374
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1375
|
9 |
|
|
|
1376
|
9 |
|
$nuO = $a / sqrt(1 - $e2 * sin($latitudeOrigin) ** 2); |
|
1377
|
9 |
|
$c = hypot($easting, $northing); |
|
1378
|
9 |
|
$alpha = atan2($easting, $northing); |
|
1379
|
9 |
|
$A = -$e2 * cos($latitudeOrigin) ** 2 * cos($alpha) ** 2 / (1 - $e2); |
|
1380
|
9 |
|
$B = 3 * $e2 * (1 - $A) * sin($latitudeOrigin) * cos($latitudeOrigin) * cos($alpha) / (1 - $e2); |
|
1381
|
9 |
|
$D = $c / $nuO; |
|
1382
|
9 |
|
$J = $D - ($A * (1 + $A) * $D ** 3 / 6) - ($B * (1 + 3 * $A) * $D ** 4 / 24); |
|
1383
|
9 |
|
$K = 1 - ($A * $J ** 2 / 2) - ($B * $J ** 3 / 6); |
|
1384
|
|
|
$psi = self::asin(sin($latitudeOrigin) * cos($J) + cos($latitudeOrigin) * sin($J) * cos($alpha)); |
|
1385
|
9 |
|
|
|
1386
|
9 |
|
$latitude = atan((1 - $e2 * $K * sin($latitudeOrigin) / sin($psi)) * tan($psi) / (1 - $e2)); |
|
1387
|
|
|
$longitude = $longitudeOrigin + self::asin(sin($alpha) * sin($J) / cos($psi)); |
|
1388
|
9 |
|
|
|
1389
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1390
|
|
|
} |
|
1391
|
|
|
|
|
1392
|
|
|
/** |
|
1393
|
|
|
* Oblique Stereographic |
|
1394
|
|
|
* This is not the same as the projection method of the same name in USGS Professional Paper no. 1395, "Map |
|
1395
|
|
|
* Projections - A Working Manual" by John P. Snyder. |
|
1396
|
27 |
|
*/ |
|
1397
|
|
|
public function obliqueStereographic( |
|
1398
|
|
|
Geographic2D|Geographic3D $to, |
|
1399
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1400
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1401
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1402
|
|
|
Length $falseEasting, |
|
1403
|
|
|
Length $falseNorthing |
|
1404
|
27 |
|
): GeographicPoint { |
|
1405
|
27 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1406
|
27 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1407
|
27 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1408
|
27 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1409
|
27 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1410
|
27 |
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1411
|
27 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1412
|
27 |
|
$e = $ellipsoid->getEccentricity(); |
|
1413
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1414
|
27 |
|
|
|
1415
|
27 |
|
$rhoOrigin = $a * (1 - $e2) / (1 - $e2 * sin($latitudeOrigin) ** 2) ** (3 / 2); |
|
1416
|
27 |
|
$nuOrigin = $a / sqrt(1 - $e2 * (sin($latitudeOrigin) ** 2)); |
|
1417
|
|
|
$R = sqrt($rhoOrigin * $nuOrigin); |
|
1418
|
27 |
|
|
|
1419
|
27 |
|
$n = sqrt(1 + ($e2 * cos($latitudeOrigin) ** 4 / (1 - $e2))); |
|
1420
|
27 |
|
$S1 = (1 + sin($latitudeOrigin)) / (1 - sin($latitudeOrigin)); |
|
1421
|
27 |
|
$S2 = (1 - $e * sin($latitudeOrigin)) / (1 + $e * sin($latitudeOrigin)); |
|
1422
|
27 |
|
$w1 = ($S1 * ($S2 ** $e)) ** $n; |
|
1423
|
27 |
|
$c = (($n + sin($latitudeOrigin)) * (1 - ($w1 - 1) / ($w1 + 1))) / (($n - sin($latitudeOrigin)) * (1 + ($w1 - 1) / ($w1 + 1))); |
|
1424
|
27 |
|
$w2 = $c * $w1; |
|
1425
|
|
|
$chiOrigin = self::asin(($w2 - 1) / ($w2 + 1)); |
|
1426
|
27 |
|
|
|
1427
|
27 |
|
$g = 2 * $R * $scaleFactorOrigin * tan(M_PI / 4 - $chiOrigin / 2); |
|
1428
|
27 |
|
$h = 4 * $R * $scaleFactorOrigin * tan($chiOrigin) + $g; |
|
1429
|
27 |
|
$i = atan2($easting, $h + $northing); |
|
1430
|
27 |
|
$j = atan2($easting, $g - $northing) - $i; |
|
1431
|
27 |
|
$chi = $chiOrigin + 2 * atan(($northing - $easting * tan($j / 2)) / (2 * $R * $scaleFactorOrigin)); |
|
1432
|
|
|
$lambda = $j + 2 * $i + $longitudeOrigin; |
|
1433
|
27 |
|
|
|
1434
|
|
|
$longitude = ($lambda - $longitudeOrigin) / $n + $longitudeOrigin; |
|
1435
|
27 |
|
|
|
1436
|
|
|
$psi = 0.5 * log((1 + sin($chi)) / ($c * (1 - sin($chi)))) / $n; |
|
1437
|
27 |
|
|
|
1438
|
|
|
$latitude = 2 * atan(M_E ** $psi) - M_PI / 2; |
|
1439
|
27 |
|
do { |
|
1440
|
27 |
|
$latitudeN = $latitude; |
|
1441
|
27 |
|
$psiN = log(tan($latitudeN / 2 + M_PI / 4) * ((1 - $e * sin($latitudeN)) / (1 + $e * sin($latitudeN))) ** ($e / 2)); |
|
1442
|
27 |
|
$latitude = $latitudeN - ($psiN - $psi) * cos($latitudeN) * (1 - $e2 * sin($latitudeN) ** 2) / (1 - $e2); |
|
1443
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1444
|
27 |
|
|
|
1445
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1446
|
|
|
} |
|
1447
|
|
|
|
|
1448
|
|
|
/** |
|
1449
|
|
|
* Polar Stereographic (variant A) |
|
1450
|
|
|
* Latitude of natural origin must be either 90 degrees or -90 degrees (or equivalent in alternative angle unit). |
|
1451
|
9 |
|
*/ |
|
1452
|
|
|
public function polarStereographicVariantA( |
|
1453
|
|
|
Geographic2D|Geographic3D $to, |
|
1454
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1455
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1456
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1457
|
|
|
Length $falseEasting, |
|
1458
|
|
|
Length $falseNorthing |
|
1459
|
9 |
|
): GeographicPoint { |
|
1460
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1461
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1462
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1463
|
9 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1464
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1465
|
9 |
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1466
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1467
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1468
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1469
|
9 |
|
$e4 = $e ** 4; |
|
1470
|
9 |
|
$e6 = $e ** 6; |
|
1471
|
|
|
$e8 = $e ** 8; |
|
1472
|
9 |
|
|
|
1473
|
9 |
|
$rho = hypot($easting, $northing); |
|
1474
|
|
|
$t = $rho * sqrt((1 + $e) ** (1 + $e) * (1 - $e) ** (1 - $e)) / (2 * $a * $scaleFactorOrigin); |
|
1475
|
9 |
|
|
|
1476
|
|
|
if ($latitudeOrigin < 0) { |
|
1477
|
|
|
$chi = 2 * atan($t) - M_PI / 2; |
|
1478
|
9 |
|
} else { |
|
1479
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1480
|
|
|
} |
|
1481
|
9 |
|
|
|
1482
|
|
|
$latitude = $chi + ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) * sin(2 * $chi) + (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) * sin(4 * $chi) + (7 * $e6 / 120 + 81 * $e8 / 1120) * sin(6 * $chi) + (4279 * $e8 / 161280) * sin(8 * $chi); |
|
1483
|
9 |
|
|
|
1484
|
|
|
if ($easting === 0.0) { |
|
|
|
|
|
|
1485
|
9 |
|
$longitude = $longitudeOrigin; |
|
1486
|
|
|
} elseif ($latitudeOrigin < 0) { |
|
1487
|
|
|
$longitude = $longitudeOrigin + atan2($easting, $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue()); |
|
1488
|
9 |
|
} else { |
|
1489
|
|
|
$longitude = $longitudeOrigin + atan2($easting, $falseNorthing->asMetres()->getValue() - $this->northing->asMetres()->getValue()); |
|
1490
|
|
|
} |
|
1491
|
9 |
|
|
|
1492
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1493
|
|
|
} |
|
1494
|
|
|
|
|
1495
|
|
|
/** |
|
1496
|
|
|
* Polar Stereographic (variant B). |
|
1497
|
9 |
|
*/ |
|
1498
|
|
|
public function polarStereographicVariantB( |
|
1499
|
|
|
Geographic2D|Geographic3D $to, |
|
1500
|
|
|
Angle $latitudeOfStandardParallel, |
|
1501
|
|
|
Angle $longitudeOfOrigin, |
|
1502
|
|
|
Length $falseEasting, |
|
1503
|
|
|
Length $falseNorthing |
|
1504
|
9 |
|
): GeographicPoint { |
|
1505
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1506
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1507
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1508
|
9 |
|
$standardParallel = $latitudeOfStandardParallel->asRadians()->getValue(); |
|
1509
|
9 |
|
$longitudeOrigin = $longitudeOfOrigin->asRadians()->getValue(); |
|
1510
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1511
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1512
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1513
|
9 |
|
$e4 = $e ** 4; |
|
1514
|
9 |
|
$e6 = $e ** 6; |
|
1515
|
|
|
$e8 = $e ** 8; |
|
1516
|
9 |
|
|
|
1517
|
9 |
|
$rho = hypot($easting, $northing); |
|
1518
|
9 |
|
if ($standardParallel < 0) { |
|
1519
|
|
|
$tF = tan(M_PI / 4 + $standardParallel / 2) / (((1 + $e * sin($standardParallel)) / (1 - $e * sin($standardParallel))) ** ($e / 2)); |
|
1520
|
|
|
} else { |
|
1521
|
|
|
$tF = tan(M_PI / 4 - $standardParallel / 2) * (((1 + $e * sin($standardParallel)) / (1 - $e * sin($standardParallel))) ** ($e / 2)); |
|
1522
|
9 |
|
} |
|
1523
|
9 |
|
$mF = cos($standardParallel) / sqrt(1 - $e2 * sin($standardParallel) ** 2); |
|
1524
|
9 |
|
$kO = $mF * sqrt((1 + $e) ** (1 + $e) * (1 - $e) ** (1 - $e)) / (2 * $tF); |
|
1525
|
|
|
$t = $rho * sqrt((1 + $e) ** (1 + $e) * (1 - $e) ** (1 - $e)) / (2 * $a * $kO); |
|
1526
|
9 |
|
|
|
1527
|
9 |
|
if ($standardParallel < 0) { |
|
1528
|
|
|
$chi = 2 * atan($t) - M_PI / 2; |
|
1529
|
|
|
} else { |
|
1530
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1531
|
|
|
} |
|
1532
|
9 |
|
|
|
1533
|
|
|
$latitude = $chi + ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) * sin(2 * $chi) + (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) * sin(4 * $chi) + (7 * $e6 / 120 + 81 * $e8 / 1120) * sin(6 * $chi) + (4279 * $e8 / 161280) * sin(8 * $chi); |
|
1534
|
9 |
|
|
|
1535
|
|
|
if ($easting === 0.0) { |
|
|
|
|
|
|
1536
|
9 |
|
$longitude = $longitudeOrigin; |
|
1537
|
9 |
|
} elseif ($standardParallel < 0) { |
|
1538
|
|
|
$longitude = $longitudeOrigin + atan2($easting, $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue()); |
|
1539
|
|
|
} else { |
|
1540
|
|
|
$longitude = $longitudeOrigin + atan2($easting, $falseNorthing->asMetres()->getValue() - $this->northing->asMetres()->getValue()); |
|
1541
|
|
|
} |
|
1542
|
9 |
|
|
|
1543
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1544
|
|
|
} |
|
1545
|
|
|
|
|
1546
|
|
|
/** |
|
1547
|
|
|
* Polar Stereographic (variant C). |
|
1548
|
9 |
|
*/ |
|
1549
|
|
|
public function polarStereographicVariantC( |
|
1550
|
|
|
Geographic2D|Geographic3D $to, |
|
1551
|
|
|
Angle $latitudeOfStandardParallel, |
|
1552
|
|
|
Angle $longitudeOfOrigin, |
|
1553
|
|
|
Length $eastingAtFalseOrigin, |
|
1554
|
|
|
Length $northingAtFalseOrigin |
|
1555
|
9 |
|
): GeographicPoint { |
|
1556
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1557
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtFalseOrigin->asMetres()->getValue(); |
|
1558
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue(); |
|
1559
|
9 |
|
$standardParallel = $latitudeOfStandardParallel->asRadians()->getValue(); |
|
1560
|
9 |
|
$longitudeOrigin = $longitudeOfOrigin->asRadians()->getValue(); |
|
1561
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1562
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1563
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1564
|
9 |
|
$e4 = $e ** 4; |
|
1565
|
9 |
|
$e6 = $e ** 6; |
|
1566
|
|
|
$e8 = $e ** 8; |
|
1567
|
9 |
|
|
|
1568
|
9 |
|
if ($standardParallel < 0) { |
|
1569
|
|
|
$tF = tan(M_PI / 4 + $standardParallel / 2) / (((1 + $e * sin($standardParallel)) / (1 - $e * sin($standardParallel))) ** ($e / 2)); |
|
1570
|
|
|
} else { |
|
1571
|
|
|
$tF = tan(M_PI / 4 - $standardParallel / 2) * (((1 + $e * sin($standardParallel)) / (1 - $e * sin($standardParallel))) ** ($e / 2)); |
|
1572
|
9 |
|
} |
|
1573
|
9 |
|
$mF = cos($standardParallel) / sqrt(1 - $e2 * sin($standardParallel) ** 2); |
|
1574
|
9 |
|
$rhoF = $a * $mF; |
|
1575
|
9 |
|
if ($standardParallel < 0) { |
|
1576
|
9 |
|
$rho = hypot($easting, $northing + $rhoF); |
|
1577
|
9 |
|
$t = $rho * $tF / $rhoF; |
|
1578
|
|
|
$chi = 2 * atan($t) - M_PI / 2; |
|
1579
|
|
|
} else { |
|
1580
|
|
|
$rho = hypot($easting, $northing - $rhoF); |
|
1581
|
|
|
$t = $rho * $tF / $rhoF; |
|
1582
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1583
|
|
|
} |
|
1584
|
9 |
|
|
|
1585
|
|
|
$latitude = $chi + ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) * sin(2 * $chi) + (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) * sin(4 * $chi) + (7 * $e6 / 120 + 81 * $e8 / 1120) * sin(6 * $chi) + (4279 * $e8 / 161280) * sin(8 * $chi); |
|
1586
|
9 |
|
|
|
1587
|
|
|
if ($easting === 0.0) { |
|
|
|
|
|
|
1588
|
9 |
|
$longitude = $longitudeOrigin; |
|
1589
|
9 |
|
} elseif ($standardParallel < 0) { |
|
1590
|
|
|
$longitude = $longitudeOrigin + atan2($easting, $this->northing->asMetres()->getValue() - $northingAtFalseOrigin->asMetres()->getValue() + $rhoF); |
|
1591
|
|
|
} else { |
|
1592
|
|
|
$longitude = $longitudeOrigin + atan2($easting, $northingAtFalseOrigin->asMetres()->getValue() - $this->northing->asMetres()->getValue() + $rhoF); |
|
1593
|
|
|
} |
|
1594
|
9 |
|
|
|
1595
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1596
|
|
|
} |
|
1597
|
|
|
|
|
1598
|
|
|
/** |
|
1599
|
|
|
* Popular Visualisation Pseudo Mercator |
|
1600
|
|
|
* Applies spherical formulas to the ellipsoid. As such does not have the properties of a true Mercator projection. |
|
1601
|
18 |
|
*/ |
|
1602
|
|
|
public function popularVisualisationPseudoMercator( |
|
1603
|
|
|
Geographic2D|Geographic3D $to, |
|
1604
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1605
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1606
|
|
|
Length $falseEasting, |
|
1607
|
|
|
Length $falseNorthing |
|
1608
|
18 |
|
): GeographicPoint { |
|
1609
|
18 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1610
|
18 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1611
|
18 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1612
|
18 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
|
|
|
|
|
1613
|
18 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1614
|
|
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1615
|
18 |
|
|
|
1616
|
18 |
|
$D = -$northing / $a; |
|
1617
|
18 |
|
$latitude = M_PI / 2 - 2 * atan(M_E ** $D); |
|
1618
|
|
|
$longitude = $easting / $a + $longitudeOrigin; |
|
1619
|
18 |
|
|
|
1620
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1621
|
|
|
} |
|
1622
|
|
|
|
|
1623
|
|
|
/** |
|
1624
|
|
|
* Similarity transformation |
|
1625
|
|
|
* Defined for two-dimensional coordinate systems. |
|
1626
|
9 |
|
*/ |
|
1627
|
|
|
public function similarityTransformation( |
|
1628
|
|
|
Projected $to, |
|
1629
|
|
|
Length $ordinate1OfEvaluationPointInTargetCRS, |
|
1630
|
|
|
Length $ordinate2OfEvaluationPointInTargetCRS, |
|
1631
|
|
|
Scale $scaleFactorForSourceCRSAxes, |
|
1632
|
|
|
Angle $rotationAngleOfSourceCRSAxes, |
|
1633
|
|
|
bool $inReverse |
|
1634
|
9 |
|
): self { |
|
1635
|
9 |
|
$xs = $this->easting->asMetres()->getValue(); |
|
1636
|
9 |
|
$ys = $this->northing->asMetres()->getValue(); |
|
1637
|
9 |
|
$xo = $ordinate1OfEvaluationPointInTargetCRS->asMetres()->getValue(); |
|
1638
|
9 |
|
$yo = $ordinate2OfEvaluationPointInTargetCRS->asMetres()->getValue(); |
|
1639
|
9 |
|
$M = $scaleFactorForSourceCRSAxes->asUnity()->getValue(); |
|
1640
|
|
|
$theta = $rotationAngleOfSourceCRSAxes->asRadians()->getValue(); |
|
1641
|
9 |
|
|
|
1642
|
|
|
if ($inReverse) { |
|
1643
|
|
|
$easting = (($xs - $xo) * cos($theta) - ($ys - $yo) * sin($theta)) / $M; |
|
1644
|
|
|
$northing = (($xs - $xo) * sin($theta) + ($ys - $yo) * cos($theta)) / $M; |
|
1645
|
9 |
|
} else { |
|
1646
|
9 |
|
$easting = $xo + $xs * $M * cos($theta) + $ys * $M * sin($theta); |
|
1647
|
|
|
$northing = $yo - $xs * $M * sin($theta) + $ys * $M * cos($theta); |
|
1648
|
|
|
} |
|
1649
|
9 |
|
|
|
1650
|
|
|
return self::create($to, new Metre($easting), new Metre($northing), new Metre(-$easting), new Metre(-$northing), $this->epoch); |
|
1651
|
|
|
} |
|
1652
|
|
|
|
|
1653
|
|
|
/** |
|
1654
|
|
|
* Mercator (variant A) |
|
1655
|
|
|
* Note that in these formulas the parameter latitude of natural origin (latO) is not used. However for this |
|
1656
|
|
|
* Mercator (variant A) method the EPSG dataset includes this parameter, which must have a value of zero, for |
|
1657
|
|
|
* completeness in CRS labelling. |
|
1658
|
18 |
|
*/ |
|
1659
|
|
|
public function mercatorVariantA( |
|
1660
|
|
|
Geographic2D|Geographic3D $to, |
|
1661
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1662
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1663
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1664
|
|
|
Length $falseEasting, |
|
1665
|
|
|
Length $falseNorthing |
|
1666
|
18 |
|
): GeographicPoint { |
|
1667
|
18 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1668
|
18 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1669
|
18 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
|
|
|
|
|
1670
|
18 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
|
|
|
|
|
1671
|
18 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1672
|
18 |
|
$scaleFactorOrigin = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1673
|
18 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1674
|
18 |
|
$e = $ellipsoid->getEccentricity(); |
|
1675
|
18 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1676
|
18 |
|
$e4 = $e ** 4; |
|
1677
|
18 |
|
$e6 = $e ** 6; |
|
1678
|
|
|
$e8 = $e ** 8; |
|
1679
|
18 |
|
|
|
1680
|
18 |
|
$t = M_E ** (($falseNorthing->asMetres()->getValue() - $this->northing->asMetres()->getValue()) / ($a * $scaleFactorOrigin)); |
|
1681
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1682
|
18 |
|
|
|
1683
|
18 |
|
$latitude = $chi + ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) * sin(2 * $chi) + (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) * sin(4 * $chi) + (7 * $e6 / 120 + 81 * $e8 / 1120) * sin(6 * $chi) + (4279 * $e8 / 161280) * sin(8 * $chi); |
|
1684
|
|
|
$longitude = $easting / ($a * $scaleFactorOrigin) + $longitudeOrigin; |
|
1685
|
18 |
|
|
|
1686
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1687
|
|
|
} |
|
1688
|
|
|
|
|
1689
|
|
|
/** |
|
1690
|
|
|
* Mercator (variant B) |
|
1691
|
|
|
* Used for most nautical charts. |
|
1692
|
9 |
|
*/ |
|
1693
|
|
|
public function mercatorVariantB( |
|
1694
|
|
|
Geographic2D|Geographic3D $to, |
|
1695
|
|
|
Angle $latitudeOf1stStandardParallel, |
|
1696
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1697
|
|
|
Length $falseEasting, |
|
1698
|
|
|
Length $falseNorthing |
|
1699
|
9 |
|
): GeographicPoint { |
|
1700
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1701
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1702
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
|
|
|
|
|
1703
|
9 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1704
|
9 |
|
$firstStandardParallel = $latitudeOf1stStandardParallel->asRadians()->getValue(); |
|
1705
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1706
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1707
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1708
|
9 |
|
$e4 = $e ** 4; |
|
1709
|
9 |
|
$e6 = $e ** 6; |
|
1710
|
|
|
$e8 = $e ** 8; |
|
1711
|
9 |
|
|
|
1712
|
|
|
$scaleFactorOrigin = cos($firstStandardParallel) / sqrt(1 - $e2 * sin($firstStandardParallel) ** 2); |
|
1713
|
9 |
|
|
|
1714
|
9 |
|
$t = M_E ** (($falseNorthing->asMetres()->getValue() - $this->northing->asMetres()->getValue()) / ($a * $scaleFactorOrigin)); |
|
1715
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1716
|
9 |
|
|
|
1717
|
9 |
|
$latitude = $chi + ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) * sin(2 * $chi) + (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) * sin(4 * $chi) + (7 * $e6 / 120 + 81 * $e8 / 1120) * sin(6 * $chi) + (4279 * $e8 / 161280) * sin(8 * $chi); |
|
1718
|
|
|
$longitude = $easting / ($a * $scaleFactorOrigin) + $longitudeOrigin; |
|
1719
|
9 |
|
|
|
1720
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1721
|
|
|
} |
|
1722
|
|
|
|
|
1723
|
|
|
/** |
|
1724
|
|
|
* Hotine Oblique Mercator (variant A). |
|
1725
|
9 |
|
*/ |
|
1726
|
|
|
public function obliqueMercatorHotineVariantA( |
|
1727
|
|
|
Geographic2D|Geographic3D $to, |
|
1728
|
|
|
Angle $latitudeOfProjectionCentre, |
|
1729
|
|
|
Angle $longitudeOfProjectionCentre, |
|
1730
|
|
|
Angle $azimuthAtProjectionCentre, |
|
1731
|
|
|
Angle $angleFromRectifiedToSkewGrid, |
|
1732
|
|
|
Scale $scaleFactorAtProjectionCentre, |
|
1733
|
|
|
Length $falseEasting, |
|
1734
|
|
|
Length $falseNorthing |
|
1735
|
9 |
|
): GeographicPoint { |
|
1736
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1737
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1738
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1739
|
9 |
|
$latC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
1740
|
9 |
|
$lonC = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
1741
|
9 |
|
$alphaC = $azimuthAtProjectionCentre->asRadians()->getValue(); |
|
1742
|
9 |
|
$kC = $scaleFactorAtProjectionCentre->asUnity()->getValue(); |
|
1743
|
9 |
|
$gammaC = $angleFromRectifiedToSkewGrid->asRadians()->getValue(); |
|
1744
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1745
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1746
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1747
|
9 |
|
$e4 = $e ** 4; |
|
1748
|
9 |
|
$e6 = $e ** 6; |
|
1749
|
|
|
$e8 = $e ** 8; |
|
1750
|
9 |
|
|
|
1751
|
9 |
|
$B = sqrt(1 + ($e2 * cos($latC) ** 4 / (1 - $e2))); |
|
1752
|
9 |
|
$A = $a * $B * $kC * sqrt(1 - $e2) / (1 - $e2 * sin($latC) ** 2); |
|
1753
|
9 |
|
$tO = tan(M_PI / 4 - $latC / 2) / ((1 - $e * sin($latC)) / (1 + $e * sin($latC))) ** ($e / 2); |
|
1754
|
9 |
|
$D = $B * sqrt(1 - $e2) / (cos($latC) * sqrt(1 - $e2 * sin($latC) ** 2)); |
|
1755
|
9 |
|
$DD = max(1, $D ** 2); |
|
1756
|
9 |
|
$F = $D + sqrt($DD - 1) * static::sign($latC); |
|
1757
|
9 |
|
$H = $F * $tO ** $B; |
|
1758
|
9 |
|
$G = ($F - 1 / $F) / 2; |
|
1759
|
9 |
|
$gammaO = self::asin(sin($alphaC) / $D); |
|
1760
|
|
|
$lonO = $lonC - self::asin($G * tan($gammaO)) / $B; |
|
1761
|
9 |
|
|
|
1762
|
9 |
|
$v = $easting * cos($gammaC) - $northing * sin($gammaC); |
|
1763
|
|
|
$u = $northing * cos($gammaC) + $easting * sin($gammaC); |
|
1764
|
9 |
|
|
|
1765
|
9 |
|
$Q = M_E ** -($B * $v / $A); |
|
1766
|
9 |
|
$S = ($Q - 1 / $Q) / 2; |
|
1767
|
9 |
|
$T = ($Q + 1 / $Q) / 2; |
|
1768
|
9 |
|
$V = sin($B * $u / $A); |
|
1769
|
9 |
|
$U = ($V * cos($gammaO) + $S * sin($gammaO)) / $T; |
|
1770
|
|
|
$t = ($H / sqrt((1 + $U) / (1 - $U))) ** (1 / $B); |
|
1771
|
9 |
|
|
|
1772
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1773
|
9 |
|
|
|
1774
|
9 |
|
$latitude = $chi + sin(2 * $chi) * ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) + sin(4 * $chi) * (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) + sin(6 * $chi) * (7 * $e6 / 120 + 81 * $e8 / 1120) + sin(8 * $chi) * (4279 * $e8 / 161280); |
|
1775
|
|
|
$longitude = $lonO - atan2($S * cos($gammaO) - $V * sin($gammaO), cos($B * $u / $A)) / $B; |
|
1776
|
9 |
|
|
|
1777
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1778
|
|
|
} |
|
1779
|
|
|
|
|
1780
|
|
|
/** |
|
1781
|
|
|
* Hotine Oblique Mercator (variant B). |
|
1782
|
9 |
|
*/ |
|
1783
|
|
|
public function obliqueMercatorHotineVariantB( |
|
1784
|
|
|
Geographic2D|Geographic3D $to, |
|
1785
|
|
|
Angle $latitudeOfProjectionCentre, |
|
1786
|
|
|
Angle $longitudeOfProjectionCentre, |
|
1787
|
|
|
Angle $azimuthAtProjectionCentre, |
|
1788
|
|
|
Angle $angleFromRectifiedToSkewGrid, |
|
1789
|
|
|
Scale $scaleFactorAtProjectionCentre, |
|
1790
|
|
|
Length $eastingAtProjectionCentre, |
|
1791
|
|
|
Length $northingAtProjectionCentre |
|
1792
|
9 |
|
): GeographicPoint { |
|
1793
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1794
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $eastingAtProjectionCentre->asMetres()->getValue(); |
|
1795
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $northingAtProjectionCentre->asMetres()->getValue(); |
|
1796
|
9 |
|
$latC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
1797
|
9 |
|
$lonC = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
1798
|
9 |
|
$alphaC = $azimuthAtProjectionCentre->asRadians()->getValue(); |
|
1799
|
9 |
|
$kC = $scaleFactorAtProjectionCentre->asUnity()->getValue(); |
|
1800
|
9 |
|
$gammaC = $angleFromRectifiedToSkewGrid->asRadians()->getValue(); |
|
1801
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1802
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1803
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1804
|
9 |
|
$e4 = $e ** 4; |
|
1805
|
9 |
|
$e6 = $e ** 6; |
|
1806
|
|
|
$e8 = $e ** 8; |
|
1807
|
9 |
|
|
|
1808
|
9 |
|
$B = sqrt(1 + ($e2 * cos($latC) ** 4 / (1 - $e2))); |
|
1809
|
9 |
|
$A = $a * $B * $kC * sqrt(1 - $e2) / (1 - $e2 * sin($latC) ** 2); |
|
1810
|
9 |
|
$tO = tan(M_PI / 4 - $latC / 2) / ((1 - $e * sin($latC)) / (1 + $e * sin($latC))) ** ($e / 2); |
|
1811
|
9 |
|
$D = $B * sqrt(1 - $e2) / (cos($latC) * sqrt(1 - $e2 * sin($latC) ** 2)); |
|
1812
|
9 |
|
$DD = max(1, $D ** 2); |
|
1813
|
9 |
|
$F = $D + sqrt($DD - 1) * static::sign($latC); |
|
1814
|
9 |
|
$H = $F * $tO ** $B; |
|
1815
|
9 |
|
$G = ($F - 1 / $F) / 2; |
|
1816
|
9 |
|
$gammaO = self::asin(sin($alphaC) / $D); |
|
1817
|
9 |
|
$lonO = $lonC - self::asin($G * tan($gammaO)) / $B; |
|
1818
|
9 |
|
$vC = 0; |
|
|
|
|
|
|
1819
|
|
|
if ($alphaC === M_PI / 2) { |
|
1820
|
|
|
$uC = $A * ($lonC - $lonO); |
|
1821
|
9 |
|
} else { |
|
1822
|
|
|
$uC = ($A / $B) * atan2(sqrt($DD - 1), cos($alphaC)) * static::sign($latC); |
|
1823
|
|
|
} |
|
1824
|
9 |
|
|
|
1825
|
9 |
|
$v = $easting * cos($gammaC) - $northing * sin($gammaC); |
|
1826
|
|
|
$u = $northing * cos($gammaC) + $easting * sin($gammaC) + (abs($uC) * static::sign($latC)); |
|
1827
|
9 |
|
|
|
1828
|
9 |
|
$Q = M_E ** -($B * $v / $A); |
|
1829
|
9 |
|
$S = ($Q - 1 / $Q) / 2; |
|
1830
|
9 |
|
$T = ($Q + 1 / $Q) / 2; |
|
1831
|
9 |
|
$V = sin($B * $u / $A); |
|
1832
|
9 |
|
$U = ($V * cos($gammaO) + $S * sin($gammaO)) / $T; |
|
1833
|
|
|
$t = ($H / sqrt((1 + $U) / (1 - $U))) ** (1 / $B); |
|
1834
|
9 |
|
|
|
1835
|
|
|
$chi = M_PI / 2 - 2 * atan($t); |
|
1836
|
9 |
|
|
|
1837
|
9 |
|
$latitude = $chi + sin(2 * $chi) * ($e2 / 2 + 5 * $e4 / 24 + $e6 / 12 + 13 * $e8 / 360) + sin(4 * $chi) * (7 * $e4 / 48 + 29 * $e6 / 240 + 811 * $e8 / 11520) + sin(6 * $chi) * (7 * $e6 / 120 + 81 * $e8 / 1120) + sin(8 * $chi) * (4279 * $e8 / 161280); |
|
1838
|
|
|
$longitude = $lonO - atan2($S * cos($gammaO) - $V * sin($gammaO), cos($B * $u / $A)) / $B; |
|
1839
|
9 |
|
|
|
1840
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1841
|
|
|
} |
|
1842
|
|
|
|
|
1843
|
|
|
/** |
|
1844
|
|
|
* Laborde Oblique Mercator. |
|
1845
|
9 |
|
*/ |
|
1846
|
|
|
public function obliqueMercatorLaborde( |
|
1847
|
|
|
Geographic2D|Geographic3D $to, |
|
1848
|
|
|
Angle $latitudeOfProjectionCentre, |
|
1849
|
|
|
Angle $longitudeOfProjectionCentre, |
|
1850
|
|
|
Angle $azimuthAtProjectionCentre, |
|
1851
|
|
|
Scale $scaleFactorAtProjectionCentre, |
|
1852
|
|
|
Length $falseEasting, |
|
1853
|
|
|
Length $falseNorthing |
|
1854
|
9 |
|
): GeographicPoint { |
|
1855
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1856
|
9 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1857
|
9 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1858
|
9 |
|
$latC = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
1859
|
9 |
|
$lonC = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
1860
|
9 |
|
$alphaC = $azimuthAtProjectionCentre->asRadians()->getValue(); |
|
1861
|
9 |
|
$kC = $scaleFactorAtProjectionCentre->asUnity()->getValue(); |
|
1862
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1863
|
9 |
|
$e = $ellipsoid->getEccentricity(); |
|
1864
|
|
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
1865
|
9 |
|
|
|
1866
|
9 |
|
$B = sqrt(1 + ($e2 * cos($latC) ** 4 / (1 - $e2))); |
|
1867
|
9 |
|
$latS = self::asin(sin($latC) / $B); |
|
1868
|
9 |
|
$R = $a * $kC * (sqrt(1 - $e2) / (1 - $e2 * sin($latC) ** 2)); |
|
1869
|
|
|
$C = log(tan(M_PI / 4 + $latS / 2)) - $B * log(tan(M_PI / 4 + $latC / 2) * ((1 - $e * sin($latC)) / (1 + $e * sin($latC))) ** ($e / 2)); |
|
1870
|
9 |
|
|
|
1871
|
|
|
$G = (new ComplexNumber(1 - cos(2 * $alphaC), sin(2 * $alphaC)))->divide(new ComplexNumber(12, 0)); |
|
1872
|
9 |
|
|
|
1873
|
9 |
|
$H0 = new ComplexNumber($northing / $R, $easting / $R); |
|
1874
|
|
|
$H = $H0->divide($H0->pow(3)->multiply($G)->add($H0)); |
|
1875
|
9 |
|
do { |
|
1876
|
9 |
|
$HN = $H; |
|
1877
|
9 |
|
$H = $HN->pow(3)->multiply($G)->multiply(new ComplexNumber(2, 0))->add($H0)->divide($HN->pow(2)->multiply($G)->multiply(new ComplexNumber(3, 0))->add(new ComplexNumber(1, 0))); |
|
1878
|
|
|
} while (abs($H0->subtract($H)->subtract($H->pow(3)->multiply($G))->getReal()) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1879
|
9 |
|
|
|
1880
|
9 |
|
$LPrime = -1 * $H->getReal(); |
|
1881
|
9 |
|
$PPrime = 2 * atan(M_E ** $H->getImaginary()) - M_PI / 2; |
|
1882
|
9 |
|
$U = cos($PPrime) * cos($LPrime) * cos($latS) + cos($PPrime) * sin($LPrime) * sin($latS); |
|
1883
|
9 |
|
$V = sin($PPrime); |
|
1884
|
|
|
$W = cos($PPrime) * cos($LPrime) * sin($latS) - cos($PPrime) * sin($LPrime) * cos($latS); |
|
1885
|
9 |
|
|
|
1886
|
9 |
|
$d = hypot($U, $V); |
|
1887
|
|
|
if ($d === 0.0) { |
|
1888
|
|
|
$L = 0; |
|
1889
|
|
|
$P = static::sign($W) * M_PI / 2; |
|
1890
|
9 |
|
} else { |
|
1891
|
9 |
|
$L = 2 * atan($V / ($U + $d)); |
|
1892
|
|
|
$P = atan($W / $d); |
|
1893
|
|
|
} |
|
1894
|
9 |
|
|
|
1895
|
|
|
$longitude = $lonC + ($L / $B); |
|
1896
|
9 |
|
|
|
1897
|
|
|
$q = (log(tan(M_PI / 4 + $P / 2)) - $C) / $B; |
|
1898
|
9 |
|
|
|
1899
|
|
|
$latitude = 2 * atan(M_E ** $q) - M_PI / 2; |
|
1900
|
9 |
|
do { |
|
1901
|
9 |
|
$latitudeN = $latitude; |
|
1902
|
9 |
|
$latitude = 2 * atan(((1 + $e * sin($latitude)) / (1 - $e * sin($latitude))) ** ($e / 2) * M_E ** $q) - M_PI / 2; |
|
1903
|
|
|
} while (abs($latitude - $latitudeN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
1904
|
9 |
|
|
|
1905
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
1906
|
|
|
} |
|
1907
|
|
|
|
|
1908
|
|
|
/** |
|
1909
|
|
|
* Transverse Mercator. |
|
1910
|
144 |
|
*/ |
|
1911
|
|
|
public function transverseMercator( |
|
1912
|
|
|
Geographic2D|Geographic3D $to, |
|
1913
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
1914
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
1915
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
1916
|
|
|
Length $falseEasting, |
|
1917
|
|
|
Length $falseNorthing |
|
1918
|
144 |
|
): GeographicPoint { |
|
1919
|
144 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
1920
|
144 |
|
$easting = $this->easting->asMetres()->getValue() - $falseEasting->asMetres()->getValue(); |
|
1921
|
144 |
|
$northing = $this->northing->asMetres()->getValue() - $falseNorthing->asMetres()->getValue(); |
|
1922
|
144 |
|
$latitudeOrigin = $latitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1923
|
144 |
|
$longitudeOrigin = $longitudeOfNaturalOrigin->asRadians()->getValue(); |
|
1924
|
144 |
|
$kO = $scaleFactorAtNaturalOrigin->asUnity()->getValue(); |
|
1925
|
144 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
1926
|
144 |
|
$e = $ellipsoid->getEccentricity(); |
|
1927
|
|
|
$f = $ellipsoid->getFlattening(); |
|
1928
|
144 |
|
|
|
1929
|
144 |
|
$n = $f / (2 - $f); |
|
1930
|
|
|
$B = ($a / (1 + $n)) * (1 + $n ** 2 / 4 + $n ** 4 / 64 + $n ** 6 / 256 + (25 / 16384) * $n ** 8); |
|
1931
|
144 |
|
|
|
1932
|
144 |
|
$h1 = $n / 2 - (2 / 3) * $n ** 2 + (5 / 16) * $n ** 3 + (41 / 180) * $n ** 4 - (127 / 288) * $n ** 5 + (7891 / 37800) * $n ** 6 + (72161 / 387072) * $n ** 7 - (18975107 / 50803200) * $n ** 8; |
|
1933
|
144 |
|
$h2 = (13 / 48) * $n ** 2 - (3 / 5) * $n ** 3 + (557 / 1440) * $n ** 4 + (281 / 630) * $n ** 5 - (1983433 / 1935360) * $n ** 6 + (13769 / 28800) * $n ** 7 + (148003883 / 174182400) * $n ** 8; |
|
1934
|
144 |
|
$h3 = (61 / 240) * $n ** 3 - (103 / 140) * $n ** 4 + (15061 / 26880) * $n ** 5 + (167603 / 181440) * $n ** 6 - (67102379 / 29030400) * $n ** 7 + (79682431 / 79833600) * $n ** 8; |
|
1935
|
144 |
|
$h4 = (49561 / 161280) * $n ** 4 - (179 / 168) * $n ** 5 + (6601661 / 7257600) * $n ** 6 + (97445 / 49896) * $n ** 7 - (40176129013 / 7664025600) * $n ** 8; |
|
1936
|
144 |
|
$h5 = (34729 / 80640) * $n ** 5 - (3418889 / 1995840) * $n ** 6 + (14644087 / 9123840) * $n ** 7 + (2605413599 / 622702080) * $n ** 8; |
|
1937
|
144 |
|
$h6 = (212378941 / 319334400) * $n ** 6 - (30705481 / 10378368) * $n ** 7 + (175214326799 / 58118860800) * $n ** 8; |
|
1938
|
144 |
|
$h7 = (1522256789 / 1383782400) * $n ** 7 - (16759934899 / 3113510400) * $n ** 8; |
|
1939
|
|
|
$h8 = (1424729850961 / 743921418240) * $n ** 8; |
|
1940
|
144 |
|
|
|
1941
|
90 |
|
if ($latitudeOrigin === 0.0) { |
|
|
|
|
|
|
1942
|
63 |
|
$mO = 0; |
|
1943
|
|
|
} elseif ($latitudeOrigin === M_PI / 2) { |
|
1944
|
63 |
|
$mO = $B * M_PI / 2; |
|
1945
|
|
|
} elseif ($latitudeOrigin === -M_PI / 2) { |
|
1946
|
|
|
$mO = $B * -M_PI / 2; |
|
1947
|
63 |
|
} else { |
|
1948
|
63 |
|
$qO = asinh(tan($latitudeOrigin)) - ($e * atanh($e * sin($latitudeOrigin))); |
|
1949
|
63 |
|
$betaO = atan(sinh($qO)); |
|
1950
|
63 |
|
$xiO0 = self::asin(sin($betaO)); |
|
1951
|
63 |
|
$xiO1 = $h1 * sin(2 * $xiO0); |
|
1952
|
63 |
|
$xiO2 = $h2 * sin(4 * $xiO0); |
|
1953
|
63 |
|
$xiO3 = $h3 * sin(6 * $xiO0); |
|
1954
|
63 |
|
$xiO4 = $h4 * sin(8 * $xiO0); |
|
1955
|
63 |
|
$xiO5 = $h5 * sin(10 * $xiO0); |
|
1956
|
63 |
|
$xiO6 = $h6 * sin(12 * $xiO0); |
|
1957
|
63 |
|
$xiO7 = $h7 * sin(14 * $xiO0); |
|
1958
|
63 |
|
$xiO8 = $h8 * sin(16 * $xiO0); |
|
1959
|
63 |
|
$xiO = $xiO0 + $xiO1 + $xiO2 + $xiO3 + $xiO4 + $xiO5 + $xiO6 + $xiO7 + $xiO8; |
|
1960
|
|
|
$mO = $B * $xiO; |
|
1961
|
|
|
} |
|
1962
|
144 |
|
|
|
1963
|
144 |
|
$h1 = $n / 2 - (2 / 3) * $n ** 2 + (37 / 96) * $n ** 3 - (1 / 360) * $n ** 4 - (81 / 512) * $n ** 5 + (96199 / 604800) * $n ** 6 - (5406467 / 38707200) * $n ** 7 + (7944359 / 67737600) * $n ** 8; |
|
1964
|
144 |
|
$h2 = (1 / 48) * $n ** 2 + (1 / 15) * $n ** 3 - (437 / 1440) * $n ** 4 + (46 / 105) * $n ** 5 - (1118711 / 3870720) * $n ** 6 + (51841 / 1209600) * $n ** 7 + (24749483 / 348364800) * $n ** 8; |
|
1965
|
144 |
|
$h3 = (17 / 480) * $n ** 3 - (37 / 840) * $n ** 4 - (209 / 4480) * $n ** 5 + (5569 / 90720) * $n ** 6 + (9261899 / 58060800) * $n ** 7 - (6457463 / 17740800) * $n ** 8; |
|
1966
|
144 |
|
$h4 = (4397 / 161280) * $n ** 4 - (11 / 504) * $n ** 5 - (830251 / 7257600) * $n ** 6 + (466511 / 2494800) * $n ** 7 + (324154477 / 7664025600) * $n ** 8; |
|
1967
|
144 |
|
$h5 = (4583 / 161280) * $n ** 5 - (108847 / 3991680) * $n ** 6 - (8005831 / 63866880) * $n ** 7 + (22894433 / 124540416) * $n ** 8; |
|
1968
|
144 |
|
$h6 = (20648693 / 638668800) * $n ** 6 - (16363163 / 518918400) * $n ** 7 - (2204645983 / 12915302400) * $n ** 8; |
|
1969
|
144 |
|
$h7 = (219941297 / 5535129600) * $n ** 7 - (497323811 / 12454041600) * $n ** 8; |
|
1970
|
|
|
$h8 = (191773887257 / 3719607091200) * $n ** 8; |
|
1971
|
144 |
|
|
|
1972
|
144 |
|
$eta = $easting / ($B * $kO); |
|
1973
|
144 |
|
$xi = ($northing + $kO * $mO) / ($B * $kO); |
|
1974
|
144 |
|
$xi1 = $h1 * sin(2 * $xi) * cosh(2 * $eta); |
|
1975
|
144 |
|
$eta1 = $h1 * cos(2 * $xi) * sinh(2 * $eta); |
|
1976
|
144 |
|
$xi2 = $h2 * sin(4 * $xi) * cosh(4 * $eta); |
|
1977
|
144 |
|
$eta2 = $h2 * cos(4 * $xi) * sinh(4 * $eta); |
|
1978
|
144 |
|
$xi3 = $h3 * sin(6 * $xi) * cosh(6 * $eta); |
|
1979
|
144 |
|
$eta3 = $h3 * cos(6 * $xi) * sinh(6 * $eta); |
|
1980
|
144 |
|
$xi4 = $h4 * sin(8 * $xi) * cosh(8 * $eta); |
|
1981
|
144 |
|
$eta4 = $h4 * cos(8 * $xi) * sinh(8 * $eta); |
|
1982
|
144 |
|
$xi5 = $h5 * sin(10 * $xi) * cosh(10 * $eta); |
|
1983
|
144 |
|
$eta5 = $h5 * cos(10 * $xi) * sinh(10 * $eta); |
|
1984
|
144 |
|
$xi6 = $h6 * sin(12 * $xi) * cosh(12 * $eta); |
|
1985
|
144 |
|
$eta6 = $h6 * cos(12 * $xi) * sinh(12 * $eta); |
|
1986
|
144 |
|
$xi7 = $h7 * sin(14 * $xi) * cosh(14 * $eta); |
|
1987
|
144 |
|
$eta7 = $h7 * cos(14 * $xi) * sinh(14 * $eta); |
|
1988
|
144 |
|
$xi8 = $h8 * sin(16 * $xi) * cosh(16 * $eta); |
|
1989
|
144 |
|
$eta8 = $h8 * cos(16 * $xi) * sinh(16 * $eta); |
|
1990
|
144 |
|
$xi0 = $xi - $xi1 - $xi2 - $xi3 - $xi4 - $xi5 - $xi6 - $xi7 - $xi8; |
|
1991
|
|
|
$eta0 = $eta - $eta1 - $eta2 - $eta3 - $eta4 - $eta5 - $eta6 - $eta7 - $eta8; |
|
1992
|
144 |
|
|
|
1993
|
|
|
$beta = self::asin(sin($xi0) / cosh($eta0)); |
|
1994
|
144 |
|
|
|
1995
|
144 |
|
$QPrime = asinh(tan($beta)); |
|
1996
|
|
|
$Q = asinh(tan($beta)); |
|
1997
|
144 |
|
do { |
|
1998
|
144 |
|
$QN = $Q; |
|
1999
|
144 |
|
$Q = $QPrime + ($e * atanh($e * tanh($Q))); |
|
2000
|
|
|
} while (abs($Q - $QN) >= static::ITERATION_CONVERGENCE_FORMULA); |
|
2001
|
144 |
|
|
|
2002
|
144 |
|
$latitude = atan(sinh($Q)); |
|
2003
|
|
|
$longitude = $longitudeOrigin + self::asin(tanh($eta0) / cos($beta)); |
|
2004
|
144 |
|
|
|
2005
|
|
|
$height = $this->height && $to instanceof Geographic3D ? $this->height : null; |
|
2006
|
144 |
|
|
|
2007
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), $height, $this->epoch); |
|
2008
|
|
|
} |
|
2009
|
|
|
|
|
2010
|
|
|
/** |
|
2011
|
|
|
* Transverse Mercator Zoned Grid System |
|
2012
|
|
|
* If locations fall outwith the fixed zones the general Transverse Mercator method (code 9807) must be used for |
|
2013
|
|
|
* each zone. |
|
2014
|
18 |
|
*/ |
|
2015
|
|
|
public function transverseMercatorZonedGrid( |
|
2016
|
|
|
Geographic2D|Geographic3D $to, |
|
2017
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
2018
|
|
|
Angle $initialLongitude, |
|
2019
|
|
|
Angle $zoneWidth, |
|
2020
|
|
|
Scale $scaleFactorAtNaturalOrigin, |
|
2021
|
|
|
Length $falseEasting, |
|
2022
|
|
|
Length $falseNorthing |
|
2023
|
18 |
|
): GeographicPoint { |
|
2024
|
18 |
|
$Z = (int) substr((string) $this->easting->asMetres()->getValue(), 0, 2); |
|
2025
|
|
|
$falseEasting = $falseEasting->add(new Metre($Z * 1000000)); |
|
2026
|
18 |
|
|
|
2027
|
18 |
|
$W = $zoneWidth->asDegrees()->getValue(); |
|
2028
|
|
|
$longitudeOrigin = $initialLongitude->add(new Degree($Z * $W - $W / 2)); |
|
2029
|
18 |
|
|
|
2030
|
|
|
return $this->transverseMercator($to, $latitudeOfNaturalOrigin, $longitudeOrigin, $scaleFactorAtNaturalOrigin, $falseEasting, $falseNorthing); |
|
2031
|
|
|
} |
|
2032
|
|
|
|
|
2033
|
|
|
/** |
|
2034
|
|
|
* General polynomial. |
|
2035
|
|
|
* @param Coefficient[] $powerCoefficients |
|
2036
|
|
|
*/ |
|
2037
|
|
|
public function generalPolynomial( |
|
2038
|
|
|
Projected $to, |
|
2039
|
|
|
Length $ordinate1OfEvaluationPointInSourceCRS, |
|
2040
|
|
|
Length $ordinate2OfEvaluationPointInSourceCRS, |
|
2041
|
|
|
Length $ordinate1OfEvaluationPointInTargetCRS, |
|
2042
|
|
|
Length $ordinate2OfEvaluationPointInTargetCRS, |
|
2043
|
|
|
Scale $scalingFactorForSourceCRSCoordDifferences, |
|
2044
|
|
|
Scale $scalingFactorForTargetCRSCoordDifferences, |
|
2045
|
|
|
Scale $A0, |
|
2046
|
|
|
Scale $B0, |
|
2047
|
|
|
array $powerCoefficients, |
|
2048
|
|
|
bool $inReverse |
|
2049
|
|
|
): self { |
|
2050
|
|
|
$xs = $this->easting->getValue(); |
|
2051
|
|
|
$ys = $this->northing->getValue(); |
|
2052
|
|
|
|
|
2053
|
|
|
$t = $this->generalPolynomialUnitless( |
|
2054
|
|
|
$xs, |
|
2055
|
|
|
$ys, |
|
2056
|
|
|
$ordinate1OfEvaluationPointInSourceCRS, |
|
2057
|
|
|
$ordinate2OfEvaluationPointInSourceCRS, |
|
2058
|
|
|
$ordinate1OfEvaluationPointInTargetCRS, |
|
2059
|
|
|
$ordinate2OfEvaluationPointInTargetCRS, |
|
2060
|
|
|
$scalingFactorForSourceCRSCoordDifferences, |
|
2061
|
|
|
$scalingFactorForTargetCRSCoordDifferences, |
|
2062
|
|
|
$A0, |
|
2063
|
|
|
$B0, |
|
2064
|
|
|
$powerCoefficients, |
|
2065
|
|
|
$inReverse |
|
2066
|
|
|
); |
|
2067
|
|
|
|
|
2068
|
|
|
$xtUnit = $to->getCoordinateSystem()->getAxes()[0]->getUnitOfMeasureId(); |
|
2069
|
|
|
$ytUnit = $to->getCoordinateSystem()->getAxes()[1]->getUnitOfMeasureId(); |
|
2070
|
|
|
|
|
2071
|
|
|
return static::createFromEastingNorthing( |
|
2072
|
|
|
$to, |
|
2073
|
|
|
Length::makeUnit($t['xt'], $xtUnit), |
|
2074
|
|
|
Length::makeUnit($t['yt'], $ytUnit), |
|
2075
|
|
|
$this->epoch |
|
2076
|
|
|
); |
|
2077
|
|
|
} |
|
2078
|
|
|
|
|
2079
|
|
|
/** |
|
2080
|
|
|
* New Zealand Map Grid. |
|
2081
|
27 |
|
*/ |
|
2082
|
|
|
public function newZealandMapGrid( |
|
2083
|
|
|
Geographic2D|Geographic3D $to, |
|
2084
|
|
|
Angle $latitudeOfNaturalOrigin, |
|
2085
|
|
|
Angle $longitudeOfNaturalOrigin, |
|
2086
|
|
|
Length $falseEasting, |
|
2087
|
|
|
Length $falseNorthing |
|
2088
|
27 |
|
): GeographicPoint { |
|
2089
|
27 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
2090
|
|
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
2091
|
27 |
|
|
|
2092
|
27 |
|
$z = new ComplexNumber( |
|
2093
|
27 |
|
$this->northing->subtract($falseNorthing)->divide($a)->asMetres()->getValue(), |
|
2094
|
27 |
|
$this->easting->subtract($falseEasting)->divide($a)->asMetres()->getValue(), |
|
2095
|
|
|
); |
|
2096
|
27 |
|
|
|
2097
|
27 |
|
$B1 = new ComplexNumber(0.7557853228, 0.0); |
|
2098
|
27 |
|
$B2 = new ComplexNumber(0.249204646, 0.003371507); |
|
2099
|
27 |
|
$B3 = new ComplexNumber(-0.001541739, 0.041058560); |
|
2100
|
27 |
|
$B4 = new ComplexNumber(-0.10162907, 0.01727609); |
|
2101
|
27 |
|
$B5 = new ComplexNumber(-0.26623489, -0.36249218); |
|
2102
|
27 |
|
$B6 = new ComplexNumber(-0.6870983, -1.1651967); |
|
2103
|
27 |
|
$b1 = new ComplexNumber(1.3231270439, 0.0); |
|
2104
|
27 |
|
$b2 = new ComplexNumber(-0.577245789, -0.007809598); |
|
2105
|
27 |
|
$b3 = new ComplexNumber(0.508307513, -0.112208952); |
|
2106
|
27 |
|
$b4 = new ComplexNumber(-0.15094762, 0.18200602); |
|
2107
|
27 |
|
$b5 = new ComplexNumber(1.01418179, 1.64497696); |
|
2108
|
|
|
$b6 = new ComplexNumber(1.9660549, 2.5127645); |
|
2109
|
27 |
|
|
|
2110
|
27 |
|
$zeta = new ComplexNumber(0, 0); |
|
2111
|
27 |
|
$zeta = $zeta->add($b1->multiply($z->pow(1))); |
|
2112
|
27 |
|
$zeta = $zeta->add($b2->multiply($z->pow(2))); |
|
2113
|
27 |
|
$zeta = $zeta->add($b3->multiply($z->pow(3))); |
|
2114
|
27 |
|
$zeta = $zeta->add($b4->multiply($z->pow(4))); |
|
2115
|
27 |
|
$zeta = $zeta->add($b5->multiply($z->pow(5))); |
|
2116
|
|
|
$zeta = $zeta->add($b6->multiply($z->pow(6))); |
|
2117
|
27 |
|
|
|
2118
|
27 |
|
for ($iterations = 0; $iterations < 2; ++$iterations) { |
|
2119
|
27 |
|
$numerator = $z; |
|
2120
|
27 |
|
$numerator = $numerator->add($B2->multiply($zeta->pow(2))->multiply(new ComplexNumber(1, 0))); |
|
2121
|
27 |
|
$numerator = $numerator->add($B3->multiply($zeta->pow(3))->multiply(new ComplexNumber(2, 0))); |
|
2122
|
27 |
|
$numerator = $numerator->add($B4->multiply($zeta->pow(4))->multiply(new ComplexNumber(3, 0))); |
|
2123
|
27 |
|
$numerator = $numerator->add($B5->multiply($zeta->pow(5))->multiply(new ComplexNumber(4, 0))); |
|
2124
|
|
|
$numerator = $numerator->add($B6->multiply($zeta->pow(6))->multiply(new ComplexNumber(5, 0))); |
|
2125
|
27 |
|
|
|
2126
|
27 |
|
$denominator = $B1; |
|
2127
|
27 |
|
$denominator = $denominator->add($B2->multiply($zeta->pow(1))->multiply(new ComplexNumber(2, 0))); |
|
2128
|
27 |
|
$denominator = $denominator->add($B3->multiply($zeta->pow(2))->multiply(new ComplexNumber(3, 0))); |
|
2129
|
27 |
|
$denominator = $denominator->add($B4->multiply($zeta->pow(3))->multiply(new ComplexNumber(4, 0))); |
|
2130
|
27 |
|
$denominator = $denominator->add($B5->multiply($zeta->pow(4))->multiply(new ComplexNumber(5, 0))); |
|
2131
|
|
|
$denominator = $denominator->add($B6->multiply($zeta->pow(5))->multiply(new ComplexNumber(6, 0))); |
|
2132
|
27 |
|
|
|
2133
|
|
|
$zeta = $numerator->divide($denominator); |
|
2134
|
|
|
} |
|
2135
|
27 |
|
|
|
2136
|
27 |
|
$deltaPsi = $zeta->getReal(); |
|
2137
|
27 |
|
$deltaLatitudeToOrigin = 0; |
|
2138
|
27 |
|
$deltaLatitudeToOrigin += 1.5627014243 * $deltaPsi ** 1; |
|
2139
|
27 |
|
$deltaLatitudeToOrigin += 0.5185406398 * $deltaPsi ** 2; |
|
2140
|
27 |
|
$deltaLatitudeToOrigin += -0.03333098 * $deltaPsi ** 3; |
|
2141
|
27 |
|
$deltaLatitudeToOrigin += -0.1052906 * $deltaPsi ** 4; |
|
2142
|
27 |
|
$deltaLatitudeToOrigin += -0.0368594 * $deltaPsi ** 5; |
|
2143
|
27 |
|
$deltaLatitudeToOrigin += 0.007317 * $deltaPsi ** 6; |
|
2144
|
27 |
|
$deltaLatitudeToOrigin += 0.01220 * $deltaPsi ** 7; |
|
2145
|
27 |
|
$deltaLatitudeToOrigin += 0.00394 * $deltaPsi ** 8; |
|
2146
|
|
|
$deltaLatitudeToOrigin += -0.0013 * $deltaPsi ** 9; |
|
2147
|
27 |
|
|
|
2148
|
27 |
|
$latitude = $latitudeOfNaturalOrigin->add(new ArcSecond($deltaLatitudeToOrigin / 0.00001)); |
|
2149
|
|
|
$longitude = $longitudeOfNaturalOrigin->add(new Radian($zeta->getImaginary())); |
|
2150
|
27 |
|
|
|
2151
|
|
|
return GeographicPoint::create($to, $latitude, $longitude, null, $this->epoch); |
|
2152
|
|
|
} |
|
2153
|
|
|
|
|
2154
|
|
|
/** |
|
2155
|
|
|
* Complex polynomial. |
|
2156
|
|
|
* Coordinate pairs treated as complex numbers. This exploits the correlation between the polynomial coefficients |
|
2157
|
|
|
* and leads to a smaller number of coefficients than the general polynomials. |
|
2158
|
9 |
|
*/ |
|
2159
|
|
|
public function complexPolynomial( |
|
2160
|
|
|
Projected $to, |
|
2161
|
|
|
Length $ordinate1OfEvaluationPointInSourceCRS, |
|
2162
|
|
|
Length $ordinate2OfEvaluationPointInSourceCRS, |
|
2163
|
|
|
Length $ordinate1OfEvaluationPointInTargetCRS, |
|
2164
|
|
|
Length $ordinate2OfEvaluationPointInTargetCRS, |
|
2165
|
|
|
Scale $scalingFactorForSourceCRSCoordDifferences, |
|
2166
|
|
|
Scale $scalingFactorForTargetCRSCoordDifferences, |
|
2167
|
|
|
Scale $A1, |
|
2168
|
|
|
Scale $A2, |
|
2169
|
|
|
Scale $A3, |
|
2170
|
|
|
Scale $A4, |
|
2171
|
|
|
Scale $A5, |
|
2172
|
|
|
Scale $A6, |
|
2173
|
|
|
?Scale $A7 = null, |
|
2174
|
|
|
?Scale $A8 = null |
|
2175
|
9 |
|
): self { |
|
2176
|
9 |
|
$xs = $this->easting->getValue(); |
|
2177
|
9 |
|
$ys = $this->northing->getValue(); |
|
2178
|
9 |
|
$xso = $ordinate1OfEvaluationPointInSourceCRS->getValue(); |
|
2179
|
9 |
|
$yso = $ordinate2OfEvaluationPointInSourceCRS->getValue(); |
|
2180
|
9 |
|
$xto = $ordinate1OfEvaluationPointInTargetCRS->getValue(); |
|
2181
|
|
|
$yto = $ordinate2OfEvaluationPointInTargetCRS->getValue(); |
|
2182
|
9 |
|
|
|
2183
|
9 |
|
$U = $scalingFactorForSourceCRSCoordDifferences->asUnity()->getValue() * ($xs - $xso); |
|
2184
|
|
|
$V = $scalingFactorForSourceCRSCoordDifferences->asUnity()->getValue() * ($ys - $yso); |
|
2185
|
9 |
|
|
|
2186
|
9 |
|
$mTdXdY = new ComplexNumber(0, 0); |
|
2187
|
9 |
|
$mTdXdY = $mTdXdY->add((new ComplexNumber($A1->getValue(), $A2->getValue()))->multiply(new ComplexNumber($U, $V))->pow(1)); |
|
2188
|
9 |
|
$mTdXdY = $mTdXdY->add((new ComplexNumber($A3->getValue(), $A4->getValue()))->multiply((new ComplexNumber($U, $V))->pow(2))); |
|
2189
|
9 |
|
$mTdXdY = $mTdXdY->add((new ComplexNumber($A5->getValue(), $A6->getValue()))->multiply((new ComplexNumber($U, $V))->pow(3))); |
|
2190
|
|
|
$mTdXdY = $mTdXdY->add((new ComplexNumber($A7 ? $A7->getValue() : 0, $A8 ? $A8->getValue() : 0))->multiply((new ComplexNumber($U, $V))->pow(4))); |
|
2191
|
9 |
|
|
|
2192
|
9 |
|
$xt = $xs - $xso + $xto + $mTdXdY->getReal() / $scalingFactorForTargetCRSCoordDifferences->asUnity()->getValue(); |
|
2193
|
|
|
$yt = $ys - $yso + $yto + $mTdXdY->getImaginary() / $scalingFactorForTargetCRSCoordDifferences->asUnity()->getValue(); |
|
2194
|
9 |
|
|
|
2195
|
9 |
|
$xtUnit = $to->getCoordinateSystem()->getAxes()[0]->getUnitOfMeasureId(); |
|
2196
|
|
|
$ytUnit = $to->getCoordinateSystem()->getAxes()[1]->getUnitOfMeasureId(); |
|
2197
|
9 |
|
|
|
2198
|
9 |
|
return static::createFromEastingNorthing( |
|
2199
|
9 |
|
$to, |
|
2200
|
9 |
|
Length::makeUnit($xt, $xtUnit), |
|
2201
|
9 |
|
Length::makeUnit($yt, $ytUnit), |
|
2202
|
9 |
|
$this->epoch |
|
2203
|
|
|
); |
|
2204
|
|
|
} |
|
2205
|
|
|
|
|
2206
|
|
|
/** |
|
2207
|
|
|
* Ordnance Survey National Transformation |
|
2208
|
|
|
* Geodetic transformation between ETRS89 (or WGS 84) and OSGB36 / National Grid. Uses ETRS89 / National Grid as |
|
2209
|
|
|
* an intermediate coordinate system for bi-linear interpolation of gridded grid coordinate differences. |
|
2210
|
|
|
*/ |
|
2211
|
|
|
public function OSTN15( |
|
2212
|
|
|
Geographic2D $to, |
|
2213
|
|
|
OSTNOSGM15Grid $eastingAndNorthingDifferenceFile |
|
2214
|
|
|
): GeographicPoint { |
|
2215
|
|
|
$asETRS89 = $eastingAndNorthingDifferenceFile->applyReverseHorizontalAdjustment($this); |
|
2216
|
|
|
|
|
2217
|
|
|
return $asETRS89->transverseMercator($to, new Degree(49), new Degree(-2), new Unity(0.9996012717), new Metre(400000), new Metre(-100000)); |
|
2218
|
|
|
} |
|
2219
|
9 |
|
|
|
2220
|
|
|
public function localOrthographic( |
|
2221
|
|
|
Geographic2D $to, |
|
2222
|
|
|
Angle $latitudeOfProjectionCentre, |
|
2223
|
|
|
Angle $longitudeOfProjectionCentre, |
|
2224
|
|
|
Angle $azimuthAtProjectionCentre, |
|
2225
|
|
|
Scale $scaleFactorAtProjectionCentre, |
|
2226
|
|
|
Length $eastingAtProjectionCentre, |
|
2227
|
|
|
Length $northingAtProjectionCentre |
|
2228
|
9 |
|
): GeographicPoint { |
|
2229
|
9 |
|
$ellipsoid = $this->crs->getDatum()->getEllipsoid(); |
|
2230
|
9 |
|
$latitudeCentre = $latitudeOfProjectionCentre->asRadians()->getValue(); |
|
2231
|
9 |
|
$longitudeCentre = $longitudeOfProjectionCentre->asRadians()->getValue(); |
|
2232
|
9 |
|
$azimuthCentre = $azimuthAtProjectionCentre->asRadians()->getValue(); |
|
2233
|
|
|
$scaleFactorCentre = $scaleFactorAtProjectionCentre->asUnity()->getValue(); |
|
2234
|
9 |
|
|
|
2235
|
9 |
|
$a = $ellipsoid->getSemiMajorAxis()->asMetres()->getValue(); |
|
2236
|
9 |
|
$e2 = $ellipsoid->getEccentricitySquared(); |
|
2237
|
|
|
$vc = $a / sqrt(1 - $e2 * sin($latitudeCentre) ** 2); |
|
2238
|
9 |
|
|
|
2239
|
9 |
|
$easting = $this->easting->subtract($eastingAtProjectionCentre)->asMetres()->getValue(); |
|
2240
|
|
|
$northing = $this->northing->subtract($northingAtProjectionCentre)->asMetres()->getValue(); |
|
2241
|
9 |
|
|
|
2242
|
9 |
|
$xp = cos($azimuthCentre) * $easting / $scaleFactorCentre + sin($azimuthCentre) * $northing / $scaleFactorCentre; |
|
2243
|
|
|
$yp = -sin($azimuthCentre) * $easting / $scaleFactorCentre + cos($azimuthCentre) * $northing / $scaleFactorCentre; |
|
2244
|
9 |
|
|
|
2245
|
9 |
|
$B = 1 - $e2 * cos($latitudeCentre) ** 2; |
|
2246
|
9 |
|
$C = $yp - $vc * sin($latitudeCentre) * cos($latitudeCentre) + $vc * (1 - $e2) * cos($latitudeCentre) * sin($latitudeCentre); |
|
2247
|
9 |
|
$D = sqrt((1 - $e2) * ($a ** 2 - $xp ** 2) * (1 - $e2 * cos($latitudeCentre) ** 2) - $C ** 2); |
|
2248
|
9 |
|
$xg = (-$C * sin($latitudeCentre) + $D * cos($latitudeCentre)) / $B; |
|
2249
|
9 |
|
$yg = $xp; |
|
2250
|
|
|
$zg = ($C * cos($latitudeCentre) * (1 - $e2) + $D * sin($latitudeCentre)) / $B; |
|
2251
|
9 |
|
|
|
2252
|
9 |
|
$latitude = atan2($zg, (1 - $e2) * sqrt($xg ** 2 + $yg ** 2)); |
|
2253
|
|
|
$longitude = $longitudeCentre + atan2($yg, $xg); |
|
2254
|
9 |
|
|
|
2255
|
|
|
return GeographicPoint::create($to, new Radian($latitude), new Radian($longitude), null, $this->epoch); |
|
2256
|
|
|
} |
|
2257
|
|
|
} |
|
2258
|
|
|
|
dvdoug /
PHPCoord
Loading history...