1

2# -*- coding: utf-8 -*-

3

4 u'''Lambert Conformal Conic (LCC) projection.

5

6 Lambert conformal conic projection for 1- or 2-Standard Parallels classes L{Conic}, L{Conics} registry, L{LCCError}

7 and position class L{Lcc}.

8

9 See U{LCC<https://WikiPedia.org/wiki/Lambert_conformal_conic_projection>}, U{Lambert

10 Conformal Conic to Geographic Transformation Formulae

11<https://www.Linz.govt.NZ/data/geodetic-system/coordinate-conversion/projection-conversions/lambert-conformal-conic-geographic>},

12 U{Lambert Conformal Conic Projection<https://MathWorld.Wolfram.com/LambertConformalConicProjection.html>}

13 and John P. Snyder U{'Map Projections - A Working Manual'<https://Pubs.USGS.gov/pp/1395/report.pdf>}, 1987, pp 107-109.

14

15@var Conics.Be08Lb: Conic(name='Be08Lb', lat0=50.797815, lon0=4.35921583, par1=49.8333339, par2=51.1666672, E0=649328, N0=665262, k0=1, SP=2, datum=Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84),

16@var Conics.Be72Lb: Conic(name='Be72Lb', lat0=90, lon0=4.3674867, par1=49.8333339, par2=51.1666672, E0=150000.013, N0=5400088.438, k0=1, SP=2, datum=Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83),

17@var Conics.Fr93Lb: Conic(name='Fr93Lb', lat0=46.5, lon0=3, par1=49, par2=44, E0=700000, N0=6600000, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),

18@var Conics.MaNLb: Conic(name='MaNLb', lat0=33.3, lon0=-5.4, par1=31.73, par2=34.87, E0=500000, N0=300000, k0=1, SP=2, datum=Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF),

19@var Conics.MxLb: Conic(name='MxLb', lat0=12, lon0=-102, par1=17.5, par2=29.5, E0=2500000, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),

20@var Conics.PyT_Lb: Conic(name='PyT_Lb', lat0=46.8, lon0=2.33722917, par1=45.8989389, par2=47.6960144, E0=600000, N0=200000, k0=1, SP=2, datum=Datum(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF),

21@var Conics.USA_Lb: Conic(name='USA_Lb', lat0=23, lon0=-96, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),

22@var Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84)

23'''

24# make sure int/int division yields float quotient, see .basics

25 from __future__ import division as _; del _ # PYCHOK semicolon

26

27 from pygeodesy.basics import copysign0, _xinstanceof, _xsubclassof

28 from pygeodesy.constants import EPS, EPS02, PI_2, _float as _F, _0_0, _0_5, \

29 _1_0, _2_0, _90_0

30 from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB

31 from pygeodesy.datums import Datums, _ellipsoidal_datum

32 from pygeodesy.errors import _IsnotError, _ValueError

33 from pygeodesy.fmath import hypot, _ALL_LAZY

34 from pygeodesy.interns import NN, _COMMASPACE_, _ellipsoidal_, _GRS80_, _k0_, \

35 _lat0_, _lon0_, _m_, _NAD83_, _NTF_, _SPACE_, \

36 _WGS84_, _C_ # PYCHOK used!

37# from pygeodesy.lazily import _ALL_LAZY # from .fmath

38 from pygeodesy.named import _lazyNamedEnumItem as _lazy, _name2__, _NamedBase, \

39 _NamedEnum, _NamedEnumItem, _xnamed

40 from pygeodesy.namedTuples import EasNor3Tuple, LatLonDatum3Tuple, \

41 LatLon2Tuple, _LL4Tuple, PhiLam2Tuple

42 from pygeodesy.props import deprecated_method, Property, Property_RO, _update_all

43 from pygeodesy.streprs import Fmt, _fstrENH2, _xzipairs

44 from pygeodesy.units import Easting, Height, _heigHt, Lam_, Northing, Phi_, \

45 Scalar_

46 from pygeodesy.utily import atan1, degrees90, degrees180, sincos2, tanPI_2_2

47

48 from math import atan, fabs, log, radians, sin, sqrt

49

50__all__ = _ALL_LAZY.lcc

51__version__ = '24.05.24'

52

53_E0_ = 'E0'

54_N0_ = 'N0'

55_par1_ = 'par1'

56_par2_ = 'par2'

57_SP_ = 'SP'

58

59

60 class Conic(_NamedEnumItem):

61 '''Lambert conformal conic projection (1- or 2-SP).

62 '''

63 _auth = NN # authorization (C{str})

64 _datum = None # datum (L{Datum})

65 _name = NN # Conic.__name__, set below

66

67 _e = _0_0 # ellipsoid excentricity (C{float})

68 _E0 = _0_0 # false easting (C{float})

69 _k0 = _1_0 # scale factor (C{float})

70 _N0 = _0_0 # false northing (C{float})

71 _SP = 0 # 1- or 2-SP (C{int})

72

73 _opt3 = _0_0 # optional, longitude (C{radians})

74 _par1 = _0_0 # 1st std parallel (C{radians})

75 _par2 = _0_0 # 2nd std parallel (C{radians})

76 _phi0 = _0_0 # origin lat (C{radians})

77 _lam0 = _0_0 # origin lon (C{radians})

78

79 _aF = _0_0 # precomputed F (C{float})

80 _n = _0_0 # precomputed n (C{float})

81 _1_n = _0_0 # precomputed 1 / n (C{float})

82 _r0 = _0_0 # precomputed rho0 (C{float})

83

84 def __init__(self, latlon0, par1, par2=None, E0=0, N0=0,

85 k0=1, opt3=0, auth=NN, **name):

86 '''New Lambert conformal conic projection.

87

88 @arg latlon0: Origin with (ellipsoidal) datum (C{LatLon}).

89 @arg par1: First standard parallel (C{degrees90}).

90 @kwarg par2: Optional, second standard parallel (C{degrees90}).

91 @kwarg E0: Optional, false easting (C{meter}).

92 @kwarg N0: Optional, false northing (C{meter}).

93 @kwarg k0: Optional scale factor (C{scalar}).

94 @kwarg opt3: Optional meridian (C{degrees180}).

95 @kwarg auth: Optional authentication authority (C{str}).

96 @kwarg name: Optional C{B{name}=NN} for the conic (C{str}).

97

98 @return: A Lambert projection (L{Conic}).

99

100 @raise TypeError: Non-ellipsoidal B{C{latlon0}}.

101

102 @raise ValueError: Invalid B{C{par1}}, B{C{par2}},

103 B{C{E0}}, B{C{N0}}, B{C{k0}}

104 or B{C{opt3}}.

105 '''

106 if latlon0 is not None:

107 _xinstanceof(_LLEB, latlon0=latlon0)

108 self._phi0, self._lam0 = latlon0.philam

109

110 self._par1 = Phi_(par1=par1)

111 self._par2 = self._par1 if par2 is None else Phi_(par2=par2)

112

113 if k0 != 1:

114 self._k0 = Scalar_(k0=k0)

115 if E0:

116 self._E0 = Northing(E0=E0, falsed=True)

117 if N0:

118 self._N0 = Easting(N0=N0, falsed=True)

119 if opt3:

120 self._opt3 = Lam_(opt3=opt3)

121

122 self.toDatum(latlon0.datum)._dup2(self)

123 self._register(Conics, name)

124 elif name:

125 self.name = name

126 if auth:

127 self._auth = str(auth)

128

129 @Property_RO

130 def auth(self):

131 '''Get the authentication authority (C{str}).

132 '''

133 return self._auth

134

135 @deprecated_method

136 def convertDatum(self, datum):

137 '''DEPRECATED, use method L{Conic.toDatum}.'''

138 return self.toDatum(datum)

139

140 @Property_RO

141 def datum(self):

142 '''Get the datum (L{Datum}).

143 '''

144 return self._datum

145

146 @Property_RO

147 def E0(self):

148 '''Get the false easting (C{meter}).

149 '''

150 return self._E0

151

152 @Property_RO

153 def k0(self):

154 '''Get scale factor (C{float}).

155 '''

156 return self._k0

157

158 @Property_RO

159 def lat0(self):

160 '''Get the origin latitude (C{degrees90}).

161 '''

162 return degrees90(self._phi0)

163

164 @Property_RO

165 def latlon0(self):

166 '''Get the central origin (L{LatLon2Tuple}C{(lat, lon)}).

167 '''

168 return LatLon2Tuple(self.lat0, self.lon0, name=self.name)

169

170 @Property_RO

171 def lam0(self):

172 '''Get the central meridian (C{radians}).

173 '''

174 return self._lam0

175

176 @Property_RO

177 def lon0(self):

178 '''Get the central meridian (C{degrees180}).

179 '''

180 return degrees180(self._lam0)

181

182 @Property_RO

183 def N0(self):

184 '''Get the false northing (C{meter}).

185 '''

186 return self._N0

187

188 @Property_RO

189 def name2(self):

190 '''Get the conic and datum names as "conic.datum" (C{str}).

191 '''

192 return self._DOT_(self.datum.name)

193

194 @Property_RO

195 def opt3(self):

196 '''Get the optional meridian (C{degrees180}).

197 '''

198 return degrees180(self._opt3)

199

200 @Property_RO

201 def par1(self):

202 '''Get the 1st standard parallel (C{degrees90}).

203 '''

204 return degrees90(self._par1)

205

206 @Property_RO

207 def par2(self):

208 '''Get the 2nd standard parallel (C{degrees90}).

209 '''

210 return degrees90(self._par2)

211

212 @Property_RO

213 def phi0(self):

214 '''Get the origin latitude (C{radians}).

215 '''

216 return self._phi0

217

218 @Property_RO

219 def philam0(self):

220 '''Get the central origin (L{PhiLam2Tuple}C{(phi, lam)}).

221 '''

222 return PhiLam2Tuple(self.phi0, self.lam0, name=self.name)

223

224 @Property_RO

225 def SP(self):

226 '''Get the number of standard parallels (C{int}).

227 '''

228 return self._SP

229

230 def toDatum(self, datum):

231 '''Convert this conic to the given datum.

232

233 @arg datum: Ellipsoidal datum to use (L{Datum}, L{Ellipsoid},

234 L{Ellipsoid2} or L{a_f2Tuple}).

235

236 @return: Converted conic, unregistered (L{Conic}).

237

238 @raise TypeError: Non-ellipsoidal B{C{datum}}.

239 '''

240 d = _ellipsoidal_datum(datum, name=self.name)

241 E = d.ellipsoid

242 if not E.isEllipsoidal:

243 raise _IsnotError(_ellipsoidal_, datum=datum)

244

245 c = self

246 if c._e != E.e or c._datum != d:

247

248 c = Conic(None, 0, name=self._name)

249 self._dup2(c)

250 c._datum = d

251 c._e = E.e

252

253 if fabs(c._par1 - c._par2) < EPS:

254 m1 = c._mdef(c._phi0)

255 t1 = c._tdef(c._phi0)

256 t0 = t1

257 k = 1 # _1_0

258 n = sin(c._phi0)

259 sp = 1

260 else:

261 m1 = c._mdef(c._par1)

262 m2 = c._mdef(c._par2)

263 t1 = c._tdef(c._par1)

264 t2 = c._tdef(c._par2)

265 t0 = c._tdef(c._phi0)

266 k = c._k0

267 n = (log(m1) - log(m2)) \

268 / (log(t1) - log(t2))

269 sp = 2

270

271 F = m1 / (n * pow(t1, n))

272

273 c._aF = k * E.a * F

274 c._n = n

275 c._1_n = _1_0 / n

276 c._r0 = c._rdef(t0)

277 c._SP = sp

278

279 return c

280

281 def toStr(self, prec=8, name=NN, **unused): # PYCHOK expected

282 '''Return this conic as a string.

283

284 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

285 @kwarg name: Overriding name (C{str}) or C{None} to exclude

286 this conic's name.

287

288 @return: Conic attributes (C{str}).

289 '''

290 a = [name, prec, _lat0_, _lon0_, _par1_, _par2_,

291 _E0_, _N0_, _k0_, _SP_]

292 if self._SP == 1:

293 _ = a.pop(a.index(_par2_))

294 return self._instr(datum=self.datum, *a)

295

296 def _dup2(self, c):

297 '''(INTERNAL) Copy this conic to C{c}.

298

299 @arg c: Duplicate (L{Conic}).

300 '''

301 _update_all(c)

302

303 c._auth = self._auth

304 c._datum = self._datum

305

306 c._e = self._e

307 c._E0 = self._E0

308 c._k0 = self._k0

309 c._N0 = self._N0

310 c._SP = self._SP

311

312 c._par1 = self._par1

313 c._par2 = self._par2

314 c._phi0 = self._phi0

315 c._lam0 = self._lam0

316 c._opt3 = self._opt3

317

318 c._aF = self._aF

319 c._n = self._n

320 c._1_n = self._1_n

321 c._r0 = self._r0

322

323 def _mdef(self, a):

324 '''(INTERNAL) Compute m(a).

325 '''

326 s, c = sincos2(a)

327 s = _1_0 - (s * self._e)**2

328 return (c / sqrt(s)) if s > EPS02 else _0_0

329

330 def _pdef(self, a):

331 '''(INTERNAL) Compute p(a).

332 '''

333 s = self._e * sin(a)

334 return pow((_1_0 - s) / (_1_0 + s), self._e * _0_5)

335

336 def _rdef(self, t):

337 '''(INTERNAL) Compute r(t).

338 '''

339 return self._aF * pow(t, self._n)

340

341 def _tdef(self, a):

342 '''(INTERNAL) Compute t(lat).

343 '''

344 return max(_0_0, tanPI_2_2(-a) / self._pdef(a))

345

346 def _xdef(self, t_x):

347 '''(INTERNAL) Compute x(t_x).

348 '''

349 return PI_2 - atan(t_x) * _2_0 # XXX + self._phi0

350

351

352 Conic._name = Conic.__name__

353

354

355 class Conics(_NamedEnum):

356 '''(INTERNAL) L{Conic} registry, I{must} be a sub-class

357 to accommodate the L{_LazyNamedEnumItem} properties.

358 '''

359 def _Lazy(self, lat, lon, datum_name, *args, **kwds):

360 '''(INTERNAL) Instantiate the L{Conic}.

361 '''

362 return Conic(_LLEB(lat, lon, datum=Datums.get(datum_name)), *args, **kwds)

363

364 Conics = Conics(Conic) # PYCHOK singleton

365'''Some pre-defined L{Conic}s, all I{lazily} instantiated.'''

366 Conics._assert( # <https://SpatialReference.org/ref/sr-org/...>

367# AsLb = _lazy('AsLb', _F(-14.2666667), _F(170), _NAD27_, _0_0, _0_0,

368# E0=_F(500000), N0=_0_0, auth='EPSG:2155'), # American Samoa ... SP=1 !

369 Be08Lb = _lazy('Be08Lb', _F(50.7978150), _F(4.359215833), _GRS80_, _F(49.8333339), _F(51.1666672),

370 E0=_F(649328.0), N0=_F(665262.0), auth='EPSG:9802'), # Belgium

371 Be72Lb = _lazy('Be72Lb', _90_0, _F(4.3674867), _NAD83_, _F(49.8333339), _F(51.1666672),

372 E0=_F(150000.013), N0=_F(5400088.438), auth='EPSG:31370'), # Belgium

373 Fr93Lb = _lazy('Fr93Lb', _F(46.5), _F(3), _WGS84_, _F(49), _F(44),

374 E0=_F(700000), N0=_F(6600000), auth='EPSG:2154'), # RFG93, France

375 MaNLb = _lazy('MaNLb', _F(33.3), _F(-5.4), _NTF_, _F(31.73), _F(34.87),

376 E0=_F(500000), N0=_F(300000)), # Marocco

377 MxLb = _lazy('MxLb', _F(12), _F(-102), _WGS84_, _F(17.5), _F(29.5),

378 E0=_F(2500000), N0=_0_0, auth='EPSG:2155'), # Mexico

379 PyT_Lb = _lazy('PyT_Lb', _F(46.8), _F(2.33722917), _NTF_, _F(45.89893890000052), _F(47.69601440000037),

380 E0=_F(600000), N0=_F(200000), auth='Test'), # France?

381 USA_Lb = _lazy('USA_Lb', _F(23), _F(-96), _WGS84_, _F(33), _F(45),

382 E0=_0_0, N0=_0_0), # Conterminous, contiguous USA?

383 WRF_Lb = _lazy('WRF_Lb', _F(40), _F(-97), _WGS84_, _F(33), _F(45),

384 E0=_0_0, N0=_0_0, auth='EPSG:4326') # World

385)

386

387

388 class LCCError(_ValueError):

389 '''Lambert Conformal Conic C{LCC} or other L{Lcc} issue.

390 '''

391 pass

392

393

394 class Lcc(_NamedBase):

395 '''Lambert conformal conic East-/Northing location.

396 '''

397 _conic = Conics.WRF_Lb # Lambert projection (L{Conic})

398 _easting = _0_0 # Easting (C{float})

399 _height = 0 # height (C{meter})

400 _northing = _0_0 # Northing (C{float})

401

402 def __init__(self, e, n, h=0, conic=Conics.WRF_Lb, **name):

403 '''New L{Lcc} Lamber conformal conic position.

404

405 @arg e: Easting (C{meter}).

406 @arg n: Northing (C{meter}).

407 @kwarg h: Optional height (C{meter}).

408 @kwarg conic: Optional, the conic projection (L{Conic}).

409 @kwarg name: Optional C{B{name}=NN} (C{str}).

410

411 @return: The Lambert location (L{Lcc}).

412

413 @raise LCCError: Invalid B{C{h}} or invalid or

414 negative B{C{e}} or B{C{n}}.

415

416 @raise TypeError: If B{C{conic}} is not L{Conic}.

417 '''

418 if conic not in (None, Lcc._conic):

419 self.conic = conic

420 self._easting = Easting(e, falsed=conic.E0 > 0, Error=LCCError)

421 self._northing = Northing(n, falsed=conic.N0 > 0, Error=LCCError)

422 if h:

423 self._height = Height(h=h, Error=LCCError)

424 if name:

425 self.name = name

426

427 @Property

428 def conic(self):

429 '''Get the conic projection (L{Conic}).

430 '''

431 return self._conic

432

433 @conic.setter # PYCHOK setter!

434 def conic(self, conic):

435 '''Set the conic projection (L{Conic}).

436

437 @raise TypeError: Invalid B{C{conic}}.

438 '''

439 _xinstanceof(Conic, conic=conic)

440 if conic != self._conic:

441 _update_all(self)

442 self._conic = conic

443

444# def dup(self, name=NN, **e_n_h_conic): # PYCHOK signature

445# '''Duplicate this location with some attributes modified.

446#

447# @kwarg e_n_h_conic: Use keyword argument C{B{e}=...}, C{B{n}=...},

448# C{B{h}=...} and/or C{B{conic}=...} to override

449# the current C{easting}, C{northing} C{height}

450# or C{conic} projection, respectively.

451# '''

452# def _args_kwds(e=None, n=None, **kwds):

453# return (e, n), kwds

454#

455# kwds = _xkwds(e_n_h_conic, e=self.easting, n=self.northing,

456# h=self.height, conic=self.conic,

457# name=name or self.name)

458# args, kwds = _args_kwds(**kwds)

459# return self.__class__(*args, **kwds) # .classof

460

461 @Property_RO

462 def easting(self):

463 '''Get the easting (C{meter}).

464 '''

465 return self._easting

466

467 @Property_RO

468 def height(self):

469 '''Get the height (C{meter}).

470 '''

471 return self._height

472

473 @Property_RO

474 def latlon(self):

475 '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}).

476 '''

477 ll = self.toLatLon(LatLon=None, datum=None)

478 return LatLon2Tuple(ll.lat, ll.lon, name=self.name)

479

480 @Property_RO

481 def latlonheight(self):

482 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).

483 '''

484 return self.latlon.to3Tuple(self.height)

485

486 @Property_RO

487 def latlonheightdatum(self):

488 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).

489 '''

490 return self.latlonheight.to4Tuple(self.conic.datum)

491

492 @Property_RO

493 def northing(self):

494 '''Get the northing (C{meter}).

495 '''

496 return self._northing

497

498 @Property_RO

499 def philam(self):

500 '''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}).

501 '''

502 return PhiLam2Tuple(radians(self.latlon.lat),

503 radians(self.latlon.lon), name=self.name)

504

505 @Property_RO

506 def philamheight(self):

507 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

508 '''

509 return self.philam.to3Tuple(self.height)

510

511 @Property_RO

512 def philamheightdatum(self):

513 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).

514 '''

515 return self.philamheight.to4Tuple(self.datum)

516

517 @deprecated_method

518 def to3lld(self, datum=None): # PYCHOK no cover

519 '''DEPRECATED, use method C{toLatLon}.

520

521 @kwarg datum: Optional datum to use, otherwise use this

522 B{C{Lcc}}'s conic.datum (C{Datum}).

523

524 @return: A L{LatLonDatum3Tuple}C{(lat, lon, datum)}.

525

526 @raise TypeError: If B{C{datum}} is not ellipsoidal.

527 '''

528 if datum in (None, self.conic.datum):

529 r = LatLonDatum3Tuple(self.latlon.lat,

530 self.latlon.lon,

531 self.conic.datum, name=self.name)

532 else:

533 r = self.toLatLon(LatLon=None, datum=datum)

534 r = LatLonDatum3Tuple(r.lat, r.lon, r.datum, name=r.name)

535 return r

536

537 def toLatLon(self, LatLon=None, datum=None, height=None, **LatLon_kwds):

538 '''Convert this L{Lcc} to an (ellipsoidal) geodetic point.

539

540 @kwarg LatLon: Optional, ellipsoidal class to return the

541 geodetic point (C{LatLon}) or C{None}.

542 @kwarg datum: Optional datum to use, otherwise use this

543 B{C{Lcc}}'s conic.datum (L{Datum}, L{Ellipsoid},

544 L{Ellipsoid2} or L{a_f2Tuple}).

545 @kwarg height: Optional height for the point, overriding

546 the default height (C{meter}).

547 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword

548 arguments, ignored if C{B{LatLon} is None}.

549

550 @return: The point (B{C{LatLon}}) or a

551 L{LatLon4Tuple}C{(lat, lon, height, datum)}

552 if B{C{LatLon}} is C{None}.

553

554 @raise TypeError: If B{C{LatLon}} or B{C{datum}} is

555 not ellipsoidal or not valid.

556 '''

557 if LatLon:

558 _xsubclassof(_LLEB, LatLon=LatLon)

559

560 c = self.conic

561 if datum not in (None, self.conic.datum):

562 c = c.toDatum(datum)

563

564 e = self.easting - c._E0

565 n = c._r0 - self.northing + c._N0

566

567 r_ = copysign0(hypot(e, n), c._n)

568 t_ = pow(r_ / c._aF, c._1_n)

569

570 x = c._xdef(t_) # XXX c._lam0

571 for self._iteration in range(10): # max 4 trips

572 p, x = x, c._xdef(t_ * c._pdef(x))

573 if fabs(x - p) < 1e-9: # XXX EPS too small?

574 break

575 lat = degrees90(x)

576 lon = degrees180((atan1(e, n) + c._opt3) * c._1_n + c._lam0)

577

578 h = _heigHt(self, height)

579 return _LL4Tuple(lat, lon, h, c.datum, LatLon, LatLon_kwds,

580 inst=self, name=self.name)

581

582 def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, m=_m_, C=False, **unused): # PYCHOK expected

583 '''Return a string representation of this L{Lcc} position.

584

585 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

586 @kwarg fmt: Enclosing backets format (C{str}).

587 @kwarg sep: Optional separator between name:values (C{str}).

588 @kwarg m: Optional unit of the height, default meter (C{str}).

589 @kwarg C: Optionally, include name of conic and datum (C{bool}).

590

591 @return: This Lcc as "[E:meter, N:meter, H:m, C:Conic.Datum]"

592 (C{str}).

593 '''

594 t, T = _fstrENH2(self, prec, m)

595 if C:

596 t += self.conic.name2,

597 T += _C_,

598 return _xzipairs(T, t, sep=sep, fmt=fmt)

599

600 def toStr(self, prec=0, sep=_SPACE_, m=_m_): # PYCHOK expected

601 '''Return a string representation of this L{Lcc} position.

602

603 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

604 @kwarg sep: Optional separator to join (C{str}) or C{None}

605 to return an unjoined C{tuple} of C{str}s.

606 @kwarg m: Optional height units, default C{meter} (C{str}).

607

608 @return: This Lcc as I{"easting nothing"} in C{meter} plus

609 I{" height"} suffixed with B{C{m}} if height is

610 non-zero (C{str}).

611 '''

612 t, _ = _fstrENH2(self, prec, m)

613 return t if sep is None else sep.join(t)

614

615

616 def toLcc(latlon, conic=Conics.WRF_Lb, height=None, Lcc=Lcc,

617 **name_Lcc_kwds):

618 '''Convert an (ellipsoidal) geodetic point to a I{Lambert} location.

619

620 @arg latlon: Ellipsoidal point (C{LatLon}).

621 @kwarg conic: Optional Lambert projection to use (L{Conic}).

622 @kwarg height: Optional height for the point, overriding the

623 default height (C{meter}).

624 @kwarg Lcc: Class to return the I{Lambert} location (L{Lcc}).

625 @kwarg name_Lcc_kwds: Optional C{B{name}=NN} (C{str}) for the

626 location and optional, additional B{C{Lcc}} keyword

627 arguments, ignored if B{C{Lcc}} is C{None}.

628

629 @return: The I{Lambert} location (L{Lcc}) or an

630 L{EasNor3Tuple}C{(easting, northing, height)} if

631 C{B{Lcc} is None}.

632

633 @raise TypeError: If B{C{latlon}} is not ellipsoidal.

634 '''

635 _xinstanceof(_LLEB, latlon=latlon)

636 name, Lcc_kwds = _name2__(name_Lcc_kwds)

637

638 a, b = latlon.philam

639 c = conic.toDatum(latlon.datum)

640

641 t = c._n * (b - c._lam0) - c._opt3

642 st, ct = sincos2(t)

643

644 r = c._rdef(c._tdef(a))

645 e = c._E0 + r * st

646 n = c._N0 + c._r0 - r * ct

647

648 h = _heigHt(latlon, height)

649 r = EasNor3Tuple(e, n, h) if Lcc is None else \

650 Lcc(e, n, h=h, conic=c, **Lcc_kwds)

651 return _xnamed(r, name) if name else r

652

653

654 if __name__ == '__main__':

655

656 from pygeodesy.interns import _NL_, _NLATvar_

657 from pygeodesy.lazily import printf

658

659 # __doc__ of this file, force all into registery

660 t = _NL_ + Conics.toRepr(all=True, asorted=True)

661 printf(_NLATvar_.join(t.split(_NL_)))

662

663# **) MIT License

664#

665# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

666#

667# Permission is hereby granted, free of charge, to any person obtaining a

668# copy of this software and associated documentation files (the "Software"),

669# to deal in the Software without restriction, including without limitation

670# the rights to use, copy, modify, merge, publish, distribute, sublicense,

671# and/or sell copies of the Software, and to permit persons to whom the

672# Software is furnished to do so, subject to the following conditions:

673#

674# The above copyright notice and this permission notice shall be included

675# in all copies or substantial portions of the Software.

676#

677# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

678# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

679# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

680# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

681# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

682# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

683# OTHER DEALINGS IN THE SOFTWARE.