1

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

3

4 u'''(INTERNAL) I{Auxiliary} latitudes' base classes, constants and functions.

5

6 Class L{AuxAngle} transcoded to Python from I{Karney}'s C++ class U{AuxAngle

7<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}

8 in I{GeographicLib version 2.2+}.

9

10 Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2022-2024) and licensed

11 under the MIT/X11 License. For more information, see the U{GeographicLib

12<https://GeographicLib.SourceForge.io>} documentation.

13'''

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

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

16

17 from pygeodesy.auxilats.auxily import Aux, _Aux2Greek, AuxError

18 from pygeodesy.basics import map1, map2, _xinstanceof

19 from pygeodesy.constants import EPS, _INF_NAN_NINF, MAX, NAN, _0_0, _0_5, _1_0, \

20 _copysign_1_0, _over, _pos_self, isfinite, isnan

21# from pygeodesy.errors import AuxError # from .auxilats.auxily

22 from pygeodesy.fmath import hypot, unstr

23 from pygeodesy.fsums import _add_op_, _iadd_op_, _isub_op_, _sub_op_

24 from pygeodesy.named import _Named, _ALL_DOCS, _MODS

25# from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS # from .named

26 from pygeodesy.props import Property, Property_RO, property_RO, property_ROver, \

27 _update_all

28# from pygeodesy.streprs import unstr # from .fmath

29 from pygeodesy.units import Degrees, Radians

30 from pygeodesy.utily import atan2, atan2d, sincos2, sincos2d

31

32 from math import asinh, copysign, degrees, fabs, radians, sinh

33

34__all__ = ()

35__version__ = '25.04.14'

36

37_0_INF_NAN_NINF = (0, _0_0) + _INF_NAN_NINF

38_MAX_2 = MAX * _0_5 # PYCHOK used!

39# del _INF_NAN_NINF, MAX

40

41

42 class AuxAngle(_Named):

43 '''U{An accurate representation of angles

44 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>}

45 '''

46 _AUX = None # overloaded/-ridden

47 _diff = NAN # default

48 _iter = None # like ._NamedBase

49 _y = _0_0

50 _x = _1_0

51

52 def __init__(self, y_angle=_0_0, x=_1_0, aux=None, **name):

53 '''New L{AuxAngle}.

54

55 @kwarg y_angle: The Y component (C{scalar}, including C{INF}, C{NAN}

56 and C{NINF}) or a previous L{AuxAngle} instance.

57 @kwarg x: The X component, required if C{B{y_angle}} is C{scalar},

58 ignored otherwise.

59 @kwarg aux: I{Auxiliary} kind (C{Aux.KIND}), like B{C{x}}.

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

61

62 @raise AuxError: Invalid B{C{y_angle}}, B{C{x}} or B{C{aux}}.

63 '''

64 try:

65 try:

66 yx = y_angle._yx

67 aux = y_angle._AUX

68 if self._diff != y_angle._diff:

69 self._diff = y_angle._diff

70 except AttributeError:

71 yx = y_angle, x

72 if aux in _AUXClass:

73 if self._AUX != aux:

74 self._AUX = aux

75 elif aux is not None:

76 raise ValueError() # _invalid_

77 except Exception as X:

78 raise AuxError(y=y_angle, x=x, aux=aux, cause=X)

79 self._y, self._x = _yx2(yx)

80 if name:

81 self.name = name

82

83 def __abs__(self):

84 '''Return this angle's absolute value (L{AuxAngle}).

85 '''

86 a = self._copy_2(self.__abs__)

87 a._yx = map2(fabs, self._yx)

88 return a

89

90 def __add__(self, other):

91 '''Return C{B{self} + B{other}} as an L{AuxAngle}.

92

93 @arg other: An L{AuxAngle}.

94

95 @return: The sum (L{AuxAngle}).

96

97 @raise TypeError: Invalid B{C{other}}.

98 '''

99 a = self._copy_2(self.__add__)

100 return a._iadd(other, _add_op_)

101

102 def __bool__(self): # PYCHOK not special in Python 2-

103 '''Return C{True} if this angle is non-zero.

104 '''

105 return bool(self.tan)

106

107 def __eq__(self, other):

108 '''Return C{B{self} == B{other}} as C{bool}.

109 '''

110 return not self.__ne__(other)

111

112 def __float__(self):

113 '''Return this angle's C{tan} (C{float}).

114 '''

115 return self.tan

116

117 def __iadd__(self, other):

118 '''Apply C{B{self} += B{other}} to this angle.

119

120 @arg other: An L{AuxAngle}.

121

122 @return: This angle, updated (L{AuxAngle}).

123

124 @raise TypeError: Invalid B{C{other}}.

125 '''

126 return self._iadd(other, _iadd_op_)

127

128 def __isub__(self, other):

129 '''Apply C{B{self} -= B{other}} to this angle.

130

131 @arg other: An L{AuxAngle}.

132

133 @return: This instance, updated (L{AuxAngle}).

134

135 @raise TypeError: Invalid B{C{other}} type.

136 '''

137 return self._iadd(-other, _isub_op_)

138

139 def __ne__(self, other):

140 '''Return C{B{self} != B{other}} as C{bool}.

141 '''

142 _xinstanceof(AuxAngle, other=other)

143 y, x, r = self._yxr_normalized()

144 s, c, t = other._yxr_normalized()

145 return fabs(y - s) > EPS or fabs(x - c) > EPS \

146 or fabs(r - t) > EPS

147

148 def __neg__(self):

149 '''Return I{a copy of} this angle, negated.

150 '''

151 a = self._copy_2(self.__neg__)

152 if a.y or not a.x:

153 a.y = -a.y

154 else:

155 a.x = -a.x

156 return a

157

158 def __pos__(self):

159 '''Return this angle I{as-is}, like C{float.__pos__()}.

160 '''

161 return self if _pos_self else self._copy_2(self.__pos__)

162

163 def __radd__(self, other):

164 '''Return C{B{other} + B{self}} as an L{AuxAngle}.

165

166 @see: Method L{AuxAngle.__add__}.

167 '''

168 a = self._copy_r2(other, self.__radd__)

169 return a._iadd(self, _add_op_)

170

171 def __rsub__(self, other):

172 '''Return C{B{other} - B{self}} as an L{AuxAngle}.

173

174 @see: Method L{AuxAngle.__sub__}.

175 '''

176 a = self._copy_r2(other, self.__rsub__)

177 return a._iadd(-self, _sub_op_)

178

179 def __str__(self):

180 n = _Aux2Greek.get(self._AUX, self.classname)

181 return unstr(n, y=self.y, x=self.x, tan=self.tan)

182

183 def __sub__(self, other):

184 '''Return C{B{self} - B{other}} as an L{AuxAngle}.

185

186 @arg other: An L{AuxAngle}.

187

188 @return: The difference (L{AuxAngle}).

189

190 @raise TypeError: Invalid B{C{other}} type.

191 '''

192 a = self._copy_2(self.__sub__)

193 return a._iadd(-other, _sub_op_)

194

195 def _iadd(self, other, *unused): # op

196 '''(INTERNAL) Apply C{B{self} += B{other}}.

197 '''

198 _xinstanceof(AuxAngle, other=other)

199 # ignore zero other to preserve signs of _y and _x

200 if other.tan:

201 s, c = other._yx

202 y, x = self._yx

203 self._yx = (y * c + x * s), \

204 (x * c - y * s)

205 return self

206

207 def _copy_2(self, which):

208 '''(INTERNAL) Copy for I{dyadic} operators.

209 '''

210 return _Named.copy(self, deep=False, name__=which)

211

212 def _copy_r2(self, other, which):

213 '''(INTERNAL) Copy for I{reverse-dyadic} operators.

214 '''

215 _xinstanceof(AuxAngle, other=other)

216 return other._copy_2(which)

217

218 def copyquadrant(self, other):

219 '''Copy an B{C{other}} angle's quadrant into this angle (L{auxAngle}).

220 '''

221 _xinstanceof(AuxAngle, other=other)

222 self._yx = copysign(self.y, other.y), \

223 copysign(self.x, other.x)

224 return self

225

226 @Property_RO

227 def diff(self):

228 '''Get derivative C{dtan(Eta) / dtan(Phi)} (C{float} or C{NAN}).

229 '''

230 return self._diff

231

232 @staticmethod

233 def fromDegrees(deg, **aux_name):

234 '''Get an L{AuxAngle} from degrees.

235 '''

236 return _AuxClass(**aux_name)(*sincos2d(deg), **aux_name)

237

238 @staticmethod

239 def fromLambertianDegrees(psi, **aux_name):

240 '''Get an L{AuxAngle} from I{Lambertian} degrees.

241 '''

242 return _AuxClass(**aux_name)(sinh(radians(psi)), **aux_name)

243

244 @staticmethod

245 def fromLambertianRadians(psi, **aux_name):

246 '''Get an L{AuxAngle} from I{Lambertian} radians.

247 '''

248 return _AuxClass(**aux_name)(sinh(psi), **aux_name)

249

250 @staticmethod

251 def fromRadians(rad, **aux_name):

252 '''Get an L{AuxAngle} from radians.

253 '''

254 return _AuxClass(**aux_name)(*sincos2(rad), **aux_name)

255

256 @Property_RO

257 def iteration(self):

258 '''Get the iteration (C{int} or C{None}).

259 '''

260 return self._iter

261

262 def normal(self):

263 '''Normalize this angle I{in-place}.

264

265 @return: This angle, normalized (L{AuxAngle}).

266 '''

267 self._yx = self._yx_normalized

268 return self

269

270 @Property_RO

271 def normalized(self):

272 '''Get a normalized copy of this angle (L{AuxAngle}).

273 '''

274 y, x = self._yx_normalized

275 return self.classof(y, x, name=self.name, aux=self._AUX)

276

277 @property_ROver

278 def _RhumbAux(self):

279 '''(INTERNAL) Import the L{RhumbAux} class, I{once}.

280 '''

281 return _MODS.rhumb.aux_.RhumbAux # overwrite property_ROver

282

283 @Property_RO

284 def tan(self):

285 '''Get this angle's C{tan} (C{float}).

286 '''

287 y, x = self._yx

288 return _over(y, x) if isfinite(y) and y else y

289

290 def toBeta(self, rhumb):

291 '''Short for C{rhumb.auxDLat.convert(Aux.BETA, self, exact=rhumb.exact)}

292 '''

293 return self._toRhumbAux(rhumb, Aux.BETA)

294

295 def toChi(self, rhumb):

296 '''Short for C{rhumb.auxDLat.convert(Aux.CHI, self, exact=rhumb.exact)}

297 '''

298 return self._toRhumbAux(rhumb, Aux.CHI)

299

300 @Property_RO

301 def toDegrees(self):

302 '''Get this angle as L{Degrees}.

303 '''

304 return Degrees(atan2d(*self._yx), name=self.name)

305

306 @Property_RO

307 def toLambertianDegrees(self): # PYCHOK no cover

308 '''Get this angle's I{Lambertian} in L{Degrees}.

309 '''

310 r = self.toLambertianRadians

311 return Degrees(degrees(r), name=r.name)

312

313 @Property_RO

314 def toLambertianRadians(self):

315 '''Get this angle's I{Lambertian} in L{Radians}.

316 '''

317 return Radians(asinh(self.tan), name=self.name)

318

319 def toMu(self, rhumb):

320 '''Short for C{rhumb.auxDLat.convert(Aux.MU, self, exact=rhumb.exact)}

321 '''

322 return self._toRhumbAux(rhumb, Aux.MU)

323

324 def toPhi(self, rhumb):

325 '''Short for C{rhumb.auxDLat.convert(Aux.PHI, self, exact=rhumb.exact)}

326 '''

327 return self._toRhumbAux(rhumb, Aux.PHI)

328

329 @Property_RO

330 def toRadians(self):

331 '''Get this angle as L{Radians}.

332 '''

333 return Radians(atan2(*self._yx), name=self.name)

334

335 def _toRhumbAux(self, rhumb, aux):

336 '''(INTERNAL) Create an C{aux}-KIND angle from this angle.

337 '''

338 _xinstanceof(self._RhumbAux, rhumb=rhumb)

339 return rhumb._auxD.convert(aux, self, exact=rhumb.exact)

340

341 @Property

342 def x(self):

343 '''Get this angle's C{x} (C{float}).

344 '''

345 return self._x

346

347 @x.setter # PYCHOK setter!

348 def x(self, x): # PYCHOK no cover

349 '''Set this angle's C{x} (C{float}).

350 '''

351 x = float(x)

352 if self._x != x:

353 _update_all(self)

354 self._x = x

355

356 @property_RO

357 def _x_normalized(self):

358 '''(INTERNAL) Get the I{normalized} C{x}.

359 '''

360 _, x = self._yx_normalized

361 return x

362

363 @Property

364 def y(self):

365 '''Get this angle's C{y} (C{float}).

366 '''

367 return self._y

368

369 @y.setter # PYCHOK setter!

370 def y(self, y): # PYCHOK no cover

371 '''Set this angle's C{y} (C{float}).

372 '''

373 y = float(y)

374 if self.y != y:

375 _update_all(self)

376 self._y = y

377

378 @Property

379 def _yx(self):

380 '''(INTERNAL) Get this angle as 2-tuple C{(y, x)}.

381 '''

382 return self._y, self._x

383

384 @_yx.setter # PYCHOK setter!

385 def _yx(self, yx):

386 '''(INTERNAL) Set this angle's C{y} and C{x}.

387 '''

388 yx = _yx2(yx)

389 if self._yx != yx:

390 _update_all(self)

391 self._y, self._x = yx

392

393 @Property_RO

394 def _yx_normalized(self):

395 '''(INTERNAL) Get this angle as 2-tuple C{(y, x)}, I{normalized}.

396 '''

397 y, x = self._yx

398 if isfinite(y) and fabs(y) < _MAX_2 \

399 and fabs(x) < _MAX_2 \

400 and isfinite(self.tan):

401 h = hypot(y, x)

402 if h > 0 and y:

403 y = y / h # /= chokes PyChecker

404 x = x / h

405 if isnan(y): # PYCHOK no cover

406 y = _copysign_1_0(self.y)

407 if isnan(x): # PYCHOK no cover

408 x = _copysign_1_0(self.x)

409 else: # scalar 0

410 y, x = _0_0, _copysign_1_0(y * x)

411 else: # scalar NAN

412 y, x = NAN, _copysign_1_0(y * x)

413 return y, x

414

415 def _yxr_normalized(self, abs_y=False):

416 '''(INTERNAL) Get 3-tuple C{(y, x, r)}, I{normalized}

417 with C{y} or C{abs(y)} and C{r} as C{.toRadians}.

418 '''

419 y, x = self._yx_normalized

420 if abs_y:

421 y = fabs(y) # only y, not x

422 return y, x, atan2(y, x) # .toRadians

423

424

425 class AuxBeta(AuxAngle):

426 '''A I{Parametric, Auxiliary} latitude.

427 '''

428 _AUX = Aux.BETA

429

430 @staticmethod

431 def fromDegrees(deg, **name):

432 '''Get an L{AuxBeta} from degrees.

433 '''

434 return AuxBeta(*sincos2d(deg), **name)

435

436 @staticmethod

437 def fromRadians(rad, **name):

438 '''Get an L{AuxBeta} from radians.

439 '''

440 return AuxBeta(*sincos2(rad), **name)

441

442

443 class AuxChi(AuxAngle):

444 '''A I{Conformal, Auxiliary} latitude.

445 '''

446 _AUX = Aux.CHI

447

448 @staticmethod

449 def fromDegrees(deg, **name):

450 '''Get an L{AuxChi} from degrees.

451 '''

452 return AuxChi(*sincos2d(deg), **name)

453

454

455 class AuxMu(AuxAngle):

456 '''A I{Rectifying, Auxiliary} latitude.

457 '''

458 _AUX = Aux.MU

459

460 @staticmethod

461 def fromDegrees(deg, **name):

462 '''Get an L{AuxMu} from degrees.

463 '''

464 return AuxMu(*sincos2d(deg), **name)

465

466

467 class AuxPhi(AuxAngle):

468 '''A I{Geodetic or Geographic, Auxiliary} latitude.

469 '''

470 _AUX = Aux.PHI

471 _diff = _1_0 # see .auxLat._Newton

472

473 @staticmethod

474 def fromDegrees(deg, **name):

475 '''Get an L{AuxPhi} from degrees.

476 '''

477 return AuxPhi(*sincos2d(deg), **name)

478

479

480 class AuxTheta(AuxAngle):

481 '''A I{Geocentric, Auxiliary} latitude.

482 '''

483 _AUX = Aux.THETA

484

485 @staticmethod

486 def fromDegrees(deg, **name):

487 '''Get an L{AuxTheta} from degrees.

488 '''

489 return AuxTheta(*sincos2d(deg), **name)

490

491

492 class AuxXi(AuxAngle):

493 '''An I{Authalic, Auxiliary} latitude.

494 '''

495 _AUX = Aux.XI

496

497 @staticmethod

498 def fromDegrees(deg, **name):

499 '''Get an L{AuxXi} from degrees.

500 '''

501 return AuxXi(*sincos2d(deg), **name)

502

503

504_AUXClass = {Aux.BETA: AuxBeta,

505 Aux.CHI: AuxChi,

506 Aux.MU: AuxMu,

507 Aux.PHI: AuxPhi,

508 Aux.THETA: AuxTheta,

509 Aux.XI: AuxXi}

510

511 def _AuxClass(aux=None, **unused): # PYCHOK C{classof(aux)}

512 return _AUXClass.get(aux, AuxAngle)

513

514

515 def _yx2(yx):

516 '''(INTERNAL) Validate 2-tuple C{(y, x)}.

517 '''

518 try:

519 y, x = yx

520 y, x = map1(float, y, x)

521 if y in _0_INF_NAN_NINF:

522 x = _copysign_1_0(x)

523 except (TypeError, ValueError) as X:

524 raise AuxError(y=y, x=x, cause=X)

525 return y, x

526

527

528__all__ += _ALL_DOCS(AuxAngle, AuxBeta, AuxChi, AuxMu, AuxPhi, AuxTheta, AuxXi)

529

530# **) MIT License

531#

532# Copyright (C) 2023-2025 -- mrJean1 at Gmail -- All Rights Reserved.

533#

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

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

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

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

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

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

540#

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

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

543#

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

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

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

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

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

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

550# OTHER DEALINGS IN THE SOFTWARE.