Coverage for pygeodesy/utily.py: 91%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Various utility functions. 

5 

6After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see 

7U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>} and 

8U{Vector-based geodesy<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. 

9''' 

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

11from __future__ import division as _; del _ # PYCHOK semicolon 

12 

13from pygeodesy.basics import _copysign, isinstanceof, isint, isstr, neg, \ 

14 _passargs 

15from pygeodesy.constants import EPS, EPS0, INF, NAN, PI, PI2, PI_2, R_M, \ 

16 _M_KM, _M_NM, _M_SM, _0_0, _1__90, _0_5, _1_0, \ 

17 _N_1_0, _2__PI, _10_0, _90_0, _N_90_0, _180_0, \ 

18 _N_180_0, _360_0, _400_0, _copysign_0_0, \ 

19 _float as _F, _isfinite, isnan, isnear0, \ 

20 _over, _umod_360, _umod_PI2 

21from pygeodesy.errors import _ValueError, _xkwds, _xkwds_get, _ALL_LAZY, _MODS 

22from pygeodesy.interns import _edge_, _radians_, _semi_circular_, _SPACE_ 

23# from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS # from .errors 

24from pygeodesy.units import Degrees, Degrees_, Feet, Float, Lam, Lam_, \ 

25 Meter, Meter2, Radians, Radians_ 

26 

27from math import acos, asin, atan2, cos, degrees, fabs, radians, sin, tan # pow 

28 

29__all__ = _ALL_LAZY.utily 

30__version__ = '24.04.04' 

31 

32# read constant name "_M_Unit" as "meter per Unit" 

33_M_CHAIN = _F( 20.1168) # yard2m(1) * 22 

34_M_FATHOM = _F( 1.8288) # yard2m(1) * 2 or _M_NM * 1e-3 

35_M_FOOT = _F( 0.3048) # Int'l (1 / 3.2808398950131 = 10_000 / (254 * 12)) 

36_M_FOOT_GE = _F( 0.31608) # German Fuss (1 / 3.1637560111364) 

37_M_FOOT_FR = _F( 0.3248406) # French Pied-du-Roi or pied (1 / 3.0784329298739) 

38_M_FOOT_USVY = _F( 0.3048006096012192) # US Survey (1200 / 3937) 

39_M_FURLONG = _F( 201.168) # 220 * yard2m(1) == 10 * m2chain(1) 

40# _M_KM = _F(1000.0) # kilo meter 

41# _M_NM = _F(1852.0) # nautical mile 

42# _M_SM = _F(1609.344) # statute mile 

43_M_TOISE = _F( 1.9490436) # French toise, 6 pieds (6 / 3.0784329298739) 

44_M_YARD_UK = _F( 0.9144) # 254 * 12 * 3 / 10_000 == 3 * ft2m(1) Int'l 

45 

46 

47def _abs1nan(x): 

48 '''(INTERNAL) Bracket C{x}. 

49 ''' 

50 return _N_1_0 < x < _1_0 or isnan(x) 

51 

52 

53def acos1(x): 

54 '''Return C{math.acos(max(-1, min(1, B{x})))}. 

55 ''' 

56 return acos(x) if _abs1nan(x) else (PI if x < 0 else _0_0) 

57 

58 

59def acre2ha(acres): 

60 '''Convert acres to hectare. 

61 

62 @arg acres: Value in acres (C{scalar}). 

63 

64 @return: Value in C{hectare} (C{float}). 

65 

66 @raise ValueError: Invalid B{C{acres}}. 

67 ''' 

68 # 0.40468564224 == acre2m2(1) / 10_000 

69 return Float(ha=Float(acres) * 0.40468564224) 

70 

71 

72def acre2m2(acres): 

73 '''Convert acres to I{square} meter. 

74 

75 @arg acres: Value in acres (C{scalar}). 

76 

77 @return: Value in C{meter^2} (C{float}). 

78 

79 @raise ValueError: Invalid B{C{acres}}. 

80 ''' 

81 # 4046.8564224 == chain2m(1) * furlong2m(1) 

82 return Meter2(Float(acres) * 4046.8564224) 

83 

84 

85def asin1(x): 

86 '''Return C{math.asin(max(-1, min(1, B{x})))}. 

87 ''' 

88 return asin(x) if _abs1nan(x) else _copysign(PI_2, x) 

89 

90 

91def atan1(y, x=_1_0): 

92 '''Return C{atan(B{y} / B{x})} angle in C{radians} M{[-PI/2..+PI/2]} 

93 using C{atan2} for consistency and to avoid C{ZeroDivisionError}. 

94 ''' 

95 return atan2(-y, -x) if x < 0 else atan2(y, x or _0_0) # -0. to 0. 

96 

97 

98def atan1d(y, x=_1_0): 

99 '''Return C{atan(B{y} / B{x})} angle in C{degrees} M{[-90..+90]} 

100 using C{atan2d} for consistency and to avoid C{ZeroDivisionError}. 

101 

102 @see: Function L{pygeodesy.atan2d}. 

103 ''' 

104 return atan2d(-y, -x) if x < 0 else atan2d(y, x or _0_0) # -0. to 0. 

105 

106 

107def atan2b(y, x): 

108 '''Return C{atan2(B{y}, B{x})} in degrees M{[0..+360]}. 

109 

110 @see: Function L{pygeodesy.atan2d}. 

111 ''' 

112 b = atan2d(y, x) 

113 if b < 0: 

114 b += _360_0 

115 return b 

116 

117 

118def atan2d(y, x, reverse=False): 

119 '''Return C{atan2(B{y}, B{x})} in degrees M{[-180..+180]}, 

120 optionally I{reversed} (by 180 degrees for C{azimuth}s). 

121 

122 @see: I{Karney}'s C++ function U{Math.atan2d 

123 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}. 

124 ''' 

125 if fabs(y) > fabs(x) > 0: 

126 if y < 0: # q = 3 

127 d = degrees(atan2(x, -y)) - _90_0 

128 else: # q = 2 

129 d = _90_0 - degrees(atan2(x, y)) 

130 elif isnan(x) or isnan(y): 

131 return NAN 

132 elif y: 

133 if x > 0: # q = 0 

134 d = degrees(atan2(y, x)) 

135 elif x < 0: # q = 1 

136 d = _copysign(_180_0, y) - degrees(atan2(y, -x)) 

137 else: # x == 0 

138 d = _copysign(_90_0, y) 

139 else: 

140 d = _180_0 if x < 0 else _0_0 

141 return _azireversed(d) if reverse else d 

142 

143 

144def _azireversed(azimuth): # in .rhumbBase 

145 '''(INTERNAL) Return the I{reverse} B{C{azimuth}} in degrees M{[-180..+180]}. 

146 ''' 

147 return azimuth + (_N_180_0 if azimuth > 0 else _180_0) 

148 

149 

150def chain2m(chains): 

151 '''Convert I{UK} chains to meter. 

152 

153 @arg chains: Value in chains (C{scalar}). 

154 

155 @return: Value in C{meter} (C{float}). 

156 

157 @raise ValueError: Invalid B{C{chains}}. 

158 ''' 

159 return Meter(Float(chains=chains) * _M_CHAIN) 

160 

161 

162def circle4(earth, lat): 

163 '''Get the equatorial or a parallel I{circle of latitude}. 

164 

165 @arg earth: The earth radius, ellipsoid or datum 

166 (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, 

167 L{Datum} or L{a_f2Tuple}). 

168 @arg lat: Geodetic latitude (C{degrees90}, C{str}). 

169 

170 @return: A L{Circle4Tuple}C{(radius, height, lat, beta)} 

171 instance. 

172 

173 @raise RangeError: Latitude B{C{lat}} outside valid range and 

174 L{pygeodesy.rangerrors} set to C{True}. 

175 

176 @raise TypeError: Invalid B{C{earth}}. 

177 

178 @raise ValueError: B{C{earth}} or B{C{lat}}. 

179 ''' 

180 E = _MODS.datums._earth_ellipsoid(earth) 

181 return E.circle4(lat) 

182 

183 

184def cot(rad, **error_kwds): 

185 '''Return the C{cotangent} of an angle in C{radians}. 

186 

187 @arg rad: Angle (C{radians}). 

188 @kwarg error_kwds: Error to raise (C{ValueError}). 

189 

190 @return: C{cot(B{rad})}. 

191 

192 @raise ValueError: L{pygeodesy.isnear0}C{(sin(B{rad})}. 

193 ''' 

194 s, c = sincos2(rad) 

195 if c: 

196 if isnear0(s): 

197 raise _valueError(cot, rad, **error_kwds) 

198 c = c / s # /= chokes PyChecker 

199 return c 

200 

201 

202def cot_(*rads, **error_kwds): 

203 '''Return the C{cotangent} of angle(s) in C{radiansresection}. 

204 

205 @arg rads: One or more angles (C{radians}). 

206 @kwarg error_kwds: Error to raise (C{ValueError}). 

207 

208 @return: Yield the C{cot(B{rad})} for each angle. 

209 

210 @raise ValueError: See L{pygeodesy.cot}. 

211 ''' 

212 try: 

213 for r in rads: 

214 yield cot(r) 

215 except ValueError: 

216 raise _valueError(cot_, r, **error_kwds) 

217 

218 

219def cotd(deg, **error_kwds): 

220 '''Return the C{cotangent} of an angle in C{degrees}. 

221 

222 @arg deg: Angle (C{degrees}). 

223 @kwarg error_kwds: Error to raise (C{ValueError}). 

224 

225 @return: C{cot(B{deg})}. 

226 

227 @raise ValueError: L{pygeodesy.isnear0}C{(sin(B{deg})}. 

228 ''' 

229 s, c = sincos2d(deg) 

230 if c: 

231 if isnear0(s): 

232 raise _valueError(cotd, deg, **error_kwds) 

233 c = c / s # /= chokes PyChecker 

234 elif s < 0: 

235 c = -c # negate-0 

236 return c 

237 

238 

239def cotd_(*degs, **error_kwds): 

240 '''Return the C{cotangent} of angle(s) in C{degrees}. 

241 

242 @arg degs: One or more angles (C{degrees}). 

243 @kwarg error_kwds: Error to raise (C{ValueError}). 

244 

245 @return: Yield the C{cot(B{deg})} for each angle. 

246 

247 @raise ValueError: See L{pygeodesy.cotd}. 

248 ''' 

249 try: 

250 for d in degs: 

251 yield cotd(d) 

252 except ValueError: 

253 raise _valueError(cotd_, d, **error_kwds) 

254 

255 

256def degrees90(rad): 

257 '''Convert radians to degrees and wrap M{[-90..+90)}. 

258 

259 @arg rad: Angle (C{radians}). 

260 

261 @return: Angle, wrapped (C{degrees90}). 

262 ''' 

263 return wrap90(degrees(rad)) 

264 

265 

266def degrees180(rad): 

267 '''Convert radians to degrees and wrap M{[-180..+180)}. 

268 

269 @arg rad: Angle (C{radians}). 

270 

271 @return: Angle, wrapped (C{degrees180}). 

272 ''' 

273 return wrap180(degrees(rad)) 

274 

275 

276def degrees360(rad): 

277 '''Convert radians to degrees and wrap M{[0..+360)}. 

278 

279 @arg rad: Angle (C{radians}). 

280 

281 @return: Angle, wrapped (C{degrees360}). 

282 ''' 

283 return _umod_360(degrees(rad)) 

284 

285 

286def degrees2grades(deg): 

287 '''Convert degrees to I{grades} (aka I{gons} or I{gradians}). 

288 

289 @arg deg: Angle (C{degrees}). 

290 

291 @return: Angle (C{grades}). 

292 ''' 

293 return Degrees(deg) * _400_0 / _360_0 

294 

295 

296def degrees2m(deg, radius=R_M, lat=0): 

297 '''Convert an angle to a distance along the equator or 

298 along the parallel at an other (geodetic) latitude. 

299 

300 @arg deg: The angle (C{degrees}). 

301 @kwarg radius: Mean earth radius, ellipsoid or datum 

302 (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, 

303 L{Datum} or L{a_f2Tuple}). 

304 @kwarg lat: Parallel latitude (C{degrees90}, C{str}). 

305 

306 @return: Distance (C{meter}, same units as B{C{radius}} 

307 or equatorial and polar radii) or C{0.0} for 

308 near-polar B{C{lat}}. 

309 

310 @raise RangeError: Latitude B{C{lat}} outside valid range and 

311 L{pygeodesy.rangerrors} set to C{True}. 

312 

313 @raise TypeError: Invalid B{C{radius}}. 

314 

315 @raise ValueError: Invalid B{C{deg}}, B{C{radius}} or 

316 B{C{lat}}. 

317 

318 @see: Function L{radians2m} and L{m2degrees}. 

319 ''' 

320 return _Radians2m(Lam_(deg=deg, clip=0), radius, lat) 

321 

322 

323def fathom2m(fathoms): 

324 '''Convert I{Imperial} fathom to meter. 

325 

326 @arg fathoms: Value in fathoms (C{scalar}). 

327 

328 @return: Value in C{meter} (C{float}). 

329 

330 @raise ValueError: Invalid B{C{fathoms}}. 

331 

332 @see: Function L{toise2m}, U{Fathom<https://WikiPedia.org/wiki/Fathom>} 

333 and U{Klafter<https://WikiPedia.org/wiki/Klafter>}. 

334 ''' 

335 return Meter(Float(fathoms=fathoms) * _M_FATHOM) 

336 

337 

338def ft2m(feet, usurvey=False, pied=False, fuss=False): 

339 '''Convert I{International}, I{US Survey}, I{French} or I{German} 

340 B{C{feet}} to C{meter}. 

341 

342 @arg feet: Value in feet (C{scalar}). 

343 @kwarg usurvey: If C{True}, convert I{US Survey} foot else ... 

344 @kwarg pied: If C{True}, convert French I{pied-du-Roi} else ... 

345 @kwarg fuss: If C{True}, convert German I{Fuss}, otherwise 

346 I{International} foot to C{meter}. 

347 

348 @return: Value in C{meter} (C{float}). 

349 

350 @raise ValueError: Invalid B{C{feet}}. 

351 ''' 

352 return Meter(Feet(feet) * (_M_FOOT_USVY if usurvey else 

353 (_M_FOOT_FR if pied else 

354 (_M_FOOT_GE if fuss else _M_FOOT)))) 

355 

356 

357def furlong2m(furlongs): 

358 '''Convert a furlong to meter. 

359 

360 @arg furlongs: Value in furlongs (C{scalar}). 

361 

362 @return: Value in C{meter} (C{float}). 

363 

364 @raise ValueError: Invalid B{C{furlongs}}. 

365 ''' 

366 return Meter(Float(furlongs=furlongs) * _M_FURLONG) 

367 

368 

369def grades(rad): 

370 '''Convert radians to I{grades} (aka I{gons} or I{gradians}). 

371 

372 @arg rad: Angle (C{radians}). 

373 

374 @return: Angle (C{grades}). 

375 ''' 

376 return Float(grades=Float(rad=rad) * _400_0 / PI2) 

377 

378 

379def grades400(rad): 

380 '''Convert radians to I{grades} (aka I{gons} or I{gradians}) and wrap M{[0..+400)}. 

381 

382 @arg rad: Angle (C{radians}). 

383 

384 @return: Angle, wrapped (C{grades}). 

385 ''' 

386 return Float(grades400=(grades(rad) % _400_0) or _0_0) # _umod_400 

387 

388 

389def grades2degrees(gon): 

390 '''Convert I{grades} (aka I{gons} or I{gradians}) to C{degrees}. 

391 

392 @arg gon: Angle (C{grades}). 

393 

394 @return: Angle (C{degrees}). 

395 ''' 

396 return Degrees(Float(gon=gon) * _360_0 / _400_0) 

397 

398 

399def grades2radians(gon): 

400 '''Convert I{grades} (aka I{gons} or I{gradians}) to C{radians}. 

401 

402 @arg gon: Angle (C{grades}). 

403 

404 @return: Angle (C{radians}). 

405 ''' 

406 return Radians(Float(gon=gon) * PI2 / _400_0) 

407 

408 

409def km2m(km): 

410 '''Convert kilo meter to meter (m). 

411 

412 @arg km: Value in kilo meter (C{scalar}). 

413 

414 @return: Value in meter (C{float}). 

415 

416 @raise ValueError: Invalid B{C{km}}. 

417 ''' 

418 return Meter(Float(km=km) * _M_KM) 

419 

420 

421def _loneg(lon): 

422 '''(INTERNAL) "Complement" of C{lon}. 

423 ''' 

424 return _180_0 - lon 

425 

426 

427def m2chain(meter): 

428 '''Convert meter to I{UK} chains. 

429 

430 @arg meter: Value in meter (C{scalar}). 

431 

432 @return: Value in C{chains} (C{float}). 

433 

434 @raise ValueError: Invalid B{C{meter}}. 

435 ''' 

436 return Float(chain=Meter(meter) / _M_CHAIN) # * 0.049709695378986715 

437 

438 

439def m2degrees(distance, radius=R_M, lat=0): 

440 '''Convert a distance to an angle along the equator or 

441 along the parallel at an other (geodetic) latitude. 

442 

443 @arg distance: Distance (C{meter}, same units as B{C{radius}}). 

444 @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, 

445 an L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or 

446 L{a_f2Tuple}). 

447 @kwarg lat: Parallel latitude (C{degrees90}, C{str}). 

448 

449 @return: Angle (C{degrees}) or C{INF} for near-polar B{C{lat}}. 

450 

451 @raise RangeError: Latitude B{C{lat}} outside valid range and 

452 L{pygeodesy.rangerrors} set to C{True}. 

453 

454 @raise TypeError: Invalid B{C{radius}}. 

455 

456 @raise ValueError: Invalid B{C{distance}}, B{C{radius}} 

457 or B{C{lat}}. 

458 

459 @see: Function L{m2radians} and L{degrees2m}. 

460 ''' 

461 return degrees(m2radians(distance, radius=radius, lat=lat)) 

462 

463 

464def m2fathom(meter): 

465 '''Convert meter to I{Imperial} fathoms. 

466 

467 @arg meter: Value in meter (C{scalar}). 

468 

469 @return: Value in C{fathoms} (C{float}). 

470 

471 @raise ValueError: Invalid B{C{meter}}. 

472 

473 @see: Function L{m2toise}, U{Fathom<https://WikiPedia.org/wiki/Fathom>} 

474 and U{Klafter<https://WikiPedia.org/wiki/Klafter>}. 

475 ''' 

476 return Float(fathom=Meter(meter) / _M_FATHOM) # * 0.546806649 

477 

478 

479def m2ft(meter, usurvey=False, pied=False, fuss=False): 

480 '''Convert meter to I{International}, I{US Survey}, I{French} or 

481 or I{German} feet (C{ft}). 

482 

483 @arg meter: Value in meter (C{scalar}). 

484 @kwarg usurvey: If C{True}, convert to I{US Survey} foot else ... 

485 @kwarg pied: If C{True}, convert to French I{pied-du-Roi} else ... 

486 @kwarg fuss: If C{True}, convert to German I{Fuss}, otherwise to 

487 I{International} foot. 

488 

489 @return: Value in C{feet} (C{float}). 

490 

491 @raise ValueError: Invalid B{C{meter}}. 

492 ''' 

493 # * 3.2808333333333333, US Survey 3937 / 1200 

494 # * 3.2808398950131235, Int'l 10_000 / (254 * 12) 

495 return Float(feet=Meter(meter) / (_M_FOOT_USVY if usurvey else 

496 (_M_FOOT_FR if pied else 

497 (_M_FOOT_GE if fuss else _M_FOOT)))) 

498 

499 

500def m2furlong(meter): 

501 '''Convert meter to furlongs. 

502 

503 @arg meter: Value in meter (C{scalar}). 

504 

505 @return: Value in C{furlongs} (C{float}). 

506 

507 @raise ValueError: Invalid B{C{meter}}. 

508 ''' 

509 return Float(furlong=Meter(meter) / _M_FURLONG) # * 0.00497096954 

510 

511 

512def m2km(meter): 

513 '''Convert meter to kilo meter (Km). 

514 

515 @arg meter: Value in meter (C{scalar}). 

516 

517 @return: Value in Km (C{float}). 

518 

519 @raise ValueError: Invalid B{C{meter}}. 

520 ''' 

521 return Float(km=Meter(meter) / _M_KM) 

522 

523 

524def m2NM(meter): 

525 '''Convert meter to nautical miles (NM). 

526 

527 @arg meter: Value in meter (C{scalar}). 

528 

529 @return: Value in C{NM} (C{float}). 

530 

531 @raise ValueError: Invalid B{C{meter}}. 

532 ''' 

533 return Float(NM=Meter(meter) / _M_NM) # * 5.39956804e-4 

534 

535 

536def m2radians(distance, radius=R_M, lat=0): 

537 '''Convert a distance to an angle along the equator or along the 

538 parallel at an other (geodetic) latitude. 

539 

540 @arg distance: Distance (C{meter}, same units as B{C{radius}}). 

541 @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, 

542 an L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or 

543 L{a_f2Tuple}). 

544 @kwarg lat: Parallel latitude (C{degrees90}, C{str}). 

545 

546 @return: Angle (C{radians}) or C{INF} for near-polar B{C{lat}}. 

547 

548 @raise RangeError: Latitude B{C{lat}} outside valid range and 

549 L{pygeodesy.rangerrors} set to C{True}. 

550 

551 @raise TypeError: Invalid B{C{radius}}. 

552 

553 @raise ValueError: Invalid B{C{distance}}, B{C{radius}} 

554 or B{C{lat}}. 

555 

556 @see: Function L{m2degrees} and L{radians2m}. 

557 ''' 

558 m = circle4(radius, lat).radius 

559 return INF if m < EPS0 else Radians(Float(distance=distance) / m) 

560 

561 

562def m2SM(meter): 

563 '''Convert meter to statute miles (SM). 

564 

565 @arg meter: Value in meter (C{scalar}). 

566 

567 @return: Value in C{SM} (C{float}). 

568 

569 @raise ValueError: Invalid B{C{meter}}. 

570 ''' 

571 return Float(SM=Meter(meter) / _M_SM) # * 6.21369949e-4 == 1 / 1609.344 

572 

573 

574def m2toise(meter): 

575 '''Convert meter to French U{toises<https://WikiPedia.org/wiki/Toise>}. 

576 

577 @arg meter: Value in meter (C{scalar}). 

578 

579 @return: Value in C{toises} (C{float}). 

580 

581 @raise ValueError: Invalid B{C{meter}}. 

582 

583 @see: Function L{m2fathom}. 

584 ''' 

585 return Float(toise=Meter(meter) / _M_TOISE) # * 0.513083632632119 

586 

587 

588def m2yard(meter): 

589 '''Convert meter to I{UK} yards. 

590 

591 @arg meter: Value in meter (C{scalar}). 

592 

593 @return: Value in C{yards} (C{float}). 

594 

595 @raise ValueError: Invalid B{C{meter}}. 

596 ''' 

597 return Float(yard=Meter(meter) / _M_YARD_UK) # * 1.0936132983377078 

598 

599 

600def NM2m(nm): 

601 '''Convert nautical miles to meter (m). 

602 

603 @arg nm: Value in nautical miles (C{scalar}). 

604 

605 @return: Value in meter (C{float}). 

606 

607 @raise ValueError: Invalid B{C{nm}}. 

608 ''' 

609 return Meter(Float(nm=nm) * _M_NM) 

610 

611 

612def radians2m(rad, radius=R_M, lat=0): 

613 '''Convert an angle to a distance along the equator or 

614 along the parallel at an other (geodetic) latitude. 

615 

616 @arg rad: The angle (C{radians}). 

617 @kwarg radius: Mean earth radius, ellipsoid or datum 

618 (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, 

619 L{Datum} or L{a_f2Tuple}). 

620 @kwarg lat: Parallel latitude (C{degrees90}, C{str}). 

621 

622 @return: Distance (C{meter}, same units as B{C{radius}} 

623 or equatorial and polar radii) or C{0.0} for 

624 near-polar B{C{lat}}. 

625 

626 @raise RangeError: Latitude B{C{lat}} outside valid range and 

627 L{pygeodesy.rangerrors} set to C{True}. 

628 

629 @raise TypeError: Invalid B{C{radius}}. 

630 

631 @raise ValueError: Invalid B{C{rad}}, B{C{radius}} or 

632 B{C{lat}}. 

633 

634 @see: Function L{degrees2m} and L{m2radians}. 

635 ''' 

636 return _Radians2m(Lam(rad=rad, clip=0), radius, lat) 

637 

638 

639def _Radians2m(rad, radius, lat): 

640 '''(INTERNAL) Helper for C{degrees2m} and C{radians2m}. 

641 ''' 

642 m = circle4(radius, lat).radius 

643 return _0_0 if m < EPS0 else (rad * m) 

644 

645 

646def radiansPI(deg): 

647 '''Convert and wrap degrees to radians M{[-PI..+PI]}. 

648 

649 @arg deg: Angle (C{degrees}). 

650 

651 @return: Radians, wrapped (C{radiansPI}) 

652 ''' 

653 return wrapPI(radians(deg)) 

654 

655 

656def radiansPI2(deg): 

657 '''Convert and wrap degrees to radians M{[0..+2PI)}. 

658 

659 @arg deg: Angle (C{degrees}). 

660 

661 @return: Radians, wrapped (C{radiansPI2}) 

662 ''' 

663 return _umod_PI2(radians(deg)) 

664 

665 

666def radiansPI_2(deg): 

667 '''Convert and wrap degrees to radians M{[-3PI/2..+PI/2]}. 

668 

669 @arg deg: Angle (C{degrees}). 

670 

671 @return: Radians, wrapped (C{radiansPI_2}) 

672 ''' 

673 return wrapPI_2(radians(deg)) 

674 

675 

676def _sin0cos2(q, r, sign): 

677 '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant C{0 <= B{q} <= 3} 

678 and C{sin} zero I{signed} with B{C{sign}}. 

679 ''' 

680 if r < PI_2: 

681 s, c = sin(r), cos(r) 

682 t = s, c, -s, -c, s 

683 else: # r == PI_2 

684 t = _1_0, _0_0, _N_1_0, _0_0, _1_0 

685# else: # r == 0, testUtility failures 

686# t = _0_0, _1_0, _0_0, _N_1_0, _0_0 

687# q &= 3 

688 s = t[q] or _copysign_0_0(sign) 

689 c = t[q + 1] or _0_0 

690 return s, c 

691 

692 

693def SinCos2(x): 

694 '''Get C{sin} and C{cos} of I{typed} angle. 

695 

696 @arg x: Angle (L{Degrees}, L{Radians} or scalar C{radians}). 

697 

698 @return: 2-Tuple (C{sin(B{x})}, C{cos(B{x})}). 

699 ''' 

700 return sincos2d(x) if isinstanceof(x, Degrees, Degrees_) else ( 

701 sincos2(x) if isinstanceof(x, Radians, Radians_) else 

702 sincos2(float(x))) # assume C{radians} 

703 

704 

705def sincos2(rad): 

706 '''Return the C{sine} and C{cosine} of an angle in C{radians}. 

707 

708 @arg rad: Angle (C{radians}). 

709 

710 @return: 2-Tuple (C{sin(B{rad})}, C{cos(B{rad})}). 

711 

712 @see: U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/ 

713 classGeographicLib_1_1Math.html#sincosd>} function U{sincosd 

714 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ 

715 python/geographiclib/geomath.py#l155>} and C++ U{sincosd 

716 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ 

717 include/GeographicLib/Math.hpp#l558>}. 

718 ''' 

719 if _isfinite(rad): 

720 q = int(rad * _2__PI) # int(math.floor) 

721 if q < 0: 

722 q -= 1 

723 t = _sin0cos2(q & 3, rad - q * PI_2, rad) 

724 else: 

725 t = NAN, NAN 

726 return t 

727 

728 

729def sincos2_(*rads): 

730 '''Return the C{sine} and C{cosine} of angle(s) in C{radians}. 

731 

732 @arg rads: One or more angles (C{radians}). 

733 

734 @return: Yield the C{sin(B{rad})} and C{cos(B{rad})} for each angle. 

735 

736 @see: function L{sincos2}. 

737 ''' 

738 for r in rads: 

739 s, c = sincos2(r) 

740 yield s 

741 yield c 

742 

743 

744def sincos2d(deg, **adeg): 

745 '''Return the C{sine} and C{cosine} of an angle in C{degrees}. 

746 

747 @arg deg: Angle (C{degrees}). 

748 @kwarg adeg: Optional correction (C{degrees}). 

749 

750 @return: 2-Tuple (C{sin(B{deg_})}, C{cos(B{deg_})}, C{B{deg_} = 

751 B{deg} + B{adeg}}). 

752 

753 @see: U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/ 

754 classGeographicLib_1_1Math.html#sincosd>} function U{sincosd 

755 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ 

756 python/geographiclib/geomath.py#l155>} and C++ U{sincosd 

757 <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ 

758 include/GeographicLib/Math.hpp#l558>}. 

759 ''' 

760 if _isfinite(deg): 

761 q = int(deg * _1__90) # int(math.floor) 

762 if q < 0: 

763 q -= 1 

764 d = deg - q * _90_0 

765 if adeg: 

766 t = _xkwds_get(adeg, adeg=_0_0) 

767 d = _MODS.karney._around(d + t) 

768 t = _sin0cos2(q & 3, radians(d), deg) 

769 else: 

770 t = NAN, NAN 

771 return t 

772 

773 

774def sincos2d_(*degs): 

775 '''Return the C{sine} and C{cosine} of angle(s) in C{degrees}. 

776 

777 @arg degs: One or more angles (C{degrees}). 

778 

779 @return: Yield the C{sin(B{deg})} and C{cos(B{deg})} for each angle. 

780 

781 @see: Function L{sincos2d}. 

782 ''' 

783 for d in degs: 

784 s, c = sincos2d(d) 

785 yield s 

786 yield c 

787 

788 

789def sincostan3(rad): 

790 '''Return the C{sine}, C{cosine} and C{tangent} of an angle in C{radians}. 

791 

792 @arg rad: Angle (C{radians}). 

793 

794 @return: 3-Tuple (C{sin(B{rad})}, C{cos(B{rad})}, C{tan(B{rad})}). 

795 

796 @see: Function L{sincos2}. 

797 ''' 

798 s, c = sincos2(float(rad)) 

799 t = NAN if s is NAN else (_over(s, c) if s else neg(s, neg0=c < 0)) 

800 return s, c, t 

801 

802 

803def SM2m(sm): 

804 '''Convert statute miles to meter (m). 

805 

806 @arg sm: Value in statute miles (C{scalar}). 

807 

808 @return: Value in meter (C{float}). 

809 

810 @raise ValueError: Invalid B{C{sm}}. 

811 ''' 

812 return Meter(Float(sm=sm) * _M_SM) 

813 

814 

815def tan_2(rad, **semi): # edge=1 

816 '''Compute the tangent of half angle. 

817 

818 @arg rad: Angle (C{radians}). 

819 @kwarg semi: Angle or edge name and index 

820 for semi-circular error. 

821 

822 @return: M{tan(rad / 2)} (C{float}). 

823 

824 @raise ValueError: If B{C{rad}} is semi-circular 

825 and B{C{semi}} is given. 

826 ''' 

827 # .formy.excessKarney_, .sphericalTrigonometry.areaOf 

828 if semi and isnear0(fabs(rad) - PI): 

829 for n, v in semi.items(): 

830 break 

831 n = _SPACE_(n, _radians_) if not isint(v) else \ 

832 _SPACE_(_MODS.streprs.Fmt.SQUARE(**semi), _edge_) 

833 raise _ValueError(n, rad, txt=_semi_circular_) 

834 

835 return tan(rad * _0_5) if _isfinite(rad) else NAN 

836 

837 

838def tand(deg, **error_kwds): 

839 '''Return the C{tangent} of an angle in C{degrees}. 

840 

841 @arg deg: Angle (C{degrees}). 

842 @kwarg error_kwds: Error to raise (C{ValueError}). 

843 

844 @return: C{tan(B{deg})}. 

845 

846 @raise ValueError: If L{pygeodesy.isnear0}C{(cos(B{deg})}. 

847 ''' 

848 s, c = sincos2d(deg) 

849 if s: 

850 if isnear0(c): 

851 raise _valueError(tand, deg, **error_kwds) 

852 s = s / c # /= chokes PyChecker 

853 elif c < 0: 

854 s = -s # negate-0 

855 return s 

856 

857 

858def tand_(*degs, **error_kwds): 

859 '''Return the C{tangent} of angle(s) in C{degrees}. 

860 

861 @arg degs: One or more angles (C{degrees}). 

862 @kwarg error_kwds: Error to raise (C{ValueError}). 

863 

864 @return: Yield the C{tan(B{deg})} for each angle. 

865 

866 @raise ValueError: See L{pygeodesy.tand}. 

867 ''' 

868 for d in degs: 

869 yield tand(d, **error_kwds) 

870 

871 

872def tanPI_2_2(rad): 

873 '''Compute the tangent of half angle, 90 degrees rotated. 

874 

875 @arg rad: Angle (C{radians}). 

876 

877 @return: M{tan((rad + PI/2) / 2)} (C{float}). 

878 ''' 

879 return tan((rad + PI_2) * _0_5) if _isfinite(rad) else ( 

880 NAN if isnan(rad) else (_N_90_0 if rad < 0 else _90_0)) 

881 

882 

883def toise2m(toises): 

884 '''Convert French U{toises<https://WikiPedia.org/wiki/Toise>} to meter. 

885 

886 @arg toises: Value in toises (C{scalar}). 

887 

888 @return: Value in C{meter} (C{float}). 

889 

890 @raise ValueError: Invalid B{C{toises}}. 

891 

892 @see: Function L{fathom2m}. 

893 ''' 

894 return Meter(Float(toises=toises) * _M_TOISE) 

895 

896 

897def truncate(x, ndigits=None): 

898 '''Truncate to the given number of digits. 

899 

900 @arg x: Value to truncate (C{scalar}). 

901 @kwarg ndigits: Number of digits (C{int}), 

902 aka I{precision}. 

903 

904 @return: Truncated B{C{x}} (C{float}). 

905 

906 @see: Python function C{round}. 

907 ''' 

908 if isint(ndigits): 

909 p = _10_0**ndigits 

910 x = int(x * p) / p 

911 return x 

912 

913 

914def unroll180(lon1, lon2, wrap=True): 

915 '''Unroll longitudinal delta and wrap longitude in degrees. 

916 

917 @arg lon1: Start longitude (C{degrees}). 

918 @arg lon2: End longitude (C{degrees}). 

919 @kwarg wrap: If C{True}, wrap and unroll to the M{(-180..+180]} 

920 range (C{bool}). 

921 

922 @return: 2-Tuple C{(B{lon2}-B{lon1}, B{lon2})} unrolled (C{degrees}, 

923 C{degrees}). 

924 

925 @see: Capability C{LONG_UNROLL} in U{GeographicLib 

926 <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. 

927 ''' 

928 d = lon2 - lon1 

929 if wrap: 

930 u = wrap180(d) 

931 if u != d: 

932 return u, (lon1 + u) 

933 return d, lon2 

934 

935 

936def _unrollon(p1, p2, wrap=False): # unroll180 == .karney._unroll2 

937 '''(INTERNAL) Wrap/normalize, unroll and replace longitude. 

938 ''' 

939 lat, lon = p2.lat, p2.lon 

940 if wrap and _Wrap.normal: 

941 lat, lon = _Wrap.latlon(lat, lon) 

942 _, lon = unroll180(p1.lon, lon, wrap=True) 

943 if lat != p2.lat or fabs(lon - p2.lon) > EPS: 

944 p2 = p2.dup(lat=lat, lon=wrap180(lon)) 

945 # p2 = p2.copy(); p2.latlon = lat, wrap180(lon) 

946 return p2 

947 

948 

949def _unrollon3(p1, p2, p3, wrap=False): 

950 '''(INTERNAL) Wrap/normalize, unroll 2 points. 

951 ''' 

952 w = wrap 

953 if w: 

954 w = _Wrap.normal 

955 p2 = _unrollon(p1, p2, wrap=w) 

956 p3 = _unrollon(p1, p3, wrap=w) 

957 p2 = _unrollon(p2, p3) 

958 return p2, p3, w # was wrapped? 

959 

960 

961def unrollPI(rad1, rad2, wrap=True): 

962 '''Unroll longitudinal delta and wrap longitude in radians. 

963 

964 @arg rad1: Start longitude (C{radians}). 

965 @arg rad2: End longitude (C{radians}). 

966 @kwarg wrap: If C{True}, wrap and unroll to the M{(-PI..+PI]} 

967 range (C{bool}). 

968 

969 @return: 2-Tuple C{(B{rad2}-B{rad1}, B{rad2})} unrolled 

970 (C{radians}, C{radians}). 

971 

972 @see: Capability C{LONG_UNROLL} in U{GeographicLib 

973 <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. 

974 ''' 

975 r = rad2 - rad1 

976 if wrap: 

977 u = wrapPI(r) 

978 if u != r: 

979 return u, (rad1 + u) 

980 return r, rad2 

981 

982 

983def _valueError(where, x, **kwds): 

984 '''(INTERNAL) Return a C{_ValueError}. 

985 ''' 

986 t = _MODS.streprs.Fmt.PAREN(where.__name__, x) 

987 return _ValueError(t, **kwds) 

988 

989 

990class _Wrap(object): 

991 

992 _normal = False # default 

993 

994 @property 

995 def normal(self): 

996 '''Get the current L{normal} setting (C{True}, 

997 C{False} or C{None}). 

998 ''' 

999 return self._normal 

1000 

1001 @normal.setter # PYCHOK setter! 

1002 def normal(self, setting): 

1003 '''Set L{normal} to C{True}, C{False} or C{None}. 

1004 ''' 

1005 t = {True: (_MODS.formy.normal, _MODS.formy.normal_), 

1006 False: (self.wraplatlon, self.wraphilam), 

1007 None: (_passargs, _passargs)}.get(setting, ()) 

1008 if t: 

1009 self.latlon, self.philam = t 

1010 self._normal = setting 

1011 

1012 def latlonDMS2(self, lat, lon, **DMS2_kwds): 

1013 if isstr(lat) or isstr(lon): 

1014 kwds = _xkwds(DMS2_kwds, clipLon=0, clipLat=0) 

1015 lat, lon = _MODS.dms.parseDMS2(lat, lon, **kwds) 

1016 return self.latlon(lat, lon) 

1017 

1018# def normalatlon(self, *latlon): 

1019# return _MODS.formy.normal(*latlon) 

1020 

1021# def normalamphi(self, *philam): 

1022# return _MODS.formy.normal_(*philam) 

1023 

1024 def wraplatlon(self, lat, lon): 

1025 return wrap90(lat), wrap180(lon) 

1026 

1027 latlon = wraplatlon # default 

1028 

1029 def latlon3(self, lon1, lat2, lon2, wrap): 

1030 if wrap: 

1031 lat2, lon2 = self.latlon(lat2, lon2) 

1032 lon21, lon2 = unroll180(lon1, lon2) 

1033 else: 

1034 lon21 = lon2 - lon1 

1035 return lon21, lat2, lon2 

1036 

1037 def _latlonop(self, wrap): 

1038 if wrap and self._normal is not None: 

1039 return self.latlon 

1040 else: 

1041 return _passargs 

1042 

1043 def wraphilam(self, phi, lam): 

1044 return wrapPI_2(phi), wrapPI(lam) 

1045 

1046 philam = wraphilam # default 

1047 

1048 def philam3(self, lam1, phi2, lam2, wrap): 

1049 if wrap: 

1050 phi2, lam2 = self.philam(phi2, lam2) 

1051 lam21, lam2 = unrollPI(lam1, lam2) 

1052 else: 

1053 lam21 = lam2 - lam1 

1054 return lam21, phi2, lam2 

1055 

1056 def _philamop(self, wrap): 

1057 if wrap and self._normal is not None: 

1058 return self.philam 

1059 else: 

1060 return _passargs 

1061 

1062 def point(self, ll, wrap=True): # in .points._fractional, -.PointsIter.iterate, ... 

1063 '''Return C{ll} or a copy, I{normalized} or I{wrap}'d. 

1064 ''' 

1065 if wrap and self._normal is not None: 

1066 lat, lon = ll.latlon 

1067 if fabs(lon) > 180 or fabs(lat) > 90: 

1068 _n = self.latlon 

1069 ll = ll.copy(name=_n.__name__) 

1070 ll.latlon = _n(lat, lon) 

1071 return ll 

1072 

1073_Wrap = _Wrap() # PYCHOK singleton 

1074 

1075 

1076# def _wrap(angle, wrap, modulo): 

1077# '''(INTERNAL) Angle wrapper M{((wrap-modulo)..+wrap]}. 

1078# 

1079# @arg angle: Angle (C{degrees}, C{radians} or C{grades}). 

1080# @arg wrap: Range (C{degrees}, C{radians} or C{grades}). 

1081# @arg modulo: Upper limit (360 C{degrees}, PI2 C{radians} or 400 C{grades}). 

1082# 

1083# @return: The B{C{angle}}, wrapped (C{degrees}, C{radians} or C{grades}). 

1084# ''' 

1085# a = float(angle) 

1086# if not (wrap - modulo) <= a < wrap: 

1087# # math.fmod(-1.5, 3.14) == -1.5, but -1.5 % 3.14 == 1.64 

1088# # math.fmod(-1.5, 360) == -1.5, but -1.5 % 360 == 358.5 

1089# a %= modulo 

1090# if a > wrap: 

1091# a -= modulo 

1092# return a 

1093 

1094 

1095def wrap90(deg): 

1096 '''Wrap degrees to M{[-90..+90]}. 

1097 

1098 @arg deg: Angle (C{degrees}). 

1099 

1100 @return: Degrees, wrapped (C{degrees90}). 

1101 ''' 

1102 w = wrap180(deg) 

1103 return (w - _180_0) if w > 90 else ((w + _180_0) if w < -90 else w) 

1104 

1105 

1106def wrap180(deg): 

1107 '''Wrap degrees to M{[-180..+180]}. 

1108 

1109 @arg deg: Angle (C{degrees}). 

1110 

1111 @return: Degrees, wrapped (C{degrees180}). 

1112 ''' 

1113 d = float(deg) 

1114 w = _umod_360(d) 

1115 if w > 180: 

1116 w -= _360_0 

1117 elif d < 0 and w == 180: 

1118 w = -w 

1119 return w 

1120 

1121 

1122def wrap360(deg): # see .streprs._umod_360 

1123 '''Wrap degrees to M{[0..+360)}. 

1124 

1125 @arg deg: Angle (C{degrees}). 

1126 

1127 @return: Degrees, wrapped (C{degrees360}). 

1128 ''' 

1129 return _umod_360(float(deg)) 

1130 

1131 

1132def wrapPI(rad): 

1133 '''Wrap radians to M{[-PI..+PI]}. 

1134 

1135 @arg rad: Angle (C{radians}). 

1136 

1137 @return: Radians, wrapped (C{radiansPI}). 

1138 ''' 

1139 r = float(rad) 

1140 w = _umod_PI2(r) 

1141 if w > PI: 

1142 w -= PI2 

1143 elif r < 0 and w == PI: 

1144 w = -PI 

1145 return w 

1146 

1147 

1148def wrapPI2(rad): 

1149 '''Wrap radians to M{[0..+2PI)}. 

1150 

1151 @arg rad: Angle (C{radians}). 

1152 

1153 @return: Radians, wrapped (C{radiansPI2}). 

1154 ''' 

1155 return _umod_PI2(float(rad)) 

1156 

1157 

1158def wrapPI_2(rad): 

1159 '''Wrap radians to M{[-PI/2..+PI/2]}. 

1160 

1161 @arg rad: Angle (C{radians}). 

1162 

1163 @return: Radians, wrapped (C{radiansPI_2}). 

1164 ''' 

1165 w = wrapPI(rad) 

1166 return (w - PI) if w > PI_2 else ((w + PI) if w < (-PI_2) else w) 

1167 

1168 

1169# def wraplatlon(lat, lon): 

1170# '''Both C{wrap90(B{lat})} and C{wrap180(B{lon})}. 

1171# ''' 

1172# return wrap90(lat), wrap180(lon) 

1173 

1174 

1175def wrap_normal(*normal): 

1176 '''Define the operation for the keyword argument C{B{wrap}=True}, 

1177 across L{pygeodesy}: I{wrap}, I{normalize} or I{no-op}. For 

1178 backward compatibility, the default is I{wrap}. 

1179 

1180 @arg normal: If C{True}, I{normalize} lat- and longitude using 

1181 L{normal} or L{normal_}, if C{False}, I{wrap} the 

1182 lat- and longitude individually by L{wrap90} or 

1183 L{wrapPI_2} respectively L{wrap180}, L{wrapPI} or 

1184 if C{None}, leave lat- and longitude I{unchanged}. 

1185 Do not supply any value to get the current setting. 

1186 

1187 @return: The previous L{wrap_normal} setting (C{bool} or C{None}). 

1188 ''' 

1189 t = _Wrap.normal 

1190 if normal: 

1191 _Wrap.normal = normal[0] 

1192 return t 

1193 

1194 

1195# def wraphilam(phi, lam,): 

1196# '''Both C{wrapPI_2(B{phi})} and C{wrapPI(B{lam})}. 

1197# ''' 

1198# return wrapPI_2(phi), wrapPI(lam) 

1199 

1200 

1201def yard2m(yards): 

1202 '''Convert I{UK} yards to meter. 

1203 

1204 @arg yards: Value in yards (C{scalar}). 

1205 

1206 @return: Value in C{meter} (C{float}). 

1207 

1208 @raise ValueError: Invalid B{C{yards}}. 

1209 ''' 

1210 return Float(yards=yards) * _M_YARD_UK 

1211 

1212# **) MIT License 

1213# 

1214# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1215# 

1216# Permission is hereby granted, free of charge, to any person obtaining a 

1217# copy of this software and associated documentation files (the "Software"), 

1218# to deal in the Software without restriction, including without limitation 

1219# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1220# and/or sell copies of the Software, and to permit persons to whom the 

1221# Software is furnished to do so, subject to the following conditions: 

1222# 

1223# The above copyright notice and this permission notice shall be included 

1224# in all copies or substantial portions of the Software. 

1225# 

1226# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1227# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1228# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1229# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1230# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1231# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1232# OTHER DEALINGS IN THE SOFTWARE.