1

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

3

4 u'''(INTERNAL) Private spherical base classes C{CartesianSphericalBase} and

5 C{LatLonSphericalBase} for L{sphericalNvector} and L{sphericalTrigonometry}.

6

7 A pure Python implementation of geodetic (lat-/longitude) functions,

8 transcoded in part from JavaScript originals by I{(C) Chris Veness 2011-2016}

9 and published under the same MIT Licence**, see

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

11'''

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

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

14

15 from pygeodesy.basics import _copysign, isbool, isinstanceof, map1

16 from pygeodesy.cartesianBase import CartesianBase, Bearing2Tuple

17 from pygeodesy.constants import EPS, PI, PI2, PI_2, R_M, \

18 _umod_360, isnear0, isnon0, _over, \

19 _0_0, _0_5, _1_0, _180_0

20 from pygeodesy.datums import Datums, _spherical_datum

21 from pygeodesy.errors import IntersectionError, _ValueError, _xError

22 from pygeodesy.fmath import favg, fdot, hypot, sqrt_a

23 from pygeodesy.interns import NN, _COMMA_, _concentric_, _datum_, \

24 _distant_, _exceed_PI_radians_, _name_, \

25 _near_, _radius_, _too_

26 from pygeodesy.latlonBase import LatLonBase, _trilaterate5 # PYCHOK passed

27 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS

28# from pygeodesy.namedTuples import Bearing2Tuple # from .cartesianBase

29 from pygeodesy.nvectorBase import NvectorBase, Fmt, _xattrs

30 from pygeodesy.props import deprecated_method, property_doc_, \

31 property_RO, _update_all

32# from pygeodesy.streprs import Fmt, _xattrs # from .nvectorBase

33 from pygeodesy.units import Bearing, Bearing_, Radians_, Radius, \

34 Radius_, Scalar_

35 from pygeodesy.utily import acos1, atan2b, atan2d, degrees90, \

36 degrees180, sincos2, sincos2d, \

37 tanPI_2_2, _unrollon, wrap360, wrapPI

38

39 from math import cos, fabs, log, sin, sqrt

40

41__all__ = _ALL_LAZY.sphericalBase

42__version__ = '23.09.28'

43

44

45 def _angular(distance, radius, low=EPS): # PYCHOK in .spherical*

46 '''(INTERNAL) Return an angular distance in C{radians}.

47

48 @raise UnitError: Invalid B{C{distance}} or B{C{radius}}.

49 '''

50 r = float(distance)

51 if radius:

52 r = r / Radius_(radius=radius) # /= chokes PyChecker

53 if low is not None:

54 # small near0 values from .rhumbDestination not exact OK

55 r = _0_0 if low < 0 and low < r < 0 else Radians_(r, low=low)

56 return r

57

58

59 def _logPI_2_2(a2, a1):

60 '''(INTERNAL) C{log} of C{tanPI_2_2}'s quotient.

61 '''

62 return log(_over(tanPI_2_2(a2), tanPI_2_2(a1)))

63

64

65 def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry

66 '''(INTERNAL) Convert radii to radians.

67 '''

68 r1 = Radius_(rad1=rad1)

69 r2 = Radius_(rad2=rad2)

70 if radius is not None: # convert radii to radians

71 r1 = _angular(r1, radius)

72 r2 = _angular(r2, radius)

73

74 x = r1 < r2

75 if x:

76 r1, r2 = r2, r1

77 if r1 > PI:

78 raise IntersectionError(rad1=rad1, rad2=rad2,

79 txt=_exceed_PI_radians_)

80 return r1, r2, x

81

82

83 class CartesianSphericalBase(CartesianBase):

84 '''(INTERNAL) Base class for spherical C{Cartesian}s.

85 '''

86 _datum = Datums.Sphere # L{Datum}

87

88 def intersections2(self, rad1, other, rad2, radius=R_M):

89 '''Compute the intersection points of two circles each defined

90 by a center point and a radius.

91

92 @arg rad1: Radius of the this circle (C{meter} or C{radians},

93 see B{C{radius}}).

94 @arg other: Center of the other circle (C{Cartesian}).

95 @arg rad2: Radius of the other circle (C{meter} or C{radians},

96 see B{C{radius}}).

97 @kwarg radius: Mean earth radius (C{meter} or C{None} if both

98 B{C{rad1}} and B{C{rad2}} are given in C{radians}).

99

100 @return: 2-Tuple of the intersection points, each C{Cartesian}.

101 For abutting circles, the intersection points are the

102 same C{Cartesian} instance, aka the I{radical center}.

103

104 @raise IntersectionError: Concentric, antipodal, invalid or

105 non-intersecting circles.

106

107 @raise TypeError: If B{C{other}} is not C{Cartesian}.

108

109 @raise ValueError: Invalid B{C{rad1}}, B{C{rad2}} or B{C{radius}}.

110

111 @see: U{Calculating intersection of two Circles

112 <https://GIS.StackExchange.com/questions/48937/

113 calculating-intersection-of-two-circles>} and method

114 or function C{trilaterate3d2}.

115 '''

116 x1, x2 = self, self.others(other)

117 r1, r2, x = _rads3(rad1, rad2, radius)

118 if x:

119 x1, x2 = x2, x1

120 try:

121 n, q = x1.cross(x2), x1.dot(x2)

122 n2, q1 = n.length2, (_1_0 - q**2)

123 if n2 < EPS or isnear0(q1):

124 raise ValueError(_near_(_concentric_))

125 c1, c2 = cos(r1), cos(r2)

126 x0 = x1.times((c1 - q * c2) / q1).plus(

127 x2.times((c2 - q * c1) / q1))

128 n1 = _1_0 - x0.length2

129 if n1 < EPS:

130 raise ValueError(_too_(_distant_))

131 except ValueError as x:

132 raise IntersectionError(center=self, rad1=rad1,

133 other=other, rad2=rad2, cause=x)

134 n = n.times(sqrt(n1 / n2))

135 if n.length > EPS:

136 x1 = x0.plus(n)

137 x2 = x0.minus(n)

138 else: # abutting circles

139 x1 = x2 = x0

140

141 return (_xattrs(x1, self, _datum_, _name_),

142 _xattrs(x2, self, _datum_, _name_))

143

144

145 class LatLonSphericalBase(LatLonBase):

146 '''(INTERNAL) Base class for spherical C{LatLon}s.

147 '''

148 _datum = Datums.Sphere # spherical L{Datum}

149

150 def __init__(self, latlonh, lon=None, height=0, datum=None, wrap=False, name=NN):

151 '''Create a spherical C{LatLon} point frome the given lat-, longitude and

152 height on the given datum.

153

154 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or

155 a previous C{LatLon} instance provided C{B{lon}=None}.

156 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or

157 C(None), indicating B{C{latlonh}} is a C{LatLon}.

158 @kwarg height: Optional height above (or below) the earth surface (C{meter},

159 same units as the datum's ellipsoid axes or radius).

160 @kwarg datum: Optional, spherical datum to use (L{Datum}, L{Ellipsoid},

161 L{Ellipsoid2}, L{a_f2Tuple}) or earth radius in C{meter},

162 conventionally).

163 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}

164 (C{bool}).

165 @kwarg name: Optional name (string).

166

167 @raise TypeError: If B{C{latlonh}} is not a C{LatLon} or B{C{datum}} not

168 spherical.

169 '''

170 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, name=name)

171 if datum not in (None, self.datum):

172 self.datum = datum

173

174 def bearingTo2(self, other, wrap=False, raiser=False):

175 '''Return the initial and final bearing (forward and reverse

176 azimuth) from this to an other point.

177

178 @arg other: The other point (C{LatLon}).

179 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

180 B{C{other}} point (C{bool}).

181

182 @return: A L{Bearing2Tuple}C{(initial, final)}.

183

184 @raise TypeError: The B{C{other}} point is not spherical.

185

186 @see: Methods C{initialBearingTo} and C{finalBearingTo}.

187 '''

188 # .initialBearingTo is inside .-Nvector and .-Trigonometry

189 i = self.initialBearingTo(other, wrap=wrap, raiser=raiser) # PYCHOK .initialBearingTo

190 f = self.finalBearingTo( other, wrap=wrap, raiser=raiser)

191 return Bearing2Tuple(i, f, name=self.name)

192

193 @property_doc_(''' this point's datum (L{Datum}).''')

194 def datum(self):

195 '''Get this point's datum (L{Datum}).

196 '''

197 return self._datum

198

199 @datum.setter # PYCHOK setter!

200 def datum(self, datum):

201 '''Set this point's datum I{without conversion} (L{Datum}, L{Ellipsoid},

202 L{Ellipsoid2}, L{a_f2Tuple}) or C{scalar} spherical earth radius).

203

204 @raise TypeError: If B{C{datum}} invalid or not not spherical.

205 '''

206 d = _spherical_datum(datum, name=self.name, raiser=_datum_)

207 if self._datum != d:

208 _update_all(self)

209 self._datum = d

210

211 def finalBearingTo(self, other, wrap=False, raiser=False):

212 '''Return the final bearing (reverse azimuth) from this to

213 an other point.

214

215 @arg other: The other point (spherical C{LatLon}).

216 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

217 the B{C{other}} point (C{bool}).

218

219 @return: Final bearing (compass C{degrees360}).

220

221 @raise TypeError: The B{C{other}} point is not spherical.

222

223 @example:

224

225 >>> p = LatLon(52.205, 0.119)

226 >>> q = LatLon(48.857, 2.351)

227 >>> b = p.finalBearingTo(q) # 157.9

228 '''

229 p = self.others(other)

230 if wrap:

231 p = _unrollon(self, p, wrap=wrap)

232 # final bearing is the reverse of the other, initial one;

233 # .initialBearingTo is inside .-Nvector and .-Trigonometry

234 b = p.initialBearingTo(self, wrap=False, raiser=raiser)

235 return _umod_360(b + _180_0)

236

237 def intersecant2(self, circle, point, bearing, radius=R_M, exact=False,

238 height=None, wrap=False): # was=True

239 '''Compute the intersections of a circle and a line.

240

241 @arg circle: Radius of the circle centered at this location

242 (C{meter}, same units as B{C{radius}}) or a point

243 on the circle (this C{LatLon}).

244 @arg point: An other point in- or outside the circle (this C{LatLon}).

245 @arg bearing: Bearing at the B{C{point}} (compass C{degrees360})

246 or a second point on the line (this C{LatLon}).

247 @kwarg radius: Mean earth radius (C{meter}, conventionally).

248 @kwarg exact: If C{True} use the I{exact} rhumb methods for azimuth,

249 destination and distance, if C{False} use the basic

250 rhumb methods (C{bool}) or if C{None} use the I{great

251 circle} methods.

252 @kwarg height: Optional height for the intersection points (C{meter},

253 conventionally) or C{None}.

254 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

255 B{C{point}}, B{C{circle}} and/or B{C{bearing}} (C{bool}).

256

257 @return: 2-Tuple of the intersection points (representing a chord),

258 each an instance of this class. For a tangent line, both

259 points are the same instance, the B{C{point}} or wrapped

260 or I{normalized}.

261

262 @raise IntersectionError: The circle and line do not intersect.

263

264 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}

265 or B{C{bearing}} invalid.

266

267 @raise ValueError: Invalid B{C{circle}}, B{C{bearing}}, B{C{radius}},

268 B{C{exact}} or B{C{height}}.

269 '''

270 p = self.others(point=point)

271 try:

272 return _intersecant2(self, circle, p, bearing, radius=radius, exact=exact,

273 height=height, wrap=wrap)

274 except (TypeError, ValueError) as x:

275 raise _xError(x, center=self, circle=circle, point=point, bearing=bearing,

276 exact=exact, wrap=wrap)

277

278 def maxLat(self, bearing):

279 '''Return the maximum latitude reached when travelling

280 on a great circle on given bearing from this point

281 based on Clairaut's formula.

282

283 The maximum latitude is independent of longitude

284 and the same for all points on a given latitude.

285

286 Negate the result for the minimum latitude (on the

287 Southern hemisphere).

288

289 @arg bearing: Initial bearing (compass C{degrees360}).

290

291 @return: Maximum latitude (C{degrees90}).

292

293 @raise ValueError: Invalid B{C{bearing}}.

294 '''

295 m = acos1(fabs(sin(Bearing_(bearing)) * cos(self.phi)))

296 return degrees90(m)

297

298 def minLat(self, bearing):

299 '''Return the minimum latitude reached when travelling

300 on a great circle on given bearing from this point.

301

302 @arg bearing: Initial bearing (compass C{degrees360}).

303

304 @return: Minimum latitude (C{degrees90}).

305

306 @see: Method L{maxLat} for more details.

307

308 @raise ValueError: Invalid B{C{bearing}}.

309 '''

310 return -self.maxLat(bearing)

311

312 def parse(self, strllh, height=0, sep=_COMMA_, name=NN):

313 '''Parse a string representing a similar, spherical C{LatLon}

314 point, consisting of C{"lat, lon[, height]"}.

315

316 @arg strllh: Lat, lon and optional height (C{str}),

317 see function L{pygeodesy.parse3llh}.

318 @kwarg height: Optional, default height (C{meter}).

319 @kwarg sep: Optional separator (C{str}).

320 @kwarg name: Optional instance name (C{str}),

321 overriding this name.

322

323 @return: The similar point (spherical C{LatLon}).

324

325 @raise ParseError: Invalid B{C{strllh}}.

326 '''

327 t = _MODS.dms.parse3llh(strllh, height=height, sep=sep)

328 r = self.classof(*t)

329 if name:

330 r.rename(name)

331 return r

332

333 @property_RO

334 def _radius(self):

335 '''(INTERNAL) Get this sphere's radius.

336 '''

337 return self.datum.ellipsoid.equatoradius

338

339 def _rhumbs3(self, other, wrap, r=False): # != .latlonBase._rhumbx3

340 '''(INTERNAL) Rhumb_ helper function.

341

342 @arg other: The other point (spherical C{LatLon}).

343 '''

344 p = self.others(other, up=2)

345 if wrap:

346 p = _unrollon(self, p, wrap=wrap)

347 a2, b2 = p.philam

348 a1, b1 = self.philam

349 # if |db| > 180 take shorter rhumb

350 # line across the anti-meridian

351 db = wrapPI(b2 - b1)

352 dp = _logPI_2_2(a2, a1)

353 da = a2 - a1

354 if r:

355 # on Mercator projection, longitude distances shrink

356 # by latitude; the 'stretch factor' q becomes ill-

357 # conditioned along E-W line (0/0); use an empirical

358 # tolerance to avoid it

359 q = (da / dp) if fabs(dp) > EPS else cos(a1)

360 da = hypot(da, q * db) # angular distance radians

361 return da, db, dp

362

363 def rhumbAzimuthTo(self, other, radius=R_M, exact=False, wrap=False):

364 '''Return the azimuth (bearing) of a rhumb line (loxodrome)

365 between this and an other (spherical) point.

366

367 @arg other: The other point (spherical C{LatLon}).

368 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},

369 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).

370 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),

371 default C{False} for backward compatibility.

372 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

373 B{C{other}} point (C{bool}).

374

375 @return: Rhumb line azimuth (compass C{degrees180}).

376

377 @raise TypeError: The B{C{other}} point is incompatible or

378 B{C{radius}} is invalid.

379

380 @example:

381

382 >>> p = LatLon(51.127, 1.338)

383 >>> q = LatLon(50.964, 1.853)

384 >>> b = p.rhumbBearingTo(q) # 116.7

385 '''

386 if exact: # use series, always

387 z = LatLonBase.rhumbAzimuthTo(self, other, exact=False, # Krüger

388 radius=radius, wrap=wrap)

389 else:

390 _, db, dp = self._rhumbs3(other, wrap)

391 z = atan2d(db, dp) # see .rhumbx.Rhumb.Inverse

392 return z

393

394 @deprecated_method

395 def rhumbBearingTo(self, other): # unwrapped

396 '''DEPRECATED, use method C{.rhumbAzimuthTo}.'''

397 return wrap360(self.rhumbAzimuthTo(other)) # [0..360)

398

399 def rhumbDestination(self, distance, bearing, radius=R_M, height=None, exact=False):

400 '''Return the destination point having travelled the given distance

401 from this point along a rhumb line (loxodrome) at the given bearing.

402

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

404 may be negative if C{B{exact}=True}.

405 @arg bearing: Bearing (azimuth) at this point (compass C{degrees360}).

406 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},

407 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if

408 C{B{exact}=True}.

409 @kwarg height: Optional height, overriding the default height

410 (C{meter}, same unit as B{C{radius}}).

411 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),

412 default C{False} for backward compatibility.

413

414 @return: The destination point (spherical C{LatLon}).

415

416 @raise ValueError: Invalid B{C{distance}}, B{C{bearing}},

417 B{C{radius}} or B{C{height}}.

418

419 @example:

420

421 >>> p = LatLon(51.127, 1.338)

422 >>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E

423 '''

424 if exact: # use series, always

425 r = LatLonBase.rhumbDestination(self, distance, bearing, exact=False, # Krüger

426 radius=radius, height=height)

427 else: # radius=None from .rhumbMidpointTo

428 if radius in (None, self._radius):

429 d, r = self.datum, radius

430 else:

431 d = _spherical_datum(radius, raiser=_radius_) # spherical only

432 r = d.ellipsoid.equatoradius

433 r = _angular(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo

434

435 a1, b1 = self.philam

436 sb, cb = sincos2(Bearing_(bearing))

437

438 da = r * cb

439 a2 = a1 + da

440 # normalize latitude if past pole

441 if fabs(a2) > PI_2:

442 a2 = _copysign(PI, a2) - a2

443

444 dp = _logPI_2_2(a2, a1)

445 # q becomes ill-conditioned on E-W course 0/0

446 q = (da / dp) if fabs(dp) > EPS else cos(a1)

447 b2 = (b1 + r * sb / q) if fabs(q) > EPS else b1

448

449 h = self._heigHt(height)

450 r = self.classof(degrees90(a2), degrees180(b2), datum=d, height=h)

451 return r

452

453 def rhumbDistanceTo(self, other, radius=R_M, exact=False, wrap=False):

454 '''Return the distance from this to an other point along

455 a rhumb line (loxodrome).

456

457 @arg other: The other point (spherical C{LatLon}).

458 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},

459 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if

460 C{B{exact}=True}.

461 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),

462 default C{False} for backward compatibility.

463 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

464 B{C{other}} point (C{bool}).

465

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

467 or C{radians} if B{C{radius}} is C{None}).

468

469 @raise TypeError: The B{C{other}} point is incompatible.

470

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

472

473 @example:

474

475 >>> p = LatLon(51.127, 1.338)

476 >>> q = LatLon(50.964, 1.853)

477 >>> d = p.rhumbDistanceTo(q) # 403100

478 '''

479 if exact: # use series, always

480 r = LatLonBase.rhumbDistanceTo(self, other, exact=False, # Krüger

481 radius=radius, wrap=wrap)

482 if radius is None: # angular distance in radians

483 r = r / self._radius # /= chokes PyChecker

484 else:

485 # see <https://www.EdWilliams.org/avform.htm#Rhumb>

486 r, _, _ = self._rhumbs3(other, wrap, r=True)

487 if radius is not None:

488 r *= Radius(radius)

489 return r

490

491 def rhumbMidpointTo(self, other, height=None, radius=R_M, exact=False,

492 fraction=_0_5, wrap=False):

493 '''Return the (loxodromic) midpoint on the rhumb line between

494 this and an other point.

495

496 @arg other: The other point (spherical LatLon).

497 @kwarg height: Optional height, overriding the mean height

498 (C{meter}).

499 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},

500 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).

501 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),

502 default C{False} for backward compatibility.

503 @kwarg fraction: Midpoint location from this point (C{scalar}),

504 may be negative if C{B{exact}=True}.

505 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

506 B{C{other}} point (C{bool}).

507

508 @return: The (mid)point at the given B{C{fraction}} along

509 the rhumb line (spherical C{LatLon}).

510

511 @raise TypeError: The B{C{other}} point is incompatible.

512

513 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}

514

515 @example:

516

517 >>> p = LatLon(51.127, 1.338)

518 >>> q = LatLon(50.964, 1.853)

519 >>> m = p.rhumb_midpointTo(q)

520 >>> m.toStr() # '51.0455°N, 001.5957°E'

521 '''

522 if exact: # use series, always

523 r = LatLonBase.rhumbMidpointTo(self, other, exact=False, # Krüger

524 radius=radius, height=height,

525 fraction=fraction, wrap=wrap)

526 elif fraction is not _0_5:

527 f = Scalar_(fraction=fraction) # low=_0_0

528 r, db, dp = self._rhumbs3(other, wrap, r=True) # radians

529 z = atan2b(db, dp)

530 h = self._havg(other, f=f, h=height)

531 r = self.rhumbDestination(r * f, z, radius=None, height=h)

532

533 else: # for backward compatibility, unwrapped

534 # see <https://MathForum.org/library/drmath/view/51822.html>

535 a1, b1 = self.philam

536 a2, b2 = self.others(other).philam

537

538 if fabs(b2 - b1) > PI:

539 b1 += PI2 # crossing anti-meridian

540

541 a3 = favg(a1, a2)

542 b3 = favg(b1, b2)

543

544 f1 = tanPI_2_2(a1)

545 if isnon0(f1):

546 f2 = tanPI_2_2(a2)

547 f = f2 / f1

548 if isnon0(f):

549 f = log(f)

550 if isnon0(f):

551 f3 = tanPI_2_2(a3)

552 b3 = fdot(map1(log, f1, f2, f3),

553 -b2, b1, b2 - b1) / f

554

555 d = self.datum if radius in (None, self._radius) else \

556 _spherical_datum(radius, name=self.name, raiser=_radius_)

557 h = self._havg(other, h=height)

558 r = self.classof(degrees90(a3), degrees180(b3), datum=d, height=h)

559 return r

560

561 def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature

562 '''Convert this point to C{Nvector} components, I{including

563 height}.

564

565 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}}

566 keyword arguments, ignored if

567 C{B{Nvector} is None}.

568

569 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}

570 if B{C{Nvector}} is C{None}.

571

572 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.

573 '''

574 return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds)

575

576

577 def _intersecant2(c, r, p, b, radius=R_M, exact=False,

578 height=None, wrap=False):

579 # (INTERNAL) Intersect a circle and bearing, see L{intersecant2}

580 # above, separated to allow callers to embellish any exceptions

581

582 if wrap:

583 p = _unrollon(c, p, wrap=wrap)

584 nonexact = exact is None

585

586 if not isinstanceof(r, c.__class__, p.__class__):

587 r = Radius_(circle=r)

588 elif nonexact:

589 r = c.distanceTo(r, radius=radius, wrap=wrap)

590 elif isbool(exact):

591 r = c.rhumbDistanceTo(r, radius=radius, exact=exact, wrap=wrap)

592 else:

593 raise _ValueError(exact=exact)

594

595 if not isinstanceof(b, c.__class__, p.__class__):

596 b = Bearing(b)

597 elif nonexact:

598 b = p.initialBearingTo(b, wrap=wrap)

599 else:

600 b = p.rhumbAzimuthTo(b, radius=radius, exact=exact, wrap=wrap)

601

602 d = p.distanceTo(c, radius=radius) if nonexact else \

603 p.rhumbDistanceTo(c, radius=radius, exact=exact)

604 if d > EPS:

605 a = p.initialBearingTo(c) if nonexact else wrap360(

606 p.rhumbAzimuthTo(c, radius=radius, exact=exact))

607 s, c = sincos2d(b - a)

608 s = sqrt_a(r, fabs(s * d))

609 if s > r:

610 raise IntersectionError(_too_(Fmt.distant(s)))

611 elif (r - s) < EPS:

612 return p, p # tangent

613 c *= d

614 else: # p and c coincide

615 s, c = r, 0

616 t = ()

617 for d, b in ((s + c, b), (s - c, b + _180_0)): # bearing direction first

618 t += (p.destination(d, b, radius=radius, height=height) if nonexact else

619 p.rhumbDestination(d, b, radius=radius, height=height, exact=exact)),

620 return t

621

622

623 def _r2m(r, radius):

624 '''(INTERNAL) Angular distance in C{radians} to C{meter}.

625 '''

626 if radius is not None: # not in (None, _0_0)

627 r *= R_M if radius is R_M else Radius(radius)

628 return r

629

630

631__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)

632

633# **) MIT License

634#

635# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

636#

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

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

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

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

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

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

643#

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

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

646#

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

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

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

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

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

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

653# OTHER DEALINGS IN THE SOFTWARE.