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, EPS0, PI, PI2, PI_2, R_M, \

18 _0_0, _0_5, _1_0, _180_0, _360_0, \

19 _over, isnear0, isnon0

20 from pygeodesy.datums import Datums, _earth_ellipsoid, _spherical_datum

21 from pygeodesy.errors import IntersectionError, _ValueError, \

22 _xattr, _xError

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

24 from pygeodesy.interns import _COMMA_, _concentric_, _datum_, _distant_, \

25 _exceed_PI_radians_, _name_, _near_, \

26 _radius_, _too_

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

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

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

30 from pygeodesy.nvectorBase import NvectorBase, Fmt, _xattrs

31 from pygeodesy.props import deprecated_method, property_doc_, property_RO, \

32 _update_all

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

34 from pygeodesy.units import Bearing, Bearing_, _isRadius, Radians_, Radius, \

35 Radius_, Scalar_, _100km

36 from pygeodesy.utily import acos1, asin1, atan2b, atan2d, degrees90, \

37 degrees180, sincos2, sincos2d, _unrollon, \

38 tanPI_2_2, wrapPI

39

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

41

42__all__ = _ALL_LAZY.sphericalBase

43__version__ = '24.06.06'

44

45

46 class CartesianSphericalBase(CartesianBase):

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

48 '''

49 _datum = Datums.Sphere # L{Datum}

50

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

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

53 by a center point and a radius.

54

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

56 see B{C{radius}}).

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

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

59 see B{C{radius}}).

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

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

62

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

64 For abutting circles, the intersection points are the

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

66

67 @raise IntersectionError: Concentric, antipodal, invalid or

68 non-intersecting circles.

69

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

71

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

73

74 @see: U{Calculating intersection of two Circles

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

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

77 or function C{trilaterate3d2}.

78 '''

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

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

81 if x:

82 x1, x2 = x2, x1

83 try:

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

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

86 if n2 < EPS or isnear0(q1):

87 raise ValueError(_near_(_concentric_))

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

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

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

91 n1 = _1_0 - x0.length2

92 if n1 < EPS:

93 raise ValueError(_too_(_distant_))

94 except ValueError as x:

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

96 other=other, rad2=rad2, cause=x)

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

98 if n.length > EPS:

99 x1 = x0.plus(n)

100 x2 = x0.minus(n)

101 else: # abutting circles

102 x1 = x2 = x0

103

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

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

106

107 @property_RO

108 def sphericalCartesian(self):

109 '''Get this C{Cartesian}'s spherical class.

110 '''

111 return type(self)

112

113

114 class LatLonSphericalBase(LatLonBase):

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

116 '''

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

118 _napieradius = _100km

119

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

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

122 height on the given datum.

123

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

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

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

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

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

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

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

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

132 conventionally).

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

134 (C{bool}).

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

136

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

138 spherical.

139 '''

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

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

142 self.datum = datum

143

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

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

146 azimuth) from this to an other point.

147

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

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

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

151

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

153

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

155

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

157 '''

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

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

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

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

162

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

164 def datum(self):

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

166 '''

167 return self._datum

168

169 @datum.setter # PYCHOK setter!

170 def datum(self, datum):

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

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

173

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

175 '''

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

177 if self._datum != d:

178 _update_all(self)

179 self._datum = d

180

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

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

183 an other point.

184

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

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

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

188

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

190

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

192 '''

193 p = self.others(other)

194 if wrap:

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

196 # final bearing is the reverse of the other, initial one

197 b = p.initialBearingTo(self, wrap=False, raiser=raiser) + _180_0

198 return b if b < 360 else (b - _360_0)

199

200 def intersecant2(self, circle, point, other, radius=R_M, exact=False, # PYCHOK signature

201 height=None, wrap=False):

202 '''Compute the intersections of a circle and a (great circle) line

203 given as two points or as a point and bearing.

204

205 @arg circle: Radius of the circle centered at this location (C{meter},

206 same units as B{C{radius}}) or a point on the circle

207 (this C{LatLon}).

208 @arg point: A point on the (great circle) line (this C{LatLon}).

209 @arg other: An other point I{on} (this {LatLon}) or the bearing at

210 B{C{point}} I{of} the (great circle) line (compass

211 C{degrees}).

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

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

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

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

216 circle} methods.

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

218 conventionally) or C{None} for interpolated heights.

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

220 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).

221

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

223 an instance of the B{C{point}} class. Both points are the same

224 instance if the (great circle) line is tangent to the circle.

225

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

227

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

229 or B{C{other}} invalid.

230

231 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},

232 B{C{exact}}, B{C{height}} or B{C{napieradius}}.

233 '''

234 p = self.others(point=point)

235 try:

236 return _intersecant2(self, circle, p, other, radius=radius, exact=exact,

237 height=height, wrap=wrap)

238 except (TypeError, ValueError) as x:

239 raise _xError(x, center=self, circle=circle, point=point, other=other,

240 radius=radius, exact=exact, height=height, wrap=wrap)

241

242 def maxLat(self, bearing):

243 '''Return the maximum latitude reached when travelling on a great circle

244 on given bearing from this point based on Clairaut's formula.

245

246 The maximum latitude is independent of longitude and the same for all

247 points on a given latitude.

248

249 Negate the result for the minimum latitude (on the Southern hemisphere).

250

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

252

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

254

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

256 '''

257 r = acos1(fabs(sin(Bearing_(bearing)) * cos(self.phi)))

258 return degrees90(r)

259

260 def minLat(self, bearing):

261 '''Return the minimum latitude reached when travelling on a great circle

262 on given bearing from this point.

263

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

265

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

267

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

269

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

271 '''

272 return -self.maxLat(bearing)

273

274 def _mpr(self, radius=R_M, exact=None): # meter per radian

275 if exact and not _isRadius(radius): # see .rhumb.ekx.Rhumb._mpr

276 radius = _earth_ellipsoid(radius)._Lpr

277 return radius

278

279 @property_doc_(''' the I{Napier} radius to apply spherical trigonometry.''')

280 def napieradius(self):

281 '''Get the I{Napier} radius (C{meter}, conventionally).

282 '''

283 return self._napieradius

284

285 @napieradius.setter # PYCHOK setter!

286 def napieradius(self, radius):

287 '''Set this I{Napier} radius (C{meter}, conventionally) or C{0}.

288

289 In methods L{intersecant2} and L{rhumbIntersecant2}, I{Napier}'s

290 spherical trigonometry is applied if the circle radius exceeds

291 the I{Napier} radius, otherwise planar trigonometry is used.

292

293 @raise UnitError: Invalid B{C{radius}}.

294 '''

295 self._napieradius = Radius(napieradius=radius or 0)

296

297# def nearestTo(self, point, other, **radius_exact_height_wrap): # PYCHOK signature

298# p = self.others(point=point)

299# try:

300# p, q = _intersecant2(self, p, p, other, **radius_exact_height_wrap)

301# except (TypeError, ValueError) as x:

302# raise _xError(x, this=self, point=point, other=other, **radius_exact_height_wrap)

303# return p.midpointTo(q)

304

305 def parse(self, strllh, height=0, sep=_COMMA_, **name):

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

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

308

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

310 L{pygeodesy.parse3llh}.

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

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

313 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.

314

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

316

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

318 '''

319 llh = _MODS.dms.parse3llh(strllh, height=height, sep=sep)

320 return self.classof(*llh, **name)

321

322 @property_RO

323 def _radius(self):

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

325 '''

326 return self.datum.ellipsoid.equatoradius

327

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

329 '''(INTERNAL) Rhumb_ helper function.

330

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

332 '''

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

334 if wrap:

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

336 a2, b2 = p.philam

337 a1, b1 = self.philam

338 # if |db| > 180 take shorter rhumb

339 # line across the anti-meridian

340 db = wrapPI(b2 - b1)

341 dp = _logPI_2_2(a2, a1)

342 da = a2 - a1

343 if r:

344 # on Mercator projection, longitude distances shrink

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

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

347 # tolerance to avoid it

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

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

350 return da, db, dp

351

352 def rhumbAzimuthTo(self, other, radius=R_M, exact=False, wrap=False, b360=False):

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

354 this and an other (spherical) point.

355

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

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

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

359 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),

360 default C{False} for backward compatibility.

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

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

363 @kwarg b360: If C{True}, return the azimuth in the bearing range.

364

365 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).

366

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

368 B{C{radius}} is invalid.

369 '''

370 if exact: # use series, always

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

372 radius=radius, wrap=wrap, b360=b360)

373 else:

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

375 z = (atan2b if b360 else atan2d)(db, dp) # see .rhumbBase.RhumbBase.Inverse

376 return z

377

378 @deprecated_method

379 def rhumbBearingTo(self, other): # unwrapped

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

381 return self.rhumbAzimuthTo(other, b360=True) # [0..360)

382

383 def rhumbDestination(self, distance, azimuth, radius=R_M, height=None,

384 exact=False, **name):

385 '''Return the destination point having travelled the given distance from

386 this point along a rhumb line (loxodrome) of the given azimuth.

387

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

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

390 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).

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

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

393 C{B{exact}=True}.

394 @kwarg height: Optional height, overriding the default height (C{meter}.

395 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),

396 default C{False} for backward compatibility.

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

398

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

400

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

402 or B{C{height}}.

403 '''

404 if exact: # use series, always

405 r = LatLonBase.rhumbDestination(self, distance, azimuth, exact=False, # Krüger

406 radius=radius, height=height, **name)

407 else: # radius=None from .rhumbMidpointTo

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

409 d, r = self.datum, radius

410 else:

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

412 r = d.ellipsoid.equatoradius

413 r = _m2radians(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo

414

415 a1, b1 = self.philam

416 sb, cb = sincos2(Bearing_(azimuth)) # radians

417

418 da = r * cb

419 a2 = a1 + da

420 # normalize latitude if past pole

421 if fabs(a2) > PI_2:

422 a2 = _copysign(PI, a2) - a2

423

424 dp = _logPI_2_2(a2, a1)

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

426 q = cos(a1) if isnear0(dp) else (da / dp)

427 b2 = b1 if isnear0(q) else (b1 + r * sb / q)

428

429 h = self._heigHt(height)

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

431 return r

432

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

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

435 a rhumb line (loxodrome).

436

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

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

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

440 C{B{exact}=True}.

441 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),

442 default C{False} for backward compatibility.

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

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

445

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

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

448

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

450

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

452 '''

453 if exact: # use series, always

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

455 radius=radius, wrap=wrap)

456 if radius is None: # angular distance in radians

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

458 else:

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

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

461 if radius is not None:

462 r *= Radius(radius)

463 return r

464

465 def rhumbIntersecant2(self, circle, point, other, radius=R_M, exact=True, # PYCHOK signature

466 height=None, wrap=False):

467 '''Compute the intersections of a circle and a rhumb line given as two

468 points and as a point and azimuth.

469

470 @arg circle: Radius of the circle centered at this location (C{meter},

471 same units as B{C{radius}}) or a point on the circle

472 (this C{LatLon}).

473 @arg point: The rhumb line's start point (this C{LatLon}).

474 @arg other: An other point (this I{on} C{LatLon}) or the azimuth I{of}

475 (compass C{degrees}) the rhumb line.

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

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

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

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

480 circle} methods.

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

482 conventionally) or C{None}.

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

484 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).

485

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

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

488 points are the same instance, wrapped or I{normalized}.

489

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

491

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

493 or B{C{other}} invalid.

494

495 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},

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

497 '''

498 m = LatLonBase.rhumbIntersecant2 if exact else \

499 LatLonSphericalBase.intersecant2

500 return m(self, circle, point, other, radius=radius, exact=exact,

501 height=height, wrap=wrap)

502

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

504 fraction=_0_5, **wrap_name):

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

506 this and an other point.

507

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

509 @kwarg height: Optional height, overriding the mean height (C{meter}).

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

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

512 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),

513 default C{False} for backward compatibility.

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

515 be negative if C{B{exact}=True}.

516 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword

517 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}

518 and unroll the B{C{other}} point (C{bool}).

519

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

521 line (spherical C{LatLon}).

522

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

524

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

526 '''

527 if exact: # use series, always

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

529 radius=radius, height=height,

530 fraction=fraction, **wrap_name)

531 elif fraction is not _0_5:

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

533 w, n = self._wrap_name2(**wrap_name)

534 r, db, dp = self._rhumbs3(other, w, r=True) # radians

535 z = atan2b(db, dp)

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

537 r = self.rhumbDestination(r * f, z, radius=None, height=h, name=n)

538

539 else: # for backward compatibility, unwrapped

540 _, n = self._wrap_name2(**wrap_name)

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

542 a1, b1 = self.philam

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

544 _, n = self._wrap_name2(**wrap_name)

545

546 if fabs(b2 - b1) > PI:

547 b1 += PI2 # crossing anti-meridian

548

549 a3 = favg(a1, a2)

550 b3 = favg(b1, b2)

551

552 f1 = tanPI_2_2(a1)

553 if isnon0(f1):

554 f2 = tanPI_2_2(a2)

555 f = f2 / f1

556 if isnon0(f):

557 f = log(f)

558 if isnon0(f):

559 f3 = tanPI_2_2(a3)

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

561 -b2, b1, b2 - b1) / f

562

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

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

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

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

567 return r

568

569 @property_RO

570 def sphericalLatLon(self):

571 '''Get this C{LatLon}'s spherical class.

572 '''

573 return type(self)

574

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

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

577 height}.

578

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

580 keyword arguments, ignored if

581 C{B{Nvector} is None}.

582

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

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

585

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

587 '''

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

589

590

591 def _intersecant2(c, r, p, b, radius=R_M, exact=False, height=None, wrap=False):

592 # (INTERNAL) Intersect a circle and line, see L{intersecant2}

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

594

595 if wrap:

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

597 nonexact = exact is None

598

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

600 r = Radius_(circle=r)

601 elif nonexact:

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

603 elif isbool(exact):

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

605 else:

606 raise _ValueError(exact=exact)

607

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

609 b = Bearing(b)

610 elif nonexact:

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

612 else:

613 b = p.rhumbAzimuthTo(b, radius=radius, exact=exact, wrap=wrap,

614 b360=True)

615

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

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

618 if d > EPS0:

619 n = _xattr(c, napieradius=0)

620 a = p.initialBearingTo(c) if nonexact else \

621 p.rhumbAzimuthTo(c, radius=radius, exact=exact, b360=True)

622 s, c = sincos2d(b - a) # Napier's sin(A), cos(A)

623 if r > n:

624 # Napier's right spherical triangle rules (R2) and (R1)

625 # <https://WikiPedia.org/wiki/Spherical_trigonometry>

626 m = p._mpr(radius=radius, exact=exact) # meter per radian

627 if fabs(c) > EPS0:

628 d = d / m # /= chokes PyChecker

629 a = asin1(sin(d) * fabs(s)) # Napier's a

630 c = _copysign(cos(a), c)

631 d = acos1(cos(d) / c) * m

632 a *= m # meter

633 else: # point and chord center coincident

634 a, d = d, 0

635 c = cos(a / m)

636 h = (acos1(cos(r / m) / c) * m) if a < r else 0

637 else: # distance from the chord center to ...

638 a = fabs(d * s) # ... the cicle center ...

639 d *= c # ... and to the point

640 h = sqrt_a(r, a) if a < r else 0 # half chord length

641 if a > r:

642 raise IntersectionError(_too_(Fmt.distant(a)))

643 else:

644 d, h = 0, r # point and circle center coincident

645

646 _intersecant1, kwds = (p.destination, {}) if nonexact else \

647 (p.rhumbDestination, dict(exact=exact))

648 kwds.update(radius=radius, height=height)

649 t = (_intersecant1(d + h, b, **kwds),)

650 if h:

651 t += (_intersecant1(d - h, b, **kwds),)

652 else: # same instance twice

653 t *= 2

654 return t

655

656

657 def _logPI_2_2(a2, a1):

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

659 '''

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

661

662

663 def _m2radians(distance, radius, low=EPS): # PYCHOK in .spherical*

664 '''(INTERNAL) Distance in C{meter} to angular distance in C{radians}.

665

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

667 '''

668 r = float(distance)

669 if radius:

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

671 if low is not None:

672 # small near0 values from .rhumbDestination not exact OK

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

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

675 return r

676

677

678 def _radians2m(rad, radius):

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

680 '''

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

682 rad *= R_M if radius is R_M else Radius(radius)

683 return rad

684

685

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

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

688 '''

689 r1 = Radius_(rad1=rad1)

690 r2 = Radius_(rad2=rad2)

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

692 r1 = _m2radians(r1, radius)

693 r2 = _m2radians(r2, radius)

694

695 x = r1 < r2

696 if x:

697 r1, r2 = r2, r1

698 if r1 > PI:

699 raise IntersectionError(rad1=rad1, rad2=rad2,

700 txt=_exceed_PI_radians_)

701 return r1, r2, x

702

703

704__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)

705

706# **) MIT License

707#

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

709#

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

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

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

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

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

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

716#

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

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

719#

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

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

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

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

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

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

726# OTHER DEALINGS IN THE SOFTWARE.