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, isscalar, 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 NN, _COMMA_, _concentric_, _datum_, \

25 _distant_, _exceed_PI_radians_, _name_, \

26 _near_, _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_, \

32 property_RO, _update_all

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

34 from pygeodesy.units import Bearing, Bearing_, 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__ = '23.12.01'

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=NN):

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 name (string).

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=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 @example:

194

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

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

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

198 '''

199 p = self.others(other)

200 if wrap:

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

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

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

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

205

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

207 height=None, wrap=False):

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

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

210

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

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

213 (this C{LatLon}).

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

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

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

217 C{degrees}).

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

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

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

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

222 circle} methods.

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

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

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

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

227

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

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

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

231

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

233

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

235 or B{C{other}} invalid.

236

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

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

239 '''

240 p = self.others(point=point)

241 try:

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

243 height=height, wrap=wrap)

244 except (TypeError, ValueError) as x:

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

246 radius=radius, exact=exact, height=height, wrap=wrap)

247

248 def maxLat(self, bearing):

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

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

251

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

253 points on a given latitude.

254

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

256

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

258

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

260

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

262 '''

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

264 return degrees90(r)

265

266 def minLat(self, bearing):

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

268 on given bearing from this point.

269

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

271

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

273

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

275

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

277 '''

278 return -self.maxLat(bearing)

279

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

281 if exact and not isscalar(radius): # see .rhumb.ekx.Rhumb._mpr

282 radius = _earth_ellipsoid(radius)._Lpr

283 return radius

284

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

286 def napieradius(self):

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

288 '''

289 return self._napieradius

290

291 @napieradius.setter # PYCHOK setter!

292 def napieradius(self, radius):

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

294

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

296 spherical trigonometry is applied if the circle radius exceeds

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

298

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

300 '''

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

302

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

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

305# try:

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

307# except (TypeError, ValueError) as x:

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

309# return p.midpointTo(q)

310

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

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

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

314

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

316 see function L{pygeodesy.parse3llh}.

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

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

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

320 overriding this name.

321

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

323

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

325 '''

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

327 r = self.classof(*t)

328 if name:

329 r.rename(name)

330 return r

331

332 @property_RO

333 def _radius(self):

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

335 '''

336 return self.datum.ellipsoid.equatoradius

337

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

339 '''(INTERNAL) Rhumb_ helper function.

340

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

342 '''

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

344 if wrap:

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

346 a2, b2 = p.philam

347 a1, b1 = self.philam

348 # if |db| > 180 take shorter rhumb

349 # line across the anti-meridian

350 db = wrapPI(b2 - b1)

351 dp = _logPI_2_2(a2, a1)

352 da = a2 - a1

353 if r:

354 # on Mercator projection, longitude distances shrink

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

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

357 # tolerance to avoid it

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

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

360 return da, db, dp

361

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

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

364 this and an other (spherical) point.

365

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

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

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

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

370 default C{False} for backward compatibility.

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

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

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

374

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

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, b360=b360)

389 else:

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

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

392 return z

393

394 @deprecated_method

395 def rhumbBearingTo(self, other): # unwrapped

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

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

398

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

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

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

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

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 (C{meter}.

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

411 default C{False} for backward compatibility.

412

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

414

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

416 or B{C{height}}.

417

418 @example:

419

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

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

422 '''

423 if exact: # use series, always

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

425 radius=radius, height=height)

426 else: # radius=None from .rhumbMidpointTo

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

428 d, r = self.datum, radius

429 else:

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

431 r = d.ellipsoid.equatoradius

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

433

434 a1, b1 = self.philam

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

436

437 da = r * cb

438 a2 = a1 + da

439 # normalize latitude if past pole

440 if fabs(a2) > PI_2:

441 a2 = _copysign(PI, a2) - a2

442

443 dp = _logPI_2_2(a2, a1)

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

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

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

447

448 h = self._heigHt(height)

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

450 return r

451

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

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

454 a rhumb line (loxodrome).

455

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

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

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

459 C{B{exact}=True}.

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

461 default C{False} for backward compatibility.

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

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

464

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

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

467

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

469

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

471

472 @example:

473

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

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

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

477 '''

478 if exact: # use series, always

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

480 radius=radius, wrap=wrap)

481 if radius is None: # angular distance in radians

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

483 else:

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

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

486 if radius is not None:

487 r *= Radius(radius)

488 return r

489

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

491 height=None, wrap=False):

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

493 points and as a point and azimuth.

494

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

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

497 (this C{LatLon}).

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

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

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

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

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

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

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

505 circle} methods.

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

507 conventionally) or C{None}.

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

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

510

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

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

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

514

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

516

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

518 or B{C{other}} invalid.

519

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

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

522 '''

523 m = LatLonBase.rhumbIntersecant2 if exact else \

524 LatLonSphericalBase.intersecant2

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

526 height=height, wrap=wrap)

527

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

529 fraction=_0_5, wrap=False):

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

531 this and an other point.

532

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

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

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

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

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

538 default C{False} for backward compatibility.

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

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

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

542 point (C{bool}).

543

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

545 line (spherical C{LatLon}).

546

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

548

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

550

551 @example:

552

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

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

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

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

557 '''

558 if exact: # use series, always

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

560 radius=radius, height=height,

561 fraction=fraction, wrap=wrap)

562 elif fraction is not _0_5:

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

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

565 z = atan2b(db, dp)

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

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

568

569 else: # for backward compatibility, unwrapped

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

571 a1, b1 = self.philam

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

573

574 if fabs(b2 - b1) > PI:

575 b1 += PI2 # crossing anti-meridian

576

577 a3 = favg(a1, a2)

578 b3 = favg(b1, b2)

579

580 f1 = tanPI_2_2(a1)

581 if isnon0(f1):

582 f2 = tanPI_2_2(a2)

583 f = f2 / f1

584 if isnon0(f):

585 f = log(f)

586 if isnon0(f):

587 f3 = tanPI_2_2(a3)

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

589 -b2, b1, b2 - b1) / f

590

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

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

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

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

595 return r

596

597 @property_RO

598 def sphericalLatLon(self):

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

600 '''

601 return type(self)

602

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

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

605 height}.

606

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

608 keyword arguments, ignored if

609 C{B{Nvector} is None}.

610

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

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

613

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

615 '''

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

617

618

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

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

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

622

623 if wrap:

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

625 nonexact = exact is None

626

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

628 r = Radius_(circle=r)

629 elif nonexact:

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

631 elif isbool(exact):

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

633 else:

634 raise _ValueError(exact=exact)

635

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

637 b = Bearing(b)

638 elif nonexact:

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

640 else:

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

642 b360=True)

643

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

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

646 if d > EPS0:

647 n = _xattr(c, napieradius=0)

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

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

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

651 if r > n:

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

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

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

655 if fabs(c) > EPS0:

656 d = d / m # /= chokes PyChecker

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

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

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

660 a *= m # meter

661 else: # point and chord center coincident

662 a, d = d, 0

663 c = cos(a / m)

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

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

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

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

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

669 if a > r:

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

671 else:

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

673

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

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

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

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

678 if h:

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

680 else: # same instance twice

681 t *= 2

682 return t

683

684

685 def _logPI_2_2(a2, a1):

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

687 '''

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

689

690

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

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

693

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

695 '''

696 r = float(distance)

697 if radius:

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

699 if low is not None:

700 # small near0 values from .rhumbDestination not exact OK

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

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

703 return r

704

705

706 def _radians2m(rad, radius):

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

708 '''

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

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

711 return rad

712

713

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

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

716 '''

717 r1 = Radius_(rad1=rad1)

718 r2 = Radius_(rad2=rad2)

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

720 r1 = _m2radians(r1, radius)

721 r2 = _m2radians(r2, radius)

722

723 x = r1 < r2

724 if x:

725 r1, r2 = r2, r1

726 if r1 > PI:

727 raise IntersectionError(rad1=rad1, rad2=rad2,

728 txt=_exceed_PI_radians_)

729 return r1, r2, x

730

731

732__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)

733

734# **) MIT License

735#

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

737#

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

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

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

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

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

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

744#

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

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

747#

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

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

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

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

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

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

754# OTHER DEALINGS IN THE SOFTWARE.