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__ = '23.10.24'

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

250 on a great circle on given bearing from this point

251 based on Clairaut's formula.

252

253 The maximum latitude is independent of longitude

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

255

256 Negate the result for the minimum latitude (on the

257 Southern hemisphere).

258

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

260

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

262

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

264 '''

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

266 return degrees90(m)

267

268 def minLat(self, bearing):

269 '''Return the minimum latitude reached when travelling

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

271

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

273

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

275

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

277

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

279 '''

280 return -self.maxLat(bearing)

281

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

283 if exact and not isscalar(radius): # see .rhumbx.Rhumb._mpr

284 radius = _earth_ellipsoid(radius)._Lpr

285 return radius

286

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

288 def napieradius(self):

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

290 '''

291 return self._napieradius

292

293 @napieradius.setter # PYCHOK setter!

294 def napieradius(self, radius):

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

296

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

298 spherical trigonometry is applied if the circle radius exceeds

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

300

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

302 '''

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

304

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

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

307# try:

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

309# except (TypeError, ValueError) as x:

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

311# return p.midpointTo(q)

312

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

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

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

316

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

318 see function L{pygeodesy.parse3llh}.

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

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

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

322 overriding this name.

323

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

325

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

327 '''

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

329 r = self.classof(*t)

330 if name:

331 r.rename(name)

332 return r

333

334 @property_RO

335 def _radius(self):

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

337 '''

338 return self.datum.ellipsoid.equatoradius

339

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

341 '''(INTERNAL) Rhumb_ helper function.

342

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

344 '''

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

346 if wrap:

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

348 a2, b2 = p.philam

349 a1, b1 = self.philam

350 # if |db| > 180 take shorter rhumb

351 # line across the anti-meridian

352 db = wrapPI(b2 - b1)

353 dp = _logPI_2_2(a2, a1)

354 da = a2 - a1

355 if r:

356 # on Mercator projection, longitude distances shrink

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

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

359 # tolerance to avoid it

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

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

362 return da, db, dp

363

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

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

366 this and an other (spherical) point.

367

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

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

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

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

372 default C{False} for backward compatibility.

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

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

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

376

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

378

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

380 B{C{radius}} is invalid.

381

382 @example:

383

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

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

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

387 '''

388 if exact: # use series, always

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

390 radius=radius, wrap=wrap, b360=b360)

391 else:

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

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

394 return z

395

396 @deprecated_method

397 def rhumbBearingTo(self, other): # unwrapped

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

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

400

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

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

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

404

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

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

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

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

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

410 C{B{exact}=True}.

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

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

413 C{False} for backward compatibility.

414

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

416

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

418 or B{C{height}}.

419

420 @example:

421

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

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

424 '''

425 if exact: # use series, always

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

427 radius=radius, height=height)

428 else: # radius=None from .rhumbMidpointTo

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

430 d, r = self.datum, radius

431 else:

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

433 r = d.ellipsoid.equatoradius

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

435

436 a1, b1 = self.philam

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

438

439 da = r * cb

440 a2 = a1 + da

441 # normalize latitude if past pole

442 if fabs(a2) > PI_2:

443 a2 = _copysign(PI, a2) - a2

444

445 dp = _logPI_2_2(a2, a1)

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

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

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

449

450 h = self._heigHt(height)

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

452 return r

453

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

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

456 a rhumb line (loxodrome).

457

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

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

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

461 C{B{exact}=True}.

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

463 default C{False} for backward compatibility.

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

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

466

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

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

469

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

471

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

473

474 @example:

475

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

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

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

479 '''

480 if exact: # use series, always

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

482 radius=radius, wrap=wrap)

483 if radius is None: # angular distance in radians

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

485 else:

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

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

488 if radius is not None:

489 r *= Radius(radius)

490 return r

491

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

493 height=None, wrap=False):

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

495 points and as a point and azimuth.

496

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

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

499 (this C{LatLon}).

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

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

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

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

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

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

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

507 circle} methods.

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

509 conventionally) or C{None}.

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

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

512

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

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

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

516

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

518

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

520 or B{C{other}} invalid.

521

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

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

524 '''

525 m = LatLonBase.rhumbIntersecant2 if exact else \

526 LatLonSphericalBase.intersecant2

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

528 height=height, wrap=wrap)

529

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

531 fraction=_0_5, wrap=False):

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

533 this and an other point.

534

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

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

537 (C{meter}).

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

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

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

541 default C{False} for backward compatibility.

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

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

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

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

546

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

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

549

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

551

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

553

554 @example:

555

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

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

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

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

560 '''

561 if exact: # use series, always

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

563 radius=radius, height=height,

564 fraction=fraction, wrap=wrap)

565 elif fraction is not _0_5:

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

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

568 z = atan2b(db, dp)

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

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

571

572 else: # for backward compatibility, unwrapped

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

574 a1, b1 = self.philam

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

576

577 if fabs(b2 - b1) > PI:

578 b1 += PI2 # crossing anti-meridian

579

580 a3 = favg(a1, a2)

581 b3 = favg(b1, b2)

582

583 f1 = tanPI_2_2(a1)

584 if isnon0(f1):

585 f2 = tanPI_2_2(a2)

586 f = f2 / f1

587 if isnon0(f):

588 f = log(f)

589 if isnon0(f):

590 f3 = tanPI_2_2(a3)

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

592 -b2, b1, b2 - b1) / f

593

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

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

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

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

598 return r

599

600 @property_RO

601 def sphericalLatLon(self):

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

603 '''

604 return type(self)

605

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

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

608 height}.

609

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

611 keyword arguments, ignored if

612 C{B{Nvector} is None}.

613

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

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

616

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

618 '''

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

620

621

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

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

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

625

626 if wrap:

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

628 nonexact = exact is None

629

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

631 r = Radius_(circle=r)

632 elif nonexact:

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

634 elif isbool(exact):

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

636 else:

637 raise _ValueError(exact=exact)

638

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

640 b = Bearing(b)

641 elif nonexact:

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

643 else:

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

645 b360=True)

646

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

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

649 if d > EPS0:

650 n = _xattr(c, napieradius=0)

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

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

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

654 if r > n:

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

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

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

658 if fabs(c) > EPS0:

659 d = d / m # /= chokes PyChecker

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

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

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

663 a *= m # meter

664 else: # point and chord center coincident

665 a, d = d, 0

666 c = cos(a / m)

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

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

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

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

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

672 if a > r:

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

674 else:

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

676

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

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

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

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

681 if h:

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

683 else: # same instance twice

684 t *= 2

685 return t

686

687

688 def _logPI_2_2(a2, a1):

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

690 '''

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

692

693

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

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

696

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

698 '''

699 r = float(distance)

700 if radius:

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

702 if low is not None:

703 # small near0 values from .rhumbDestination not exact OK

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

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

706 return r

707

708

709 def _radians2m(rad, radius):

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

711 '''

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

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

714 return rad

715

716

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

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

719 '''

720 r1 = Radius_(rad1=rad1)

721 r2 = Radius_(rad2=rad2)

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

723 r1 = _m2radians(r1, radius)

724 r2 = _m2radians(r2, radius)

725

726 x = r1 < r2

727 if x:

728 r1, r2 = r2, r1

729 if r1 > PI:

730 raise IntersectionError(rad1=rad1, rad2=rad2,

731 txt=_exceed_PI_radians_)

732 return r1, r2, x

733

734

735__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)

736

737# **) MIT License

738#

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

740#

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

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

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

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

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

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

747#

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

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

750#

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

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

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

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

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

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

757# OTHER DEALINGS IN THE SOFTWARE.