Coverage for pygeodesy/sphericalBase.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

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

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

6 

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

8transcoded in part from JavaScript originals by I{(C) Chris Veness 2011-2024} 

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

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

11''' 

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

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

14 

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

16from pygeodesy.cartesianBase import CartesianBase, Bearing2Tuple 

17from 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 

20from pygeodesy.datums import Datums, _earth_ellipsoid, _spherical_datum 

21from pygeodesy.errors import IntersectionError, _ValueError, \ 

22 _xattr, _xattrs, _xError 

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

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

25 _exceed_PI_radians_, _name_, _near_, \ 

26 _radius_, _too_ 

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

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

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

30from pygeodesy.nvectorBase import NvectorBase, Fmt 

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

32 _update_all 

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

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

35 Radius_, Scalar_, _100km 

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

37 degrees180, sincos2, sincos2d, _unrollon, \ 

38 tanPI_2_2, wrapPI 

39 

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

41 

42__all__ = _ALL_LAZY.sphericalBase 

43__version__ = '25.04.14' 

44 

45 

46class 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 

114class 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 radius or axes). 

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

131 L{Ellipsoid2}, L{a_f2Tuple}) or the mean earth radius 

132 (C{meter}, 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: Invalid B{C{latlonh}} or B{C{datum}} not spherical. 

138 ''' 

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

140 if not _isin(datum, None, self.datum): 

141 self.datum = datum 

142 

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

144 '''Return the initial and final bearing (forward and reverse azimuth) 

145 from this to an other point. 

146 

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

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

149 B{C{other}} point (C{bool}). 

150 

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

152 

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

154 

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

156 ''' 

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

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

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

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

161 

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

163 def datum(self): 

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

165 ''' 

166 return self._datum 

167 

168 @datum.setter # PYCHOK setter! 

169 def datum(self, datum): 

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

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

172 

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

174 ''' 

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

176 if self._datum != d: 

177 _update_all(self) 

178 self._datum = d 

179 

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

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

182 an other point. 

183 

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

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

186 the B{C{other}} point (C{bool}). 

187 

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

189 

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

191 ''' 

192 p = self.others(other) 

193 if wrap: 

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

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

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

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

198 

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

200 height=None, wrap=False): 

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

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

203 

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

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

206 (same C{LatLon} class). 

207 @arg point: A point on the (great circle) line (same C{LatLon} class). 

208 @arg other: An other point I{on} (same C{LatLon} class) or the bearing 

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

210 C{degrees}). 

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

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

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

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

215 circle} methods. 

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

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

218 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{circle}}, 

219 B{C{point}} and B{C{other}} iff points (C{bool}). 

220 

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

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

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

224 

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

226 

227 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}. 

228 

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

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

231 ''' 

232 p = self.others(point=point) 

233 try: 

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

235 height=height, wrap=wrap) 

236 except (TypeError, ValueError) as x: 

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

238 radius=radius, exact=exact, height=height, wrap=wrap) 

239 

240 def maxLat(self, bearing): 

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

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

243 

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

245 points on a given latitude. 

246 

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

248 

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

250 

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

252 

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

254 ''' 

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

256 return degrees90(r) 

257 

258 def minLat(self, bearing): 

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

260 on given bearing from this point. 

261 

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

263 

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

265 

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

267 

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

269 ''' 

270 return -self.maxLat(bearing) 

271 

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

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

274 radius = _earth_ellipsoid(radius)._Lpr 

275 return radius 

276 

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

278 def napieradius(self): 

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

280 ''' 

281 return self._napieradius 

282 

283 @napieradius.setter # PYCHOK setter! 

284 def napieradius(self, radius): 

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

286 

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

288 spherical trigonometry is applied if the circle radius exceeds 

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

290 

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

292 ''' 

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

294 

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

296# p = self.others(point=point) 

297# try: 

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

299# except (TypeError, ValueError) as x: 

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

301# return p.midpointTo(q) 

302 

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

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

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

306 

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

308 L{pygeodesy.parse3llh}. 

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

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

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

312 

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

314 

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

316 ''' 

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

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

319 

320 @property_RO 

321 def _radius(self): 

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

323 ''' 

324 return self.datum.ellipsoid.equatoradius 

325 

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

327 '''(INTERNAL) Rhumb_ helper function. 

328 

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

330 ''' 

331 p = self.others(other, up=2) 

332 if wrap: 

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

334 a2, b2 = p.philam 

335 a1, b1 = self.philam 

336 # if |db| > 180 take shorter rhumb 

337 # line across the anti-meridian 

338 db = wrapPI(b2 - b1) 

339 dp = _logPI_2_2(a2, a1) 

340 da = a2 - a1 

341 if r: 

342 # on Mercator projection, longitude distances shrink 

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

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

345 # tolerance to avoid it 

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

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

348 return da, db, dp 

349 

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

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

352 this and an other (spherical) point. 

353 

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

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

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

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

358 default C{False} for backward compatibility. 

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

360 B{C{other}} point (C{bool}). 

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

362 

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

364 

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

366 B{C{radius}} is invalid. 

367 ''' 

368 if exact: # use series, always 

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

370 radius=radius, wrap=wrap, b360=b360) 

371 else: 

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

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

374 return z 

375 

376 @deprecated_method 

377 def rhumbBearingTo(self, other): # unwrapped 

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

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

380 

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

382 exact=False, **name): 

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

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

385 

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

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

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

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

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

391 C{B{exact}=True}. 

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

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

394 default C{False} for backward compatibility. 

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

396 

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

398 

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

400 or B{C{height}}. 

401 ''' 

402 if exact: # use series, always 

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

404 radius=radius, height=height, **name) 

405 else: # radius=None from .rhumbMidpointTo 

406 if _isin(radius, None, self._radius): 

407 d, r = self.datum, radius 

408 else: 

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

410 r = d.ellipsoid.equatoradius 

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

412 

413 a1, b1 = self.philam 

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

415 

416 da = r * cb 

417 a2 = a1 + da 

418 # normalize latitude if past pole 

419 if fabs(a2) > PI_2: 

420 a2 = _copysign(PI, a2) - a2 

421 

422 dp = _logPI_2_2(a2, a1) 

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

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

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

426 

427 h = self._heigHt(height) 

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

429 return r 

430 

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

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

433 a rhumb line (loxodrome). 

434 

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

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

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

438 C{B{exact}=True}. 

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

440 default C{False} for backward compatibility. 

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

442 B{C{other}} point (C{bool}). 

443 

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

445 C{radians} if C{B{radius} is None}). 

446 

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

448 

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

450 ''' 

451 if exact: # use series, always 

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

453 radius=radius, wrap=wrap) 

454 if radius is None: # angular distance in radians 

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

456 else: 

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

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

459 if radius is not None: 

460 r *= Radius(radius) 

461 return r 

462 

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

464 height=None, wrap=False): 

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

466 points and as a point and azimuth. 

467 

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

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

470 (same C{LatLon} class). 

471 @arg point: The rhumb line's start point (same C{LatLon} class). 

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

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

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

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

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

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

478 circle} methods. 

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

480 conventionally) or C{None}. 

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

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

483 

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

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

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

487 

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

489 

490 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}. 

491 

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

493 B{C{exact}} or B{C{height}}. 

494 ''' 

495 m = LatLonBase.rhumbIntersecant2 if exact else \ 

496 LatLonSphericalBase.intersecant2 

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

498 height=height, wrap=wrap) 

499 

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

501 fraction=_0_5, **wrap_name): 

502 '''Return the (loxodromic) midpoint on the rhumb line between this 

503 and an other point. 

504 

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

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

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

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

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

510 default C{False} for backward compatibility. 

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

512 be negative if C{B{exact}=True}. 

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

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

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

516 

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

518 line (spherical C{LatLon}). 

519 

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

521 

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

523 ''' 

524 if exact: # use series, always 

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

526 radius=radius, height=height, 

527 fraction=fraction, **wrap_name) 

528 elif fraction is not _0_5: 

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

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

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

532 z = atan2b(db, dp) 

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

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

535 

536 else: # for backward compatibility, unwrapped 

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

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

539 a1, b1 = self.philam 

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

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

542 

543 if fabs(b2 - b1) > PI: 

544 b1 += PI2 # crossing anti-meridian 

545 

546 a3 = favg(a1, a2) 

547 b3 = favg(b1, b2) 

548 

549 f1 = tanPI_2_2(a1) 

550 if isnon0(f1): 

551 f2 = tanPI_2_2(a2) 

552 f = f2 / f1 

553 if isnon0(f): 

554 f = log(f) 

555 if isnon0(f): 

556 f3 = tanPI_2_2(a3) 

557 b3 = fdot(map1(log, f1, f2, f3), 

558 -b2, b1, b2 - b1) / f 

559 

560 d = self.datum if _isin(radius, None, self._radius) else \ 

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

562 h = self._havg(other, h=height) 

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

564 return r 

565 

566 @property_RO 

567 def sphericalLatLon(self): 

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

569 ''' 

570 return type(self) 

571 

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

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

574 height}. 

575 

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

577 arguments, ignored if C{B{Nvector} is None}. 

578 

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

580 B{C{Nvector} is None}. 

581 

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

583 ''' 

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

585 

586 

587def _intersecant2(c, r, p, b, radius=R_M, exact=False, height=None, wrap=False): 

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

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

590 

591 if wrap: 

592 p = _unrollon(c, p, wrap=wrap) 

593 nonexact = exact is None 

594 

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

596 r = Radius_(circle=r) 

597 elif nonexact: 

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

599 elif isbool(exact): 

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

601 else: 

602 raise _ValueError(exact=exact) 

603 

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

605 b = Bearing(b) 

606 elif nonexact: 

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

608 else: 

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

610 b360=True) 

611 

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

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

614 if d > EPS0: 

615 n = _xattr(c, napieradius=0) 

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

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

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

619 if r > n: 

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

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

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

623 if fabs(c) > EPS0: 

624 d = d / m # /= chokes PyChecker 

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

626 c = _copysign(cos(a), c) 

627 d = acos1(cos(d) / c) * m 

628 a *= m # meter 

629 else: # point and chord center coincident 

630 a, d = d, 0 

631 c = cos(a / m) 

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

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

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

635 d *= c # ... and to the point 

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

637 if a > r: 

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

639 else: 

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

641 

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

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

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

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

646 if h: 

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

648 else: # same instance twice 

649 t *= 2 

650 return t 

651 

652 

653def _logPI_2_2(a2, a1): 

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

655 ''' 

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

657 

658 

659def _m2radians(distance, radius, low=EPS): # PYCHOK in .spherical* 

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

661 

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

663 ''' 

664 r = float(distance) 

665 if radius: 

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

667 if low is not None: 

668 # small near0 values from .rhumbDestination not exact OK 

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

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

671 return r 

672 

673 

674def _radians2m(rad, radius): 

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

676 ''' 

677 if radius is not None: # not _isin(radius, None, _0_0) 

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

679 return rad 

680 

681 

682def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry 

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

684 ''' 

685 r1 = Radius_(rad1=rad1) 

686 r2 = Radius_(rad2=rad2) 

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

688 r1 = _m2radians(r1, radius) 

689 r2 = _m2radians(r2, radius) 

690 

691 x = r1 < r2 

692 if x: 

693 r1, r2 = r2, r1 

694 if r1 > PI: 

695 raise IntersectionError(rad1=rad1, rad2=rad2, 

696 txt=_exceed_PI_radians_) 

697 return r1, r2, x 

698 

699 

700__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase) 

701 

702# **) MIT License 

703# 

704# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

705# 

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

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

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

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

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

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

712# 

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

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

715# 

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

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

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

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

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

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

722# OTHER DEALINGS IN THE SOFTWARE.