Coverage for pygeodesy/sphericalBase.py: 91%

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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 2011-2016} 

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 isbool, isinstanceof, map1 

16from pygeodesy.cartesianBase import CartesianBase, Bearing2Tuple 

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

18 _umod_360, isnear0, isnon0, _0_0, \ 

19 _0_5, _1_0, _180_0 

20from pygeodesy.datums import Datums, _spherical_datum 

21from pygeodesy.errors import IntersectionError, _ValueError, _xError 

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

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

24 _distant_, _exceed_PI_radians_, _name_, \ 

25 _near_, _radius_, _too_ 

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

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

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

29from pygeodesy.nvectorBase import NvectorBase, Fmt, _xattrs 

30from pygeodesy.props import deprecated_method, property_doc_, \ 

31 property_RO, _update_all 

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

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

34 Radius_, Scalar_ 

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

36 degrees180, sincos2, sincos2d, tanPI_2_2, \ 

37 _unrollon, wrap360, wrapPI 

38 

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

40 

41__all__ = _ALL_LAZY.sphericalBase 

42__version__ = '23.06.05' 

43 

44 

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

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

47 

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

49 ''' 

50 r = _1_0 if radius is None else Radius_(radius=radius) 

51 return Radians_(distance / r, low=low) 

52 

53 

54def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry 

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

56 ''' 

57 r1 = Radius_(rad1=rad1) 

58 r2 = Radius_(rad2=rad2) 

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

60 r1 = _angular(r1, radius) 

61 r2 = _angular(r2, radius) 

62 

63 x = r1 < r2 

64 if x: 

65 r1, r2 = r2, r1 

66 if r1 > PI: 

67 raise IntersectionError(rad1=rad1, rad2=rad2, 

68 txt=_exceed_PI_radians_) 

69 return r1, r2, x 

70 

71 

72class CartesianSphericalBase(CartesianBase): 

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

74 ''' 

75 _datum = Datums.Sphere # L{Datum} 

76 

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

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

79 by a center point and a radius. 

80 

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

82 see B{C{radius}}). 

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

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

85 see B{C{radius}}). 

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

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

88 

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

90 For abutting circles, the intersection points are the 

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

92 

93 @raise IntersectionError: Concentric, antipodal, invalid or 

94 non-intersecting circles. 

95 

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

97 

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

99 

100 @see: U{Calculating intersection of two Circles 

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

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

103 or function C{trilaterate3d2}. 

104 ''' 

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

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

107 if x: 

108 x1, x2 = x2, x1 

109 try: 

110 n, q = x1.cross(x2), x1.dot(x2) 

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

112 if n2 < EPS or isnear0(q1): 

113 raise ValueError(_near_(_concentric_)) 

114 c1, c2 = cos(r1), cos(r2) 

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

116 x2.times((c2 - q * c1) / q1)) 

117 n1 = _1_0 - x0.length2 

118 if n1 < EPS: 

119 raise ValueError(_too_(_distant_)) 

120 except ValueError as x: 

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

122 other=other, rad2=rad2, cause=x) 

123 n = n.times(sqrt(n1 / n2)) 

124 if n.length > EPS: 

125 x1 = x0.plus(n) 

126 x2 = x0.minus(n) 

127 else: # abutting circles 

128 x1 = x2 = x0 

129 

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

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

132 

133 

134class LatLonSphericalBase(LatLonBase): 

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

136 ''' 

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

138 

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

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

141 height on the given datum. 

142 

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

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

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

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

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

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

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

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

151 conventionally). 

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

153 (C{bool}). 

154 @kwarg name: Optional name (string). 

155 

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

157 spherical. 

158 ''' 

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

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

161 self.datum = datum 

162 

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

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

165 azimuth) from this to an other point. 

166 

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

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

169 B{C{other}} point (C{bool}). 

170 

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

172 

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

174 

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

176 ''' 

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

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

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

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

181 

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

183 def datum(self): 

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

185 ''' 

186 return self._datum 

187 

188 @datum.setter # PYCHOK setter! 

189 def datum(self, datum): 

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

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

192 

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

194 ''' 

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

196 if self._datum != d: 

197 _update_all(self) 

198 self._datum = d 

199 

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

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

202 an other point. 

203 

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

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

206 the B{C{other}} point (C{bool}). 

207 

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

209 

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

211 

212 @example: 

213 

214 >>> p = LatLon(52.205, 0.119) 

215 >>> q = LatLon(48.857, 2.351) 

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

217 ''' 

218 p = self.others(other) 

219 if wrap: 

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

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

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

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

224 return _umod_360(b + _180_0) 

225 

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

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

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

229 

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

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

232 on the circle (this C{LatLon}). 

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

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

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

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

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

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

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

240 circle} methods. 

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

242 conventionally) or C{None}. 

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

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

245 

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

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

248 point C{is} this very instance. 

249 

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

251 

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

253 or B{C{bearing}} invalid. 

254 

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

256 B{C{exact}} or B{C{height}}. 

257 ''' 

258 p = self.others(point=point) 

259 try: 

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

261 height=height, wrap=wrap) 

262 except (TypeError, ValueError) as x: 

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

264 exact=exact, wrap=wrap) 

265 

266 def maxLat(self, bearing): 

267 '''Return the maximum latitude reached when travelling 

268 on a great circle on given bearing from this point 

269 based on Clairaut's formula. 

270 

271 The maximum latitude is independent of longitude 

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

273 

274 Negate the result for the minimum latitude (on the 

275 Southern hemisphere). 

276 

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

278 

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

280 

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

282 ''' 

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

284 return degrees90(m) 

285 

286 def minLat(self, bearing): 

287 '''Return the minimum latitude reached when travelling 

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

289 

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

291 

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

293 

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

295 

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

297 ''' 

298 return -self.maxLat(bearing) 

299 

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

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

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

303 

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

305 see function L{pygeodesy.parse3llh}. 

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

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

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

309 overriding this name. 

310 

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

312 

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

314 ''' 

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

316 r = self.classof(*t) 

317 if name: 

318 r.rename(name) 

319 return r 

320 

321 @property_RO 

322 def _radius(self): 

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

324 ''' 

325 return self.datum.ellipsoid.equatoradius 

326 

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

328 '''(INTERNAL) Rhumb_ helper function. 

329 

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

331 ''' 

332 p = self.others(other, up=2) 

333 if wrap: 

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

335 a2, b2 = p.philam 

336 a1, b1 = self.philam 

337 # if |db| > 180 take shorter rhumb 

338 # line across the anti-meridian 

339 db = wrapPI(b2 - b1) 

340 dp = log(tanPI_2_2(a2) / tanPI_2_2(a1)) 

341 da = a2 - a1 

342 if r: 

343 # on Mercator projection, longitude distances shrink 

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

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

346 # tolerance to avoid it 

347 q = (da / dp) if fabs(dp) > EPS else cos(self.phi) 

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

349 return da, db, dp 

350 

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

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

353 between this and an other (spherical) point. 

354 

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

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

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

358 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

359 default C{False} for backward compatibility. 

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

361 B{C{other}} point (C{bool}). 

362 

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

364 

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

366 B{C{radius}} is invalid. 

367 

368 @example: 

369 

370 >>> p = LatLon(51.127, 1.338) 

371 >>> q = LatLon(50.964, 1.853) 

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

373 ''' 

374 if exact: # use series, always 

375 z = LatLonBase.rhumbAzimuthTo(self, other, exact=False, 

376 radius=radius, wrap=wrap) 

377 else: 

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

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

380 return z 

381 

382 @deprecated_method 

383 def rhumbBearingTo(self, other): # unwrapped 

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

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

386 

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

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

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

390 

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

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

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

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

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

396 C{B{exact}=True}. 

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

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

399 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

400 default C{False} for backward compatibility. 

401 

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

403 

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

405 B{C{radius}} or B{C{height}}. 

406 

407 @example: 

408 

409 >>> p = LatLon(51.127, 1.338) 

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

411 ''' 

412 if exact: # use series, always 

413 r = LatLonBase.rhumbDestination(self, distance, bearing, exact=False, 

414 radius=radius, height=height) 

415 else: # radius=None from .rhumbMidpointTo 

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

417 d, r = self.datum, radius 

418 else: 

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

420 r = d.ellipsoid.equatoradius 

421 r = _angular(distance, r, low=_0_0) # distance=0 from .rhumbMidpointTo 

422 

423 a1, b1 = self.philam 

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

425 

426 da = r * cb 

427 a2 = a1 + da 

428 # normalize latitude if past pole 

429 if a2 > PI_2: 

430 a2 = PI - a2 

431 elif a2 < -PI_2: 

432 a2 = -PI - a2 

433 

434 dp = log(tanPI_2_2(a2) / tanPI_2_2(a1)) 

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

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

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

438 

439 h = self._heigHt(height) 

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

441 return r 

442 

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

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

445 a rhumb line (loxodrome). 

446 

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

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

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

450 C{B{exact}=True}. 

451 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

452 default C{False} for backward compatibility. 

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

454 B{C{other}} point (C{bool}). 

455 

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

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

458 

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

460 

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

462 

463 @example: 

464 

465 >>> p = LatLon(51.127, 1.338) 

466 >>> q = LatLon(50.964, 1.853) 

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

468 ''' 

469 if exact: # use series, always 

470 r = LatLonBase.rhumbDistanceTo(self, other, exact=False, 

471 radius=radius, wrap=wrap) 

472 if radius is None: # angular distance in radians 

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

474 else: 

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

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

477 if radius is not None: 

478 r *= Radius(radius) 

479 return r 

480 

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

482 fraction=_0_5, wrap=False): 

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

484 this and an other point. 

485 

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

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

488 (C{meter}). 

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

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

491 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}), 

492 default C{False} for backward compatibility. 

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

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

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

496 B{C{other}} point (C{bool}). 

497 

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

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

500 

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

502 

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

504 

505 @example: 

506 

507 >>> p = LatLon(51.127, 1.338) 

508 >>> q = LatLon(50.964, 1.853) 

509 >>> m = p.rhumb_midpointTo(q) 

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

511 ''' 

512 if exact: # use series, always 

513 r = LatLonBase.rhumbMidpointTo(self, other, exact=False, 

514 radius=radius, height=height, 

515 fraction=fraction, wrap=wrap) 

516 elif fraction is not _0_5: 

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

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

519 z = atan2b(db, dp) 

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

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

522 

523 else: # for backward compatibility, unwrapped 

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

525 a1, b1 = self.philam 

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

527 

528 if fabs(b2 - b1) > PI: 

529 b1 += PI2 # crossing anti-meridian 

530 

531 a3 = favg(a1, a2) 

532 b3 = favg(b1, b2) 

533 

534 f1 = tanPI_2_2(a1) 

535 if isnon0(f1): 

536 f2 = tanPI_2_2(a2) 

537 f = f2 / f1 

538 if isnon0(f): 

539 f = log(f) 

540 if isnon0(f): 

541 f3 = tanPI_2_2(a3) 

542 b3 = fdot(map1(log, f1, f2, f3), 

543 -b2, b1, b2 - b1) / f 

544 

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

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

547 h = self._havg(other, h=height) 

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

549 return r 

550 

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

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

553 height}. 

554 

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

556 keyword arguments, ignored if 

557 C{B{Nvector} is None}. 

558 

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

560 if B{C{Nvector}} is C{None}. 

561 

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

563 ''' 

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

565 

566 def toWm(self, radius=R_MA): 

567 '''Convert this point to a I{WM} coordinate. 

568 

569 @kwarg radius: Optional earth radius (C{meter}). 

570 

571 @return: The WM coordinate (L{Wm}). 

572 

573 @see: Function L{pygeodesy.toWm} in module L{webmercator} for details. 

574 ''' 

575 return _MODS.webmercator.toWm(self, radius=radius) 

576 

577 

578def _intersecant2(c, r, p, b, radius=R_M, exact=False, 

579 height=None, wrap=False): 

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

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

582 

583 if wrap: 

584 p = _unrollon(c, p, wrap=wrap) 

585 nonexact = exact is None 

586 

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

588 r = Radius_(circle=r) 

589 elif nonexact: 

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

591 elif isbool(exact): 

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

593 else: 

594 raise _ValueError(exact=exact) 

595 

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

597 b = Bearing(b) 

598 elif nonexact: 

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

600 else: 

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

602 

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

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

605 if d > EPS: 

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

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

608 s, c = sincos2d(b - a) 

609 s = sqrt_a(r, fabs(s * d)) 

610 if s > r: 

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

612 elif (r - s) < EPS: 

613 return p, p # tangent 

614 c *= d 

615 else: # coincindent 

616 s, c = r, 0 

617 

618 a = b + _180_0 

619 if nonexact: 

620 b = p.destination(s + c, b, radius=radius, height=height) 

621 a = p.destination(s - c, a, radius=radius, height=height) 

622 else: 

623 b = p.rhumbDestination(s + c, b, radius=radius, height=height, exact=exact) 

624 a = p.rhumbDestination(s - c, a, radius=radius, height=height, exact=exact) 

625 return b, a # in bearing direction first 

626 

627 

628__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase) 

629 

630# **) MIT License 

631# 

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

633# 

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

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

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

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

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

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

640# 

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

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

643# 

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

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

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

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

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

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

650# OTHER DEALINGS IN THE SOFTWARE.