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 isbool, isinstanceof, map1

16 from pygeodesy.cartesianBase import CartesianBase, Bearing2Tuple

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

18 _umod_360, isnear0, isnon0, _0_0, \

19 _0_5, _1_0, _180_0

20 from pygeodesy.datums import Datums, _spherical_datum

21 from pygeodesy.errors import IntersectionError, _ValueError, _xError

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

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

24 _distant_, _exceed_PI_radians_, _name_, \

25 _near_, _radius_, _too_

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

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

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

29 from pygeodesy.nvectorBase import NvectorBase, Fmt, _xattrs

30 from pygeodesy.props import deprecated_method, property_doc_, \

31 property_RO, _update_all

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

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

34 Radius_, Scalar_

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

36 degrees180, sincos2, sincos2d, tanPI_2_2, \

37 _unrollon, wrap360, wrapPI

38

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

40

41__all__ = _ALL_LAZY.sphericalBase

42__version__ = '23.07.01'

43

44

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

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

47

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

49 '''

50 r = float(distance)

51 if radius:

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

53 if low is not None:

54 # small near0 values from .rhumbDestination not exact OK

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

56 return r

57

58

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

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

61 '''

62 r1 = Radius_(rad1=rad1)

63 r2 = Radius_(rad2=rad2)

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

65 r1 = _angular(r1, radius)

66 r2 = _angular(r2, radius)

67

68 x = r1 < r2

69 if x:

70 r1, r2 = r2, r1

71 if r1 > PI:

72 raise IntersectionError(rad1=rad1, rad2=rad2,

73 txt=_exceed_PI_radians_)

74 return r1, r2, x

75

76

77 class CartesianSphericalBase(CartesianBase):

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

79 '''

80 _datum = Datums.Sphere # L{Datum}

81

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

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

84 by a center point and a radius.

85

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

87 see B{C{radius}}).

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

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

90 see B{C{radius}}).

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

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

93

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

95 For abutting circles, the intersection points are the

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

97

98 @raise IntersectionError: Concentric, antipodal, invalid or

99 non-intersecting circles.

100

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

102

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

104

105 @see: U{Calculating intersection of two Circles

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

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

108 or function C{trilaterate3d2}.

109 '''

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

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

112 if x:

113 x1, x2 = x2, x1

114 try:

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

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

117 if n2 < EPS or isnear0(q1):

118 raise ValueError(_near_(_concentric_))

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

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

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

122 n1 = _1_0 - x0.length2

123 if n1 < EPS:

124 raise ValueError(_too_(_distant_))

125 except ValueError as x:

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

127 other=other, rad2=rad2, cause=x)

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

129 if n.length > EPS:

130 x1 = x0.plus(n)

131 x2 = x0.minus(n)

132 else: # abutting circles

133 x1 = x2 = x0

134

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

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

137

138

139 class LatLonSphericalBase(LatLonBase):

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

141 '''

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

143

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

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

146 height on the given datum.

147

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

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

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

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

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

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

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

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

156 conventionally).

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

158 (C{bool}).

159 @kwarg name: Optional name (string).

160

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

162 spherical.

163 '''

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

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

166 self.datum = datum

167

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

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

170 azimuth) from this to an other point.

171

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

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

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

175

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

177

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

179

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

181 '''

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

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

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

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

186

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

188 def datum(self):

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

190 '''

191 return self._datum

192

193 @datum.setter # PYCHOK setter!

194 def datum(self, datum):

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

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

197

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

199 '''

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

201 if self._datum != d:

202 _update_all(self)

203 self._datum = d

204

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

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

207 an other point.

208

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

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

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

212

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

214

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

216

217 @example:

218

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

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

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

222 '''

223 p = self.others(other)

224 if wrap:

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

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

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

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

229 return _umod_360(b + _180_0)

230

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

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

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

234

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

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

237 on the circle (this C{LatLon}).

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

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

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

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

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

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

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

245 circle} methods.

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

247 conventionally) or C{None}.

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

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

250

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

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

253 points are the same instance, the B{C{point}} or wrapped

254 or I{normalized}.

255

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

257

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

259 or B{C{bearing}} invalid.

260

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

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

263 '''

264 p = self.others(point=point)

265 try:

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

267 height=height, wrap=wrap)

268 except (TypeError, ValueError) as x:

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

270 exact=exact, wrap=wrap)

271

272 def maxLat(self, bearing):

273 '''Return the maximum latitude reached when travelling

274 on a great circle on given bearing from this point

275 based on Clairaut's formula.

276

277 The maximum latitude is independent of longitude

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

279

280 Negate the result for the minimum latitude (on the

281 Southern hemisphere).

282

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

284

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

286

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

288 '''

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

290 return degrees90(m)

291

292 def minLat(self, bearing):

293 '''Return the minimum latitude reached when travelling

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

295

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

297

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

299

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

301

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

303 '''

304 return -self.maxLat(bearing)

305

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

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

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

309

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

311 see function L{pygeodesy.parse3llh}.

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

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

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

315 overriding this name.

316

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

318

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

320 '''

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

322 r = self.classof(*t)

323 if name:

324 r.rename(name)

325 return r

326

327 @property_RO

328 def _radius(self):

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

330 '''

331 return self.datum.ellipsoid.equatoradius

332

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

334 '''(INTERNAL) Rhumb_ helper function.

335

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

337 '''

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

339 if wrap:

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

341 a2, b2 = p.philam

342 a1, b1 = self.philam

343 # if |db| > 180 take shorter rhumb

344 # line across the anti-meridian

345 db = wrapPI(b2 - b1)

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

347 da = a2 - a1

348 if r:

349 # on Mercator projection, longitude distances shrink

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

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

352 # tolerance to avoid it

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

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

355 return da, db, dp

356

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

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

359 between this and an other (spherical) point.

360

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

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

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

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

365 default C{False} for backward compatibility.

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

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

368

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

370

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

372 B{C{radius}} is invalid.

373

374 @example:

375

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

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

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

379 '''

380 if exact: # use series, always

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

382 radius=radius, wrap=wrap)

383 else:

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

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

386 return z

387

388 @deprecated_method

389 def rhumbBearingTo(self, other): # unwrapped

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

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

392

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

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

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

396

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

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

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

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

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

402 C{B{exact}=True}.

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

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

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

406 default C{False} for backward compatibility.

407

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

409

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

411 B{C{radius}} or B{C{height}}.

412

413 @example:

414

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

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

417 '''

418 if exact: # use series, always

419 r = LatLonBase.rhumbDestination(self, distance, bearing, exact=False, # Krüger

420 radius=radius, height=height)

421 else: # radius=None from .rhumbMidpointTo

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

423 d, r = self.datum, radius

424 else:

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

426 r = d.ellipsoid.equatoradius

427 r = _angular(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo

428

429 a1, b1 = self.philam

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

431

432 da = r * cb

433 a2 = a1 + da

434 # normalize latitude if past pole

435 if a2 > PI_2:

436 a2 = PI - a2

437 elif a2 < -PI_2:

438 a2 = -PI - a2

439

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

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

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

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

444

445 h = self._heigHt(height)

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

447 return r

448

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

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

451 a rhumb line (loxodrome).

452

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

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

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

456 C{B{exact}=True}.

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

458 default C{False} for backward compatibility.

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

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

461

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

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

464

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

466

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

468

469 @example:

470

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

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

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

474 '''

475 if exact: # use series, always

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

477 radius=radius, wrap=wrap)

478 if radius is None: # angular distance in radians

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

480 else:

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

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

483 if radius is not None:

484 r *= Radius(radius)

485 return r

486

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

488 fraction=_0_5, wrap=False):

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

490 this and an other point.

491

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

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

494 (C{meter}).

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

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

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

498 default C{False} for backward compatibility.

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

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

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

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

503

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

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

506

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

508

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

510

511 @example:

512

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

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

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

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

517 '''

518 if exact: # use series, always

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

520 radius=radius, height=height,

521 fraction=fraction, wrap=wrap)

522 elif fraction is not _0_5:

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

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

525 z = atan2b(db, dp)

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

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

528

529 else: # for backward compatibility, unwrapped

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

531 a1, b1 = self.philam

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

533

534 if fabs(b2 - b1) > PI:

535 b1 += PI2 # crossing anti-meridian

536

537 a3 = favg(a1, a2)

538 b3 = favg(b1, b2)

539

540 f1 = tanPI_2_2(a1)

541 if isnon0(f1):

542 f2 = tanPI_2_2(a2)

543 f = f2 / f1

544 if isnon0(f):

545 f = log(f)

546 if isnon0(f):

547 f3 = tanPI_2_2(a3)

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

549 -b2, b1, b2 - b1) / f

550

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

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

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

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

555 return r

556

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

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

559 height}.

560

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

562 keyword arguments, ignored if

563 C{B{Nvector} is None}.

564

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

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

567

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

569 '''

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

571

572

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

574 height=None, wrap=False):

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

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

577

578 if wrap:

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

580 nonexact = exact is None

581

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

583 r = Radius_(circle=r)

584 elif nonexact:

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

586 elif isbool(exact):

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

588 else:

589 raise _ValueError(exact=exact)

590

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

592 b = Bearing(b)

593 elif nonexact:

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

595 else:

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

597

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

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

600 if d > EPS:

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

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

603 s, c = sincos2d(b - a)

604 s = sqrt_a(r, fabs(s * d))

605 if s > r:

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

607 elif (r - s) < EPS:

608 return p, p # tangent

609 c *= d

610 else: # p and c coincide

611 s, c = r, 0

612 t = ()

613 for d, b in ((s + c, b), (s - c, b + _180_0)): # bearing direction first

614 t += (p.destination(d, b, radius=radius, height=height) if nonexact else

615 p.rhumbDestination(d, b, radius=radius, height=height, exact=exact)),

616 return t

617

618

619 def _r2m(r, radius):

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

621 '''

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

623 r *= R_M if radius is R_M else Radius(radius)

624 return r

625

626

627__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)

628

629# **) MIT License

630#

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

632#

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

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

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

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

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

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

639#

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

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

642#

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

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

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

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

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

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

649# OTHER DEALINGS IN THE SOFTWARE.