1

2# -*- coding: utf-8 -*-

3

4 u'''(INTERNAL) Private, ellipsoidal Direct/Inverse geodesy base

5 class C{LatLonEllipsoidalBaseDI} and functions.

6'''

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

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

9

10 from pygeodesy.basics import isLatLon, issubclassof, map2

11 from pygeodesy.constants import EPS, MAX, PI, PI2, PI_4, isnear0, isnear1, \

12 _EPSqrt as _TOL, _0_0, _0_5, _1_5, _3_0

13# from pygeodesy.dms import F_DMS # _MODS

14 from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase, _TOL_M, property_RO

15 from pygeodesy.errors import _AssertionError, IntersectionError, _IsnotError, \

16 _or, _ValueError, _xellipsoidal, _xError, _xkwds_not

17 from pygeodesy.fmath import favg, fmean_

18 from pygeodesy.fsums import Fmt, fsumf_

19 from pygeodesy.formy import _isequalTo, opposing, _radical2

20 from pygeodesy.interns import _antipodal_, _concentric_, _dunder_nameof, \

21 _ellipsoidal_, _exceed_PI_radians_, _low_, \

22 _near_, _SPACE_, _too_

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

24 from pygeodesy.namedTuples import Bearing2Tuple, Destination2Tuple, \

25 Intersection3Tuple, NearestOn2Tuple, \

26 NearestOn8Tuple, _LL4Tuple

27# from pygeodesy.props import property_RO # from .ellipsoidalBase

28# from pygeodesy.streprs import Fmt # from .fsums

29 from pygeodesy.units import _fi_j2, _isDegrees, _isHeight, _isRadius, \

30 Radius_, Scalar

31 from pygeodesy.utily import m2km, unroll180, _unrollon, _unrollon3, \

32 _Wrap, wrap360

33

34 from math import degrees, radians

35

36__all__ = _ALL_LAZY.ellipsoidalBaseDI

37__version__ = '24.02.14'

38

39_polar__ = 'polar?'

40_B2END = _1_5 # _intersect3 bearing to pseudo-end point factor

41_TRIPS = 33 # _intersect3, _intersects2, _nearestOn interations, 6..9 sufficient?

42

43

44 class LatLonEllipsoidalBaseDI(LatLonEllipsoidalBase):

45 '''(INTERNAL) Base class for C{ellipsoidal*.LatLon} classes

46 with I{overloaded} C{Direct} and C{Inverse} methods.

47 '''

48

49 def bearingTo2(self, other, wrap=False):

50 '''Compute the initial and final bearing (forward and reverse

51 azimuth) from this to an other point, using this C{Inverse}

52 method. See methods L{initialBearingTo} and L{finalBearingTo}

53 for more details.

54

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

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

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

58

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

60

61 @raise TypeError: The B{C{other}} point is not C{LatLon}.

62

63 @raise ValueError: If this and the B{C{other}} point's L{Datum}

64 ellipsoids are not compatible.

65 '''

66 r = self._Inverse(other, wrap)

67 return Bearing2Tuple(r.initial, r.final, name=self.name)

68

69 def destination(self, distance, bearing, height=None):

70 '''Compute the destination point after having travelled for

71 the given distance from this point along a geodesic given

72 by an initial bearing, using this C{Direct} method. See

73 method L{destination2} for more details.

74

75 @arg distance: Distance (C{meter}).

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

77 @kwarg height: Optional height, overriding the default

78 height (C{meter}, same units as C{distance}).

79

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

81 '''

82 return self._Direct(distance, bearing, self.classof, height).destination

83

84 def destination2(self, distance, bearing, height=None):

85 '''Compute the destination point and the final bearing (reverse

86 azimuth) after having travelled for the given distance from

87 this point along a geodesic given by an initial bearing,

88 using this C{Direct} method.

89

90 The distance must be in the same units as this point's datum

91 axes, conventionally C{meter}. The distance is measured on

92 the surface of the ellipsoid, ignoring this point's height.

93

94 The initial and final bearing (forward and reverse azimuth)

95 are in compass C{degrees360}.

96

97 The destination point's height and datum are set to this

98 point's height and datum, unless the former is overridden.

99

100 @arg distance: Distance (C{meter}).

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

102 @kwarg height: Optional height, overriding the default

103 height (C{meter}, same units as C{distance}).

104

105 @return: A L{Destination2Tuple}C{(destination, final)}.

106 '''

107 r = self._Direct(distance, bearing, self.classof, height)

108 return self._xnamed(r)

109

110 def _Direct(self, distance, bearing, LL, height): # overloaded by I{Vincenty}

111 '''(INTERNAL) I{Karney}'s C{Direct} method.

112

113 @return: A L{Destination2Tuple}C{(destination, final)} or

114 a L{Destination3Tuple}C{(lat, lon, final)} if

115 B{C{LL}} is C{None}.

116 '''

117 g = self.geodesic

118 r = g.Direct3(self.lat, self.lon, bearing, distance)

119 if LL:

120 r = self._Direct2Tuple(LL, height, r)

121 return r

122

123 def _Direct2Tuple(self, LL, height, r):

124 '''(INTERNAL) Helper for C{._Direct} result L{Destination2Tuple}.

125 '''

126 h = self.height if height is None else height

127 d = LL(*_Wrap.latlon(r.lat, r.lon), height=h, **_xkwds_not(None,

128 datum=self.datum, name=self.name,

129 epoch=self.epoch, reframe=self.reframe))

130 return Destination2Tuple(d, wrap360(r.final))

131

132 def distanceTo(self, other, wrap=False, **unused): # ignore radius=R_M

133 '''Compute the distance between this and an other point along

134 a geodesic, using this C{Inverse} method. See method

135 L{distanceTo3} for more details.

136

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

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

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

140

141 @return: Distance (C{meter}).

142

143 @raise TypeError: The B{C{other}} point is not C{LatLon}.

144

145 @raise ValueError: If this and the B{C{other}} point's L{Datum}

146 ellipsoids are not compatible.

147 '''

148 return self._Inverse(other, wrap, azis=False).distance

149

150 def distanceTo3(self, other, wrap=False):

151 '''Compute the distance, the initial and final bearing along

152 a geodesic between this and an other point, using this

153 C{Inverse} method.

154

155 The distance is in the same units as this point's datum axes,

156 conventionally meter. The distance is measured on the surface

157 of the ellipsoid, ignoring this point's height.

158

159 The initial and final bearing (forward and reverse azimuth)

160 are in compass C{degrees360} from North.

161

162 @arg other: Destination point (C{LatLon}).

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

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

165

166 @return: A L{Distance3Tuple}C{(distance, initial, final)}.

167

168 @raise TypeError: The B{C{other}} point is not C{LatLon}.

169

170 @raise ValueError: If this and the B{C{other}} point's L{Datum}

171 ellipsoids are not compatible.

172 '''

173 return self._xnamed(self._Inverse(other, wrap))

174

175 def finalBearingOn(self, distance, bearing):

176 '''Compute the final bearing (reverse azimuth) after having

177 travelled for the given distance along a geodesic given by

178 an initial bearing from this point, using this C{Direct}

179 method. See method L{destination2} for more details.

180

181 @arg distance: Distance (C{meter}).

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

183

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

185 '''

186 return self._Direct(distance, bearing, None, None).final

187

188 def finalBearingTo(self, other, wrap=False):

189 '''Compute the final bearing (reverse azimuth) after having

190 travelled along a geodesic from this point to an other

191 point, using this C{Inverse} method. See method

192 L{distanceTo3} for more details.

193

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

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

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

197

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

199

200 @raise TypeError: The B{C{other}} point is not C{LatLon}.

201

202 @raise ValueError: If this and the B{C{other}} point's L{Datum}

203 ellipsoids are not compatible.

204 '''

205 return self._Inverse(other, wrap).final

206

207 @property_RO

208 def geodesic(self): # overloaded by I{Karney}'s, N/A for I{Vincenty}

209 '''N/A, invalid (C{None} I{always}).

210 '''

211 return None # PYCHOK no cover

212

213 def _g_gl_p3(self, point, other, exact, wrap):

214 '''(INTERNAL) Helper for methods C{.intersecant2} and C{.plumbTo}.

215 '''

216 p = _unrollon(self, self.others(point=point), wrap=wrap)

217 g = self.datum.ellipsoid.geodesic_(exact=exact)

218 gl = g._DirectLine( p, other) if _isDegrees(other) else \

219 g._InverseLine(p, self.others(other), wrap)

220 return g, gl, p

221

222 def initialBearingTo(self, other, wrap=False):

223 '''Compute the initial bearing (forward azimuth) to travel

224 along a geodesic from this point to an other point,

225 using this C{Inverse} method. See method L{distanceTo3}

226 for more details.

227

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

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

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

231

232 @return: Initial bearing (compass C{degrees360}).

233

234 @raise TypeError: The B{C{other}} point is not C{LatLon}.

235

236 @raise ValueError: If this and the B{C{other}} point's L{Datum}

237 ellipsoids are not compatible.

238 '''

239 return self._Inverse(other, wrap).initial

240

241 def intermediateTo(self, other, fraction, height=None, wrap=False):

242 '''Return the point at given fraction along the geodesic between

243 this and an other point, using this C{Direct} and C{Inverse}

244 methods.

245

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

247 @arg fraction: Fraction between both points (C{scalar}, 0.0

248 at this and 1.0 at the other point.

249 @kwarg height: Optional height, overriding the fractional

250 height (C{meter}).

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

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

253

254 @return: Intermediate point (C{LatLon}).

255

256 @raise TypeError: The B{C{other}} point is not C{LatLon}.

257

258 @raise UnitError: Invalid B{C{fraction}} or B{C{height}}.

259

260 @raise ValueError: If this and the B{C{other}} point's L{Datum}

261 ellipsoids are not compatible.

262

263 @see: Methods L{distanceTo3}, L{destination}, C{midpointTo} and

264 C{rhumbMidpointTo}.

265 '''

266 f = Scalar(fraction=fraction)

267 if isnear0(f):

268 r = self

269 elif isnear1(f) and not wrap:

270 r = self.others(other)

271 else: # negative fraction OK

272 t = self.distanceTo3(other, wrap=wrap)

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

274 r = self.destination(t.distance * f, t.initial, height=h)

275 return r

276

277 def intersecant2(self, circle, point, other, exact=False, height=None, # PYCHOK signature

278 wrap=False, tol=_TOL):

279 '''Compute the intersections of a circle and a geodesic (line) given as

280 two points or as a point and bearing.

281

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

283 conventionally) or a point on the circle (this C{LatLon}).

284 @arg point: A location on the geodesic (this C{LatLon}).

285 @arg other: An other point on the geodesic (this C{LatLon}) or the

286 (forward) bearing at the B{C{point}} (compass C{degrees}).

287 @kwarg exact: Exact C{geodesic...} to use (C{bool} or C{Geodesic...}), see

288 method L{Ellipsoid.geodesic_}.

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

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

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

292 B{C{circle}} and/or B{C{other}} (C{bool}).

293 @kwarg tol: Convergence tolerance (C{scalar}).

294

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

296 each an instance of this C{LatLon}. Both points are the same

297 instance if the geodesic (line) is tangential to the circle.

298

299 @raise IntersectionError: The circle and geodesic do not intersect.

300

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

302 or B{C{other}} invalid.

303

304 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{exact}} or

305 B{C{height}}.

306

307 @see: Method L{rhumbIntersecant2<LatLonBase.rhumbIntersecant2>}.

308 '''

309 try:

310 g, gl, p = self._g_gl_p3(point, other, exact, wrap)

311 r = Radius_(circle=circle) if _isRadius(circle) else \

312 g._Inverse(self, self.others(circle=circle), wrap).s12

313

314 P, Q = _MODS.geodesicw._Intersecant2(gl, self.lat, self.lon, r, tol=tol,

315 form=_MODS.dms.F_DMS)

316 return self._intersecend2(p, other, wrap, height, g, P, Q,

317 self.intersecant2)

318 except (TypeError, ValueError) as x:

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

320 exact=exact, wrap=wrap)

321

322 def _Inverse(self, other, wrap, **unused): # azis=False, overloaded by I{Vincenty}

323 '''(INTERNAL) I{Karney}'s C{Inverse} method.

324

325 @return: A L{Distance3Tuple}C{(distance, initial, final)}.

326 '''

327 _ = self.ellipsoids(other)

328 g = self.geodesic

329 _, lon = unroll180(self.lon, other.lon, wrap=wrap)

330 return g.Inverse3(self.lat, self.lon, other.lat, lon)

331

332 def nearestOn8(self, points, closed=False, height=None, wrap=False,

333 equidistant=None, tol=_TOL_M):

334 '''I{Iteratively} locate the point on a path or polygon closest

335 to this point.

336

337 @arg points: The path or polygon points (C{LatLon}[]).

338 @kwarg closed: Optionally, close the polygon (C{bool}).

339 @kwarg height: Optional height, overriding the height of this and

340 all other points (C{meter}, conventionally). If

341 B{C{height}} is C{None}, the height of each point

342 is taken into account for distances.

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

344 B{C{points}} (C{bool}).

345

346 @return: A L{NearestOn8Tuple}C{(closest, distance, fi, j, start,

347 end, initial, final)} with C{distance} in C{meter},

348 conventionally and with the C{closest}, the C{start}

349 the C{end} point each an instance of this C{LatLon}.

350

351 @raise PointsError: Insufficient number of B{C{points}}.

352

353 @raise TypeError: Some B{C{points}} or B{C{equidistant}} invalid.

354

355 @raise ValueError: Some B{C{points}}' datum or ellipsoid incompatible

356 or no convergence for the given B{C{tol}}.

357

358 @see: Function L{pygeodesy.nearestOn6} and method C{nearestOn6}.

359 '''

360 _d3 = self.distanceTo3 # Distance3Tuple

361 _n3 = _nearestOn3

362 try:

363 Ps = self.PointsIter(points, loop=1, wrap=wrap)

364 p1 = c = s = e = Ps[0]

365 _ = self.ellipsoids(p1)

366 c3 = _d3(c, wrap=wrap) # XXX wrap=False?

367

368 except (TypeError, ValueError) as x:

369 raise _xError(x, Fmt.SQUARE(points=0), p1, this=self, tol=tol,

370 closed=closed, height=height, wrap=wrap)

371

372 # get the azimuthal equidistant projection, once

373 A = _Equidistant00(equidistant, c)

374 b = _Box(c, c3.distance)

375 m = f = i = 0 # p1..p2 == points[i]..[j]

376

377 kwds = dict(within=True, height=height, tol=tol,

378 LatLon=self.classof, # this LatLon

379 datum=self.datum, epoch=self.epoch, reframe=self.reframe)

380 try:

381 for j, p2 in Ps.enumerate(closed=closed):

382 if wrap and j != 0: # not Ps.looped

383 p2 = _unrollon(p1, p2)

384 # skip edge if no overlap with box around closest

385 if j < 4 or b.overlaps(p1.lat, p1.lon, p2.lat, p2.lon):

386 p, t, _ = _n3(self, p1, p2, A, **kwds)

387 d3 = _d3(p, wrap=False) # already unrolled

388 if d3.distance < c3.distance:

389 c3, c, s, e, f = d3, p, p1, p2, (i + t)

390 b = _Box(c, c3.distance)

391 m = max(m, c.iteration)

392 p1, i = p2, j

393

394 except (TypeError, ValueError) as x:

395 raise _xError(x, Fmt.SQUARE(points=i), p1,

396 Fmt.SQUARE(points=j), p2, this=self, tol=tol,

397 closed=closed, height=height, wrap=wrap)

398

399 f, j = _fi_j2(f, len(Ps)) # like .vector3d.nearestOn6

400

401 n = self.nearestOn8.__name__

402 c.rename(n)

403 if s is not c:

404 s = s.copy(name=n)

405 if e is not c:

406 e = e.copy(name=n)

407 return NearestOn8Tuple(c, c3.distance, f, j, s, e, c3.initial, c3.final,

408 iteration=m) # ._iteration for tests

409

410 def plumbTo(self, point, other, exact=False, height=None, # PYCHOK signature

411 wrap=False, tol=_TOL):

412 '''Compute the I{perpendicular} intersection of a geodesic (line) with

413 a geodesic from this point.

414

415 @arg point: A location (C{LatLon}) on the geodesic (line).

416 @arg other: An other point (C{LatLon}) on the geodesic (line) or the

417 (forward) bearing at the B{C{point}} (compass C{degrees}).

418 @kwarg exact: Exact C{geodesic...} to use (C{bool} or C{Geodesic...}),

419 see method L{Ellipsoid.geodesic_}.

420 @kwarg height: Optional height for the intersection point (C{meter},

421 conventionally) or C{None} for an interpolated height.

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

423 and/or B{C{other}} (C{bool}).

424 @kwarg tol: Convergence tolerance (C{scalar}).

425

426 @return: The intersection point, an instance of this C{LatLon}.

427

428 @raise TypeError: If B{C{point}} or B{C{other}} not this C{LatLon}.

429

430 @raise UnitError: Invalid B{C{other}}, B{C{exact}} or B{C{height}}.

431 '''

432 try:

433 g, gl, p = self._g_gl_p3(point, other, exact, wrap)

434

435 P = _MODS.geodesicw._PlumbTo(gl, self.lat, self.lon, tol=tol)

436 h = self._havg(p, h=height)

437 p = self.classof(P.lat2, P.lon2, datum=self.datum, height=h) # name=n

438 p._iteration = P.iteration

439 except (TypeError, ValueError) as x:

440 raise _xError(x, plumb=self, point=point, other=other,

441 exact=exact, wrap=wrap)

442 return p

443

444

445 class _Box(object):

446 '''Bounding box around a C{LatLon} point.

447

448 @see: Function C{_box4} in .clipy.py.

449 '''

450 def __init__(self, center, distance):

451 '''New L{_Box} around point.

452

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

454 @arg distance: Radius, half-size of the box

455 (C{meter}, conventionally)

456 '''

457 m = Radius_(distance=distance)

458 E = center.ellipsoid() # XXX see above

459 d = E.m2degrees(m) + _0_5 # some margin

460 self._N = center.lat + d

461 self._S = center.lat - d

462 self._E = center.lon + d

463 self._W = center.lon - d

464

465 def overlaps(self, lat1, lon1, lat2, lon2):

466 '''Check whether this box overlaps an other box.

467

468 @arg lat1: Latitude of a box corner (C{degrees}).

469 @arg lon1: Longitude of a box corner (C{degrees}).

470 @arg lat2: Latitude of the opposing corner (C{degrees}).

471 @arg lon2: Longitude of the opposing corner (C{degrees}).

472

473 @return: C{True} if there is some overlap, C{False}

474 otherwise (C{bool}).

475 '''

476 if lat1 > lat2:

477 lat1, lat2 = lat2, lat1

478 if lat1 > self._N or lat2 < self._S:

479 return False

480 if lon1 > lon2:

481 lon1, lon2 = lon2, lon1

482 if lon1 > self._E or lon2 < self._W:

483 return False

484 return True

485

486

487 class _Tol(object):

488 '''Handle a tolerance in C{meter} as C{degrees} and C{meter}.

489 '''

490 _deg = 0 # tol in degrees

491 _lat = 0

492 _m = 0 # tol in meter

493 _min = MAX # degrees

494 _prev = None

495 _r = 0

496

497 def __init__(self, tol_m, E, lat, *lats):

498 '''New L{_Tol}.

499

500 @arg tol_m: Tolerance (C{meter}, only).

501 @arg E: Earth ellipsoid (L{Ellipsoid}).

502 @arg lat: Latitude (C{degrees}).

503 @arg lats: Additional latitudes (C{degrees}).

504 '''

505 self._lat = fmean_(lat, *lats) if lats else lat

506 self._r = max(EPS, E.rocMean(self._lat))

507 self._m = max(EPS, tol_m)

508 self._deg = max(EPS, degrees(self._m / self._r)) # avoid m2degrees!

509

510 @property_RO

511 def degrees(self):

512 '''Get this tolerance in C{degrees}.

513 '''

514 return self._deg

515

516 def degrees2m(self, deg):

517 '''Convert B{C{deg}} to meter at the same C{lat} and earth radius.

518 '''

519 return self.radius * radians(deg) / PI2 # avoid degrees2m!

520

521 def degError(self, Error=_ValueError):

522 '''Compose an error with the C{deg}rees minimum.

523 '''

524 return self.mError(self.degrees2m(self._min), Error=Error)

525

526 def done(self, deg):

527 '''Check C{deg} vs. tolerance and previous value.

528 '''

529 if deg < self._deg or deg == self._prev:

530 return True

531 self._min = min(self._min, deg)

532 self._prev = deg

533 return False

534

535 @property_RO

536 def lat(self):

537 '''Get the mean latitude in C{degrees}.

538 '''

539 return self._lat

540

541 def mError(self, m, Error=_ValueError):

542 '''Compose an error with B{C{m}}eter minimum.

543 '''

544 t = _SPACE_(Fmt.tolerance(self.meter), _too_(_low_))

545 if m2km(m) > self.meter:

546 t = _or(t, _antipodal_, _near_(_polar__))

547 return Error(Fmt.no_convergence(m), txt=t)

548

549 @property_RO

550 def meter(self):

551 '''Get this tolerance in C{meter}.

552 '''

553 return self._m

554

555 @property_RO

556 def radius(self):

557 '''Get the earth radius in C{meter}.

558 '''

559 return self._r

560

561 def reset(self):

562 '''Reset tolerances.

563 '''

564 self._min = MAX

565 self._prev = None

566

567

568 def _Equidistant00(equidistant, p1):

569 '''(INTERNAL) Get an C{Equidistant*(0, 0, ...)} instance.

570 '''

571 if equidistant is None or not callable(equidistant):

572 equidistant = p1.Equidistant

573 else:

574 Eqs = _MODS.azimuthal._Equidistants

575 if not issubclassof(equidistant, *Eqs): # PYCHOK no cover

576 t = map2(_dunder_nameof, Eqs)

577 raise _IsnotError(*t, equidistant=equidistant)

578 return equidistant(0, 0, p1.datum)

579

580

581 def intersecant2(center, circle, point, other, **exact_height_wrap_tol):

582 '''Compute the intersections of a circle and a geodesic given as two points

583 or as a point and (forward) bearing.

584

585 @arg center: Center of the circle (C{LatLon}).

586 @arg circle: Radius of the circle (C{meter}, conventionally) or a point on

587 the circle (C{LatLon}, as B{C{center}}).

588 @arg point: A point of the geodesic (C{LatLon}, as B{C{center}}).

589 @arg other: An other point of the geodesic (C{LatLon}, as B{C{center}}) or

590 the (forward) bearing at the B{C{point}} (compass C{degrees}).

591 @kwarg exact_height_wrap_tol: Optional keyword arguments, see below.

592

593 @raise NotImplementedError: Method C{intersecant2} not available.

594

595 @raise TypeError: If B{C{center}}, B{C{point}} or B{C{circle}} or B{C{other}}

596 points not ellipsoidal or not compatible with B{C{center}}.

597

598 @see: Method C{LatLon.intersecant2} of class L{ellipsoidalExact.LatLon},

599 L{ellipsoidalKarney.LatLon} or L{ellipsoidalVincenty.LatLon}.

600 '''

601 if not isLatLon(center, ellipsoidal=True): # isinstance(center, LatLonEllipsoidalBase)

602 raise _IsnotError(_ellipsoidal_, center=center)

603 return center.intersecant2(circle, point, other, **exact_height_wrap_tol)

604

605

606 def _intersect3(s1, end1, s2, end2, height=None, wrap=False, # MCCABE 16 was=True

607 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds):

608 '''(INTERNAL) Intersect two (ellipsoidal) lines, see ellipsoidal method

609 L{intersection3}, separated to allow callers to embellish any exceptions.

610 '''

611 _LLS = _MODS.sphericalTrigonometry.LatLon

612 _si = _MODS.sphericalTrigonometry._intersect

613 _vi3 = _MODS.vector3d._intersect3d3

614

615 def _b_d(s, e, w, t, h=_0_0):

616 # compute opposing and distance

617 t = s.classof(t.lat, t.lon, height=h, name=t.name)

618 t = s.distanceTo3(t, wrap=w) # Distance3Tuple

619 b = opposing(e, t.initial) # "before" start

620 return b, t.distance

621

622 def _b_e(s, e, w, t):

623 # compute an end point along the initial bearing about

624 # 1.5 times the distance to the gu-/estimate, at least

625 # 1/8 and at most 3/8 of the earth perimeter like the

626 # radians in .sphericalTrigonometry._int3d2 and bearing

627 # comparison in .sphericaltrigonometry._intb

628 b, d = _b_d(s, e, w, t, h=t.height)

629 m = s.ellipsoid().R2x * PI_4 # authalic exact

630 d = min(max(d * _B2END, m), m * _3_0)

631 e = s.destination(d, e)

632 return b, (_unrollon(s, e) if w else e)

633

634 def _e_ll(s, e, w, **end):

635 # return 2-tuple (end, False if bearing else True)

636 ll = not _isDegrees(e)

637 if ll:

638 e = s.others(**end)

639 if w: # unroll180 == .karney._unroll2

640 e = _unrollon(s, e)

641 return e, ll

642

643 def _o(o, b, n, s, t, e):

644 # determine C{o}utside before, on or after start point

645 if not o: # intersection may be on start

646 if _isequalTo(s, t, eps=e.degrees):

647 return o

648 return -n if b else n

649

650 E = s1.ellipsoids(s2)

651

652 e1, ll1 = _e_ll(s1, end1, wrap, end1=end1)

653 e2, ll2 = _e_ll(s2, end2, wrap, end2=end2)

654

655 e = _Tol(tol, E, s1.lat, (e1.lat if ll1 else s1.lat),

656 s2.lat, (e2.lat if ll2 else s2.lat))

657

658 # get the azimuthal equidistant projection

659 A = _Equidistant00(equidistant, s1)

660

661 # gu-/estimate initial intersection, spherically ...

662 t = _si(_LLS(s1), (_LLS(e1) if ll1 else e1),

663 _LLS(s2), (_LLS(e2) if ll2 else e2),

664 height=height, wrap=False, LatLon=_LLS) # unrolled already

665 h, n = t.height, t.name

666

667 if not ll1:

668 b1, e1 = _b_e(s1, e1, wrap, t)

669 if not ll2:

670 b2, e2 = _b_e(s2, e2, wrap, t)

671

672 # ... and iterate as Karney describes, for references

673 # @see: Function L{ellipsoidalKarney.intersection3}.

674 for i in range(1, _TRIPS):

675 A.reset(t.lat, t.lon) # gu-/estimate as origin

676 # convert start and end points to projection

677 # space and compute an intersection there

678 v, o1, o2 = _vi3(*A._forwards(s1, e1, s2, e2),

679 eps=e.meter, useZ=False)

680 # convert intersection back to geodetic

681 t, d = A._reverse2(v)

682 if e.done(d): # below tol or unchanged?

683 break

684 else:

685 raise e.degError(Error=IntersectionError)

686

687 # like .sphericalTrigonometry._intersect, if this intersection

688 # is "before" the first point, use the antipodal intersection

689 if not (ll1 or ll2): # end1 and end2 are an initial bearing

690 b1, _ = _b_d(s1, end1, wrap, t)

691 if b1:

692 t = t.antipodal()

693 b1 = not b1

694 b2, _ = _b_d(s2, end2, wrap, t)

695

696 r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=s1,

697 iteration=i, name=n)

698 return Intersection3Tuple(r, (o1 if ll1 else _o(o1, b1, 1, s1, t, e)),

699 (o2 if ll2 else _o(o2, b2, 2, s2, t, e)))

700

701

702 def _intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True

703 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds):

704 '''(INTERNAL) Iteratively compute the intersection point of two lines,

705 each defined by two (ellipsoidal) points or an (ellipsoidal) start

706 point and an initial bearing from North.

707 '''

708 s1 = _xellipsoidal(start1=start1)

709 s2 = s1.others(start2=start2)

710 try:

711 return _intersect3(s1, end1, s2, end2, height=height, wrap=wrap,

712 equidistant=equidistant, tol=tol,

713 LatLon=LatLon, **LatLon_kwds)

714 except (TypeError, ValueError) as x:

715 raise _xError(x, start1=start1, end1=end1, start2=start2, end2=end2)

716

717

718 def _intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True

719 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds):

720 '''(INTERNAL) Iteratively compute the intersection points of two circles,

721 each defined by an (ellipsoidal) center point and a radius.

722 '''

723 c1 = _xellipsoidal(center1=center1)

724 c2 = c1.others(center2=center2)

725 try:

726 return _intersects2(c1, radius1, c2, radius2, height=height, wrap=wrap,

727 equidistant=equidistant, tol=tol,

728 LatLon=LatLon, **LatLon_kwds)

729 except (TypeError, ValueError) as x:

730 raise _xError(x, center1=center1, radius1=radius1,

731 center2=center2, radius2=radius2)

732

733

734 def _intersects2(c1, radius1, c2, radius2, height=None, wrap=False, # MCCABE 16 was=True

735 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds):

736 '''(INTERNAL) Intersect two (ellipsoidal) circles, see L{_intersections2}

737 above, separated to allow callers to embellish any exceptions.

738 '''

739 _LLS = _MODS.sphericalTrigonometry.LatLon

740 _si2 = _MODS.sphericalTrigonometry._intersects2

741 _vi2 = _MODS.vector3d._intersects2

742

743 def _ll4(t, h, n, c):

744 return _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=c,

745 iteration=t.iteration, name=n)

746

747 r1 = Radius_(radius1=radius1)

748 r2 = Radius_(radius2=radius2)

749

750 E = c1.ellipsoids(c2)

751 # get the azimuthal equidistant projection

752 A = _Equidistant00(equidistant, c1)

753

754 if r1 < r2:

755 c1, c2 = c2, c1

756 r1, r2 = r2, r1

757

758 if r1 > (min(E.b, E.a) * PI):

759 raise _ValueError(_exceed_PI_radians_)

760

761 if wrap: # unroll180 == .karney._unroll2

762 c2 = _unrollon(c1, c2)

763

764 # distance between centers and radii are

765 # measured along the ellipsoid's surface

766 m = c1.distanceTo(c2, wrap=False) # meter

767 if m < max(r1 - r2, EPS):

768 raise IntersectionError(_near_(_concentric_)) # XXX ConcentricError?

769 if fsumf_(r1, r2, -m) < 0:

770 raise IntersectionError(_too_(Fmt.distant(m)))

771

772 f = _radical2(m, r1, r2).ratio # "radical fraction"

773 e = _Tol(tol, E, favg(c1.lat, c2.lat, f=f))

774

775 # gu-/estimate initial intersections, spherically ...

776 t1, t2 = _si2(_LLS(c1), r1, _LLS(c2), r2, radius=e.radius,

777 height=height, wrap=False, too_d=m) # unrolled already

778 h, n = t1.height, t1.name

779

780 # ... and iterate as Karney describes, for references

781 # @see: Function L{ellipsoidalKarney.intersections2}.

782 ts, ta = [], None

783 for t in ((t1,) if t1 is t2 else (t1, t2)):

784 for i in range(1, _TRIPS):

785 A.reset(t.lat, t.lon) # gu-/estimate as origin

786 # convert centers to projection space and

787 # compute the intersections there

788 t1, t2 = A._forwards(c1, c2)

789 v1, v2 = _vi2(t1, r1, # XXX * t1.scale?,

790 t2, r2, # XXX * t2.scale?,

791 sphere=False, too_d=m)

792 # convert intersections back to geodetic

793 if v1 is v2: # abutting

794 t, d = A._reverse2(v1)

795 else: # consider the closer intersection

796 t1, d1 = A._reverse2(v1)

797 t2, d2 = A._reverse2(v2)

798 t, d = (t1, d1) if d1 < d2 else (t2, d2)

799 if e.done(d): # below tol or unchanged?

800 t._iteration = i # _NamedTuple._iteration

801 ts.append(t)

802 if v1 is v2: # abutting

803 ta = t

804 break

805 else:

806 raise e.degError(Error=IntersectionError)

807 e.reset()

808

809 if ta: # abutting circles

810 pass # PYCHOK no cover

811 elif len(ts) == 2:

812 return (_ll4(ts[0], h, n, c1),

813 _ll4(ts[1], h, n, c2))

814 elif len(ts) == 1: # PYCHOK no cover

815 ta = ts[0] # assume abutting

816 else: # PYCHOK no cover

817 raise _AssertionError(ts=ts)

818 r = _ll4(ta, h, n, c1)

819 return r, r

820

821

822 def _nearestOn2(p, point1, point2, within=True, height=None, wrap=False, # was=True

823 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

824 '''(INTERNAL) Closest point and fraction, like L{_intersects2} above,

825 separated to allow callers to embellish any exceptions.

826 '''

827 p1 = p.others(point1=point1)

828 p2 = p.others(point2=point2)

829

830 _ = p.ellipsoids(p1)

831# E = p.ellipsoids(p2) # done in _nearestOn3

832

833 # get the azimuthal equidistant projection

834 A = _Equidistant00(equidistant, p)

835

836 p1, p2, _ = _unrollon3(p, p1, p2, wrap) # XXX don't unroll?

837 r, f, _ = _nearestOn3(p, p1, p2, A, within=within, height=height,

838 tol=tol, **LatLon_and_kwds)

839 return NearestOn2Tuple(r, f)

840

841

842 def _nearestOn3(p, p1, p2, A, within=True, height=None, tol=_TOL_M,

843 LatLon=None, **LatLon_kwds):

844 # Only in function C{_nearestOn2} and method C{nearestOn8} above

845 _LLS = _MODS.sphericalNvector.LatLon

846 _V3d = _MODS.vector3d.Vector3d

847 _vn2 = _MODS.vector3d._nearestOn2

848

849 E = p.ellipsoids(p2)

850 e = _Tol(tol, E, p.lat, p1.lat, p2.lat)

851

852 # gu-/estimate initial nearestOn, spherically ... wrap=False, only!

853 # using sphericalNvector.LatLon.nearestOn for within=False support

854 t = _LLS(p).nearestOn(_LLS(p1), _LLS(p2), within=within,

855 height=height)

856 n, h = t.name, t.height

857 if height is None:

858 h1 = p1.height # use heights as pseudo-Z in projection space

859 h2 = p2.height # to be included in the closest function

860 h0 = favg(h1, h2)

861 else: # ignore heights in distances, Z=0

862 h0 = h1 = h2 = _0_0

863

864 # ... and iterate to find the closest (to the origin with .z

865 # to interpolate height) as Karney describes, for references

866 # @see: Function L{ellipsoidalKarney.nearestOn}.

867 vp, f = _V3d(_0_0, _0_0, h0), None

868 for i in range(1, _TRIPS):

869 A.reset(t.lat, t.lon) # gu-/estimate as origin

870 # convert points to projection space and compute

871 # the nearest one (and its height) there

872 s, t = A._forwards(p1, p2)

873 v, f = _vn2(vp, _V3d(s.x, s.y, h1),

874 _V3d(t.x, t.y, h2), within=within)

875 # convert nearest one back to geodetic

876 t, d = A._reverse2(v)

877 if e.done(d): # below tol or unchanged?

878 break

879 else:

880 raise e.degError()

881

882 if height is None:

883 h = v.z # nearest

884 elif _isHeight(height):

885 h = height

886 r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=p,

887 iteration=i, name=n)

888 return r, f, e # fraction or None

889

890

891__all__ += _ALL_DOCS(LatLonEllipsoidalBaseDI, intersecant2)

892

893# **) MIT License

894#

895# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

896#

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

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

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

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

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

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

903#

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

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

906#

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

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

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

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

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

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

913# OTHER DEALINGS IN THE SOFTWARE.