1

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

3

4 u'''(INTERNAL) Private C{CartesianBase} class for elliposiodal, spherical and N-/vectorial

5 C{Cartesian}s and public functions L{rtp2xyz}, L{rtp2xyz_}, L{xyz2rtp} and L{xyz2rtp_}.

6

7 After I{(C) Chris Veness 2011-2024} published under the same MIT Licence**, see

8 U{https://www.Movable-Type.co.UK/scripts/latlong.html},

9 U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and

10 U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}.

11'''

12

13# from pygeodesy.basics import _xinstanceof # from .datums

14 from pygeodesy.constants import EPS, EPS0, INT0, PI2, _isfinite, isnear0, \

15 _0_0, _1_0, _N_1_0, _2_0, _4_0, _6_0

16 from pygeodesy.datums import Datum, _earth_ellipsoid, _spherical_datum, \

17 Transform, _WGS84, _xinstanceof

18# from pygeodesy.ecef import EcefKarney # _MODS

19 from pygeodesy.errors import _IsnotError, _TypeError, _ValueError, _xattr, \

20 _xdatum, _xkwds, _xkwds_get, _xkwds_pop2

21 from pygeodesy.fmath import cbrt, hypot, hypot_, hypot2, fabs, sqrt # hypot

22# from pygeodesy.formy import _hartzell # _MODS

23 from pygeodesy.fsums import fsumf_, Fmt

24 from pygeodesy.interns import _COMMASPACE_, _datum_, _no_, _phi_

25 from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used!

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

27 from pygeodesy.named import _name2__, _NamedLocal, _Pass

28 from pygeodesy.namedTuples import LatLon4Tuple, _NamedTupleTo , Vector3Tuple, \

29 Vector4Tuple, Bearing2Tuple # PYCHOK .sphericalBase

30# from pygeodesy.nvectorBase import _N_vector # _MODS

31 from pygeodesy.props import deprecated_method, Property, Property_RO, property_doc_, \

32 property_RO, _update_all

33# from pygeodesy,resections import cassini, collins5, pierlot, pierlotx, \

34# tienstra7 # _MODS

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

36# from pygeodesy.triaxials import Triaxial_ # _MODS

37 from pygeodesy.units import Degrees, Height, _heigHt, _isMeter, Meter, Radians

38 from pygeodesy.utily import acos1, atan2, sincos2d, sincos2_, degrees, radians

39 from pygeodesy.vector3d import Vector3d, _xyzhdlln4

40# from pygeodesy.vector3dBase import _xyz3 # _MODS

41# from pygeodesy import ltp # _MODS

42

43# from math import degrees, fabs, radians, sqrt # from .fmath, .utily

44

45__all__ = _ALL_LAZY.cartesianBase

46__version__ = '24.12.04'

47

48_r_ = 'r'

49_theta_ = 'theta'

50

51

52 class CartesianBase(Vector3d, _NamedLocal):

53 '''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}.

54 '''

55 _datum = None # L{Datum}, to be overriden

56 _height = None # height (L{Height}), set or approximated

57

58 def __init__(self, x_xyz, y=None, z=None, datum=None, **ll_name):

59 '''New C{Cartesian...}.

60

61 @arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian},

62 L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}.

63 @kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}}

64 is not C{scalar}, otherwise same units as B{C{x_xyz}}.

65 @kwarg z: Cartesian Z coordinate (C{scalar}), like B{C{y}}.

66 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

67 or L{a_f2Tuple}).

68 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original

69 latlon C{B{ll}=None} (C{LatLon}).

70

71 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate

72 or B{C{x_xyz}} not a C{Cartesian}, L{Ecef9Tuple},

73 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is

74 not a L{Datum}.

75 '''

76 h, d, ll, n = _xyzhdlln4(x_xyz, None, datum, **ll_name)

77 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=n)

78 if h is not None:

79 self._height = Height(h)

80 if d is not None:

81 self.datum = d

82

83# def __matmul__(self, other): # PYCHOK Python 3.5+

84# '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}.

85# '''

86# return NotImplemented if isinstance(other, (Datum, Transform)) else \

87# _NotImplemented(self, other)

88

89 def cassini(self, pointB, pointC, alpha, beta, useZ=False):

90 '''3-Point resection between this and 2 other points using U{Cassini

91 <https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method.

92

93 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

94 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

95 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

96 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

97 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to

98 B{C{pointC}} (C{degrees}, non-negative).

99 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to

100 B{C{pointC}} (C{degrees}, non-negative).

101 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise

102 force C{z=INT0} (C{bool}).

103

104 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.

105

106 @return: The survey point, an instance of this (sub-)class.

107

108 @raise ResectionError: Near-coincident, -colinear or -concyclic points

109 or negative or invalid B{C{alpha}} or B{C{beta}}.

110

111 @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}.

112

113 @see: Function L{pygeodesy.cassini} for references and more details.

114 '''

115 return _MODS.resections.cassini(self, pointB, pointC, alpha, beta,

116 useZ=useZ, datum=self.datum)

117

118 @deprecated_method

119 def collins(self, pointB, pointC, alpha, beta, useZ=False):

120 '''DEPRECATED, use method L{collins5}.'''

121 return self.collins5(pointB, pointC, alpha, beta, useZ=useZ)

122

123 def collins5(self, pointB, pointC, alpha, beta, useZ=False):

124 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/

125 documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method.

126

127 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

128 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

129 @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

130 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

131 @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to

132 B{C{pointC}} (C{degrees}, non-negative).

133 @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to

134 B{C{pointC}} (C{degrees}, non-negative).

135 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise

136 force C{z=INT0} (C{bool}).

137

138 @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.

139

140 @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP},

141 auxiliary C{pointH}, each an instance of this (sub-)class and

142 triangle sides C{a}, C{b} and C{c}.

143

144 @raise ResectionError: Near-coincident, -colinear or -concyclic points

145 or negative or invalid B{C{alpha}} or B{C{beta}}.

146

147 @raise TypeError: Invalid B{C{pointB}} or B{C{pointM}}.

148

149 @see: Function L{pygeodesy.collins5} for references and more details.

150 '''

151 return _MODS.resections.collins5(self, pointB, pointC, alpha, beta,

152 useZ=useZ, datum=self.datum)

153

154 @deprecated_method

155 def convertDatum(self, datum2, **datum):

156 '''DEPRECATED, use method L{toDatum}.'''

157 return self.toDatum(datum2, **datum)

158

159 @property_doc_(''' this cartesian's datum (L{Datum}).''')

160 def datum(self):

161 '''Get this cartesian's datum (L{Datum}).

162 '''

163 return self._datum

164

165 @datum.setter # PYCHOK setter!

166 def datum(self, datum):

167 '''Set this cartesian's C{datum} I{without conversion}

168 (L{Datum}), ellipsoidal or spherical.

169

170 @raise TypeError: The B{C{datum}} is not a L{Datum}.

171 '''

172 d = _spherical_datum(datum, name=self.name)

173 if self._datum: # is not None

174 if d.isEllipsoidal and not self._datum.isEllipsoidal:

175 raise _IsnotError(_ellipsoidal_, datum=datum)

176 elif d.isSpherical and not self._datum.isSpherical:

177 raise _IsnotError(_spherical_, datum=datum)

178 if self._datum != d:

179 _update_all(self)

180 self._datum = d

181

182 def destinationXyz(self, delta, Cartesian=None, **name_Cartesian_kwds):

183 '''Calculate the destination using a I{local} delta from this cartesian.

184

185 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, L{Ned}

186 or L{Local9Tuple}).

187 @kwarg Cartesian: Optional (geocentric) class to return the destination

188 or C{None}.

189 @kwarg name_Cartesian_kwds: Optional C{B{name}=NN} (C{str}) and optionally,

190 additional B{C{Cartesian}} keyword arguments, ignored if

191 C{B{Cartesian} is None}.

192

193 @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})}

194 instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y,

195 z, lat, lon, height, C, M, datum)} with C{M=None} always.

196

197 @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or B{C{Cartesian_kwds}}

198 item or C{datum} missing or incompatible.

199 '''

200 n, kwds = _name2__(name_Cartesian_kwds, _or_nameof=self)

201 if Cartesian is None:

202 r = self._Ltp._local2ecef(delta, nine=True)

203 else:

204 d = self.datum

205 if not d:

206 raise _TypeError(delta=delta, txt=_no_(_datum_))

207 t = _xkwds_get(kwds, datum=d)

208 if _xattr(t, ellipsoid=None) != d.ellipsoid:

209 raise _TypeError(datum=t, txt=str(d))

210 c = self._Ltp._local2ecef(delta, nine=False)

211 r = Cartesian(*c, **kwds)

212 return r.renamed(n) if n else r

213

214 @Property_RO

215 def _ecef9(self):

216 '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).

217 '''

218 return self.Ecef(self.datum, name=self.name).reverse(self, M=True)

219

220 @property_RO

221 def ellipsoidalCartesian(self):

222 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.

223 '''

224 return False

225

226 def hartzell(self, los=False, earth=None):

227 '''Compute the intersection of a Line-Of-Sight from this cartesian Point-Of-View

228 (pov) and this cartesian's C{datum} ellipsoid surface.

229

230 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),

231 C{True} for the I{normal, plumb} onto the surface or I{False} or

232 C{None} to point to the center of the ellipsoid.

233 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}

234 or C{scalar} radius in C{meter}), overriding this cartesian's

235 datum.

236

237 @return: The intersection (C{Cartesian}) with C{.height} set to the distance to

238 this C{pov}.

239

240 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside

241 the ellipsoid or B{C{los}} points outside or away from

242 the ellipsoid.

243

244 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.

245

246 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.

247 '''

248 return _MODS.formy._hartzell(self, los, earth)

249

250 @Property

251 def height(self):

252 '''Get the height (C{meter}).

253 '''

254 return self._height4.h if self._height is None else self._height

255

256 @height.setter # PYCHOK setter!

257 def height(self, height):

258 '''Set the height (C{meter}).

259

260 @raise TypeError: Invalid B{C{height}} C{type}.

261

262 @raise ValueError: Invalid B{C{height}}.

263 '''

264 h = Height(height)

265 if self._height != h:

266 _update_all(self)

267 self._height = h

268

269 def _height2C(self, r, Cartesian=None, datum=None, height=INT0, **kwds):

270 '''(INTERNAL) Helper for methods C{.height3} and C{.height4}.

271 '''

272 if Cartesian is not None:

273 r = Cartesian(r, **kwds)

274 if datum is not None:

275 r.datum = datum

276 if height is not None:

277 r.height = height # Height(height)

278 return r

279

280 def height3(self, earth=None, height=None, **Cartesian_and_kwds):

281 '''Compute the cartesian at a height above or below this certesian's

282 C{datum} ellipsoid surface.

283

284 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,

285 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},

286 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).

287 @kwarg height: The height (C{meter}, conventionally), overriding this

288 cartesian's height.

289 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return

290 the cartesian I{at height} and additional B{C{Cartesian}}

291 keyword arguments.

292

293 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None},

294 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z}

295 coordinates I{at height} in C{meter}, conventionally.

296

297 @note: This cartesian's coordinates are returned if B{C{earth}} and this

298 datum or B{C{height}} and/or this height are C{None} or undefined.

299

300 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}

301 does not accept a B{C{datum}} keyword agument.

302

303 @raise TriaxialError: No convergence in triaxial root finding.

304

305 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.

306 '''

307 n = self.height3.__name__

308 d = self.datum if earth is None else _spherical_datum(earth, name=n)

309 c, h = self, _heigHt(self, height)

310 if h and d:

311 R, r = self.Roc2(earth=d)

312 if R > EPS0:

313 R = (R + h) / R

314 r = ((r + h) / r) if r > EPS0 else _1_0

315 c = c.times_(R, R, r)

316

317 r = Vector3Tuple(c.x, c.y, c.z, name=n)

318 if Cartesian_and_kwds:

319 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))

320 return r

321

322 @Property_RO

323 def _height4(self):

324 '''(INTERNAL) Get this C{height4}-tuple.

325 '''

326 try:

327 r = self.datum.ellipsoid.height4(self, normal=True)

328 except (AttributeError, ValueError): # no datum, null cartesian,

329 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4)

330 return r

331

332 def height4(self, earth=None, normal=True, **Cartesian_and_kwds):

333 '''Compute the projection of this point on and the height above or below

334 this datum's ellipsoid surface.

335

336 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,

337 I{overriding} this datum (L{Datum}, L{Ellipsoid},

338 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},

339 L{JacobiConformal} or C{meter}, conventionally).

340 @kwarg normal: If C{True}, the projection is the nearest point on the

341 ellipsoid's surface, otherwise the intersection of the

342 radial line to the ellipsoid's center and surface C{bool}).

343 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return

344 the I{projection} and additional B{C{Cartesian}} keyword

345 arguments.

346

347 @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a

348 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}

349 and C{z} coordinates and height C{h} in C{meter}, conventionally.

350

351 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}}

352 does not accept a B{C{datum}} keyword agument.

353

354 @raise TriaxialError: No convergence in triaxial root finding.

355

356 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.

357

358 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.

359 '''

360 n = self.height4.__name__

361 d = self.datum if earth is None else earth

362 if normal and d is self.datum:

363 r = self._height4

364 elif isinstance(d, _MODS.triaxials.Triaxial_):

365 r = d.height4(self, normal=normal)

366 try:

367 d = d.toEllipsoid(name=n)

368 except (TypeError, ValueError): # TriaxialError

369 d = None

370 else:

371 r = _earth_ellipsoid(d).height4(self, normal=normal)

372

373 if Cartesian_and_kwds:

374 if d and not isinstance(d, Datum):

375 d = _spherical_datum(d, name=n)

376 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d))

377 return r

378

379 @Property_RO

380 def isEllipsoidal(self):

381 '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).

382 '''

383 return _xattr(self.datum, isEllipsoidal=None)

384

385 @Property_RO

386 def isSpherical(self):

387 '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).

388 '''

389 return _xattr(self.datum, isSpherical=None)

390

391 @Property_RO

392 def latlon(self):

393 '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).

394 '''

395 return self.toEcef().latlon

396

397 @Property_RO

398 def latlonheight(self):

399 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).

400 '''

401 return self.toEcef().latlonheight

402

403 @Property_RO

404 def latlonheightdatum(self):

405 '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).

406 '''

407 return self.toEcef().latlonheightdatum

408

409 @Property_RO

410 def _N_vector(self):

411 '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).

412 '''

413 _N = _MODS.nvectorBase._N_vector_

414 x, y, z, h = self._n_xyzh4(self.datum)

415 return _N(x, y, z, h=h, name=self.name)

416

417 def _n_xyzh4(self, datum):

418 '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.

419 '''

420 def _ErrorEPS0(x):

421 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x))

422

423 _xinstanceof(Datum, datum=datum)

424 # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/

425 # latlon-nvector-ellipsoidal.js.html#line309>,

426 # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>

427 # _equation23 and <https://www.NavLab.net/nvector>

428 E = datum.ellipsoid

429 x, y, z = self.xyz3

430

431 # Kenneth Gade eqn 23

432 p = hypot2(x, y) * E.a2_

433 q = z**2 * E.e21 * E.a2_

434 r = fsumf_(p, q, -E.e4) / _6_0

435 s = (p * q * E.e4) / (_4_0 * r**3)

436 t = cbrt(fsumf_(_1_0, s, sqrt(s * (_2_0 + s))))

437 if isnear0(t):

438 raise _ErrorEPS0(t)

439 u = fsumf_(_1_0, t, _1_0 / t) * r

440 v = sqrt(u**2 + E.e4 * q)

441 t = v * _2_0

442 if t < EPS0: # isnear0

443 raise _ErrorEPS0(t)

444 w = fsumf_(u, v, -q) * E.e2 / t

445 k = sqrt(fsumf_(u, v, w**2)) - w

446 if isnear0(k):

447 raise _ErrorEPS0(k)

448 t = k + E.e2

449 if isnear0(t):

450 raise _ErrorEPS0(t)

451 e = k / t

452# d = e * hypot(x, y)

453# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)

454 t = hypot_(x * e, y * e, z) # == 1 / tmp

455 if t < EPS0: # isnear0

456 raise _ErrorEPS0(t)

457 h = fsumf_(k, E.e2, _N_1_0) / k * t

458 s = e / t # == e * tmp

459 return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)

460

461 @Property_RO

462 def philam(self):

463 '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).

464 '''

465 return self.toEcef().philam

466

467 @Property_RO

468 def philamheight(self):

469 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).

470 '''

471 return self.toEcef().philamheight

472

473 @Property_RO

474 def philamheightdatum(self):

475 '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).

476 '''

477 return self.toEcef().philamheightdatum

478

479 def pierlot(self, point2, point3, alpha12, alpha23, useZ=False, eps=EPS):

480 '''3-Point resection between this and two other points using U{Pierlot

481 <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal} with

482 I{approximate} limits for the (pseudo-)singularities.

483

484 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

485 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

486 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

487 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

488 @arg alpha12: Angle subtended from this point to B{C{point2}} or

489 B{C{alpha2 - alpha}} (C{degrees}).

490 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or

491 B{C{alpha3 - alpha2}} (C{degrees}).

492 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}

493 (C{bool}).

494 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).

495

496 @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.

497

498 @return: The survey (or robot) point, an instance of this (sub-)class.

499

500 @raise ResectionError: Near-coincident, -colinear or -concyclic points

501 or invalid B{C{alpha12}} or B{C{alpha23}}.

502

503 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

504

505 @see: Function L{pygeodesy.pierlot} for references and more details.

506 '''

507 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,

508 useZ=useZ, eps=eps, datum=self.datum)

509

510 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):

511 '''3-Point resection between this and two other points using U{Pierlot

512 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s

513 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.

514

515 @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

516 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

517 @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},

518 C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).

519 @arg alpha1: Angle at B{C{point1}} (C{degrees}).

520 @arg alpha2: Angle at B{C{point2}} (C{degrees}).

521 @arg alpha3: Angle at B{C{point3}} (C{degrees}).

522 @kwarg useZ: If C{True}, interpolate the survey point's Z component,

523 otherwise use C{z=INT0} (C{bool}).

524

525 @return: The survey (or robot) point, an instance of this (sub-)class.

526

527 @raise ResectionError: Near-coincident, -colinear or -concyclic points or

528 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.

529

530 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

531

532 @see: Function L{pygeodesy.pierlotx} for references and more details.

533 '''

534 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,

535 useZ=useZ, datum=self.datum)

536

537 def Roc2(self, earth=None):

538 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature.

539

540 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,

541 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid},

542 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally).

543

544 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of

545 curvature C{R} respectively C{r}, both in C{meter} conventionally.

546

547 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}.

548 '''

549 r = z = fabs( self.z)

550 R, _0 = hypot(self.x, self.y), EPS0

551 if R < _0: # polar

552 R = z

553 elif z > _0: # non-equatorial

554 d = self.datum if earth is None else _spherical_datum(earth)

555 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple

556 M = e.M # EcefMatrix

557 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat))

558 if ca < _0: # polar

559 R = z

560 else: # prime-vertical, normal roc R

561 R = R / ca # /= chokes PyChecker

562 r = R if sa < _0 else (r / sa) # non-/equatorial

563 return R, r

564

565 @property_RO

566 def sphericalCartesian(self):

567 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.

568 '''

569 return False

570

571 @deprecated_method

572 def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):

573 '''DEPRECATED, use method L{tienstra7}.'''

574 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)

575

576 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):

577 '''3-Point resection between this and two other points using U{Tienstra

578 <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.

579

580 @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or

581 C{Vector2Tuple} if C{B{useZ}=False}).

582 @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or

583 C{Vector2Tuple} if C{B{useZ}=False}).

584 @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},

585 non-negative).

586 @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},

587 non-negative) or C{None} if C{B{gamma} is not None}.

588 @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},

589 non-negative) or C{None} if C{B{beta} is not None}.

590 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}

591 (C{bool}).

592

593 @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.

594

595 @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},

596 an instance of this (sub-)class and triangle angle C{A} at this point,

597 C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and

598 triangle sides C{a}, C{b} and C{c}.

599

600 @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of

601 B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or

602 negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.

603

604 @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.

605

606 @see: Function L{pygeodesy.tienstra7} for references and more details.

607 '''

608 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,

609 useZ=useZ, datum=self.datum)

610

611 @deprecated_method

612 def to2ab(self): # PYCHOK no cover

613 '''DEPRECATED, use property C{philam}.

614

615 @return: A L{PhiLam2Tuple}C{(phi, lam)}.

616 '''

617 return self.philam

618

619 @deprecated_method

620 def to2ll(self): # PYCHOK no cover

621 '''DEPRECATED, use property C{latlon}.

622

623 @return: A L{LatLon2Tuple}C{(lat, lon)}.

624 '''

625 return self.latlon

626

627 @deprecated_method

628 def to3llh(self, datum=None): # PYCHOK no cover

629 '''DEPRECATED, use property L{latlonheight} or L{latlonheightdatum}.

630

631 @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.

632

633 @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}

634 as its name may suggest.

635 '''

636 t = self.toLatLon(datum=datum, LatLon=None)

637 return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)

638

639# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE

640# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.

641# '''

642# r = self.to3llh(datum) # LatLon3Tuple

643# if LL is not None:

644# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)

645# for n, v in pairs.items():

646# setattr(r, n, v)

647# return r

648

649 def toDatum(self, datum2, datum=None):

650 '''Convert this cartesian from one datum to an other.

651

652 @arg datum2: Datum to convert I{to} (L{Datum}).

653 @kwarg datum: Datum to convert I{from} (L{Datum}).

654

655 @return: The converted point (C{Cartesian}).

656

657 @raise TypeError: B{C{datum2}} or B{C{datum}}

658 invalid.

659 '''

660 _xinstanceof(Datum, datum2=datum2)

661

662 c = self if datum in (None, self.datum) else \

663 self.toDatum(datum)

664

665 i, d = False, c.datum

666 if d == datum2:

667 return c.copy() if c is self else c

668

669 elif d is None or (d.transform.isunity and

670 datum2.transform.isunity):

671 return c.dup(datum=datum2)

672

673 elif d == _WGS84:

674 d = datum2 # convert from WGS84 to datum2

675

676 elif datum2 == _WGS84:

677 i = True # convert to WGS84 by inverse transformation

678

679 else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first

680 c = c.toTransform(d.transform, inverse=True, datum=_WGS84)

681 d = datum2

682

683 return c.toTransform(d.transform, inverse=i, datum=datum2)

684

685 def toEcef(self):

686 '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.

687

688 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

689 with C{C} and C{M} if available.

690

691 @raise EcefError: A C{.datum} or an ECEF issue.

692 '''

693 return self._ecef9

694

695 def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum

696 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.

697

698 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).

699 @kwarg height: Optional height, overriding the converted height (C{meter}), only if

700 C{B{LatLon} is not None}.

701 @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}.

702 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if

703 C{B{LatLon} is None}.

704

705 @return: The geodetic point (B{C{LatLon}}) or if C{B{LatLon}is None}, an

706 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C}

707 and C{M} if available.

708

709 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.

710 '''

711 d = _spherical_datum(datum or self.datum, name=self.name)

712 if d == self.datum:

713 r = self.toEcef()

714 else:

715 c = self.toDatum(d)

716 r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)

717

718 if LatLon: # class or .classof

719 h = _heigHt(r, height)

720 r = LatLon(r.lat, r.lon, datum=r.datum, height=h,

721 **_xkwds(LatLon_kwds, name=r.name))

722 _xdatum(r.datum, d)

723 return r

724

725 def toNvector(self, Nvector=None, datum=None, **name_Nvector_kwds):

726 '''Convert this cartesian to C{n-vector} components, I{including height}.

727

728 @kwarg Nvector: Optional class to return the C{n-vector} components

729 (C{Nvector}) or C{None}.

730 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

731 or L{a_f2Tuple}) overriding this cartesian's datum.

732 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,

733 additional B{C{Nvector}} keyword arguments, ignored if

734 C{B{Nvector} is None}.

735

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

737 C{B{Nvector} is None}.

738

739 @raise TypeError: Invalid B{C{Nvector}}, B{C{datum}} or

740 B{C{name_Nvector_kwds}} item.

741

742 @raise ValueError: B{C{Cartesian}} at origin.

743 '''

744 r, d = self._N_vector.xyzh, self.datum

745 if datum is not None:

746 d = _spherical_datum(datum, name=self.name)

747 if d != self.datum:

748 r = self._n_xyzh4(d)

749

750 if Nvector is None:

751 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)

752 if n:

753 r = r.dup(name=n)

754 else:

755 kwds = _xkwds(name_Nvector_kwds, h=r.h, datum=d)

756 r = Nvector(r.x, r.y, r.z, **self._name1__(kwds))

757 return r

758

759 def toRtp(self):

760 '''Convert this cartesian to I{spherical, polar} coordinates.

761

762 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}

763 and C{phi}, both in L{Degrees}.

764

765 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}.

766 '''

767 return _rtp3(self.toRtp, Degrees, self, name=self.name)

768

769 def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected

770 '''Return the string representation of this cartesian.

771

772 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

773 @kwarg fmt: Enclosing backets format (C{letter}).

774 @kwarg sep: Separator to join (C{str}).

775

776 @return: Cartesian represented as "[x, y, z]" (C{str}).

777 '''

778 return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)

779

780 def toTransform(self, transform, inverse=False, datum=None):

781 '''Apply a Helmert transform to this cartesian.

782

783 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).

784 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}).

785 @kwarg datum: Datum for the transformed cartesian (L{Datum}), overriding

786 this cartesian's datum but I{not} taken it into account.

787

788 @return: A transformed cartesian (C{Cartesian}) or a copy of this

789 cartesian if C{B{transform}.isunity}.

790

791 @raise TypeError: Invalid B{C{transform}}.

792 '''

793 _xinstanceof(Transform, transform=transform)

794 if transform.isunity:

795 c = self.dup(datum=datum or self.datum)

796 else:

797 # if inverse and d != _WGS84:

798 # raise _ValueError(inverse=inverse, datum=d,

799 # txt_not_=_WGS84.name)

800 xyz = transform.transform(*self.xyz3, inverse=inverse)

801 c = self.dup(xyz=xyz, datum=datum or self.datum)

802 return c

803

804 def toVector(self, Vector=None, **Vector_kwds):

805 '''Return this cartesian's I{geocentric} components as vector.

806

807 @kwarg Vector: Optional class to return the I{geocentric}

808 components (L{Vector3d}) or C{None}.

809 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword

810 arguments, ignored if C{B{Vector} is None}.

811

812 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if

813 C{B{Vector} is None}.

814

815 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.

816 '''

817 return self.xyz if Vector is None else Vector(

818 self.x, self.y, self.z, **self._name1__(Vector_kwds))

819

820

821 class RadiusThetaPhi3Tuple(_NamedTupleTo):

822 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination

823 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in

824 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position

825 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}.

826 '''

827 _Names_ = (_r_, _theta_, _phi_)

828 _Units_ = ( Meter, _Pass, _Pass)

829

830 def toCartesian(self, **name_Cartesian_and_kwds):

831 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector.

832

833 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this

834 name and optional class C{B{Cartesian}=None} and additional

835 C{B{Cartesian}} keyword arguments.

836

837 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword

838 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y}

839 and C{z} in the same units as radius C{r}, C{meter} conventionally.

840

841 @see: Function L{rtp2xyz_}.

842 '''

843 r, t, p = self

844 t, p, _ = _NamedTupleTo._Radians3(self, t, p)

845 return rtp2xyz_(r, t, p, **name_Cartesian_and_kwds)

846

847 def toDegrees(self, **name):

848 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}.

849

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

851

852 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}

853 and C{phi} both in L{Degrees}.

854 '''

855 return self._toX3U(_NamedTupleTo._Degrees3, Degrees, name)

856

857 def toRadians(self, **name):

858 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}.

859

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

861

862 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta}

863 and C{phi} both in L{Radians}.

864 '''

865 return self._toX3U(_NamedTupleTo._Radians3, Radians, name)

866

867 def _toU(self, U):

868 M = RadiusThetaPhi3Tuple._Units_[0] # Meter

869 return self.reUnit(M, U, U).toUnits()

870

871 def _toX3U(self, _X3, U, name):

872 r, t, p = self

873 t, p, s = _X3(self, t, p)

874 if s is None or name:

875 n = self._name__(name)

876 s = self.classof(r, t, p, name=n)._toU(U)

877 return s

878

879

880 def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):

881 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.

882

883 @arg theta: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis),

884 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.

885 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), like B{C{theta}}.

886

887 @see: Function L{rtp2xyz_} for further details.

888 '''

889 if isinstance(r_rtp, RadiusThetaPhi3Tuple):

890 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)

891 else:

892 c = rtp2xyz_(r_rtp, radians(theta), radians(phi), **name_Cartesian_and_kwds)

893 return c

894

895

896 def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds):

897 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates.

898

899 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous

900 L{RadiusThetaPhi3Tuple} instance.

901 @arg theta: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis),

902 required if C{B{r_rtp}} is C{scalar}, ignored otherwise.

903 @arg phi: Azimuthal angle B{C{phi}} (C{radians}), like B{C{theta}}.

904 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), C{B{Cartesian}=None}

905 class to return the coordinates and optionally, additional C{B{Cartesian}}

906 keyword arguments.

907

908 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword argument

909 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same

910 units as radius C{r}, C{meter} conventionally.

911

912 @raise TypeError: Invalid B{C{r_rtp}}, B{C{theta}}, B{C{phi}} or

913 B{C{name_Cartesian_and_kwds}} item.

914

915 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}

916 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and functions L{rtp2xyz}

917 and L{xyz2rtp}.

918 '''

919 if isinstance(r_rtp, RadiusThetaPhi3Tuple):

920 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)

921 elif _isMeter(r_rtp):

922 r = r_rtp

923 if r and _isfinite(r):

924 s, z, y, x = sincos2_(theta, phi)

925 s *= r

926 z *= r

927 y *= s

928 x *= s

929 else:

930 x = y = z = r

931

932 n, kwds = _name2__(**name_Cartesian_and_kwds)

933 C, kwds = _xkwds_pop2(kwds, Cartesian=None)

934 c = Vector3Tuple(x, y, z, name=n) if C is None else \

935 C(x, y, z, name=n, **kwds)

936 else:

937 raise _TypeError(r_rtp=r_rtp, theta=theta, phi=phi)

938 return c

939

940

941 def _rtp3(where, U, *x_y_z, **name):

942 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}.

943 '''

944 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z)

945 r = hypot_(x, y, z)

946 if r > 0:

947 t = acos1(z / r)

948 p = atan2(y, x)

949 while p < 0:

950 p += PI2

951 if U is Degrees:

952 t = degrees(t)

953 p = degrees(p)

954 else:

955 t = p = _0_0

956 return RadiusThetaPhi3Tuple(r, t, p, **name)._toU(U)

957

958

959 def xyz2rtp(x_xyz, y=0, z=0, **name):

960 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.

961

962 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both

963 in L{Degrees}.

964

965 @see: Function L{xyz2rtp_} for further details.

966 '''

967 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name)

968

969

970 def xyz2rtp_(x_xyz, y=0, z=0, **name):

971 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.

972

973 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},

974 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or

975 C{list} of 3+ C{scalar} items) if no C{y_z} specified.

976 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise.

977 @arg z: Z component (C{scalar}), like B{C{y}}.

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

979

980 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter},

981 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the

982 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}.

983

984 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}

985 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}.

986 '''

987 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name)

988

989

990__all__ += _ALL_DOCS(CartesianBase)

991

992# **) MIT License

993#

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

995#

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

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

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

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

1000# and/or sell copies of the Software, and to permit persons to whom the

1001# Software is furnished to do so, subject to the following conditions:

1002#

1003# The above copyright notice and this permission notice shall be included

1004# in all copies or substantial portions of the Software.

1005#

1006# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1007# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1008# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1009# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1010# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1011# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1012# OTHER DEALINGS IN THE SOFTWARE.