1

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

3

4 u'''I{Local Tangent Plane} (LTP) and I{local} cartesian coordinates.

5

6 I{Local cartesian} and I{local tangent plane} classes L{LocalCartesian}, approximations L{ChLVa}

7 and L{ChLVe} and L{Ltp}, L{ChLV}, L{LocalError}, L{Attitude} and L{Frustum}.

8

9@see: U{Local tangent plane coordinates<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>}

10 and class L{LocalCartesian}, transcoded from I{Charles Karney}'s C++ classU{LocalCartesian

11 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>}.

12'''

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

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

15

16 from pygeodesy.basics import isscalar, issubclassof, map1, _xargs_names

17 from pygeodesy.constants import EPS, INT0, _umod_360, _0_0, _0_01, _0_5, _1_0, \

18 _2_0, _60_0, _90_0, _100_0, _180_0, _3600_0, \

19 _N_1_0 # PYCHOK used!

20 from pygeodesy.datums import _WGS84, _xinstanceof

21 from pygeodesy.ecef import _EcefBase, EcefKarney, _llhn4, _xyzn4

22 from pygeodesy.errors import _NotImplementedError, _TypesError, _ValueError, \

23 _xattr, _xkwds, _xkwds_get

24 from pygeodesy.fmath import fabs, fdot, Fhorner

25 from pygeodesy.fsums import _floor, Fsum, fsumf_, fsum1f_

26 from pygeodesy.interns import NN, _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, \

27 _invalid_, _lat0_, _lon0_, _ltp_, _M_, _name_, _too_

28# from pygeodesy.lazily import _ALL_LAZY # from vector3d

29 from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \

30 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \

31 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple

32 from pygeodesy.named import _NamedBase, notOverloaded

33 from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple

34 from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \

35 _update_all

36 from pygeodesy.streprs import Fmt, strs, unstr

37 from pygeodesy.units import Bearing, Degrees, Meter

38 from pygeodesy.utily import cotd, sincos2d, sincos2d_, tand, tand_, wrap180, wrap360

39 from pygeodesy.vector3d import _ALL_LAZY, Vector3d

40

41# from math import fabs, floor as _floor # from .fmath, .fsums

42

43__all__ = _ALL_LAZY.ltp

44__version__ = '23.08.06'

45

46_height0_ = _height_ + _0_

47_narrow_ = 'narrow'

48_wide_ = 'wide'

49_Xyz_ = 'Xyz'

50

51

52 def _fov_2(**fov):

53 # Half a field-of-view angle in C{degrees}.

54 f = Degrees(Error=LocalError, **fov) * _0_5

55 if EPS < f < _90_0:

56 return f

57 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)

58 raise LocalError(txt=t, **fov)

59

60

61 class Attitude(_NamedBase):

62 '''The orientation of a plane or camera in space.

63 '''

64 _alt = Meter( alt =_0_0)

65 _roll = Degrees(roll=_0_0)

66 _tilt = Degrees(tilt=_0_0)

67 _yaw = Bearing(yaw =_0_0)

68

69 def __init__(self, alt_attitude=INT0, tilt=INT0, yaw=INT0, roll=INT0, name=NN):

70 '''New L{Attitude}.

71

72 @kwarg alt_attitude: An altitude (C{meter}) above earth or an attitude

73 (L{Attitude} or L{Attitude4Tuple}) with the

74 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.

75 @kwarg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down

76 (clockwise rotation along and around the x- or East axis).

77 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North

78 (counter-clockwise rotation along and around the z- or Up axis).

79 @kwarg roll: Roll, bank (C{degrees180}), positive to the right and down

80 (clockwise rotation along and around the y- or North axis).

81 @kwarg name: Optional name C{str}).

82

83 @raise AttitudeError: Invalid B{C{alt_attitude}}, B{C{tilt}}, B{C{yaw}} or

84 B{C{roll}}.

85

86 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>} and

87 U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.

88 '''

89 if isscalar(alt_attitude):

90 t = Attitude4Tuple(alt_attitude, tilt, yaw, roll)

91 else:

92 try:

93 t = alt_attitude.atyr

94 except AttributeError:

95 raise AttitudeError(alt=alt_attitude, tilt=tilt, yaw=yaw, rol=roll)

96 for n, v in t.items():

97 if v:

98 setattr(self, n, v)

99 n = name or t.name

100 if n:

101 self.name = n

102

103 @property_doc_(' altitude above earth in C{meter}.')

104 def alt(self):

105 return self._alt

106

107 @alt.setter # PYCHOK setter!

108 def alt(self, alt): # PYCHOK no cover

109 a = Meter(alt=alt, Error=AttitudeError)

110 if self._alt != a:

111 _update_all(self)

112 self._alt = a

113

114 altitude = alt

115

116 @Property_RO

117 def atyr(self):

118 '''Return this attitude's alt[itude], tilt, yaw and roll as an L{Attitude4Tuple}.

119 '''

120 return Attitude4Tuple(self.alt, self.tilt, self.yaw, self.roll, name=self.name)

121

122 @Property_RO

123 def matrix(self):

124 '''Get the 3x3 rotation matrix C{R(yaw)·R(tilt)·R(roll)}, aka I{ZYX} (C{float}, row-order).

125

126 @see: The matrix M of case 10 in U{Appendix A

127 <https://ntrs.NASA.gov/api/citations/19770019231/downloads/19770019231.pdf>}.

128 '''

129 def _5to3(x, y, _y, z, _z):

130 return x, fsum1f_(y, _y), fsum1f_(z, _z)

131

132 r0, r1, r2 = self._rows3

133 return _5to3(*r0), _5to3(*r1), r2

134

135 @property_doc_(' roll/bank in C{degrees180}, positive to the right and down.')

136 def roll(self):

137 return self._roll

138

139 @roll.setter # PYCHOK setter!

140 def roll(self, roll):

141 r = Degrees(roll=roll, wrap=wrap180, Error=AttitudeError)

142 if self._roll != r:

143 _update_all(self)

144 self._roll = r

145

146 bank = roll

147

148 @Property_RO

149 def _rows3(self):

150 # to follow the definitions of rotation angles alpha, beta and gamma:

151 # negate yaw since yaw is counter-clockwise around the z-axis, swap

152 # tilt and roll since tilt is around the x- and roll around the y-axis

153 sa, ca, sb, cb, sg, cg = sincos2d_(-self.yaw, self.roll, self.tilt)

154 return ((ca * cb, ca * sb * sg, -sa * cg, ca * sb * cg, sa * sg),

155 (sa * cb, sa * sb * sg, ca * cg, sa * sb * cg, -ca * sg),

156 ( -sb, cb * sg, cb * cg))

157

158 def rotate(self, x_xyz, y=None, z=None, Vector=None, **Vector_kwds):

159 '''Transform a (local) cartesian by this attitude's matrix.

160

161 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector

162 (C{Cartesian}, L{Vector3d} or L{Vector3Tuple}).

163 @kwarg y: Y component of vector (C{scalar}), same units as B{C{x}}.

164 @kwarg z: Z component of vector (C{scalar}), same units as B{C{x}}.

165 @kwarg Vector: Class to return transformed point (C{Cartesian},

166 L{Vector3d} or C{Vector3Tuple}) or C{None}.

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

168 ignored if C{B{Vector} is None}.

169

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

171 C{B{Vector}=None}.

172

173 @raise AttitudeError: Invalid B{C{x_xyz}}, B{C{y}} or B{C{z}}.

174

175 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.

176 '''

177 try:

178 try:

179 x, y, z = map( float, x_xyz.xyz)

180 except AttributeError:

181 x, y, z = map1(float, x_xyz, y, z)

182 except (TypeError, ValueError) as x:

183 raise AttitudeError(x_xyz=x_xyz, y=y, z=z, cause=x)

184

185 X, Y, Z = self._rows3

186 X = fdot(X, x, y, y, z, z)

187 Y = fdot(Y, x, y, y, z, z)

188 Z = fdot(Z, x, y, z)

189 return Vector3Tuple(X, Y, Z, name=self.name) if Vector is None else \

190 Vector(X, Y, Z, **_xkwds(Vector_kwds, name=self.name))

191

192 @property_doc_(' tilt/pitch/elevation from horizontal in C{degrees180}, negative down.')

193 def tilt(self):

194 return self._tilt

195

196 @tilt.setter # PYCHOK setter!

197 def tilt(self, tilt):

198 t = Degrees(tilt=tilt, wrap=wrap180, Error=AttitudeError)

199 if self._tilt != t:

200 _update_all(self)

201 self._tilt = t

202

203 elevation = pitch = tilt

204

205 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature

206 '''Format this attitude as string.

207

208 @kwarg prec: The C{float} precision, number of decimal digits (0..9).

209 Trailing zero decimals are stripped for B{C{prec}} values

210 of 1 and above, but kept for negative B{C{prec}} values.

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

212

213 @return: This attitude (C{str}).

214 '''

215 return self.atyr.toStr(prec=prec, sep=sep)

216

217 @Property_RO

218 def tyr3d(self):

219 '''Get this attitude's (3-D) directional vector (L{Vector3d}).

220

221 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.

222 '''

223 def _r2d(r):

224 return fsumf_(_N_1_0, *r)

225

226 return Vector3d(*map(_r2d, self._rows3), name=tyr3d.__name__)

227

228 @property_doc_(' yaw/bearing/heading in compass C{degrees360}, clockwise from North.')

229 def yaw(self):

230 return self._yaw

231

232 @yaw.setter # PYCHOK setter!

233 def yaw(self, yaw):

234 y = Bearing(yaw=yaw, Error=AttitudeError)

235 if self._yaw != y:

236 _update_all(self)

237 self._yaw = y

238

239 bearing = heading = yaw

240

241

242 class AttitudeError(_ValueError):

243 '''An L{Attitude} or L{Attitude4Tuple} issue.

244 '''

245 pass

246

247

248 class Frustum(_NamedBase):

249 '''A rectangular pyramid, typically representing a camera's I{field-of-view}

250 (fov) and the intersection with (or projection to) a I{local tangent plane}.

251

252 @see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}.

253 '''

254 _h_2 = _0_0 # half hfov in degrees

255 _ltp = None # local tangent plane

256 _tan_h_2 = _0_0 # tan(_h_2)

257 _v_2 = _0_0 # half vfov in degrees

258

259 def __init__(self, hfov, vfov, ltp=None):

260 '''New L{Frustum}.

261

262 @arg hfov: Horizontal field-of-view (C{degrees180}).

263 @arg vfov: Vertical field-of-view (C{degrees180}).

264 @kwarg ltp: Optional I{local tangent plane} (L{Ltp}).

265

266 @raise LocalError: Invalid B{C{hfov}} or B{C{vfov}}.

267 '''

268 self._h_2 = h = _fov_2(hfov=hfov)

269 self._v_2 = _fov_2(vfov=vfov)

270

271 self._tan_h_2 = tand(h, fov_2=h)

272

273 if ltp:

274 self._ltp = _xLtp(ltp)

275

276 def footprint5(self, alt_attitude, tilt=0, yaw=0, roll=0, z=_0_0, ltp=None): # MCCABE 15

277 '''Compute the center and corners of the intersection with (or projection

278 to) the I{local tangent plane} (LTP).

279

280 @arg alt_attitude: An altitude (C{meter}) above I{local tangent plane} or

281 an attitude (L{Attitude} or L{Attitude4Tuple}) with the

282 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.

283 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down

284 (clockwise rotation along and around the x- or East axis).

285 @kwarg yaw: Bearing, heading (compass C{degrees}), clockwise from North

286 (counter-clockwise rotation along and around the z- or Up axis).

287 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down

288 (clockwise rotation along and around the y- or North axis).

289 @kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}.

290 @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this

291 frustum's C{ltp}.

292

293 @return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright,

294 lowerleft)} with the C{center} and 4 corners, each an L{Xyz4Tuple}.

295

296 @raise TypeError: Invalid B{C{ltp}}.

297

298 @raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}.

299

300 @raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}}

301 or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}-

302 over the horizon.

303

304 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}.

305 '''

306 def _xy2(a, e, h_2, tan_h_2, r):

307 # left and right corners, or swapped

308 if r < EPS: # no roll

309 r = a * tan_h_2

310 l = -r # PYCHOK l is ell

311 else: # roll

312 r, l = tand_(r - h_2, r + h_2, roll_hfov=r) # PYCHOK l is ell

313 r *= -a # negate right positive

314 l *= -a # PYCHOK l is ell

315 y = a * cotd(e, tilt_vfov=e)

316 return (l, y), (r, y)

317

318 def _xyz5(b, xy5, z, ltp):

319 # rotate (x, y)'s by bearing, clockwise

320 s, c = sincos2d(b)

321 for x, y in xy5:

322 yield Xyz4Tuple(fsum1f_(x * c, y * s),

323 fsum1f_(y * c, -x * s), z, ltp)

324

325 try:

326 a, t, y, r = alt_attitude.atyr

327 except AttributeError:

328 a, t, y, r = alt_attitude, tilt, yaw, roll

329

330 a = Meter(altitude=a)

331 if a < EPS: # too low

332 raise _ValueError(altitude=a)

333 if z: # PYCHOK no cover

334 z = Meter(z=z)

335 a -= z

336 if a < EPS: # z above a

337 raise _ValueError(altitude_z=a)

338 else:

339 z = _0_0

340

341 b = Degrees(yaw=y, wrap=wrap360) # bearing

342 e = -Degrees(tilt=t, wrap=wrap180) # elevation, pitch

343 if not EPS < e < _180_0:

344 raise _ValueError(tilt=t)

345 if e > _90_0:

346 e = _180_0 - e

347 b = _umod_360(b + _180_0)

348

349 r = Degrees(roll=r, wrap=wrap180) # roll center

350 x = (-a * tand(r, roll=r)) if r else _0_0

351 y = a * cotd(e, tilt=t) # ground range

352 if fabs(y) < EPS:

353 y = _0_0

354

355 # center and corners, clockwise from upperleft, rolled

356 xy5 = ((x, y),) + _xy2(a, e - self._v_2, self._h_2, self._tan_h_2, r) \

357 + _xy2(a, e + self._v_2, -self._h_2, -self._tan_h_2, r) # swapped

358 # turn center and corners by yaw, clockwise

359 p = self.ltp if ltp is None else ltp # None OK

360 return Footprint5Tuple(_xyz5(b, xy5, z, p)) # *_xyz5

361

362 @Property_RO

363 def hfov(self):

364 '''Get the horizontal C{fov} (C{degrees}).

365 '''

366 return Degrees(hfov=self._h_2 * _2_0)

367

368 @Property_RO

369 def ltp(self):

370 '''Get the I{local tangent plane} (L{Ltp}) or C{None}.

371 '''

372 return self._ltp

373

374 def toStr(self, prec=3, fmt=Fmt.F, sep=_COMMASPACE_): # PYCHOK signature

375 '''Convert this frustum to a "hfov, vfov, ltp" string.

376

377 @kwarg prec: Number of (decimal) digits, unstripped (0..8 or C{None}).

378 @kwarg fmt: Optional, C{float} format (C{str}).

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

380

381 @return: Frustum in the specified form (C{str}).

382 '''

383 t = self.hfov, self.vfov

384 if self.ltp:

385 t += self.ltp,

386 t = strs(t, prec=prec, fmt=fmt)

387 return sep.join(t) if sep else t

388

389 @Property_RO

390 def vfov(self):

391 '''Get the vertical C{fov} (C{degrees}).

392 '''

393 return Degrees(vfov=self._v_2 * _2_0)

394

395

396 class LocalError(_ValueError):

397 '''A L{LocalCartesian} or L{Ltp} related issue.

398 '''

399 pass

400

401

402 class LocalCartesian(_NamedBase):

403 '''Conversion between geodetic C{(lat, lon, height)} and I{local

404 cartesian} C{(x, y, z)} coordinates with I{geodetic} origin

405 C{(lat0, lon0, height0)}, transcoded from I{Karney}'s C++ class

406 U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/

407 classGeographicLib_1_1LocalCartesian.html>}.

408

409 The C{z} axis is normal to the ellipsoid, the C{y} axis points due

410 North. The plane C{z = -height0} is tangent to the ellipsoid.

411

412 The conversions all take place via geocentric coordinates using a

413 geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid.

414

415 @see: Class L{Ltp}.

416 '''

417 _ecef = EcefKarney(_WGS84)

418 _EcefClass = EcefKarney

419 _lon00 = INT0 # self.lon0

420 _t0 = None # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple}

421 _9Tuple = Local9Tuple

422

423 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):

424 '''New L{LocalCartesian} converter.

425

426 @kwarg latlonh0: The (geodetic) origin (C{LatLon}, L{LatLon4Tuple}, L{Ltp}

427 L{LocalCartesian} or L{Ecef9Tuple}) or the C{scalar}

428 latitude of the (goedetic) origin (C{degrees}).

429 @kwarg lon0: Longitude of the (goedetic) origin (C{degrees}) for C{scalar}

430 B{C{latlonh0}}, ignored otherwise.

431 @kwarg height0: Optional height (C{meter}, conventionally) at the (goedetic)

432 origin perpendicular to and above (or below) the ellipsoid's

433 surface and for C{scalar} B{C{latlonh0}}, ignored otherwise.

434 @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}) for C{scalar}

435 B{C{latlonh0}}, ignored otherwise.

436 @kwarg name: Optional name (C{str}).

437 @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), overriding

438 the default C{B{lon00}=B{lon0}}, see method C{reverse}.

439

440 @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{LatLon4Tuple}, L{Ltp},

441 L{LocalCartesian} or L{Ecef9Tuple} or B{C{latlonh0}},

442 B{C{lon0}}, B{C{height0}} or B{C{lon00}} invalid.

443

444 @raise TypeError: Invalid B{C{ecef}} or not L{EcefKarney}.

445

446 @note: If BC{latlonh0} is an L{Ltp} or L{LocalCartesian}, only C{lat0}, C{lon0},

447 C{height0} and I{polar} C{lon00} are copied, I{not} the ECEF converter.

448 '''

449 self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, name=name, **lon00)

450

451 def __eq__(self, other):

452 '''Compare this and an other instance.

453

454 @arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}).

455

456 @return: C{True} if equal, C{False} otherwise.

457 '''

458 return other is self or (isinstance(other, self.__class__) and

459 other.ecef == self.ecef and

460 other._t0 == self._t0)

461

462 @Property_RO

463 def datum(self):

464 '''Get the ECEF converter's datum (L{Datum}).

465 '''

466 return self.ecef.datum

467

468 @Property_RO

469 def ecef(self):

470 '''Get the ECEF converter (L{EcefKarney}).

471 '''

472 return self._ecef

473

474 def _ecef2local(self, ecef, Xyz, Xyz_kwds):

475 '''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}.

476

477 @arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}).

478 @arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}.

479 @arg Xyz_kwds: B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}.

480

481 @return: An C{B{Xyz}(x, y, z, ltp, **B{Xyz_kwds}} instance or if

482 C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon,

483 height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}}

484 (L{Ecef9Tuple}) converted to this C{datum} and C{M=None},

485 always.

486 '''

487 ltp = self

488 if ecef.datum != ltp.datum:

489 ecef = ecef.toDatum(ltp.datum)

490 x, y, z = self.M.rotate(ecef.xyz, *ltp._t0_xyz)

491 r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height,

492 ltp, ecef, None, name=ecef.name)

493 if Xyz:

494 if not issubclassof(Xyz, *_XyzLocals4): # Vector3d

495 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4)

496 r = r.toXyz(Xyz=Xyz, **Xyz_kwds)

497 return r

498

499 @Property_RO

500 def ellipsoid(self):

501 '''Get the ECEF converter's ellipsoid (L{Ellipsoid}).

502 '''

503 return self.ecef.datum.ellipsoid

504

505 def forward(self, latlonh, lon=None, height=0, M=False, name=NN):

506 '''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian

507 C{(x, y, z)}.

508

509 @arg latlonh: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or C{scalar}

510 (geodetic) latitude (C{degrees}).

511 @kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar}

512 B{C{latlonh}} (C{degrees}).

513 @kwarg height: Optional height (C{meter}, conventionally) perpendicular

514 to and above (or below) the ellipsoid's surface.

515 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix},

516 iff available (C{bool}).

517 @kwarg name: Optional name (C{str}).

518

519 @return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)}

520 with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon},

521 C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with

522 I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat},

523 C{lon}, C{height}) and the I{concatenated} rotation matrix

524 C{M} (L{EcefMatrix}) if requested.

525

526 @raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp},

527 L{Ecef9Tuple} or invalid or if B{C{lon}} not

528 C{scalar} for C{scalar} B{C{latlonh}} or invalid

529 or if B{C{height}} invalid.

530 '''

531 lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, name=name)

532 t = self.ecef._forward(lat, lon, h, n, M=M)

533 x, y, z = self.M.rotate(t.xyz, *self._t0_xyz)

534 m = self.M.multiply(t.M) if M else None

535 return self._9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name)

536

537 @Property_RO

538 def height0(self):

539 '''Get the origin's height (C{meter}).

540 '''

541 return self._t0.height

542

543 @Property_RO

544 def lat0(self):

545 '''Get the origin's latitude (C{degrees}).

546 '''

547 return self._t0.lat

548

549 @Property_RO

550 def latlonheight0(self):

551 '''Get the origin's lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).

552 '''

553 return LatLon3Tuple(self.lat0, self.lon0, self.height0, name=self.name)

554

555 def _local2ecef(self, local, nine=False, M=False):

556 '''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}.

557

558 @arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}).

559 @kwarg nine: Return 3- or 9-tuple (C{bool}).

560 @kwarg M: Include the rotation matrix (C{bool}).

561

562 @return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True},

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

564 optionally including rotation matrix C{M} or C{None}.

565 '''

566 t = self.M.unrotate(local.xyz, *self._t0_xyz)

567 if nine:

568 t = self.ecef.reverse(*t, M=M)

569 return t

570

571 @Property_RO

572 def lon0(self):

573 '''Get the origin's longitude (C{degrees}).

574 '''

575 return self._t0.lon

576

577 @Property

578 def lon00(self):

579 '''Get the arbitrary, I{polar} longitude (C{degrees}).

580 '''

581 return self._lon00

582

583 @lon00.setter # PYCHOK setter!

584 def lon00(self, lon00):

585 '''Set the arbitrary, I{polar} longitude (C{degrees}).

586 '''

587 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>

588 self._lon00 = Degrees(lon00=lon00)

589

590 @Property_RO

591 def M(self):

592 '''Get the rotation matrix (C{EcefMatrix}).

593 '''

594 return self._t0.M

595

596 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):

597 '''Reset this converter, see L{LocalCartesian.__init__} and L{Ltp.__init__} for more details.

598 '''

599 if isinstance(latlonh0, LocalCartesian):

600 if self._t0:

601 _update_all(self)

602 self._ecef = latlonh0.ecef

603 self._lon00 = latlonh0.lon00

604 self._t0 = latlonh0._t0

605 n = name or latlonh0.name

606 else:

607 lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_,

608 Error=LocalError, name=name or self.name)

609 if ecef: # PYCHOK no cover

610 _xinstanceof(self._EcefClass, ecef=ecef)

611 _update_all(self)

612 self._ecef = ecef

613 elif self._t0:

614 _update_all(self)

615 self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True)

616 self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00, lon00=lon0))

617 if n:

618 self.rename(n)

619

620 def reverse(self, xyz, y=None, z=None, M=False, name=NN, **lon00):

621 '''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}.

622

623 @arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or

624 local C{x} coordinate (C{scalar}).

625 @kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

626 @kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

627 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, iff

628 available (C{bool}).

629 @kwarg name: Optional name (C{str}).

630 @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), returned for local

631 C{B{x}=0} and C{B{y}=0} at I{polar} latitudes C{abs(B{lat0}) == 90},

632 overriding property C{lon00} and default C{B{lon00}=B{lon0}}.

633

634 @return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with

635 I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height},

636 this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x},

637 C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the

638 I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested.

639

640 @raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}

641 not C{scalar} for C{scalar} B{C{xyz}}.

642 '''

643 x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name)

644 c = self.M.unrotate((x, y, z), *self._t0_xyz)

645 t = self.ecef.reverse(*c, M=M, lon00=_xkwds_get(lon00, lon00=self.lon00))

646 m = self.M.multiply(t.M) if M else None

647 return self._9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name)

648

649 @Property_RO

650 def _t0_xyz(self):

651 '''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}.

652 '''

653 return self._t0.xyz

654

655 def toStr(self, prec=9, **unused): # PYCHOK signature

656 '''Return this L{LocalCartesian} as a string.

657

658 @kwarg prec: Precision, number of (decimal) digits (0..9).

659

660 @return: This L{LocalCartesian} representation (C{str}).

661 '''

662 return self.attrs(_lat0_, _lon0_, _height0_, _M_, _ecef_, _name_, prec=prec)

663

664

665 class Ltp(LocalCartesian):

666 '''A I{local tangent plan} (LTP), a sub-class of C{LocalCartesian} with

667 (re-)configurable ECEF converter.

668 '''

669 _EcefClass = _EcefBase

670

671 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):

672 '''New C{Ltp}, see L{LocalCartesian.__init__} for more details.

673

674 @kwarg ecef: Optional ECEF converter (L{EcefKarney}, L{EcefFarrell21},

675 L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or

676 L{EcefYou} I{instance}), overriding the default

677 L{EcefKarney}C{(datum=Datums.WGS84)} for C{scalar}.

678

679 @raise TypeError: Invalid B{C{ecef}}.

680 '''

681 LocalCartesian.reset(self, latlonh0, lon0=lon0, height0=height0,

682 ecef=ecef, name=name, **lon00)

683

684 @Property

685 def ecef(self):

686 '''Get this LTP's ECEF converter (C{Ecef...} I{instance}).

687 '''

688 return self._ecef

689

690 @ecef.setter # PYCHOK setter!

691 def ecef(self, ecef):

692 '''Set this LTP's ECEF converter (C{Ecef...} I{instance}).

693

694 @raise TypeError: Invalid B{C{ecef}}.

695 '''

696 _xinstanceof(_EcefBase, ecef=ecef)

697 if ecef != self._ecef: # PYCHOK no cover

698 self.reset(self._t0)

699 self._ecef = ecef

700

701

702 class _ChLV(object):

703 '''(INTERNAL) Base class for C{ChLV*} classes.

704 '''

705 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)

706# _92_falsing = ChLVYX2Tuple(2.0e6, 1.0e6) # _95_ - _03_

707 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)

708

709 def _ChLV9Tuple(self, fw, M, name, *Y_X_h_lat_lon_h):

710 '''(INTERNAL) Helper for C{ChLVa/e.forward} and C{.reverse}.

711 '''

712 if bool(M): # PYCHOK no cover

713 m = self.forward if fw else self.reverse # PYCHOK attr

714 n = _DOT_(self.__class__.__name__, m.__name__)

715 raise _NotImplementedError(unstr(n, M=M), txt=None)

716 t = Y_X_h_lat_lon_h + (self, self._t0, None) # PYCHOK _t0

717 return ChLV9Tuple(t, name=name)

718

719 @property_RO

720 def _enh_n_h(self):

721 '''(INTERNAL) Get C{ChLV*.reverse} args[1:4] names, I{once}.

722 '''

723 t = _xargs_names(_ChLV.reverse)[1:4]

724 _ChLV._enh_n_h = t # overwrite this property_RO

725 # assert _xargs_names( ChLV.reverse)[1:4] == t

726 # assert _xargs_names(ChLVa.reverse)[1:4] == t

727 # assert _xargs_names(ChLVe.reverse)[1:4] == t

728 return t

729

730 def forward(self, latlonh, lon=None, height=0, M=None, name=NN): # PYCHOK no cover

731 '''Convert WGS84 geodetic to I{Swiss} projection coordinates.

732

733 @arg latlonh: Either a C{LatLon}, L{Ltp} or C{scalar} (geodetic) latitude (C{degrees}).

734 @kwarg lon: Optional, C{scalar} (geodetic) longitude for C{scalar} B{C{latlonh}} (C{degrees}).

735 @kwarg height: Optional, height, vertically above (or below) the surface of the ellipsoid

736 (C{meter}) for C{scalar} B{C{latlonh}} and B{C{lon}}.

737 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available

738 for C{ChLV} only, C{None} otherwise (C{bool}).

739 @kwarg name: Optional name (C{str}).

740

741 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed

742 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},

743 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at

744 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},

745 C{ChLVa} or C{ChLVe} instance.

746

747 @raise LocalError: Invalid or non-C{scalar} B{C{latlonh}}, B{C{lon}} or B{C{height}}.

748 '''

749 notOverloaded(self, latlonh, lon=lon, height=height, M=M, name=name)

750

751 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK no cover

752 '''Convert I{Swiss} projection to WGS84 geodetic coordinates.

753

754 @arg enh_: A Swiss projection (L{ChLV9Tuple}) or the C{scalar}, falsed I{Swiss E_LV95}

755 or I{y_LV03} easting (C{meter}).

756 @kwarg n: Falsed I{Swiss N_LV85} or I{x_LV03} northing for C{scalar} B{C{enh_}} and

757 B{C{h_}} (C{meter}).

758 @kwarg h_: I{Swiss h'} height for C{scalar} B{C{enh_}} and B{C{n}} (C{meter}).

759 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available

760 for C{ChLV} only, C{None} otherwise (C{bool}).

761 @kwarg name: Optional name (C{str}).

762

763 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed

764 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},

765 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at

766 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},

767 C{ChLVa} or C{ChLVe} instance.

768

769 @raise LocalError: Invalid or non-C{scalar} B{C{enh_}}, B{C{n}} or B{C{h_}}.

770 '''

771 notOverloaded(self, enh_, n=n, h_=h_, M=M, **name)

772

773 @staticmethod

774 def _falsing2(LV95):

775 '''(INTERNAL) Get the C{LV95} or C{LV03} falsing.

776 '''

777 return _ChLV._95_falsing if LV95 in (True, 95) else (

778 _ChLV._03_falsing if LV95 in (False, 3) else ChLVYX2Tuple(0, 0))

779

780 @staticmethod

781 def _llh2abh_3(lat, lon, h):

782 '''(INTERNAL) Helper for C{ChLVa/e.forward}.

783 '''

784 def _deg2ab(deg, sLL):

785 # convert degrees to arc-seconds

786 def _dms(ds, p, q, swap):

787 d = _floor(ds)

788 t = (ds - d) * p

789 m = _floor(t)

790 s = (t - m) * p

791 if swap:

792 d, s = s, d

793 return d + (m + s * q) * q

794

795 s = _dms(deg, _60_0, _0_01, False) # deg2sexag

796 s = _dms( s, _100_0, _60_0, True) # sexag2asec

797 return (s - sLL) / ChLV._s_ab

798

799 a = _deg2ab(lat, ChLV._sLat) # phi', lat_aux

800 b = _deg2ab(lon, ChLV._sLon) # lam', lng_aux

801 h_ = fsumf_(h, -ChLV.Bern.height, 2.73 * b, 6.94 * a)

802 return a, b, h_

803

804 @staticmethod

805 def _YXh_2abh3(Y, X, h_):

806 '''(INTERNAL) Helper for C{ChLVa/e.reverse}.

807 '''

808 def _YX2ab(YX):

809 return YX * ChLV._ab_m

810

811 a, b = map1(_YX2ab, Y, X)

812 h = fsumf_(h_, ChLV.Bern.height, -12.6 * a, -22.64 * b)

813 return a, b, h

814

815 def _YXh_n4(self, enh_, n, h_, **name):

816 '''(INTERNAL) Helper for C{ChLV*.reverse}.

817 '''

818 Y, X, h_, name = _xyzn4(enh_, n, h_, ChLV9Tuple,

819 _xyz_y_z_names=self._enh_n_h, **name)

820 if isinstance(enh_, ChLV9Tuple):

821 Y, X = enh_.Y, enh_.X

822 else: # isscalar(enh_)

823 Y, X = ChLV.unfalse2(Y, X) # PYCHOK ChLVYX2Tuple

824 return Y, X, h_, name

825

826

827 class ChLV(_ChLV, Ltp):

828 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates using

829 L{pygeodesy.EcefKarney}'s Earth-Centered, Earth-Fixed (ECEF) methods.

830

831 @see: U{Swiss projection formulas<https://www.SwissTopo.admin.CH/en/maps-data-online/

832 calculation-services.html>}, page 7ff, U{NAVREF<https://www.SwissTopo.admin.CH/en/

833 maps-data-online/calculation-services/navref.html>}, U{REFRAME<https://www.SwissTopo.admin.CH/

834 en/maps-data-online/calculation-services/reframe.html>} and U{SwissTopo Scripts GPS WGS84

835 <-> LV03<https://GitHub.com/ValentinMinder/Swisstopo-WGS84-LV03>}.

836 '''

837 _9Tuple = ChLV9Tuple

838

839 _ab_d = 0.36 # a, b units per degree, ...

840 _ab_m = 1.0e-6 # ... per meter and ...

841 _ab_M = _1_0 # ... per 1,000 kilometer

842 _s_d = _3600_0 # arc-seconds per degree ...

843 _s_ab = _s_d / _ab_d # ... and per a, b unit

844 _sLat = 169028.66 # Bern, Ch in ...

845 _sLon = 26782.5 # ... arc-seconds ...

846 # lat, lon, height == 46°57'08.66", 7°26'22.50", 49.55m ("new" 46°57'07.89", 7°26'22.335")

847 Bern = LatLon4Tuple(_sLat / _s_d, _sLon / _s_d, 49.55, _WGS84, name='Bern')

848

849 def __init__(self, latlonh0=Bern, **other_Ltp_kwds):

850 '''New ECEF-based I{WGS84-Swiss} L{ChLV} converter, centered at I{Bern, Ch}.

851

852 @kwarg latlonh0: The I{geodetic} origin and height, overriding C{Bern, Ch}.

853 @kwarg other_Ltp_kwds: Optional, other L{Ltp.__init__} keyword arguments.

854

855 @see: L{Ltp.__init__} for more information.

856 '''

857 Ltp.__init__(self, latlonh0, **_xkwds(other_Ltp_kwds, ecef=None, name=ChLV.Bern.name))

858

859 def forward(self, latlonh, lon=None, height=0, M=None, name=NN): # PYCHOK unused M

860 # overloaded for the _ChLV.forward.__doc__

861 return Ltp.forward(self, latlonh, lon=lon, height=height, M=M, name=name)

862

863 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature

864 # overloaded for the _ChLV.reverse.__doc__

865 Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)

866 return Ltp.reverse(self, Y, X, h_, M=M, name=name)

867

868 @staticmethod

869 def false2(Y, X, LV95=True, name=NN):

870 '''Add the I{Swiss LV95} or I{LV03} falsing.

871

872 @arg Y: Unfalsed I{Swiss Y} easting (C{meter}).

873 @arg X: Unfalsed I{Swiss X} northing (C{meter}).

874 @kwarg LV95: If C{True} add C{LV95} falsing, if C{False} add

875 C{LV03} falsing, otherwise leave unfalsed.

876 @kwarg name: Optional name (C{str}).

877

878 @return: A L{ChLVEN2Tuple}C{(E_LV95, N_LV95)} or a

879 L{ChLVyx2Tuple}C{(y_LV03, x_LV03)} with falsed B{C{Y}}

880 and B{C{X}}, otherwise a L{ChLVYX2Tuple}C{(Y, X)}

881 with B{C{Y}} and B{C{X}} as-is.

882 '''

883 e, n = t = _ChLV._falsing2(LV95)

884 return t.classof(e + Y, n + X, name=name)

885

886 @staticmethod

887 def isLV03(e, n):

888 '''Is C{(B{e}, B{n})} a valid I{Swiss LV03} projection?

889

890 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).

891 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).

892

893 @return: C{True} if C{(B{e}, B{n})} is a valid, falsed I{Swiss

894 LV03}, projection C{False} otherwise.

895 '''

896 # @see: U{Map<https://www.SwissTopo.admin.CH/en/knowledge-facts/

897 # surveying-geodesy/reference-frames/local/lv95.html>}

898 return 400.0e3 < e < 900.0e3 and 40.0e3 < n < 400.0e3

899

900 @staticmethod

901 def isLV95(e, n, raiser=True):

902 '''Is C{(B{e}, B{n})} a valid I{Swiss LV95} or I{LV03} projection?

903

904 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).

905 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).

906 @kwarg raiser: If C{True}, throw a L{LocalError} if B{C{e}} and

907 B{C{n}} are invalid I{Swiss LV95} nor I{LV03}.

908

909 @return: C{True} or C{False} if C{(B{e}, B{n})} is a valid I{Swiss

910 LV95} respectively I{LV03} projection, C{None} otherwise.

911 '''

912 if ChLV.isLV03(e, n):

913 return False

914 elif ChLV.isLV03(e - 2.0e6, n - 1.0e6): # _92_falsing = _95_ - _03_

915 return True

916 elif raiser: # PYCHOK no cover

917 raise LocalError(unstr(ChLV.isLV95, e=e, n=n))

918 return None

919

920 @staticmethod

921 def unfalse2(e, n, LV95=None, name=NN):

922 '''Remove the I{Swiss LV95} or I{LV03} falsing.

923

924 @arg e: Falsed I{Swiss E_LV95} or I{y_LV03} easting (C{meter}).

925 @arg n: Falsed I{Swiss N_LV95} or I{x_LV03} northing (C{meter}).

926 @kwarg LV95: If C{True} remove I{LV95} falsing, if C{False} remove

927 I{LV03} falsing, otherwise use method C{isLV95(B{e},

928 B{n})}.

929 @kwarg name: Optional name (C{str}).

930

931 @return: A L{ChLVYX2Tuple}C{(Y, X)} with the unfalsed B{C{e}}

932 respectively B{C{n}}.

933 '''

934 Y, X = _ChLV._falsing2(ChLV.isLV95(e, n) if LV95 is None else LV95)

935 return ChLVYX2Tuple(e - Y, n - X, name=name)

936

937

938 class ChLVa(_ChLV, LocalCartesian):

939 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates

940 using the U{Approximate<https://www.SwissTopo.admin.CH/en/maps-data-online/

941 calculation-services.html>} formulas, page 13.

942

943 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.

944 '''

945 def __init__(self, name=ChLV.Bern.name):

946 '''New I{Approximate WGS84-Swiss} L{ChLVa} converter, centered at I{Bern, Ch}.

947

948 @kwarg name: Optional name (C{str}), overriding C{Bern.name}.

949 '''

950 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

951

952 def forward(self, latlonh, lon=None, height=0, M=None, name=NN):

953 # overloaded for the _ChLV.forward.__doc__

954 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)

955 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)

956 a2, b2 = a**2, b**2

957

958 Y = fsumf_( 72.37, 211455.93 * b,

959 -10938.51 * b * a,

960 -0.36 * b * a2,

961 -44.54 * b * b2) # + 600_000

962 X = fsumf_(147.07, 308807.95 * a,

963 3745.25 * b2,

964 76.63 * a2,

965 -194.56 * b2 * a,

966 119.79 * a2 * a) # + 200_000

967 return self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)

968

969 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature

970 # overloaded for the _ChLV.reverse.__doc__

971 Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)

972 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)

973 ab_d, a2, b2 = ChLV._ab_d, a**2, b**2

974

975 lat = Fsum(16.9023892, 3.238272 * b,

976 -0.270978 * a2,

977 -0.002528 * b2,

978 -0.0447 * a2 * b,

979 -0.014 * b2 * b).fover(ab_d)

980 lon = Fsum( 2.6779094, 4.728982 * a,

981 0.791484 * a * b,

982 0.1306 * a * b2,

983 -0.0436 * a * a2).fover(ab_d)

984 return self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)

985

986

987 class ChLVe(_ChLV, LocalCartesian):

988 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates

989 using the U{Ellipsoidal approximate<https://www.SwissTopo.admin.CH/en/

990 maps-data-online/calculation-services.html>} formulas, pp 10-11 and U{Bolliger,

991 J.<https://eMuseum.GGGS.CH/literatur-lv/liste-Dateien/1967_Bolliger_a.pdf>}

992 pp 148-151 (also U{GGGS<https://eMuseum.GGGS.CH/literatur-lv/liste.htm>}).

993

994 @note: Methods L{ChLVe.forward} and L{ChLVe.reverse} have an additional keyword

995 argument C{B{gamma}=False} to approximate the I{meridian convergence}.

996 If C{B{gamma}=True} a 2-tuple C{(t, gamma)} is returned with C{t} the

997 usual result (C{ChLV9Tuple}) and C{gamma}, the I{meridian convergence}

998 (decimal C{degrees}). To convert C{gamma} to C{grades} or C{gons},

999 use function L{pygeodesy.degrees2grades}.

1000

1001 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.

1002 '''

1003 def __init__(self, name=ChLV.Bern.name):

1004 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.

1005

1006 @kwarg name: Optional name (C{str}), overriding C{Bern.name}.

1007 '''

1008 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

1009

1010 def forward(self, latlonh, lon=None, height=0, M=None, name=NN, gamma=False): # PYCHOK gamma

1011 # overloaded for the _ChLV.forward.__doc__

1012 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)

1013 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)

1014 ab_M, z, _F = ChLV._ab_M, 0, Fhorner

1015

1016 B1 = _F(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)

1017 B3 = _F(a, -44.232717, 4.291740, -0.309883, 0.013924)

1018 B5 = _F(a, 0.019784, -0.004277)

1019 Y = _F(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!

1020

1021 B0 = _F(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)

1022 B2 = _F(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)

1023 B4 = _F(a, -0.734684, 0.144466, -0.011842)

1024 B6 = 0.000488

1025 X = _F(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!

1026

1027 t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)

1028 if gamma:

1029 U1 = _F(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)

1030 U3 = _F(a, -412.991934, 64.106344, -2.679566, 0.123833)

1031 U5 = _F(a, 0.204129, -0.037725)

1032 g = _F(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?

1033 t = t, g

1034 return t

1035

1036 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma

1037 # overloaded for the _ChLV.reverse.__doc__

1038 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name)

1039 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)

1040 s_d, _F, z = ChLV._s_d, Fhorner, 0

1041

1042 A0 = _F(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)

1043 A2 = _F(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)

1044 A4 = _F(b, 24.42786, 13.20703, 4.7476)

1045 A6 = -0.4249

1046 lat = _F(a, A0, z, A2, z, A4, z, A6).fover(s_d)

1047

1048 A1 = _F(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)

1049 A3 = _F(b, -442.709889, -255.02202, -96.34947, -30.0808)

1050 A5 = _F(b, 9.63495, 9.0243)

1051 lon = _F(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)

1052 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d

1053

1054 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)

1055 if gamma:

1056 U1 = _F(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)

1057 U3 = _F(b, -1435.508, -794.8777, -296.309, -92.908)

1058 U5 = _F(b, 29.631, 27.873)

1059 g = _F(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees

1060 t = t, g

1061 return t

1062

1063

1064 def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds):

1065 '''Convert an attitude oriention into a (3-D) direction vector.

1066

1067 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down

1068 (clockwise rotation along and around the x-axis).

1069 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North

1070 (counter-clockwise rotation along and around the z-axis).

1071 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down

1072 (clockwise rotation along and around the y-axis).

1073

1074 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},

1075 a named L{Vector3Tuple}C{(x, y, z)}.

1076

1077 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}

1078 and function L{pygeodesy.hartzell} argument C{los}.

1079 '''

1080 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d

1081 return d if Vector is type(d) else (

1082 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else

1083 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent

1084

1085

1086 def _xLtp(ltp, *dflt):

1087 '''(INTERNAL) Validate B{C{ltp}}.

1088 '''

1089 if dflt and ltp is None:

1090 ltp = dflt[0]

1091 if isinstance(ltp, (LocalCartesian, Ltp)):

1092 return ltp

1093 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)

1094

1095# **) MIT License

1096#

1097# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1098#

1099# Permission is hereby granted, free of charge, to any person obtaining a

1100# copy of this software and associated documentation files (the "Software"),

1101# to deal in the Software without restriction, including without limitation

1102# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1103# and/or sell copies of the Software, and to permit persons to whom the

1104# Software is furnished to do so, subject to the following conditions:

1105#

1106# The above copyright notice and this permission notice shall be included

1107# in all copies or substantial portions of the Software.

1108#

1109# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1110# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1111# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

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