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 _args_kwds_names, issubclassof, map1, map2 # .datums

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, _isHeight, Meter

38 from pygeodesy.utily import cotd, _loneg, sincos2d, sincos2d_, tand, tand_, \

39 wrap180, wrap360

40 from pygeodesy.vector3d import _ALL_LAZY, Vector3d

41

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

43

44__all__ = _ALL_LAZY.ltp

45__version__ = '24.02.16'

46

47_height0_ = _height_ + _0_

48_narrow_ = 'narrow'

49_wide_ = 'wide'

50_Xyz_ = 'Xyz'

51

52

53 def _fov_2(**fov):

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

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

56 if EPS < f < _90_0:

57 return f

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

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

60

61

62 class Attitude(_NamedBase):

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

64 '''

65 _alt = Meter( alt =_0_0)

66 _roll = Degrees(roll=_0_0)

67 _tilt = Degrees(tilt=_0_0)

68 _yaw = Bearing(yaw =_0_0)

69

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

71 '''New L{Attitude}.

72

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

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

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

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

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

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

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

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

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

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

83

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

85 B{C{roll}}.

86

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

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

89 '''

90 if _isHeight(alt_attitude):

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

92 else:

93 try:

94 t = alt_attitude.atyr

95 except AttributeError:

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

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

98 if v:

99 setattr(self, n, v)

100 n = name or t.name

101 if n:

102 self.name = n

103

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

105 def alt(self):

106 return self._alt

107

108 @alt.setter # PYCHOK setter!

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

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

111 if self._alt != a:

112 _update_all(self)

113 self._alt = a

114

115 altitude = alt

116

117 @Property_RO

118 def atyr(self):

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

120 '''

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

122

123 @Property_RO

124 def matrix(self):

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

126

127 @see: Matrix M of case 10 in U{Appendix A

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

129 '''

130 _f = fsum1f_

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

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

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

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

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

136 (sa * cb, _f(sa * sb * sg, ca * cg), _f(sa * sb * cg, -ca * sg)),

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

138

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

140 def roll(self):

141 return self._roll

142

143 @roll.setter # PYCHOK setter!

144 def roll(self, roll):

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

146 if self._roll != r:

147 _update_all(self)

148 self._roll = r

149

150 bank = roll

151

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

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

154

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

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

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

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

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

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

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

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

163

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

165 C{B{Vector}=None}.

166

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

168

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

170 '''

171 try:

172 try:

173 xyz = map2(float, x_xyz.xyz)

174 except AttributeError:

175 xyz = map1(float, x_xyz, y, z)

176 except (TypeError, ValueError) as x:

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

178

179 x, y, z = (fdot(r, *xyz) for r in self.matrix)

180 return Vector3Tuple(x, y, z, name=self.name) if Vector is None else \

181 Vector(x, y, z, **_xkwds(Vector_kwds, name=self.name))

182

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

184 def tilt(self):

185 return self._tilt

186

187 @tilt.setter # PYCHOK setter!

188 def tilt(self, tilt):

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

190 if self._tilt != t:

191 _update_all(self)

192 self._tilt = t

193

194 elevation = pitch = tilt

195

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

197 '''Format this attitude as string.

198

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

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

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

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

203

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

205 '''

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

207

208 @Property_RO

209 def tyr3d(self):

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

211

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

213 '''

214 def _r2d(r):

215 return fsumf_(_N_1_0, *r)

216

217 return Vector3d(*map(_r2d, self.matrix), name=tyr3d.__name__)

218

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

220 def yaw(self):

221 return self._yaw

222

223 @yaw.setter # PYCHOK setter!

224 def yaw(self, yaw):

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

226 if self._yaw != y:

227 _update_all(self)

228 self._yaw = y

229

230 bearing = heading = yaw

231

232

233 class AttitudeError(_ValueError):

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

235 '''

236 pass

237

238

239 class Frustum(_NamedBase):

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

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

242

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

244 '''

245 _h_2 = _0_0 # half hfov in degrees

246 _ltp = None # local tangent plane

247 _tan_h_2 = _0_0 # tan(_h_2)

248 _v_2 = _0_0 # half vfov in degrees

249

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

251 '''New L{Frustum}.

252

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

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

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

256

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

258 '''

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

260 self._v_2 = _fov_2(vfov=vfov)

261

262 self._tan_h_2 = tand(h, hfov_2=h)

263

264 if ltp:

265 self._ltp = _xLtp(ltp)

266

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

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

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

270

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

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

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

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

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

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

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

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

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

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

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

282 frustum's C{ltp}.

283

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

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

286

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

288

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

290

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

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

293 over the horizon.

294

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

296 '''

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

298 # left and right corners, or swapped

299 if r < EPS: # no roll

300 r = a * tan_h_2

301 l = -r # PYCHOK l is ell

302 else: # roll

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

304 r *= -a # negate right positive

305 l *= -a # PYCHOK l is ell

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

307 return (l, y), (r, y)

308

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

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

311 s, c = sincos2d(b)

312 _f = fsum1f_

313 for x, y in xy5:

314 yield Xyz4Tuple(_f(x * c, y * s),

315 _f(y * c, -x * s), z, ltp)

316

317 try:

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

319 except AttributeError:

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

321

322 a = Meter(altitude=a)

323 if a < EPS: # too low

324 raise _ValueError(altitude=a)

325 if z: # PYCHOK no cover

326 z = Meter(z=z)

327 a -= z

328 if a < EPS: # z above a

329 raise _ValueError(altitude_z=a)

330 else:

331 z = _0_0

332

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

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

335 if not EPS < e < _180_0:

336 raise _ValueError(tilt=t)

337 if e > _90_0:

338 e = _loneg(e)

339 b = _umod_360(b + _180_0)

340

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

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

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

344 if fabs(y) < EPS:

345 y = _0_0

346

347 v, h, t = self._v_2, self._h_2, self._tan_h_2

348 # center and corners, clockwise from upperleft, rolled

349 xy5 = ((x, y),) + _xy2(a, e - v, h, t, r) \

350 + _xy2(a, e + v, -h, -t, r) # swapped

351 # turn center and corners by yaw, clockwise

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

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

354

355 @Property_RO

356 def hfov(self):

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

358 '''

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

360

361 @Property_RO

362 def ltp(self):

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

364 '''

365 return self._ltp

366

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

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

369

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

371 @kwarg fmt: Optional, C{float} format (C{letter}).

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

373

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

375 '''

376 t = self.hfov, self.vfov

377 if self.ltp:

378 t += self.ltp,

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

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

381

382 @Property_RO

383 def vfov(self):

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

385 '''

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

387

388

389 class LocalError(_ValueError):

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

391 '''

392 pass

393

394

395 class LocalCartesian(_NamedBase):

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

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

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

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

400 classGeographicLib_1_1LocalCartesian.html>}.

401

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

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

404

405 The conversions all take place via geocentric coordinates using a

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

407

408 @see: Class L{Ltp}.

409 '''

410 _ecef = EcefKarney(_WGS84)

411 _Ecef = EcefKarney

412 _lon00 = INT0 # self.lon0

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

414 _9Tuple = Local9Tuple

415

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

417 '''New L{LocalCartesian} converter.

418

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

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

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

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

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

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

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

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

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

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

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

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

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

432

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

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

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

436

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

438

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

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

441 '''

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

443

444 def __eq__(self, other):

445 '''Compare this and an other instance.

446

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

448

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

450 '''

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

452 other.ecef == self.ecef and

453 other._t0 == self._t0)

454

455 @Property_RO

456 def datum(self):

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

458 '''

459 return self.ecef.datum

460

461 @Property_RO

462 def ecef(self):

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

464 '''

465 return self._ecef

466

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

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

469

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

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

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

473

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

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

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

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

478 always.

479 '''

480 ltp = self

481 if ecef.datum != ltp.datum:

482 ecef = ecef.toDatum(ltp.datum)

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

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

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

486 if Xyz:

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

488 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4)

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

490 return r

491

492 @Property_RO

493 def ellipsoid(self):

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

495 '''

496 return self.ecef.datum.ellipsoid

497

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

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

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

501

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

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

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

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

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

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

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

509 iff available (C{bool}).

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

511

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

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

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

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

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

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

518

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

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

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

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

523 '''

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

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

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

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

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

529

530 @Property_RO

531 def height0(self):

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

533 '''

534 return self._t0.height

535

536 @Property_RO

537 def lat0(self):

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

539 '''

540 return self._t0.lat

541

542 @Property_RO

543 def latlonheight0(self):

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

545 '''

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

547

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

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

550

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

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

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

554

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

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

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

558 '''

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

560 if nine:

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

562 return t

563

564 @Property_RO

565 def lon0(self):

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

567 '''

568 return self._t0.lon

569

570 @Property

571 def lon00(self):

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

573 '''

574 return self._lon00

575

576 @lon00.setter # PYCHOK setter!

577 def lon00(self, lon00):

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

579 '''

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

581 self._lon00 = Degrees(lon00=lon00)

582

583 @Property_RO

584 def M(self):

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

586 '''

587 return self._t0.M

588

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

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

591 '''

592 if isinstance(latlonh0, LocalCartesian):

593 if self._t0:

594 _update_all(self)

595 self._ecef = latlonh0.ecef

596 self._lon00 = latlonh0.lon00

597 self._t0 = latlonh0._t0

598 n = name or latlonh0.name

599 else:

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

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

602 if ecef: # PYCHOK no cover

603 _xinstanceof(self._Ecef, ecef=ecef)

604 _update_all(self)

605 self._ecef = ecef

606 elif self._t0:

607 _update_all(self)

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

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

610 if n:

611 self.rename(n)

612

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

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

615

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

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

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

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

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

621 available (C{bool}).

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

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

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

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

626

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

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

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

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

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

632

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

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

635 '''

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

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

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

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

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

641

642 @Property_RO

643 def _t0_xyz(self):

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

645 '''

646 return self._t0.xyz

647

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

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

650

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

652

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

654 '''

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

656

657

658 class Ltp(LocalCartesian):

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

660 (re-)configurable ECEF converter.

661 '''

662 _Ecef = _EcefBase

663

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

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

666

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

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

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

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

671

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

673 '''

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

675 ecef=ecef, name=name, **lon00)

676

677 @Property

678 def ecef(self):

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

680 '''

681 return self._ecef

682

683 @ecef.setter # PYCHOK setter!

684 def ecef(self, ecef):

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

686

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

688 '''

689 _xinstanceof(_EcefBase, ecef=ecef)

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

691 self.reset(self._t0)

692 self._ecef = ecef

693

694

695 class _ChLV(object):

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

697 '''

698 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)

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

700 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)

701

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

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

704 '''

705 if bool(M): # PYCHOK no cover

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

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

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

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

710 return ChLV9Tuple(t, name=name)

711

712 @property_RO

713 def _enh_n_h(self):

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

715 '''

716 _ChLV._enh_n_h = t = _args_kwds_names(_ChLV.reverse)[1:4] # overwrite property_RO

717 # assert _args_kwds_names( ChLV.reverse)[1:4] == t

718 # assert _args_kwds_names(ChLVa.reverse)[1:4] == t

719 # assert _args_kwds_names(ChLVe.reverse)[1:4] == t

720 return t

721

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

723 '''Convert WGS84 geodetic to I{Swiss} projection coordinates. I{Must be overloaded}.

724

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

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

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

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

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

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

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

732

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

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

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

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

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

738

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

740 '''

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

742

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

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

745

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

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

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

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

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

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

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

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

754

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

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

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

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

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

760

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

762 '''

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

764

765 @staticmethod

766 def _falsing2(LV95):

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

768 '''

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

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

771

772 @staticmethod

773 def _llh2abh_3(lat, lon, h):

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

775 '''

776 def _deg2ab(deg, sLL):

777 # convert degrees to arc-seconds

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

779 d = _floor(ds)

780 t = (ds - d) * p

781 m = _floor(t)

782 s = (t - m) * p

783 if swap:

784 d, s = s, d

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

786

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

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

789 return (s - sLL) / ChLV._s_ab

790

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

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

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

794 return a, b, h_

795

796 @staticmethod

797 def _YXh_2abh3(Y, X, h_):

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

799 '''

800 def _YX2ab(YX):

801 return YX * ChLV._ab_m

802

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

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

805 return a, b, h

806

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

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

809 '''

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

811 _xyz_y_z_names=self._enh_n_h, **name)

812 if isinstance(enh_, ChLV9Tuple):

813 Y, X = enh_.Y, enh_.X

814 else: # isscalar(enh_)

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

816 return Y, X, h_, name

817

818

819 class ChLV(_ChLV, Ltp):

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

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

822

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

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

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

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

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

828 '''

829 _9Tuple = ChLV9Tuple

830

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

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

833 _ab_M = _1_0 # ... per 1,000 Km or 1 Mm

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

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

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

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

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

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

840

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

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

843

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

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

846

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

848 '''

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

850

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

852 # overloaded for the _ChLV.forward.__doc__

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

854

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

856 # overloaded for the _ChLV.reverse.__doc__

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

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

859

860 @staticmethod

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

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

863

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

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

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

867 C{LV03} falsing, otherwise leave unfalsed.

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

869

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

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

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

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

874 '''

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

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

877

878 @staticmethod

879 def isLV03(e, n):

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

881

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

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

884

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

886 LV03}, projection C{False} otherwise.

887 '''

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

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

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

891

892 @staticmethod

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

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

895

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

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

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

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

900

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

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

903 '''

904 if ChLV.isLV03(e, n):

905 return False

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

907 return True

908 elif raiser: # PYCHOK no cover

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

910 return None

911

912 @staticmethod

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

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

915

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

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

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

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

920 B{n})}.

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

922

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

924 respectively B{C{n}}.

925 '''

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

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

928

929

930 class ChLVa(_ChLV, LocalCartesian):

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

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

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

934

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

936 '''

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

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

939

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

941 '''

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

943

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

945 # overloaded for the _ChLV.forward.__doc__

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

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

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

949

950 Y = fsumf_( 72.37, 211455.93 * b,

951 -10938.51 * b * a,

952 -0.36 * b * a2,

953 -44.54 * b * b2) # + 600_000

954 X = fsumf_(147.07, 308807.95 * a,

955 3745.25 * b2,

956 76.63 * a2,

957 -194.56 * b2 * a,

958 119.79 * a2 * a) # + 200_000

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

960

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

962 # overloaded for the _ChLV.reverse.__doc__

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

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

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

966

967 lat = Fsum(16.9023892, 3.238272 * b,

968 -0.270978 * a2,

969 -0.002528 * b2,

970 -0.0447 * a2 * b,

971 -0.014 * b2 * b).fover(ab_d)

972 lon = Fsum( 2.6779094, 4.728982 * a,

973 0.791484 * a * b,

974 0.1306 * a * b2,

975 -0.0436 * a * a2).fover(ab_d)

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

977

978

979 class ChLVe(_ChLV, LocalCartesian):

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

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

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

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

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

985

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

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

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

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

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

991 use function L{pygeodesy.degrees2grades}.

992

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

994 '''

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

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

997

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

999 '''

1000 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

1001

1002 def forward(self, latlonh, lon=None, height=0, M=None, name=NN, gamma=False): # PYCHOK gamma

1003 # overloaded for the _ChLV.forward.__doc__

1004 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)

1005 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)

1006 ab_M, z, _H = ChLV._ab_M, 0, Fhorner

1007

1008 B1 = _H(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)

1009 B3 = _H(a, -44.232717, 4.291740, -0.309883, 0.013924)

1010 B5 = _H(a, 0.019784, -0.004277)

1011 Y = _H(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!

1012

1013 B0 = _H(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)

1014 B2 = _H(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)

1015 B4 = _H(a, -0.734684, 0.144466, -0.011842)

1016 B6 = 0.000488

1017 X = _H(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!

1018

1019 t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)

1020 if gamma:

1021 U1 = _H(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)

1022 U3 = _H(a, -412.991934, 64.106344, -2.679566, 0.123833)

1023 U5 = _H(a, 0.204129, -0.037725)

1024 g = _H(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?

1025 t = t, g

1026 return t

1027

1028 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma

1029 # overloaded for the _ChLV.reverse.__doc__

1030 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name)

1031 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)

1032 s_d, _H, z = ChLV._s_d, Fhorner, 0

1033

1034 A0 = _H(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)

1035 A2 = _H(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)

1036 A4 = _H(b, 24.42786, 13.20703, 4.7476)

1037 A6 = -0.4249

1038 lat = _H(a, A0, z, A2, z, A4, z, A6).fover(s_d)

1039

1040 A1 = _H(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)

1041 A3 = _H(b, -442.709889, -255.02202, -96.34947, -30.0808)

1042 A5 = _H(b, 9.63495, 9.0243)

1043 lon = _H(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)

1044 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d

1045

1046 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)

1047 if gamma:

1048 U1 = _H(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)

1049 U3 = _H(b, -1435.508, -794.8777, -296.309, -92.908)

1050 U5 = _H(b, 29.631, 27.873)

1051 g = _H(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees

1052 t = t, g

1053 return t

1054

1055

1056 def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds):

1057 '''Convert an attitude oriention into a (3-D) direction vector.

1058

1059 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down

1060 (clockwise rotation along and around the x-axis).

1061 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North

1062 (counter-clockwise rotation along and around the z-axis).

1063 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down

1064 (clockwise rotation along and around the y-axis).

1065

1066 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},

1067 a named L{Vector3Tuple}C{(x, y, z)}.

1068

1069 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}

1070 and function L{pygeodesy.hartzell} argument C{los}.

1071 '''

1072 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d

1073 return d if Vector is type(d) else (

1074 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else

1075 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent

1076

1077

1078 def _xLtp(ltp, *dflt):

1079 '''(INTERNAL) Validate B{C{ltp}}.

1080 '''

1081 if dflt and ltp is None:

1082 ltp = dflt[0]

1083 if isinstance(ltp, (LocalCartesian, Ltp)):

1084 return ltp

1085 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)

1086

1087# **) MIT License

1088#

1089# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1090#

1091# Permission is hereby granted, free of charge, to any person obtaining a

1092# copy of this software and associated documentation files (the "Software"),

1093# to deal in the Software without restriction, including without limitation

1094# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1095# and/or sell copies of the Software, and to permit persons to whom the

1096# Software is furnished to do so, subject to the following conditions:

1097#

1098# The above copyright notice and this permission notice shall be included

1099# in all copies or substantial portions of the Software.

1100#

1101# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1102# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1103# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

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