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, map1, map2, _xinstanceof, \

17 _xsubclassof # .datums

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

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

20 _N_1_0 # PYCHOK used!

21# from pygeodesy.datums import _WGS84 # from .ecef

22 from pygeodesy.ecef import _EcefBase, EcefKarney, Ecef9Tuple, _llhn4, \

23 _xyzn4, _WGS84

24 from pygeodesy.errors import _NotImplementedError, _ValueError, _xattr, \

25 _xkwds, _xkwds_get, _xkwds_pop2

26 from pygeodesy.fmath import fabs, fdot, fdot_, Fhorner

27 from pygeodesy.fsums import _floor, fsumf_

28 from pygeodesy.interns import _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, _M_, \

29 _invalid_, _lat0_, _lon0_, _name_, _too_

30# from pygeodesy.lazily import _ALL_LAZY # from vector3d

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

32 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \

33 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple

34 from pygeodesy.named import _name__, _name2__, _NamedBase, notOverloaded

35 from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple

36 from pygeodesy.props import Property, Property_RO, property_doc_, \

37 property_ROver, _update_all

38 from pygeodesy.streprs import Fmt, strs, unstr

39 from pygeodesy.units import Bearing, Degrees, _isHeight, Meter

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

41 wrap180, wrap360

42 from pygeodesy.vector3d import _ALL_LAZY, Vector3d

43

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

45

46__all__ = _ALL_LAZY.ltp

47__version__ = '24.12.12'

48

49_height0_ = _height_ + _0_

50_narrow_ = 'narrow'

51_wide_ = 'wide'

52

53

54 class Attitude(_NamedBase):

55 '''The pose of a plane or camera in space.

56 '''

57 _alt = Meter( alt =_0_0)

58 _roll = Degrees(roll=_0_0)

59 _tilt = Degrees(tilt=_0_0)

60 _yaw = Bearing(yaw =_0_0)

61

62 def __init__(self, alt_attitude=INT0, tilt=INT0, yaw=INT0, roll=INT0, **name):

63 '''New L{Attitude}.

64

65 @kwarg alt_attitude: Altitude (C{meter}) above earth or previous attitude

66 (L{Attitude} or L{Attitude4Tuple}) with the C{B{alt}itude},

67 B{C{tilt}}, B{C{yaw}} and B{C{roll}}.

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

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

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

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

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

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

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

75

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

77 B{C{roll}}.

78

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

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

81 '''

82 if _isHeight(alt_attitude):

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

84 else:

85 try:

86 t = alt_attitude.atyr

87 except AttributeError:

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

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

90 if v:

91 setattr(self, n, v)

92 n = _name__(name, _or_nameof=t)

93 if n:

94 self.name = n

95

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

97 def alt(self):

98 return self._alt

99

100 @alt.setter # PYCHOK setter!

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

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

103 if self._alt != a:

104 _update_all(self)

105 self._alt = a

106

107 altitude = alt

108

109 @Property_RO

110 def atyr(self):

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

112 '''

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

114

115 @Property_RO

116 def matrix(self):

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

118

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

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

121 '''

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

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

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

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

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

127 (sa * cb, fdot_(sa, sb * sg, ca, cg), fdot_(sa, sb * cg, -ca, sg)),

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

129

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

131 def roll(self):

132 return self._roll

133

134 @roll.setter # PYCHOK setter!

135 def roll(self, roll):

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

137 if self._roll != r:

138 _update_all(self)

139 self._roll = r

140

141 bank = roll

142

143 def rotate(self, x_xyz, y=None, z=None, Vector=None, **name_Vector_kwds):

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

145

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

147 L{Vector3d} or L{Vector3Tuple}).

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

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

150 @kwarg Vector: Class to return transformed point (C{Cartesian}, L{Vector3d}

151 or C{Vector3Tuple}) or C{None}.

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

153 additional B{C{Vector}} keyword arguments, ignored if C{B{Vector}

154 is None}.

155

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

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

158

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

160

161 @raise TypeError: Invalid B{C{Vector}} or B{C{name_Vector_kwds}} item.

162

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

164 '''

165 try:

166 try:

167 xyz = map2(float, x_xyz.xyz3)

168 except AttributeError:

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

170 except (TypeError, ValueError) as x:

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

172

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

174 n, kwds = _name2__(name_Vector_kwds, _or_nameof=self)

175 return Vector3Tuple(x, y, z, name=n) if Vector is None else \

176 Vector(x, y, z, name=n, **kwds)

177

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

179 def tilt(self):

180 return self._tilt

181

182 @tilt.setter # PYCHOK setter!

183 def tilt(self, tilt):

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

185 if self._tilt != t:

186 _update_all(self)

187 self._tilt = t

188

189 elevation = pitch = tilt

190

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

192 '''Format this attitude as string.

193

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

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

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

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

198

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

200 '''

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

202

203 @Property_RO

204 def tyr3d(self):

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

206

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

208 '''

209 def _r2d(r):

210 return fsumf_(_N_1_0, *r)

211

212 return Vector3d(*map(_r2d, self.matrix), name__=tyr3d)

213

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

215 def yaw(self):

216 return self._yaw

217

218 @yaw.setter # PYCHOK setter!

219 def yaw(self, yaw):

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

221 if self._yaw != y:

222 _update_all(self)

223 self._yaw = y

224

225 bearing = heading = yaw

226

227

228 class AttitudeError(_ValueError):

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

230 '''

231 pass

232

233

234 class Frustum(_NamedBase):

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

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

237

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

239 '''

240 _h_2 = _0_0 # half hfov in degrees

241 _ltp = None # local tangent plane

242 _tan_h_2 = _0_0 # tan(_h_2)

243 _v_2 = _0_0 # half vfov in degrees

244

245 def __init__(self, hfov, vfov, ltp=None, **name):

246 '''New L{Frustum}.

247

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

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

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

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

252

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

254 '''

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

256 self._v_2 = _fov_2(vfov=vfov)

257

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

259

260 if ltp:

261 self._ltp = _xLtp(ltp)

262 if name:

263 self.name # PYCHOK effect

264

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

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

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

268

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

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

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

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

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

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

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

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

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

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

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

280 frustum's C{ltp}.

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

282

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

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

285

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

287

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

289

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

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

292 over the horizon.

293

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

295 '''

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

297 # left and right corners, or swapped

298 if r < EPS: # no roll

299 r = a * tan_h_2

300 l = -r # PYCHOK l is ell

301 else: # roll

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

303 r *= -a # negate right positive

304 l *= -a # PYCHOK l is ell

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

306 return (l, y), (r, y)

307

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

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

310 sc = sincos2d(b)

311 for x, y in xy5:

312 yield Xyz4Tuple(fdot(sc, x, y),

313 fdot(sc, -x, y), z, ltp)

314

315 try:

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

317 except AttributeError:

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

319

320 a = Meter(altitude=a)

321 if a < EPS: # too low

322 raise _ValueError(altitude=a)

323 if z: # PYCHOK no cover

324 z = Meter(z=z)

325 a -= z

326 if a < EPS: # z above a

327 raise _ValueError(altitude_z=a)

328 else:

329 z = _0_0

330

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

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

333 if not EPS < e < _180_0:

334 raise _ValueError(tilt=t)

335 if e > _90_0:

336 e = _loneg(e)

337 b = _umod_360(b + _180_0)

338

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

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

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

342 if fabs(y) < EPS:

343 y = _0_0

344

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

346 # center and corners, clockwise from upperleft, rolled

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

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

349 # turn center and corners by yaw, clockwise

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

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

352

353 @Property_RO

354 def hfov(self):

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

356 '''

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

358

359 @Property_RO

360 def ltp(self):

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

362 '''

363 return self._ltp

364

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

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

367

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

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

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

371

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

373 '''

374 t = self.hfov, self.vfov

375 if self.ltp:

376 t += self.ltp,

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

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

379

380 @Property_RO

381 def vfov(self):

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

383 '''

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

385

386

387 class LocalError(_ValueError):

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

389 '''

390 pass

391

392

393 class LocalCartesian(_NamedBase):

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

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

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

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

398 classGeographicLib_1_1LocalCartesian.html>}.

399

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

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

402

403 The conversions all take place via geocentric coordinates using a

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

405

406 @see: Class L{Ltp}.

407 '''

408 _ecef = EcefKarney(_WGS84)

409 _Ecef = EcefKarney

410 _lon00 = INT0 # self.lon0

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

412 _9Tuple = Local9Tuple

413

414 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):

415 '''New L{LocalCartesian} converter.

416

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

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

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

420 @kwarg lon0: Longitude of the (goedetic) origin (C{degrees}), required if

421 B{C{latlonh0}} is C{scalar}, ignored otherwise.

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

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

424 surface, like B{C{lon0}}.

425 @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}), like B{C{lon0}}.

426 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and keyword argument

427 C{B{lon00}=B{lon0}} for the arbitrary I{polar} longitude

428 (C{degrees}), see method C{reverse} and property C{lon00}

429 for further details.

430

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

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

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

434

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

436

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

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

439 '''

440 self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, **lon00_name)

441

442 def __eq__(self, other):

443 '''Compare this and an other instance.

444

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

446

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

448 '''

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

450 other.ecef == self.ecef and

451 other._t0 == self._t0)

452

453 @Property_RO

454 def datum(self):

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

456 '''

457 return self.ecef.datum

458

459 @Property_RO

460 def ecef(self):

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

462 '''

463 return self._ecef

464

465 def _ecef2local(self, ecef, Xyz, name_Xyz_kwds):

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

467

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

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

470 @arg name_Xyz_kwds: Optional C{B{name}=NN} (C{str}) and optionally,

471 additional B{C{Xyz}} keyword arguments, ignored if C{B{Xyz}

472 is None}.

473

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

475 if 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 @raise TypeError: Invalid B{C{Xyz}} or B{C{name_Xyz_kwds}} item.

481 '''

482 _xinstanceof(Ecef9Tuple, ecef=ecef)

483 if ecef.datum != self.datum:

484 ecef = ecef.toDatum(self.datum)

485 n, kwds = _name2__(name_Xyz_kwds, _or_nameof=ecef)

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

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

488 self, ecef, None, name=n)

489 if Xyz:

490 _xsubclassof(*_XyzLocals4, Xyz=Xyz) # Vector3d

491 r = r.toXyz(Xyz=Xyz, name=n, **kwds)

492 return r

493

494 @Property_RO

495 def ellipsoid(self):

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

497 '''

498 return self.ecef.datum.ellipsoid

499

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

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

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

503

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

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

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

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

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

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

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

511 iff available (C{bool}).

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

513

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

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

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

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

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

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

520

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

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

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

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

525 '''

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

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

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

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

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

531

532 @Property_RO

533 def height0(self):

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

535 '''

536 return self._t0.height

537

538 @Property_RO

539 def lat0(self):

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

541 '''

542 return self._t0.lat

543

544 @Property_RO

545 def latlonheight0(self):

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

547 '''

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

549

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

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

552

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

554 @kwarg nine: If C{True}, return a 9-, otherwise a 3-tuple (C{bool}).

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

556

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

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

559 rotation matrix C{M} (L{EcefMatrix}) if requested.

560 '''

561 _xinstanceof(*_XyzLocals5, local=local)

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

563 if nine:

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

565 return t

566

567 @Property_RO

568 def lon0(self):

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

570 '''

571 return self._t0.lon

572

573 @Property

574 def lon00(self):

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

576 '''

577 return self._lon00

578

579 @lon00.setter # PYCHOK setter!

580 def lon00(self, lon00):

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

582 '''

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

584 self._lon00 = Degrees(lon00=lon00)

585

586 @Property_RO

587 def M(self):

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

589 '''

590 return self._t0.M

591

592 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):

593 '''Reset this converter, see L{LocalCartesian.__init__} for more details.

594 '''

595 _, name = _xkwds_pop2(lon00_name, lon00=None) # PYCHOK get **name

596 if isinstance(latlonh0, LocalCartesian):

597 if self._t0:

598 _update_all(self)

599 self._ecef = latlonh0.ecef

600 self._lon00 = latlonh0.lon00

601 self._t0 = latlonh0._t0

602 n = _name__(name, _or_nameof=latlonh0)

603 else:

604 n = _name__(name, _or_nameof=self)

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

606 Error=LocalError, name=n)

607 if ecef: # PYCHOK no cover

608 _xinstanceof(self._Ecef, ecef=ecef)

609 _update_all(self)

610 self._ecef = ecef

611 elif self._t0:

612 _update_all(self)

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

614 self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00_name, lon00=lon0))

615 if n:

616 self.rename(n)

617

618 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name):

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

620

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

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

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

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

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

626 available (C{bool}).

627 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and keyword argument

628 C{B{lon00}=B{lon0}} for the arbitrary I{polar} longitude

629 (C{degrees}), overriding see the property C{B{lon00}=B{lon0}}

630 value. The I{polar} longitude (C{degrees}) is returned with

631 I{polar} latitudes C{abs(B{lat0}) == 90} for local C{B{x}=0}

632 and C{B{y}=0} locations.

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 lon00, name =_xkwds_pop2(lon00_name, lon00=self.lon00)

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

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

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

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

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

649

650 @Property_RO

651 def _t0_xyz(self):

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

653 '''

654 return self._t0.xyz

655

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

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

658

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

660

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

662 '''

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

664

665

666 class Ltp(LocalCartesian):

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

668 (re-)configurable ECEF converter.

669 '''

670 _Ecef = _EcefBase

671

672 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):

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

674

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

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

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

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

679

680 @see: Class L{LocalCartesian<LocalCartesian.__init__>} for further details.

681

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

683 '''

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

685 ecef=ecef, **lon00_name)

686

687 @Property

688 def ecef(self):

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

690 '''

691 return self._ecef

692

693 @ecef.setter # PYCHOK setter!

694 def ecef(self, ecef):

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

696

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

698 '''

699 _xinstanceof(_EcefBase, ecef=ecef)

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

701 self.reset(self._t0)

702 self._ecef = ecef

703

704

705 class _ChLV(object):

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

707 '''

708 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)

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

710 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)

711

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

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

714 '''

715 if bool(M): # PYCHOK no cover

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

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

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

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

720 return ChLV9Tuple(t, name=name)

721

722 @property_ROver

723 def _enh_n_h(self):

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

725 '''

726 t = _args_kwds_names(_ChLV.reverse)[1:4]

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

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

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

730 return t # overwrite property_ROver

731

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

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

734

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

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

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

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

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

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

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

742

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

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

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

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

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

748

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

750 '''

751 notOverloaded(self, latlonh, lon=lon, height=height, M=M, **name)

752

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

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

755

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

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

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

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

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

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

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

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

764

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

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

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

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

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

770

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

772 '''

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

774

775 @staticmethod

776 def _falsing2(LV95):

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

778 '''

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

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

781

782 @staticmethod

783 def _llh2abh_3(lat, lon, h):

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

785 '''

786 def _deg2ab(deg, sLL):

787 # convert degrees to arc-seconds

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

789 d = _floor(ds)

790 t = (ds - d) * p

791 m = _floor(t)

792 s = (t - m) * p

793 if swap:

794 d, s = s, d

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

796

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

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

799 return (s - sLL) / ChLV._s_ab

800

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

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

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

804 return a, b, h_

805

806 @staticmethod

807 def _YXh_2abh3(Y, X, h_):

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

809 '''

810 def _YX2ab(YX):

811 return YX * ChLV._ab_m

812

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

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

815 return a, b, h

816

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

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

819 '''

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

821 _xyz_y_z_names=self._enh_n_h, **name)

822 if isinstance(enh_, ChLV9Tuple):

823 Y, X = enh_.Y, enh_.X

824 else: # isscalar(enh_)

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

826 return Y, X, h_, name

827

828

829 class ChLV(_ChLV, Ltp):

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

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

832

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

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

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

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

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

838 '''

839 _9Tuple = ChLV9Tuple

840

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

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

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

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

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

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

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

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

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

850

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

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

853

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

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

856

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

858 '''

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

860

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

862 # overloaded for the _ChLV.forward.__doc__

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

864

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

866 # overloaded for the _ChLV.reverse.__doc__

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

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

869

870 @staticmethod

871 def false2(Y, X, LV95=True, **name):

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

873

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

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

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

877 C{LV03} falsing, otherwise leave unfalsed.

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

879

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

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

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

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

884 '''

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

886 return t.classof(e + Y, n + X, **name)

887

888 @staticmethod

889 def isLV03(e, n):

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

891

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

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

894

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

896 LV03}, projection C{False} otherwise.

897 '''

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

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

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

901

902 @staticmethod

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

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

905

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

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

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

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

910

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

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

913 '''

914 if ChLV.isLV03(e, n):

915 return False

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

917 return True

918 elif raiser: # PYCHOK no cover

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

920 return None

921

922 @staticmethod

923 def unfalse2(e, n, LV95=None, **name):

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

925

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

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

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

929 I{LV03} falsing, otherwise use method C{isLV95(B{e}, B{n})}.

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

931

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

933 respectively B{C{n}}.

934 '''

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

936 return ChLVYX2Tuple(e - Y, n - X, **name)

937

938

939 class ChLVa(_ChLV, LocalCartesian):

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

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

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

943

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

945 '''

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

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

948

949 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).

950 '''

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

952

953 def forward(self, latlonh, lon=None, height=0, M=None, **name):

954 # overloaded for the _ChLV.forward.__doc__

955 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)

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

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

958

959 Y = fdot_(211455.93, b,

960 -10938.51, b * a,

961 -0.36, b * a2,

962 -44.54, b * b2, start=72.37) # + 600_000

963 X = fdot_(308807.95, a,

964 3745.25, b2,

965 76.63, a2,

966 -194.56, b2 * a,

967 119.79, a2 * a, start=147.07) # + 200_000

968 return self._ChLV9Tuple(True, M, n, Y, X, h_, lat, lon, h)

969

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

971 # overloaded for the _ChLV.reverse.__doc__

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

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

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

975

976 lat = fdot_(3.238272, b,

977 -0.270978, a2,

978 -0.002528, b2,

979 -0.0447, a2 * b,

980 -0.014, b2 * b, start=16.9023892) / ab_d

981 lon = fdot_(4.728982, a,

982 0.791484, a * b,

983 0.1306, a * b2,

984 -0.0436, a * a2, start=2.6779094) / ab_d

985 return self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)

986

987

988 class ChLVe(_ChLV, LocalCartesian):

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

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

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

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

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

994

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

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

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

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

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

1000 use function L{pygeodesy.degrees2grades}.

1001

1002 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.

1003 '''

1004 def __init__(self, name=ChLV.Bern.name):

1005 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.

1006

1007 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).

1008 '''

1009 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

1010

1011 def forward(self, latlonh, lon=None, height=0, M=None, gamma=False, **name): # PYCHOK gamma

1012 # overloaded for the _ChLV.forward.__doc__

1013 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)

1014 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)

1015 ab_M, z, _H = ChLV._ab_M, 0, Fhorner

1016

1017 B1 = _H(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)

1018 B3 = _H(a, -44.232717, 4.291740, -0.309883, 0.013924)

1019 B5 = _H(a, 0.019784, -0.004277)

1020 Y = _H(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!

1021

1022 B0 = _H(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)

1023 B2 = _H(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)

1024 B4 = _H(a, -0.734684, 0.144466, -0.011842)

1025 X = _H(b, B0, z, B2, z, B4, z, 0.000488).fover(ab_M) # 1,000 Km!

1026

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

1028 if gamma:

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

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

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

1032 g = _H(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, gamma=False, **name): # PYCHOK gamma

1037 # overloaded for the _ChLV.reverse.__doc__

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

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

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

1041

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

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

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

1045 lat = _H(a, A0, z, A2, z, A4, z, -0.4249).fover(s_d)

1046

1047 A1 = _H(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)

1048 A3 = _H(b, -442.709889, -255.02202, -96.34947, -30.0808)

1049 A5 = _H(b, 9.63495, 9.0243)

1050 lon = _H(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)

1051 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d

1052

1053 t = self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)

1054 if gamma:

1055 U1 = _H(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)

1056 U3 = _H(b, -1435.508, -794.8777, -296.309, -92.908)

1057 U5 = _H(b, 29.631, 27.873)

1058 g = _H(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees

1059 t = t, g

1060 return t

1061

1062

1063 def _fov_2(**fov):

1064 # Half a field-of-view angle in C{degrees}.

1065 f = Degrees(Error=LocalError, **fov) * _0_5

1066 if EPS < f < _90_0:

1067 return f

1068 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)

1069 raise LocalError(txt=t, **fov)

1070

1071

1072 def _toLocal(inst, ltp, Xyz, Xyz_kwds):

1073 '''(INTERNAL) Helper for C{CartesianBase.toAer}, C{CartesianBase.toEnu},

1074 C{CartesianBase.toLocal}, C{CartesianBase.toNed} and C{latLonBase.toLocal}.

1075 '''

1076 return _xLtp(ltp, inst._Ltp)._ecef2local(inst._ecef9, Xyz, Xyz_kwds)

1077

1078

1079 def _toLtp(inst, Ecef, ecef9, name):

1080 '''(INTERNAL) Helper for C{CartesianBase.toLtp}, C{ecef.toLtp} and C{latLonBase.toLtp}.

1081 '''

1082 return inst._Ltp if (not name) and Ecef in (None, inst.Ecef) else \

1083 Ltp(ecef9, ecef=Ecef(inst.datum), name=inst._name__(name))

1084

1085

1086 def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **name_Vector_kwds):

1087 '''Convert an attitude pose into a (3-D) direction vector.

1088

1089 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down

1090 (clockwise rotation along and around the x-axis).

1091 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North

1092 (counter-clockwise rotation along and around the z-axis).

1093 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down

1094 (clockwise rotation along and around the y-axis).

1095 @kwarg Vector: Class to return the direction vector (C{Cartesian},

1096 L{Vector3d} or C{Vector3Tuple}) or C{None}.

1097 @kwarg name_Vector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,

1098 additional B{C{Vector}} keyword arguments, ignored if C{B{Vector}

1099 is None}.

1100

1101 @return: A named B{C{Vector}} instance or if C{B{Vector} is None},

1102 a named L{Vector3Tuple}C{(x, y, z)}.

1103

1104 @raise AttitudeError: Invalid B{C{tilt}}, B{C{yaw}} or B{C{roll}}.

1105

1106 @raise TypeError: Invalid B{C{Vector}} or B{C{name_Vector_kwds}}.

1107

1108 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}

1109 and function L{pygeodesy.hartzell} argument C{los}, Line-Of-Sight.

1110 '''

1111 v = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d

1112 if Vector is not type(v):

1113 n, kwds = _name2__(name_Vector_kwds, name__=tyr3d)

1114 v = Vector3Tuple(v.x, v.y, v.z, name=n) if Vector is None else \

1115 Vector(v.x, v.y, v.z, name=n, **kwds)

1116 elif name_Vector_kwds:

1117 n, _ = _name2__(name_Vector_kwds)

1118 if n:

1119 v = v.copy(name=n)

1120 return v

1121

1122

1123 def _xLtp(ltp, *dflt):

1124 '''(INTERNAL) Validate B{C{ltp}} if not C{None} else B{C{dflt}}.

1125 '''

1126 if dflt and ltp is None:

1127 ltp = dflt[0]

1128 _xinstanceof(Ltp, LocalCartesian, ltp=ltp)

1129 return ltp

1130

1131# **) MIT License

1132#

1133# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

1134#

1135# Permission is hereby granted, free of charge, to any person obtaining a

1136# copy of this software and associated documentation files (the "Software"),

1137# to deal in the Software without restriction, including without limitation

1138# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1139# and/or sell copies of the Software, and to permit persons to whom the

1140# Software is furnished to do so, subject to the following conditions:

1141#

1142# The above copyright notice and this permission notice shall be included

1143# in all copies or substantial portions of the Software.

1144#

1145# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1146# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1147# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1148# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1149# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1150# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1151# OTHER DEALINGS IN THE SOFTWARE.