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, _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__ = '23.09.06'

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 isscalar(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: The matrix M of case 10 in U{Appendix A

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

129 '''

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

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

132

133 r0, r1, r2 = self._rows3

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

135

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

137 def roll(self):

138 return self._roll

139

140 @roll.setter # PYCHOK setter!

141 def roll(self, roll):

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

143 if self._roll != r:

144 _update_all(self)

145 self._roll = r

146

147 bank = roll

148

149 @Property_RO

150 def _rows3(self):

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

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

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

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

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

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

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

158

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

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

161

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

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

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

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

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

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

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

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

170

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

172 C{B{Vector}=None}.

173

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

175

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

177 '''

178 try:

179 try:

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

181 except AttributeError:

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

183 except (TypeError, ValueError) as x:

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

185

186 X, Y, Z = self._rows3

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

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

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

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

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

192

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

194 def tilt(self):

195 return self._tilt

196

197 @tilt.setter # PYCHOK setter!

198 def tilt(self, tilt):

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

200 if self._tilt != t:

201 _update_all(self)

202 self._tilt = t

203

204 elevation = pitch = tilt

205

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

207 '''Format this attitude as string.

208

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

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

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

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

213

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

215 '''

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

217

218 @Property_RO

219 def tyr3d(self):

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

221

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

223 '''

224 def _r2d(r):

225 return fsumf_(_N_1_0, *r)

226

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

228

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

230 def yaw(self):

231 return self._yaw

232

233 @yaw.setter # PYCHOK setter!

234 def yaw(self, yaw):

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

236 if self._yaw != y:

237 _update_all(self)

238 self._yaw = y

239

240 bearing = heading = yaw

241

242

243 class AttitudeError(_ValueError):

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

245 '''

246 pass

247

248

249 class Frustum(_NamedBase):

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

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

252

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

254 '''

255 _h_2 = _0_0 # half hfov in degrees

256 _ltp = None # local tangent plane

257 _tan_h_2 = _0_0 # tan(_h_2)

258 _v_2 = _0_0 # half vfov in degrees

259

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

261 '''New L{Frustum}.

262

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

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

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

266

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

268 '''

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

270 self._v_2 = _fov_2(vfov=vfov)

271

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

273

274 if ltp:

275 self._ltp = _xLtp(ltp)

276

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

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

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

280

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

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

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

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

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

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

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

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

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

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

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

292 frustum's C{ltp}.

293

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

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

296

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

298

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

300

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

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

303 over the horizon.

304

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

306 '''

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

308 # left and right corners, or swapped

309 if r < EPS: # no roll

310 r = a * tan_h_2

311 l = -r # PYCHOK l is ell

312 else: # roll

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

314 r *= -a # negate right positive

315 l *= -a # PYCHOK l is ell

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

317 return (l, y), (r, y)

318

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

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

321 s, c = sincos2d(b)

322 for x, y in xy5:

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

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

325

326 try:

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

328 except AttributeError:

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

330

331 a = Meter(altitude=a)

332 if a < EPS: # too low

333 raise _ValueError(altitude=a)

334 if z: # PYCHOK no cover

335 z = Meter(z=z)

336 a -= z

337 if a < EPS: # z above a

338 raise _ValueError(altitude_z=a)

339 else:

340 z = _0_0

341

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

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

344 if not EPS < e < _180_0:

345 raise _ValueError(tilt=t)

346 if e > _90_0:

347 e = _loneg(e)

348 b = _umod_360(b + _180_0)

349

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

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

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

353 if fabs(y) < EPS:

354 y = _0_0

355

356 # center and corners, clockwise from upperleft, rolled

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

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

359 # turn center and corners by yaw, clockwise

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

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

362

363 @Property_RO

364 def hfov(self):

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

366 '''

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

368

369 @Property_RO

370 def ltp(self):

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

372 '''

373 return self._ltp

374

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

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

377

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

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

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

381

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

383 '''

384 t = self.hfov, self.vfov

385 if self.ltp:

386 t += self.ltp,

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

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

389

390 @Property_RO

391 def vfov(self):

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

393 '''

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

395

396

397 class LocalError(_ValueError):

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

399 '''

400 pass

401

402

403 class LocalCartesian(_NamedBase):

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

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

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

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

408 classGeographicLib_1_1LocalCartesian.html>}.

409

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

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

412

413 The conversions all take place via geocentric coordinates using a

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

415

416 @see: Class L{Ltp}.

417 '''

418 _ecef = EcefKarney(_WGS84)

419 _EcefClass = EcefKarney

420 _lon00 = INT0 # self.lon0

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

422 _9Tuple = Local9Tuple

423

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

425 '''New L{LocalCartesian} converter.

426

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

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

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

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

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

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

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

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

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

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

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

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

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

440

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

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

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

444

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

446

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

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

449 '''

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

451

452 def __eq__(self, other):

453 '''Compare this and an other instance.

454

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

456

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

458 '''

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

460 other.ecef == self.ecef and

461 other._t0 == self._t0)

462

463 @Property_RO

464 def datum(self):

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

466 '''

467 return self.ecef.datum

468

469 @Property_RO

470 def ecef(self):

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

472 '''

473 return self._ecef

474

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

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

477

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

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

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

481

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

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

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

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

486 always.

487 '''

488 ltp = self

489 if ecef.datum != ltp.datum:

490 ecef = ecef.toDatum(ltp.datum)

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

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

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

494 if Xyz:

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

496 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4)

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

498 return r

499

500 @Property_RO

501 def ellipsoid(self):

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

503 '''

504 return self.ecef.datum.ellipsoid

505

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

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

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

509

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

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

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

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

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

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

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

517 iff available (C{bool}).

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

519

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

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

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

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

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

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

526

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

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

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

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

531 '''

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

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

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

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

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

537

538 @Property_RO

539 def height0(self):

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

541 '''

542 return self._t0.height

543

544 @Property_RO

545 def lat0(self):

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

547 '''

548 return self._t0.lat

549

550 @Property_RO

551 def latlonheight0(self):

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

553 '''

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

555

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

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

558

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

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

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

562

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

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

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

566 '''

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

568 if nine:

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

570 return t

571

572 @Property_RO

573 def lon0(self):

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

575 '''

576 return self._t0.lon

577

578 @Property

579 def lon00(self):

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

581 '''

582 return self._lon00

583

584 @lon00.setter # PYCHOK setter!

585 def lon00(self, lon00):

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

587 '''

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

589 self._lon00 = Degrees(lon00=lon00)

590

591 @Property_RO

592 def M(self):

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

594 '''

595 return self._t0.M

596

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

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

599 '''

600 if isinstance(latlonh0, LocalCartesian):

601 if self._t0:

602 _update_all(self)

603 self._ecef = latlonh0.ecef

604 self._lon00 = latlonh0.lon00

605 self._t0 = latlonh0._t0

606 n = name or latlonh0.name

607 else:

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

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

610 if ecef: # PYCHOK no cover

611 _xinstanceof(self._EcefClass, ecef=ecef)

612 _update_all(self)

613 self._ecef = ecef

614 elif self._t0:

615 _update_all(self)

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

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

618 if n:

619 self.rename(n)

620

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

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

623

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

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

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

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

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

629 available (C{bool}).

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

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

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

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

634

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

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

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

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

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

640

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

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

643 '''

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=_xkwds_get(lon00, lon00=self.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 _EcefClass = _EcefBase

671

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

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

681 '''

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

683 ecef=ecef, name=name, **lon00)

684

685 @Property

686 def ecef(self):

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

688 '''

689 return self._ecef

690

691 @ecef.setter # PYCHOK setter!

692 def ecef(self, ecef):

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

694

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

696 '''

697 _xinstanceof(_EcefBase, ecef=ecef)

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

699 self.reset(self._t0)

700 self._ecef = ecef

701

702

703 class _ChLV(object):

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

705 '''

706 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)

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

708 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)

709

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

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

712 '''

713 if bool(M): # PYCHOK no cover

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

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

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

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

718 return ChLV9Tuple(t, name=name)

719

720 @property_RO

721 def _enh_n_h(self):

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

723 '''

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

725 _ChLV._enh_n_h = t # overwrite this property_RO

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

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

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

729 return t

730

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

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

733

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

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

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

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

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

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

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

741

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

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

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

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

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

747

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

749 '''

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

751

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

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

754

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

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

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

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

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

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

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

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

763

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

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

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

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

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

769

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

771 '''

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

773

774 @staticmethod

775 def _falsing2(LV95):

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

777 '''

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

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

780

781 @staticmethod

782 def _llh2abh_3(lat, lon, h):

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

784 '''

785 def _deg2ab(deg, sLL):

786 # convert degrees to arc-seconds

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

788 d = _floor(ds)

789 t = (ds - d) * p

790 m = _floor(t)

791 s = (t - m) * p

792 if swap:

793 d, s = s, d

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

795

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

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

798 return (s - sLL) / ChLV._s_ab

799

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

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

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

803 return a, b, h_

804

805 @staticmethod

806 def _YXh_2abh3(Y, X, h_):

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

808 '''

809 def _YX2ab(YX):

810 return YX * ChLV._ab_m

811

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

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

814 return a, b, h

815

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

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

818 '''

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

820 _xyz_y_z_names=self._enh_n_h, **name)

821 if isinstance(enh_, ChLV9Tuple):

822 Y, X = enh_.Y, enh_.X

823 else: # isscalar(enh_)

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

825 return Y, X, h_, name

826

827

828 class ChLV(_ChLV, Ltp):

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

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

831

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

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

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

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

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

837 '''

838 _9Tuple = ChLV9Tuple

839

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

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

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

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

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

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

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

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

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

849

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

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

852

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

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

855

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

857 '''

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

859

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

861 # overloaded for the _ChLV.forward.__doc__

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

863

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

865 # overloaded for the _ChLV.reverse.__doc__

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

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

868

869 @staticmethod

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

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

872

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

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

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

876 C{LV03} falsing, otherwise leave unfalsed.

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

878

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

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

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

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

883 '''

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

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

886

887 @staticmethod

888 def isLV03(e, n):

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

890

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

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

893

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

895 LV03}, projection C{False} otherwise.

896 '''

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

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

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

900

901 @staticmethod

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

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

904

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

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

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

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

909

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

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

912 '''

913 if ChLV.isLV03(e, n):

914 return False

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

916 return True

917 elif raiser: # PYCHOK no cover

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

919 return None

920

921 @staticmethod

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

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

924

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

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

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

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

929 B{n})}.

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

950 '''

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

952

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

954 # overloaded for the _ChLV.forward.__doc__

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

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

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

958

959 Y = fsumf_( 72.37, 211455.93 * b,

960 -10938.51 * b * a,

961 -0.36 * b * a2,

962 -44.54 * b * b2) # + 600_000

963 X = fsumf_(147.07, 308807.95 * a,

964 3745.25 * b2,

965 76.63 * a2,

966 -194.56 * b2 * a,

967 119.79 * a2 * a) # + 200_000

968 return self._ChLV9Tuple(True, M, name, 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_, name = 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 = Fsum(16.9023892, 3.238272 * b,

977 -0.270978 * a2,

978 -0.002528 * b2,

979 -0.0447 * a2 * b,

980 -0.014 * b2 * b).fover(ab_d)

981 lon = Fsum( 2.6779094, 4.728982 * a,

982 0.791484 * a * b,

983 0.1306 * a * b2,

984 -0.0436 * a * a2).fover(ab_d)

985 return self._ChLV9Tuple(False, M, name, 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 name (C{str}), overriding C{Bern.name}.

1008 '''

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

1010

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

1012 # overloaded for the _ChLV.forward.__doc__

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

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

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

1016

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

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

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

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

1021

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

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

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

1025 B6 = 0.000488

1026 X = _F(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!

1027

1028 t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)

1029 if gamma:

1030 U1 = _F(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)

1031 U3 = _F(a, -412.991934, 64.106344, -2.679566, 0.123833)

1032 U5 = _F(a, 0.204129, -0.037725)

1033 g = _F(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?

1034 t = t, g

1035 return t

1036

1037 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma

1038 # overloaded for the _ChLV.reverse.__doc__

1039 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name)

1040 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)

1041 s_d, _F, z = ChLV._s_d, Fhorner, 0

1042

1043 A0 = _F(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)

1044 A2 = _F(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)

1045 A4 = _F(b, 24.42786, 13.20703, 4.7476)

1046 A6 = -0.4249

1047 lat = _F(a, A0, z, A2, z, A4, z, A6).fover(s_d)

1048

1049 A1 = _F(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)

1050 A3 = _F(b, -442.709889, -255.02202, -96.34947, -30.0808)

1051 A5 = _F(b, 9.63495, 9.0243)

1052 lon = _F(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)

1053 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d

1054

1055 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)

1056 if gamma:

1057 U1 = _F(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)

1058 U3 = _F(b, -1435.508, -794.8777, -296.309, -92.908)

1059 U5 = _F(b, 29.631, 27.873)

1060 g = _F(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees

1061 t = t, g

1062 return t

1063

1064

1065 def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds):

1066 '''Convert an attitude oriention into a (3-D) direction vector.

1067

1068 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down

1069 (clockwise rotation along and around the x-axis).

1070 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North

1071 (counter-clockwise rotation along and around the z-axis).

1072 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down

1073 (clockwise rotation along and around the y-axis).

1074

1075 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},

1076 a named L{Vector3Tuple}C{(x, y, z)}.

1077

1078 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}

1079 and function L{pygeodesy.hartzell} argument C{los}.

1080 '''

1081 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d

1082 return d if Vector is type(d) else (

1083 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else

1084 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent

1085

1086

1087 def _xLtp(ltp, *dflt):

1088 '''(INTERNAL) Validate B{C{ltp}}.

1089 '''

1090 if dflt and ltp is None:

1091 ltp = dflt[0]

1092 if isinstance(ltp, (LocalCartesian, Ltp)):

1093 return ltp

1094 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)

1095

1096# **) MIT License

1097#

1098# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1099#

1100# Permission is hereby granted, free of charge, to any person obtaining a

1101# copy of this software and associated documentation files (the "Software"),

1102# to deal in the Software without restriction, including without limitation

1103# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1104# and/or sell copies of the Software, and to permit persons to whom the

1105# Software is furnished to do so, subject to the following conditions:

1106#

1107# The above copyright notice and this permission notice shall be included

1108# in all copies or substantial portions of the Software.

1109#

1110# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1111# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1112# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1113# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1114# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1115# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1116# OTHER DEALINGS IN THE SOFTWARE.