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, _xsubclassof # .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, _xkwds_pop2

24 from pygeodesy.fmath import fabs, fdot, Fhorner

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

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

27 _invalid_, _lat0_, _lon0_, _ltp_, _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 _name__, _name2__, _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__ = '24.05.31'

46

47_height0_ = _height_ + _0_

48_narrow_ = 'narrow'

49_wide_ = 'wide'

50

51

52 class Attitude(_NamedBase):

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

54 '''

55 _alt = Meter( alt =_0_0)

56 _roll = Degrees(roll=_0_0)

57 _tilt = Degrees(tilt=_0_0)

58 _yaw = Bearing(yaw =_0_0)

59

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

61 '''New L{Attitude}.

62

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

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

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

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

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

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

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

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

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

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

73

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

75 B{C{roll}}.

76

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

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

79 '''

80 if _isHeight(alt_attitude):

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

82 else:

83 try:

84 t = alt_attitude.atyr

85 except AttributeError:

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

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

88 if v:

89 setattr(self, n, v)

90 n = _name__(name, _or_nameof=t)

91 if n:

92 self.name = n

93

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

95 def alt(self):

96 return self._alt

97

98 @alt.setter # PYCHOK setter!

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

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

101 if self._alt != a:

102 _update_all(self)

103 self._alt = a

104

105 altitude = alt

106

107 @Property_RO

108 def atyr(self):

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

110 '''

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

112

113 @Property_RO

114 def matrix(self):

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

116

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

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

119 '''

120 _f = fsum1f_

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

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

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

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

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

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

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

128

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

130 def roll(self):

131 return self._roll

132

133 @roll.setter # PYCHOK setter!

134 def roll(self, roll):

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

136 if self._roll != r:

137 _update_all(self)

138 self._roll = r

139

140 bank = roll

141

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

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

144

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

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

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

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

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

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

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

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

153 C{B{Vector} is None}.

154

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

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

157

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

159

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

161

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

163 '''

164 try:

165 try:

166 xyz = map2(float, x_xyz.xyz)

167 except AttributeError:

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

169 except (TypeError, ValueError) as x:

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

171

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

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

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

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

176

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

178 def tilt(self):

179 return self._tilt

180

181 @tilt.setter # PYCHOK setter!

182 def tilt(self, tilt):

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

184 if self._tilt != t:

185 _update_all(self)

186 self._tilt = t

187

188 elevation = pitch = tilt

189

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

191 '''Format this attitude as string.

192

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

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

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

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

197

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

199 '''

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

201

202 @Property_RO

203 def tyr3d(self):

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

205

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

207 '''

208 def _r2d(r):

209 return fsumf_(_N_1_0, *r)

210

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

212

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

214 def yaw(self):

215 return self._yaw

216

217 @yaw.setter # PYCHOK setter!

218 def yaw(self, yaw):

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

220 if self._yaw != y:

221 _update_all(self)

222 self._yaw = y

223

224 bearing = heading = yaw

225

226

227 class AttitudeError(_ValueError):

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

229 '''

230 pass

231

232

233 class Frustum(_NamedBase):

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

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

236

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

238 '''

239 _h_2 = _0_0 # half hfov in degrees

240 _ltp = None # local tangent plane

241 _tan_h_2 = _0_0 # tan(_h_2)

242 _v_2 = _0_0 # half vfov in degrees

243

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

245 '''New L{Frustum}.

246

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

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

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

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

251

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

253 '''

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

255 self._v_2 = _fov_2(vfov=vfov)

256

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

258

259 if ltp:

260 self._ltp = _xLtp(ltp)

261 if name:

262 self.name # PYCHOK effect

263

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

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

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

267

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

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

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

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

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

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

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

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

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

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

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

279 frustum's C{ltp}.

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

281

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

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

284

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

286

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

288

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

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

291 over the horizon.

292

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

294 '''

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

296 # left and right corners, or swapped

297 if r < EPS: # no roll

298 r = a * tan_h_2

299 l = -r # PYCHOK l is ell

300 else: # roll

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

302 r *= -a # negate right positive

303 l *= -a # PYCHOK l is ell

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

305 return (l, y), (r, y)

306

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

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

309 s, c = sincos2d(b)

310 _f = fsum1f_

311 for x, y in xy5:

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

313 _f(y * c, -x * s), 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}) for C{scalar}

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

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

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

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

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

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

430 for further details.

431

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

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

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

435

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

437

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

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

440 '''

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

442

443 def __eq__(self, other):

444 '''Compare this and an other instance.

445

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

447

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

449 '''

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

451 other.ecef == self.ecef and

452 other._t0 == self._t0)

453

454 @Property_RO

455 def datum(self):

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

457 '''

458 return self.ecef.datum

459

460 @Property_RO

461 def ecef(self):

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

463 '''

464 return self._ecef

465

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

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

468

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

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

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

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

473 C{B{Xyz} is None}.

474

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

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

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

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

479 always.

480

481 @raise TypeError: Invalid B{C{Xyz}} or B{C{name_Xyz_kwds}}.

482 '''

483 ltp = self

484 if ecef.datum != ltp.datum:

485 ecef = ecef.toDatum(ltp.datum)

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

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

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

489 ltp, ecef, None, name=n)

490 if Xyz:

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

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

493 return r

494

495 @Property_RO

496 def ellipsoid(self):

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

498 '''

499 return self.ecef.datum.ellipsoid

500

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

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

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

504

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

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

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

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

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

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

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

512 iff available (C{bool}).

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

514

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

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

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

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

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

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

521

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

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

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

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

526 '''

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

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

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

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

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

532

533 @Property_RO

534 def height0(self):

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

536 '''

537 return self._t0.height

538

539 @Property_RO

540 def lat0(self):

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

542 '''

543 return self._t0.lat

544

545 @Property_RO

546 def latlonheight0(self):

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

548 '''

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

550

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

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

553

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

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

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

557

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

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

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

561 '''

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_RO

723 def _enh_n_h(self):

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

725 '''

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

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

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},

930 B{n})}.

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

932

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

934 respectively B{C{n}}.

935 '''

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

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

938

939

940 class ChLVa(_ChLV, LocalCartesian):

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

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

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

944

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

946 '''

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

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

949

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

951 '''

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

953

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

955 # overloaded for the _ChLV.forward.__doc__

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

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

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

959

960 Y = fsumf_( 72.37, 211455.93 * b,

961 -10938.51 * b * a,

962 -0.36 * b * a2,

963 -44.54 * b * b2) # + 600_000

964 X = fsumf_(147.07, 308807.95 * a,

965 3745.25 * b2,

966 76.63 * a2,

967 -194.56 * b2 * a,

968 119.79 * a2 * a) # + 200_000

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

970

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

972 # overloaded for the _ChLV.reverse.__doc__

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

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

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

976

977 lat = _Fsumf_(16.9023892, 3.238272 * b,

978 -0.270978 * a2,

979 -0.002528 * b2,

980 -0.0447 * a2 * b,

981 -0.014 * b2 * b).fover(ab_d)

982 lon = _Fsumf_( 2.6779094, 4.728982 * a,

983 0.791484 * a * b,

984 0.1306 * a * b2,

985 -0.0436 * a * a2).fover(ab_d)

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

987

988

989 class ChLVe(_ChLV, LocalCartesian):

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

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

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

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

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

995

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

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

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

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

1000 (decimal C{degrees}). To convert C{gamma} to C{grades} or C{gons},

1001 use function L{pygeodesy.degrees2grades}.

1002

1003 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.

1004 '''

1005 def __init__(self, name=ChLV.Bern.name):

1006 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.

1007

1008 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).

1009 '''

1010 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

1011

1012 def forward(self, latlonh, lon=None, height=0, M=None, gamma=False, **name): # PYCHOK gamma

1013 # overloaded for the _ChLV.forward.__doc__

1014 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)

1015 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)

1016 ab_M, z, _H = ChLV._ab_M, 0, Fhorner

1017

1018 B1 = _H(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)

1019 B3 = _H(a, -44.232717, 4.291740, -0.309883, 0.013924)

1020 B5 = _H(a, 0.019784, -0.004277)

1021 Y = _H(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!

1022

1023 B0 = _H(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)

1024 B2 = _H(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)

1025 B4 = _H(a, -0.734684, 0.144466, -0.011842)

1026 B6 = 0.000488

1027 X = _H(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!

1028

1029 t = self._ChLV9Tuple(True, M, n, Y, X, h_, lat, lon, h)

1030 if gamma:

1031 U1 = _H(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)

1032 U3 = _H(a, -412.991934, 64.106344, -2.679566, 0.123833)

1033 U5 = _H(a, 0.204129, -0.037725)

1034 g = _H(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?

1035 t = t, g

1036 return t

1037

1038 def reverse(self, enh_, n=None, h_=0, M=None, gamma=False, **name): # PYCHOK gamma

1039 # overloaded for the _ChLV.reverse.__doc__

1040 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)

1041 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)

1042 s_d, _H, z = ChLV._s_d, Fhorner, 0

1043

1044 A0 = _H(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)

1045 A2 = _H(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)

1046 A4 = _H(b, 24.42786, 13.20703, 4.7476)

1047 A6 = -0.4249

1048 lat = _H(a, A0, z, A2, z, A4, z, A6).fover(s_d)

1049

1050 A1 = _H(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)

1051 A3 = _H(b, -442.709889, -255.02202, -96.34947, -30.0808)

1052 A5 = _H(b, 9.63495, 9.0243)

1053 lon = _H(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)

1054 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d

1055

1056 t = self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)

1057 if gamma:

1058 U1 = _H(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)

1059 U3 = _H(b, -1435.508, -794.8777, -296.309, -92.908)

1060 U5 = _H(b, 29.631, 27.873)

1061 g = _H(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees

1062 t = t, g

1063 return t

1064

1065

1066 def _fov_2(**fov):

1067 # Half a field-of-view angle in C{degrees}.

1068 f = Degrees(Error=LocalError, **fov) * _0_5

1069 if EPS < f < _90_0:

1070 return f

1071 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)

1072 raise LocalError(txt=t, **fov)

1073

1074

1075 def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **name_Vector_kwds):

1076 '''Convert an attitude pose into a (3-D) direction vector.

1077

1078 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down

1079 (clockwise rotation along and around the x-axis).

1080 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North

1081 (counter-clockwise rotation along and around the z-axis).

1082 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down

1083 (clockwise rotation along and around the y-axis).

1084 @kwarg Vector: Class to return the direction vector (C{Cartesian},

1085 L{Vector3d} or C{Vector3Tuple}) or C{None}.

1086 @kwarg name_Vector_kwds: Optional C{B{name}=NN} (C{str}) and optional,

1087 additional B{C{Vector}} keyword arguments, ignored if

1088 C{B{Vector} is None}.

1089

1090 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},

1091 a named L{Vector3Tuple}C{(x, y, z)}.

1092

1093 @raise AttitudeError: Invalid B{C{tilt}}, B{C{yaw}} or B{C{roll}}.

1094

1095 @raise TypeError: Invalid B{C{Vector}} or B{C{name_Vector_kwds}}.

1096

1097 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}

1098 and function L{pygeodesy.hartzell} argument C{los}, Line-Of-Sight.

1099 '''

1100 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d

1101 if Vector is not type(d):

1102 n, kwds = _name2__(name_Vector_kwds, name__=tyr3d)

1103 d = Vector3Tuple(d.x, d.y, d.z, name=n) if Vector is None else \

1104 Vector(d.x, d.y, d.z, name=n, **kwds)

1105 return d

1106

1107

1108 def _xLtp(ltp, *dflt):

1109 '''(INTERNAL) Validate B{C{ltp}}.

1110 '''

1111 if dflt and ltp is None:

1112 ltp = dflt[0]

1113 if isinstance(ltp, (LocalCartesian, Ltp)):

1114 return ltp

1115 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)

1116

1117# **) MIT License

1118#

1119# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1120#

1121# Permission is hereby granted, free of charge, to any person obtaining a

1122# copy of this software and associated documentation files (the "Software"),

1123# to deal in the Software without restriction, including without limitation

1124# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1125# and/or sell copies of the Software, and to permit persons to whom the

1126# Software is furnished to do so, subject to the following conditions:

1127#

1128# The above copyright notice and this permission notice shall be included

1129# in all copies or substantial portions of the Software.

1130#

1131# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1132# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1133# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1134# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1135# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1136# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1137# OTHER DEALINGS IN THE SOFTWARE.