Coverage for pygeodesy/ltp.py: 97%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5 

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

7and 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 

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

15 

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

17from 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! 

20from pygeodesy.datums import _WGS84, _xinstanceof 

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

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

23from pygeodesy.fmath import fabs, fdot, Fhorner 

24from pygeodesy.fsums import _floor, Fsum, fsum_, fsum1_ 

25from pygeodesy.interns import NN, _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, \ 

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

27# from pygeodesy.lazily import _ALL_LAZY # from vector3d 

28from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \ 

29 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \ 

30 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple 

31from pygeodesy.named import _NamedBase, notOverloaded 

32from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple 

33from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \ 

34 _update_all 

35from pygeodesy.streprs import Fmt, strs, unstr 

36from pygeodesy.units import Bearing, Degrees, Meter 

37from pygeodesy.utily import cotd, sincos2d, sincos2d_, tand, tand_, wrap180, wrap360 

38from pygeodesy.vector3d import _ALL_LAZY, Vector3d 

39 

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

41 

42__all__ = _ALL_LAZY.ltp 

43__version__ = '23.03.19' 

44 

45_height0_ = _height_ + _0_ 

46_narrow_ = 'narrow' 

47_wide_ = 'wide' 

48_Xyz_ = 'Xyz' 

49 

50 

51def _fov_2(**fov): 

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

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

54 if EPS < f < _90_0: 

55 return f 

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

57 raise LocalError(txt=t, **fov) 

58 

59 

60class Attitude(_NamedBase): 

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

62 ''' 

63 _alt = Meter( alt =_0_0) 

64 _roll = Degrees(roll=_0_0) 

65 _tilt = Degrees(tilt=_0_0) 

66 _yaw = Bearing(yaw =_0_0) 

67 

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

69 '''New L{Attitude}. 

70 

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

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

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

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

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

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

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

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

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

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

81 

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

83 B{C{roll}}. 

84 

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

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

87 ''' 

88 if isscalar(alt_attitude): 

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

90 else: 

91 try: 

92 t = alt_attitude.atyr 

93 except AttributeError: 

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

95 for n, v in t.items(): 

96 if v: 

97 setattr(self, n, v) 

98 n = name or t.name 

99 if n: 

100 self.name = n 

101 

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

103 def alt(self): 

104 return self._alt 

105 

106 @alt.setter # PYCHOK setter! 

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

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

109 if self._alt != a: 

110 _update_all(self) 

111 self._alt = a 

112 

113 altitude = alt 

114 

115 @Property_RO 

116 def atyr(self): 

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

118 ''' 

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

120 

121 @Property_RO 

122 def matrix(self): 

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

124 

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

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

127 ''' 

128 def _5to3(x, y, _y, z, _z): 

129 return x, fsum1_(y, _y), fsum1_(z, _z) 

130 

131 r0, r1, r2 = self._rows3 

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

133 

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

135 def roll(self): 

136 return self._roll 

137 

138 @roll.setter # PYCHOK setter! 

139 def roll(self, roll): 

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

141 if self._roll != r: 

142 _update_all(self) 

143 self._roll = r 

144 

145 bank = roll 

146 

147 @Property_RO 

148 def _rows3(self): 

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

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

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

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

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

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

155 ( -sb, cb * sg, cb * cg)) 

156 

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

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

159 

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

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

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

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

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

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

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

167 ignored if C{B{Vector} is None}. 

168 

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

170 C{B{Vector}=None}. 

171 

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

173 ''' 

174 try: 

175 x, y, z = map( float, x_xyz.xyz) 

176 except AttributeError: 

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

178 

179 r0, r1, r2 = self._rows3 

180 X = fdot(r0, x, y, y, z, z) 

181 Y = fdot(r1, x, y, y, z, z) 

182 Z = fdot(r2, x, y, z) 

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

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

185 

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

187 def tilt(self): 

188 return self._tilt 

189 

190 @tilt.setter # PYCHOK setter! 

191 def tilt(self, tilt): 

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

193 if self._tilt != t: 

194 _update_all(self) 

195 self._tilt = t 

196 

197 elevation = pitch = tilt 

198 

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

200 '''Format this attitude as string. 

201 

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

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

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

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

206 

207 @return: This attitude (C{str}). 

208 ''' 

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

210 

211 @Property_RO 

212 def tyr3d(self): 

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

214 

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

216 ''' 

217 def _r2d(r): 

218 return fsum_(_N_1_0, *r) 

219 

220 return Vector3d(*map1(_r2d, *self._rows3), name=tyr3d.__name__) 

221 

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

223 def yaw(self): 

224 return self._yaw 

225 

226 @yaw.setter # PYCHOK setter! 

227 def yaw(self, yaw): 

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

229 if self._yaw != y: 

230 _update_all(self) 

231 self._yaw = y 

232 

233 bearing = heading = yaw 

234 

235 

236class AttitudeError(_ValueError): 

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

238 ''' 

239 pass 

240 

241 

242class Frustum(_NamedBase): 

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

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

245 

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

247 ''' 

248 _h_2 = _0_0 # half hfov in degrees 

249 _ltp = None # local tangent plane 

250 _tan_h_2 = _0_0 # tan(_h_2) 

251 _v_2 = _0_0 # half vfov in degrees 

252 

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

254 '''New L{Frustum}. 

255 

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

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

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

259 

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

261 ''' 

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

263 self._v_2 = _fov_2(vfov=vfov) 

264 

265 self._tan_h_2 = tand(h, fov_2=h) 

266 

267 if ltp: 

268 self._ltp = _xLtp(ltp) 

269 

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

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

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

273 

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

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

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

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

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

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

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

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

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

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

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

285 frustum's C{ltp}. 

286 

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

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

289 

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

291 

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

293 

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

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

296 over the horizon. 

297 

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

299 ''' 

300 def _xy2(a, e, h_2, tan_h_2, r): 

301 # left and right corners, or swapped 

302 if r < EPS: # no roll 

303 r = a * tan_h_2 

304 l = -r # PYCHOK l is ell 

305 else: # roll 

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

307 r *= -a # negate right positive 

308 l *= -a # PYCHOK l is ell 

309 y = a * cotd(e, tilt_vfov=e) 

310 return (l, y), (r, y) 

311 

312 def _xyz5(b, xy5, z, ltp): 

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

314 s, c = sincos2d(b) 

315 for x, y in xy5: 

316 yield Xyz4Tuple(fsum1_(x * c, y * s), 

317 fsum1_(y * c, -x * s), z, ltp) 

318 

319 try: 

320 a, t, y, r = alt_attitude.atyr 

321 except AttributeError: 

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

323 

324 a = Meter(altitude=a) 

325 if a < EPS: # too low 

326 raise _ValueError(altitude=a) 

327 if z: # PYCHOK no cover 

328 z = Meter(z=z) 

329 a -= z 

330 if a < EPS: # z above a 

331 raise _ValueError(altitude_z=a) 

332 else: 

333 z = _0_0 

334 

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

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

337 if not EPS < e < _180_0: 

338 raise _ValueError(tilt=t) 

339 if e > _90_0: 

340 e = _180_0 - e 

341 b = _umod_360(b + _180_0) 

342 

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

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

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

346 if fabs(y) < EPS: 

347 y = _0_0 

348 

349 # center and corners, clockwise from upperleft, rolled 

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

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

352 # turn center and corners by yaw, clockwise 

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

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

355 

356 @Property_RO 

357 def hfov(self): 

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

359 ''' 

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

361 

362 @Property_RO 

363 def ltp(self): 

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

365 ''' 

366 return self._ltp 

367 

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

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

370 

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

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

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

374 

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

376 ''' 

377 t = self.hfov, self.vfov 

378 if self.ltp: 

379 t += self.ltp, 

380 t = strs(t, prec=prec, fmt=fmt) 

381 return sep.join(t) if sep else t 

382 

383 @Property_RO 

384 def vfov(self): 

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

386 ''' 

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

388 

389 

390class LocalError(_ValueError): 

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

392 ''' 

393 pass 

394 

395 

396class LocalCartesian(_NamedBase): 

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

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

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

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

401 classGeographicLib_1_1LocalCartesian.html>}. 

402 

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

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

405 

406 The conversions all take place via geocentric coordinates using a 

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

408 

409 @see: Class L{Ltp}. 

410 ''' 

411 _ecef = EcefKarney(_WGS84) 

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

413 _9Tuple = Local9Tuple 

414 

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

416 '''New L{LocalCartesian} converter. 

417 

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

419 L{Ltp} or L{Ecef9Tuple}) or latitude of the 

420 (goedetic) origin (C{degrees}). 

421 @kwarg lon0: Optional longitude of the (goedetic) origin for 

422 C{scalar} B{C{latlonh0}} and B{C{height0}} (C{degrees}). 

423 @kwarg height0: Optional origin height (C{meter}), vertically 

424 above (or below) the surface of the ellipsoid. 

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

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

427 

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

429 L{Ltp} or L{Ecef9Tuple} or B{C{latlonh0}}, B{C{lon0}} 

430 or B{C{height0}} invalid, non-C{scalar}. 

431 

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

433 

434 @note: If BC{latlonh0} is an L{Ltp}, only the lat-, longitude and 

435 height are duplicated, I{not} the ECEF converter. 

436 ''' 

437 if isinstance(latlonh0, LocalCartesian): 

438 self._ecef = latlonh0.ecef 

439 self._t0 = latlonh0._t0 

440 self.name = name or latlonh0.name 

441 else: 

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

443 if ecef: # PYCHOK no cover 

444 _xinstanceof(EcefKarney, ecef=ecef) 

445 self._ecef = ecef 

446 

447 def __eq__(self, other): 

448 '''Compare this and an other instance. 

449 

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

451 

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

453 ''' 

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

455 other.ecef == self.ecef and 

456 other._t0 == self._t0) 

457 

458 @Property_RO 

459 def datum(self): 

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

461 ''' 

462 return self.ecef.datum 

463 

464 @Property_RO 

465 def ecef(self): 

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

467 ''' 

468 return self._ecef 

469 

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

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

472 

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

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

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

476 

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

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

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

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

481 always. 

482 ''' 

483 ltp = self 

484 if ecef.datum != ltp.datum: 

485 ecef = ecef.toDatum(ltp.datum) 

486 x, y, z = self.M.rotate(ecef.xyz, *ltp._xyz0) 

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

488 ltp, ecef, None, name=ecef.name) 

489 if Xyz: 

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

491 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4) 

492 r = r.toXyz(Xyz=Xyz, **Xyz_kwds) 

493 return r 

494 

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

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

497 C{(x, y, z)}. 

498 

499 @arg latlonh: Either a C{LatLon}, an L{Ltp}, an L{Ecef9Tuple} or 

500 C{scalar} (geodetic) latitude (C{degrees}). 

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

502 B{C{latlonh}} (C{degrees}). 

503 @kwarg height: Optional height (C{meter}), vertically above (or below) 

504 the surface of the ellipsoid. 

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

506 iff available (C{bool}). 

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

508 

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

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

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

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

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

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

515 

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

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

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

519 or if B{C{height}} invalid. 

520 ''' 

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

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

523 x, y, z = self.M.rotate(t.xyz, *self._xyz0) 

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

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

526 

527 @Property_RO 

528 def height0(self): 

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

530 ''' 

531 return self._t0.height 

532 

533 @Property_RO 

534 def lat0(self): 

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

536 ''' 

537 return self._t0.lat 

538 

539 @Property_RO 

540 def latlonheight0(self): 

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

542 ''' 

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

544 

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

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

547 

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

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

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

551 

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

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

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

555 ''' 

556 t = self.M.unrotate(local.xyz, *self._xyz0) 

557 if nine: 

558 t = self.ecef.reverse(*t, M=M) 

559 return t 

560 

561 @Property_RO 

562 def lon0(self): 

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

564 ''' 

565 return self._t0.lon 

566 

567 @Property_RO 

568 def M(self): 

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

570 ''' 

571 return self._t0.M 

572 

573 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, name=NN): 

574 '''Reset the (geodetic) origin. 

575 

576 @kwarg latlonh0: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} 

577 latitude of the origin (C{degrees}). 

578 @kwarg lon0: Optional C{scalar} longitude of the origin for 

579 C{scalar} B{C{latlonh0}} (C{degrees}). 

580 @kwarg height0: Optional origin height (C{meter}), vertically 

581 above (or below) the surface of the ellipsoid. 

582 @kwarg name: Optional, new name (C{str}). 

583 

584 @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

585 C{scalar} or invalid or if B{C{lon0}} not 

586 C{scalar} for C{scalar} B{C{latlonh0}} or 

587 invalid or if B{C{height0}} invalid. 

588 ''' 

589 _update_all(self) # force reset 

590 

591 lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, 

592 suffix=_0_, Error=LocalError, name=name) 

593 if n: 

594 self.rename(n) 

595 else: 

596 n = self.name 

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

598 

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

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

601 

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

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

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

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

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

607 available (C{bool}). 

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

609 

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

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

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

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

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

615 

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

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

618 ''' 

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

620 c = self.M.unrotate((x, y, z), *self._xyz0) 

621 t = self.ecef.reverse(*c, M=M) 

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

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

624 

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

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

627 

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

629 

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

631 ''' 

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

633 

634 @Property_RO 

635 def _xyz0(self): 

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

637 ''' 

638 return self._t0.xyz 

639 

640 

641class Ltp(LocalCartesian): 

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

643 configurable ECEF converter and without optional rotation matrix. 

644 ''' 

645 def __init__(self, latlonh0=0, lon0=0, height0=0, ecef=None, name=NN): 

646 '''New C{Ltp}. 

647 

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

649 L{Ltp} or L{Ecef9Tuple}) or latitude of the 

650 (goedetic) origin (C{degrees}). 

651 @kwarg lon0: Optional longitude of the (goedetic) origin for 

652 C{scalar} B{C{latlonh0}} and B{C{height0}} (C{degrees}). 

653 @kwarg height0: Optional origin height (C{meter}), vertically 

654 above (or below) the surface of the ellipsoid. 

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

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

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

658 L{EcefKarney}C{(datum=Datums.WGS84)}. 

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

660 

661 @return: New instance (C{Ltp}). 

662 

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

664 L{Ltp} or L{Ecef9Tuple} or B{C{latlonh0}}, B{C{lon0}} 

665 or B{C{height0}} invalid, non-C{scalar}. 

666 

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

668 

669 @note: If BC{latlonh0} is an L{Ltp}, only the lat-, longitude and 

670 height are duplicated, I{not} the ECEF converter. 

671 ''' 

672 LocalCartesian.__init__(self, latlonh0, lon0=lon0, height0=height0, name=name) 

673 if ecef: 

674 self.ecef = ecef 

675 

676 @Property 

677 def ecef(self): 

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

679 ''' 

680 return self._ecef 

681 

682 @ecef.setter # PYCHOK setter! 

683 def ecef(self, ecef): 

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

685 

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

687 ''' 

688 _xinstanceof(_EcefBase, ecef=ecef) 

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

690 self.reset(self._t0) 

691 self._ecef = ecef 

692 

693 

694class _ChLV(object): 

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

696 ''' 

697 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6) 

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

699 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6) 

700 

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

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

703 ''' 

704 if bool(M): # PYCHOK no cover 

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

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

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

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

709 return ChLV9Tuple(t, name=name) 

710 

711 @property_RO 

712 def _enh_n_h(self): 

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

714 ''' 

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

716 _ChLV._enh_n_h = t # overwrite this property_RO 

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

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

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

720 return t 

721 

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

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

724 

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

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

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

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

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

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

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

732 

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

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

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

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

737 C{ChLVa} or C{ChLVe} instance. 

738 

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

740 ''' 

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

742 

743 def reverse(self, enh_, n=None, h_=0, M=None, name=NN): 

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

745 

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

747 or I{y_LV03} easting (C{meter}). 

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

749 B{C{h_}} (C{meter}). 

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

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

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

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

754 

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

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

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

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

759 C{ChLVa} or C{ChLVe} instance. 

760 

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

762 ''' 

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

764 

765 @staticmethod 

766 def _falsing2(LV95): 

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

768 ''' 

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

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

771 

772 @staticmethod 

773 def _llh2abh_3(lat, lon, h): 

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

775 ''' 

776 def _deg2ab(deg, sLL): 

777 # convert degrees to arc-seconds 

778 def _dms(ds, p, q, swap): 

779 d = _floor(ds) 

780 t = (ds - d) * p 

781 m = _floor(t) 

782 s = (t - m) * p 

783 if swap: 

784 d, s = s, d 

785 return d + (m + s * q) * q 

786 

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

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

789 return (s - sLL) / ChLV._s_ab 

790 

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

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

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

794 return a, b, h_ 

795 

796 @staticmethod 

797 def _YXh_2abh3(Y, X, h_): 

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

799 ''' 

800 def _YX2ab(YX): 

801 return YX * ChLV._ab_m 

802 

803 a, b = map1(_YX2ab, Y, X) 

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

805 return a, b, h 

806 

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

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

809 ''' 

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

811 _xyz_y_z_names=self._enh_n_h) 

812 if isinstance(enh_, ChLV9Tuple): 

813 Y, X = enh_.Y, enh_.X 

814 else: # isscalar(enh_) 

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

816 return Y, X, h_, name 

817 

818 

819class ChLV(_ChLV, Ltp): 

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

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

822 

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

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

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

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

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

828 ''' 

829 _9Tuple = ChLV9Tuple 

830 

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

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

833 _ab_M = _1_0 # ... per 1000 kilometer 

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

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

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

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

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

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

840 

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

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

843 

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

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

846 

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

848 ''' 

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

850 

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

852 # overloaded for the _ChLV.forward.__doc__ 

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

854 

855 def reverse(self, enh_, n=None, h_=0, M=None, name=NN): 

856 # overloaded for the _ChLV.reverse.__doc__ 

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

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

859 

860 @staticmethod 

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

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

863 

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

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

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

867 C{LV03} falsing, otherwise leave unfalsed. 

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

869 

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

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

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

873 with B{C{Y}} and B{C{X}} as-is. 

874 ''' 

875 e, n = t = _ChLV._falsing2(LV95) 

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

877 

878 @staticmethod 

879 def isLV03(e, n): 

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

881 

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

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

884 

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

886 LV03}, projection C{False} otherwise. 

887 ''' 

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

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

890 return 400.e3 < e < 900.e3 and 40.e3 < n < 400.e3 

891 

892 @staticmethod 

893 def isLV95(e, n, raiser=True): 

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

895 

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

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

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

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

900 

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

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

903 ''' 

904 if ChLV.isLV03(e, n): 

905 return False 

906 elif ChLV.isLV03(e - 2.e6, n - 1.e6): # _92_falsing = _95_ - _03_ 

907 return True 

908 elif raiser: # PYCHOK no cover 

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

910 return None 

911 

912 @staticmethod 

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

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

915 

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

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

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

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

920 B{n})}. 

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

922 

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

924 respectively B{C{n}}. 

925 ''' 

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

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

928 

929 

930class ChLVa(_ChLV, LocalCartesian): 

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

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

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

934 

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

936 ''' 

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

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

939 

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

941 ''' 

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

943 

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

945 # overloaded for the _ChLV.forward.__doc__ 

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

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

948 a2, b2 = a**2, b**2 

949 

950 Y = fsum_( 72.37, 211455.93 * b, 

951 -10938.51 * b * a, 

952 -0.36 * b * a2, 

953 -44.54 * b * b2) # + 600_000 

954 X = fsum_(147.07, 308807.95 * a, 

955 3745.25 * b2, 

956 76.63 * a2, 

957 -194.56 * b2 * a, 

958 119.79 * a2 * a) # + 200_000 

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

960 

961 def reverse(self, enh_, n=None, h_=0, M=None, name=NN): 

962 # overloaded for the _ChLV.reverse.__doc__ 

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

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

965 a2, b2 = a**2, b**2 

966 

967 lon = Fsum( 2.6779094, 4.728982 * a, 

968 0.791484 * a * b, 

969 0.1306 * a * b2, 

970 -0.0436 * a * a2).fover(ChLV._ab_d) 

971 lat = Fsum(16.9023892, 3.238272 * b, 

972 -0.270978 * a2, 

973 -0.002528 * b2, 

974 -0.0447 * a2 * b, 

975 -0.014 * b2 * b).fover(ChLV._ab_d) 

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

977 

978 

979class ChLVe(_ChLV, LocalCartesian): 

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

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

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

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

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

985 

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

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

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

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

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

991 use function L{pygeodesy.degrees2grades}. 

992 

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

994 ''' 

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

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

997 

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

999 ''' 

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

1001 

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

1003 # overloaded for the _ChLV.forward.__doc__ 

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

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

1006 F = Fhorner 

1007 

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

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

1010 B5 = F(a, 0.019784, -0.004277) 

1011 Y = F(b, 0, B1, 0, B3, 0, B5).fover(ChLV._ab_M) # 1000 km! 

1012 

1013 B0 = F(a, 0, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001) 

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

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

1016 B6 = 0.000488 

1017 X = F(b, B0, 0, B2, 0, B4, 0, B6).fover(ChLV._ab_M) # 1000 km! 

1018 

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

1020 if gamma: 

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

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

1023 U5 = F(a, 0.204129, -0.037725) 

1024 t = t, F(b, 0, U1, 0, U3, 0, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees? 

1025 return t 

1026 

1027 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma 

1028 # overloaded for the _ChLV.reverse.__doc__ 

1029 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name) 

1030 a, b, h = _ChLV._YXh_2abh3(Y, X, h_) 

1031 F = Fhorner 

1032 

1033 A1 = F(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243) 

1034 A3 = F(b, -442.709889, -255.02202, -96.34947, -30.0808) 

1035 A5 = F(b, 9.63495, 9.0243) 

1036 lon = F(a, ChLV._sLon, A1, 0, A3, 0, A5).fover(ChLV._s_d) 

1037 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / ChLV._s_d 

1038 

1039 A0 = F(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069) 

1040 A2 = F(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604) 

1041 A4 = F(b, 24.42786, 13.20703, 4.7476) 

1042 A6 = -0.4249 

1043 lat = F(a, A0, 0, A2, 0, A4, 0, A6).fover(ChLV._s_d) 

1044 

1045 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h) 

1046 if gamma: 

1047 U1 = F(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725) 

1048 U3 = F(b, -1435.508, -794.8777, -296.309, -92.908) 

1049 U5 = F(b, 29.631, 27.873) 

1050 t = t, F(a, 0, U1, 0, U3, 0, U5).fover(ChLV._s_ab) # degrees 

1051 return t 

1052 

1053 

1054def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds): 

1055 '''Convert an attitude oriention into a (3-D) direction vector. 

1056 

1057 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down 

1058 (clockwise rotation along and around the x-axis). 

1059 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North 

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

1061 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down 

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

1063 

1064 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None}, 

1065 a named L{Vector3Tuple}C{(x, y, z)}. 

1066 

1067 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>} 

1068 and function L{pygeodesy.hartzell} argument C{los}. 

1069 ''' 

1070 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d 

1071 return d if Vector is type(d) else ( 

1072 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else 

1073 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent 

1074 

1075 

1076def _xLtp(ltp, *dflt): 

1077 '''(INTERNAL) Validate B{C{ltp}}. 

1078 ''' 

1079 if dflt and ltp is None: 

1080 ltp = dflt[0] 

1081 if isinstance(ltp, (LocalCartesian, Ltp)): 

1082 return ltp 

1083 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian) 

1084 

1085# **) MIT License 

1086# 

1087# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1088# 

1089# Permission is hereby granted, free of charge, to any person obtaining a 

1090# copy of this software and associated documentation files (the "Software"), 

1091# to deal in the Software without restriction, including without limitation 

1092# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1093# and/or sell copies of the Software, and to permit persons to whom the 

1094# Software is furnished to do so, subject to the following conditions: 

1095# 

1096# The above copyright notice and this permission notice shall be included 

1097# in all copies or substantial portions of the Software. 

1098# 

1099# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1100# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1101# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1102# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1103# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1104# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1105# OTHER DEALINGS IN THE SOFTWARE.