Coverage for pygeodesy/ltp.py: 96%

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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, map2, \ 

17 _xargs_kwds_names 

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

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

20 _N_1_0 # PYCHOK used! 

21from pygeodesy.datums import _WGS84, _xinstanceof 

22from pygeodesy.ecef import _EcefBase, EcefKarney, _llhn4, _xyzn4 

23from pygeodesy.errors import _NotImplementedError, _TypesError, _ValueError, \ 

24 _xattr, _xkwds, _xkwds_get 

25from pygeodesy.fmath import fabs, fdot, Fhorner 

26from pygeodesy.fsums import _floor, Fsum, fsumf_, fsum1f_ 

27from pygeodesy.interns import NN, _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, \ 

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

29# from pygeodesy.lazily import _ALL_LAZY # from vector3d 

30from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \ 

31 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \ 

32 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple 

33from pygeodesy.named import _NamedBase, notOverloaded 

34from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple 

35from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \ 

36 _update_all 

37from pygeodesy.streprs import Fmt, strs, unstr 

38from pygeodesy.units import Bearing, Degrees, Meter 

39from pygeodesy.utily import cotd, _loneg, sincos2d, sincos2d_, tand, tand_, \ 

40 wrap180, wrap360 

41from pygeodesy.vector3d import _ALL_LAZY, Vector3d 

42 

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

44 

45__all__ = _ALL_LAZY.ltp 

46__version__ = '23.11.16' 

47 

48_height0_ = _height_ + _0_ 

49_narrow_ = 'narrow' 

50_wide_ = 'wide' 

51_Xyz_ = 'Xyz' 

52 

53 

54def _fov_2(**fov): 

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

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

57 if EPS < f < _90_0: 

58 return f 

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

60 raise LocalError(txt=t, **fov) 

61 

62 

63class Attitude(_NamedBase): 

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

65 ''' 

66 _alt = Meter( alt =_0_0) 

67 _roll = Degrees(roll=_0_0) 

68 _tilt = Degrees(tilt=_0_0) 

69 _yaw = Bearing(yaw =_0_0) 

70 

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

72 '''New L{Attitude}. 

73 

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

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

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

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

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

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

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

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

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

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

84 

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

86 B{C{roll}}. 

87 

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

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

90 ''' 

91 if isscalar(alt_attitude): 

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

93 else: 

94 try: 

95 t = alt_attitude.atyr 

96 except AttributeError: 

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

98 for n, v in t.items(): 

99 if v: 

100 setattr(self, n, v) 

101 n = name or t.name 

102 if n: 

103 self.name = n 

104 

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

106 def alt(self): 

107 return self._alt 

108 

109 @alt.setter # PYCHOK setter! 

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

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

112 if self._alt != a: 

113 _update_all(self) 

114 self._alt = a 

115 

116 altitude = alt 

117 

118 @Property_RO 

119 def atyr(self): 

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

121 ''' 

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

123 

124 @Property_RO 

125 def matrix(self): 

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

127 

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

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

130 ''' 

131 _f = fsum1f_ 

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

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

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

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

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

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

138 ( -sb, cb * sg, cb * cg)) 

139 

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

141 def roll(self): 

142 return self._roll 

143 

144 @roll.setter # PYCHOK setter! 

145 def roll(self, roll): 

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

147 if self._roll != r: 

148 _update_all(self) 

149 self._roll = r 

150 

151 bank = roll 

152 

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

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

155 

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

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

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

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

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

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

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

163 ignored if C{B{Vector} is None}. 

164 

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

166 C{B{Vector}=None}. 

167 

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

169 

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

171 ''' 

172 try: 

173 try: 

174 xyz = map2(float, x_xyz.xyz) 

175 except AttributeError: 

176 xyz = map1(float, x_xyz, y, z) 

177 except (TypeError, ValueError) as x: 

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

179 

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

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

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

183 

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

185 def tilt(self): 

186 return self._tilt 

187 

188 @tilt.setter # PYCHOK setter! 

189 def tilt(self, tilt): 

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

191 if self._tilt != t: 

192 _update_all(self) 

193 self._tilt = t 

194 

195 elevation = pitch = tilt 

196 

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

198 '''Format this attitude as string. 

199 

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

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

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

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

204 

205 @return: This attitude (C{str}). 

206 ''' 

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

208 

209 @Property_RO 

210 def tyr3d(self): 

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

212 

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

214 ''' 

215 def _r2d(r): 

216 return fsumf_(_N_1_0, *r) 

217 

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

219 

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

221 def yaw(self): 

222 return self._yaw 

223 

224 @yaw.setter # PYCHOK setter! 

225 def yaw(self, yaw): 

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

227 if self._yaw != y: 

228 _update_all(self) 

229 self._yaw = y 

230 

231 bearing = heading = yaw 

232 

233 

234class AttitudeError(_ValueError): 

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

236 ''' 

237 pass 

238 

239 

240class Frustum(_NamedBase): 

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

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

243 

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

245 ''' 

246 _h_2 = _0_0 # half hfov in degrees 

247 _ltp = None # local tangent plane 

248 _tan_h_2 = _0_0 # tan(_h_2) 

249 _v_2 = _0_0 # half vfov in degrees 

250 

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

252 '''New L{Frustum}. 

253 

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

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

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

257 

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

259 ''' 

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

261 self._v_2 = _fov_2(vfov=vfov) 

262 

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

264 

265 if ltp: 

266 self._ltp = _xLtp(ltp) 

267 

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

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

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

271 

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

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

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

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

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

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

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

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

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

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

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

283 frustum's C{ltp}. 

284 

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

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

287 

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

289 

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

291 

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

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

294 over the horizon. 

295 

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

297 ''' 

298 def _xy2(a, e, h_2, tan_h_2, r): 

299 # left and right corners, or swapped 

300 if r < EPS: # no roll 

301 r = a * tan_h_2 

302 l = -r # PYCHOK l is ell 

303 else: # roll 

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

305 r *= -a # negate right positive 

306 l *= -a # PYCHOK l is ell 

307 y = a * cotd(e, tilt_vfov=e) 

308 return (l, y), (r, y) 

309 

310 def _xyz5(b, xy5, z, ltp): 

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

312 s, c = sincos2d(b) 

313 _f = fsum1f_ 

314 for x, y in xy5: 

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

316 _f(y * c, -x * s), z, ltp) 

317 

318 try: 

319 a, t, y, r = alt_attitude.atyr 

320 except AttributeError: 

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

322 

323 a = Meter(altitude=a) 

324 if a < EPS: # too low 

325 raise _ValueError(altitude=a) 

326 if z: # PYCHOK no cover 

327 z = Meter(z=z) 

328 a -= z 

329 if a < EPS: # z above a 

330 raise _ValueError(altitude_z=a) 

331 else: 

332 z = _0_0 

333 

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

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

336 if not EPS < e < _180_0: 

337 raise _ValueError(tilt=t) 

338 if e > _90_0: 

339 e = _loneg(e) 

340 b = _umod_360(b + _180_0) 

341 

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

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

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

345 if fabs(y) < EPS: 

346 y = _0_0 

347 

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

349 # center and corners, clockwise from upperleft, rolled 

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

351 + _xy2(a, e + v, -h, -t, 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 _Ecef = EcefKarney 

413 _lon00 = INT0 # self.lon0 

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

415 _9Tuple = Local9Tuple 

416 

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

418 '''New L{LocalCartesian} converter. 

419 

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

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

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

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

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

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

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

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

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

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

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

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

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

433 

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

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

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

437 

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

439 

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

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

442 ''' 

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

444 

445 def __eq__(self, other): 

446 '''Compare this and an other instance. 

447 

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

449 

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

451 ''' 

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

453 other.ecef == self.ecef and 

454 other._t0 == self._t0) 

455 

456 @Property_RO 

457 def datum(self): 

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

459 ''' 

460 return self.ecef.datum 

461 

462 @Property_RO 

463 def ecef(self): 

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

465 ''' 

466 return self._ecef 

467 

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

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

470 

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

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

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

474 

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

476 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 ltp = self 

482 if ecef.datum != ltp.datum: 

483 ecef = ecef.toDatum(ltp.datum) 

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

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

486 ltp, ecef, None, name=ecef.name) 

487 if Xyz: 

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

489 raise _TypesError(_Xyz_, Xyz, *_XyzLocals4) 

490 r = r.toXyz(Xyz=Xyz, **Xyz_kwds) 

491 return r 

492 

493 @Property_RO 

494 def ellipsoid(self): 

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

496 ''' 

497 return self.ecef.datum.ellipsoid 

498 

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

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

501 C{(x, y, z)}. 

502 

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

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

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

506 B{C{latlonh}} (C{degrees}). 

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

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

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

510 iff available (C{bool}). 

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

512 

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

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

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

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

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

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

519 

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

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

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

523 or if B{C{height}} invalid. 

524 ''' 

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

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

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

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

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

530 

531 @Property_RO 

532 def height0(self): 

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

534 ''' 

535 return self._t0.height 

536 

537 @Property_RO 

538 def lat0(self): 

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

540 ''' 

541 return self._t0.lat 

542 

543 @Property_RO 

544 def latlonheight0(self): 

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

546 ''' 

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

548 

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

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

551 

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

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

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

555 

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

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

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

559 ''' 

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

561 if nine: 

562 t = self.ecef.reverse(*t, M=M) 

563 return t 

564 

565 @Property_RO 

566 def lon0(self): 

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

568 ''' 

569 return self._t0.lon 

570 

571 @Property 

572 def lon00(self): 

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

574 ''' 

575 return self._lon00 

576 

577 @lon00.setter # PYCHOK setter! 

578 def lon00(self, lon00): 

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

580 ''' 

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

582 self._lon00 = Degrees(lon00=lon00) 

583 

584 @Property_RO 

585 def M(self): 

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

587 ''' 

588 return self._t0.M 

589 

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

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

592 ''' 

593 if isinstance(latlonh0, LocalCartesian): 

594 if self._t0: 

595 _update_all(self) 

596 self._ecef = latlonh0.ecef 

597 self._lon00 = latlonh0.lon00 

598 self._t0 = latlonh0._t0 

599 n = name or latlonh0.name 

600 else: 

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

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

603 if ecef: # PYCHOK no cover 

604 _xinstanceof(self._Ecef, ecef=ecef) 

605 _update_all(self) 

606 self._ecef = ecef 

607 elif self._t0: 

608 _update_all(self) 

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

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

611 if n: 

612 self.rename(n) 

613 

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

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

616 

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

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

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

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

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

622 available (C{bool}). 

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

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

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

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

627 

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

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

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

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

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

633 

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

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

636 ''' 

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

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

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

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

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

642 

643 @Property_RO 

644 def _t0_xyz(self): 

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

646 ''' 

647 return self._t0.xyz 

648 

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

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

651 

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

653 

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

655 ''' 

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

657 

658 

659class Ltp(LocalCartesian): 

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

661 (re-)configurable ECEF converter. 

662 ''' 

663 _Ecef = _EcefBase 

664 

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

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

667 

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

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

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

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

672 

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

674 ''' 

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

676 ecef=ecef, name=name, **lon00) 

677 

678 @Property 

679 def ecef(self): 

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

681 ''' 

682 return self._ecef 

683 

684 @ecef.setter # PYCHOK setter! 

685 def ecef(self, ecef): 

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

687 

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

689 ''' 

690 _xinstanceof(_EcefBase, ecef=ecef) 

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

692 self.reset(self._t0) 

693 self._ecef = ecef 

694 

695 

696class _ChLV(object): 

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

698 ''' 

699 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6) 

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

701 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6) 

702 

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

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

705 ''' 

706 if bool(M): # PYCHOK no cover 

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

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

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

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

711 return ChLV9Tuple(t, name=name) 

712 

713 @property_RO 

714 def _enh_n_h(self): 

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

716 ''' 

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

718 # assert _xargs_kwds_names( ChLV.reverse)[1:4] == t 

719 # assert _xargs_kwds_names(ChLVa.reverse)[1:4] == t 

720 # assert _xargs_kwds_names(ChLVe.reverse)[1:4] == t 

721 return t 

722 

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

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

725 

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

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

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

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

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

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

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

733 

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

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

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

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

738 C{ChLVa} or C{ChLVe} instance. 

739 

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

741 ''' 

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

743 

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

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

746 

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

748 or I{y_LV03} easting (C{meter}). 

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

750 B{C{h_}} (C{meter}). 

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

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

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

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

755 

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

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

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

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

760 C{ChLVa} or C{ChLVe} instance. 

761 

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

763 ''' 

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

765 

766 @staticmethod 

767 def _falsing2(LV95): 

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

769 ''' 

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

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

772 

773 @staticmethod 

774 def _llh2abh_3(lat, lon, h): 

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

776 ''' 

777 def _deg2ab(deg, sLL): 

778 # convert degrees to arc-seconds 

779 def _dms(ds, p, q, swap): 

780 d = _floor(ds) 

781 t = (ds - d) * p 

782 m = _floor(t) 

783 s = (t - m) * p 

784 if swap: 

785 d, s = s, d 

786 return d + (m + s * q) * q 

787 

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

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

790 return (s - sLL) / ChLV._s_ab 

791 

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

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

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

795 return a, b, h_ 

796 

797 @staticmethod 

798 def _YXh_2abh3(Y, X, h_): 

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

800 ''' 

801 def _YX2ab(YX): 

802 return YX * ChLV._ab_m 

803 

804 a, b = map1(_YX2ab, Y, X) 

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

806 return a, b, h 

807 

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

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

810 ''' 

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

812 _xyz_y_z_names=self._enh_n_h, **name) 

813 if isinstance(enh_, ChLV9Tuple): 

814 Y, X = enh_.Y, enh_.X 

815 else: # isscalar(enh_) 

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

817 return Y, X, h_, name 

818 

819 

820class ChLV(_ChLV, Ltp): 

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

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

823 

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

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

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

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

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

829 ''' 

830 _9Tuple = ChLV9Tuple 

831 

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

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

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

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

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

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

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

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

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

841 

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

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

844 

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

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

847 

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

849 ''' 

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

851 

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

853 # overloaded for the _ChLV.forward.__doc__ 

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

855 

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

857 # overloaded for the _ChLV.reverse.__doc__ 

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

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

860 

861 @staticmethod 

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

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

864 

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

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

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

868 C{LV03} falsing, otherwise leave unfalsed. 

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

870 

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

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

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

874 with B{C{Y}} and B{C{X}} as-is. 

875 ''' 

876 e, n = t = _ChLV._falsing2(LV95) 

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

878 

879 @staticmethod 

880 def isLV03(e, n): 

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

882 

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

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

885 

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

887 LV03}, projection C{False} otherwise. 

888 ''' 

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

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

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

892 

893 @staticmethod 

894 def isLV95(e, n, raiser=True): 

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

896 

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

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

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

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

901 

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

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

904 ''' 

905 if ChLV.isLV03(e, n): 

906 return False 

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

908 return True 

909 elif raiser: # PYCHOK no cover 

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

911 return None 

912 

913 @staticmethod 

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

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

916 

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

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

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

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

921 B{n})}. 

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

923 

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

925 respectively B{C{n}}. 

926 ''' 

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

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

929 

930 

931class ChLVa(_ChLV, LocalCartesian): 

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

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

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

935 

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

937 ''' 

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

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

940 

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

942 ''' 

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

944 

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

946 # overloaded for the _ChLV.forward.__doc__ 

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

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

949 a2, b2 = a**2, b**2 

950 

951 Y = fsumf_( 72.37, 211455.93 * b, 

952 -10938.51 * b * a, 

953 -0.36 * b * a2, 

954 -44.54 * b * b2) # + 600_000 

955 X = fsumf_(147.07, 308807.95 * a, 

956 3745.25 * b2, 

957 76.63 * a2, 

958 -194.56 * b2 * a, 

959 119.79 * a2 * a) # + 200_000 

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

961 

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

963 # overloaded for the _ChLV.reverse.__doc__ 

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

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

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

967 

968 lat = Fsum(16.9023892, 3.238272 * b, 

969 -0.270978 * a2, 

970 -0.002528 * b2, 

971 -0.0447 * a2 * b, 

972 -0.014 * b2 * b).fover(ab_d) 

973 lon = Fsum( 2.6779094, 4.728982 * a, 

974 0.791484 * a * b, 

975 0.1306 * a * b2, 

976 -0.0436 * a * a2).fover(ab_d) 

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

978 

979 

980class ChLVe(_ChLV, LocalCartesian): 

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

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

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

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

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

986 

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

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

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

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

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

992 use function L{pygeodesy.degrees2grades}. 

993 

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

995 ''' 

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

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

998 

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

1000 ''' 

1001 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name) 

1002 

1003 def forward(self, latlonh, lon=None, height=0, M=None, name=NN, gamma=False): # PYCHOK gamma 

1004 # overloaded for the _ChLV.forward.__doc__ 

1005 lat, lon, h, name = _llhn4(latlonh, lon, height, name=name) 

1006 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h) 

1007 ab_M, z, _F = ChLV._ab_M, 0, Fhorner 

1008 

1009 B1 = _F(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992) 

1010 B3 = _F(a, -44.232717, 4.291740, -0.309883, 0.013924) 

1011 B5 = _F(a, 0.019784, -0.004277) 

1012 Y = _F(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km! 

1013 

1014 B0 = _F(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001) 

1015 B2 = _F(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053) 

1016 B4 = _F(a, -0.734684, 0.144466, -0.011842) 

1017 B6 = 0.000488 

1018 X = _F(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km! 

1019 

1020 t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h) 

1021 if gamma: 

1022 U1 = _F(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165) 

1023 U3 = _F(a, -412.991934, 64.106344, -2.679566, 0.123833) 

1024 U5 = _F(a, 0.204129, -0.037725) 

1025 g = _F(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees? 

1026 t = t, g 

1027 return t 

1028 

1029 def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False): # PYCHOK gamma 

1030 # overloaded for the _ChLV.reverse.__doc__ 

1031 Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name) 

1032 a, b, h = _ChLV._YXh_2abh3(Y, X, h_) 

1033 s_d, _F, z = ChLV._s_d, Fhorner, 0 

1034 

1035 A0 = _F(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069) 

1036 A2 = _F(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604) 

1037 A4 = _F(b, 24.42786, 13.20703, 4.7476) 

1038 A6 = -0.4249 

1039 lat = _F(a, A0, z, A2, z, A4, z, A6).fover(s_d) 

1040 

1041 A1 = _F(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243) 

1042 A3 = _F(b, -442.709889, -255.02202, -96.34947, -30.0808) 

1043 A5 = _F(b, 9.63495, 9.0243) 

1044 lon = _F(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d) 

1045 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d 

1046 

1047 t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h) 

1048 if gamma: 

1049 U1 = _F(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725) 

1050 U3 = _F(b, -1435.508, -794.8777, -296.309, -92.908) 

1051 U5 = _F(b, 29.631, 27.873) 

1052 g = _F(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees 

1053 t = t, g 

1054 return t 

1055 

1056 

1057def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds): 

1058 '''Convert an attitude oriention into a (3-D) direction vector. 

1059 

1060 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down 

1061 (clockwise rotation along and around the x-axis). 

1062 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North 

1063 (counter-clockwise rotation along and around the z-axis). 

1064 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down 

1065 (clockwise rotation along and around the y-axis). 

1066 

1067 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None}, 

1068 a named L{Vector3Tuple}C{(x, y, z)}. 

1069 

1070 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>} 

1071 and function L{pygeodesy.hartzell} argument C{los}. 

1072 ''' 

1073 d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d 

1074 return d if Vector is type(d) else ( 

1075 Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else 

1076 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent 

1077 

1078 

1079def _xLtp(ltp, *dflt): 

1080 '''(INTERNAL) Validate B{C{ltp}}. 

1081 ''' 

1082 if dflt and ltp is None: 

1083 ltp = dflt[0] 

1084 if isinstance(ltp, (LocalCartesian, Ltp)): 

1085 return ltp 

1086 raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian) 

1087 

1088# **) MIT License 

1089# 

1090# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1091# 

1092# Permission is hereby granted, free of charge, to any person obtaining a 

1093# copy of this software and associated documentation files (the "Software"), 

1094# to deal in the Software without restriction, including without limitation 

1095# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1096# and/or sell copies of the Software, and to permit persons to whom the 

1097# Software is furnished to do so, subject to the following conditions: 

1098# 

1099# The above copyright notice and this permission notice shall be included 

1100# in all copies or substantial portions of the Software. 

1101# 

1102# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1103# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1104# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1105# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1106# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1107# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1108# OTHER DEALINGS IN THE SOFTWARE.