Coverage for pyrdnap/rdnap2018.py: 93%

2# -*- coding: utf-8 -*-

4u'''Main classes L{RDNAP2018v1} and L{RDNAP2018v2} follow C{variant 1} respectively C{variant 2} of

5the U{RDNAPTRANS(tm)2018_v220627<https://formulieren.kadaster.nl/aanvragen_rdnaptrans>} specification.

6Each provide a C{forward} method to convert geodetic lat-/longitudes and heights to C{RD} coodinates

7and C{NAP} heights and a C{reverse} method for converting the other way.

9The L{RDNAP2018v1.forward} and C{.reverse} results are within the C{RDNAPTRANS(tm)2018_v220627}

10self-validation requirements of C{0.000000010 degrees} respectively C{0.0010 meter} for points inside

11the C{RD} region, see B{C{Note below}}. Class L{RDNAP2018v2} does not.

13@note: L{RDNAP2018v1}, C{PyRDNAP} and C{pyrdnap} have B{not been formally validated} and are

14 B{not certified} to carry the trademark C{RDNAPTRANS(tm)}.

15'''

16# make sure int/int division yields float quotient, see .basics

17from __future__ import division as _; del _ # noqa: E702 ;

19from pyrdnap.rd0 import _RD, _RD0 as A0, RDNAP7Tuple

20from pyrdnap.v_grids import RDNAPError, _V_grid, _v_gridz_import

21from pyrdnap.__pygeodesy import (_0_0, _0_5, _1_0, _2_0,

22 _isNAN, _isNAN0, _earth_datum,

23 _ALL_DOCS, _ALL_OTHER, _FOR_DOCS,

24 _NamedBase, notOverloaded)

25from pygeodesy import (map1, EPS0, EPS1, NAN, PI_2, PI, PI2, # "consterns"

26 Datum, Ellipsoid, LatLonDatum3Tuple, # datums, ellipsoids

27 property_RO, property_ROnce, # props

28 Lamd, Lat, Lon, Phid, # units

29 sincos2, sincos2d) # utily

31from math import asin, atan, copysign, degrees, exp, \

32 fabs, floor, hypot, radians, sin, sqrt

34__all__ = ()

35__version__ = '26.06.06'

37_TOL_D = 1e-9 # degrees 2.3.3f+

38_TOL_M = 1e-6 # meter

39_TOL_R = radians(_TOL_D) # 2e-11

40_TRIPS = 16 # 5..6 sufficient

43class _RDNAPbase(_NamedBase): # in .rd0._RD.regionB

44 '''(INTERNAL) L{RDNAP2018v1}C{/-v2} base class.

45 '''

46 _datum = None # forward, v1 reverse Datum, lazily (GRS80)

47 _EETRS = None # forward, v1 reverse Ellipsoid, lazily

48 _raiser = False

50 def __init__(self, a_ellipsoid=None, f=None, raiser=False, **name):

51 '''New C{RDNAP2018v1} or C{-v2} instance.

53 @kwarg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or the ellipsoid's equatorial

54 radius (C{scalar}, conventionally in C{meter}), see B{C{f}}

55 or a datum (L{Datum}). Default C{Datums.GRS80} for ETRS89.

56 @kwarg f: The flattening of the ellipsoid (C{scalar}) if B{C{a_ellipsoid}} is

57 specified as C{scalar}, ignored otherwise.

58 @kwarg raiser: If C{True} raise an L{RDNAPError} for lat-/longitudes outside

59 the C{RD} region (C{bool}).

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

62 @raise RDNAPError: Ellipsoid (or datum) is not oblate (i.e. is spherical or

63 prolate) or the datum's C{transform} is not C{unity}.

64 '''

65 if a_ellipsoid is f is None:

66 self._datum = A0.D80 # GRS80 (ETRS89)

67 else:

68 _earth_datum(self, a_ellipsoid, f, **name) # sets self._datum

69 self._EETRS = E = self._datum.ellipsoid

70 if not E.isOblate:

71 raise RDNAPError('not oblate: %r' % (E,))

72 if raiser: # PYCHOK no cover

73 T = self._datum.transform

74 if not T.isunity:

75 raise RDNAPError('not unity: %r' % (T,))

76 self._raiser = True

77 if name:

78 self.name = name

80 def forward(self, lat, lon, height=0, raiser=None, name='forward'):

81 '''Convert GRS80 (ETRS98) geodetic C{(B{lat}, B{lon})} and B{C{height}}

82 to local C{(RDx, RDy)} coordinates and C{NAPh} quasi-geoid-height.

84 @arg lat: Latitude (C{degrees} geodetic).

85 @arg lon: Longitude (C{degrees} geodetic).

86 @kwarg height: Height, optional (C{meter} above geoid) or C{NAN}

87 to ignore C{NAPh} interpolation.

88 @kwarg raiser: If C{True} raise an L{RDNAPError} if B{C{lat}} or

89 B{C{lon}} is outside the C{RD} region (C{bool}),

90 if C{False} don't, overriding property C{raiser}.

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

93 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}

94 with local C{RDx}, C{RDy} coordinates and C{NAPh} height.

95 '''

96 lat, lon = Lat(lat), Lon(lon)

97 lat0, lon0 = \

98 lat_, lon_ = self._forwardXform2(raiser, lat, lon)

99 for _ in range(_TRIPS): # 2.3.3a-f, 1..2

100 latc, lonc = self._rdlatlon2(lat_, lon_, lat0, lon0)

101 if fabs(latc - lat_) < _TOL_D and \

102 fabs(lonc - lon_) < _TOL_D:

103 break

104 lat_, lon_ = latc, lonc

105

106 phiClamC = _ellipsoidal2spherical(latc, lonc)

107 RDx, RDy = _spherical2oblique(*phiClamC)

108 NAPh = NAN if _isNAN(height) else (height - # NOT lat0, lon0

109 self._rdNAPh_v(lat, lon, latc, lonc)) # 2.5.2

110 return RDNAP7Tuple(RDx, RDy, NAPh,

111 lat, lon, height, self.forwardDatum, name=name)

112

113 def forward3(self, lat, lon, name='forward3'):

114 '''Datum transform C{(B{lat}, B{lon})} from GRS80 (ETRS98) to Bessel1841 (RD-Bessel).

115

116 @return: A L{LatLonDatum3Tuple}C{(lat, lon, datum)}.

117 '''

118 x, y, z = _geodetic2cartesian(lat, lon, A0.H0_ETRS, self._EETRS)

119 x, y, z = _RD._xETRS2RD.transform(x, y, z)

120 lat, lon = _cartesian2geodetic(x, y, z, A0.E0)

121 return LatLonDatum3Tuple(lat, lon, A0.D0, name=name)

122

123 @property_RO

124 def forwardDatum(self):

125 '''Get the C{forward} datum (L{Datum}, default GRS80).

126 '''

127 return self._datum

128

129 def _inside2(self, raiser, lat, lon):

130 # default and variant 2: no datum Xform

131 if (raiser or (raiser is None and self._raiser)) and \

132 not _RD.isinside(lat, lon):

133 raise self._outsidError(lat, lon)

134 return lat, lon

135

136 _forwardXform2 = _inside2 # no datum Xform

137

138 def isinside(self, lat, lon, eps=0, B=False):

139 '''Is geodetic C{(B{lat}, B{lon})} inside the C{RD} region (C{bool})?

140

141 @kwarg eps: Over-/undersize the C{RD} region (C{degrees}).

142 @kwarg B: Use C{B{B}=True} for the C{RD-Bessel} regionB in case

143 C{(B{lat}, B{lon})} are Bessel1841 and not GRS80.

144 '''

145 return _RD.isinside(Lat(lat), Lon(lon), eps, B)

146

147 def _outsidError(self, *lat_lon):

148 # format an RDNAPError for C{lat_lon} outside C{RD} region

149 return RDNAPError('%r outside %s' % (lat_lon, self.region))

150

151 @property_RO

152 def _rdgrid(self): # PYCHOK no cover

153 raise notOverloaded(self)

154

155 def _rdlatlon2(self, lat, lon, lat0=None, lon0=None): # 2.3.2

156 # return the RD-corrected C{(lat, lon)}

157 if _RD.isinside(lat, lon):

158 c_f_N_f6 = _RD._c_f_N_f6(lat, lon)

159 lat_corr = _bilinear(self._rdgrid._lat_corr, *c_f_N_f6)

160 lon_corr = _bilinear(self._rdgrid._lon_corr, *c_f_N_f6)

161

162 if lat0 is lon0 is None: # reverse

163 lat += lat_corr

164 lon += lon_corr

165 else: # forward

166 lat = lat0 - lat_corr

167 lon = lon0 - lon_corr

168 return lat, lon # NAN, NAN?

169

170 def rdNAPh(self, lat, lon, raiser=False): # 2.5.1 and 3.5

171 '''Interpolate the C{NAPh} quasi-geoid-height I{within} the C{RD} region.

172

173 @arg lat: Latitude (C{degrees} geodetic).

174 @arg lon: Longitude (C{degrees} geodetic).

175 @kwarg raiser: If C{True} raise an L{RDNAPError} if B{C{lat}} or

176 B{C{lon}} is outside the C{RD} region (C{bool}),

177 otherwise don't and return C{NAN}.

178

179 @return: C{NAPh} (C{meter}) or C{NAN} if C{B{raiser} is False} and

180 B{C{lat}} or B{C{lon}} is outside the C{RD} region.

181 '''

182 return self._rdNAPh(Lat(lat), Lon(lon), raiser)

183

184 def _rdNAPh(self, lat, lon, raiser):

185 # return C{NAPh} at C{(lat, lon)} or C{NAN} if outside

186 if _RD.isinside(lat, lon): # eps=0

187 c_f_N_f6 = _RD._c_f_N_f6(lat, lon)

188 return _bilinear(self._rdgrid._NAP_h, *c_f_N_f6)

189 elif raiser:

190 raise self._outsidError(lat, lon)

191 return NAN # c0 2.5.1e+

192

193 def _rdNAPh_v(self, lat1, lon1, lat2, lon2):

194 # get C{NAPh} at geodetic C{lat1, lon1} for variant 1 or at the

195 # RD-corrected or inverse-projected C{lat2, lon2} for variant 2

196 if self.variant == 2:

197 lat1, lon1 = lat2, lon2

198 return self._rdNAPh(lat1, lon1, False)

199

200 @property_ROnce

201 def region(self):

202 '''Get the C{RD} region as L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}, all C{GRS80 (ETRS89) degrees}.

203 '''

204 return _RD.region

205

206 @property_ROnce

207 def regionB(self): # in .rd0._RD.regionB

208 '''Get the C{RD} region as L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}, all C{Bessel1841 (RD-Bessel) degrees}.

209 '''

210 S, W, N, E = r = self.region # Bounds4Tuple

211 _R = _RDNAPbase

212 _f = _R().forward3

213 nB = r.name.replace(_R.region.name, _R.regionB.name)

214 s, w, _ = _f(S, W)

215 n, e, _ = _f(N, E)

216 return r.classof(s, w, n, e, name=nB) # r.dup(latS=S, ...)

217

218 def reverse3(self, lat, lon, name='reverse3'):

219 '''Datum transform C{(B{lat}, B{lon})} from Bessel1841 (RD-Bessel) to GRS80 (ETRS98).

220

221 @return: A L{LatLon3Tuple}C{(lat, lon, datum)}.

222 '''

223 x, y, z = _geodetic2cartesian(lat, lon, A0.H0, A0.E0)

224 x, y, z = _RD._xRD2ETRS.transform(x, y, z)

225 lat, lon = _cartesian2geodetic(x, y, z, self._EETRS)

226 return LatLonDatum3Tuple(lat, lon, self.forwardDatum, name=name)

227

228 def _reverse(self, RDx, RDy, NAPh, toRD, raiser=None, name='reverse'):

229 '''(INTERNAL) Convert local C{(B{RDx}, B{RDy})} coordinates and

230 B{C{NAPh}} quasi-geoid-height to GRS80 (ETRS89) or Bessel1841

231 (RD-Bessel) geodetic C{lat}, C{lon} and C{height}.

232 '''

233 phiClamC = _oblique2spherical(RDx, RDy)

234 latlon = _spherical2ellipsoidal(*phiClamC)

235

236 latc, lonc = self._rdlatlon2(*latlon)

237 lat, lon, _ = self._reverseXform3(raiser, latc, lonc)

238 h = NAN if _isNAN(NAPh) else (NAPh +

239 self._rdNAPh_v(lat, lon, *latlon))

240

241 if toRD: # RD_Bessel

242 lat, lon, d = latc, lonc, A0.D0

243 else: # GRS80 (ETRS89)

244 d = self._EETRS

245 return RDNAP7Tuple(RDx, RDy, NAPh,

246 lat, lon, h, d, name=name)

247

248 @property_RO

249 def reverseDatum(self):

250 '''Get the I{default} C{reverse} datum (L{Datum}), GRS80 or Bessel1841.

251 '''

252 return {1: self._datum, # A0.D80

253 2: A0.D0}.get(self.variant)

254

255 def _reverseXform3(self, *raiser_lat_lon):

256 # datum transform C{(lat, lon)} from RD-Bessel to GRS80 (ETRS89)

257 # and raise an C{RDNAPError} if outside the C{RD} region

258 lat, lon = self._inside2(*raiser_lat_lon)

259 return self.reverse3(lat, lon)

260

261 def similarity(self, inverse=None): # PYCHOK no cover

262 raise notOverloaded(self, inverse=inverse) # PYCHOK None

263

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

265 '''Return this C{RDNAP20181v1} or C{-v2} instance as a string.

266

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

268

269 @return: This C{RDNAP2018v1} or C{-v2} (C{str}).

270 '''

271 return self.attrs('name', 'variant', 'forwardDatum', prec=prec) # _ellipsoid_, _name__

272

273 @property_RO

274 def variant(self): # PYCHOK no cover

275 raise notOverloaded(self)

276

277

278class RDNAP2018v1(_RDNAPbase):

279 '''Transformer implementing C{variant 1} of U{RD NAP 2018 v220627

280 <https://formulieren.kadaster.nl/aanvragen_rdnaptrans>}.

281

282 @note: Method L{RDNAP2018v1.reverse} returns B{GRS80 (ETRS89)}

283 geodetic lat- and longitudes.

284

285 @note: L{RDNAP2018v1} has B{not been formally validated} and is

286 B{not certified} to carry the trademark C{RDNAPTRANS(tm)}.

287 '''

288 if _FOR_DOCS:

289 __init__ = _RDNAPbase.__init__

290 forward = _RDNAPbase.forward

291 forward3 = _RDNAPbase.forward3

292 reverse3 = _RDNAPbase.reverse3

293

294 def _forwardXform2(self, raiser, lat, lon):

295 # datum transform C{(lat, lon)} from GRS80 (ETRS89) to RD-Bessel

296 # and raise an C{RDNAPError} if outside the C{RD} region

297 lat, lon, _ = self.forward3(lat, lon)

298 return self._inside2(raiser, lat, lon)

299

300 @property_ROnce

301 def _rdgrid(self):

302 try:

303 from pyrdnap import v1grid

304 except (AttributeError, ImportError, RDNAPError):

305 v1grid = _v_gridz_import(self.variant)

306 return v1grid

307

308 def reverse(self, RDx, RDy, NAPh=0, toRD=False, **raiser_name):

309 '''Convert a local C{(B{RDx}, B{RDy})} point and B{C{NAPh}} height to

310 B{GRS80 (ETRS89)} geodetic C{(lat, lon, height)}, by default.

311

312 @arg RDx: Local C{RD} X (C{meter}, conventionally).

313 @arg RDy: Local C{RD} Y (C{meter}, conventionally).

314 @kwarg NAPh: C{NAP} quasi-geoid-height (C{meter}, conventionally)

315 or C{NAN} to ignore C{NAPh} interpolation.

316 @kwarg toRD: Use C{B{toRD}=True} to return Bessel1841 (RD-Bessel)

317 lat- and longitudes instead of GRS80 (ETRS89) (C{bool}).

318 @kwarg raiser_name: Like the C{forward} method, C{B{raiser}=None}

319 (C{bool}) and optional C{B{name}='reverse'} (C{str}).

320

321 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}

322 with geodetic C{lat} and C{lon}, C{height} and C{datum}

323 B{GRS80 (ETRS89)} or C{Bessel1841 (RD-Bessel)}.

324 '''

325 return self._reverse(RDx, RDy, NAPh, toRD, **raiser_name)

326

327 def similarity(self, inverse=False):

328 '''Get the similarity transform (C{Similarity}).

329

330 @kwarg inverse: Use C{True} for the C{reverse} or C{False}

331 for the C{forward} transform (C{bool}).

332 '''

333 return _RD._xRD2ETRS if inverse else _RD._xETRS2RD

334

335 @property_ROnce

336 def variant(self):

337 '''Get this C{RDNAP2018}'s variant (C{int}).

338 '''

339 return 1

340

341

342class RDNAP2018v2(_RDNAPbase):

343 '''Transformer implementing C{variant 2} of U{RD NAP 2018 v220627

344 <https://formulieren.kadaster.nl/aanvragen_rdnaptrans>}.

345

346 @note: Method L{RDNAP2018v2.reverse} returns by default B{Bessel1841

347 (RD-Bessel)} and optionally GRS80 (ETRS89) geodetic lat- and

348 longitudes.

349

350 @note: L{RDNAP2018v2} has B{not been formally validated} and is

351 B{not certified} to carry the trademark C{RDNAPTRANS(tm)}.

352 '''

353 if _FOR_DOCS:

354 __init__ = _RDNAPbase.__init__

355 forward = _RDNAPbase.forward

356 forward3 = _RDNAPbase.forward3

357 reverse3 = _RDNAPbase.reverse3

358

359 @property_ROnce

360 def _rdgrid(self):

361 try:

362 from pyrdnap import v2grid

363 except (AttributeError, ImportError, RDNAPError):

364 v2grid = _v_gridz_import(self.variant)

365 return v2grid

366

367 def reverse(self, RDx, RDy, NAPh=0, toRD=True, **raiser_name):

368 '''Convert a local C{(B{RDx}, B{RDy})} point and B{C{NAPh}} height to

369 B{Bessel1841 (RD-Bessel)} geodetic C{(lat, lon, height)}, by default.

370

371 @arg RDx: Local C{RD} X (C{meter}, conventionally).

372 @arg RDy: Local C{RD} Y (C{meter}, conventionally).

373 @kwarg NAPh: C{NAP} quasi-geoid-height (C{meter}, conventionally)

374 or C{NAN} to ignore C{NAPh} interpolation.

375 @kwarg toRD: Use C{B{toRD}=False} to return GRS80 (ETRS89) lat- and

376 longitudes instead of Bessel1841 (RD-Bessel) (C{bool}).

377 @kwarg raiser_name: Like the C{forward} method, C{B{raiser}=None}

378 (C{bool}) and optional C{B{name}='reverse'} (C{str}).

379

380 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}

381 with geodetic C{lat} and C{lon}, C{height} and C{datum}

382 B{Bessel1841 (RD-Bessel)} or C{GRS80 (ETRS89)}.

383 '''

384 return self._reverse(RDx, RDy, NAPh, toRD, **raiser_name)

385

386 def similarity(self, *unused): # PYCHOK signature

387 '''Get the similarity transform, always C{None}.

388 '''

389 return None

390

391 @property_ROnce

392 def variant(self):

393 '''Get this C{RDNAP2018}'s variant (C{int}).

394 '''

395 return 2

396

397

398def _atan3(y, x, x0): # 2.2.3e and 3.1.1i

399 # equiv to math.atan2 iff x0 is y

400 if x > 0:

401 r = atan(y / x)

402 elif x < 0:

403 r = atan(y / x) + copysign(PI, x0)

404 else:

405 r = copysign(PI_2, x0) if x0 else _0_0

406 return r

407

408

409def _atan_exp(w): # 2.4.1c

410 return atan(exp(w)) * _2_0 - PI_2

411

412

413def _bilinear(v_grid, c_latI, f_latI, latN_f, # 2.3.1f and g

414 c_lonI, f_lonI, lonN_f):

415 # interpolate a lat_corr_, lon_corr_ or NAP_...

416 assert isinstance(v_grid, _V_grid), v_grid

417 ne = v_grid(c_latI, c_lonI)

418 nw = v_grid(c_latI, f_lonI)

419 se = v_grid(f_latI, c_lonI)

420 sw = v_grid(f_latI, f_lonI)

421 lonN_f1 = _1_0 - lonN_f # == 1 - (lonN - f_lonN)

422 return (ne * lonN_f + nw * lonN_f1) * latN_f + \

423 (se * lonN_f + sw * lonN_f1) * (_1_0 - latN_f)

424

425

426def _cartesian2geodetic(x, y, z, E): # 2.2.3 == EcefUPC.reverse?

427 # convert cartesian C{(x, y, z)} to C{E}-geodetic C{(lat, lon)}

428 r = hypot(x, y)

429 if r > _TOL_M:

430 a = E.a * E.e2

431 phi_ = atan(z / r) # atan2(z, r)

432 for _ in range(_TRIPS): # 4..6

433 s = sin(phi_)

434 s *= a / sqrt(_1_0 - s**2 * E.e2)

435 phi = atan((z + s) / r) # atan2(z + s, r)

436 if fabs(phi - phi_) < _TOL_R:

437 break

438 phi_ = phi

439 else:

440 phi = copysign(PI_2, z)

441 lam = _atan3(y, x, y)

442 return map1(degrees, phi, lam) # lat, lon

443

444

445def _ellipsoidal2spherical(lat, lon): # 2.4.1

446 # convert geodetic C{(lat, lon)} to spherical C{(𝛷, 𝛬)}

447 phiC = phi = Phid(lat)

448 if PI_2 > phi > -PI_2: # 2.4.1c

449 q = A0.log_tan(phi) - A0.log_e_2(phi)

450 w = A0.N0 * q + A0.M0 # 2.4.1b

451 phiC = _atan_exp(w)

452 lamC = (Lamd(lon) - A0.LAM0) * A0.N0 + A0.LAM0C # 2.4.1d

453 return phiC, lamC # -Capital 𝛷, 𝛬

454

455

456def _eq0(r, r0=_0_0):

457 return fabs(r - r0) < _TOL_R

458

459

460# def _eq0d(d, d0=_0_0):

461# return fabs(d - d0) < _TOL_D

462

463

464def _geodetic2cartesian(lat, lon, h, E): # 2.2.1

465 # convert C{E}-geodetic C{(lat, lon)} to cartesian C{(x, y, z)}

466 y, x = sincos2d(lon)

467 z, c = sincos2d(lat)

468 n = E.a / sqrt(_1_0 - z**2 * E.e2)

469 H = _isNAN0(h)

470 c *= n + H

471 x *= c

472 y *= c

473 z *= n * (_1_0 - E.e2) + H

474 return x, y, z

475

476

477def _ne0(r, r0=_0_0):

478 return fabs(r - r0) > _TOL_R

479

480

481# def _ne0d(d, d0=_0_0):

482# return fabs(d - d0) > _TOL_D

483

484

485def _oblique2spherical(x, y): # 3.1.1

486 # inverse oblique stereographic conformal projection from

487 # C{RD (x, y)} to spherical C{(𝛷, 𝛬)}, see C++ function

488 # sterea_e_inverse in U{Proj/src/projections/sterea.cpp

489 # <https://Proj.org/en/stable/operations/projections/sterea.html>}

490 x -= A0.X0

491 y -= A0.Y0

492 r = hypot(x, y)

493 if r > _TOL_M: # x and y

494 s0, c0 = A0.sincos2PHI0C

495 sp, cp = sincos2(atan(r / A0.RK2) * _2_0) # psi atan2(r, A0.RK2)

496 ca = sp * y / r

497 xN = cp * c0 - ca * s0

498 yN = sp * x / r

499 zN = cp * s0 + ca * c0

500 phiC = asin(zN)

501 else:

502 _, xN = A0.sincos2PHI0C

503 yN = _0_0

504 phiC = A0.PHI0C # asin(sin(PHI0C))

505 lamC = _atan3(yN, xN, x) + A0.LAM0C

506 return phiC, lamC # -Capital 𝛷, 𝛬

507

508

509def _spherical2ellipsoidal(phiC, lamC): # 3.1.2

510 # inverse Gauss conformal projection from

511 # spherical C{(𝛷, 𝛬)} to geodetic C{(lat, lon)}

512 phi = phiC

513 if PI_2 > phi > -PI_2:

514 q = (A0.log_tan(phi) - A0.M0) / A0.N0

515# w = A0.log_tan(phi)

516 for _ in range(_TRIPS): # 3..6

517 phi_ = phi

518 phi = _atan_exp(A0.log_e_2(phi) + q)

519 if fabs(phi - phi_) < _TOL_R:

520 break

521 lam = (lamC - A0.LAM0C) / A0.N0 + A0.LAM0

522 lam += floor((PI - lam) / PI2) * PI2

523 return map1(degrees, phi, lam) # lat, lon

524

525

526def _spherical2oblique(phiC, lamC): # 2.4.2

527 # oblique stereographic conformal projection

528 # from spherical C{(𝛷, 𝛬)} to C{RD (x, y)}

529 x = A0.X0 # 2.4.2g

530 y = A0.Y0 # 2.4.2h

531 a = phiC - A0.PHI0C # 𝛷 - 𝛷0

532 b = lamC - A0.LAM0C # 𝛬 - 𝛬0

533 if (_ne0(a) or _ne0(b)) and (_ne0(phiC, -A0.PHI0C) or

534 _ne0(lamC, -A0.LAM0C + PI)):

535 s0, c0 = A0.sincos2PHI0C # sin(𝛷0), cos(𝛷0)

536 s, c = sincos2(phiC) # sin(𝛷), cos(𝛷)

537 sp_22 = sin(a * _0_5)**2 + \

538 sin(b * _0_5)**2 * c * c0 # sin(𝜓/2)**2

539 if EPS0 < sp_22 < EPS1:

540 # r = 2kR * tan(𝜓/2)

541 # q = r / (sin(𝜓/2) * cos(𝜓/2) * 2)

542 # = 2kR * sin(𝜓/2) / (sin(𝜓/2) * cos(𝜓/2)**2 * 2)

543 # = 2kR / (cos(𝜓/2)**2 * 2)

544 # = 2kR / ((1 - sin(𝜓/2)**2) * 2)

545 # = 2kR / (2 - sin(𝜓/2)**2 * 2)

546 t = sp_22 * _2_0 # 0 < t < 2

547 q = A0.RK2 / (_2_0 - t)

548 x += q * (c * sin(b))

549 y += q * (s - s0 + s0 * t) / c0

550 elif _eq0(a) and _eq0(b):

551 pass

552 else: # if _eq0(phiC, -A0.PHI0C) and _eq0(lamC, A0.LAM0C - PI):

553 x = y = NAN

554# else:

555# raise RDNAPError(str((phiC, lamC)))

556 return x, y

557

558

559__all__ += _ALL_DOCS(_RDNAPbase)

560__all__ += _ALL_OTHER(RDNAP2018v1, RDNAP2018v2, RDNAPError,

561 Datum, Ellipsoid, LatLonDatum3Tuple) # passed along from PyGeodesy

562

563# **) MIT License

564#

566#

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

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

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

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

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

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

573#

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

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

576#

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

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

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

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

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

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

583# OTHER DEALINGS IN THE SOFTWARE.

Coverage for pyrdnap / rdnap2018.py: 93%

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