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}}.

13@note: L{RDNAP2018v1}, L{RDNAP2018v2}, C{PyRDNAP} and C{pyrdnap} have B{not been formally validated}

14 and are 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)

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

26 Datum, Ellipsoid, LatLonDatum3Tuple, # datums, ellipsoids

27 Property_RO, 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__ = '26.06.09'

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) # pseudo

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

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 _forwardXform2(self, *args): # PYCHOK no cover

130 return self._notOverloaded(*args)

131

132 def _inside2(self, raiser, lat, lon, **as89):

133 # if RD-Bessel C{(lat, lon)} is not inside C{RD} region

134 # raise an error if C{raiser} or self.raiser is True

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

136 not _RD.isinside(lat, lon, **as89):

137 raise self._outsidError(lat, lon)

138 return lat, lon

139

140 def isinside(self, lat, lon, as89=False, eps=0):

141 '''Is geodetic C{(B{lat}, B{lon})} inside the C{RD} region[89] (C{bool})?

142

143 @kwarg as89: Use C{B{as89}=True} for C{RD} region89 and in case

144 C{(B{lat}, B{lon})} are ETRS89 (GRS80), not Bessel1841.

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

146 '''

147 return _RD.isinside(Lat(lat), Lon(lon), as89, eps)

148

149 def _outsidError(self, *lat_lon):

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

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

152

153 @property_RO

154 def _rdgrid(self): # PYCHOK no cover

155 return self._notOverloaded()

156

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

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

159 if _RD.isinside(lat, lon):

160 c_f_N_f6 = _RD._c_f_N_f6(lat, lon)

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

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

163

164 if lat0 is lon0 is None: # reverse

165 lat += lat_corr

166 lon += lon_corr

167 else: # forward

168 lat = lat0 - lat_corr

169 lon = lon0 - lon_corr

170 return lat, lon # NAN, NAN?

171

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

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

174

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

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

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

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

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

180

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

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

183 '''

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

185

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

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

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

189 c_f_N_f6 = _RD._c_f_N_f6(lat, lon)

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

191 elif raiser:

192 raise self._outsidError(lat, lon)

193 return NAN # c0 2.5.1e+

194

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

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

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

198 if self.variant == 2:

199 lat1, lon1 = lat2, lon2

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

201

202 @property_ROnce

203 def region(self):

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

205 '''

206 return _RD.region

207

208 @Property_RO

209 def region89(self): # in .rd0._RD.region89

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

211 '''

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

213 _R = _RDNAPbase

214 _r = _R().reverse3

215 nB = r.name.replace(_R.region.name, _R.region89.name)

216 s, w, _ = _r(S, W)

217 n, e, _ = _r(N, E)

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

219

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

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

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

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

224 '''

225 phiClamC = _oblique2spherical(RDx, RDy)

226 latlon = _spherical2ellipsoidal(*phiClamC)

227

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

229 lat, lon, d = self._reverseXform3(raiser, latc, lonc)

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

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

232

233 if (asRD if toRD is None else toRD): # backward comp'y toRD

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

235 return RDNAP7Tuple(RDx, RDy, NAPh,

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

237

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

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

240

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

242 '''

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

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

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

246 return LatLonDatum3Tuple(lat, lon, self.forwardDatum, 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, # self.forwardDatum

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 return self._notOverloaded(inverse=inverse)

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 return self._notOverloaded()

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

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

284 '''

285 if _FOR_DOCS:

286 __init__ = _RDNAPbase.__init__

287 forward = _RDNAPbase.forward

288 forward3 = _RDNAPbase.forward3

289 reverse3 = _RDNAPbase.reverse3

290

291 def _forwardXform2(self, raiser, *lat_lon): # PYCHOK signature

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

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

294 lat, lon, _ = self.forward3(*lat_lon)

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

296

297 @property_ROnce

298 def _rdgrid(self):

299 try:

300 from pyrdnap import v1grid

301 except (AttributeError, ImportError, RDNAPError):

302 v1grid = _v_gridz_import(self.variant)

303 return v1grid

304

305 def reverse(self, RDx, RDy, NAPh=0, asRD=False, **raiser_name):

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

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

308

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

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

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

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

313 @kwarg asRD: Use C{B{asRD}=True} to return Bessel1841 (RD-Bessel) lat-

314 and longitudes instead of GRS80 (ETRS89) (C{bool}).

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

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

317

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

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

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

321 '''

322 return self._reverse(RDx, RDy, NAPh, asRD, **raiser_name)

323

324 def similarity(self, inverse=False):

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

326

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

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

329 '''

330 return _RD._xRD2ETRS if inverse else _RD._xETRS2RD

331

332 @property_ROnce

333 def variant(self):

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

335 '''

336 return 1

337

338

339class RDNAP2018v2(_RDNAPbase):

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

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

342

343 @note: Method L{RDNAP2018v2.reverse} returns by default GRS80

344 (ETRS89) geodetic lat- and longitudes and datum.

345

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

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

348 '''

349 if _FOR_DOCS:

350 __init__ = _RDNAPbase.__init__

351 forward = _RDNAPbase.forward

352 forward3 = _RDNAPbase.forward3

353 reverse3 = _RDNAPbase.reverse3

354

355 def _forwardXform2(self, *raiser_lat_lon):

356 # no datum transform C{(lat, lon)} to RD-Bessel, but

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

358 return self._inside2(*raiser_lat_lon) # as89=True

359

360 @property_ROnce

361 def _rdgrid(self):

362 try:

363 from pyrdnap import v2grid

364 except (AttributeError, ImportError, RDNAPError):

365 v2grid = _v_gridz_import(self.variant)

366 return v2grid

367

368 def reverse(self, RDx, RDy, NAPh=0, asRD=True, **raiser_name):

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

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

371

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

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

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

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

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

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

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

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

380

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

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

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

384 '''

385 return self._reverse(RDx, RDy, NAPh, asRD, **raiser_name)

386

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

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

389 '''

390 return None

391

392 @property_ROnce

393 def variant(self):

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

395 '''

396 return 2

397

398

399def _atan3(y, x, x0): # 2.2.3e and 3.1.1i

400 # equiv to math.atan2 iff x0 is y

401 if x > 0:

402 r = atan(y / x)

403 elif x < 0:

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

405 else:

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

407 return r

408

409

410def _atan_exp(w): # 2.4.1c

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

412

413

414def _bilinear(v_grid, c_latI, f_latI, latN_f, # 2.3.1f and g

415 c_lonI, f_lonI, lonN_f):

416 # interpolate a lat_corr_, lon_corr_ or NAP_h...

417 assert isinstance(v_grid, _V_grid), v_grid

418 ne = v_grid(c_latI, c_lonI)

419 nw = v_grid(c_latI, f_lonI)

420 se = v_grid(f_latI, c_lonI)

421 sw = v_grid(f_latI, f_lonI)

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

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

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

425

426

427def _cartesian2geodetic(x, y, z, E): # 2.2.3 == EcefUPC.reverse?

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

429 r = hypot(x, y)

430 if r > _TOL_M:

431 a = E.a * E.e2

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

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

434 s = sin(phi_)

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

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

437 if fabs(phi - phi_) < _TOL_R:

438 break

439 phi_ = phi

440 else:

441 phi = copysign(PI_2, z)

442 lam = _atan3(y, x, y)

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

444

445

446def _ellipsoidal2spherical(lat, lon): # 2.4.1

447 # convert RD-Bessel C{(lat, lon)} to spherical C{(𝛷, 𝛬)}

448 phiC = phi = Phid(lat)

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

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

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

452 phiC = _atan_exp(w)

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

454 return phiC, lamC # -Capital 𝛷, 𝛬

455

456

457def _eq0(r, r0=_0_0):

458 return fabs(r - r0) < _TOL_R

459

460

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

462# return fabs(d - d0) < _TOL_D

463

464

465def _geodetic2cartesian(lat, lon, h, E): # 2.2.1

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

467 y, x = sincos2d(lon)

468 z, c = sincos2d(lat)

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

470 H = _isNAN0(h)

471 c *= n + H

472 x *= c

473 y *= c

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

475 return x, y, z

476

477

478def _ne0(r, r0=_0_0):

479 return fabs(r - r0) > _TOL_R

480

481

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

483# return fabs(d - d0) > _TOL_D

484

485

486def _oblique2spherical(x, y): # 3.1.1

487 # inverse oblique stereographic conformal projection from

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

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

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

491 x -= A0.X0

492 y -= A0.Y0

493 r = hypot(x, y)

494 if r > _TOL_M: # x and y

495 s0, c0 = A0.sincos2PHI0C

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

497 ca = sp * y / r

498 xN = cp * c0 - ca * s0

499 yN = sp * x / r

500 zN = cp * s0 + ca * c0

501 phiC = asin(zN)

502 else:

503 _, xN = A0.sincos2PHI0C

504 yN = _0_0

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

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

507 return phiC, lamC # -Capital 𝛷, 𝛬

508

509

510def _spherical2ellipsoidal(phiC, lamC): # 3.1.2

511 # inverse Gauss conformal projection from

512 # spherical C{(𝛷, 𝛬)} to RD-Bessel C{(lat, lon)}

513 phi = phiC

514 if PI_2 > phi > -PI_2:

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

516# w = A0.log_tan(phi)

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

518 phi_ = phi

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

520 if fabs(phi - phi_) < _TOL_R:

521 break

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

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

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

525

526

527def _spherical2oblique(phiC, lamC): # 2.4.2

528 # oblique stereographic conformal projection

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

530 x = A0.X0 # 2.4.2g

531 y = A0.Y0 # 2.4.2h

532 a = phiC - A0.PHI0C # 𝛷 - 𝛷0

533 b = lamC - A0.LAM0C # 𝛬 - 𝛬0

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

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

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

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

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

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

540 if EPS0 < sp_22 < EPS1:

541 # r = 2kR * tan(𝜓/2)

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

543 # = 2kR * sin(𝜓/2) / (sin(𝜓/2) * cos(𝜓/2)**2 * 2)

544 # = 2kR / (cos(𝜓/2)**2 * 2)

545 # = 2kR / ((1 - sin(𝜓/2)**2) * 2)

546 # = 2kR / (2 - sin(𝜓/2)**2 * 2)

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

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

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

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

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

552 pass

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

554 x = y = NAN

555# else:

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

557 return x, y

558

559

560__all__ += _ALL_DOCS(_RDNAPbase)

561__all__ += _ALL_OTHER(RDNAP2018v1, RDNAP2018v2, RDNAPError,

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

563

564# **) MIT License

565#

567#

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

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

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

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

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

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

574#

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

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

577#

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

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

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

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

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

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

584# OTHER DEALINGS IN THE SOFTWARE.

Coverage for pyrdnap / rdnap2018.py: 93%

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