Coverage for pygeodesy/points.py: 91%

618 statements  

« prev     ^ index     » next       coverage.py v7.2.2, created at 2023-06-07 08:37 -0400

1 

2# -*- coding: utf-8 -*- 

3 

4u'''Utilities for point lists, tuples, etc. 

5 

6Functions to handle collections and sequences of C{LatLon} points 

7specified as 2-d U{NumPy<https://www.NumPy.org>}, C{arrays} or tuples 

8as C{LatLon} or as C{pseudo-x/-y} pairs. 

9 

10C{NumPy} arrays are assumed to contain rows of points with a lat-, a 

11longitude -and possibly other- values in different columns. While 

12iterating over the array rows, create an instance of a given C{LatLon} 

13class "on-the-fly" for each row with the row's lat- and longitude. 

14 

15The original C{NumPy} array is read-accessed only and never duplicated, 

16except to return a I{subset} of the original array. 

17 

18For example, to process a C{NumPy} array, wrap the array by instantiating 

19class L{Numpy2LatLon} and specifying the column index for the lat- and 

20longitude in each row. Then, pass the L{Numpy2LatLon} instance to any 

21L{pygeodesy} function or method accepting a I{points} argument. 

22 

23Similarly, class L{Tuple2LatLon} is used to instantiate a C{LatLon} from 

24each 2+tuple in a sequence of such 2+tuples using the C{ilat} lat- and 

25C{ilon} longitude index in each 2+tuple. 

26''' 

27 

28from pygeodesy.basics import isclass, isint, isscalar, issequence, \ 

29 issubclassof, _Sequence, _xcopy, _xdup, \ 

30 _xinstanceof 

31from pygeodesy.constants import EPS, EPS1, PI_2, R_M, isnear0, isnear1, \ 

32 _umod_360, _0_0, _0_5, _1_0, _2_0, _6_0, \ 

33 _90_0, _N_90_0, _180_0, _360_0 

34# from pygeodesy.datums import _spherical_datum # from .formy 

35from pygeodesy.dms import F_D, latDMS, lonDMS, parseDMS, S_DEG, S_DMS, \ 

36 S_MIN, S_SEC, S_SEP 

37from pygeodesy.errors import CrossError, crosserrors, _IndexError, \ 

38 _IsnotError, _TypeError, _ValueError, \ 

39 _xattr, _xkwds, _xkwds_pop 

40from pygeodesy.fmath import favg, fdot, hypot, Fsum, fsum 

41# from pygeodesy.fsums import Fsum, fsum # from .fmath 

42from pygeodesy.formy import _bearingTo2, equirectangular_, _isequalTo, \ 

43 isnormal, latlon2n_xyz, normal, _spherical_datum 

44from pygeodesy.interns import NN, _colinear_, _COMMASPACE_, _composite_, \ 

45 _DEQUALSPACED_, _ELLIPSIS_, _EW_, _immutable_, \ 

46 _lat_, _lon_, _LatLon_, _near_, _no_, _not_, \ 

47 _NS_, _point_, _SPACE_, _UNDER_, _valid_ 

48from pygeodesy.iters import LatLon2PsxyIter, PointsIter, points2 

49from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

50from pygeodesy.named import classname, nameof, notImplemented, notOverloaded, \ 

51 _NamedTuple, _xnamed, _xother3, _xotherError 

52from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, \ 

53 LatLon2Tuple, NearestOn3Tuple, \ 

54 NearestOn5Tuple, PhiLam2Tuple, \ 

55 Point3Tuple, Vector3Tuple, Vector4Tuple 

56from pygeodesy.nvectorBase import NvectorBase, _N_vector_ 

57from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

58 property_doc_, property_RO, _update_all 

59from pygeodesy.streprs import Fmt, hstr, instr, pairs 

60from pygeodesy.units import Number_, Radius, Scalar, Scalar_ 

61from pygeodesy.utily import atan2b, degrees90, degrees180, degrees2m, \ 

62 unroll180, _unrollon, unrollPI, _Wrap, wrap180 

63 

64from math import cos, fabs, fmod, radians, sin 

65 

66__all__ = _ALL_LAZY.points 

67__version__ = '23.05.26' 

68 

69_ilat_ = 'ilat' 

70_ilon_ = 'ilon' 

71_ncols_ = 'ncols' 

72_nrows_ = 'nrows' 

73 

74 

75class LatLon_(object): # XXX in heights._HeightBase.height 

76 '''Low-overhead C{LatLon} class for L{Numpy2LatLon} and L{Tuple2LatLon}. 

77 ''' 

78 # __slots__ efficiency is voided if the __slots__ class attribute 

79 # is used in a subclass of a class with the traditional __dict__, 

80 # see <https://docs.Python.org/2/reference/datamodel.html#slots> 

81 # and __slots__ must be repeated in sub-classes, see "Problems 

82 # with __slots__" in Luciano Ramalho, "Fluent Python", page 

83 # 276+, O'Reilly, 2016, also at <https://Books.Google.ie/ 

84 # books?id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg= 

85 # PT364#v=onepage&q=“Problems%20with%20__slots__”&f=false> 

86 # 

87 # __slots__ = (_lat_, _lon_, _height_, _datum_, _name_) 

88 # Property_RO = property_RO # no __dict__ with __slots__! 

89 # 

90 # However, sys.getsizeof(LatLon_(1, 2)) is 72-88 with __slots__ 

91 # but only 48-56 bytes without in Python 2.7.18+ and Python 3+. 

92 

93 def __init__(self, latlonh, lon=None, name=NN, height=0, 

94 datum=None, wrap=False): 

95 '''Creat a new, mininal, low-overhead L{LatLon_} instance. 

96 

97 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or 

98 a previous C{LatLon} instance provided C{B{lon}=None}. 

99 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or 

100 C(None), indicating B{C{latlonh}} is a C{LatLon}. 

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

102 @kwarg height: Optional height (C{meter}, conventionally). 

103 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, 

104 L{a_f2Tuple} or I{scalar} radius) or C{None}. 

105 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} 

106 (C{bool}). 

107 

108 @raise TypeError: Invalid B{C{datum}} or B{C{latlonh}} not a C{LatLon}. 

109 

110 @note: The lat- and longitude are taken as-given, 

111 un-clipped and un-validated . 

112 ''' 

113 if lon is None: 

114 try: 

115 ll = latlonh.lat, latlonh.lon 

116 height = _xattr(latlonh, height=height) 

117 except AttributeError: 

118 raise _IsnotError(_LatLon_, latlonh=latlonh) 

119 if wrap: 

120 ll = _Wrap.latlon(*ll) 

121 elif wrap: 

122 ll = _Wrap.latlonDMS2(latlonh, lon) 

123 else: # must be latNS, lonEW 

124 ll = parseDMS(latlonh, suffix=_NS_), parseDMS(lon, suffix=_EW_) 

125 

126 self.lat, self.lon = ll 

127 self.name = str(name) if name else NN 

128 self.height = height 

129 self.datum = datum if datum is None else \ 

130 _spherical_datum(datum, name=self.name) 

131 

132 def __eq__(self, other): 

133 return isinstance(other, LatLon_) and \ 

134 other.lat == self.lat and \ 

135 other.lon == self.lon 

136 

137 def __ne__(self, other): 

138 return not self.__eq__(other) 

139 

140 def __repr__(self): 

141 return self.toRepr() 

142 

143 def __str__(self): 

144 return self.toStr() 

145 

146 def classof(self, *args, **kwds): 

147 '''Instantiate this very class. 

148 

149 @arg args: Optional, positional arguments. 

150 @kwarg kwds: Optional, keyword arguments. 

151 

152 @return: New instance (C{self.__class__}). 

153 ''' 

154 return _xnamed(self.__class__(*args, **kwds), self.name) 

155 

156 def copy(self, deep=False): 

157 '''Make a shallow or deep copy of this instance. 

158 

159 @kwarg deep: If C{True} make a deep, otherwise a 

160 shallow copy (C{bool}). 

161 

162 @return: The copy (C{This} (sub-)class). 

163 ''' 

164 return _xcopy(self, deep=deep) 

165 

166 def dup(self, **items): 

167 '''Duplicate this instance, replacing some items. 

168 

169 @kwarg items: Attributes to be changed (C{any}). 

170 

171 @return: The duplicate (C{This} (sub-)class). 

172 

173 @raise AttributeError: Some B{C{items}} invalid. 

174 ''' 

175 d = _xdup(self, **items) 

176 if items: 

177 _update_all(d) 

178 return d 

179 

180 def heightStr(self, prec=-2): 

181 '''Return a string for the height B{C{height}}. 

182 

183 @kwarg prec: Number of (decimal) digits, unstripped (C{int}). 

184 

185 @see: Function L{pygeodesy.hstr}. 

186 ''' 

187 return hstr(self.height, prec=prec) 

188 

189 def intermediateTo(self, other, fraction, height=None, wrap=False): 

190 '''Locate the point at a given fraction between (or along) this 

191 and an other point. 

192 

193 @arg other: The other point (C{LatLon}). 

194 @arg fraction: Fraction between both points (C{float}, 

195 0.0 for this and 1.0 for the other point). 

196 @kwarg height: Optional height (C{meter}), overriding the 

197 intermediate height. 

198 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

199 the B{C{other}} point (C{bool}). 

200 

201 @return: Intermediate point (this C{LatLon}). 

202 

203 @raise TypeError: Incompatible B{C{other}} C{type}. 

204 ''' 

205 f = Scalar(fraction=fraction) 

206 if isnear0(f): 

207 r = self 

208 elif isnear1(f) and not wrap: 

209 r = self.others(other) 

210 else: 

211 p = self.others(other) 

212 h = favg(self.height, p.height, f=f) if height is None else height 

213 _, lat, lon = _Wrap.latlon3(self.lon, p.lat, p.lon, wrap=wrap) 

214 r = self.classof(favg(self.lat, lat, f=f), 

215 favg(self.lon, lon, f=f), 

216 height=h, datum=self.datum, 

217 name=self.intermediateTo.__name__) 

218 return r 

219 

220 @Property_RO # PYCHOK no cover 

221 def isEllipsoidal(self): 

222 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown). 

223 ''' 

224 return self.datum.isEllipsoidal if self.datum else None 

225 

226 @Property_RO # PYCHOK no cover 

227 def isEllipsoidalLatLon(self): 

228 '''Get C{LatLon} base. 

229 ''' 

230 return False 

231 

232 def isequalTo(self, other, eps=None): 

233 '''Compare this point with an other point, I{ignoring} height. 

234 

235 @arg other: The other point (C{LatLon}). 

236 @kwarg eps: Tolerance for equality (C{degrees}). 

237 

238 @return: C{True} if both points are identical, 

239 I{ignoring} height, C{False} otherwise. 

240 

241 @raise UnitError: Invalid B{C{eps}}. 

242 ''' 

243 return _isequalTo(self, self.others(other), eps=eps) 

244 

245 @Property_RO 

246 def isnormal(self): 

247 '''Return C{True} if this point is normal (C{bool}), 

248 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}. 

249 

250 @see: Methods L{normal}, L{toNormal} and functions 

251 L{pygeodesy.isnormal} and L{pygeodesy.normal}. 

252 ''' 

253 return isnormal(self.lat, self.lon, eps=0) 

254 

255 @Property_RO 

256 def isSpherical(self): # PYCHOK no cover 

257 '''Check whether this point is spherical (C{bool} or C{None} if unknown). 

258 ''' 

259 return self.datum.isSpherical if self.datum else None 

260 

261 @Property_RO 

262 def lam(self): 

263 '''Get the longitude (B{C{radians}}). 

264 ''' 

265 return radians(self.lon) 

266 

267 @Property 

268 def latlon(self): 

269 '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). 

270 ''' 

271 return LatLon2Tuple(self.lat, self.lon, name=self.name) 

272 

273 @latlon.setter # PYCHOK setter! 

274 def latlon(self, latlon): 

275 '''Set the lat- and longitude. 

276 

277 @arg latlon: New lat- and longitude in C{degrees} (C{2-tuple} or {-list}). 

278 ''' 

279 if self.latlon != latlon[:2]: 

280 _update_all(self) 

281 self.lat, self.lon = latlon[:2] 

282 

283 @Property_RO 

284 def latlonheight(self): 

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

286 ''' 

287 return self.latlon.to3Tuple(self.height) 

288 

289 @Property_RO 

290 def _N_vector(self): 

291 '''(INTERNAL) Get the minimal, low-overhead (C{nvectorBase._N_vector_}) 

292 ''' 

293 return _N_vector_(*latlon2n_xyz(self.lat, self.lon), 

294 h=self.height, name=self.name) 

295 

296 def others(self, *other, **name_other_up): # see .named._namedBase.others 

297 '''Refined class comparison. 

298 

299 @arg other: The other instance (any C{type}). 

300 @kwarg name_other_up: Overriding C{name=other} and C{up=1} 

301 keyword arguments. 

302 

303 @return: The B{C{other}} if compatible. 

304 

305 @raise TypeError: Incompatible B{C{other}} C{type}. 

306 ''' 

307 other, name, up = _xother3(self, other, **name_other_up) 

308 if isinstance(other, self.__class__) or (hasattr(other, _lat_) 

309 and hasattr(other, _lon_)): 

310 return other 

311 raise _xotherError(self, other, name=name, up=up + 1) 

312 

313 def normal(self): 

314 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and 

315 C{abs(lon) <= 180}. 

316 

317 @return: C{True} if this point was I{normal}, C{False} if it 

318 wasn't (but is now). 

319 

320 @see: Property L{isnormal} and method L{toNormal}. 

321 ''' 

322 n = self.isnormal 

323 if not n: 

324 self.latlon = normal(*self.latlon) 

325 return n 

326 

327 @Property_RO 

328 def phi(self): 

329 '''Get the latitude (B{C{radians}}). 

330 ''' 

331 return radians(self.lat) 

332 

333 @Property_RO 

334 def philam(self): 

335 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}). 

336 ''' 

337 return PhiLam2Tuple(self.phi, self.lam, name=self.name) 

338 

339 @Property_RO 

340 def philamheight(self): 

341 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

342 ''' 

343 return self.philam.to3Tuple(self.height) 

344 

345 @deprecated_method 

346 def points(self, points, closed=False, base=None): # PYCHOK no cover 

347 '''DEPRECATED, use method C{points2}.''' 

348 return points2(points, closed=closed, base=base) 

349 

350 def points2(self, points, closed=False, base=None): 

351 '''Check a path or polygon represented by points. 

352 

353 @arg points: The path or polygon points (C{LatLon}[]) 

354 @kwarg closed: Optionally, consider the polygon closed, 

355 ignoring any duplicate or closing final 

356 B{C{points}} (C{bool}). 

357 @kwarg base: Optionally, check all B{C{points}} against 

358 this base class, if C{None} don't check. 

359 

360 @return: A L{Points2Tuple}C{(number, points)} with the number 

361 of points and the points C{list} or C{tuple}. 

362 

363 @raise PointsError: Insufficient number of B{C{points}}. 

364 

365 @raise TypeError: Some B{C{points}} are not B{C{base}}. 

366 ''' 

367 return points2(points, closed=closed, base=base) 

368 

369 def PointsIter(self, points, loop=0, dedup=False): 

370 '''Return a points iterator. 

371 

372 @arg points: The path or polygon points (C{LatLon}[]) 

373 @kwarg loop: Number of loop-back points (non-negative C{int}). 

374 @kwarg dedup: Skip duplicate points (C{bool}). 

375 

376 @return: A new C{PointsIter} iterator. 

377 

378 @raise PointsError: Insufficient number of B{C{points}}. 

379 ''' 

380 return PointsIter(points, base=self, loop=loop, dedup=dedup) 

381 

382 @deprecated_method 

383 def to2ab(self): # PYCHOK no cover 

384 '''DEPRECATED, use property L{philam}.''' 

385 return self.philam 

386 

387 def toNormal(self, deep=False, name=NN): 

388 '''Get a copy of this point normalized to C{abs(lat) <= 90} 

389 and C{abs(lon) <= 180}. 

390 

391 @kwarg deep: If C{True} make a deep, otherwise a 

392 shallow copy (C{bool}). 

393 @kwarg name: Optional name of the copy (C{str}). 

394 

395 @return: A copy of this point, I{normalized} and 

396 optionally renamed (C{LatLon}). 

397 

398 @see: Property L{isnormal}, method L{normal} and 

399 function L{pygeodesy.normal}. 

400 ''' 

401 ll = self.copy(deep=deep) 

402 _ = ll.normal() 

403 if name: 

404 ll.name = str(name) 

405 return ll 

406 

407 def toNvector(self, h=None, Nvector=NvectorBase, **Nvector_kwds): 

408 '''Convert this point to C{n-vector} (normal to the earth's 

409 surface) components, I{including height}. 

410 

411 @kwarg h: Optional height, overriding this point's height 

412 (C{meter}). 

413 @kwarg Nvector: Optional class to return the C{n-vector} 

414 components (C{Nvector}) or C{None}. 

415 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword 

416 arguments, ignored if C{B{Nvector} is None}. 

417 

418 @return: The C{n-vector} components B{C{Nvector}} or if 

419 B{C{Nvector}} is C{None}, a L{Vector4Tuple}C{(x, 

420 y, z, h)}. 

421 

422 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}} 

423 argument. 

424 ''' 

425 x, y, z = latlon2n_xyz(self.lat, self.lon) 

426 r = Vector4Tuple(x, y, z, self.height if h is None else h) 

427 if Nvector is not None: 

428 r = Nvector(x, y, z, **_xkwds(Nvector_kwds, h=r.h, ll=self)) 

429 return _xnamed(r, self.name) 

430 

431 def toRepr(self, **kwds): 

432 '''This L{LatLon_} as a string "class(<degrees>, ...)". 

433 

434 @kwarg kwds: Optional, keyword arguments. 

435 

436 @return: Class instance (C{str}). 

437 ''' 

438 _ = _xkwds_pop(kwds, std=None) # PYCHOK std unused 

439 return Fmt.PAREN(classname(self), self.toStr(**kwds)) 

440 

441 def toStr(self, form=F_D, joined=_COMMASPACE_, **prec_sep_s_D_M_S_kwds): 

442 '''Convert this point to a "lat, lon[, height][, name][, ...]" string, 

443 formatted in the given C{B{form}at}. 

444 

445 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see 

446 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. 

447 @kwarg joined: Separator to join the lat-, longitude, heigth, name 

448 and other strings (C{str} or C{None} or C{NN} for 

449 non-joined). 

450 @kwarg prec_sep_s_D_M_S_kwds: Optional C{B{prec}ision}, C{B{sep}arator}, 

451 B{C{s_D}}, B{C{s_M}}, B{C{s_S}}, B{C{s_DMS}} and possibly 

452 other keyword arguments, see functions L{pygeodesy.latDMS} 

453 or L{pygeodesy.lonDMS}. 

454 

455 @return: This point in the specified C{B{form}at}, etc. (C{str} or 

456 a 2- or 3+tuple C{(lat_str, lon_str[, height_str][, name_str][, 

457 ...])} if C{B{joined}=NN} or C{B{joined}=None} and with the 

458 C{height_str} and C{name_str} only included if non-zero 

459 respectively non-empty). 

460 

461 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more 

462 details about keyword arguments C{B{form}at}, C{B{prec}ision}, 

463 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. 

464 ''' 

465 def _t3(prec=None, sep=S_SEP, s_D=S_DEG, s_M=S_MIN, s_S=S_SEC, s_DMS=S_DMS, **kwds): 

466 return dict(prec=prec, sep=sep, s_D=s_D, s_M=s_M, s_S=s_S, s_DMS=s_DMS), kwds, prec 

467 

468 prec_sep_s_D_M_S, kwds, prec = _t3(**prec_sep_s_D_M_S_kwds) 

469 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), 

470 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) 

471 if self.height: 

472 t += (self.heightStr(),) 

473 if self.name: 

474 t += (repr(self.name),) 

475 if kwds: 

476 t += pairs(kwds) if prec is None else pairs(kwds, prec=prec) 

477 return joined.join(t) if joined else t 

478 

479 @deprecated_method 

480 def toStr2(self, **kwds): # PYCHOK no cover 

481 '''DEPRECATED, used method L{toRepr}.''' 

482 return self.toRepr(**kwds) 

483 

484 

485def _isLatLon(inst): 

486 '''(INTERNAL) Check a C{LatLon} or C{LatLon_} instance. 

487 ''' 

488 return isinstance(inst, (LatLon_, _MODS.latlonBase.LatLonBase)) 

489 

490 

491def _isLatLon_(LL): 

492 '''(INTERNAL) Check a (sub-)class of C{LatLon_}. 

493 ''' 

494 return issubclassof(LL, LatLon_) or (isclass(LL) and 

495 all(hasattr(LL, a) for a in _ALL_ATTRS_)) 

496 

497 

498# get all pseudo-slots for class C{LatLon_} 

499_ALL_ATTRS_ = tuple(LatLon_(0, 0).__dict__.keys()) 

500 

501 

502class _Basequence(_Sequence): # immutable, on purpose 

503 '''(INTERNAL) Base class. 

504 ''' 

505 _array = [] 

506 _epsilon = EPS 

507 _itemname = _point_ 

508 

509 def _contains(self, point): 

510 '''(INTERNAL) Check for a matching point. 

511 ''' 

512 return any(self._findall(point, ())) 

513 

514 def copy(self, deep=False): # PYCHOK no cover 

515 '''Make a shallow or deep copy of this instance. 

516 

517 @kwarg deep: If C{True} make a deep, otherwise a 

518 shallow copy (C{bool}). 

519 

520 @return: The copy (C{This class} or subclass thereof). 

521 ''' 

522 return _xcopy(self, deep=deep) 

523 

524 def _count(self, point): 

525 '''(INTERNAL) Count the number of matching points. 

526 ''' 

527 return sum(1 for _ in self._findall(point, ())) # NOT len()! 

528 

529 def dup(self, **items): # PYCHOK no cover 

530 '''Duplicate this instance, I{without replacing items}. 

531 

532 @kwarg items: No attributes (I{not allowed}). 

533 

534 @return: The duplicate (C{This} (sub-)class). 

535 

536 @raise TypeError: Any B{C{items}} invalid. 

537 ''' 

538 if items: 

539 t = _SPACE_(classname(self), _immutable_) 

540 raise _TypeError(txt=t, this=self, **items) 

541 return _xdup(self) 

542 

543 @property_doc_(''' the equality tolerance (C{float}).''') 

544 def epsilon(self): 

545 '''Get the tolerance for equality tests (C{float}). 

546 ''' 

547 return self._epsilon 

548 

549 @epsilon.setter # PYCHOK setter! 

550 def epsilon(self, tol): 

551 '''Set the tolerance for equality tests (C{scalar}). 

552 

553 @raise UnitError: Non-scalar or invalid B{C{tol}}. 

554 ''' 

555 self._epsilon = Scalar_(tolerance=tol) 

556 

557 def _find(self, point, start_end): 

558 '''(INTERNAL) Find the first matching point index. 

559 ''' 

560 for i in self._findall(point, start_end): 

561 return i 

562 return -1 

563 

564 def _findall(self, point, start_end): # PYCHOK no cover 

565 '''(INTERNAL) I{Must be implemented/overloaded}. 

566 ''' 

567 notImplemented(self, point, start_end) 

568 

569 def _getitem(self, index): 

570 '''(INTERNAL) Return point [index] or return a slice. 

571 ''' 

572 # Luciano Ramalho, "Fluent Python", page 290+, O'Reilly, 2016 

573 if isinstance(index, slice): 

574 # XXX an numpy.[nd]array slice is a view, not a copy 

575 return self.__class__(self._array[index], **self._slicekwds()) 

576 else: 

577 return self.point(self._array[index]) 

578 

579 def _index(self, point, start_end): 

580 '''(INTERNAL) Find the first matching point index. 

581 ''' 

582 for i in self._findall(point, start_end): 

583 return i 

584 raise _IndexError(self._itemname, point, txt=_not_('found')) 

585 

586 @property_RO 

587 def isNumpy2(self): # PYCHOK no cover 

588 '''Is this a Numpy2 wrapper? 

589 ''' 

590 return False # isinstance(self, (Numpy2LatLon, ...)) 

591 

592 @property_RO 

593 def isPoints2(self): # PYCHOK no cover 

594 '''Is this a LatLon2 wrapper/converter? 

595 ''' 

596 return False # isinstance(self, (LatLon2psxy, ...)) 

597 

598 @property_RO 

599 def isTuple2(self): # PYCHOK no cover 

600 '''Is this a Tuple2 wrapper? 

601 ''' 

602 return False # isinstance(self, (Tuple2LatLon, ...)) 

603 

604 def _iter(self): 

605 '''(INTERNAL) Yield all points. 

606 ''' 

607 _array, _point = self._array, self.point 

608 for i in range(len(self)): 

609 yield _point(_array[i]) 

610 

611 def point(self, *attrs): # PYCHOK no cover 

612 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded in}. 

613 

614 @arg attrs: Optional arguments. 

615 ''' 

616 notOverloaded(self, *attrs) 

617 

618 def _range(self, start=None, end=None, step=1): 

619 '''(INTERNAL) Return the range. 

620 ''' 

621 if step > 0: 

622 if start is None: 

623 start = 0 

624 if end is None: 

625 end = len(self) 

626 elif step < 0: 

627 if start is None: 

628 start = len(self) - 1 

629 if end is None: 

630 end = -1 

631 else: 

632 raise _ValueError(step=step) 

633 return range(start, end, step) 

634 

635 def _repr(self): 

636 '''(INTERNAL) Return a string representation. 

637 ''' 

638 # XXX use Python 3+ reprlib.repr 

639 t = repr(self._array[:1]) # only first row 

640 t = _SPACE_(t[:-1], _ELLIPSIS_, Fmt.SQUARE(t[-1:], len(self))) 

641 t = _SPACE_.join(t.split()) # coalesce spaces 

642 return instr(self, t, **self._slicekwds()) 

643 

644 def _reversed(self): # PYCHOK false 

645 '''(INTERNAL) Yield all points in reverse order. 

646 ''' 

647 _array, point = self._array, self.point 

648 for i in range(len(self) - 1, -1, -1): 

649 yield point(_array[i]) 

650 

651 def _rfind(self, point, start_end): 

652 '''(INTERNAL) Find the last matching point index. 

653 ''' 

654 def _r3(start=None, end=None, step=-1): 

655 return (start, end, step) # PYCHOK returns 

656 

657 for i in self._findall(point, _r3(*start_end)): 

658 return i 

659 return -1 

660 

661 def _slicekwds(self): # PYCHOK no cover 

662 '''(INTERNAL) I{Should be overloaded}. 

663 ''' 

664 return {} 

665 

666 

667class _Array2LatLon(_Basequence): # immutable, on purpose 

668 '''(INTERNAL) Base class for Numpy2LatLon or Tuple2LatLon. 

669 ''' 

670 _array = () 

671 _ilat = 0 # row column index 

672 _ilon = 0 # row column index 

673 _LatLon = LatLon_ # default 

674 _shape = () 

675 

676 def __init__(self, array, ilat=0, ilon=1, LatLon=None, shape=()): 

677 '''Handle a C{NumPy} or C{Tuple} array as a sequence of C{LatLon} points. 

678 ''' 

679 ais = (_ilat_, ilat), (_ilon_, ilon) 

680 

681 if len(shape) != 2 or shape[0] < 1 or shape[1] < len(ais): 

682 raise _IndexError('array.shape', shape) 

683 

684 self._array = array 

685 self._shape = Shape2Tuple(shape) # *shape 

686 

687 if LatLon: # check the point class 

688 if not _isLatLon_(LatLon): 

689 raise _IsnotError(_valid_, LatLon=LatLon) 

690 self._LatLon = LatLon 

691 

692 # check the attr indices 

693 for n, (ai, i) in enumerate(ais): 

694 if not isint(i): 

695 raise _IsnotError(int.__name__, **{ai: i}) 

696 i = int(i) 

697 if not 0 <= i < shape[1]: 

698 raise _ValueError(ai, i) 

699 for aj, j in ais[:n]: 

700 if int(j) == i: 

701 raise _ValueError(_DEQUALSPACED_(ai, aj, i)) 

702 setattr(self, NN(_UNDER_, ai), i) 

703 

704 def __contains__(self, latlon): 

705 '''Check for a specific lat-/longitude. 

706 

707 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

708 C{(lat, lon)}). 

709 

710 @return: C{True} if B{C{latlon}} is present, C{False} otherwise. 

711 

712 @raise TypeError: Invalid B{C{latlon}}. 

713 ''' 

714 return self._contains(latlon) 

715 

716 def __getitem__(self, index): 

717 '''Return row[index] as C{LatLon} or return a L{Numpy2LatLon} slice. 

718 ''' 

719 return self._getitem(index) 

720 

721 def __iter__(self): 

722 '''Yield rows as C{LatLon}. 

723 ''' 

724 return self._iter() 

725 

726 def __len__(self): 

727 '''Return the number of rows. 

728 ''' 

729 return self._shape[0] 

730 

731 def __repr__(self): 

732 '''Return a string representation. 

733 ''' 

734 return self._repr() 

735 

736 def __reversed__(self): # PYCHOK false 

737 '''Yield rows as C{LatLon} in reverse order. 

738 ''' 

739 return self._reversed() 

740 

741 __str__ = __repr__ 

742 

743 def count(self, latlon): 

744 '''Count the number of rows with a specific lat-/longitude. 

745 

746 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

747 C{(lat, lon)}). 

748 

749 @return: Count (C{int}). 

750 

751 @raise TypeError: Invalid B{C{latlon}}. 

752 ''' 

753 return self._count(latlon) 

754 

755 def find(self, latlon, *start_end): 

756 '''Find the first row with a specific lat-/longitude. 

757 

758 @arg latlon: Point (C{LatLon}) or 2-tuple (lat, lon). 

759 @arg start_end: Optional C{[start[, end]]} index (integers). 

760 

761 @return: Index or -1 if not found (C{int}). 

762 

763 @raise TypeError: Invalid B{C{latlon}}. 

764 ''' 

765 return self._find(latlon, start_end) 

766 

767 def _findall(self, latlon, start_end): 

768 '''(INTERNAL) Yield indices of all matching rows. 

769 ''' 

770 try: 

771 lat, lon = latlon.lat, latlon.lon 

772 except AttributeError: 

773 try: 

774 lat, lon = latlon 

775 except (TypeError, ValueError): 

776 raise _IsnotError(_valid_, latlon=latlon) 

777 

778 _ilat, _ilon = self._ilat, self._ilon 

779 _array, _eps = self._array, self._epsilon 

780 for i in self._range(*start_end): 

781 row = _array[i] 

782 if fabs(row[_ilat] - lat) <= _eps and \ 

783 fabs(row[_ilon] - lon) <= _eps: 

784 yield i 

785 

786 def findall(self, latlon, *start_end): 

787 '''Yield indices of all rows with a specific lat-/longitude. 

788 

789 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

790 C{(lat, lon)}). 

791 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

792 

793 @return: Indices (C{iterable}). 

794 

795 @raise TypeError: Invalid B{C{latlon}}. 

796 ''' 

797 return self._findall(latlon, start_end) 

798 

799 def index(self, latlon, *start_end): # PYCHOK Python 2- issue 

800 '''Find index of the first row with a specific lat-/longitude. 

801 

802 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

803 C{(lat, lon)}). 

804 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

805 

806 @return: Index (C{int}). 

807 

808 @raise IndexError: Point not found. 

809 

810 @raise TypeError: Invalid B{C{latlon}}. 

811 ''' 

812 return self._index(latlon, start_end) 

813 

814 @Property_RO 

815 def ilat(self): 

816 '''Get the latitudes column index (C{int}). 

817 ''' 

818 return self._ilat 

819 

820 @Property_RO 

821 def ilon(self): 

822 '''Get the longitudes column index (C{int}). 

823 ''' 

824 return self._ilon 

825 

826# next = __iter__ 

827 

828 def point(self, row): # PYCHOK *attrs 

829 '''Instantiate a point C{LatLon}. 

830 

831 @arg row: Array row (numpy.array). 

832 

833 @return: Point (C{LatLon}). 

834 ''' 

835 return self._LatLon(row[self._ilat], row[self._ilon]) 

836 

837 def rfind(self, latlon, *start_end): 

838 '''Find the last row with a specific lat-/longitude. 

839 

840 @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

841 C{(lat, lon)}). 

842 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

843 

844 @note: Keyword order, first stop, then start. 

845 

846 @return: Index or -1 if not found (C{int}). 

847 

848 @raise TypeError: Invalid B{C{latlon}}. 

849 ''' 

850 return self._rfind(latlon, start_end) 

851 

852 def _slicekwds(self): 

853 '''(INTERNAL) Slice kwds. 

854 ''' 

855 return dict(ilat=self._ilat, ilon=self._ilon) 

856 

857 @Property_RO 

858 def shape(self): 

859 '''Get the shape of the C{NumPy} array or the C{Tuples} as 

860 L{Shape2Tuple}C{(nrows, ncols)}. 

861 ''' 

862 return self._shape 

863 

864 def _subset(self, indices): # PYCHOK no cover 

865 '''(INTERNAL) I{Must be implemented/overloaded}. 

866 ''' 

867 notImplemented(self, indices) 

868 

869 def subset(self, indices): 

870 '''Return a subset of the C{NumPy} array. 

871 

872 @arg indices: Row indices (C{range} or C{int}[]). 

873 

874 @note: A C{subset} is different from a C{slice} in 2 ways: 

875 (a) the C{subset} is typically specified as a list of 

876 (un-)ordered indices and (b) the C{subset} allocates 

877 a new, separate C{NumPy} array while a C{slice} is 

878 just an other C{view} of the original C{NumPy} array. 

879 

880 @return: Sub-array (C{numpy.array}). 

881 

882 @raise IndexError: Out-of-range B{C{indices}} value. 

883 

884 @raise TypeError: If B{C{indices}} is not a C{range} 

885 nor an C{int}[]. 

886 ''' 

887 if not issequence(indices, tuple): # NO tuple, only list 

888 # and range work properly to get Numpy array sub-sets 

889 raise _IsnotError(_valid_, indices=type(indices)) 

890 

891 n = len(self) 

892 for i, v in enumerate(indices): 

893 if not isint(v): 

894 raise _TypeError(Fmt.SQUARE(indices=i), v) 

895 elif not 0 <= v < n: 

896 raise _IndexError(Fmt.SQUARE(indices=i), v) 

897 

898 return self._subset(indices) 

899 

900 

901class LatLon2psxy(_Basequence): 

902 '''Wrapper for C{LatLon} points as "on-the-fly" pseudo-xy coordinates. 

903 ''' 

904 _closed = False 

905 _len = 0 

906 _deg2m = None # default, keep degrees 

907 _radius = None 

908 _wrap = True 

909 

910 def __init__(self, latlons, closed=False, radius=None, wrap=True): 

911 '''Handle C{LatLon} points as pseudo-xy coordinates. 

912 

913 @note: The C{LatLon} latitude is considered the I{pseudo-y} 

914 and longitude the I{pseudo-x} coordinate, likewise 

915 for L{LatLon2Tuple}. However, 2-tuples C{(x, y)} are 

916 considered as I{(longitude, latitude)}. 

917 

918 @arg latlons: Points C{list}, C{sequence}, C{set}, C{tuple}, 

919 etc. (C{LatLon[]}). 

920 @kwarg closed: Optionally, close the polygon (C{bool}). 

921 @kwarg radius: Mean earth radius (C{meter}). 

922 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

923 the B{C{latlons}} points (C{bool}). 

924 

925 @raise PointsError: Insufficient number of B{C{latlons}}. 

926 

927 @raise TypeError: Some B{C{points}} are not B{C{base}}. 

928 ''' 

929 self._closed = closed 

930 self._len, self._array = points2(latlons, closed=closed) 

931 if radius: 

932 self._radius = r = Radius(radius) 

933 self._deg2m = degrees2m(_1_0, r) 

934 if not wrap: 

935 self._wrap = False 

936 

937 def __contains__(self, xy): 

938 '''Check for a matching point. 

939 

940 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

941 C{(x, y)}) in (C{degrees}. 

942 

943 @return: C{True} if B{C{xy}} is present, C{False} otherwise. 

944 

945 @raise TypeError: Invalid B{C{xy}}. 

946 ''' 

947 return self._contains(xy) 

948 

949 def __getitem__(self, index): 

950 '''Return the pseudo-xy or return a L{LatLon2psxy} slice. 

951 ''' 

952 return self._getitem(index) 

953 

954 def __iter__(self): 

955 '''Yield all pseudo-xy's. 

956 ''' 

957 return self._iter() 

958 

959 def __len__(self): 

960 '''Return the number of pseudo-xy's. 

961 ''' 

962 return self._len 

963 

964 def __repr__(self): 

965 '''Return a string representation. 

966 ''' 

967 return self._repr() 

968 

969 def __reversed__(self): # PYCHOK false 

970 '''Yield all pseudo-xy's in reverse order. 

971 ''' 

972 return self._reversed() 

973 

974 __str__ = __repr__ 

975 

976 def count(self, xy): 

977 '''Count the number of matching points. 

978 

979 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

980 C{(x, y)}) in (C{degrees}. 

981 

982 @return: Count (C{int}). 

983 

984 @raise TypeError: Invalid B{C{xy}}. 

985 ''' 

986 return self._count(xy) 

987 

988 def find(self, xy, *start_end): 

989 '''Find the first matching point. 

990 

991 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

992 C{(x, y)}) in (C{degrees}. 

993 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

994 

995 @return: Index or -1 if not found (C{int}). 

996 

997 @raise TypeError: Invalid B{C{xy}}. 

998 ''' 

999 return self._find(xy, start_end) 

1000 

1001 def _findall(self, xy, start_end): 

1002 '''(INTERNAL) Yield indices of all matching points. 

1003 ''' 

1004 try: 

1005 x, y = xy.lon, xy.lat 

1006 

1007 def _x_y_ll3(ll): # match LatLon 

1008 return ll.lon, ll.lat, ll 

1009 

1010 except AttributeError: 

1011 try: 

1012 x, y = xy[:2] 

1013 except (IndexError, TypeError, ValueError): 

1014 raise _IsnotError(_valid_, xy=xy) 

1015 

1016 _x_y_ll3 = self.point # PYCHOK expected 

1017 

1018 _array, _eps = self._array, self._epsilon 

1019 for i in self._range(*start_end): 

1020 xi, yi, _ = _x_y_ll3(_array[i]) 

1021 if fabs(xi - x) <= _eps and \ 

1022 fabs(yi - y) <= _eps: 

1023 yield i 

1024 

1025 def findall(self, xy, *start_end): 

1026 '''Yield indices of all matching points. 

1027 

1028 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

1029 C{(x, y)}) in (C{degrees}. 

1030 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

1031 

1032 @return: Indices (C{iterator}). 

1033 

1034 @raise TypeError: Invalid B{C{xy}}. 

1035 ''' 

1036 return self._findall(xy, start_end) 

1037 

1038 def index(self, xy, *start_end): # PYCHOK Python 2- issue 

1039 '''Find the first matching point. 

1040 

1041 @arg xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}). 

1042 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

1043 

1044 @return: Index (C{int}). 

1045 

1046 @raise IndexError: Point not found. 

1047 

1048 @raise TypeError: Invalid B{C{xy}}. 

1049 ''' 

1050 return self._index(xy, start_end) 

1051 

1052 @property_RO 

1053 def isPoints2(self): 

1054 '''Is this a LatLon2 wrapper/converter? 

1055 ''' 

1056 return True # isinstance(self, (LatLon2psxy, ...)) 

1057 

1058 def point(self, ll): # PYCHOK *attrs 

1059 '''Create a pseudo-xy. 

1060 

1061 @arg ll: Point (C{LatLon}). 

1062 

1063 @return: An L{Point3Tuple}C{(x, y, ll)}. 

1064 ''' 

1065 x, y = ll.lon, ll.lat # note, x, y = lon, lat 

1066 if self._wrap: 

1067 y, x = _Wrap.latlon(y, x) 

1068 d = self._deg2m 

1069 if d: # convert degrees to meter (or radians) 

1070 x *= d 

1071 y *= d 

1072 return Point3Tuple(x, y, ll) 

1073 

1074 def rfind(self, xy, *start_end): 

1075 '''Find the last matching point. 

1076 

1077 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple 

1078 C{(x, y)}) in (C{degrees}. 

1079 @arg start_end: Optional C{[start[, end]]} index (C{int}). 

1080 

1081 @return: Index or -1 if not found (C{int}). 

1082 

1083 @raise TypeError: Invalid B{C{xy}}. 

1084 ''' 

1085 return self._rfind(xy, start_end) 

1086 

1087 def _slicekwds(self): 

1088 '''(INTERNAL) Slice kwds. 

1089 ''' 

1090 return dict(closed=self._closed, radius=self._radius, wrap=self._wrap) 

1091 

1092 

1093class Numpy2LatLon(_Array2LatLon): # immutable, on purpose 

1094 '''Wrapper for C{NumPy} arrays as "on-the-fly" C{LatLon} points. 

1095 ''' 

1096 def __init__(self, array, ilat=0, ilon=1, LatLon=None): 

1097 '''Handle a C{NumPy} array as a sequence of C{LatLon} points. 

1098 

1099 @arg array: C{NumPy} array (C{numpy.array}). 

1100 @kwarg ilat: Optional index of the latitudes column (C{int}). 

1101 @kwarg ilon: Optional index of the longitudes column (C{int}). 

1102 @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). 

1103 

1104 @raise IndexError: If B{C{array.shape}} is not (1+, 2+). 

1105 

1106 @raise TypeError: If B{C{array}} is not a C{NumPy} array or 

1107 C{LatLon} is not a class with C{lat} 

1108 and C{lon} attributes. 

1109 

1110 @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values 

1111 are the same or out of range. 

1112 

1113 @example: 

1114 

1115 >>> type(array) 

1116 <type 'numpy.ndarray'> # <class ...> in Python 3+ 

1117 >>> points = Numpy2LatLon(array, lat=0, lon=1) 

1118 >>> simply = simplifyRDP(points, ...) 

1119 >>> type(simply) 

1120 <type 'numpy.ndarray'> # <class ...> in Python 3+ 

1121 >>> sliced = points[1:-1] 

1122 >>> type(sliced) 

1123 <class '...Numpy2LatLon'> 

1124 ''' 

1125 try: # get shape and check some other numpy.array attrs 

1126 s, _, _ = array.shape, array.nbytes, array.ndim # PYCHOK expected 

1127 except AttributeError: 

1128 raise _IsnotError('NumPy', array=type(array)) 

1129 

1130 _Array2LatLon.__init__(self, array, ilat=ilat, ilon=ilon, 

1131 LatLon=LatLon, shape=s) 

1132 

1133 @property_RO 

1134 def isNumpy2(self): 

1135 '''Is this a Numpy2 wrapper? 

1136 ''' 

1137 return True # isinstance(self, (Numpy2LatLon, ...)) 

1138 

1139 def _subset(self, indices): 

1140 return self._array[indices] # NumPy special 

1141 

1142 

1143class Shape2Tuple(_NamedTuple): 

1144 '''2-Tuple C{(nrows, ncols)}, the number of rows and columns, 

1145 both C{int}. 

1146 ''' 

1147 _Names_ = (_nrows_, _ncols_) 

1148 _Units_ = ( Number_, Number_) 

1149 

1150 

1151class Tuple2LatLon(_Array2LatLon): 

1152 '''Wrapper for tuple sequences as "on-the-fly" C{LatLon} points. 

1153 ''' 

1154 def __init__(self, tuples, ilat=0, ilon=1, LatLon=None): 

1155 '''Handle a list of tuples, each containing a lat- and longitude 

1156 and perhaps other values as a sequence of C{LatLon} points. 

1157 

1158 @arg tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]). 

1159 @kwarg ilat: Optional index of the latitudes value (C{int}). 

1160 @kwarg ilon: Optional index of the longitudes value (C{int}). 

1161 @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). 

1162 

1163 @raise IndexError: If C{(len(B{tuples}), min(len(t) for t 

1164 in B{tuples}))} is not (1+, 2+). 

1165 

1166 @raise TypeError: If B{C{tuples}} is not a C{list}, C{tuple} 

1167 or C{sequence} or if B{C{LatLon}} is not a 

1168 C{LatLon} with C{lat}, C{lon} and C{name} 

1169 attributes. 

1170 

1171 @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values 

1172 are the same or out of range. 

1173 

1174 @example: 

1175 

1176 >>> tuples = [(0, 1), (2, 3), (4, 5)] 

1177 >>> type(tuples) 

1178 <type 'list'> # <class ...> in Python 3+ 

1179 >>> points = Tuple2LatLon(tuples, lat=0, lon=1) 

1180 >>> simply = simplifyRW(points, 0.5, ...) 

1181 >>> type(simply) 

1182 <type 'list'> # <class ...> in Python 3+ 

1183 >>> simply 

1184 [(0, 1), (4, 5)] 

1185 >>> sliced = points[1:-1] 

1186 >>> type(sliced) 

1187 <class '...Tuple2LatLon'> 

1188 >>> sliced 

1189 ...Tuple2LatLon([(2, 3), ...][1], ilat=0, ilon=1) 

1190 

1191 >>> closest, _ = nearestOn2(LatLon_(2, 1), points, adjust=False) 

1192 >>> closest 

1193 LatLon_(lat=1.0, lon=2.0) 

1194 

1195 >>> closest, _ = nearestOn2(LatLon_(3, 2), points) 

1196 >>> closest 

1197 LatLon_(lat=2.001162, lon=3.001162) 

1198 ''' 

1199 _xinstanceof(list, tuple, tuples=tuples) 

1200 s = len(tuples), min(len(_) for _ in tuples) 

1201 _Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon, 

1202 LatLon=LatLon, shape=s) 

1203 

1204 @property_RO 

1205 def isTuple2(self): 

1206 '''Is this a Tuple2 wrapper? 

1207 ''' 

1208 return True # isinstance(self, (Tuple2LatLon, ...)) 

1209 

1210 def _subset(self, indices): 

1211 return type(self._array)(self._array[i] for i in indices) 

1212 

1213 

1214def _area2(points, adjust, wrap): 

1215 '''(INTERNAL) Approximate the area in radians squared, I{signed}. 

1216 ''' 

1217 if adjust: 

1218 # approximate trapezoid by a rectangle, adjusting 

1219 # the top width by the cosine of the latitudinal 

1220 # average and bottom width by some fudge factor 

1221 def _adjust(w, h): 

1222 c = cos(h) if fabs(h) < PI_2 else _0_0 

1223 return w * h * (c + 1.2876) * _0_5 

1224 else: 

1225 def _adjust(w, h): # PYCHOK expected 

1226 return w * h 

1227 

1228 # setting radius=1 converts degrees to radians 

1229 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap) 

1230 x1, y1, ll = Ps[0] 

1231 pts = [ll] # for _areaError 

1232 

1233 A2 = Fsum() # trapezoidal area in radians**2 

1234 for p in Ps.iterate(closed=True): 

1235 x2, y2, ll = p 

1236 if len(pts) < 4: 

1237 pts.append(ll) 

1238 w, x2 = unrollPI(x1, x2, wrap=wrap and not Ps.looped) 

1239 A2 += _adjust(w, (y2 + y1) * _0_5) 

1240 x1, y1 = x2, y2 

1241 

1242 return A2.fsum(), tuple(pts) 

1243 

1244 

1245def _areaError(pts, near_=NN): # imported by .ellipsoidalKarney 

1246 '''(INTERNAL) Area issue. 

1247 ''' 

1248 t = _ELLIPSIS_(pts[:3], NN) 

1249 return _ValueError(NN(near_, 'zero or polar area'), txt=t) 

1250 

1251 

1252def areaOf(points, adjust=True, radius=R_M, wrap=True): 

1253 '''Approximate the area of a polygon or composite. 

1254 

1255 @arg points: The polygon points or clips (C{LatLon}[], 

1256 L{BooleanFHP} or L{BooleanGH}). 

1257 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta 

1258 by the cosine of the mean latitude (C{bool}). 

1259 @kwarg radius: Mean earth radius (C{meter}) or C{None}. 

1260 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1261 the B{C{points}} (C{bool}). 

1262 

1263 @return: Approximate area (I{square} C{meter}, same units as 

1264 B{C{radius}} or C{radians} I{squared} if B{C{radius}} 

1265 is C{None}). 

1266 

1267 @raise PointsError: Insufficient number of B{C{points}} 

1268 

1269 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1270 

1271 @raise ValueError: Invalid B{C{radius}}. 

1272 

1273 @note: This area approximation has limited accuracy and is 

1274 ill-suited for regions exceeding several hundred Km 

1275 or Miles or with near-polar latitudes. 

1276 

1277 @see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf}, 

1278 L{ellipsoidalExact.areaOf} and L{ellipsoidalKarney.areaOf}. 

1279 ''' 

1280 if _MODS.booleans.isBoolean(points): 

1281 a = points._sum1(areaOf, adjust=adjust, radius=None, wrap=wrap) 

1282 else: 

1283 a, _ = _area2(points, adjust, wrap) 

1284 return fabs(a if radius is None else (Radius(radius)**2 * a)) 

1285 

1286 

1287def boundsOf(points, wrap=False, LatLon=None): # was=True 

1288 '''Determine the bottom-left SW and top-right NE corners of a 

1289 path or polygon. 

1290 

1291 @arg points: The path or polygon points (C{LatLon}[]). 

1292 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1293 the B{C{points}} (C{bool}). 

1294 @kwarg LatLon: Optional class to return the C{bounds} 

1295 corners (C{LatLon}) or C{None}. 

1296 

1297 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as 

1298 B{C{LatLon}}s if B{C{LatLon}} is C{None} a 

1299 L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}. 

1300 

1301 @raise PointsError: Insufficient number of B{C{points}} 

1302 

1303 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1304 

1305 @see: Function L{quadOf}. 

1306 

1307 @example: 

1308 

1309 >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) 

1310 >>> boundsOf(b) # False 

1311 >>> 45.0, 1.0, 46.0, 2.0 

1312 ''' 

1313 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap) 

1314 w, s, _ = e, n, _ = Ps[0] 

1315 

1316 v = w 

1317 for x, y, _ in Ps.iterate(closed=False): # [1:] 

1318 if wrap: 

1319 _, x = unroll180(v, x, wrap=True) 

1320 v = x 

1321 

1322 if w > x: 

1323 w = x 

1324 elif e < x: 

1325 e = x 

1326 

1327 if s > y: 

1328 s = y 

1329 elif n < y: 

1330 n = y 

1331 

1332 return Bounds4Tuple(s, w, n, e) if LatLon is None else \ 

1333 Bounds2Tuple(LatLon(s, w), LatLon(n, e)) # PYCHOK inconsistent 

1334 

1335 

1336def _distanceTo(Error, **name_points): # .frechet, .hausdorff, .heights 

1337 '''(INTERNAL) Chech callable C{distanceTo} methods. 

1338 ''' 

1339 name, ps = name_points.popitem() 

1340 for i, p in enumerate(ps): 

1341 if not callable(_xattr(p, distanceTo=None)): 

1342 n = _distanceTo.__name__[1:] 

1343 t = _SPACE_(_no_, callable.__name__, n) 

1344 raise Error(Fmt.SQUARE(name, i), p, txt=t) 

1345 return ps 

1346 

1347 

1348def centroidOf(points, wrap=False, LatLon=None): # was=True 

1349 '''Determine the centroid of a polygon. 

1350 

1351 @arg points: The polygon points (C{LatLon}[]). 

1352 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1353 B{C{points}} (C{bool}). 

1354 @kwarg LatLon: Optional class to return the centroid (C{LatLon}) 

1355 or C{None}. 

1356 

1357 @return: Centroid (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)} 

1358 if C{B{LatLon} is None}. 

1359 

1360 @raise PointsError: Insufficient number of B{C{points}} 

1361 

1362 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1363 

1364 @raise ValueError: The B{C{points}} enclose a pole or 

1365 near-zero area. 

1366 

1367 @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and 

1368 Paul Bourke's U{Calculating The Area And Centroid Of A Polygon 

1369 <https://www.SEAS.UPenn.edu/~ese502/lab-content/extra_materials/ 

1370 Polygon%20Area%20and%20Centroid.pdf>}, 1988. 

1371 ''' 

1372 A, X, Y = Fsum(), Fsum(), Fsum() 

1373 

1374 # setting radius=1 converts degrees to radians 

1375 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap) 

1376 x1, y1, ll = Ps[0] 

1377 pts = [ll] # for _areaError 

1378 for p in Ps.iterate(closed=True): 

1379 x2, y2, ll = p 

1380 if len(pts) < 4: 

1381 pts.append(ll) 

1382 if wrap and not Ps.looped: 

1383 _, x2 = unrollPI(x1, x2, wrap=True) 

1384 t = x1 * y2 - x2 * y1 

1385 A += t 

1386 X += t * (x1 + x2) 

1387 Y += t * (y1 + y2) 

1388 # XXX more elaborately: 

1389 # t1, t2 = x1 * y2, -(x2 * y1) 

1390 # A.fadd_(t1, t2) 

1391 # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2) 

1392 # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2) 

1393 x1, y1 = x2, y2 

1394 

1395 a = A.fmul(_6_0).fover(_2_0) 

1396 if isnear0(a): 

1397 raise _areaError(pts, near_=_near_) 

1398 y, x = degrees90(Y.fover(a)), degrees180(X.fover(a)) 

1399 return LatLon2Tuple(y, x) if LatLon is None else LatLon(y, x) 

1400 

1401 

1402def fractional(points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds): 

1403 '''Return the point at a given I{fractional} index. 

1404 

1405 @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[], 

1406 L{Tuple2LatLon}[], C{Cartesian}[], C{Vector3d}[], 

1407 L{Vector3Tuple}[]). 

1408 @arg fi: The fractional index (L{FIx}, C{float} or C{int}). 

1409 @kwarg j: Optionally, index of the other point (C{int}). 

1410 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1411 B{{points}} (C{bool}) or C{None} for a backward 

1412 compatible L{LatLon2Tuple} or B{C{LatLon}} with 

1413 averaged lat- and longitudes. Use C{True} or 

1414 C{False} to get the I{fractional} point computed 

1415 by method C{B{points}[fi].intermediateTo}. 

1416 @kwarg LatLon: Optional class to return the I{intermediate}, 

1417 I{fractional} point (C{LatLon}) or C{None}. 

1418 @kwarg Vector: Optional class to return the I{intermediate}, 

1419 I{fractional} point (C{Cartesian}, C{Vector3d}) 

1420 or C{None}. 

1421 @kwarg kwds: Optional, additional B{C{LatLon}} I{or} B{C{Vector}} 

1422 keyword arguments, ignored if both C{B{LatLon}} and 

1423 C{B{Vector}} are C{None}. 

1424 

1425 @return: A L{LatLon2Tuple}C{(lat, lon)} if B{C{wrap}}, B{C{LatLon}} 

1426 and B{C{Vector}} all are C{None}, the defaults. 

1427 

1428 An instance of B{C{LatLon}} if not C{None} I{or} an instance 

1429 of B{C{Vector}} if not C{None}. 

1430 

1431 Otherwise with B{C{wrap}} either C{True} or C{False} and 

1432 B{C{LatLon}} and B{C{Vector}} both C{None}, an instance of 

1433 B{C{points}}' (sub-)class C{intermediateTo} I{fractional}. 

1434 

1435 Summarized as follows: 

1436 

1437 >>> wrap | LatLon | Vector | returned type/value 

1438 # -------+--------+--------+--------------+------ 

1439 # | | | LatLon2Tuple | favg 

1440 # None | None | None | or** | 

1441 # | | | Vector3Tuple | favg 

1442 # None | LatLon | None | LatLon | favg 

1443 # None | None | Vector | Vector | favg 

1444 # -------+--------+--------+--------------+------ 

1445 # True | None | None | points' | .iTo 

1446 # True | LatLon | None | LatLon | .iTo 

1447 # True | None | Vector | Vector | .iTo 

1448 # -------+--------+--------+--------------+------ 

1449 # False | None | None | points' | .iTo 

1450 # False | LatLon | None | LatLon | .iTo 

1451 # False | None | Vector | Vector | .iTo 

1452 # _____ 

1453 # favg) averaged lat, lon or x, y, z values 

1454 # .iTo) value from points[fi].intermediateTo 

1455 # **) depends on base class of points[fi] 

1456 

1457 @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}} 

1458 not subscriptable or not closed. 

1459 

1460 @raise TypeError: Invalid B{C{LatLon}}, B{C{Vector}} or B{C{kwds}} 

1461 argument. 

1462 

1463 @see: Class L{FIx} and method L{FIx.fractional}. 

1464 ''' 

1465 if LatLon and Vector: # PYCHOK no cover 

1466 kwds = _xkwds(kwds, fi=fi, LatLon=LatLon, Vector=Vector) 

1467 raise _TypeError(txt=fractional.__name__, **kwds) 

1468 w = wrap if LatLon else False # intermediateTo 

1469 try: 

1470 if not isscalar(fi) or fi < 0: 

1471 raise IndexError 

1472 n = _xattr(fi, fin=0) 

1473 p = _fractional(points, fi, j, fin=n, wrap=w) # see .units.FIx 

1474 if LatLon: 

1475 p = LatLon(p.lat, p.lon, **kwds) 

1476 elif Vector: 

1477 p = Vector(p.x, p.y, p.z, **kwds) 

1478 except (IndexError, TypeError): 

1479 raise _IndexError(fi=fi, points=points, wrap=w, txt=fractional.__name__) 

1480 return p 

1481 

1482 

1483def _fractional(points, fi, j, fin=None, wrap=None): # in .frechet.py 

1484 '''(INTERNAL) Compute point at L{fractional} index C{fi} and C{j}. 

1485 ''' 

1486 i = int(fi) 

1487 p = points[i] 

1488 r = fi - float(i) 

1489 if r > EPS: # EPS0? 

1490 if j is None: # in .frechet.py 

1491 j = i + 1 

1492 if fin: 

1493 j %= fin 

1494 q = points[j] 

1495 if r >= EPS1: # PYCHOK no cover 

1496 p = q 

1497 elif wrap is not None: # in (True, False) 

1498 p = p.intermediateTo(q, r, wrap=wrap) 

1499 elif _isLatLon(p): # backward compatible default 

1500 p = LatLon2Tuple(favg(p.lat, q.lat, f=r), 

1501 favg(p.lon, q.lon, f=r), 

1502 name=fractional.__name__) 

1503 else: # assume p and q are cartesian or vectorial 

1504 z = p.z if p.z is q.z else favg(p.z, q.z, f=r) 

1505 p = Vector3Tuple(favg(p.x, q.x, f=r), 

1506 favg(p.y, q.y, f=r), z, 

1507 name=fractional.__name__) 

1508 return p 

1509 

1510 

1511def isclockwise(points, adjust=False, wrap=True): 

1512 '''Determine the direction of a path or polygon. 

1513 

1514 @arg points: The path or polygon points (C{LatLon}[]). 

1515 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta 

1516 by the cosine of the mean latitude (C{bool}). 

1517 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1518 B{C{points}} (C{bool}). 

1519 

1520 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise. 

1521 

1522 @raise PointsError: Insufficient number of B{C{points}} 

1523 

1524 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1525 

1526 @raise ValueError: The B{C{points}} enclose a pole or zero area. 

1527 

1528 @example: 

1529 

1530 >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) 

1531 >>> isclockwise(f) # False 

1532 >>> isclockwise(reversed(f)) # True 

1533 ''' 

1534 a, pts = _area2(points, adjust, wrap) 

1535 if a > 0: # opposite of ellipsoidalExact and -Karney 

1536 return True 

1537 elif a < 0: 

1538 return False 

1539 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> 

1540 raise _areaError(pts) 

1541 

1542 

1543def isconvex(points, adjust=False, wrap=False): # was=True 

1544 '''Determine whether a polygon is convex. 

1545 

1546 @arg points: The polygon points (C{LatLon}[]). 

1547 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta 

1548 by the cosine of the mean latitude (C{bool}). 

1549 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1550 B{C{points}} (C{bool}). 

1551 

1552 @return: C{True} if B{C{points}} are convex, C{False} otherwise. 

1553 

1554 @raise CrossError: Some B{C{points}} are colinear. 

1555 

1556 @raise PointsError: Insufficient number of B{C{points}} 

1557 

1558 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1559 

1560 @example: 

1561 

1562 >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) 

1563 >>> isconvex(t) # True 

1564 

1565 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) 

1566 >>> isconvex(f) # False 

1567 ''' 

1568 return bool(isconvex_(points, adjust=adjust, wrap=wrap)) 

1569 

1570 

1571def isconvex_(points, adjust=False, wrap=False): # was=True 

1572 '''Determine whether a polygon is convex I{and clockwise}. 

1573 

1574 @arg points: The polygon points (C{LatLon}[]). 

1575 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta 

1576 by the cosine of the mean latitude (C{bool}). 

1577 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1578 B{C{points}} (C{bool}). 

1579 

1580 @return: C{+1} if B{C{points}} are convex clockwise, C{-1} for 

1581 convex counter-clockwise B{C{points}}, C{0} otherwise. 

1582 

1583 @raise CrossError: Some B{C{points}} are colinear. 

1584 

1585 @raise PointsError: Insufficient number of B{C{points}} 

1586 

1587 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1588 

1589 @example: 

1590 

1591 >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) 

1592 >>> isconvex_(t) # +1 

1593 

1594 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) 

1595 >>> isconvex_(f) # 0 

1596 ''' 

1597 if adjust: 

1598 def _unroll2(x1, x2, w, y1, y2): 

1599 x21, x2 = unroll180(x1, x2, wrap=w) 

1600 y = radians(y1 + y2) * _0_5 

1601 x21 *= cos(y) if fabs(y) < PI_2 else _0_0 

1602 return x21, x2 

1603 else: 

1604 def _unroll2(x1, x2, w, *unused): # PYCHOK expected 

1605 return unroll180(x1, x2, wrap=w) 

1606 

1607 c, s = crosserrors(), 0 

1608 

1609 Ps = LatLon2PsxyIter(points, loop=2, wrap=wrap) 

1610 x1, y1, _ = Ps[0] 

1611 x2, y2, _ = Ps[1] 

1612 

1613 x21, x2 = _unroll2(x1, x2, False, y1, y2) 

1614 for i, p in Ps.enumerate(closed=True): 

1615 x3, y3, ll = p 

1616 x32, x3 = _unroll2(x2, x3, bool(wrap and not Ps.looped), y2, y3) 

1617 

1618 # get the sign of the distance from point 

1619 # x3, y3 to the line from x1, y1 to x2, y2 

1620 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line> 

1621 s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2) 

1622 if s3 > 0: # x3, y3 on the right 

1623 if s < 0: # non-convex 

1624 return 0 

1625 s = +1 

1626 

1627 elif s3 < 0: # x3, y3 on the left 

1628 if s > 0: # non-convex 

1629 return 0 

1630 s = -1 

1631 

1632 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # PYCHOK no cover 

1633 # colinear u-turn: x3, y3 not on the 

1634 # opposite side of x2, y2 as x1, y1 

1635 t = Fmt.SQUARE(points=i) 

1636 raise CrossError(t, ll, txt=_colinear_) 

1637 

1638 x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32 

1639 

1640 return s # all points on the same side 

1641 

1642 

1643def isenclosedBy(point, points, wrap=False): # MCCABE 15 

1644 '''Determine whether a point is enclosed by a polygon or composite. 

1645 

1646 @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}). 

1647 @arg points: The polygon points or clips (C{LatLon}[], L{BooleanFHP} 

1648 or L{BooleanGH}). 

1649 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1650 B{C{points}} (C{bool}). 

1651 

1652 @return: C{True} if the B{C{point}} is inside the polygon or 

1653 composite, C{False} otherwise. 

1654 

1655 @raise PointsError: Insufficient number of B{C{points}} 

1656 

1657 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1658 

1659 @raise ValueError: Invalid B{C{point}}, lat- or longitude. 

1660 

1661 @see: Functions L{pygeodesy.isconvex} and L{pygeodesy.ispolar} especially 

1662 if the B{C{points}} may enclose a pole or wrap around the earth 

1663 I{longitudinally}, methods L{sphericalNvector.LatLon.isenclosedBy}, 

1664 L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop 

1665 GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et.al. 2009, 

1666 JTECH<https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>} 

1667 and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/ 

1668 10.1175/JTECH-D-11-00019.1>}). 

1669 ''' 

1670 try: 

1671 y0, x0 = point.lat, point.lon 

1672 except AttributeError: 

1673 try: 

1674 y0, x0 = map(float, point[:2]) 

1675 except (IndexError, TypeError, ValueError) as x: 

1676 raise _ValueError(point=point, cause=x) 

1677 

1678 if wrap: 

1679 y0, x0 = _Wrap.latlon(y0, x0) 

1680 

1681 def _dxy3(x, x2, y2, Ps): 

1682 dx, x2 = unroll180(x, x2, wrap=not Ps.looped) 

1683 return dx, x2, y2 

1684 

1685 else: 

1686 x0 = fmod(x0, _360_0) # not x0 % 360! 

1687 x0_180_ = x0 - _180_0 

1688 x0_180 = x0 + _180_0 

1689 

1690 def _dxy3(x1, x, y, unused): # PYCHOK expected 

1691 x = _umod_360(float(x)) 

1692 if x < x0_180_: 

1693 x += _360_0 

1694 elif x >= x0_180: 

1695 x -= _360_0 

1696 return (x - x1), x, y 

1697 

1698 if _MODS.booleans.isBoolean(points): 

1699 return points._encloses(y0, x0, wrap=wrap) 

1700 

1701 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap) 

1702 p = Ps[0] 

1703 e = m = False 

1704 S = Fsum() 

1705 

1706 _, x1, y1 = _dxy3(x0, p.x, p.y, False) 

1707 for p in Ps.iterate(closed=True): 

1708 dx, x2, y2 = _dxy3(x1, p.x, p.y, Ps) 

1709 # ignore duplicate and near-duplicate pts 

1710 if fabs(dx) > EPS or fabs(y2 - y1) > EPS: 

1711 # determine if polygon edge (x1, y1)..(x2, y2) straddles 

1712 # point (lat, lon) or is on boundary, but do not count 

1713 # edges on boundary as more than one crossing 

1714 if fabs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1): 

1715 m = not m 

1716 dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx 

1717 if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0): 

1718 e = not e 

1719 

1720 S += sin(radians(y2)) 

1721 x1, y1 = x2, y2 

1722 

1723 # An odd number of meridian crossings means, the polygon 

1724 # contains a pole. Assume it is the pole on the hemisphere 

1725 # containing the polygon mean point and if the polygon does 

1726 # contain the North Pole, flip the result. 

1727 if m and S.fsum() > 0: 

1728 e = not e 

1729 return e 

1730 

1731 

1732def ispolar(points, wrap=False): 

1733 '''Check whether a polygon encloses a pole. 

1734 

1735 @arg points: The polygon points (C{LatLon}[]). 

1736 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1737 the B{C{points}} (C{bool}). 

1738 

1739 @return: C{True} if the polygon encloses a pole, C{False} 

1740 otherwise. 

1741 

1742 @raise PointsError: Insufficient number of B{C{points}} 

1743 

1744 @raise TypeError: Some B{C{points}} are not C{LatLon} or don't 

1745 have C{bearingTo2}, C{initialBearingTo} 

1746 and C{finalBearingTo} methods. 

1747 ''' 

1748 def _cds(ps, w): # iterate over course deltas 

1749 Ps = PointsIter(ps, loop=2, wrap=w) 

1750 p2, p1 = Ps[0:2] 

1751 b1, _ = _bearingTo2(p2, p1, wrap=False) 

1752 for p2 in Ps.iterate(closed=True): 

1753 if not p2.isequalTo(p1, EPS): 

1754 if w and not Ps.looped: 

1755 p2 = _unrollon(p1, p2) 

1756 b, b2 = _bearingTo2(p1, p2, wrap=False) 

1757 yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180 

1758 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180 

1759 p1, b1 = p2, b2 

1760 

1761 # summation of course deltas around pole is 0° rather than normally ±360° 

1762 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> 

1763 s = fsum(_cds(points, wrap), floats=True) 

1764 # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90) 

1765 return fabs(s) < 90 # "zero-ish" 

1766 

1767 

1768def luneOf(lon1, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds): 

1769 '''Generate an ellipsoidal or spherical U{lune 

1770 <https://WikiPedia.org/wiki/Spherical_lune>}-shaped path or polygon. 

1771 

1772 @arg lon1: Left longitude (C{degrees90}). 

1773 @arg lon2: Right longitude (C{degrees90}). 

1774 @kwarg closed: Optionally, close the path (C{bool}). 

1775 @kwarg LatLon: Class to use (L{LatLon_}). 

1776 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

1777 keyword arguments. 

1778 

1779 @return: A tuple of 4 or 5 B{C{LatLon}} instances outlining 

1780 the lune shape. 

1781 

1782 @see: U{Latitude-longitude quadrangle 

1783 <https://www.MathWorks.com/help/map/ref/areaquad.html>}. 

1784 ''' 

1785 t = (LatLon( _0_0, lon1, **LatLon_kwds), 

1786 LatLon( _90_0, lon1, **LatLon_kwds), 

1787 LatLon( _0_0, lon2, **LatLon_kwds), 

1788 LatLon(_N_90_0, lon2, **LatLon_kwds)) 

1789 if closed: 

1790 t += t[:1] 

1791 return t 

1792 

1793 

1794def nearestOn5(point, points, closed=False, wrap=False, adjust=True, 

1795 limit=9, **LatLon_and_kwds): 

1796 '''Locate the point on a path or polygon closest to a reference point. 

1797 

1798 The closest point on each polygon edge is either the nearest of that 

1799 edge's end points or a point in between. 

1800 

1801 @arg point: The reference point (C{LatLon}). 

1802 @arg points: The path or polygon points (C{LatLon}[]). 

1803 @kwarg closed: Optionally, close the path or polygon (C{bool}). 

1804 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1805 B{C{points}} (C{bool}). 

1806 @kwarg adjust: See function L{pygeodesy.equirectangular_} (C{bool}). 

1807 @kwarg limit: See function L{pygeodesy.equirectangular_} (C{degrees}), 

1808 default C{9 degrees} is about C{1,000 Kmeter} (for mean 

1809 spherical earth radius L{R_KM}). 

1810 @kwarg LatLon_and_kwds: Optional, C{B{LatLon}=None} class to use for 

1811 the closest point and additional B{C{LatLon}} keyword 

1812 arguments, ignored if C{B{LatLon}=None} or not given. 

1813 

1814 @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the 

1815 {closest} point (B{C{LatLon}}) or if C{B{LatLon} is None}, 

1816 a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}. 

1817 The C{distance} is the L{pygeodesy.equirectangular} distance 

1818 between the C{closest} and reference B{C{point}} in C{degrees}. 

1819 The C{angle} from the B{C{point}} to the C{closest} is in 

1820 compass C{degrees}, like function L{pygeodesy.compassAngle}. 

1821 

1822 @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}}, 

1823 see function L{pygeodesy.equirectangular_}. 

1824 

1825 @raise PointsError: Insufficient number of B{C{points}} 

1826 

1827 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1828 

1829 @note: Distances are I{approximated} by function L{pygeodesy.equirectangular_}. 

1830 For more accuracy use one of the C{LatLon.nearestOn6} methods. 

1831 

1832 @see: Function L{pygeodesy.degrees2m}. 

1833 ''' 

1834 def _d2yx4(p2, p1, u, alw): 

1835 # w = wrap if (i < (n - 1) or not closed) else False 

1836 # equirectangular_ returns a Distance4Tuple(distance 

1837 # in degrees squared, delta lat, delta lon, p2.lon 

1838 # unroll/wrap'd); the previous p2.lon unroll/wrap'd 

1839 # is also applied to the next edge's p1.lon 

1840 return equirectangular_(p1.lat, p1.lon + u, 

1841 p2.lat, p2.lon, **alw) 

1842 

1843 def _h(p): # get height or default 0 

1844 return _xattr(p, height=0) or 0 

1845 

1846 # 3-D version used in .vector3d._nearestOn2 

1847 # 

1848 # point (x, y) on axis rotated ccw by angle a: 

1849 # x' = y * sin(a) + x * cos(a) 

1850 # y' = y * cos(a) - x * sin(a) 

1851 # 

1852 # distance (w) along and (h) perpendicular to 

1853 # a line thru point (dx, dy) and the origin: 

1854 # w = (y * dy + x * dx) / hypot(dx, dy) 

1855 # h = (y * dx - x * dy) / hypot(dx, dy) 

1856 # 

1857 # closest point on that line thru (dx, dy): 

1858 # xc = dx * w / hypot(dx, dy) 

1859 # yc = dy * w / hypot(dx, dy) 

1860 # or 

1861 # xc = dx * f 

1862 # yc = dy * f 

1863 # with 

1864 # f = w / hypot(dx, dy) 

1865 # or 

1866 # f = (y * dy + x * dx) / hypot2(dx, dy) 

1867 # 

1868 # i.e. no need for sqrt or hypot 

1869 

1870 Ps = PointsIter(points, loop=1, wrap=wrap) 

1871 p1 = c = Ps[0] 

1872 u1 = u = _0_0 

1873 kw = dict(adjust=adjust, limit=limit, wrap=False) 

1874 d, dy, dx, _ = _d2yx4(p1, point, u1, kw) 

1875 for p2 in Ps.iterate(closed=closed): 

1876 # iff wrapped, unroll lon1 (actually previous 

1877 # lon2) like function unroll180/-PI would've 

1878 if wrap: 

1879 kw.update(wrap=not (closed and Ps.looped)) 

1880 d21, y21, x21, u2 = _d2yx4(p2, p1, u1, kw) 

1881 if d21 > EPS: 

1882 # distance point to p1, y01 and x01 negated 

1883 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw) 

1884 if d2 > EPS: 

1885 w2 = y01 * y21 + x01 * x21 

1886 if w2 > 0: 

1887 if w2 < d21: 

1888 # closest is between p1 and p2, use 

1889 # original delta's, not y21 and x21 

1890 f = w2 / d21 

1891 p1 = LatLon_(favg(p1.lat, p2.lat, f=f), 

1892 favg(p1.lon, p2.lon + u2, f=f), 

1893 height=favg(_h(p1), _h(p2), f=f)) 

1894 u1 = _0_0 

1895 else: # p2 is closest 

1896 p1, u1 = p2, u2 

1897 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw) 

1898 if d2 < d: # p1 is closer, y01 and x01 negated 

1899 c, u, d, dy, dx = p1, u1, d2, -y01, -x01 

1900 p1, u1 = p2, u2 

1901 

1902 a = atan2b(dx, dy) 

1903 d = hypot(dx, dy) 

1904 h = _h(c) 

1905 n = nameof(point) or nearestOn5.__name__ 

1906 if LatLon_and_kwds: 

1907 kwds = _xkwds(LatLon_and_kwds, height=h, name=n) 

1908 LL = _xkwds_pop(kwds, LatLon=None) 

1909 if LL is not None: 

1910 r = LL(c.lat, c.lon + u, **kwds) 

1911 return NearestOn3Tuple(r, d, a, name=n) 

1912 return NearestOn5Tuple(c.lat, c.lon + u, d, a, h, name=n) # PYCHOK expected 

1913 

1914 

1915def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True): 

1916 '''I{Approximate} the perimeter of a path, polygon. or composite. 

1917 

1918 @arg points: The path or polygon points or clips (C{LatLon}[], 

1919 L{BooleanFHP} or L{BooleanGH}). 

1920 @kwarg closed: Optionally, close the path or polygon (C{bool}). 

1921 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta 

1922 by the cosine of the mean latitude (C{bool}). 

1923 @kwarg radius: Mean earth radius (C{meter}). 

1924 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

1925 B{C{points}} (C{bool}). 

1926 

1927 @return: Approximate perimeter (C{meter}, same units as 

1928 B{C{radius}}). 

1929 

1930 @raise PointsError: Insufficient number of B{C{points}} 

1931 

1932 @raise TypeError: Some B{C{points}} are not C{LatLon}. 

1933 

1934 @raise ValueError: Invalid B{C{radius}} or C{B{closed}=False} with 

1935 C{B{points}} a composite. 

1936 

1937 @note: This perimeter is based on the L{pygeodesy.equirectangular_} 

1938 distance approximation and is ill-suited for regions exceeding 

1939 several hundred Km or Miles or with near-polar latitudes. 

1940 

1941 @see: Functions L{sphericalTrigonometry.perimeterOf} and 

1942 L{ellipsoidalKarney.perimeterOf}. 

1943 ''' 

1944 def _degs(ps, c, a, w): # angular edge lengths in degrees 

1945 Ps = LatLon2PsxyIter(ps, loop=1) # wrap=w 

1946 p1, u = Ps[0], _0_0 # previous x2's unroll/wrap 

1947 for p2 in Ps.iterate(closed=c): 

1948 if w and c: 

1949 w = not Ps.looped 

1950 # apply previous x2's unroll/wrap'd to new x1 

1951 _, dy, dx, u = equirectangular_(p1.y, p1.x + u, 

1952 p2.y, p2.x, 

1953 adjust=a, limit=None, 

1954 wrap=w) # PYCHOK non-seq 

1955 yield hypot(dx, dy) 

1956 p1 = p2 

1957 

1958 if _MODS.booleans.isBoolean(points): 

1959 if not closed: 

1960 notImplemented(None, closed=closed, points=_composite_) 

1961 d = points._sum1(perimeterOf, closed=True, adjust=adjust, 

1962 radius=radius, wrap=wrap) 

1963 else: 

1964 d = fsum(_degs(points, closed, adjust, wrap), floats=True) 

1965 return degrees2m(d, radius=radius) 

1966 

1967 

1968def quadOf(latS, lonW, latN, lonE, closed=False, LatLon=LatLon_, **LatLon_kwds): 

1969 '''Generate a quadrilateral path or polygon from two points. 

1970 

1971 @arg latS: Souther-nmost latitude (C{degrees90}). 

1972 @arg lonW: Western-most longitude (C{degrees180}). 

1973 @arg latN: Norther-nmost latitude (C{degrees90}). 

1974 @arg lonE: Eastern-most longitude (C{degrees180}). 

1975 @kwarg closed: Optionally, close the path (C{bool}). 

1976 @kwarg LatLon: Class to use (L{LatLon_}). 

1977 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

1978 keyword arguments. 

1979 

1980 @return: Return a tuple of 4 or 5 B{C{LatLon}} instances 

1981 outlining the quadrilateral. 

1982 

1983 @see: Function L{boundsOf}. 

1984 ''' 

1985 t = (LatLon(latS, lonW, **LatLon_kwds), 

1986 LatLon(latN, lonW, **LatLon_kwds), 

1987 LatLon(latN, lonE, **LatLon_kwds), 

1988 LatLon(latS, lonE, **LatLon_kwds)) 

1989 if closed: 

1990 t += t[:1] 

1991 return t 

1992 

1993 

1994__all__ += _ALL_DOCS(_Array2LatLon, _Basequence) 

1995 

1996# **) MIT License 

1997# 

1998# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1999# 

2000# Permission is hereby granted, free of charge, to any person obtaining a 

2001# copy of this software and associated documentation files (the "Software"), 

2002# to deal in the Software without restriction, including without limitation 

2003# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

2004# and/or sell copies of the Software, and to permit persons to whom the 

2005# Software is furnished to do so, subject to the following conditions: 

2006# 

2007# The above copyright notice and this permission notice shall be included 

2008# in all copies or substantial portions of the Software. 

2009# 

2010# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

2011# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

2012# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

2013# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

2014# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

2015# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

2016# OTHER DEALINGS IN THE SOFTWARE.