1

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

3

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

5

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

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

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

9

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

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

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

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

14

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

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

17

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

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

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

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

22

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

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

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

26'''

27

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

29 issubclassof, _Sequence, _xcopy, _xdup, \

30 _xinstanceof

31 from 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

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

36 S_MIN, S_SEC, S_SEP

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

38 _IsnotError, _TypeError, _ValueError, \

39 _xattr, _xkwds, _xkwds_pop

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

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

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

43 isnormal, latlon2n_xyz, normal, _spherical_datum

44 from 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_

48 from pygeodesy.iters import LatLon2PsxyIter, PointsIter, points2

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

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

51 _NamedTuple, _xnamed, _xother3, _xotherError

52 from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, \

53 LatLon2Tuple, NearestOn3Tuple, \

54 NearestOn5Tuple, PhiLam2Tuple, \

55 Point3Tuple, Vector3Tuple, Vector4Tuple

56 from pygeodesy.nvectorBase import NvectorBase, _N_vector_

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

58 property_doc_, property_RO, _update_all

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

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

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

62 unroll180, _unrollon, unrollPI, _Wrap, wrap180

63

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

65

66__all__ = _ALL_LAZY.points

67__version__ = '23.08.23'

68

69_ilat_ = 'ilat'

70_ilon_ = 'ilon'

71_ncols_ = 'ncols'

72_nrows_ = 'nrows'

73

74

75 class 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 Luciano

82 # Ramalho, "Fluent Python", O'Reilly, 2016 p. 276+ "Problems

83 # with __slots__" (also at <https://Books.Google.ie/books?

84 # id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg=PT364#

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

86 # 2022 p. 390 "Summarizing the Issues with __slots__".

87 #

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

89 # Property_RO = property_RO # no __dict__ with __slots__!

90 #

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

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

93

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

95 datum=None, wrap=False):

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

97

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

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

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

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

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

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

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

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

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

107 (C{bool}).

108

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

110

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

112 un-clipped and un-validated .

113 '''

114 if lon is None: # PYCHOK no cover

115 try:

116 ll = latlonh.lat, latlonh.lon

117 height = _xattr(latlonh, height=height)

118 except AttributeError:

119 raise _IsnotError(_LatLon_, latlonh=latlonh)

120 if wrap:

121 ll = _Wrap.latlon(*ll)

122 elif wrap: # PYCHOK no cover

123 ll = _Wrap.latlonDMS2(latlonh, lon)

124 else: # must be latNS, lonEW

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

126

127 self.lat, self.lon = ll

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

129 self.height = height

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

131 _spherical_datum(datum, name=self.name)

132

133 def __eq__(self, other):

134 return isinstance(other, LatLon_) and \

135 other.lat == self.lat and \

136 other.lon == self.lon

137

138 def __ne__(self, other):

139 return not self.__eq__(other)

140

141 def __repr__(self):

142 return self.toRepr()

143

144 def __str__(self):

145 return self.toStr()

146

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

148 '''Instantiate this very class.

149

150 @arg args: Optional, positional arguments.

151 @kwarg kwds: Optional, keyword arguments.

152

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

154 '''

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

156

157 def copy(self, deep=False):

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

159

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

161 shallow copy (C{bool}).

162

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

164 '''

165 return _xcopy(self, deep=deep)

166

167 def dup(self, **items):

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

169

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

171

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

173

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

175 '''

176 d = _xdup(self, **items)

177 if items:

178 _update_all(d)

179 return d

180

181 def heightStr(self, prec=-2):

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

183

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

185

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

187 '''

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

189

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

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

192 and an other point.

193

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

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

196 0.0 for this and 1.0 for the other point).

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

198 intermediate height.

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

200 the B{C{other}} point (C{bool}).

201

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

203

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

205 '''

206 f = Scalar(fraction=fraction)

207 if isnear0(f):

208 r = self

209 elif isnear1(f) and not wrap:

210 r = self.others(other)

211 else:

212 p = self.others(other)

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

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

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

216 favg(self.lon, lon, f=f),

217 height=h, datum=self.datum,

218 name=self.intermediateTo.__name__)

219 return r

220

221 @Property_RO # PYCHOK no cover

222 def isEllipsoidal(self):

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

224 '''

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

226

227 @Property_RO # PYCHOK no cover

228 def isEllipsoidalLatLon(self):

229 '''Get C{LatLon} base.

230 '''

231 return False

232

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

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

235

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

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

238

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

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

241

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

243 '''

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

245

246 @Property_RO

247 def isnormal(self):

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

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

250

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

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

253 '''

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

255

256 @Property_RO

257 def isSpherical(self): # PYCHOK no cover

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

259 '''

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

261

262 @Property_RO

263 def lam(self):

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

265 '''

266 return radians(self.lon)

267

268 @Property

269 def latlon(self):

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

271 '''

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

273

274 @latlon.setter # PYCHOK setter!

275 def latlon(self, latlon):

276 '''Set the lat- and longitude.

277

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

279 '''

280 if self.latlon != latlon[:2]:

281 _update_all(self)

282 self.lat, self.lon = latlon[:2]

283

284 @Property_RO

285 def latlonheight(self):

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

287 '''

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

289

290 @Property_RO

291 def _N_vector(self):

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

293 '''

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

295 h=self.height, name=self.name)

296

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

298 '''Refined class comparison.

299

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

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

302 keyword arguments.

303

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

305

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

307 '''

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

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

310 and hasattr(other, _lon_)):

311 return other

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

313

314 def normal(self):

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

316 C{abs(lon) <= 180}.

317

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

319 wasn't (but is now).

320

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

322 '''

323 n = self.isnormal

324 if not n:

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

326 return n

327

328 @Property_RO

329 def phi(self):

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

331 '''

332 return radians(self.lat)

333

334 @Property_RO

335 def philam(self):

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

337 '''

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

339

340 @Property_RO

341 def philamheight(self):

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

343 '''

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

345

346 @deprecated_method

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

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

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

350

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

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

353

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

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

356 ignoring any duplicate or closing final

357 B{C{points}} (C{bool}).

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

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

360

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

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

363

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

365

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

367 '''

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

369

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

371 '''Return a points iterator.

372

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

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

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

376

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

378

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

380 '''

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

382

383 @deprecated_method

384 def to2ab(self): # PYCHOK no cover

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

386 return self.philam

387

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

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

390 and C{abs(lon) <= 180}.

391

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

393 shallow copy (C{bool}).

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

395

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

397 optionally renamed (C{LatLon}).

398

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

400 function L{pygeodesy.normal}.

401 '''

402 ll = self.copy(deep=deep)

403 _ = ll.normal()

404 if name:

405 ll.name = str(name)

406 return ll

407

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

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

410 surface) components, I{including height}.

411

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

413 (C{meter}).

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

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

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

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

418

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

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

421 y, z, h)}.

422

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

424 argument.

425 '''

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

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

428 if Nvector is not None:

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

430 return _xnamed(r, self.name)

431

432 def toRepr(self, **kwds):

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

434

435 @kwarg kwds: Optional, keyword arguments.

436

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

438 '''

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

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

441

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

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

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

445

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

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

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

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

450 non-joined).

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

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

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

454 or L{pygeodesy.lonDMS}.

455

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

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

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

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

460 respectively non-empty).

461

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

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

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

465 '''

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

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

468

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

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

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

472 if self.height:

473 t += (self.heightStr(),)

474 if self.name:

475 t += (repr(self.name),)

476 if kwds:

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

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

479

480 @deprecated_method

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

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

483 return self.toRepr(**kwds)

484

485

486 def _isLatLon(inst):

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

488 '''

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

490

491

492 def _isLatLon_(LL):

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

494 '''

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

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

497

498

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

500_ALL_ATTRS_ = tuple(LatLon_(0, 0).__dict__.keys())

501

502

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

504 '''(INTERNAL) Base class.

505 '''

506 _array = []

507 _epsilon = EPS

508 _itemname = _point_

509

510 def _contains(self, point):

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

512 '''

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

514

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

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

517

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

519 shallow copy (C{bool}).

520

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

522 '''

523 return _xcopy(self, deep=deep)

524

525 def _count(self, point):

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

527 '''

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

529

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

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

532

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

534

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

536

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

538 '''

539 if items:

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

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

542 return _xdup(self)

543

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

545 def epsilon(self):

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

547 '''

548 return self._epsilon

549

550 @epsilon.setter # PYCHOK setter!

551 def epsilon(self, tol):

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

553

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

555 '''

556 self._epsilon = Scalar_(tolerance=tol)

557

558 def _find(self, point, start_end):

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

560 '''

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

562 return i

563 return -1

564

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

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

567 '''

568 notImplemented(self, point, start_end)

569

570 def _getitem(self, index):

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

572 '''

573 # Luciano Ramalho, "Fluent Python", O'Reilly, 2016 p. 290+, 2022 p. 405+

574 if isinstance(index, slice):

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

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

577 else:

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

579

580 def _index(self, point, start_end):

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

582 '''

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

584 return i

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

586

587 @property_RO

588 def isNumpy2(self): # PYCHOK no cover

589 '''Is this a Numpy2 wrapper?

590 '''

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

592

593 @property_RO

594 def isPoints2(self): # PYCHOK no cover

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

596 '''

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

598

599 @property_RO

600 def isTuple2(self): # PYCHOK no cover

601 '''Is this a Tuple2 wrapper?

602 '''

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

604

605 def _iter(self):

606 '''(INTERNAL) Yield all points.

607 '''

608 _array, _point = self._array, self.point

609 for i in range(len(self)):

610 yield _point(_array[i])

611

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

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

614

615 @arg attrs: Optional arguments.

616 '''

617 notOverloaded(self, *attrs)

618

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

620 '''(INTERNAL) Return the range.

621 '''

622 if step > 0:

623 if start is None:

624 start = 0

625 if end is None:

626 end = len(self)

627 elif step < 0:

628 if start is None:

629 start = len(self) - 1

630 if end is None:

631 end = -1

632 else:

633 raise _ValueError(step=step)

634 return range(start, end, step)

635

636 def _repr(self):

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

638 '''

639 # XXX use Python 3+ reprlib.repr

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

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

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

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

644

645 def _reversed(self): # PYCHOK false

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

647 '''

648 _array, point = self._array, self.point

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

650 yield point(_array[i])

651

652 def _rfind(self, point, start_end):

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

654 '''

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

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

657

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

659 return i

660 return -1

661

662 def _slicekwds(self): # PYCHOK no cover

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

664 '''

665 return {}

666

667

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

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

670 '''

671 _array = ()

672 _ilat = 0 # row column index

673 _ilon = 0 # row column index

674 _LatLon = LatLon_ # default

675 _shape = ()

676

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

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

679 '''

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

681

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

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

684

685 self._array = array

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

687

688 if LatLon: # check the point class

689 if not _isLatLon_(LatLon):

690 raise _IsnotError(_valid_, LatLon=LatLon)

691 self._LatLon = LatLon

692

693 # check the attr indices

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

695 if not isint(i):

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

697 i = int(i)

698 if not 0 <= i < shape[1]:

699 raise _ValueError(ai, i)

700 for aj, j in ais[:n]:

701 if int(j) == i:

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

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

704

705 def __contains__(self, latlon):

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

707

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

709 C{(lat, lon)}).

710

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

712

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

714 '''

715 return self._contains(latlon)

716

717 def __getitem__(self, index):

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

719 '''

720 return self._getitem(index)

721

722 def __iter__(self):

723 '''Yield rows as C{LatLon}.

724 '''

725 return self._iter()

726

727 def __len__(self):

728 '''Return the number of rows.

729 '''

730 return self._shape[0]

731

732 def __repr__(self):

733 '''Return a string representation.

734 '''

735 return self._repr()

736

737 def __reversed__(self): # PYCHOK false

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

739 '''

740 return self._reversed()

741

742 __str__ = __repr__

743

744 def count(self, latlon):

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

746

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

748 C{(lat, lon)}).

749

750 @return: Count (C{int}).

751

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

753 '''

754 return self._count(latlon)

755

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

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

758

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

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

761

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

763

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

765 '''

766 return self._find(latlon, start_end)

767

768 def _findall(self, latlon, start_end):

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

770 '''

771 try:

772 lat, lon = latlon.lat, latlon.lon

773 except AttributeError:

774 try:

775 lat, lon = latlon

776 except (TypeError, ValueError):

777 raise _IsnotError(_valid_, latlon=latlon)

778

779 _ilat, _ilon = self._ilat, self._ilon

780 _array, _eps = self._array, self._epsilon

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

782 row = _array[i]

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

784 fabs(row[_ilon] - lon) <= _eps:

785 yield i

786

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

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

789

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

791 C{(lat, lon)}).

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

793

794 @return: Indices (C{iterable}).

795

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

797 '''

798 return self._findall(latlon, start_end)

799

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

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

802

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

804 C{(lat, lon)}).

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

806

807 @return: Index (C{int}).

808

809 @raise IndexError: Point not found.

810

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

812 '''

813 return self._index(latlon, start_end)

814

815 @Property_RO

816 def ilat(self):

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

818 '''

819 return self._ilat

820

821 @Property_RO

822 def ilon(self):

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

824 '''

825 return self._ilon

826

827# next = __iter__

828

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

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

831

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

833

834 @return: Point (C{LatLon}).

835 '''

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

837

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

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

840

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

842 C{(lat, lon)}).

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

844

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

846

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

848

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

850 '''

851 return self._rfind(latlon, start_end)

852

853 def _slicekwds(self):

854 '''(INTERNAL) Slice kwds.

855 '''

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

857

858 @Property_RO

859 def shape(self):

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

861 L{Shape2Tuple}C{(nrows, ncols)}.

862 '''

863 return self._shape

864

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

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

867 '''

868 notImplemented(self, indices)

869

870 def subset(self, indices):

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

872

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

874

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

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

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

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

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

880

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

882

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

884

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

886 nor an C{int}[].

887 '''

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

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

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

891

892 n = len(self)

893 for i, v in enumerate(indices):

894 if not isint(v):

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

896 elif not 0 <= v < n:

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

898

899 return self._subset(indices)

900

901

902 class LatLon2psxy(_Basequence):

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

904 '''

905 _closed = False

906 _len = 0

907 _deg2m = None # default, keep degrees

908 _radius = None

909 _wrap = True

910

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

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

913

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

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

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

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

918

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

920 etc. (C{LatLon[]}).

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

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

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

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

925

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

927

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

929 '''

930 self._closed = closed

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

932 if radius:

933 self._radius = r = Radius(radius)

934 self._deg2m = degrees2m(_1_0, r)

935 if not wrap:

936 self._wrap = False

937

938 def __contains__(self, xy):

939 '''Check for a matching point.

940

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

942 C{(x, y)}) in (C{degrees}.

943

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

945

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

947 '''

948 return self._contains(xy)

949

950 def __getitem__(self, index):

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

952 '''

953 return self._getitem(index)

954

955 def __iter__(self):

956 '''Yield all pseudo-xy's.

957 '''

958 return self._iter()

959

960 def __len__(self):

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

962 '''

963 return self._len

964

965 def __repr__(self):

966 '''Return a string representation.

967 '''

968 return self._repr()

969

970 def __reversed__(self): # PYCHOK false

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

972 '''

973 return self._reversed()

974

975 __str__ = __repr__

976

977 def count(self, xy):

978 '''Count the number of matching points.

979

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

981 C{(x, y)}) in (C{degrees}.

982

983 @return: Count (C{int}).

984

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

986 '''

987 return self._count(xy)

988

989 def find(self, xy, *start_end):

990 '''Find the first matching point.

991

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

993 C{(x, y)}) in (C{degrees}.

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

995

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

997

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

999 '''

1000 return self._find(xy, start_end)

1001

1002 def _findall(self, xy, start_end):

1003 '''(INTERNAL) Yield indices of all matching points.

1004 '''

1005 try:

1006 x, y = xy.lon, xy.lat

1007

1008 def _x_y_ll3(ll): # match LatLon

1009 return ll.lon, ll.lat, ll

1010

1011 except AttributeError:

1012 try:

1013 x, y = xy[:2]

1014 except (IndexError, TypeError, ValueError):

1015 raise _IsnotError(_valid_, xy=xy)

1016

1017 _x_y_ll3 = self.point # PYCHOK expected

1018

1019 _array, _eps = self._array, self._epsilon

1020 for i in self._range(*start_end):

1021 xi, yi, _ = _x_y_ll3(_array[i])

1022 if fabs(xi - x) <= _eps and \

1023 fabs(yi - y) <= _eps:

1024 yield i

1025

1026 def findall(self, xy, *start_end):

1027 '''Yield indices of all matching points.

1028

1029 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple

1030 C{(x, y)}) in (C{degrees}.

1031 @arg start_end: Optional C{[start[, end]]} index (C{int}).

1032

1033 @return: Indices (C{iterator}).

1034

1035 @raise TypeError: Invalid B{C{xy}}.

1036 '''

1037 return self._findall(xy, start_end)

1038

1039 def index(self, xy, *start_end): # PYCHOK Python 2- issue

1040 '''Find the first matching point.

1041

1042 @arg xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}).

1043 @arg start_end: Optional C{[start[, end]]} index (C{int}).

1044

1045 @return: Index (C{int}).

1046

1047 @raise IndexError: Point not found.

1048

1049 @raise TypeError: Invalid B{C{xy}}.

1050 '''

1051 return self._index(xy, start_end)

1052

1053 @property_RO

1054 def isPoints2(self):

1055 '''Is this a LatLon2 wrapper/converter?

1056 '''

1057 return True # isinstance(self, (LatLon2psxy, ...))

1058

1059 def point(self, ll): # PYCHOK *attrs

1060 '''Create a pseudo-xy.

1061

1062 @arg ll: Point (C{LatLon}).

1063

1064 @return: An L{Point3Tuple}C{(x, y, ll)}.

1065 '''

1066 x, y = ll.lon, ll.lat # note, x, y = lon, lat

1067 if self._wrap:

1068 y, x = _Wrap.latlon(y, x)

1069 d = self._deg2m

1070 if d: # convert degrees to meter (or radians)

1071 x *= d

1072 y *= d

1073 return Point3Tuple(x, y, ll)

1074

1075 def rfind(self, xy, *start_end):

1076 '''Find the last matching point.

1077

1078 @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple

1079 C{(x, y)}) in (C{degrees}.

1080 @arg start_end: Optional C{[start[, end]]} index (C{int}).

1081

1082 @return: Index or -1 if not found (C{int}).

1083

1084 @raise TypeError: Invalid B{C{xy}}.

1085 '''

1086 return self._rfind(xy, start_end)

1087

1088 def _slicekwds(self):

1089 '''(INTERNAL) Slice kwds.

1090 '''

1091 return dict(closed=self._closed, radius=self._radius, wrap=self._wrap)

1092

1093

1094 class Numpy2LatLon(_Array2LatLon): # immutable, on purpose

1095 '''Wrapper for C{NumPy} arrays as "on-the-fly" C{LatLon} points.

1096 '''

1097 def __init__(self, array, ilat=0, ilon=1, LatLon=None):

1098 '''Handle a C{NumPy} array as a sequence of C{LatLon} points.

1099

1100 @arg array: C{NumPy} array (C{numpy.array}).

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

1102 @kwarg ilon: Optional index of the longitudes column (C{int}).

1103 @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}).

1104

1105 @raise IndexError: If B{C{array.shape}} is not (1+, 2+).

1106

1107 @raise TypeError: If B{C{array}} is not a C{NumPy} array or

1108 C{LatLon} is not a class with C{lat}

1109 and C{lon} attributes.

1110

1111 @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values

1112 are the same or out of range.

1113

1114 @example:

1115

1116 >>> type(array)

1117 <type 'numpy.ndarray'> # <class ...> in Python 3+

1118 >>> points = Numpy2LatLon(array, lat=0, lon=1)

1119 >>> simply = simplifyRDP(points, ...)

1120 >>> type(simply)

1121 <type 'numpy.ndarray'> # <class ...> in Python 3+

1122 >>> sliced = points[1:-1]

1123 >>> type(sliced)

1124 <class '...Numpy2LatLon'>

1125 '''

1126 try: # get shape and check some other numpy.array attrs

1127 s, _, _ = array.shape, array.nbytes, array.ndim # PYCHOK expected

1128 except AttributeError:

1129 raise _IsnotError('NumPy', array=type(array))

1130

1131 _Array2LatLon.__init__(self, array, ilat=ilat, ilon=ilon,

1132 LatLon=LatLon, shape=s)

1133

1134 @property_RO

1135 def isNumpy2(self):

1136 '''Is this a Numpy2 wrapper?

1137 '''

1138 return True # isinstance(self, (Numpy2LatLon, ...))

1139

1140 def _subset(self, indices):

1141 return self._array[indices] # NumPy special

1142

1143

1144 class Shape2Tuple(_NamedTuple):

1145 '''2-Tuple C{(nrows, ncols)}, the number of rows and columns,

1146 both C{int}.

1147 '''

1148 _Names_ = (_nrows_, _ncols_)

1149 _Units_ = ( Number_, Number_)

1150

1151

1152 class Tuple2LatLon(_Array2LatLon):

1153 '''Wrapper for tuple sequences as "on-the-fly" C{LatLon} points.

1154 '''

1155 def __init__(self, tuples, ilat=0, ilon=1, LatLon=None):

1156 '''Handle a list of tuples, each containing a lat- and longitude

1157 and perhaps other values as a sequence of C{LatLon} points.

1158

1159 @arg tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]).

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

1161 @kwarg ilon: Optional index of the longitudes value (C{int}).

1162 @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}).

1163

1164 @raise IndexError: If C{(len(B{tuples}), min(len(t) for t

1165 in B{tuples}))} is not (1+, 2+).

1166

1167 @raise TypeError: If B{C{tuples}} is not a C{list}, C{tuple}

1168 or C{sequence} or if B{C{LatLon}} is not a

1169 C{LatLon} with C{lat}, C{lon} and C{name}

1170 attributes.

1171

1172 @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values

1173 are the same or out of range.

1174

1175 @example:

1176

1177 >>> tuples = [(0, 1), (2, 3), (4, 5)]

1178 >>> type(tuples)

1179 <type 'list'> # <class ...> in Python 3+

1180 >>> points = Tuple2LatLon(tuples, lat=0, lon=1)

1181 >>> simply = simplifyRW(points, 0.5, ...)

1182 >>> type(simply)

1183 <type 'list'> # <class ...> in Python 3+

1184 >>> simply

1185 [(0, 1), (4, 5)]

1186 >>> sliced = points[1:-1]

1187 >>> type(sliced)

1188 <class '...Tuple2LatLon'>

1189 >>> sliced

1190 ...Tuple2LatLon([(2, 3), ...][1], ilat=0, ilon=1)

1191

1192 >>> closest, _ = nearestOn2(LatLon_(2, 1), points, adjust=False)

1193 >>> closest

1194 LatLon_(lat=1.0, lon=2.0)

1195

1196 >>> closest, _ = nearestOn2(LatLon_(3, 2), points)

1197 >>> closest

1198 LatLon_(lat=2.001162, lon=3.001162)

1199 '''

1200 _xinstanceof(list, tuple, tuples=tuples)

1201 s = len(tuples), min(len(_) for _ in tuples)

1202 _Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon,

1203 LatLon=LatLon, shape=s)

1204

1205 @property_RO

1206 def isTuple2(self):

1207 '''Is this a Tuple2 wrapper?

1208 '''

1209 return True # isinstance(self, (Tuple2LatLon, ...))

1210

1211 def _subset(self, indices):

1212 return type(self._array)(self._array[i] for i in indices)

1213

1214

1215 def _area2(points, adjust, wrap):

1216 '''(INTERNAL) Approximate the area in radians squared, I{signed}.

1217 '''

1218 if adjust:

1219 # approximate trapezoid by a rectangle, adjusting

1220 # the top width by the cosine of the latitudinal

1221 # average and bottom width by some fudge factor

1222 def _adjust(w, h):

1223 c = cos(h) if fabs(h) < PI_2 else _0_0

1224 return w * h * (c + 1.2876) * _0_5

1225 else:

1226 def _adjust(w, h): # PYCHOK expected

1227 return w * h

1228

1229 # setting radius=1 converts degrees to radians

1230 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap)

1231 x1, y1, ll = Ps[0]

1232 pts = [ll] # for _areaError

1233

1234 A2 = Fsum() # trapezoidal area in radians**2

1235 for p in Ps.iterate(closed=True):

1236 x2, y2, ll = p

1237 if len(pts) < 4:

1238 pts.append(ll)

1239 w, x2 = unrollPI(x1, x2, wrap=wrap and not Ps.looped)

1240 A2 += _adjust(w, (y2 + y1) * _0_5)

1241 x1, y1 = x2, y2

1242

1243 return A2.fsum(), tuple(pts)

1244

1245

1246 def _areaError(pts, near_=NN): # imported by .ellipsoidalKarney

1247 '''(INTERNAL) Area issue.

1248 '''

1249 t = _ELLIPSIS_(pts[:3], NN)

1250 return _ValueError(NN(near_, 'zero or polar area'), txt=t)

1251

1252

1253 def areaOf(points, adjust=True, radius=R_M, wrap=True):

1254 '''Approximate the area of a polygon or composite.

1255

1256 @arg points: The polygon points or clips (C{LatLon}[],

1257 L{BooleanFHP} or L{BooleanGH}).

1258 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1259 by the cosine of the mean latitude (C{bool}).

1260 @kwarg radius: Mean earth radius (C{meter}) or C{None}.

1261 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1262 the B{C{points}} (C{bool}).

1263

1264 @return: Approximate area (I{square} C{meter}, same units as

1265 B{C{radius}} or C{radians} I{squared} if B{C{radius}}

1266 is C{None}).

1267

1268 @raise PointsError: Insufficient number of B{C{points}}

1269

1270 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1271

1272 @raise ValueError: Invalid B{C{radius}}.

1273

1274 @note: This area approximation has limited accuracy and is

1275 ill-suited for regions exceeding several hundred Km

1276 or Miles or with near-polar latitudes.

1277

1278 @see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf},

1279 L{ellipsoidalExact.areaOf} and L{ellipsoidalKarney.areaOf}.

1280 '''

1281 if _MODS.booleans.isBoolean(points):

1282 a = points._sum1(areaOf, adjust=adjust, radius=None, wrap=wrap)

1283 else:

1284 a, _ = _area2(points, adjust, wrap)

1285 return fabs(a if radius is None else (Radius(radius)**2 * a))

1286

1287

1288 def boundsOf(points, wrap=False, LatLon=None): # was=True

1289 '''Determine the bottom-left SW and top-right NE corners of a

1290 path or polygon.

1291

1292 @arg points: The path or polygon points (C{LatLon}[]).

1293 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1294 the B{C{points}} (C{bool}).

1295 @kwarg LatLon: Optional class to return the C{bounds}

1296 corners (C{LatLon}) or C{None}.

1297

1298 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as

1299 B{C{LatLon}}s if B{C{LatLon}} is C{None} a

1300 L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}.

1301

1302 @raise PointsError: Insufficient number of B{C{points}}

1303

1304 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1305

1306 @see: Function L{quadOf}.

1307

1308 @example:

1309

1310 >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)

1311 >>> boundsOf(b) # False

1312 >>> 45.0, 1.0, 46.0, 2.0

1313 '''

1314 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap)

1315 w, s, _ = e, n, _ = Ps[0]

1316

1317 v = w

1318 for x, y, _ in Ps.iterate(closed=False): # [1:]

1319 if wrap:

1320 _, x = unroll180(v, x, wrap=True)

1321 v = x

1322

1323 if w > x:

1324 w = x

1325 elif e < x:

1326 e = x

1327

1328 if s > y:

1329 s = y

1330 elif n < y:

1331 n = y

1332

1333 return Bounds4Tuple(s, w, n, e) if LatLon is None else \

1334 Bounds2Tuple(LatLon(s, w), LatLon(n, e)) # PYCHOK inconsistent

1335

1336

1337 def _distanceTo(Error, **name_points): # .frechet, .hausdorff, .heights

1338 '''(INTERNAL) Chech callable C{distanceTo} methods.

1339 '''

1340 name, ps = name_points.popitem()

1341 for i, p in enumerate(ps):

1342 if not callable(_xattr(p, distanceTo=None)):

1343 n = _distanceTo.__name__[1:]

1344 t = _SPACE_(_no_, callable.__name__, n)

1345 raise Error(Fmt.SQUARE(name, i), p, txt=t)

1346 return ps

1347

1348

1349 def centroidOf(points, wrap=False, LatLon=None): # was=True

1350 '''Determine the centroid of a polygon.

1351

1352 @arg points: The polygon points (C{LatLon}[]).

1353 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1354 B{C{points}} (C{bool}).

1355 @kwarg LatLon: Optional class to return the centroid (C{LatLon})

1356 or C{None}.

1357

1358 @return: Centroid (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)}

1359 if C{B{LatLon} is None}.

1360

1361 @raise PointsError: Insufficient number of B{C{points}}

1362

1363 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1364

1365 @raise ValueError: The B{C{points}} enclose a pole or

1366 near-zero area.

1367

1368 @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and

1369 Paul Bourke's U{Calculating The Area And Centroid Of A Polygon

1370 <https://www.SEAS.UPenn.edu/~ese502/lab-content/extra_materials/

1371 Polygon%20Area%20and%20Centroid.pdf>}, 1988.

1372 '''

1373 A, X, Y = Fsum(), Fsum(), Fsum()

1374

1375 # setting radius=1 converts degrees to radians

1376 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap)

1377 x1, y1, ll = Ps[0]

1378 pts = [ll] # for _areaError

1379 for p in Ps.iterate(closed=True):

1380 x2, y2, ll = p

1381 if len(pts) < 4:

1382 pts.append(ll)

1383 if wrap and not Ps.looped:

1384 _, x2 = unrollPI(x1, x2, wrap=True)

1385 t = x1 * y2 - x2 * y1

1386 A += t

1387 X += t * (x1 + x2)

1388 Y += t * (y1 + y2)

1389 # XXX more elaborately:

1390 # t1, t2 = x1 * y2, -(x2 * y1)

1391 # A.fadd_(t1, t2)

1392 # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2)

1393 # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2)

1394 x1, y1 = x2, y2

1395

1396 a = A.fmul(_6_0).fover(_2_0)

1397 if isnear0(a):

1398 raise _areaError(pts, near_=_near_)

1399 y, x = degrees90(Y.fover(a)), degrees180(X.fover(a))

1400 return LatLon2Tuple(y, x) if LatLon is None else LatLon(y, x)

1401

1402

1403 def fractional(points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds):

1404 '''Return the point at a given I{fractional} index.

1405

1406 @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[],

1407 L{Tuple2LatLon}[], C{Cartesian}[], C{Vector3d}[],

1408 L{Vector3Tuple}[]).

1409 @arg fi: The fractional index (L{FIx}, C{float} or C{int}).

1410 @kwarg j: Optionally, index of the other point (C{int}).

1411 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1412 B{{points}} (C{bool}) or C{None} for a backward

1413 compatible L{LatLon2Tuple} or B{C{LatLon}} with

1414 averaged lat- and longitudes. Use C{True} or

1415 C{False} to get the I{fractional} point computed

1416 by method C{B{points}[fi].intermediateTo}.

1417 @kwarg LatLon: Optional class to return the I{intermediate},

1418 I{fractional} point (C{LatLon}) or C{None}.

1419 @kwarg Vector: Optional class to return the I{intermediate},

1420 I{fractional} point (C{Cartesian}, C{Vector3d})

1421 or C{None}.

1422 @kwarg kwds: Optional, additional B{C{LatLon}} I{or} B{C{Vector}}

1423 keyword arguments, ignored if both C{B{LatLon}} and

1424 C{B{Vector}} are C{None}.

1425

1426 @return: A L{LatLon2Tuple}C{(lat, lon)} if B{C{wrap}}, B{C{LatLon}}

1427 and B{C{Vector}} all are C{None}, the defaults.

1428

1429 An instance of B{C{LatLon}} if not C{None} I{or} an instance

1430 of B{C{Vector}} if not C{None}.

1431

1432 Otherwise with B{C{wrap}} either C{True} or C{False} and

1433 B{C{LatLon}} and B{C{Vector}} both C{None}, an instance of

1434 B{C{points}}' (sub-)class C{intermediateTo} I{fractional}.

1435

1436 Summarized as follows:

1437

1438 >>> wrap | LatLon | Vector | returned type/value

1439 # -------+--------+--------+--------------+------

1440 # | | | LatLon2Tuple | favg

1441 # None | None | None | or** |

1442 # | | | Vector3Tuple | favg

1443 # None | LatLon | None | LatLon | favg

1444 # None | None | Vector | Vector | favg

1445 # -------+--------+--------+--------------+------

1446 # True | None | None | points' | .iTo

1447 # True | LatLon | None | LatLon | .iTo

1448 # True | None | Vector | Vector | .iTo

1449 # -------+--------+--------+--------------+------

1450 # False | None | None | points' | .iTo

1451 # False | LatLon | None | LatLon | .iTo

1452 # False | None | Vector | Vector | .iTo

1453 # _____

1454 # favg) averaged lat, lon or x, y, z values

1455 # .iTo) value from points[fi].intermediateTo

1456 # **) depends on base class of points[fi]

1457

1458 @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}}

1459 not subscriptable or not closed.

1460

1461 @raise TypeError: Invalid B{C{LatLon}}, B{C{Vector}} or B{C{kwds}}

1462 argument.

1463

1464 @see: Class L{FIx} and method L{FIx.fractional}.

1465 '''

1466 if LatLon and Vector: # PYCHOK no cover

1467 kwds = _xkwds(kwds, fi=fi, LatLon=LatLon, Vector=Vector)

1468 raise _TypeError(txt=fractional.__name__, **kwds)

1469 w = wrap if LatLon else False # intermediateTo

1470 try:

1471 if not isscalar(fi) or fi < 0:

1472 raise IndexError

1473 n = _xattr(fi, fin=0)

1474 p = _fractional(points, fi, j, fin=n, wrap=w) # see .units.FIx

1475 if LatLon:

1476 p = LatLon(p.lat, p.lon, **kwds)

1477 elif Vector:

1478 p = Vector(p.x, p.y, p.z, **kwds)

1479 except (IndexError, TypeError):

1480 raise _IndexError(fi=fi, points=points, wrap=w, txt=fractional.__name__)

1481 return p

1482

1483

1484 def _fractional(points, fi, j, fin=None, wrap=None): # in .frechet.py

1485 '''(INTERNAL) Compute point at L{fractional} index C{fi} and C{j}.

1486 '''

1487 i = int(fi)

1488 p = points[i]

1489 r = fi - float(i)

1490 if r > EPS: # EPS0?

1491 if j is None: # in .frechet.py

1492 j = i + 1

1493 if fin:

1494 j %= fin

1495 q = points[j]

1496 if r >= EPS1: # PYCHOK no cover

1497 p = q

1498 elif wrap is not None: # in (True, False)

1499 p = p.intermediateTo(q, r, wrap=wrap)

1500 elif _isLatLon(p): # backward compatible default

1501 p = LatLon2Tuple(favg(p.lat, q.lat, f=r),

1502 favg(p.lon, q.lon, f=r),

1503 name=fractional.__name__)

1504 else: # assume p and q are cartesian or vectorial

1505 z = p.z if p.z is q.z else favg(p.z, q.z, f=r)

1506 p = Vector3Tuple(favg(p.x, q.x, f=r),

1507 favg(p.y, q.y, f=r), z,

1508 name=fractional.__name__)

1509 return p

1510

1511

1512 def isclockwise(points, adjust=False, wrap=True):

1513 '''Determine the direction of a path or polygon.

1514

1515 @arg points: The path or polygon points (C{LatLon}[]).

1516 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1517 by the cosine of the mean latitude (C{bool}).

1518 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1519 B{C{points}} (C{bool}).

1520

1521 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.

1522

1523 @raise PointsError: Insufficient number of B{C{points}}

1524

1525 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1526

1527 @raise ValueError: The B{C{points}} enclose a pole or zero area.

1528

1529 @example:

1530

1531 >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)

1532 >>> isclockwise(f) # False

1533 >>> isclockwise(reversed(f)) # True

1534 '''

1535 a, pts = _area2(points, adjust, wrap)

1536 if a > 0: # opposite of ellipsoidalExact and -Karney

1537 return True

1538 elif a < 0:

1539 return False

1540 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html>

1541 raise _areaError(pts)

1542

1543

1544 def isconvex(points, adjust=False, wrap=False): # was=True

1545 '''Determine whether a polygon is convex.

1546

1547 @arg points: The polygon points (C{LatLon}[]).

1548 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1549 by the cosine of the mean latitude (C{bool}).

1550 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1551 B{C{points}} (C{bool}).

1552

1553 @return: C{True} if B{C{points}} are convex, C{False} otherwise.

1554

1555 @raise CrossError: Some B{C{points}} are colinear.

1556

1557 @raise PointsError: Insufficient number of B{C{points}}

1558

1559 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1560

1561 @example:

1562

1563 >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)

1564 >>> isconvex(t) # True

1565

1566 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)

1567 >>> isconvex(f) # False

1568 '''

1569 return bool(isconvex_(points, adjust=adjust, wrap=wrap))

1570

1571

1572 def isconvex_(points, adjust=False, wrap=False): # was=True

1573 '''Determine whether a polygon is convex I{and clockwise}.

1574

1575 @arg points: The polygon points (C{LatLon}[]).

1576 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1577 by the cosine of the mean latitude (C{bool}).

1578 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1579 B{C{points}} (C{bool}).

1580

1581 @return: C{+1} if B{C{points}} are convex clockwise, C{-1} for

1582 convex counter-clockwise B{C{points}}, C{0} otherwise.

1583

1584 @raise CrossError: Some B{C{points}} are colinear.

1585

1586 @raise PointsError: Insufficient number of B{C{points}}

1587

1588 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1589

1590 @example:

1591

1592 >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)

1593 >>> isconvex_(t) # +1

1594

1595 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)

1596 >>> isconvex_(f) # 0

1597 '''

1598 if adjust:

1599 def _unroll2(x1, x2, w, y1, y2):

1600 x21, x2 = unroll180(x1, x2, wrap=w)

1601 y = radians(y1 + y2) * _0_5

1602 x21 *= cos(y) if fabs(y) < PI_2 else _0_0

1603 return x21, x2

1604 else:

1605 def _unroll2(x1, x2, w, *unused): # PYCHOK expected

1606 return unroll180(x1, x2, wrap=w)

1607

1608 c, s = crosserrors(), 0

1609

1610 Ps = LatLon2PsxyIter(points, loop=2, wrap=wrap)

1611 x1, y1, _ = Ps[0]

1612 x2, y2, _ = Ps[1]

1613

1614 x21, x2 = _unroll2(x1, x2, False, y1, y2)

1615 for i, p in Ps.enumerate(closed=True):

1616 x3, y3, ll = p

1617 x32, x3 = _unroll2(x2, x3, bool(wrap and not Ps.looped), y2, y3)

1618

1619 # get the sign of the distance from point

1620 # x3, y3 to the line from x1, y1 to x2, y2

1621 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line>

1622 s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2)

1623 if s3 > 0: # x3, y3 on the right

1624 if s < 0: # non-convex

1625 return 0

1626 s = +1

1627

1628 elif s3 < 0: # x3, y3 on the left

1629 if s > 0: # non-convex

1630 return 0

1631 s = -1

1632

1633 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # PYCHOK no cover

1634 # colinear u-turn: x3, y3 not on the

1635 # opposite side of x2, y2 as x1, y1

1636 t = Fmt.SQUARE(points=i)

1637 raise CrossError(t, ll, txt=_colinear_)

1638

1639 x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32

1640

1641 return s # all points on the same side

1642

1643

1644 def isenclosedBy(point, points, wrap=False): # MCCABE 15

1645 '''Determine whether a point is enclosed by a polygon or composite.

1646

1647 @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}).

1648 @arg points: The polygon points or clips (C{LatLon}[], L{BooleanFHP}

1649 or L{BooleanGH}).

1650 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1651 B{C{points}} (C{bool}).

1652

1653 @return: C{True} if the B{C{point}} is inside the polygon or

1654 composite, C{False} otherwise.

1655

1656 @raise PointsError: Insufficient number of B{C{points}}

1657

1658 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1659

1660 @raise ValueError: Invalid B{C{point}}, lat- or longitude.

1661

1662 @see: Functions L{pygeodesy.isconvex} and L{pygeodesy.ispolar} especially

1663 if the B{C{points}} may enclose a pole or wrap around the earth

1664 I{longitudinally}, methods L{sphericalNvector.LatLon.isenclosedBy},

1665 L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop

1666 GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et.al. 2009,

1667 JTECH<https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>}

1668 and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/

1669 10.1175/JTECH-D-11-00019.1>}).

1670 '''

1671 try:

1672 y0, x0 = point.lat, point.lon

1673 except AttributeError:

1674 try:

1675 y0, x0 = map(float, point[:2])

1676 except (IndexError, TypeError, ValueError) as x:

1677 raise _ValueError(point=point, cause=x)

1678

1679 if wrap:

1680 y0, x0 = _Wrap.latlon(y0, x0)

1681

1682 def _dxy3(x, x2, y2, Ps):

1683 dx, x2 = unroll180(x, x2, wrap=not Ps.looped)

1684 return dx, x2, y2

1685

1686 else:

1687 x0 = fmod(x0, _360_0) # not x0 % 360!

1688 x0_180_ = x0 - _180_0

1689 x0_180 = x0 + _180_0

1690

1691 def _dxy3(x1, x, y, unused): # PYCHOK expected

1692 x = _umod_360(float(x))

1693 if x < x0_180_:

1694 x += _360_0

1695 elif x >= x0_180:

1696 x -= _360_0

1697 return (x - x1), x, y

1698

1699 if _MODS.booleans.isBoolean(points):

1700 return points._encloses(y0, x0, wrap=wrap)

1701

1702 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap)

1703 p = Ps[0]

1704 e = m = False

1705 S = Fsum()

1706

1707 _, x1, y1 = _dxy3(x0, p.x, p.y, False)

1708 for p in Ps.iterate(closed=True):

1709 dx, x2, y2 = _dxy3(x1, p.x, p.y, Ps)

1710 # ignore duplicate and near-duplicate pts

1711 if fabs(dx) > EPS or fabs(y2 - y1) > EPS:

1712 # determine if polygon edge (x1, y1)..(x2, y2) straddles

1713 # point (lat, lon) or is on boundary, but do not count

1714 # edges on boundary as more than one crossing

1715 if fabs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1):

1716 m = not m

1717 dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx

1718 if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0):

1719 e = not e

1720

1721 S += sin(radians(y2))

1722 x1, y1 = x2, y2

1723

1724 # An odd number of meridian crossings means, the polygon

1725 # contains a pole. Assume it is the pole on the hemisphere

1726 # containing the polygon mean point and if the polygon does

1727 # contain the North Pole, flip the result.

1728 if m and S.fsum() > 0:

1729 e = not e

1730 return e

1731

1732

1733 def ispolar(points, wrap=False):

1734 '''Check whether a polygon encloses a pole.

1735

1736 @arg points: The polygon points (C{LatLon}[]).

1737 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1738 the B{C{points}} (C{bool}).

1739

1740 @return: C{True} if the polygon encloses a pole, C{False}

1741 otherwise.

1742

1743 @raise PointsError: Insufficient number of B{C{points}}

1744

1745 @raise TypeError: Some B{C{points}} are not C{LatLon} or don't

1746 have C{bearingTo2}, C{initialBearingTo}

1747 and C{finalBearingTo} methods.

1748 '''

1749 def _cds(ps, w): # iterate over course deltas

1750 Ps = PointsIter(ps, loop=2, wrap=w)

1751 p2, p1 = Ps[0:2]

1752 b1, _ = _bearingTo2(p2, p1, wrap=False)

1753 for p2 in Ps.iterate(closed=True):

1754 if not p2.isequalTo(p1, EPS):

1755 if w and not Ps.looped:

1756 p2 = _unrollon(p1, p2)

1757 b, b2 = _bearingTo2(p1, p2, wrap=False)

1758 yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180

1759 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180

1760 p1, b1 = p2, b2

1761

1762 # summation of course deltas around pole is 0° rather than normally ±360°

1763 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html>

1764 s = fsum(_cds(points, wrap), floats=True)

1765 # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90)

1766 return fabs(s) < 90 # "zero-ish"

1767

1768

1769 def luneOf(lon1, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds):

1770 '''Generate an ellipsoidal or spherical U{lune

1771 <https://WikiPedia.org/wiki/Spherical_lune>}-shaped path or polygon.

1772

1773 @arg lon1: Left longitude (C{degrees90}).

1774 @arg lon2: Right longitude (C{degrees90}).

1775 @kwarg closed: Optionally, close the path (C{bool}).

1776 @kwarg LatLon: Class to use (L{LatLon_}).

1777 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}

1778 keyword arguments.

1779

1780 @return: A tuple of 4 or 5 B{C{LatLon}} instances outlining

1781 the lune shape.

1782

1783 @see: U{Latitude-longitude quadrangle

1784 <https://www.MathWorks.com/help/map/ref/areaquad.html>}.

1785 '''

1786 t = (LatLon( _0_0, lon1, **LatLon_kwds),

1787 LatLon( _90_0, lon1, **LatLon_kwds),

1788 LatLon( _0_0, lon2, **LatLon_kwds),

1789 LatLon(_N_90_0, lon2, **LatLon_kwds))

1790 if closed:

1791 t += t[:1]

1792 return t

1793

1794

1795 def nearestOn5(point, points, closed=False, wrap=False, adjust=True,

1796 limit=9, **LatLon_and_kwds):

1797 '''Locate the point on a path or polygon closest to a reference point.

1798

1799 The closest point on each polygon edge is either the nearest of that

1800 edge's end points or a point in between.

1801

1802 @arg point: The reference point (C{LatLon}).

1803 @arg points: The path or polygon points (C{LatLon}[]).

1804 @kwarg closed: Optionally, close the path or polygon (C{bool}).

1805 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1806 B{C{points}} (C{bool}).

1807 @kwarg adjust: See function L{pygeodesy.equirectangular_} (C{bool}).

1808 @kwarg limit: See function L{pygeodesy.equirectangular_} (C{degrees}),

1809 default C{9 degrees} is about C{1,000 Kmeter} (for mean

1810 spherical earth radius L{R_KM}).

1811 @kwarg LatLon_and_kwds: Optional, C{B{LatLon}=None} class to use for

1812 the closest point and additional B{C{LatLon}} keyword

1813 arguments, ignored if C{B{LatLon}=None} or not given.

1814

1815 @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the

1816 {closest} point (B{C{LatLon}}) or if C{B{LatLon} is None},

1817 a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}.

1818 The C{distance} is the L{pygeodesy.equirectangular} distance

1819 between the C{closest} and reference B{C{point}} in C{degrees}.

1820 The C{angle} from the B{C{point}} to the C{closest} is in

1821 compass C{degrees}, like function L{pygeodesy.compassAngle}.

1822

1823 @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}},

1824 see function L{pygeodesy.equirectangular_}.

1825

1826 @raise PointsError: Insufficient number of B{C{points}}

1827

1828 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1829

1830 @note: Distances are I{approximated} by function L{pygeodesy.equirectangular_}.

1831 For more accuracy use one of the C{LatLon.nearestOn6} methods.

1832

1833 @see: Function L{pygeodesy.degrees2m}.

1834 '''

1835 def _d2yx4(p2, p1, u, alw):

1836 # w = wrap if (i < (n - 1) or not closed) else False

1837 # equirectangular_ returns a Distance4Tuple(distance

1838 # in degrees squared, delta lat, delta lon, p2.lon

1839 # unroll/wrap'd); the previous p2.lon unroll/wrap'd

1840 # is also applied to the next edge's p1.lon

1841 return equirectangular_(p1.lat, p1.lon + u,

1842 p2.lat, p2.lon, **alw)

1843

1844 def _h(p): # get height or default 0

1845 return _xattr(p, height=0) or 0

1846

1847 # 3-D version used in .vector3d._nearestOn2

1848 #

1849 # point (x, y) on axis rotated ccw by angle a:

1850 # x' = y * sin(a) + x * cos(a)

1851 # y' = y * cos(a) - x * sin(a)

1852 #

1853 # distance (w) along and (h) perpendicular to

1854 # a line thru point (dx, dy) and the origin:

1855 # w = (y * dy + x * dx) / hypot(dx, dy)

1856 # h = (y * dx - x * dy) / hypot(dx, dy)

1857 #

1858 # closest point on that line thru (dx, dy):

1859 # xc = dx * w / hypot(dx, dy)

1860 # yc = dy * w / hypot(dx, dy)

1861 # or

1862 # xc = dx * f

1863 # yc = dy * f

1864 # with

1865 # f = w / hypot(dx, dy)

1866 # or

1867 # f = (y * dy + x * dx) / hypot2(dx, dy)

1868 #

1869 # i.e. no need for sqrt or hypot

1870

1871 Ps = PointsIter(points, loop=1, wrap=wrap)

1872 p1 = c = Ps[0]

1873 u1 = u = _0_0

1874 kw = dict(adjust=adjust, limit=limit, wrap=False)

1875 d, dy, dx, _ = _d2yx4(p1, point, u1, kw)

1876 for p2 in Ps.iterate(closed=closed):

1877 # iff wrapped, unroll lon1 (actually previous

1878 # lon2) like function unroll180/-PI would've

1879 if wrap:

1880 kw.update(wrap=not (closed and Ps.looped))

1881 d21, y21, x21, u2 = _d2yx4(p2, p1, u1, kw)

1882 if d21 > EPS:

1883 # distance point to p1, y01 and x01 negated

1884 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw)

1885 if d2 > EPS:

1886 w2 = y01 * y21 + x01 * x21

1887 if w2 > 0:

1888 if w2 < d21:

1889 # closest is between p1 and p2, use

1890 # original delta's, not y21 and x21

1891 f = w2 / d21

1892 p1 = LatLon_(favg(p1.lat, p2.lat, f=f),

1893 favg(p1.lon, p2.lon + u2, f=f),

1894 height=favg(_h(p1), _h(p2), f=f))

1895 u1 = _0_0

1896 else: # p2 is closest

1897 p1, u1 = p2, u2

1898 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw)

1899 if d2 < d: # p1 is closer, y01 and x01 negated

1900 c, u, d, dy, dx = p1, u1, d2, -y01, -x01

1901 p1, u1 = p2, u2

1902

1903 a = atan2b(dx, dy)

1904 d = hypot(dx, dy)

1905 h = _h(c)

1906 n = nameof(point) or nearestOn5.__name__

1907 if LatLon_and_kwds:

1908 kwds = _xkwds(LatLon_and_kwds, height=h, name=n)

1909 LL = _xkwds_pop(kwds, LatLon=None)

1910 if LL is not None:

1911 r = LL(c.lat, c.lon + u, **kwds)

1912 return NearestOn3Tuple(r, d, a, name=n)

1913 return NearestOn5Tuple(c.lat, c.lon + u, d, a, h, name=n) # PYCHOK expected

1914

1915

1916 def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True):

1917 '''I{Approximate} the perimeter of a path, polygon. or composite.

1918

1919 @arg points: The path or polygon points or clips (C{LatLon}[],

1920 L{BooleanFHP} or L{BooleanGH}).

1921 @kwarg closed: Optionally, close the path or polygon (C{bool}).

1922 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1923 by the cosine of the mean latitude (C{bool}).

1924 @kwarg radius: Mean earth radius (C{meter}).

1925 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1926 B{C{points}} (C{bool}).

1927

1928 @return: Approximate perimeter (C{meter}, same units as

1929 B{C{radius}}).

1930

1931 @raise PointsError: Insufficient number of B{C{points}}

1932

1933 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1934

1935 @raise ValueError: Invalid B{C{radius}} or C{B{closed}=False} with

1936 C{B{points}} a composite.

1937

1938 @note: This perimeter is based on the L{pygeodesy.equirectangular_}

1939 distance approximation and is ill-suited for regions exceeding

1940 several hundred Km or Miles or with near-polar latitudes.

1941

1942 @see: Functions L{sphericalTrigonometry.perimeterOf} and

1943 L{ellipsoidalKarney.perimeterOf}.

1944 '''

1945 def _degs(ps, c, a, w): # angular edge lengths in degrees

1946 Ps = LatLon2PsxyIter(ps, loop=1) # wrap=w

1947 p1, u = Ps[0], _0_0 # previous x2's unroll/wrap

1948 for p2 in Ps.iterate(closed=c):

1949 if w and c:

1950 w = not Ps.looped

1951 # apply previous x2's unroll/wrap'd to new x1

1952 _, dy, dx, u = equirectangular_(p1.y, p1.x + u,

1953 p2.y, p2.x,

1954 adjust=a, limit=None,

1955 wrap=w) # PYCHOK non-seq

1956 yield hypot(dx, dy)

1957 p1 = p2

1958

1959 if _MODS.booleans.isBoolean(points):

1960 if not closed:

1961 notImplemented(None, closed=closed, points=_composite_)

1962 d = points._sum1(perimeterOf, closed=True, adjust=adjust,

1963 radius=radius, wrap=wrap)

1964 else:

1965 d = fsum(_degs(points, closed, adjust, wrap), floats=True)

1966 return degrees2m(d, radius=radius)

1967

1968

1969 def quadOf(latS, lonW, latN, lonE, closed=False, LatLon=LatLon_, **LatLon_kwds):

1970 '''Generate a quadrilateral path or polygon from two points.

1971

1972 @arg latS: Souther-nmost latitude (C{degrees90}).

1973 @arg lonW: Western-most longitude (C{degrees180}).

1974 @arg latN: Norther-nmost latitude (C{degrees90}).

1975 @arg lonE: Eastern-most longitude (C{degrees180}).

1976 @kwarg closed: Optionally, close the path (C{bool}).

1977 @kwarg LatLon: Class to use (L{LatLon_}).

1978 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}

1979 keyword arguments.

1980

1981 @return: Return a tuple of 4 or 5 B{C{LatLon}} instances

1982 outlining the quadrilateral.

1983

1984 @see: Function L{boundsOf}.

1985 '''

1986 t = (LatLon(latS, lonW, **LatLon_kwds),

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

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

1989 LatLon(latS, lonE, **LatLon_kwds))

1990 if closed:

1991 t += t[:1]

1992 return t

1993

1994

1995__all__ += _ALL_DOCS(_Array2LatLon, _Basequence)

1996

1997# **) MIT License

1998#

1999# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

2000#

2001# Permission is hereby granted, free of charge, to any person obtaining a

2002# copy of this software and associated documentation files (the "Software"),

2003# to deal in the Software without restriction, including without limitation

2004# the rights to use, copy, modify, merge, publish, distribute, sublicense,

2005# and/or sell copies of the Software, and to permit persons to whom the

2006# Software is furnished to do so, subject to the following conditions:

2007#

2008# The above copyright notice and this permission notice shall be included

2009# in all copies or substantial portions of the Software.

2010#

2011# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

2012# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

2013# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

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