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 _xdup, issubclassof, _Sequence, _xcopy, \

30 _xinstanceof, typename

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, parseDMS

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

37 _IsnotError, _TypeError, _ValueError, \

38 _xattr, _xkwds, _xkwds_item2, _xkwds_pop2

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

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

41 from pygeodesy.formy import _bearingTo2, equirectangular4, _spherical_datum

42# from pygeodesy.internals import typename # from .basics

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

44 _DEQUALSPACED_, _ELLIPSIS_, _EW_, _immutable_, \

45 _near_, _no_, _NS_, _point_, _SPACE_, _UNDER_, \

46 _valid_ # _lat_, _lon_

47 from pygeodesy.iters import LatLon2PsxyIter, PointsIter, points2

48 from pygeodesy.latlonBase import LatLonBase, _latlonheight3, \

49 _ALL_DOCS, _ALL_LAZY, _MODS

50# from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS

51 from pygeodesy.named import classname, _NamedTuple, nameof, \

52 notImplemented, notOverloaded

53 from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, LatLon2Tuple, \

54 NearestOn3Tuple, NearestOn5Tuple, \

55 Point3Tuple, Vector3Tuple, \

56 PhiLam2Tuple # PYCHOK shared

57 from pygeodesy.props import Property_RO, property_doc_, property_RO

58 from pygeodesy.streprs import Fmt, instr

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

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

61 unroll180, _unrollon, unrollPI, _Wrap, wrap180

62

63 from math import cos, fabs, fmod as _fmod, radians, sin

64

65__all__ = _ALL_LAZY.points

66__version__ = '25.04.18'

67

68_ilat_ = 'ilat'

69_ilon_ = 'ilon'

70_ncols_ = 'ncols'

71_nrows_ = 'nrows'

72

73

74 class LatLon_(LatLonBase): # XXX in heights._HeightBase.height

75 '''Low-overhead C{LatLon} class, mainly for L{Numpy2LatLon} and L{Tuple2LatLon}.

76 '''

77 # __slots__ efficiency is voided if the __slots__ class attribute is

78 # used in a subclass of a class with the traditional __dict__, @see

79 # <https://docs.Python.org/2/reference/datamodel.html#slots> plus ...

80 #

81 # __slots__ must be repeated in sub-classes, @see Luciano Ramalho,

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

83 # 2nd Ed, 2022 p. 390 "Summarizing the Issues with __slots__".

84 #

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

86 # Property_RO = property_RO # no __dict__ with __slots__!

87 #

88 # In addition, both size and overhead have shrunk in recent Python:

89 #

90 # sys.getsizeof(LatLon_(1, 2)) is 72-88 I{with} __slots__, but

91 # only 48-56 bytes I{without in Python 2.7.18+ and Python 3+}.

92 #

93 # python3 -m timeit -s "from pygeodesy... import LatLonBase as LL" "LL(0, 0)" 2.14 usec

94 # python3 -m timeit -s "from pygeodesy import LatLon_" "LatLon_(0, 0)" 216 nsec

95

96 def __init__(self, latlonh, lon=None, height=0, wrap=False, datum=None, **name):

97 '''New L{LatLon_}.

98

99 @note: The lat- and longitude values are taken I{as-given,

100 un-clipped and un-validated}.

101

102 @see: L{latlonBase.LatLonBase} for further details.

103 '''

104 if name:

105 self.name = name

106

107 if lon is None: # PYCHOK no cover

108 lat, lon, height = _latlonheight3(latlonh, height, wrap)

109 elif wrap: # PYCHOK no cover

110 lat, lon = _Wrap.latlonDMS2(latlonh, lon)

111 else: # must be latNS, lonEW

112 try:

113 lat, lon = float(latlonh), float(lon)

114 except (TypeError, ValueError):

115 lat = parseDMS(latlonh, suffix=_NS_)

116 lon = parseDMS(lon, suffix=_EW_)

117

118 # get the minimal __dict__, see _isLatLon_ below

119 self._lat = lat # un-clipped and ...

120 self._lon = lon # ... un-validated

121 self._datum = None if datum is None else \

122 _spherical_datum(datum, name=self.name)

123 self._height = height

124

125 def __eq__(self, other):

126 return isinstance(other, LatLon_) and \

127 other.lat == self.lat and \

128 other.lon == self.lon

129

130 def __ne__(self, other):

131 return not self.__eq__(other)

132

133 @Property_RO

134 def datum(self):

135 '''Get the C{datum} (L{Datum}) or C{None}.

136 '''

137 return self._datum

138

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

140 '''Locate the point at a given fraction, I{linearly} between

141 (or along) this and an other point.

142

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

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

145 0.0 for this and 1.0 for the other point).

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

147 intermediate height.

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

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

150

151 @return: Intermediate point (same C{LatLon} class).

152

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

154 '''

155 f = Scalar(fraction=fraction)

156 if isnear0(f):

157 r = self

158 else:

159 r = self.others(other)

160 if wrap or not isnear1(f):

161 _, lat, lon = _Wrap.latlon3(self.lon, r.lat, r.lon, wrap)

162 lat = favg(self.lat, lat, f=f)

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

164 h = height if height is not None else \

165 favg(self.height, r.height, f=f)

166 # = self._havg(r, f=f, h=height)

167 r = self.classof(lat, lon, height=h, datum=r.datum,

168 name=typename(r.intermediateTo))

169 return r

170

171 def toRepr(self, **kwds):

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

173 ignoring keyword argument C{B{std}=N/A}.

174

175 @see: L{latlonBase.LatLonBase.toRepr} for further details.

176 '''

177 _, kwds = _xkwds_pop2(kwds, std=NotImplemented)

178 return LatLonBase.toRepr(self, **kwds)

179

180 def toStr(self, form=F_D, joined=_COMMASPACE_, **m_prec_sep_s_D_M_S): # PYCHOK expected

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

182 string, formatted in the given C{B{form}at}.

183

184 @see: L{latlonBase.LatLonBase.toStr} for further details.

185 '''

186 t = LatLonBase.toStr(self, form=form, joined=NN,

187 **_xkwds(m_prec_sep_s_D_M_S, m=NN))

188 if self.name:

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

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

191

192

193 def _isLatLon(inst):

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

195 '''

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

197

198

199 def _isLatLon_(LL):

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

201 '''

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

203 all(hasattr(LL, _) for _ in LatLon_(0, 0).__dict__.keys()))

204

205

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

207 '''(INTERNAL) Base class.

208 '''

209 _array = []

210 _epsilon = EPS

211 _itemname = _point_

212

213 def _contains(self, point):

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

215 '''

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

217

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

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

220

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

222 shallow copy (C{bool}).

223

224 @return: The copy (C{This class}).

225 '''

226 return _xcopy(self, deep=deep)

227

228 def _count(self, point):

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

230 '''

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

232

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

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

235

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

237

238 @return: The duplicate (C{This class}).

239

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

241 '''

242 if items:

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

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

245 return _xdup(self)

246

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

248 def epsilon(self):

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

250 '''

251 return self._epsilon

252

253 @epsilon.setter # PYCHOK setter!

254 def epsilon(self, tol):

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

256

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

258 '''

259 self._epsilon = Scalar_(tolerance=tol)

260

261 def _find(self, point, start_end):

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

263 '''

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

265 return i

266 return -1

267

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

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

270 notImplemented(self, point, start_end)

271

272 def _getitem(self, index):

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

274 '''

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

276 if isinstance(index, slice):

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

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

279 else:

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

281

282 def _index(self, point, start_end):

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

284 '''

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

286 return i

287 raise _IndexError(self._itemname, point, txt_not_='found')

288

289 @property_RO

290 def isNumpy2(self): # PYCHOK no cover

291 '''Is this a Numpy2 wrapper?

292 '''

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

294

295 @property_RO

296 def isPoints2(self): # PYCHOK no cover

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

298 '''

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

300

301 @property_RO

302 def isTuple2(self): # PYCHOK no cover

303 '''Is this a Tuple2 wrapper?

304 '''

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

306

307 def _iter(self):

308 '''(INTERNAL) Yield all points.

309 '''

310 _array, _point = self._array, self.point

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

312 yield _point(_array[i])

313

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

315 '''I{Must be overloaded}.'''

316 notOverloaded(self, *attrs)

317

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

319 '''(INTERNAL) Return the range.

320 '''

321 if step > 0:

322 if start is None:

323 start = 0

324 if end is None:

325 end = len(self)

326 elif step < 0:

327 if start is None:

328 start = len(self) - 1

329 if end is None:

330 end = -1

331 else:

332 raise _ValueError(step=step)

333 return range(start, end, step)

334

335 def _repr(self):

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

337 '''

338 # XXX use Python 3+ reprlib.repr

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

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

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

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

343

344 def _reversed(self): # PYCHOK false

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

346 '''

347 _array, point = self._array, self.point

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

349 yield point(_array[i])

350

351 def _rfind(self, point, start_end):

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

353 '''

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

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

356

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

358 return i

359 return -1

360

361 def _slicekwds(self): # PYCHOK no cover

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

363 '''

364 return {}

365

366

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

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

369 '''

370 _array = ()

371 _ilat = 0 # row column index

372 _ilon = 0 # row column index

373 _LatLon = LatLon_ # default

374 _shape = ()

375

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

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

378 '''

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

380

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

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

383

384 self._array = array

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

386

387 if LatLon: # check the point class

388 if not _isLatLon_(LatLon):

389 raise _IsnotError(_valid_, LatLon=LatLon)

390 self._LatLon = LatLon

391

392 # check the attr indices

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

394 if not isint(i):

395 raise _IsnotError(int, **{ai: i})

396 i = int(i)

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

398 raise _ValueError(ai, i)

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

400 if int(j) == i:

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

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

403

404 def __contains__(self, latlon):

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

406

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

408 C{(lat, lon)}).

409

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

411

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

413 '''

414 return self._contains(latlon)

415

416 def __getitem__(self, index):

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

418 '''

419 return self._getitem(index)

420

421 def __iter__(self):

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

423 '''

424 return self._iter()

425

426 def __len__(self):

427 '''Return the number of rows.

428 '''

429 return self._shape[0]

430

431 def __repr__(self):

432 '''Return a string representation.

433 '''

434 return self._repr()

435

436 def __reversed__(self): # PYCHOK false

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

438 '''

439 return self._reversed()

440

441 __str__ = __repr__

442

443 def count(self, latlon):

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

445

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

447 C{(lat, lon)}).

448

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

450

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

452 '''

453 return self._count(latlon)

454

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

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

457

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

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

460

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

462

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

464 '''

465 return self._find(latlon, start_end)

466

467 def _findall(self, latlon, start_end):

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

469 '''

470 try:

471 lat, lon = latlon.lat, latlon.lon

472 except AttributeError:

473 try:

474 lat, lon = latlon

475 except (TypeError, ValueError):

476 raise _IsnotError(_valid_, latlon=latlon)

477

478 _ilat, _ilon = self._ilat, self._ilon

479 _array, _eps = self._array, self._epsilon

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

481 row = _array[i]

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

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

484 yield i

485

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

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

488

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

490 C{(lat, lon)}).

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

492

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

494

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

496 '''

497 return self._findall(latlon, start_end)

498

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

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

501

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

503 C{(lat, lon)}).

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

505

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

507

508 @raise IndexError: Point not found.

509

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

511 '''

512 return self._index(latlon, start_end)

513

514 @Property_RO

515 def ilat(self):

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

517 '''

518 return self._ilat

519

520 @Property_RO

521 def ilon(self):

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

523 '''

524 return self._ilon

525

526# next = __iter__

527

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

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

530

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

532

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

534 '''

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

536

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

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

539

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

541 C{(lat, lon)}).

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

543

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

545

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

547

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

549 '''

550 return self._rfind(latlon, start_end)

551

552 def _slicekwds(self):

553 '''(INTERNAL) Slice kwds.

554 '''

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

556

557 @Property_RO

558 def shape(self):

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

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

561 '''

562 return self._shape

563

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

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

566 notImplemented(self, indices)

567

568 def subset(self, indices):

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

570

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

572

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

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

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

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

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

578

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

580

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

582

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

584 nor an C{int}[].

585 '''

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

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

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

589

590 n = len(self)

591 for i, v in enumerate(indices):

592 if not isint(v):

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

594 elif not 0 <= v < n:

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

596

597 return self._subset(indices)

598

599

600 class LatLon2psxy(_Basequence):

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

602 '''

603 _closed = False

604 _len = 0

605 _deg2m = None # default, keep degrees

606 _radius = None

607 _wrap = True

608

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

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

611

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

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

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

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

616

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

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

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

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

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

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

623

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

625

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

627 '''

628 self._closed = closed

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

630 if radius:

631 self._radius = r = Radius(radius)

632 self._deg2m = degrees2m(_1_0, r)

633 if not wrap:

634 self._wrap = False

635

636 def __contains__(self, xy):

637 '''Check for a matching point.

638

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

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

641

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

643

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

645 '''

646 return self._contains(xy)

647

648 def __getitem__(self, index):

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

650 '''

651 return self._getitem(index)

652

653 def __iter__(self):

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

655 '''

656 return self._iter()

657

658 def __len__(self):

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

660 '''

661 return self._len

662

663 def __repr__(self):

664 '''Return a string representation.

665 '''

666 return self._repr()

667

668 def __reversed__(self): # PYCHOK false

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

670 '''

671 return self._reversed()

672

673 __str__ = __repr__

674

675 def count(self, xy):

676 '''Count the number of matching points.

677

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

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

680

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

682

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

684 '''

685 return self._count(xy)

686

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

688 '''Find the first matching point.

689

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

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

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

693

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

695

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

697 '''

698 return self._find(xy, start_end)

699

700 def _findall(self, xy, start_end):

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

702 '''

703 try:

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

705

706 def _x_y_ll3(ll): # match LatLon

707 return ll.lon, ll.lat, ll

708

709 except AttributeError:

710 try:

711 x, y = xy[:2]

712 except (IndexError, TypeError, ValueError):

713 raise _IsnotError(_valid_, xy=xy)

714

715 _x_y_ll3 = self.point # PYCHOK expected

716

717 _array, _eps = self._array, self._epsilon

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

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

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

721 fabs(yi - y) <= _eps:

722 yield i

723

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

725 '''Yield indices of all matching points.

726

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

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

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

730

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

732

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

734 '''

735 return self._findall(xy, start_end)

736

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

738 '''Find the first matching point.

739

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

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

742

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

744

745 @raise IndexError: Point not found.

746

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

748 '''

749 return self._index(xy, start_end)

750

751 @property_RO

752 def isPoints2(self):

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

754 '''

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

756

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

758 '''Create a pseudo-xy.

759

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

761

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

763 '''

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

765 if self._wrap:

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

767 d = self._deg2m

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

769 x *= d

770 y *= d

771 return Point3Tuple(x, y, ll)

772

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

774 '''Find the last matching point.

775

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

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

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

779

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

781

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

783 '''

784 return self._rfind(xy, start_end)

785

786 def _slicekwds(self):

787 '''(INTERNAL) Slice kwds.

788 '''

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

790

791

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

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

794 '''

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

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

797

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

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

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

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

802

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

804

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

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

807 and C{lon} attributes.

808

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

810 are the same or out of range.

811

812 @example:

813

814 >>> type(array)

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

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

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

818 >>> type(simply)

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

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

821 >>> type(sliced)

822 <class '...Numpy2LatLon'>

823 '''

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

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

826 except AttributeError:

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

828

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

830 LatLon=LatLon, shape=s)

831

832 @property_RO

833 def isNumpy2(self):

834 '''Is this a Numpy2 wrapper?

835 '''

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

837

838 def _subset(self, indices):

839 return self._array[indices] # NumPy special

840

841

842 class Shape2Tuple(_NamedTuple):

843 '''2-Tuple C{(nrows, ncols)}, the number of rows and columns,

844 both C{int}.

845 '''

846 _Names_ = (_nrows_, _ncols_)

847 _Units_ = ( Number_, Number_)

848

849

850 class Tuple2LatLon(_Array2LatLon):

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

852 '''

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

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

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

856

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

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

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

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

861

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

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

864

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

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

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

868 attributes.

869

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

871 are the same or out of range.

872

873 @example:

874

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

876 >>> type(tuples)

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

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

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

880 >>> type(simply)

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

882 >>> simply

883 [(0, 1), (4, 5)]

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

885 >>> type(sliced)

886 <class '...Tuple2LatLon'>

887 >>> sliced

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

889

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

891 >>> closest

892 LatLon_(lat=1.0, lon=2.0)

893

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

895 >>> closest

896 LatLon_(lat=2.001162, lon=3.001162)

897 '''

898 _xinstanceof(list, tuple, tuples=tuples)

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

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

901 LatLon=LatLon, shape=s)

902

903 @property_RO

904 def isTuple2(self):

905 '''Is this a Tuple2 wrapper?

906 '''

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

908

909 def _subset(self, indices):

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

911

912

913 def _area2(points, adjust, wrap):

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

915 '''

916 if adjust:

917 # approximate trapezoid by a rectangle, adjusting

918 # the top width by the cosine of the latitudinal

919 # average and bottom width by some fudge factor

920 def _adjust(w, h):

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

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

923 else:

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

925 return w * h

926

927 # setting radius=1 converts degrees to radians

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

929 x1, y1, ll = Ps[0]

930 pts = [ll] # for _areaError

931

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

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

934 x2, y2, ll = p

935 if len(pts) < 4:

936 pts.append(ll)

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

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

939 x1, y1 = x2, y2

940

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

942

943

944 def _areaError(pts, near_=NN): # in .ellipsoidalKarney

945 '''(INTERNAL) Area issue.

946 '''

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

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

949

950

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

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

953

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

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

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

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

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

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

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

961

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

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

964 is None}).

965

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

967

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

969

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

971

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

973 ill-suited for regions exceeding several hundred Km

974 or Miles or with near-polar latitudes.

975

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

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

978 '''

979 if _MODS.booleans.isBoolean(points):

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

981 else:

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

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

984

985

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

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

988 path or polygon.

989

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

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

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

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

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

995

996 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, each

997 a B{C{LatLon}} or if C{B{LatLon} is None}, a

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

999

1000 @raise PointsError: Insufficient number of B{C{points}}

1001

1002 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1003

1004 @see: Function L{quadOf}.

1005 '''

1006 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap)

1007 w, s, _ = e, n, _ = Ps[0]

1008

1009 v = w

1010 for x, y, _ in Ps.iterate(closed=False): # [1:]

1011 if wrap:

1012 _, x = unroll180(v, x, wrap=True)

1013 v = x

1014

1015 if w > x:

1016 w = x

1017 elif e < x:

1018 e = x

1019

1020 if s > y:

1021 s = y

1022 elif n < y:

1023 n = y

1024

1025 return Bounds4Tuple(s, w, n, e) if LatLon is None else \

1026 Bounds2Tuple(LatLon(s, w), LatLon(n, e)) # PYCHOK inconsistent

1027

1028

1029 def centroidOf(points, wrap=False, LatLon=None): # was=True

1030 '''Determine the centroid of a polygon.

1031

1032 @arg points: The polygon points (C{LatLon}[]).

1033 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1034 B{C{points}} (C{bool}).

1035 @kwarg LatLon: Optional class to return the centroid (C{LatLon})

1036 or C{None}.

1037

1038 @return: Centroid (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)}

1039 if C{B{LatLon} is None}.

1040

1041 @raise PointsError: Insufficient number of B{C{points}}

1042

1043 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1044

1045 @raise ValueError: The B{C{points}} enclose a pole or

1046 near-zero area.

1047

1048 @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and

1049 Paul Bourke's U{Calculating The Area And Centroid Of A Polygon

1050 <https://www.SEAS.UPenn.edu/~ese502/lab-content/extra_materials/

1051 Polygon%20Area%20and%20Centroid.pdf>}, 1988.

1052 '''

1053 A, X, Y = Fsum(), Fsum(), Fsum()

1054

1055 # setting radius=1 converts degrees to radians

1056 Ps = LatLon2PsxyIter(points, loop=1, radius=_1_0, wrap=wrap)

1057 x1, y1, ll = Ps[0]

1058 pts = [ll] # for _areaError

1059 for p in Ps.iterate(closed=True):

1060 x2, y2, ll = p

1061 if len(pts) < 4:

1062 pts.append(ll)

1063 if wrap and not Ps.looped:

1064 _, x2 = unrollPI(x1, x2, wrap=True)

1065 t = x1 * y2 - x2 * y1

1066 A += t

1067 X += t * (x1 + x2)

1068 Y += t * (y1 + y2)

1069 # XXX more elaborately:

1070 # t1, t2 = x1 * y2, -(x2 * y1)

1071 # A.fadd_(t1, t2)

1072 # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2)

1073 # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2)

1074 x1, y1 = x2, y2

1075

1076 a = A.fmul(_6_0).fover(_2_0)

1077 if isnear0(a):

1078 raise _areaError(pts, near_=_near_)

1079 y, x = degrees90(Y.fover(a)), degrees180(X.fover(a))

1080 return LatLon2Tuple(y, x) if LatLon is None else LatLon(y, x)

1081

1082

1083 def _distanceTo(Error, **name_points): # .frechet, .hausdorff, .heights

1084 '''(INTERNAL) Check all callable C{distanceTo} methods.

1085 '''

1086 name, ps = _xkwds_item2(name_points)

1087 for i, p in enumerate(ps):

1088 if not callable(_xattr(p, distanceTo=None)):

1089 n = typename(_distanceTo)[1:]

1090 t = _SPACE_(_no_, typename(callable), n)

1091 raise Error(Fmt.SQUARE(name, i), p, txt=t)

1092 return ps

1093

1094

1095 def fractional(points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds):

1096 '''Return the point at a given I{fractional} index.

1097

1098 @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[],

1099 L{Tuple2LatLon}[], C{Cartesian}[], C{Vector3d}[],

1100 L{Vector3Tuple}[]).

1101 @arg fi: The fractional index (L{FIx}, C{float} or C{int}).

1102 @kwarg j: Optionally, index of the other point (C{int}).

1103 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1104 B{{points}} (C{bool}) or C{None} for a backward

1105 compatible L{LatLon2Tuple} or B{C{LatLon}} with

1106 averaged lat- and longitudes. Use C{True} or

1107 C{False} to get the I{fractional} point computed

1108 by method C{B{points}[fi].intermediateTo}.

1109 @kwarg LatLon: Optional class to return the I{intermediate},

1110 I{fractional} point (C{LatLon}) or C{None}.

1111 @kwarg Vector: Optional class to return the I{intermediate},

1112 I{fractional} point (C{Cartesian}, C{Vector3d})

1113 or C{None}.

1114 @kwarg kwds: Optional, additional B{C{LatLon}} I{or} B{C{Vector}}

1115 keyword arguments, ignored if both C{B{LatLon}} and

1116 C{B{Vector}} are C{None}.

1117

1118 @return: A L{LatLon2Tuple}C{(lat, lon)} if B{C{wrap}}, B{C{LatLon}}

1119 and B{C{Vector}} all are C{None}, the defaults.

1120

1121 An instance of B{C{LatLon}} if not C{None} I{or} an instance

1122 of B{C{Vector}} if not C{None}.

1123

1124 Otherwise with B{C{wrap}} either C{True} or C{False} and

1125 B{C{LatLon}} and B{C{Vector}} both C{None}, an instance of

1126 B{C{points}}' (sub-)class C{intermediateTo} I{fractional}.

1127

1128 Summarized as follows:

1129

1130 >>> wrap | LatLon | Vector | returned type/value

1131 # -------+--------+--------+--------------+------

1132 # | | | LatLon2Tuple | favg

1133 # None | None | None | or** |

1134 # | | | Vector3Tuple | favg

1135 # None | LatLon | None | LatLon | favg

1136 # None | None | Vector | Vector | favg

1137 # -------+--------+--------+--------------+------

1138 # True | None | None | points' | .iTo

1139 # True | LatLon | None | LatLon | .iTo

1140 # True | None | Vector | Vector | .iTo

1141 # -------+--------+--------+--------------+------

1142 # False | None | None | points' | .iTo

1143 # False | LatLon | None | LatLon | .iTo

1144 # False | None | Vector | Vector | .iTo

1145 # _____

1146 # favg) averaged lat, lon or x, y, z values

1147 # .iTo) value from points[fi].intermediateTo

1148 # **) depends on base class of points[fi]

1149

1150 @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}}

1151 not subscriptable or not closed.

1152

1153 @raise TypeError: Invalid B{C{LatLon}}, B{C{Vector}} or B{C{kwds}}

1154 argument.

1155

1156 @see: Class L{FIx} and method L{FIx.fractional}.

1157 '''

1158 if LatLon and Vector: # PYCHOK no cover

1159 kwds = _xkwds(kwds, fi=fi, LatLon=LatLon, Vector=Vector)

1160 raise _TypeError(txt__=fractional, **kwds)

1161 w = wrap if LatLon else False # intermediateTo

1162 try:

1163 if (not isscalar(fi)) or fi < 0:

1164 raise IndexError

1165 n = _xattr(fi, fin=0)

1166 p = _fractional(points, fi, j, fin=n, wrap=w) # see .units.FIx

1167 if LatLon:

1168 p = LatLon(p.lat, p.lon, **kwds)

1169 elif Vector:

1170 p = Vector(p.x, p.y, p.z, **kwds)

1171 except (IndexError, TypeError):

1172 raise _IndexError(fi=fi, points=points, wrap=w, txt__=fractional)

1173 return p

1174

1175

1176 def _fractional(points, fi, j, fin=None, wrap=None, dup=False): # in .frechet.py

1177 '''(INTERNAL) Compute point at L{fractional} index C{fi} and C{j}.

1178 '''

1179 i = int(fi)

1180 p = points[i]

1181 r = fi - float(i)

1182 if r > EPS: # EPS0?

1183 if j is None: # in .frechet.py

1184 j = i + 1

1185 if fin:

1186 j %= fin

1187 q = points[j]

1188 if r >= EPS1: # PYCHOK no cover

1189 p = q

1190 elif wrap is not None: # isbool(wrap)

1191 p = p.intermediateTo(q, r, wrap=wrap)

1192 elif _isLatLon(p): # backward compatible default

1193 t = LatLon2Tuple(favg(p.lat, q.lat, f=r),

1194 favg(p.lon, q.lon, f=r),

1195 name__=fractional)

1196 p = p.dup(lat=t.lat, lon=t.lon, name=t.name) if dup else t # PYCHOK lat, lon

1197 else: # assume p and q are cartesian or vectorial

1198 z = p.z if p.z is q.z else favg(p.z, q.z, f=r)

1199 p = Vector3Tuple(favg(p.x, q.x, f=r),

1200 favg(p.y, q.y, f=r), z,

1201 name__=fractional)

1202 return p

1203

1204

1205 def isclockwise(points, adjust=False, wrap=True):

1206 '''Determine the direction of a path or polygon.

1207

1208 @arg points: The path or polygon points (C{LatLon}[]).

1209 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1210 by the cosine of the mean latitude (C{bool}).

1211 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1212 B{C{points}} (C{bool}).

1213

1214 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.

1215

1216 @raise PointsError: Insufficient number of B{C{points}}

1217

1218 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1219

1220 @raise ValueError: The B{C{points}} enclose a pole or zero area.

1221 '''

1222 a, pts = _area2(points, adjust, wrap)

1223 if a > 0: # opposite of ellipsoidalExact and -Karney

1224 return True

1225 elif a < 0:

1226 return False

1227 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html>

1228 raise _areaError(pts)

1229

1230

1231 def isconvex(points, adjust=False, wrap=False): # was=True

1232 '''Determine whether a polygon is convex.

1233

1234 @arg points: The polygon points (C{LatLon}[]).

1235 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1236 by the cosine of the mean latitude (C{bool}).

1237 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1238 B{C{points}} (C{bool}).

1239

1240 @return: C{True} if B{C{points}} are convex, C{False} otherwise.

1241

1242 @raise CrossError: Some B{C{points}} are colinear.

1243

1244 @raise PointsError: Insufficient number of B{C{points}}

1245

1246 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1247 '''

1248 return bool(isconvex_(points, adjust=adjust, wrap=wrap))

1249

1250

1251 def isconvex_(points, adjust=False, wrap=False): # was=True

1252 '''Determine whether a polygon is convex I{and clockwise}.

1253

1254 @arg points: The polygon points (C{LatLon}[]).

1255 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1256 by the cosine of the mean latitude (C{bool}).

1257 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1258 B{C{points}} (C{bool}).

1259

1260 @return: C{+1} if B{C{points}} are convex clockwise, C{-1} for

1261 convex counter-clockwise B{C{points}}, C{0} otherwise.

1262

1263 @raise CrossError: Some B{C{points}} are colinear.

1264

1265 @raise PointsError: Insufficient number of B{C{points}}

1266

1267 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1268 '''

1269 if adjust:

1270 def _unroll2(x1, x2, w, y1, y2):

1271 x21, x2 = unroll180(x1, x2, wrap=w)

1272 y = radians(y1 + y2) * _0_5

1273 x21 *= cos(y) if fabs(y) < PI_2 else _0_0

1274 return x21, x2

1275 else:

1276 def _unroll2(x1, x2, w, *unused): # PYCHOK expected

1277 return unroll180(x1, x2, wrap=w)

1278

1279 c, s = crosserrors(), 0

1280

1281 Ps = LatLon2PsxyIter(points, loop=2, wrap=wrap)

1282 x1, y1, _ = Ps[0]

1283 x2, y2, _ = Ps[1]

1284

1285 x21, x2 = _unroll2(x1, x2, False, y1, y2)

1286 for i, p in Ps.enumerate(closed=True):

1287 x3, y3, ll = p

1288 x32, x3 = _unroll2(x2, x3, bool(wrap and not Ps.looped), y2, y3)

1289

1290 # get the sign of the distance from point

1291 # x3, y3 to the line from x1, y1 to x2, y2

1292 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line>

1293 s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2)

1294 if s3 > 0: # x3, y3 on the right

1295 if s < 0: # non-convex

1296 return 0

1297 s = +1

1298

1299 elif s3 < 0: # x3, y3 on the left

1300 if s > 0: # non-convex

1301 return 0

1302 s = -1

1303

1304 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # PYCHOK no cover

1305 # colinear u-turn: x3, y3 not on the

1306 # opposite side of x2, y2 as x1, y1

1307 t = Fmt.SQUARE(points=i)

1308 raise CrossError(t, ll, txt=_colinear_)

1309

1310 x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32

1311

1312 return s # all points on the same side

1313

1314

1315 def isenclosedBy(point, points, wrap=False): # MCCABE 15

1316 '''Determine whether a point is enclosed by a polygon or composite.

1317

1318 @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}).

1319 @arg points: The polygon points or clips (C{LatLon}[], L{BooleanFHP}

1320 or L{BooleanGH}).

1321 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1322 B{C{points}} (C{bool}).

1323

1324 @return: C{True} if the B{C{point}} is inside the polygon or

1325 composite, C{False} otherwise.

1326

1327 @raise PointsError: Insufficient number of B{C{points}}

1328

1329 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1330

1331 @raise ValueError: Invalid B{C{point}}, lat- or longitude.

1332

1333 @see: Functions L{pygeodesy.isconvex} and L{pygeodesy.ispolar} especially

1334 if the B{C{points}} may enclose a pole or wrap around the earth

1335 I{longitudinally}, methods L{sphericalNvector.LatLon.isenclosedBy},

1336 L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop

1337 GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et.al. 2009,

1338 JTECH<https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>}

1339 and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/

1340 10.1175/JTECH-D-11-00019.1>}).

1341 '''

1342 try:

1343 y0, x0 = point.lat, point.lon

1344 except AttributeError:

1345 try:

1346 y0, x0 = map(float, point[:2])

1347 except (IndexError, TypeError, ValueError) as x:

1348 raise _ValueError(point=point, cause=x)

1349

1350 if wrap:

1351 y0, x0 = _Wrap.latlon(y0, x0)

1352

1353 def _dxy3(x, x2, y2, Ps):

1354 dx, x2 = unroll180(x, x2, wrap=not Ps.looped)

1355 return dx, x2, y2

1356

1357 else:

1358 x0 = _fmod(x0, _360_0) # not x0 % 360!

1359 x0_180_ = x0 - _180_0

1360 x0_180 = x0 + _180_0

1361

1362 def _dxy3(x1, x, y, unused): # PYCHOK expected

1363 x = _umod_360(float(x))

1364 if x < x0_180_:

1365 x += _360_0

1366 elif x >= x0_180:

1367 x -= _360_0

1368 return (x - x1), x, y

1369

1370 if _MODS.booleans.isBoolean(points):

1371 return points._encloses(y0, x0, wrap=wrap)

1372

1373 Ps = LatLon2PsxyIter(points, loop=1, wrap=wrap)

1374 p = Ps[0]

1375 e = m = False

1376 S = Fsum()

1377

1378 _, x1, y1 = _dxy3(x0, p.x, p.y, False)

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

1380 dx, x2, y2 = _dxy3(x1, p.x, p.y, Ps)

1381 # ignore duplicate and near-duplicate pts

1382 if fabs(dx) > EPS or fabs(y2 - y1) > EPS:

1383 # determine if polygon edge (x1, y1)..(x2, y2) straddles

1384 # point (lat, lon) or is on boundary, but do not count

1385 # edges on boundary as more than one crossing

1386 if fabs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1):

1387 m = not m

1388 dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx

1389 if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0):

1390 e = not e

1391

1392 S += sin(radians(y2))

1393 x1, y1 = x2, y2

1394

1395 # An odd number of meridian crossings means, the polygon

1396 # contains a pole. Assume it is the pole on the hemisphere

1397 # containing the polygon mean point and if the polygon does

1398 # contain the North Pole, flip the result.

1399 if m and S.fsum() > 0:

1400 e = not e

1401 return e

1402

1403

1404 def ispolar(points, wrap=False):

1405 '''Check whether a polygon encloses a pole.

1406

1407 @arg points: The polygon points (C{LatLon}[]).

1408 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1409 the B{C{points}} (C{bool}).

1410

1411 @return: C{True} if the polygon encloses a pole, C{False}

1412 otherwise.

1413

1414 @raise PointsError: Insufficient number of B{C{points}}

1415

1416 @raise TypeError: Some B{C{points}} are not C{LatLon} or don't

1417 have C{bearingTo2}, C{initialBearingTo}

1418 and C{finalBearingTo} methods.

1419 '''

1420 def _cds(ps, w): # iterate over course deltas

1421 Ps = PointsIter(ps, loop=2, wrap=w)

1422 p2, p1 = Ps[0:2]

1423 b1, _ = _bearingTo2(p2, p1, wrap=False)

1424 for p2 in Ps.iterate(closed=True):

1425 if not p2.isequalTo(p1, EPS):

1426 if w and not Ps.looped:

1427 p2 = _unrollon(p1, p2)

1428 b, b2 = _bearingTo2(p1, p2, wrap=False)

1429 yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180

1430 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180

1431 p1, b1 = p2, b2

1432

1433 # summation of course deltas around pole is 0° rather than normally ±360°

1434 # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html>

1435 s = fsum(_cds(points, wrap))

1436 # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90)

1437 return fabs(s) < 90 # "zero-ish"

1438

1439

1440 def luneOf(lon1, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds):

1441 '''Generate an ellipsoidal or spherical U{lune

1442 <https://WikiPedia.org/wiki/Spherical_lune>}-shaped path or polygon.

1443

1444 @arg lon1: Left longitude (C{degrees90}).

1445 @arg lon2: Right longitude (C{degrees90}).

1446 @kwarg closed: Optionally, close the path (C{bool}).

1447 @kwarg LatLon: Class to use (L{LatLon_}).

1448 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}

1449 keyword arguments.

1450

1451 @return: A tuple of 4 or 5 B{C{LatLon}} instances outlining

1452 the lune shape.

1453

1454 @see: U{Latitude-longitude quadrangle

1455 <https://www.MathWorks.com/help/map/ref/areaquad.html>}.

1456 '''

1457 t = (LatLon( _0_0, lon1, **LatLon_kwds),

1458 LatLon( _90_0, lon1, **LatLon_kwds),

1459 LatLon( _0_0, lon2, **LatLon_kwds),

1460 LatLon(_N_90_0, lon2, **LatLon_kwds))

1461 if closed:

1462 t += t[:1]

1463 return t

1464

1465

1466 def nearestOn5(point, points, closed=False, wrap=False, adjust=True,

1467 limit=9, **LatLon_and_kwds):

1468 '''Locate the point on a path or polygon closest to a reference point.

1469

1470 The closest point on each polygon edge is either the nearest of that

1471 edge's end points or a point in between.

1472

1473 @arg point: The reference point (C{LatLon}).

1474 @arg points: The path or polygon points (C{LatLon}[]).

1475 @kwarg closed: Optionally, close the path or polygon (C{bool}).

1476 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1477 B{C{points}} (C{bool}).

1478 @kwarg adjust: See function L{pygeodesy.equirectangular4} (C{bool}).

1479 @kwarg limit: See function L{pygeodesy.equirectangular4} (C{degrees}),

1480 default C{9 degrees} is about C{1,000 Kmeter} (for mean

1481 spherical earth radius L{R_KM}).

1482 @kwarg LatLon_and_kwds: Optional, C{B{LatLon}=None} class to use for

1483 the closest point and additional B{C{LatLon}} keyword

1484 arguments, ignored if C{B{LatLon} is None} or not given.

1485

1486 @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the

1487 {closest} point (B{C{LatLon}}) or if C{B{LatLon} is None},

1488 a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}.

1489 The C{distance} is the L{pygeodesy.equirectangular} distance

1490 between the C{closest} and reference B{C{point}} in C{degrees}.

1491 The C{angle} from the B{C{point}} to the C{closest} is in

1492 compass C{degrees}, like function L{pygeodesy.compassAngle}.

1493

1494 @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}},

1495 see function L{pygeodesy.equirectangular4}.

1496

1497 @raise PointsError: Insufficient number of B{C{points}}

1498

1499 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1500

1501 @note: Distances are I{approximated} by function L{pygeodesy.equirectangular4}.

1502 For more accuracy use one of the C{LatLon.nearestOn6} methods.

1503

1504 @see: Function L{pygeodesy.degrees2m}.

1505 '''

1506 def _d2yx4(p2, p1, u, alw):

1507 # w = wrap if (i < (n - 1) or not closed) else False

1508 # equirectangular4 returns a Distance4Tuple(distance

1509 # in degrees squared, delta lat, delta lon, p2.lon

1510 # unroll/wrap'd); the previous p2.lon unroll/wrap'd

1511 # is also applied to the next edge's p1.lon

1512 return equirectangular4(p1.lat, p1.lon + u,

1513 p2.lat, p2.lon, **alw)

1514

1515 def _h(p): # get height or default 0

1516 return _xattr(p, height=0) or 0

1517

1518 # 3-D version used in .vector3d._nearestOn2

1519 #

1520 # point (x, y) on axis rotated ccw by angle a:

1521 # x' = x * cos(a) + y * sin(a)

1522 # y' = y * cos(a) - x * sin(a)

1523 #

1524 # distance (w) along and (h) perpendicular to

1525 # a line thru point (dx, dy) and the origin:

1526 # d = hypot(dx, dy)

1527 # w = (x * dx + y * dy) / d

1528 # h = (y * dx - x * dy) / d

1529 #

1530 # closest point on that line thru (dx, dy):

1531 # xc = dx * w / d

1532 # yc = dy * w / d

1533 # or

1534 # xc = dx * f

1535 # yc = dy * f

1536 # with

1537 # f = w / d

1538 # or

1539 # f = (y * dy + x * dx) / hypot2(dx, dy)

1540 #

1541 # i.e. no need for sqrt or hypot

1542

1543 Ps = PointsIter(points, loop=1, wrap=wrap)

1544 p1 = c = Ps[0]

1545 u1 = u = _0_0

1546 kw = dict(adjust=adjust, limit=limit, wrap=False)

1547 d, dy, dx, _ = _d2yx4(p1, point, u1, kw)

1548 for p2 in Ps.iterate(closed=closed):

1549 # iff wrapped, unroll lon1 (actually previous

1550 # lon2) like function unroll180/-PI would've

1551 if wrap:

1552 kw.update(wrap=not (closed and Ps.looped))

1553 d21, y21, x21, u2 = _d2yx4(p2, p1, u1, kw)

1554 if d21 > EPS:

1555 # distance point to p1, y01 and x01 negated

1556 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw)

1557 if d2 > EPS:

1558 w2 = y01 * y21 + x01 * x21

1559 if w2 > 0:

1560 if w2 < d21:

1561 # closest is between p1 and p2, use

1562 # original delta's, not y21 and x21

1563 f = w2 / d21

1564 p1 = LatLon_(favg(p1.lat, p2.lat, f=f),

1565 favg(p1.lon, p2.lon + u2, f=f),

1566 height=favg(_h(p1), _h(p2), f=f))

1567 u1 = _0_0

1568 else: # p2 is closest

1569 p1, u1 = p2, u2

1570 d2, y01, x01, _ = _d2yx4(point, p1, u1, kw)

1571 if d2 < d: # p1 is closer, y01 and x01 negated

1572 c, u, d, dy, dx = p1, u1, d2, -y01, -x01

1573 p1, u1 = p2, u2

1574

1575 a = atan2b(dx, dy) # azimuth

1576 d = hypot( dx, dy)

1577 h = _h(c)

1578 n = nameof(point) or typename(nearestOn5)

1579 if LatLon_and_kwds:

1580 LL, kwds = _xkwds_pop2(LatLon_and_kwds, LatLon=None)

1581 if LL is not None:

1582 r = LL(c.lat, c.lon + u, **_xkwds(kwds, height=h, name=n))

1583 return NearestOn3Tuple(r, d, a, name=n)

1584 return NearestOn5Tuple(c.lat, c.lon + u, d, a, h, name=n) # PYCHOK expected

1585

1586

1587 def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True):

1588 '''I{Approximate} the perimeter of a path, polygon. or composite.

1589

1590 @arg points: The path or polygon points or clips (C{LatLon}[],

1591 L{BooleanFHP} or L{BooleanGH}).

1592 @kwarg closed: Optionally, close the path or polygon (C{bool}).

1593 @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta

1594 by the cosine of the mean latitude (C{bool}).

1595 @kwarg radius: Mean earth radius (C{meter}).

1596 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1597 B{C{points}} (C{bool}).

1598

1599 @return: Approximate perimeter (C{meter}, same units as

1600 B{C{radius}}).

1601

1602 @raise PointsError: Insufficient number of B{C{points}}

1603

1604 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1605

1606 @raise ValueError: Invalid B{C{radius}} or C{B{closed}=False} with

1607 C{B{points}} a composite.

1608

1609 @note: This perimeter is based on the L{pygeodesy.equirectangular4}

1610 distance approximation and is ill-suited for regions exceeding

1611 several hundred Km or Miles or with near-polar latitudes.

1612

1613 @see: Functions L{sphericalTrigonometry.perimeterOf} and

1614 L{ellipsoidalKarney.perimeterOf}.

1615 '''

1616 def _degs(ps, c, a, w): # angular edge lengths in degrees

1617 Ps = LatLon2PsxyIter(ps, loop=1) # wrap=w

1618 p1, u = Ps[0], _0_0 # previous x2's unroll/wrap

1619 for p2 in Ps.iterate(closed=c):

1620 if w and c:

1621 w = not Ps.looped

1622 # apply previous x2's unroll/wrap'd to new x1

1623 _, dy, dx, u = equirectangular4(p1.y, p1.x + u,

1624 p2.y, p2.x,

1625 adjust=a, limit=None,

1626 wrap=w) # PYCHOK non-seq

1627 yield hypot(dx, dy)

1628 p1 = p2

1629

1630 if _MODS.booleans.isBoolean(points):

1631 if not closed:

1632 notImplemented(None, closed=closed, points=_composite_)

1633 d = points._sum1(perimeterOf, closed=True, adjust=adjust,

1634 radius=radius, wrap=wrap)

1635 else:

1636 d = fsum(_degs(points, closed, adjust, wrap))

1637 return degrees2m(d, radius=radius)

1638

1639

1640 def quadOf(latS, lonW, latN, lonE, closed=False, LatLon=LatLon_, **LatLon_kwds):

1641 '''Generate a quadrilateral path or polygon from two points.

1642

1643 @arg latS: Souther-nmost latitude (C{degrees90}).

1644 @arg lonW: Western-most longitude (C{degrees180}).

1645 @arg latN: Norther-nmost latitude (C{degrees90}).

1646 @arg lonE: Eastern-most longitude (C{degrees180}).

1647 @kwarg closed: Optionally, close the path (C{bool}).

1648 @kwarg LatLon: Class to use (L{LatLon_}).

1649 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}

1650 keyword arguments.

1651

1652 @return: Return a tuple of 4 or 5 B{C{LatLon}} instances

1653 outlining the quadrilateral.

1654

1655 @see: Function L{boundsOf}.

1656 '''

1657 t = (LatLon(latS, lonW, **LatLon_kwds),

1658 LatLon(latN, lonW, **LatLon_kwds),

1659 LatLon(latN, lonE, **LatLon_kwds),

1660 LatLon(latS, lonE, **LatLon_kwds))

1661 if closed:

1662 t += t[:1]

1663 return t

1664

1665

1666__all__ += _ALL_DOCS(_Array2LatLon, _Basequence)

1667

1668# **) MIT License

1669#

1670# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

1671#

1672# Permission is hereby granted, free of charge, to any person obtaining a

1673# copy of this software and associated documentation files (the "Software"),

1674# to deal in the Software without restriction, including without limitation

1675# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1676# and/or sell copies of the Software, and to permit persons to whom the

1677# Software is furnished to do so, subject to the following conditions:

1678#

1679# The above copyright notice and this permission notice shall be included

1680# in all copies or substantial portions of the Software.

1681#

1682# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1683# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1684# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1685# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1686# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1687# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1688# OTHER DEALINGS IN THE SOFTWARE.