1

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

3

4 u'''Fréchet distances.

5

6 Classes L{Frechet}, L{FrechetDegrees}, L{FrechetRadians},

7 L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert},

8 L{FrechetCosineLaw}, L{FrechetDistanceTo}< L{FrechetEquirectangular},

9 L{FrechetEuclidean}, L{FrechetExact}, L{FrechetFlatLocal}, L{FrechetFlatPolar},

10 L{FrechetHaversine}, L{FrechetHubeny}, L{FrechetKarney}, L{FrechetThomas}

11 and L{FrechetVincentys} to compute I{discrete} U{Fréchet

12<https://WikiPedia.org/wiki/Frechet_distance>} distances between two sets

13 of C{LatLon}, C{NumPy}, C{tuples} or other types of points.

14

15 Only L{FrechetDistanceTo} -iff used with L{ellipsoidalKarney.LatLon}

16 points- and L{FrechetKarney} requires installation of I{Charles Karney}'s

17 U{geographiclib<https://PyPI.org/project/geographiclib>}.

18

19 Typical usage is as follows. First, create a C{Frechet} calculator

20 from one set of C{LatLon} points.

21

22 C{f = FrechetXyz(point1s, ...)}

23

24 Get the I{discrete} Fréchet distance to another set of C{LatLon} points

25 by

26

27 C{t6 = f.discrete(point2s)}

28

29 Or, use function C{frechet_} with a proper C{distance} function passed

30 as keyword arguments as follows

31

32 C{t6 = frechet_(point1s, point2s, ..., distance=...)}.

33

34 In both cases, the returned result C{t6} is a L{Frechet6Tuple}.

35

36 For C{(lat, lon, ...)} points in a C{NumPy} array or plain C{tuples},

37 wrap the points in a L{Numpy2LatLon} respectively L{Tuple2LatLon}

38 instance, more details in the documentation thereof.

39

40 For other points, create a L{Frechet} sub-class with the appropriate

41 C{distance} method overloading L{Frechet.distance} as in this example.

42

43 >>> from pygeodesy import Frechet, hypot_

44 >>>

45 >>> class F3D(Frechet):

46 >>> """Custom Frechet example.

47 >>> """

48 >>> def distance(self, p1, p2):

49 >>> return hypot_(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z)

50 >>>

51 >>> f3D = F3D(xyz1, ..., units="...")

52 >>> t6 = f3D.discrete(xyz2)

53

54 Transcribed from the original U{Computing Discrete Fréchet Distance

55<https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>} by

56 Eiter, T. and Mannila, H., 1994, April 25, Technical Report CD-TR 94/64,

57 Information Systems Department/Christian Doppler Laboratory for Expert

58 Systems, Technical University Vienna, Austria.

59

60 This L{Frechet.discrete} implementation optionally generates intermediate

61 points for each point set separately. For example, using keyword argument

62 C{fraction=0.5} adds one additional point halfway between each pair of

63 points. Or using C{fraction=0.1} interpolates nine additional points

64 between each points pair.

65

66 The L{Frechet6Tuple} attributes C{fi1} and/or C{fi2} will be I{fractional}

67 indices of type C{float} if keyword argument C{fraction} is used. Otherwise,

68 C{fi1} and/or C{fi2} are simply type C{int} indices into the respective

69 points set.

70

71 For example, C{fractional} index value 2.5 means an intermediate point

72 halfway between points[2] and points[3]. Use function L{fractional}

73 to obtain the intermediate point for a I{fractional} index in the

74 corresponding set of points.

75

76 The C{Fréchet} distance was introduced in 1906 by U{Maurice Fréchet

77<https://WikiPedia.org/wiki/Maurice_Rene_Frechet>}, see U{reference

78[6]<https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>}.

79 It is a measure of similarity between curves that takes into account the

80 location and ordering of the points. Therefore, it is often a better metric

81 than the well-known C{Hausdorff} distance, see the L{hausdorff} module.

82'''

83

84# from pygeodesy.basics import isscalar # from .points

85 from pygeodesy.constants import EPS, EPS1, INF, NINF

86 from pygeodesy.datums import _ellipsoidal_datum, _WGS84

87 from pygeodesy.errors import _IsnotError, PointsError, _xattr, \

88 _xkwds, _xkwds_get

89 import pygeodesy.formy as _formy

90 from pygeodesy.interns import NN, _DOT_, _n_, _units_

91# from pygeodesy.iters import points2 as _points2 # from .points

92 from pygeodesy.lazily import _ALL_LAZY, _FOR_DOCS

93 from pygeodesy.named import _Named, _NamedTuple, notOverloaded, _Pass

94# from pygeodesy.namedTuples import PhiLam2Tuple # from .points

95 from pygeodesy.points import _distanceTo, _fractional, isscalar, \

96 PhiLam2Tuple, points2 as _points2, radians

97 from pygeodesy.props import property_doc_, property_RO

98 from pygeodesy.units import FIx, Float, Number_, _xUnit, _xUnits

99 from pygeodesy.unitsBase import _Str_degrees, _Str_meter, _Str_NN, \

100 _Str_radians, _Str_radians2

101

102 from collections import defaultdict as _defaultdict

103# from math import radians # from .points

104

105__all__ = _ALL_LAZY.frechet

106__version__ = '23.05.14'

107

108

109 def _fraction(fraction, n):

110 f = 1 # int, no fractional indices

111 if fraction in (None, 1):

112 pass

113 elif not (isscalar(fraction) and EPS < fraction < EPS1

114 and (float(n) - fraction) < n):

115 raise FrechetError(fraction=fraction)

116 elif fraction < EPS1:

117 f = float(fraction)

118 return f

119

120

121 class FrechetError(PointsError):

122 '''Fréchet issue.

123 '''

124 pass

125

126

127 class Frechet(_Named):

128 '''Frechet base class, requires method L{Frechet.distance} to

129 be overloaded.

130 '''

131 _datum = _WGS84

132 _func = None # formy function

133 _f1 = 1

134 _kwds = {} # func_ options

135 _n1 = 0

136 _ps1 = None

137 _units = _Str_NN # XXX Str to _Pass and for backward compatibility

138

139 def __init__(self, point1s, fraction=None, name=NN, units=NN, **kwds):

140 '''New C{Frechet...} calculator/interpolator.

141

142 @arg point1s: First set of points (C{LatLon}[], L{Numpy2LatLon}[],

143 L{Tuple2LatLon}[] or C{other}[]).

144 @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to

145 interpolate intermediate B{C{point1s}} or use

146 C{None}, C{0} or C{1} for no intermediate

147 B{C{point1s}} and no I{fractional} indices.

148 @kwarg name: Optional calculator/interpolator name (C{str}).

149 @kwarg units: Optional distance units (C{Unit} or C{str}).

150 @kwarg kwds: Optional keyword argument for distance function,

151 retrievable with property C{kwds}.

152

153 @raise FrechetError: Insufficient number of B{C{point1s}} or

154 an invalid B{C{point1}}, B{C{fraction}}

155 or B{C{units}}.

156 '''

157 self._n1, self._ps1 = self._points2(point1s)

158 if fraction:

159 self.fraction = fraction

160 if name:

161 self.name = name

162 if units: # and not self.units:

163 self.units = units

164 if kwds:

165 self._kwds = kwds

166

167 @property_RO

168 def adjust(self):

169 '''Get the C{adjust} setting (C{bool} or C{None}).

170 '''

171 return _xkwds_get(self._kwds, adjust=None)

172

173 @property_RO

174 def datum(self):

175 '''Get the datum (L{Datum} or C{None} if not applicable).

176 '''

177 return self._datum

178

179 def _datum_setter(self, datum):

180 '''(INTERNAL) Set the datum.

181 '''

182 d = datum or _xattr(self._ps1[0], datum=None)

183 if d and d is not self._datum: # PYCHOK no cover

184 self._datum = _ellipsoidal_datum(d, name=self.name)

185

186 def discrete(self, point2s, fraction=None):

187 '''Compute the C{forward, discrete Fréchet} distance.

188

189 @arg point2s: Second set of points (C{LatLon}[], L{Numpy2LatLon}[],

190 L{Tuple2LatLon}[] or C{other}[]).

191 @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to

192 interpolate intermediate B{C{point2s}} or use

193 C{None}, C{0} or C{1} for no intermediate

194 B{C{point2s}} and no I{fractional} indices.

195

196 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)}.

197

198 @raise FrechetError: Insufficient number of B{C{point2s}} or

199 an invalid B{C{point2}} or B{C{fraction}}.

200

201 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit

202 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}.

203 '''

204 return self._discrete(point2s, fraction, self.distance)

205

206 def _discrete(self, point2s, fraction, distance):

207 '''(INTERNAL) Detailed C{discrete} with C{disance}.

208 '''

209 n2, ps2 = self._points2(point2s)

210

211 f2 = _fraction(fraction, n2)

212 p2 = self.points_fraction if f2 < EPS1 else self.points_ # PYCHOK expected

213

214 f1 = self.fraction

215 p1 = self.points_fraction if f1 < EPS1 else self.points_ # PYCHOK expected

216

217 def _dF(fi1, fi2):

218 return distance(p1(self._ps1, fi1), p2(ps2, fi2))

219

220 try:

221 return _frechet_(self._n1, f1, n2, f2, _dF, self.units)

222 except TypeError as x:

223 t = _DOT_(self.classname, self.discrete.__name__)

224 raise FrechetError(t, cause=x)

225

226 def distance(self, point1, point2):

227 '''Return the distance between B{C{point1}} and B{C{point2s}},

228 subject to the supplied optional keyword arguments, see

229 property C{kwds}.

230 '''

231 return self._func(point1.lat, point1.lon,

232 point2.lat, point2.lon, **self._kwds)

233

234 @property_doc_(''' the index fraction (C{float}).''')

235 def fraction(self):

236 '''Get the index fraction (C{float} or C{1}).

237 '''

238 return self._f1

239

240 @fraction.setter # PYCHOK setter!

241 def fraction(self, fraction):

242 '''Set the index fraction (C{float} in C{EPS}..L{EPS1}) to interpolate

243 intermediate B{C{point1s}} or use C{None}, C{0} or C{1} for no

244 intermediate B{C{point1s}} and no I{fractional} indices.

245

246 @raise FrechetError: Invalid B{C{fraction}}.

247 '''

248 self._f1 = _fraction(fraction, self._n1)

249

250 def _func(self, *args, **kwds):

251 notOverloaded(self, *args, **kwds)

252

253 @property_RO

254 def kwds(self):

255 '''Get the supplied, optional keyword arguments (C{dict}).

256 '''

257 return self._kwds

258

259 def point(self, point):

260 '''Convert a point for the C{.distance} method.

261

262 @arg point: The point to convert ((C{LatLon}, L{Numpy2LatLon},

263 L{Tuple2LatLon} or C{other}).

264

265 @return: The converted B{C{point}}.

266 '''

267 return point # pass thru

268

269 def points_(self, points, i):

270 '''Get and convert a point for the C{.distance} method.

271

272 @arg points: The orignal B{C{points}} to convert ((C{LatLon}[],

273 L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]).

274 @arg i: The B{C{points}} index (C{int}).

275

276 @return: The converted B{C{points[i]}}.

277 '''

278 return self.point(points[i])

279

280 def points_fraction(self, points, fi):

281 '''Get and convert a I{fractional} point for the C{.distance} method.

282

283 @arg points: The orignal B{C{points}} to convert ((C{LatLon}[],

284 L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]).

285 @arg fi: The I{fractional} index in B{C{points}} (C{float} or C{int}).

286

287 @return: The interpolated, converted, intermediate B{C{points[fi]}}.

288 '''

289 return self.point(_fractional(points, fi, None, wrap=None)) # was=self.wrap

290

291 def _points2(self, points):

292 '''(INTERNAL) Check a set of points, overloaded in L{FrechetDistanceTo}.

293 '''

294 return _points2(points, closed=False, Error=FrechetError)

295

296 @property_doc_(''' the distance units (C{Unit} or C{str}).''')

297 def units(self):

298 '''Get the distance units (C{Unit} or C{str}).

299 '''

300 return self._units

301

302 @units.setter # PYCHOK setter!

303 def units(self, units):

304 '''Set the distance units (C{Unit} or C{str}).

305

306 @raise TypeError: Invalid B{C{units}}.

307 '''

308 self._units = _xUnits(units, Base=Float)

309

310 @property_RO

311 def wrap(self):

312 '''Get the C{wrap} setting (C{bool} or C{None}).

313 '''

314 return _xkwds_get(self._kwds, wrap=None)

315

316

317 class FrechetDegrees(Frechet):

318 '''DEPRECATED, use an other C{Frechet*} class.

319 '''

320 _units = _Str_degrees

321

322 if _FOR_DOCS:

323 __init__ = Frechet.__init__

324 discrete = Frechet.discrete

325

326 def distance(self, point1, point2, *args, **kwds): # PYCHOK signature

327 '''I{Must be overloaded} to return the distance between

328 B{C{point1}} and B{C{point2}} in C{degrees}.

329 '''

330 notOverloaded(self, point1, point2, *args, **kwds)

331

332

333 class FrechetRadians(Frechet):

334 '''DEPRECATED, use an other C{Frechet*} class.

335 '''

336 _units = _Str_radians

337

338 if _FOR_DOCS:

339 __init__ = Frechet.__init__

340 discrete = Frechet.discrete

341

342 def distance(self, point1, point2, *args, **kwds): # PYCHOK signature

343 '''I{Must be overloaded} to return the distance between

344 B{C{point1}} and B{C{point2}} in C{radians}.

345 '''

346 notOverloaded(self, point1, point2, *args, **kwds)

347

348 def point(self, point):

349 '''Return B{C{point}} as L{PhiLam2Tuple} to maintain

350 I{backward compatibility} of L{FrechetRadians}.

351

352 @return: A L{PhiLam2Tuple}C{(phi, lam)}.

353 '''

354 try:

355 return point.philam

356 except AttributeError:

357 return PhiLam2Tuple(radians(point.lat), radians(point.lon))

358

359

360 class _FrechetMeterRadians(Frechet):

361 '''(INTERNAL) Returning C{meter} or C{radians} depending on

362 the optional keyword arguments supplied at instantiation

363 of the C{Frechet*} sub-class.

364 '''

365 _units = _Str_meter

366 _units_ = _Str_radians

367

368 def discrete(self, point2s, fraction=None):

369 '''Overloaded method L{Frechet.discrete} to determine

370 the distance function and units from the optional

371 keyword arguments given at this instantiation, see

372 property C{kwds}.

373

374 @see: L{Frechet.discrete} for other details.

375 '''

376 return self._discrete(point2s, fraction, _formy._radistance(self))

377

378 def _func_(self, *args, **kwds):

379 notOverloaded(self, *args, **kwds)

380

381

382 class FrechetCosineAndoyerLambert(_FrechetMeterRadians):

383 '''Compute the C{Frechet} distance based on the I{angular} distance

384 in C{radians} from function L{pygeodesy.cosineAndoyerLambert}.

385 '''

386 def __init__(self, point1s, fraction=None, name=NN, **datum_wrap):

387 '''New L{FrechetCosineAndoyerLambert} calculator/interpolator.

388

389 @kwarg datum_wrap: Optional keyword arguments for function

390 L{pygeodesy.cosineAndoyerLambert}.

391

392 @see: L{Frechet.__init__} for details about B{C{point1s}},

393 B{C{fraction}}, B{C{name}} and other exceptions.

394 '''

395 Frechet.__init__(self, point1s, fraction=fraction, name=name,

396 **datum_wrap)

397 self._func = _formy.cosineAndoyerLambert

398 self._func_ = _formy.cosineAndoyerLambert_

399

400 if _FOR_DOCS:

401 discrete = Frechet.discrete

402

403

404 class FrechetCosineForsytheAndoyerLambert(_FrechetMeterRadians):

405 '''Compute the C{Frechet} distance based on the I{angular} distance

406 in C{radians} from function L{pygeodesy.cosineForsytheAndoyerLambert}.

407 '''

408 def __init__(self, point1s, fraction=None, name=NN, **datum_wrap):

409 '''New L{FrechetCosineForsytheAndoyerLambert} calculator/interpolator.

410

411 @kwarg datum_wrap: Optional keyword arguments for function

412 L{pygeodesy.cosineAndoyerLambert}.

413

414 @see: L{Frechet.__init__} for details about B{C{point1s}},

415 B{C{fraction}}, B{C{name}} and other exceptions.

416 '''

417 Frechet.__init__(self, point1s, fraction=fraction, name=name,

418 **datum_wrap)

419 self._func = _formy.cosineForsytheAndoyerLambert

420 self._func_ = _formy.cosineForsytheAndoyerLambert_

421

422 if _FOR_DOCS:

423 discrete = Frechet.discrete

424

425

426 class FrechetCosineLaw(_FrechetMeterRadians):

427 '''Compute the C{Frechet} distance based on the I{angular} distance

428 in C{radians} from function L{pygeodesy.cosineLaw}.

429

430 @note: See note at function L{pygeodesy.vincentys_}.

431 '''

432 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap):

433 '''New L{FrechetCosineLaw} calculator/interpolator.

434

435 @kwarg radius_wrap: Optional keyword arguments for function

436 L{pygeodesy.cosineLaw}.

437

438 @see: L{Frechet.__init__} for details about B{C{point1s}},

439 B{C{fraction}}, B{C{name}} and other exceptions.

440 '''

441 Frechet.__init__(self, point1s, fraction=fraction, name=name,

442 **radius_wrap)

443 self._func = _formy.cosineLaw

444 self._func_ = _formy.cosineLaw_

445

446 if _FOR_DOCS:

447 discrete = Frechet.discrete

448

449

450 class FrechetDistanceTo(Frechet): # FrechetMeter

451 '''Compute the C{Frechet} distance based on the distance from the

452 point1s' C{LatLon.distanceTo} method, conventionally in C{meter}.

453 '''

454 _units = _Str_meter

455

456 def __init__(self, point1s, fraction=None, name=NN, **distanceTo_kwds):

457 '''New L{FrechetDistanceTo} calculator/interpolator.

458

459 @kwarg distanceTo_kwds: Optional keyword arguments for each

460 B{C{point1s}}' C{LatLon.distanceTo}

461 method.

462

463 @see: L{Frechet.__init__} for details about B{C{point1s}},

464 B{C{fraction}}, B{C{name}} and other exceptions.

465

466 @note: All B{C{point1s}} I{must} be instances of the same

467 ellipsoidal or spherical C{LatLon} class.

468 '''

469 Frechet.__init__(self, point1s, fraction=fraction, name=name,

470 **distanceTo_kwds)

471

472 if _FOR_DOCS:

473 discrete = Frechet.discrete

474

475 def distance(self, p1, p2):

476 '''Return the distance in C{meter}.

477 '''

478 return p1.distanceTo(p2, **self._kwds)

479

480 def _points2(self, points):

481 '''(INTERNAL) Check a set of points.

482 '''

483 np, ps = Frechet._points2(self, points)

484 return np, _distanceTo(FrechetError, points=ps)

485

486

487 class FrechetEquirectangular(Frechet):

488 '''Compute the C{Frechet} distance based on the I{equirectangular}

489 distance in C{radians squared} like function L{pygeodesy.equirectangular}.

490 '''

491 _units = _Str_radians2

492

493 def __init__(self, point1s, fraction=None, name=NN, **adjust_limit_wrap):

494 '''New L{FrechetEquirectangular} calculator/interpolator.

495

496 @kwarg adjust_limit_wrap: Optional keyword arguments for function

497 L{pygeodesy.equirectangular_} I{with default}

498 C{B{limit}=0} for I{backward compatibility}.

499

500 @see: L{Frechet.__init__} for details about B{C{point1s}},

501 B{C{fraction}}, B{C{name}} and other exceptions.

502 '''

503 adjust_limit_wrap = _xkwds(adjust_limit_wrap, limit=0)

504 Frechet.__init__(self, point1s, fraction=fraction, name=name,

505 **adjust_limit_wrap)

506 self._func = _formy._equirectangular # helper

507

508 if _FOR_DOCS:

509 discrete = Frechet.discrete

510

511

512 class FrechetEuclidean(_FrechetMeterRadians):

513 '''Compute the C{Frechet} distance based on the I{Euclidean}

514 distance in C{radians} from function L{pygeodesy.euclidean}.

515 '''

516 def __init__(self, point1s, fraction=None, name=NN, **adjust_radius_wrap): # was=True

517 '''New L{FrechetEuclidean} calculator/interpolator.

518

519 @kwarg adjust_radius_wrap: Optional keyword arguments for

520 function L{pygeodesy.euclidean}.

521

522 @see: L{Frechet.__init__} for details about B{C{point1s}},

523 B{C{fraction}}, B{C{name}} and other exceptions.

524 '''

525 Frechet.__init__(self, point1s, fraction=fraction, name=name,

526 **adjust_radius_wrap)

527 self._func = _formy.euclidean

528 self._func_ = _formy.euclidean_

529

530 if _FOR_DOCS:

531 discrete = Frechet.discrete

532

533

534 class FrechetExact(Frechet):

535 '''Compute the C{Frechet} distance based on the I{angular} distance

536 in C{degrees} from method L{GeodesicExact}C{.Inverse}.

537 '''

538 _units = _Str_degrees

539

540 def __init__(self, point1s, fraction=None, name=NN, datum=None, **wrap):

541 '''New L{FrechetExact} calculator/interpolator.

542

543 @kwarg datum: Datum to override the default C{Datums.WGS84} and

544 first B{C{point1s}}' datum (L{Datum}, L{Ellipsoid},

545 L{Ellipsoid2} or L{a_f2Tuple}).

546 @kwarg wrap: Optional keyword argument for method C{Inverse1}

547 of class L{geodesicx.GeodesicExact}.

548

549 @raise TypeError: Invalid B{C{datum}}.

550

551 @see: L{Frechet.__init__} for details about B{C{point1s}},

552 B{C{fraction}}, B{C{name}} and other exceptions.

553 '''

554 Frechet.__init__(self, point1s, fraction=fraction, name=name,

555 **wrap)

556 self._datum_setter(datum)

557 self._func = self.datum.ellipsoid.geodesicx.Inverse1 # note -x

558

559 if _FOR_DOCS:

560 discrete = Frechet.discrete

561

562

563 class FrechetFlatLocal(_FrechetMeterRadians):

564 '''Compute the C{Frechet} distance based on the I{angular} distance in

565 C{radians squared} like function L{pygeodesy.flatLocal_}/L{pygeodesy.hubeny}.

566 '''

567 _units_ = _Str_radians2 # see L{flatLocal_}

568

569 def __init__(self, point1s, fraction=None, name=NN, **datum_scaled_wrap):

570 '''New L{FrechetFlatLocal}/L{FrechetHubeny} calculator/interpolator.

571

572 @kwarg datum_scaled_wrap: Optional keyword arguments for

573 function L{pygeodesy.flatLocal}.

574

575 @see: L{Frechet.__init__} for details about B{C{point1s}},

576 B{C{fraction}}, B{C{name}} and other exceptions.

577

578 @note: The distance C{units} are C{radians squared}, not C{radians}.

579 '''

580 Frechet.__init__(self, point1s, fraction=fraction, name=name,

581 **datum_scaled_wrap)

582 self._func = _formy.flatLocal

583 self._func_ = self.datum.ellipsoid._hubeny_2

584

585 if _FOR_DOCS:

586 discrete = Frechet.discrete

587

588

589 class FrechetFlatPolar(_FrechetMeterRadians):

590 '''Compute the C{Frechet} distance based on the I{angular} distance

591 in C{radians} from function L{flatPolar_}.

592 '''

593 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap):

594 '''New L{FrechetFlatPolar} calculator/interpolator.

595

596 @kwarg radius_wrap: Optional keyword arguments for function

597 L{pygeodesy.flatPolar}.

598

599 @see: L{Frechet.__init__} for details about B{C{point1s}},

600 B{C{fraction}}, B{C{name}} and other exceptions.

601 '''

602 Frechet.__init__(self, point1s, fraction=fraction, name=name,

603 **radius_wrap)

604 self._func = _formy.flatPolar

605 self._func_ = _formy.flatPolar_

606

607 if _FOR_DOCS:

608 discrete = Frechet.discrete

609

610

611 class FrechetHaversine(_FrechetMeterRadians):

612 '''Compute the C{Frechet} distance based on the I{angular}

613 distance in C{radians} from function L{pygeodesy.haversine_}.

614

615 @note: See note at function L{pygeodesy.vincentys_}.

616 '''

617 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap):

618 '''New L{FrechetHaversine} calculator/interpolator.

619

620 @kwarg radius_wrap: Optional keyword arguments for function

621 L{pygeodesy.haversine}.

622

623 @see: L{Frechet.__init__} for details about B{C{point1s}},

624 B{C{fraction}}, B{C{name}} and other exceptions.

625 '''

626 Frechet.__init__(self, point1s, fraction=fraction, name=name,

627 **radius_wrap)

628 self._func = _formy.haversine

629 self._func_ = _formy.haversine_

630

631 if _FOR_DOCS:

632 discrete = Frechet.discrete

633

634

635 class FrechetHubeny(FrechetFlatLocal): # for Karl Hubeny

636 if _FOR_DOCS:

637 __doc__ = FrechetFlatLocal.__doc__

638 __init__ = FrechetFlatLocal.__init__

639 discrete = FrechetFlatLocal.discrete

640 distance = FrechetFlatLocal.discrete

641

642

643 class FrechetKarney(Frechet):

644 '''Compute the C{Frechet} distance based on the I{angular}

645 distance in C{degrees} from I{Karney}'s U{geographiclib

646 <https://PyPI.org/project/geographiclib>} U{geodesic.Geodesic

647 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}

648 C{Inverse} method.

649 '''

650 _units = _Str_degrees

651

652 def __init__(self, point1s, fraction=None, name=NN, datum=None, **wrap):

653 '''New L{FrechetKarney} calculator/interpolator.

654

655 @kwarg datum: Datum to override the default C{Datums.WGS84} and

656 first B{C{knots}}' datum (L{Datum}, L{Ellipsoid},

657 L{Ellipsoid2} or L{a_f2Tuple}).

658 @kwarg wrap: Optional keyword argument for method C{Inverse1}

659 of class L{geodesicw.Geodesic}.

660

661 @raise ImportError: Package U{geographiclib

662 <https://PyPI.org/project/geographiclib>} missing.

663

664 @raise TypeError: Invalid B{C{datum}}.

665

666 @see: L{Frechet.__init__} for details about B{C{point1s}},

667 B{C{fraction}}, B{C{name}} and other exceptions.

668 '''

669 Frechet.__init__(self, point1s, fraction=fraction, name=name,

670 **wrap)

671 self._datum_setter(datum)

672 self._func = self.datum.ellipsoid.geodesic.Inverse1

673

674 if _FOR_DOCS:

675 discrete = Frechet.discrete

676

677

678 class FrechetThomas(_FrechetMeterRadians):

679 '''Compute the C{Frechet} distance based on the I{angular} distance

680 in C{radians} from function L{pygeodesy.thomas_}.

681 '''

682 def __init__(self, point1s, fraction=None, name=NN, **datum_wrap):

683 '''New L{FrechetThomas} calculator/interpolator.

684

685 @kwarg datum_wrap: Optional keyword argument for function

686 L{pygeodesy.thomas}.

687

688 @see: L{Frechet.__init__} for details about B{C{point1s}},

689 B{C{fraction}}, B{C{name}} and other exceptions.

690 '''

691 Frechet.__init__(self, point1s, fraction=fraction, name=name,

692 **datum_wrap)

693 self._func = _formy.thomas

694 self._func_ = _formy.thomas_

695

696 if _FOR_DOCS:

697 discrete = Frechet.discrete

698

699

700 class FrechetVincentys(_FrechetMeterRadians):

701 '''Compute the C{Frechet} distance based on the I{angular}

702 distance in C{radians} from function L{pygeodesy.vincentys_}.

703

704 @note: See note at function L{pygeodesy.vincentys_}.

705 '''

706 def __init__(self, point1s, fraction=None, name=NN, **radius_wrap):

707 '''New L{FrechetVincentys} calculator/interpolator.

708

709 @kwarg radius_wrap: Optional keyword arguments for function

710 L{pygeodesy.vincentys}.

711

712 @see: L{Frechet.__init__} for details about B{C{point1s}},

713 B{C{fraction}}, B{C{name}} and other exceptions.

714 '''

715 Frechet.__init__(self, point1s, fraction=fraction, name=name,

716 **radius_wrap)

717 self._func = _formy.vincentys

718 self._func_ = _formy.vincentys_

719

720 if _FOR_DOCS:

721 discrete = Frechet.discrete

722

723

724 def _frechet_(ni, fi, nj, fj, dF, units): # MCCABE 14

725 '''(INTERNAL) Recursive core of function L{frechet_}

726 and method C{discrete} of C{Frechet...} classes.

727 '''

728 iFs = {}

729

730 def iF(i): # cache index, depth ints and floats

731 return iFs.setdefault(i, i)

732

733 cF = _defaultdict(dict)

734

735 def _rF(i, j, r): # recursive Fréchet

736 i = iF(i)

737 j = iF(j)

738 try:

739 t = cF[i][j]

740 except KeyError:

741 r = iF(r + 1)

742 try:

743 if i > 0:

744 if j > 0:

745 t = min(_rF(i - fi, j, r),

746 _rF(i - fi, j - fj, r),

747 _rF(i, j - fj, r))

748 elif j < 0:

749 raise IndexError

750 else: # j == 0

751 t = _rF(i - fi, 0, r)

752 elif i < 0:

753 raise IndexError

754

755 elif j > 0: # i == 0

756 t = _rF(0, j - fj, r)

757 elif j < 0: # i == 0

758 raise IndexError

759 else: # i == j == 0

760 t = (NINF, i, j, r)

761

762 d = dF(i, j)

763 if d > t[0]:

764 t = (d, i, j, r)

765 except IndexError:

766 t = (INF, i, j, r)

767 cF[i][j] = t

768 return t

769

770 t = _rF(ni - 1, nj - 1, 0)

771 t += (sum(map(len, cF.values())), units)

772# del cF, iFs

773 return Frechet6Tuple(t) # *t

774

775

776 def frechet_(point1s, point2s, distance=None, units=NN):

777 '''Compute the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>}

778 distance between two paths, each given as a set of points.

779

780 @arg point1s: First set of points (C{LatLon}[], L{Numpy2LatLon}[],

781 L{Tuple2LatLon}[] or C{other}[]).

782 @arg point2s: Second set of points (C{LatLon}[], L{Numpy2LatLon}[],

783 L{Tuple2LatLon}[] or C{other}[]).

784 @kwarg distance: Callable returning the distance between a B{C{point1s}}

785 and a B{C{point2s}} point (signature C{(point1, point2)}).

786 @kwarg units: Optional, the distance units (C{Unit} or C{str}).

787

788 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)} where C{fi1}

789 and C{fi2} are type C{int} indices into B{C{point1s}} respectively

790 B{C{point2s}}.

791

792 @raise FrechetError: Insufficient number of B{C{point1s}} or B{C{point2s}}.

793

794 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit()

795 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}.

796

797 @raise TypeError: If B{C{distance}} is not a callable.

798

799 @note: Function L{frechet_} does I{not} support I{fractional} indices

800 for intermediate B{C{point1s}} and B{C{point2s}}.

801 '''

802 if not callable(distance):

803 raise _IsnotError(callable.__name__, distance=distance)

804

805 n1, ps1 = _points2(point1s, closed=False, Error=FrechetError)

806 n2, ps2 = _points2(point2s, closed=False, Error=FrechetError)

807

808 def _dF(i1, i2):

809 return distance(ps1[i1], ps2[i2])

810

811 return _frechet_(n1, 1, n2, 1, _dF, units)

812

813

814 class Frechet6Tuple(_NamedTuple):

815 '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete}

816 U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance

817 C{fd}, I{fractional} indices C{fi1} and C{fi2} as C{FIx}, the

818 recursion depth C{r}, the number of distances computed C{n} and

819 the L{units} class or class or name of the distance C{units}.

820

821 If I{fractional} indices C{fi1} and C{fi2} are C{int}, the

822 returned C{fd} is the distance between C{point1s[fi1]} and

823 C{point2s[fi2]}. For C{float} indices, the distance is

824 between an intermediate point along C{point1s[int(fi1)]} and

825 C{point1s[int(fi1) + 1]} respectively an intermediate point

826 along C{point2s[int(fi2)]} and C{point2s[int(fi2) + 1]}.

827

828 Use function L{fractional} to compute the point at a

829 I{fractional} index.

830 '''

831 _Names_ = ('fd', 'fi1', 'fi2', 'r', _n_, _units_)

832 _Units_ = (_Pass, FIx, FIx, Number_, Number_, _Pass)

833

834 def toUnits(self, **Error): # PYCHOK expected

835 '''Overloaded C{_NamedTuple.toUnits} for C{fd} units.

836 '''

837 U = _xUnit(self.units, Float) # PYCHOK expected

838 self._Units_ = (U,) + Frechet6Tuple._Units_[1:]

839 return _NamedTuple.toUnits(self, **Error)

840

841# def __gt__(self, other):

842# _xinstanceof(Frechet6Tuple, other=other)

843# return self if self.fd > other.fd else other # PYCHOK .fd=[0]

844#

845# def __lt__(self, other):

846# _xinstanceof(Frechet6Tuple, other=other)

847# return self if self.fd < other.fd else other # PYCHOK .fd=[0]

848

849# **) MIT License

850#

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

852#

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

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

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

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

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

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

859#

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

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

862#

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

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

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

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

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

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

869# OTHER DEALINGS IN THE SOFTWARE.