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 PointsError, _xattr, _xcallable, _xkwds, _xkwds_get

88 import pygeodesy.formy as _formy

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

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

91 from pygeodesy.lazily import _ALL_LAZY, _FOR_DOCS

92 from pygeodesy.named import _Named, _NamedTuple, _Pass

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

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

95 PhiLam2Tuple, points2 as _points2, radians

96 from pygeodesy.props import property_doc_, property_RO

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

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

99 _Str_radians, _Str_radians2

100

101 from collections import defaultdict as _defaultdict

102# from math import radians # from .points

103

104__all__ = _ALL_LAZY.frechet

105__version__ = '24.04.07'

106

107

108 def _fraction(fraction, n):

109 f = 1 # int, no fractional indices

110 if fraction in (None, 1):

111 pass

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

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

114 raise FrechetError(fraction=fraction)

115 elif fraction < EPS1:

116 f = float(fraction)

117 return f

118

119

120 class FrechetError(PointsError):

121 '''Fréchet issue.

122 '''

123 pass

124

125

126 class Frechet(_Named):

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

128 be overloaded.

129 '''

130 _datum = _WGS84

131 _func = None # formy function

132 _f1 = 1

133 _kwds = {} # func_ options

134 _n1 = 0

135 _ps1 = None

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

137

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

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

140

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

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

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

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

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

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

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

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

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

150 retrievable with property C{kwds}.

151

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

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

154 or B{C{units}}.

155 '''

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

157 if fraction:

158 self.fraction = fraction

159 if name:

160 self.name = name

161 if units: # and not self.units:

162 self.units = units

163 if kwds:

164 self._kwds = kwds

165

166 @property_RO

167 def adjust(self):

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

169 '''

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

171

172 @property_RO

173 def datum(self):

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

175 '''

176 return self._datum

177

178 def _datum_setter(self, datum):

179 '''(INTERNAL) Set the datum.

180 '''

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

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

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

184

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

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

187

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

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

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

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

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

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

194

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

196

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

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

199

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

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

202 '''

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

204

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

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

207 '''

208 n2, ps2 = self._points2(point2s)

209

210 f2 = _fraction(fraction, n2)

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

212

213 f1 = self.fraction

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

215

216 def _dF(fi1, fi2):

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

218

219 try:

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

221 except TypeError as x:

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

223 raise FrechetError(t, cause=x)

224

225 def distance(self, point1, point2):

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

227 subject to the supplied optional keyword arguments, see

228 property C{kwds}.

229 '''

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

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

232

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

234 def fraction(self):

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

236 '''

237 return self._f1

238

239 @fraction.setter # PYCHOK setter!

240 def fraction(self, fraction):

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

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

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

244

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

246 '''

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

248

249 def _func(self, *args, **kwds): # PYCHOK no cover

250 '''(INTERNAL) I{Must be overloaded}.'''

251 self._notOverloaded(*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 no cover

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

328 self._notOverloaded(point1, point2, *args, **kwds)

329

330

331 class FrechetRadians(Frechet):

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

333 '''

334 _units = _Str_radians

335

336 if _FOR_DOCS:

337 __init__ = Frechet.__init__

338 discrete = Frechet.discrete

339

340 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover

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

342 self._notOverloaded(point1, point2, *args, **kwds)

343

344 def point(self, point):

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

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

347

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

349 '''

350 try:

351 return point.philam

352 except AttributeError:

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

354

355

356 class _FrechetMeterRadians(Frechet):

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

358 the optional keyword arguments supplied at instantiation

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

360 '''

361 _units = _Str_meter

362 _units_ = _Str_radians

363

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

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

366 the distance function and units from the optional

367 keyword arguments given at this instantiation, see

368 property C{kwds}.

369

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

371 '''

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

373

374 def _func_(self, *args, **kwds): # PYCHOK no cover

375 '''(INTERNAL) I{Must be overloaded}.'''

376 self._notOverloaded(*args, **kwds)

377

378

379 class FrechetCosineAndoyerLambert(_FrechetMeterRadians):

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

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

382 '''

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

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

385

386 @kwarg datum_wrap: Optional keyword arguments for function

387 L{pygeodesy.cosineAndoyerLambert}.

388

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

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

391 '''

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

393 **datum_wrap)

394 self._func = _formy.cosineAndoyerLambert

395 self._func_ = _formy.cosineAndoyerLambert_

396

397 if _FOR_DOCS:

398 discrete = Frechet.discrete

399

400

401 class FrechetCosineForsytheAndoyerLambert(_FrechetMeterRadians):

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

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

404 '''

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

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

407

408 @kwarg datum_wrap: Optional keyword arguments for function

409 L{pygeodesy.cosineAndoyerLambert}.

410

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

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

413 '''

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

415 **datum_wrap)

416 self._func = _formy.cosineForsytheAndoyerLambert

417 self._func_ = _formy.cosineForsytheAndoyerLambert_

418

419 if _FOR_DOCS:

420 discrete = Frechet.discrete

421

422

423 class FrechetCosineLaw(_FrechetMeterRadians):

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

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

426

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

428 '''

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

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

431

432 @kwarg radius_wrap: Optional keyword arguments for function

433 L{pygeodesy.cosineLaw}.

434

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

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

437 '''

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

439 **radius_wrap)

440 self._func = _formy.cosineLaw

441 self._func_ = _formy.cosineLaw_

442

443 if _FOR_DOCS:

444 discrete = Frechet.discrete

445

446

447 class FrechetDistanceTo(Frechet): # FrechetMeter

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

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

450 '''

451 _units = _Str_meter

452

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

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

455

456 @kwarg distanceTo_kwds: Optional keyword arguments for each

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

458 method.

459

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

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

462

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

464 ellipsoidal or spherical C{LatLon} class.

465 '''

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

467 **distanceTo_kwds)

468

469 if _FOR_DOCS:

470 discrete = Frechet.discrete

471

472 def distance(self, p1, p2):

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

474 '''

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

476

477 def _points2(self, points):

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

479 '''

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

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

482

483

484 class FrechetEquirectangular(Frechet):

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

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

487 '''

488 _units = _Str_radians2

489

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

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

492

493 @kwarg adjust_limit_wrap: Optional keyword arguments for function

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

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

496

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

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

499 '''

500 adjust_limit_wrap = _xkwds(adjust_limit_wrap, limit=0)

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

502 **adjust_limit_wrap)

503 self._func = _formy._equirectangular # helper

504

505 if _FOR_DOCS:

506 discrete = Frechet.discrete

507

508

509 class FrechetEuclidean(_FrechetMeterRadians):

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

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

512 '''

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

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

515

516 @kwarg adjust_radius_wrap: Optional keyword arguments for

517 function L{pygeodesy.euclidean}.

518

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

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

521 '''

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

523 **adjust_radius_wrap)

524 self._func = _formy.euclidean

525 self._func_ = _formy.euclidean_

526

527 if _FOR_DOCS:

528 discrete = Frechet.discrete

529

530

531 class FrechetExact(Frechet):

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

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

534 '''

535 _units = _Str_degrees

536

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

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

539

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

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

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

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

544 of class L{geodesicx.GeodesicExact}.

545

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

547

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

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

550 '''

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

552 **wrap)

553 self._datum_setter(datum)

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

555

556 if _FOR_DOCS:

557 discrete = Frechet.discrete

558

559

560 class FrechetFlatLocal(_FrechetMeterRadians):

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

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

563 '''

564 _units_ = _Str_radians2 # see L{flatLocal_}

565

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

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

568

569 @kwarg datum_scaled_wrap: Optional keyword arguments for

570 function L{pygeodesy.flatLocal}.

571

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

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

574

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

576 '''

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

578 **datum_scaled_wrap)

579 self._func = _formy.flatLocal

580 self._func_ = self.datum.ellipsoid._hubeny_2

581

582 if _FOR_DOCS:

583 discrete = Frechet.discrete

584

585

586 class FrechetFlatPolar(_FrechetMeterRadians):

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

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

589 '''

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

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

592

593 @kwarg radius_wrap: Optional keyword arguments for function

594 L{pygeodesy.flatPolar}.

595

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

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

598 '''

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

600 **radius_wrap)

601 self._func = _formy.flatPolar

602 self._func_ = _formy.flatPolar_

603

604 if _FOR_DOCS:

605 discrete = Frechet.discrete

606

607

608 class FrechetHaversine(_FrechetMeterRadians):

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

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

611

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

613 '''

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

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

616

617 @kwarg radius_wrap: Optional keyword arguments for function

618 L{pygeodesy.haversine}.

619

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

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

622 '''

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

624 **radius_wrap)

625 self._func = _formy.haversine

626 self._func_ = _formy.haversine_

627

628 if _FOR_DOCS:

629 discrete = Frechet.discrete

630

631

632 class FrechetHubeny(FrechetFlatLocal): # for Karl Hubeny

633 if _FOR_DOCS:

634 __doc__ = FrechetFlatLocal.__doc__

635 __init__ = FrechetFlatLocal.__init__

636 discrete = FrechetFlatLocal.discrete

637 distance = FrechetFlatLocal.discrete

638

639

640 class FrechetKarney(Frechet):

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

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

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

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

645 C{Inverse} method.

646 '''

647 _units = _Str_degrees

648

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

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

651

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

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

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

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

656 of class L{geodesicw.Geodesic}.

657

658 @raise ImportError: Package U{geographiclib

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

660

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

662

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

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

665 '''

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

667 **wrap)

668 self._datum_setter(datum)

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

670

671 if _FOR_DOCS:

672 discrete = Frechet.discrete

673

674

675 class FrechetThomas(_FrechetMeterRadians):

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

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

678 '''

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

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

681

682 @kwarg datum_wrap: Optional keyword argument for function

683 L{pygeodesy.thomas}.

684

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

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

687 '''

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

689 **datum_wrap)

690 self._func = _formy.thomas

691 self._func_ = _formy.thomas_

692

693 if _FOR_DOCS:

694 discrete = Frechet.discrete

695

696

697 class FrechetVincentys(_FrechetMeterRadians):

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

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

700

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

702 '''

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

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

705

706 @kwarg radius_wrap: Optional keyword arguments for function

707 L{pygeodesy.vincentys}.

708

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

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

711 '''

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

713 **radius_wrap)

714 self._func = _formy.vincentys

715 self._func_ = _formy.vincentys_

716

717 if _FOR_DOCS:

718 discrete = Frechet.discrete

719

720

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

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

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

724 '''

725 iFs = {}

726

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

728 return iFs.setdefault(i, i)

729

730 cF = _defaultdict(dict)

731

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

733 i = iF(i)

734 j = iF(j)

735 try:

736 t = cF[i][j]

737 except KeyError:

738 r = iF(r + 1)

739 try:

740 if i > 0:

741 if j > 0:

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

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

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

745 elif j < 0:

746 raise IndexError

747 else: # j == 0

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

749 elif i < 0:

750 raise IndexError

751

752 elif j > 0: # i == 0

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

754 elif j < 0: # i == 0

755 raise IndexError

756 else: # i == j == 0

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

758

759 d = dF(i, j)

760 if d > t[0]:

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

762 except IndexError:

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

764 cF[i][j] = t

765 return t

766

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

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

769# del cF, iFs

770 return Frechet6Tuple(t) # *t

771

772

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

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

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

776

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

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

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

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

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

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

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

784

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

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

787 B{C{point2s}}.

788

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

790

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

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

793

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

795

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

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

798 '''

799 _xcallable(distance=distance)

800

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

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

803

804 def _dF(i1, i2):

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

806

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

808

809

810 class Frechet6Tuple(_NamedTuple):

811 '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete}

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

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

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

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

816

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

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

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

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

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

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

823

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

825 I{fractional} index.

826 '''

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

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

829

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

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

832 '''

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

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

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

836

837# def __gt__(self, other):

838# _xinstanceof(Frechet6Tuple, other=other)

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

840#

841# def __lt__(self, other):

842# _xinstanceof(Frechet6Tuple, other=other)

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

844

845# **) MIT License

846#

847# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

848#

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

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

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

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

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

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

855#

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

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

858#

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

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

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

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

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

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

865# OTHER DEALINGS IN THE SOFTWARE.