Coverage for pygeodesy/frechet.py: 96%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Fréchet distances. 

5 

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

7L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, 

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

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

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

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

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

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

14 

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

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

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

18 

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

20from one set of C{LatLon} points. 

21 

22C{f = FrechetXyz(point1s, ...)} 

23 

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

25by 

26 

27C{t6 = f.discrete(point2s)} 

28 

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

30as keyword arguments as follows 

31 

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

33 

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

35 

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

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

38instance, more details in the documentation thereof. 

39 

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

41C{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 

54Transcribed from the original U{Computing Discrete Fréchet Distance 

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

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

57Information Systems Department/Christian Doppler Laboratory for Expert 

58Systems, Technical University Vienna, Austria. 

59 

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

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

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

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

64between each points pair. 

65 

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

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

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

69points set. 

70 

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

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

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

74corresponding set of points. 

75 

76The 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>}. 

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

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

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

82''' 

83 

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

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

86from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

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

88 _xkwds, _xkwds_get 

89import pygeodesy.formy as _formy 

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

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

92from pygeodesy.lazily import _ALL_LAZY, _FOR_DOCS 

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

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

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

96 PhiLam2Tuple, points2 as _points2, radians 

97from pygeodesy.props import property_doc_, property_RO 

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

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

100 _Str_radians, _Str_radians2 

101 

102from collections import defaultdict as _defaultdict 

103# from math import radians # from .points 

104 

105__all__ = _ALL_LAZY.frechet 

106__version__ = '23.10.31' 

107 

108 

109def _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 

121class FrechetError(PointsError): 

122 '''Fréchet issue. 

123 ''' 

124 pass 

125 

126 

127class 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): # PYCHOK no cover 

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

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

253 

254 @property_RO 

255 def kwds(self): 

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

257 ''' 

258 return self._kwds 

259 

260 def point(self, point): 

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

262 

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

264 L{Tuple2LatLon} or C{other}). 

265 

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

267 ''' 

268 return point # pass thru 

269 

270 def points_(self, points, i): 

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

272 

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

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

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

276 

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

278 ''' 

279 return self.point(points[i]) 

280 

281 def points_fraction(self, points, fi): 

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

283 

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

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

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

287 

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

289 ''' 

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

291 

292 def _points2(self, points): 

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

294 ''' 

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

296 

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

298 def units(self): 

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

300 ''' 

301 return self._units 

302 

303 @units.setter # PYCHOK setter! 

304 def units(self, units): 

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

306 

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

308 ''' 

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

310 

311 @property_RO 

312 def wrap(self): 

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

314 ''' 

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

316 

317 

318class FrechetDegrees(Frechet): 

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

320 ''' 

321 _units = _Str_degrees 

322 

323 if _FOR_DOCS: 

324 __init__ = Frechet.__init__ 

325 discrete = Frechet.discrete 

326 

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

328 '''I{Must be overloaded}.''' 

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

330 

331 

332class FrechetRadians(Frechet): 

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

334 ''' 

335 _units = _Str_radians 

336 

337 if _FOR_DOCS: 

338 __init__ = Frechet.__init__ 

339 discrete = Frechet.discrete 

340 

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

342 '''I{Must be overloaded}.''' 

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

344 

345 def point(self, point): 

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

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

348 

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

350 ''' 

351 try: 

352 return point.philam 

353 except AttributeError: 

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

355 

356 

357class _FrechetMeterRadians(Frechet): 

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

359 the optional keyword arguments supplied at instantiation 

360 of the C{Frechet*} sub-class. 

361 ''' 

362 _units = _Str_meter 

363 _units_ = _Str_radians 

364 

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

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

367 the distance function and units from the optional 

368 keyword arguments given at this instantiation, see 

369 property C{kwds}. 

370 

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

372 ''' 

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

374 

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

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

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

378 

379 

380class FrechetCosineAndoyerLambert(_FrechetMeterRadians): 

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

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

383 ''' 

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

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

386 

387 @kwarg datum_wrap: Optional keyword arguments for function 

388 L{pygeodesy.cosineAndoyerLambert}. 

389 

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

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

392 ''' 

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

394 **datum_wrap) 

395 self._func = _formy.cosineAndoyerLambert 

396 self._func_ = _formy.cosineAndoyerLambert_ 

397 

398 if _FOR_DOCS: 

399 discrete = Frechet.discrete 

400 

401 

402class FrechetCosineForsytheAndoyerLambert(_FrechetMeterRadians): 

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

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

405 ''' 

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

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

408 

409 @kwarg datum_wrap: Optional keyword arguments for function 

410 L{pygeodesy.cosineAndoyerLambert}. 

411 

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

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

414 ''' 

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

416 **datum_wrap) 

417 self._func = _formy.cosineForsytheAndoyerLambert 

418 self._func_ = _formy.cosineForsytheAndoyerLambert_ 

419 

420 if _FOR_DOCS: 

421 discrete = Frechet.discrete 

422 

423 

424class FrechetCosineLaw(_FrechetMeterRadians): 

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

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

427 

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

429 ''' 

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

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

432 

433 @kwarg radius_wrap: Optional keyword arguments for function 

434 L{pygeodesy.cosineLaw}. 

435 

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

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

438 ''' 

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

440 **radius_wrap) 

441 self._func = _formy.cosineLaw 

442 self._func_ = _formy.cosineLaw_ 

443 

444 if _FOR_DOCS: 

445 discrete = Frechet.discrete 

446 

447 

448class FrechetDistanceTo(Frechet): # FrechetMeter 

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

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

451 ''' 

452 _units = _Str_meter 

453 

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

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

456 

457 @kwarg distanceTo_kwds: Optional keyword arguments for each 

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

459 method. 

460 

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

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

463 

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

465 ellipsoidal or spherical C{LatLon} class. 

466 ''' 

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

468 **distanceTo_kwds) 

469 

470 if _FOR_DOCS: 

471 discrete = Frechet.discrete 

472 

473 def distance(self, p1, p2): 

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

475 ''' 

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

477 

478 def _points2(self, points): 

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

480 ''' 

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

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

483 

484 

485class FrechetEquirectangular(Frechet): 

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

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

488 ''' 

489 _units = _Str_radians2 

490 

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

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

493 

494 @kwarg adjust_limit_wrap: Optional keyword arguments for function 

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

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

497 

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

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

500 ''' 

501 adjust_limit_wrap = _xkwds(adjust_limit_wrap, limit=0) 

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

503 **adjust_limit_wrap) 

504 self._func = _formy._equirectangular # helper 

505 

506 if _FOR_DOCS: 

507 discrete = Frechet.discrete 

508 

509 

510class FrechetEuclidean(_FrechetMeterRadians): 

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

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

513 ''' 

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

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

516 

517 @kwarg adjust_radius_wrap: Optional keyword arguments for 

518 function L{pygeodesy.euclidean}. 

519 

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

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

522 ''' 

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

524 **adjust_radius_wrap) 

525 self._func = _formy.euclidean 

526 self._func_ = _formy.euclidean_ 

527 

528 if _FOR_DOCS: 

529 discrete = Frechet.discrete 

530 

531 

532class FrechetExact(Frechet): 

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

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

535 ''' 

536 _units = _Str_degrees 

537 

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

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

540 

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

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

543 L{Ellipsoid2} or L{a_f2Tuple}). 

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

545 of class L{geodesicx.GeodesicExact}. 

546 

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

548 

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

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

551 ''' 

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

553 **wrap) 

554 self._datum_setter(datum) 

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

556 

557 if _FOR_DOCS: 

558 discrete = Frechet.discrete 

559 

560 

561class FrechetFlatLocal(_FrechetMeterRadians): 

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

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

564 ''' 

565 _units_ = _Str_radians2 # see L{flatLocal_} 

566 

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

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

569 

570 @kwarg datum_scaled_wrap: Optional keyword arguments for 

571 function L{pygeodesy.flatLocal}. 

572 

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

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

575 

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

577 ''' 

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

579 **datum_scaled_wrap) 

580 self._func = _formy.flatLocal 

581 self._func_ = self.datum.ellipsoid._hubeny_2 

582 

583 if _FOR_DOCS: 

584 discrete = Frechet.discrete 

585 

586 

587class FrechetFlatPolar(_FrechetMeterRadians): 

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

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

590 ''' 

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

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

593 

594 @kwarg radius_wrap: Optional keyword arguments for function 

595 L{pygeodesy.flatPolar}. 

596 

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

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

599 ''' 

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

601 **radius_wrap) 

602 self._func = _formy.flatPolar 

603 self._func_ = _formy.flatPolar_ 

604 

605 if _FOR_DOCS: 

606 discrete = Frechet.discrete 

607 

608 

609class FrechetHaversine(_FrechetMeterRadians): 

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

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

612 

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

614 ''' 

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

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

617 

618 @kwarg radius_wrap: Optional keyword arguments for function 

619 L{pygeodesy.haversine}. 

620 

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

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

623 ''' 

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

625 **radius_wrap) 

626 self._func = _formy.haversine 

627 self._func_ = _formy.haversine_ 

628 

629 if _FOR_DOCS: 

630 discrete = Frechet.discrete 

631 

632 

633class FrechetHubeny(FrechetFlatLocal): # for Karl Hubeny 

634 if _FOR_DOCS: 

635 __doc__ = FrechetFlatLocal.__doc__ 

636 __init__ = FrechetFlatLocal.__init__ 

637 discrete = FrechetFlatLocal.discrete 

638 distance = FrechetFlatLocal.discrete 

639 

640 

641class FrechetKarney(Frechet): 

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

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

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

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

646 C{Inverse} method. 

647 ''' 

648 _units = _Str_degrees 

649 

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

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

652 

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

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

655 L{Ellipsoid2} or L{a_f2Tuple}). 

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

657 of class L{geodesicw.Geodesic}. 

658 

659 @raise ImportError: Package U{geographiclib 

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

661 

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

663 

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

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

666 ''' 

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

668 **wrap) 

669 self._datum_setter(datum) 

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

671 

672 if _FOR_DOCS: 

673 discrete = Frechet.discrete 

674 

675 

676class FrechetThomas(_FrechetMeterRadians): 

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

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

679 ''' 

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

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

682 

683 @kwarg datum_wrap: Optional keyword argument for function 

684 L{pygeodesy.thomas}. 

685 

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

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

688 ''' 

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

690 **datum_wrap) 

691 self._func = _formy.thomas 

692 self._func_ = _formy.thomas_ 

693 

694 if _FOR_DOCS: 

695 discrete = Frechet.discrete 

696 

697 

698class FrechetVincentys(_FrechetMeterRadians): 

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

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

701 

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

703 ''' 

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

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

706 

707 @kwarg radius_wrap: Optional keyword arguments for function 

708 L{pygeodesy.vincentys}. 

709 

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

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

712 ''' 

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

714 **radius_wrap) 

715 self._func = _formy.vincentys 

716 self._func_ = _formy.vincentys_ 

717 

718 if _FOR_DOCS: 

719 discrete = Frechet.discrete 

720 

721 

722def _frechet_(ni, fi, nj, fj, dF, units): # MCCABE 14 

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

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

725 ''' 

726 iFs = {} 

727 

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

729 return iFs.setdefault(i, i) 

730 

731 cF = _defaultdict(dict) 

732 

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

734 i = iF(i) 

735 j = iF(j) 

736 try: 

737 t = cF[i][j] 

738 except KeyError: 

739 r = iF(r + 1) 

740 try: 

741 if i > 0: 

742 if j > 0: 

743 t = min(_rF(i - fi, j, r), 

744 _rF(i - fi, j - fj, r), 

745 _rF(i, j - fj, r)) 

746 elif j < 0: 

747 raise IndexError 

748 else: # j == 0 

749 t = _rF(i - fi, 0, r) 

750 elif i < 0: 

751 raise IndexError 

752 

753 elif j > 0: # i == 0 

754 t = _rF(0, j - fj, r) 

755 elif j < 0: # i == 0 

756 raise IndexError 

757 else: # i == j == 0 

758 t = (NINF, i, j, r) 

759 

760 d = dF(i, j) 

761 if d > t[0]: 

762 t = (d, i, j, r) 

763 except IndexError: 

764 t = (INF, i, j, r) 

765 cF[i][j] = t 

766 return t 

767 

768 t = _rF(ni - 1, nj - 1, 0) 

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

770# del cF, iFs 

771 return Frechet6Tuple(t) # *t 

772 

773 

774def frechet_(point1s, point2s, distance=None, units=NN): 

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

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

777 

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

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

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

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

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

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

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

785 

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

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

788 B{C{point2s}}. 

789 

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

791 

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

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

794 

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

796 

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

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

799 ''' 

800 if not callable(distance): 

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

802 

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

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

805 

806 def _dF(i1, i2): 

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

808 

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

810 

811 

812class Frechet6Tuple(_NamedTuple): 

813 '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete} 

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

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

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

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

818 

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

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

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

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

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

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

825 

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

827 I{fractional} index. 

828 ''' 

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

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

831 

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

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

834 ''' 

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

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

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

838 

839# def __gt__(self, other): 

840# _xinstanceof(Frechet6Tuple, other=other) 

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

842# 

843# def __lt__(self, other): 

844# _xinstanceof(Frechet6Tuple, other=other) 

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

846 

847# **) MIT License 

848# 

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

850# 

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

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

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

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

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

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

857# 

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

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

860# 

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

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

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

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

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

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

867# OTHER DEALINGS IN THE SOFTWARE.