Coverage for pygeodesy/frechet.py: 96%
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2# -*- coding: utf-8 -*-
4u'''Fréchet distances.
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.
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>}.
19Typical usage is as follows. First, create a C{Frechet} calculator
20from one set of C{LatLon} points.
22C{f = FrechetXyz(point1s, ...)}
24Get the I{discrete} Fréchet distance to another set of C{LatLon} points
25by
27C{t6 = f.discrete(point2s)}
29Or, use function C{frechet_} with a proper C{distance} function passed
30as keyword arguments as follows
32C{t6 = frechet_(point1s, point2s, ..., distance=...)}.
34In both cases, the returned result C{t6} is a L{Frechet6Tuple}.
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.
40For other points, create a L{Frechet} sub-class with the appropriate
41C{distance} method overloading L{Frechet.distance} as in this example.
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)
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.
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.
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.
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.
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'''
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 PointsError, _xattr, _xcallable, _xkwds, \
88 _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 _name2__, _Named, _NamedTuple, _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, 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
102from collections import defaultdict as _defaultdict
103# from math import radians # from .points
105__all__ = _ALL_LAZY.frechet
106__version__ = '24.06.10'
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
121class FrechetError(PointsError):
122 '''Fréchet issue.
123 '''
124 pass
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/property
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
139 def __init__(self, point1s, fraction=None, units=NN, **name__kwds):
140 '''New C{Frechet...} calculator/interpolator.
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 C{None},
146 C{0} or C{1} for no intermediate B{C{point1s}} and no
147 I{fractional} indices.
148 @kwarg units: Optional distance units (C{Unit} or C{str}).
149 @kwarg name__kwds: Optional C{B{name}=NN} for this calculator/interpolator
150 (C{str}) and any keyword arguments for the distance function,
151 retrievable with property C{kwds}.
153 @raise FrechetError: Insufficient number of B{C{point1s}} or an invalid
154 B{C{point1}}, B{C{fraction}} or B{C{units}}.
155 '''
156 name, kwds = _name2__(**name__kwds) # name__=self.__class__
157 if name:
158 self.name = name
160 self._n1, self._ps1 = self._points2(point1s)
161 if fraction:
162 self.fraction = fraction
163 if units: # and not self.units:
164 self.units = units
165 if kwds:
166 self._kwds = kwds
168 @property_RO
169 def adjust(self):
170 '''Get the C{adjust} setting (C{bool} or C{None}).
171 '''
172 return _xkwds_get(self._kwds, adjust=None)
174 @property_RO
175 def datum(self):
176 '''Get the datum (L{Datum} or C{None} if not applicable).
177 '''
178 return self._datum
180 def _datum_setter(self, datum):
181 '''(INTERNAL) Set the datum.
182 '''
183 d = datum or _xattr(self._ps1[0], datum=None)
184 if d and d is not self._datum: # PYCHOK no cover
185 self._datum = _ellipsoidal_datum(d, name=self.name)
187 def discrete(self, point2s, fraction=None):
188 '''Compute the C{forward, discrete Fréchet} distance.
190 @arg point2s: Second set of points (C{LatLon}[], L{Numpy2LatLon}[],
191 L{Tuple2LatLon}[] or C{other}[]).
192 @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to
193 interpolate intermediate B{C{point2s}} or use
194 C{None}, C{0} or C{1} for no intermediate
195 B{C{point2s}} and no I{fractional} indices.
197 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)}.
199 @raise FrechetError: Insufficient number of B{C{point2s}} or
200 an invalid B{C{point2}} or B{C{fraction}}.
202 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit
203 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}.
204 '''
205 return self._discrete(point2s, fraction, self.distance)
207 def _discrete(self, point2s, fraction, distance):
208 '''(INTERNAL) Detailed C{discrete} with C{disance}.
209 '''
210 n2, ps2 = self._points2(point2s)
212 f2 = _fraction(fraction, n2)
213 p2 = self.points_fraction if f2 < EPS1 else self.points_ # PYCHOK expected
215 f1 = self.fraction
216 p1 = self.points_fraction if f1 < EPS1 else self.points_ # PYCHOK expected
218 def _dF(fi1, fi2):
219 return distance(p1(self._ps1, fi1), p2(ps2, fi2))
221 try:
222 return _frechet_(self._n1, f1, n2, f2, _dF, self.units)
223 except TypeError as x:
224 t = _DOT_(self.classname, self.discrete.__name__)
225 raise FrechetError(t, cause=x)
227 def distance(self, point1, point2):
228 '''Return the distance between B{C{point1}} and B{C{point2s}},
229 subject to the supplied optional keyword arguments, see
230 property C{kwds}.
231 '''
232 return self._func(point1.lat, point1.lon,
233 point2.lat, point2.lon, **self._kwds)
235 @property_doc_(''' the index fraction (C{float}).''')
236 def fraction(self):
237 '''Get the index fraction (C{float} or C{1}).
238 '''
239 return self._f1
241 @fraction.setter # PYCHOK setter!
242 def fraction(self, fraction):
243 '''Set the index fraction (C{float} in C{EPS}..L{EPS1}) to interpolate
244 intermediate B{C{point1s}} or use C{None}, C{0} or C{1} for no
245 intermediate B{C{point1s}} and no I{fractional} indices.
247 @raise FrechetError: Invalid B{C{fraction}}.
248 '''
249 self._f1 = _fraction(fraction, self._n1)
251# def _func(self, *args, **kwds): # PYCHOK no cover
252# '''(INTERNAL) I{Must be overloaded}.'''
253# self._notOverloaded(*args, **kwds)
255 @Property
256 def _func(self):
257 '''(INTERNAL) I{Must be overloaded}.'''
258 self._notOverloaded(**self.kwds)
260 @_func.setter_ # PYCHOK setter_underscore!
261 def _func(self, func):
262 return _formy._Propy(func, 4, self.kwds)
264 @property_RO
265 def kwds(self):
266 '''Get the supplied, optional keyword arguments (C{dict}).
267 '''
268 return self._kwds
270 def point(self, point):
271 '''Convert a point for the C{.distance} method.
273 @arg point: The point to convert ((C{LatLon}, L{Numpy2LatLon},
274 L{Tuple2LatLon} or C{other}).
276 @return: The converted B{C{point}}.
277 '''
278 return point # pass thru
280 def points_(self, points, i):
281 '''Get and convert a point for the C{.distance} method.
283 @arg points: The orignal B{C{points}} to convert ((C{LatLon}[],
284 L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]).
285 @arg i: The B{C{points}} index (C{int}).
287 @return: The converted B{C{points[i]}}.
288 '''
289 return self.point(points[i])
291 def points_fraction(self, points, fi):
292 '''Get and convert a I{fractional} point for the C{.distance} method.
294 @arg points: The orignal B{C{points}} to convert ((C{LatLon}[],
295 L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]).
296 @arg fi: The I{fractional} index in B{C{points}} (C{float} or C{int}).
298 @return: The interpolated, converted, intermediate B{C{points[fi]}}.
299 '''
300 return self.point(_fractional(points, fi, None, wrap=None)) # was=self.wrap
302 def _points2(self, points):
303 '''(INTERNAL) Check a set of points, overloaded in L{FrechetDistanceTo}.
304 '''
305 return _points2(points, closed=False, Error=FrechetError)
307 @property_doc_(''' the distance units (C{Unit} or C{str}).''')
308 def units(self):
309 '''Get the distance units (C{Unit} or C{str}).
310 '''
311 return self._units
313 @units.setter # PYCHOK setter!
314 def units(self, units):
315 '''Set the distance units (C{Unit} or C{str}).
317 @raise TypeError: Invalid B{C{units}}.
318 '''
319 self._units = _xUnits(units, Base=Float)
321 @property_RO
322 def wrap(self):
323 '''Get the C{wrap} setting (C{bool} or C{None}).
324 '''
325 return _xkwds_get(self._kwds, wrap=None)
328class FrechetDegrees(Frechet):
329 '''DEPRECATED, use an other C{Frechet*} class.
330 '''
331 _units = _Str_degrees
333 if _FOR_DOCS:
334 __init__ = Frechet.__init__
335 discrete = Frechet.discrete
337 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover
338 '''I{Must be overloaded}.'''
339 self._notOverloaded(point1, point2, *args, **kwds)
342class FrechetRadians(Frechet):
343 '''DEPRECATED, use an other C{Frechet*} class.
344 '''
345 _units = _Str_radians
347 if _FOR_DOCS:
348 __init__ = Frechet.__init__
349 discrete = Frechet.discrete
351 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover
352 '''I{Must be overloaded}.'''
353 self._notOverloaded(point1, point2, *args, **kwds)
355 def point(self, point):
356 '''Return B{C{point}} as L{PhiLam2Tuple} to maintain
357 I{backward compatibility} of L{FrechetRadians}.
359 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
360 '''
361 try:
362 return point.philam
363 except AttributeError:
364 return PhiLam2Tuple(radians(point.lat), radians(point.lon))
367class _FrechetMeterRadians(Frechet):
368 '''(INTERNAL) Returning C{meter} or C{radians} depending on
369 the optional keyword arguments supplied at instantiation
370 of the C{Frechet*} sub-class.
371 '''
372 _units = _Str_meter
373 _units_ = _Str_radians
375 def discrete(self, point2s, fraction=None):
376 '''Overloaded method L{Frechet.discrete} to determine
377 the distance function and units from the optional
378 keyword arguments given at this instantiation, see
379 property C{kwds}.
381 @see: L{Frechet.discrete} for other details.
382 '''
383 return self._discrete(point2s, fraction, _formy._radistance(self))
385 @Property
386 def _func_(self):
387 '''(INTERNAL) I{Must be overloaded}.'''
388 self._notOverloaded(**self.kwds)
390 @_func_.setter_ # PYCHOK setter_underscore!
391 def _func_(self, func):
392 return _formy._Propy(func, 3, self.kwds)
395class FrechetCosineAndoyerLambert(_FrechetMeterRadians):
396 '''Compute the C{Frechet} distance based on the I{angular} distance
397 in C{radians} from function L{pygeodesy.cosineAndoyerLambert}.
398 '''
399 def __init__(self, point1s, **fraction_name__datum_wrap):
400 '''New L{FrechetCosineAndoyerLambert} calculator/interpolator.
402 @kwarg fraction_name__datum_wrap: Optional C{B{fraction}=None}
403 and C{B{name}=NN} and keyword arguments for
404 function L{pygeodesy.cosineAndoyerLambert}.
406 @see: L{Frechet.__init__} for details about B{C{point1s}},
407 B{C{fraction}}, B{C{name}} and other exceptions.
408 '''
409 Frechet.__init__(self, point1s, **fraction_name__datum_wrap)
410 self._func = _formy.cosineAndoyerLambert
411 self._func_ = _formy.cosineAndoyerLambert_
413 if _FOR_DOCS:
414 discrete = Frechet.discrete
417class FrechetCosineForsytheAndoyerLambert(_FrechetMeterRadians):
418 '''Compute the C{Frechet} distance based on the I{angular} distance
419 in C{radians} from function L{pygeodesy.cosineForsytheAndoyerLambert}.
420 '''
421 def __init__(self, point1s, **fraction_name__datum_wrap):
422 '''New L{FrechetCosineForsytheAndoyerLambert} calculator/interpolator.
424 @kwarg fraction_name__datum_wrap: Optional C{B{fraction}=None} and
425 C{B{name}=NN} and keyword arguments for function
426 L{pygeodesy.cosineForsytheAndoyerLambert}.
428 @see: L{Frechet.__init__} for details about B{C{point1s}},
429 B{C{fraction}}, B{C{name}} and other exceptions.
430 '''
431 Frechet.__init__(self, point1s, **fraction_name__datum_wrap)
432 self._func = _formy.cosineForsytheAndoyerLambert
433 self._func_ = _formy.cosineForsytheAndoyerLambert_
435 if _FOR_DOCS:
436 discrete = Frechet.discrete
439class FrechetCosineLaw(_FrechetMeterRadians):
440 '''Compute the C{Frechet} distance based on the I{angular} distance
441 in C{radians} from function L{pygeodesy.cosineLaw}.
443 @note: See note at function L{pygeodesy.vincentys_}.
444 '''
445 def __init__(self, point1s, **fraction_name__radius_wrap):
446 '''New L{FrechetCosineLaw} calculator/interpolator.
448 @kwarg fraction_name__radius_wrap: Optional C{B{fraction}=None}
449 and C{B{name}=NN} and keyword arguments
450 for function L{pygeodesy.cosineLaw}.
452 @see: L{Frechet.__init__} for details about B{C{point1s}},
453 B{C{fraction}}, B{C{name}} and other exceptions.
454 '''
455 Frechet.__init__(self, point1s, **fraction_name__radius_wrap)
456 self._func = _formy.cosineLaw
457 self._func_ = _formy.cosineLaw_
459 if _FOR_DOCS:
460 discrete = Frechet.discrete
463class FrechetDistanceTo(Frechet): # FrechetMeter
464 '''Compute the C{Frechet} distance based on the distance from the
465 point1s' C{LatLon.distanceTo} method, conventionally in C{meter}.
466 '''
467 _units = _Str_meter
469 def __init__(self, point1s, **fraction_name__distanceTo_kwds):
470 '''New L{FrechetDistanceTo} calculator/interpolator.
472 @kwarg fraction_name__distanceTo_kwds: Optional C{B{fraction}=None}
473 and C{B{name}=NN} and keyword arguments for
474 each B{C{point1s}}' C{LatLon.distanceTo} method.
476 @see: L{Frechet.__init__} for details about B{C{point1s}}, B{C{fraction}},
477 B{C{name}} and other exceptions.
479 @note: All B{C{point1s}} I{must} be instances of the same ellipsoidal
480 or spherical C{LatLon} class.
481 '''
482 Frechet.__init__(self, point1s, **fraction_name__distanceTo_kwds)
484 if _FOR_DOCS:
485 discrete = Frechet.discrete
487 def distance(self, p1, p2):
488 '''Return the distance in C{meter}.
489 '''
490 return p1.distanceTo(p2, **self._kwds)
492 def _points2(self, points):
493 '''(INTERNAL) Check a set of points.
494 '''
495 np, ps = Frechet._points2(self, points)
496 return np, _distanceTo(FrechetError, points=ps)
499class FrechetEquirectangular(Frechet):
500 '''Compute the C{Frechet} distance based on the I{equirectangular}
501 distance in C{radians squared} like function L{pygeodesy.equirectangular}.
502 '''
503 _units = _Str_radians2
505 def __init__(self, point1s, **fraction_name__adjust_limit_wrap):
506 '''New L{FrechetEquirectangular} calculator/interpolator.
508 @kwarg fraction_name__adjust_limit_wrap: Optional C{B{fraction}=None}
509 and C{B{name}=NN} and keyword arguments for
510 function L{pygeodesy.equirectangular} I{with
511 default} C{B{limit}=0} for I{backward compatibility}.
513 @see: L{Frechet.__init__} for details about B{C{point1s}}, B{C{fraction}},
514 B{C{name}} and other exceptions.
515 '''
516 Frechet.__init__(self, point1s, **_xkwds(fraction_name__adjust_limit_wrap,
517 limit=0))
518 self._func = _formy._equirectangular # helper
520 if _FOR_DOCS:
521 discrete = Frechet.discrete
524class FrechetEuclidean(_FrechetMeterRadians):
525 '''Compute the C{Frechet} distance based on the I{Euclidean}
526 distance in C{radians} from function L{pygeodesy.euclidean}.
527 '''
528 def __init__(self, point1s, **fraction_name__adjust_radius_wrap): # was=True
529 '''New L{FrechetEuclidean} calculator/interpolator.
531 @kwarg fraction_name__adjust_radius_wrap: Optional C{B{fraction}=None}
532 and C{B{name}=NN} and keyword arguments for
533 function L{pygeodesy.euclidean}.
535 @see: L{Frechet.__init__} for details about B{C{point1s}}, B{C{fraction}},
536 B{C{name}} and other exceptions.
537 '''
538 Frechet.__init__(self, point1s, **fraction_name__adjust_radius_wrap)
539 self._func = _formy.euclidean
540 self._func_ = _formy.euclidean_
542 if _FOR_DOCS:
543 discrete = Frechet.discrete
546class FrechetExact(Frechet):
547 '''Compute the C{Frechet} distance based on the I{angular} distance
548 in C{degrees} from method L{GeodesicExact}C{.Inverse}.
549 '''
550 _units = _Str_degrees
552 def __init__(self, point1s, datum=None, **fraction_name__wrap):
553 '''New L{FrechetExact} calculator/interpolator.
555 @kwarg datum: Datum to override the default C{Datums.WGS84} and first
556 B{C{point1s}}' datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
557 or L{a_f2Tuple}).
558 @kwarg fraction_name__wrap: Optional C{B{fraction}=None} and C{B{name}=NN}
559 and keyword argument for method C{Inverse1} of class
560 L{geodesicx.GeodesicExact}.
562 @raise TypeError: Invalid B{C{datum}}.
564 @see: L{Frechet.__init__} for details about B{C{point1s}}, B{C{fraction}},
565 B{C{name}} and other exceptions.
566 '''
567 Frechet.__init__(self, point1s, **fraction_name__wrap)
568 self._datum_setter(datum)
569 self._func = self.datum.ellipsoid.geodesicx.Inverse1 # note -x
571 if _FOR_DOCS:
572 discrete = Frechet.discrete
575class FrechetFlatLocal(_FrechetMeterRadians):
576 '''Compute the C{Frechet} distance based on the I{angular} distance in
577 C{radians squared} like function L{pygeodesy.flatLocal_}/L{pygeodesy.hubeny}.
578 '''
579 _units_ = _Str_radians2 # see L{flatLocal_}
581 def __init__(self, point1s, **fraction_name__datum_scaled_wrap):
582 '''New L{FrechetFlatLocal}/L{FrechetHubeny} calculator/interpolator.
584 @kwarg fraction_name__datum_scaled_wrap: Optional C{B{fraction}=None}
585 and C{B{name}=NN} and keyword arguments for
586 function L{pygeodesy.flatLocal}.
588 @see: L{Frechet.__init__} for details about B{C{point1s}}, B{C{fraction}},
589 B{C{name}} and other exceptions.
591 @note: The distance C{units} are C{radians squared}, not C{radians}.
592 '''
593 Frechet.__init__(self, point1s, **fraction_name__datum_scaled_wrap)
594 self._func = _formy.flatLocal
595 self._func_ = self.datum.ellipsoid._hubeny_2
597 if _FOR_DOCS:
598 discrete = Frechet.discrete
601class FrechetFlatPolar(_FrechetMeterRadians):
602 '''Compute the C{Frechet} distance based on the I{angular} distance
603 in C{radians} from function L{flatPolar_}.
604 '''
605 def __init__(self, point1s, **fraction_name__radius_wrap):
606 '''New L{FrechetFlatPolar} calculator/interpolator.
608 @kwarg fraction_name__radius_wrap: Optional C{B{fraction}=None}
609 and C{B{name}=NN} and keyword arguments
610 for function L{pygeodesy.flatPolar}.
612 @see: L{Frechet.__init__} for details about B{C{point1s}},
613 B{C{fraction}}, B{C{name}} and other exceptions.
614 '''
615 Frechet.__init__(self, point1s, **fraction_name__radius_wrap)
616 self._func = _formy.flatPolar
617 self._func_ = _formy.flatPolar_
619 if _FOR_DOCS:
620 discrete = Frechet.discrete
623class FrechetHaversine(_FrechetMeterRadians):
624 '''Compute the C{Frechet} distance based on the I{angular}
625 distance in C{radians} from function L{pygeodesy.haversine_}.
627 @note: See note at function L{pygeodesy.vincentys_}.
628 '''
629 def __init__(self, point1s, **fraction_name__radius_wrap):
630 '''New L{FrechetHaversine} calculator/interpolator.
632 @kwarg fraction_name__radius_wrap: Optional C{B{fraction}=None}
633 and C{B{name}=NN} and keyword arguments
634 for function L{pygeodesy.haversine}.
636 @see: L{Frechet.__init__} for details about B{C{point1s}},
637 B{C{fraction}}, B{C{name}} and other exceptions.
638 '''
639 Frechet.__init__(self, point1s, **fraction_name__radius_wrap)
640 self._func = _formy.haversine
641 self._func_ = _formy.haversine_
643 if _FOR_DOCS:
644 discrete = Frechet.discrete
647class FrechetHubeny(FrechetFlatLocal): # for Karl Hubeny
648 if _FOR_DOCS:
649 __doc__ = FrechetFlatLocal.__doc__
650 __init__ = FrechetFlatLocal.__init__
651 discrete = FrechetFlatLocal.discrete
652 distance = FrechetFlatLocal.discrete
655class FrechetKarney(Frechet):
656 '''Compute the C{Frechet} distance based on the I{angular}
657 distance in C{degrees} from I{Karney}'s U{geographiclib
658 <https://PyPI.org/project/geographiclib>} U{geodesic.Geodesic
659 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}
660 C{Inverse} method.
661 '''
662 _units = _Str_degrees
664 def __init__(self, point1s, datum=None, **fraction_name__wrap):
665 '''New L{FrechetKarney} calculator/interpolator.
667 @kwarg datum: Datum to override the default C{Datums.WGS84} and
668 first B{C{knots}}' datum (L{Datum}, L{Ellipsoid},
669 L{Ellipsoid2} or L{a_f2Tuple}).
670 @kwarg fraction_name__wrap: Optional C{B{fraction}=None} and
671 C{B{name}=NN} and keyword arguments for
672 method C{Inverse1} of class L{geodesicw.Geodesic}.
674 @raise ImportError: Package U{geographiclib
675 <https://PyPI.org/project/geographiclib>} missing.
677 @raise TypeError: Invalid B{C{datum}}.
679 @see: L{Frechet.__init__} for details about B{C{point1s}},
680 B{C{fraction}}, B{C{name}} and other exceptions.
681 '''
682 Frechet.__init__(self, point1s, **fraction_name__wrap)
683 self._datum_setter(datum)
684 self._func = self.datum.ellipsoid.geodesic.Inverse1
686 if _FOR_DOCS:
687 discrete = Frechet.discrete
690class FrechetThomas(_FrechetMeterRadians):
691 '''Compute the C{Frechet} distance based on the I{angular} distance
692 in C{radians} from function L{pygeodesy.thomas_}.
693 '''
694 def __init__(self, point1s, **fraction_name__datum_wrap):
695 '''New L{FrechetThomas} calculator/interpolator.
697 @kwarg fraction_name__datum_wrap: Optional C{B{fraction}=None}
698 and C{B{name}=NN} and keyword arguments
699 for function L{pygeodesy.thomas}.
701 @see: L{Frechet.__init__} for details about B{C{point1s}},
702 B{C{fraction}}, B{C{name}} and other exceptions.
703 '''
704 Frechet.__init__(self, point1s, **fraction_name__datum_wrap)
705 self._func = _formy.thomas
706 self._func_ = _formy.thomas_
708 if _FOR_DOCS:
709 discrete = Frechet.discrete
712class FrechetVincentys(_FrechetMeterRadians):
713 '''Compute the C{Frechet} distance based on the I{angular}
714 distance in C{radians} from function L{pygeodesy.vincentys_}.
716 @note: See note at function L{pygeodesy.vincentys_}.
717 '''
718 def __init__(self, point1s, **fraction_name__radius_wrap):
719 '''New L{FrechetVincentys} calculator/interpolator.
721 @kwarg fraction_name__radius_wrap: Optional C{B{fraction}=None}
722 and C{B{name}=NN} and keyword arguments
723 for function L{pygeodesy.vincentys}.
725 @see: L{Frechet.__init__} for details about B{C{point1s}},
726 B{C{fraction}}, B{C{name}} and other exceptions.
727 '''
728 Frechet.__init__(self, point1s, **fraction_name__radius_wrap)
729 self._func = _formy.vincentys
730 self._func_ = _formy.vincentys_
732 if _FOR_DOCS:
733 discrete = Frechet.discrete
736def _frechet_(ni, fi, nj, fj, dF, units): # MCCABE 14
737 '''(INTERNAL) Recursive core of function L{frechet_}
738 and method C{discrete} of C{Frechet...} classes.
739 '''
740 iFs = {}
742 def iF(i): # cache index, depth ints and floats
743 return iFs.setdefault(i, i)
745 cF = _defaultdict(dict)
747 def _rF(i, j, r): # recursive Fréchet
748 i = iF(i)
749 j = iF(j)
750 try:
751 t = cF[i][j]
752 except KeyError:
753 r = iF(r + 1)
754 try:
755 if i > 0:
756 if j > 0:
757 t = min(_rF(i - fi, j, r),
758 _rF(i - fi, j - fj, r),
759 _rF(i, j - fj, r))
760 elif j < 0:
761 raise IndexError
762 else: # j == 0
763 t = _rF(i - fi, 0, r)
764 elif i < 0:
765 raise IndexError
767 elif j > 0: # i == 0
768 t = _rF(0, j - fj, r)
769 elif j < 0: # i == 0
770 raise IndexError
771 else: # i == j == 0
772 t = (NINF, i, j, r)
774 d = dF(i, j)
775 if d > t[0]:
776 t = (d, i, j, r)
777 except IndexError:
778 t = (INF, i, j, r)
779 cF[i][j] = t
780 return t
782 t = _rF(ni - 1, nj - 1, 0)
783 t += (sum(map(len, cF.values())), units)
784# del cF, iFs
785 return Frechet6Tuple(t) # *t
788def frechet_(point1s, point2s, distance=None, units=NN):
789 '''Compute the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>}
790 distance between two paths, each given as a set of points.
792 @arg point1s: First set of points (C{LatLon}[], L{Numpy2LatLon}[],
793 L{Tuple2LatLon}[] or C{other}[]).
794 @arg point2s: Second set of points (C{LatLon}[], L{Numpy2LatLon}[],
795 L{Tuple2LatLon}[] or C{other}[]).
796 @kwarg distance: Callable returning the distance between a B{C{point1s}}
797 and a B{C{point2s}} point (signature C{(point1, point2)}).
798 @kwarg units: Optional, the distance units (C{Unit} or C{str}).
800 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)} where C{fi1}
801 and C{fi2} are type C{int} indices into B{C{point1s}} respectively
802 B{C{point2s}}.
804 @raise FrechetError: Insufficient number of B{C{point1s}} or B{C{point2s}}.
806 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit()
807 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}.
809 @raise TypeError: If B{C{distance}} is not a callable.
811 @note: Function L{frechet_} does I{not} support I{fractional} indices
812 for intermediate B{C{point1s}} and B{C{point2s}}.
813 '''
814 _xcallable(distance=distance)
816 n1, ps1 = _points2(point1s, closed=False, Error=FrechetError)
817 n2, ps2 = _points2(point2s, closed=False, Error=FrechetError)
819 def _dF(i1, i2):
820 return distance(ps1[i1], ps2[i2])
822 return _frechet_(n1, 1, n2, 1, _dF, units)
825class Frechet6Tuple(_NamedTuple):
826 '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete}
827 U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance
828 C{fd}, I{fractional} indices C{fi1} and C{fi2} as C{FIx}, the
829 recursion depth C{r}, the number of distances computed C{n} and
830 the L{units} class or class or name of the distance C{units}.
832 If I{fractional} indices C{fi1} and C{fi2} are C{int}, the
833 returned C{fd} is the distance between C{point1s[fi1]} and
834 C{point2s[fi2]}. For C{float} indices, the distance is
835 between an intermediate point along C{point1s[int(fi1)]} and
836 C{point1s[int(fi1) + 1]} respectively an intermediate point
837 along C{point2s[int(fi2)]} and C{point2s[int(fi2) + 1]}.
839 Use function L{fractional} to compute the point at a
840 I{fractional} index.
841 '''
842 _Names_ = ('fd', 'fi1', 'fi2', 'r', _n_, _units_)
843 _Units_ = (_Pass, FIx, FIx, Number_, Number_, _Pass)
845 def toUnits(self, **Error_name): # PYCHOK expected
846 '''Overloaded C{_NamedTuple.toUnits} for C{fd} units.
847 '''
848 U = _xUnit(self.units, Float) # PYCHOK expected
849 return _NamedTuple.toUnits(self.reUnit(U), **Error_name) # PYCHOK self
851# def __gt__(self, other):
852# _xinstanceof(Frechet6Tuple, other=other)
853# return self if self.fd > other.fd else other # PYCHOK .fd=[0]
854#
855# def __lt__(self, other):
856# _xinstanceof(Frechet6Tuple, other=other)
857# return self if self.fd < other.fd else other # PYCHOK .fd=[0]
859# **) MIT License
860#
861# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
862#
863# Permission is hereby granted, free of charge, to any person obtaining a
864# copy of this software and associated documentation files (the "Software"),
865# to deal in the Software without restriction, including without limitation
866# the rights to use, copy, modify, merge, publish, distribute, sublicense,
867# and/or sell copies of the Software, and to permit persons to whom the
868# Software is furnished to do so, subject to the following conditions:
869#
870# The above copyright notice and this permission notice shall be included
871# in all copies or substantial portions of the Software.
872#
873# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
874# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
875# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
876# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
877# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
878# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
879# OTHER DEALINGS IN THE SOFTWARE.