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 _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
102from collections import defaultdict as _defaultdict
103# from math import radians # from .points
105__all__ = _ALL_LAZY.frechet
106__version__ = '23.10.31'
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
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, name=NN, units=NN, **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
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}.
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
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)
173 @property_RO
174 def datum(self):
175 '''Get the datum (L{Datum} or C{None} if not applicable).
176 '''
177 return self._datum
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)
186 def discrete(self, point2s, fraction=None):
187 '''Compute the C{forward, discrete Fréchet} distance.
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.
196 @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)}.
198 @raise FrechetError: Insufficient number of B{C{point2s}} or
199 an invalid B{C{point2}} or B{C{fraction}}.
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)
206 def _discrete(self, point2s, fraction, distance):
207 '''(INTERNAL) Detailed C{discrete} with C{disance}.
208 '''
209 n2, ps2 = self._points2(point2s)
211 f2 = _fraction(fraction, n2)
212 p2 = self.points_fraction if f2 < EPS1 else self.points_ # PYCHOK expected
214 f1 = self.fraction
215 p1 = self.points_fraction if f1 < EPS1 else self.points_ # PYCHOK expected
217 def _dF(fi1, fi2):
218 return distance(p1(self._ps1, fi1), p2(ps2, fi2))
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)
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)
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
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.
246 @raise FrechetError: Invalid B{C{fraction}}.
247 '''
248 self._f1 = _fraction(fraction, self._n1)
250 def _func(self, *args, **kwds): # PYCHOK no cover
251 '''(INTERNAL) I{Must be overloaded}.'''
252 notOverloaded(self, *args, **kwds)
254 @property_RO
255 def kwds(self):
256 '''Get the supplied, optional keyword arguments (C{dict}).
257 '''
258 return self._kwds
260 def point(self, point):
261 '''Convert a point for the C{.distance} method.
263 @arg point: The point to convert ((C{LatLon}, L{Numpy2LatLon},
264 L{Tuple2LatLon} or C{other}).
266 @return: The converted B{C{point}}.
267 '''
268 return point # pass thru
270 def points_(self, points, i):
271 '''Get and convert a point for the C{.distance} method.
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}).
277 @return: The converted B{C{points[i]}}.
278 '''
279 return self.point(points[i])
281 def points_fraction(self, points, fi):
282 '''Get and convert a I{fractional} point for the C{.distance} method.
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}).
288 @return: The interpolated, converted, intermediate B{C{points[fi]}}.
289 '''
290 return self.point(_fractional(points, fi, None, wrap=None)) # was=self.wrap
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)
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
303 @units.setter # PYCHOK setter!
304 def units(self, units):
305 '''Set the distance units (C{Unit} or C{str}).
307 @raise TypeError: Invalid B{C{units}}.
308 '''
309 self._units = _xUnits(units, Base=Float)
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)
318class FrechetDegrees(Frechet):
319 '''DEPRECATED, use an other C{Frechet*} class.
320 '''
321 _units = _Str_degrees
323 if _FOR_DOCS:
324 __init__ = Frechet.__init__
325 discrete = Frechet.discrete
327 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover
328 '''I{Must be overloaded}.'''
329 notOverloaded(self, point1, point2, *args, **kwds)
332class FrechetRadians(Frechet):
333 '''DEPRECATED, use an other C{Frechet*} class.
334 '''
335 _units = _Str_radians
337 if _FOR_DOCS:
338 __init__ = Frechet.__init__
339 discrete = Frechet.discrete
341 def distance(self, point1, point2, *args, **kwds): # PYCHOK no cover
342 '''I{Must be overloaded}.'''
343 notOverloaded(self, point1, point2, *args, **kwds)
345 def point(self, point):
346 '''Return B{C{point}} as L{PhiLam2Tuple} to maintain
347 I{backward compatibility} of L{FrechetRadians}.
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))
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
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}.
371 @see: L{Frechet.discrete} for other details.
372 '''
373 return self._discrete(point2s, fraction, _formy._radistance(self))
375 def _func_(self, *args, **kwds): # PYCHOK no cover
376 '''(INTERNAL) I{Must be overloaded}.'''
377 notOverloaded(self, *args, **kwds)
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.
387 @kwarg datum_wrap: Optional keyword arguments for function
388 L{pygeodesy.cosineAndoyerLambert}.
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_
398 if _FOR_DOCS:
399 discrete = Frechet.discrete
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.
409 @kwarg datum_wrap: Optional keyword arguments for function
410 L{pygeodesy.cosineAndoyerLambert}.
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_
420 if _FOR_DOCS:
421 discrete = Frechet.discrete
424class FrechetCosineLaw(_FrechetMeterRadians):
425 '''Compute the C{Frechet} distance based on the I{angular} distance
426 in C{radians} from function L{pygeodesy.cosineLaw}.
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.
433 @kwarg radius_wrap: Optional keyword arguments for function
434 L{pygeodesy.cosineLaw}.
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_
444 if _FOR_DOCS:
445 discrete = Frechet.discrete
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
454 def __init__(self, point1s, fraction=None, name=NN, **distanceTo_kwds):
455 '''New L{FrechetDistanceTo} calculator/interpolator.
457 @kwarg distanceTo_kwds: Optional keyword arguments for each
458 B{C{point1s}}' C{LatLon.distanceTo}
459 method.
461 @see: L{Frechet.__init__} for details about B{C{point1s}},
462 B{C{fraction}}, B{C{name}} and other exceptions.
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)
470 if _FOR_DOCS:
471 discrete = Frechet.discrete
473 def distance(self, p1, p2):
474 '''Return the distance in C{meter}.
475 '''
476 return p1.distanceTo(p2, **self._kwds)
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)
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
491 def __init__(self, point1s, fraction=None, name=NN, **adjust_limit_wrap):
492 '''New L{FrechetEquirectangular} calculator/interpolator.
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}.
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
506 if _FOR_DOCS:
507 discrete = Frechet.discrete
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.
517 @kwarg adjust_radius_wrap: Optional keyword arguments for
518 function L{pygeodesy.euclidean}.
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_
528 if _FOR_DOCS:
529 discrete = Frechet.discrete
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
538 def __init__(self, point1s, fraction=None, name=NN, datum=None, **wrap):
539 '''New L{FrechetExact} calculator/interpolator.
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}.
547 @raise TypeError: Invalid B{C{datum}}.
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
557 if _FOR_DOCS:
558 discrete = Frechet.discrete
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_}
567 def __init__(self, point1s, fraction=None, name=NN, **datum_scaled_wrap):
568 '''New L{FrechetFlatLocal}/L{FrechetHubeny} calculator/interpolator.
570 @kwarg datum_scaled_wrap: Optional keyword arguments for
571 function L{pygeodesy.flatLocal}.
573 @see: L{Frechet.__init__} for details about B{C{point1s}},
574 B{C{fraction}}, B{C{name}} and other exceptions.
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
583 if _FOR_DOCS:
584 discrete = Frechet.discrete
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.
594 @kwarg radius_wrap: Optional keyword arguments for function
595 L{pygeodesy.flatPolar}.
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_
605 if _FOR_DOCS:
606 discrete = Frechet.discrete
609class FrechetHaversine(_FrechetMeterRadians):
610 '''Compute the C{Frechet} distance based on the I{angular}
611 distance in C{radians} from function L{pygeodesy.haversine_}.
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.
618 @kwarg radius_wrap: Optional keyword arguments for function
619 L{pygeodesy.haversine}.
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_
629 if _FOR_DOCS:
630 discrete = Frechet.discrete
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
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
650 def __init__(self, point1s, fraction=None, name=NN, datum=None, **wrap):
651 '''New L{FrechetKarney} calculator/interpolator.
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}.
659 @raise ImportError: Package U{geographiclib
660 <https://PyPI.org/project/geographiclib>} missing.
662 @raise TypeError: Invalid B{C{datum}}.
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
672 if _FOR_DOCS:
673 discrete = Frechet.discrete
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.
683 @kwarg datum_wrap: Optional keyword argument for function
684 L{pygeodesy.thomas}.
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_
694 if _FOR_DOCS:
695 discrete = Frechet.discrete
698class FrechetVincentys(_FrechetMeterRadians):
699 '''Compute the C{Frechet} distance based on the I{angular}
700 distance in C{radians} from function L{pygeodesy.vincentys_}.
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.
707 @kwarg radius_wrap: Optional keyword arguments for function
708 L{pygeodesy.vincentys}.
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_
718 if _FOR_DOCS:
719 discrete = Frechet.discrete
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 = {}
728 def iF(i): # cache index, depth ints and floats
729 return iFs.setdefault(i, i)
731 cF = _defaultdict(dict)
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
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)
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
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
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.
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}).
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}}.
790 @raise FrechetError: Insufficient number of B{C{point1s}} or B{C{point2s}}.
792 @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit()
793 <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}.
795 @raise TypeError: If B{C{distance}} is not a callable.
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)
803 n1, ps1 = _points2(point1s, closed=False, Error=FrechetError)
804 n2, ps2 = _points2(point2s, closed=False, Error=FrechetError)
806 def _dF(i1, i2):
807 return distance(ps1[i1], ps2[i2])
809 return _frechet_(n1, 1, n2, 1, _dF, units)
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}.
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]}.
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)
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)
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]
847# **) MIT License
848#
849# Copyright (C) 2016-2023 -- 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.