# Coverage for pygeodesy/frechet.py : 97%

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Only L{FrechetDistanceTo} -iff used with L{ellipsoidalKarney.LatLon} points- and L{FrechetKarney} requires installation of I{Charles Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>}. Typical usage is as follows. First, create a C{Frechet} calculator from one set of C{LatLon} points. C{f = FrechetXyz(points1, ...)} Get the I{discrete} Fréchet distance to another set of C{LatLon} points by C{t6 = f.discrete(points2)} Or, use function C{frechet_} with a proper C{distance} function passed as keyword arguments as follows C{t6 = frechet_(points1, points2, ..., distance=...)}. In both cases, the returned result C{t6} is a L{Frechet6Tuple}. For C{(lat, lon, ...)} points in a C{NumPy} array or plain C{tuples}, wrap the points in a L{Numpy2LatLon} respectively L{Tuple2LatLon} instance, more details in the documentation thereof. For other points, create a L{Frechet} sub-class with the appropriate C{distance} method overloading L{Frechet.distance} as in this example. >>> from pygeodesy import Frechet, hypot_ >>> >>> class F3D(Frechet): >>> """Custom Frechet example. >>> """ >>> def distance(self, p1, p2): >>> return hypot_(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z) >>> >>> f3D = F3D(xyz1, ..., units="...") >>> t6 = f3D.discrete(xyz2) Transcribed from the original U{Computing Discrete Fréchet Distance <https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>} by Eiter, T. and Mannila, H., 1994, April 25, Technical Report CD-TR 94/64, Information Systems Department/Christian Doppler Laboratory for Expert Systems, Technical University Vienna, Austria. This L{Frechet.discrete} implementation optionally generates intermediate points for each point set separately. For example, using keyword argument C{fraction=0.5} adds one additional point halfway between each pair of points. Or using C{fraction=0.1} interpolates nine additional points between each points pair. The L{Frechet6Tuple} attributes C{fi1} and/or C{fi2} will be I{fractional} indices of type C{float} if keyword argument C{fraction} is used. Otherwise, C{fi1} and/or C{fi2} are simply type C{int} indices into the respective points set. For example, C{fractional} index value 2.5 means an intermediate point halfway between points[2] and points[3]. Use function L{fractional} to obtain the intermediate point for a I{fractional} index in the corresponding set of points. The C{Fréchet} distance was introduced in 1906 by U{Maurice Fréchet <https://WikiPedia.org/wiki/Maurice_Rene_Frechet>}, see U{reference [6]<https://www.kr.TUWien.ac.AT/staff/eiter/et-archive/cdtr9464.pdf>}. It is a measure of similarity between curves that takes into account the location and ordering of the points. Therefore, it is often a better metric than the well-known C{Hausdorff} distance, see the L{hausdorff} module. ''' from pygeodesy.basics import _bkwds, EPS, EPS1, INF, isscalar, \ property_doc_, property_RO, _xinstanceof from pygeodesy.datum import Datums, Datum from pygeodesy.errors import _AssertionError, _IndexError, _IsnotError, \ PointsError from pygeodesy.fmath import favg, hypot2 from pygeodesy.formy import cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, \ cosineLaw_, euclidean_, flatPolar_, haversine_, \ points2 as _points2, _scale_rad, thomas_, vincentys_ from pygeodesy.interns import _datum_, _degrees_, _distanceTo_, _dot_, _item_sq, \ _meter_, NN, _points_, _radians_, _radians2_, _units_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import LatLon2Tuple, _Named, _NamedTuple, \ notOverloaded, PhiLam2Tuple from pygeodesy.utily import unrollPI from collections import defaultdict from math import radians __all__ = _ALL_LAZY.frechet __version__ = '20.08.06' if not 0 < EPS < EPS1 < 1: raise _AssertionError('%s < %s: 0 < %.6g < %.6g < 1' % ('EPS', 'EPS1', EPS, EPS1)) def _fraction(fraction, n): f = 1 # int, no fractional indices if fraction in (None, 1): pass elif not (isscalar(fraction) and EPS < fraction < EPS1 and (float(n) - fraction) < n): raise FrechetError(fraction=fraction) elif fraction < EPS1: f = float(fraction) return f class FrechetError(PointsError): '''Fréchet issue. ''' pass class Frechet6Tuple(_NamedTuple): '''6-Tuple C{(fd, fi1, fi2, r, n, units)} with the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance C{fd}, I{fractional} indices C{fi1} and C{fi2}, the recursion depth C{r}, the number of distances computed C{n} and the name of the distance C{units}. If I{fractional} indices C{fi1} and C{fi2} are type C{int}, the returned C{fd} is the distance between C{points1[fi1]} and C{points2[fi2]}. For type C{float} indices, the distance is between an intermediate point along C{points1[int(fi1)]} and C{points1[int(fi1) + 1]} respectively an intermediate point along C{points2[int(fi2)]} and C{points2[int(fi2) + 1]}. Use function L{fractional} to compute the point at a I{fractional} index. ''' _Names_ = ('fd', 'fi1', 'fi2', 'r', 'n', _units_) # def __gt__(self, other): # _xinstanceof(Frechet6Tuple, other=other) # return self if self.fd > other.fd else other # PYCHOK .fd=[0] # # def __lt__(self, other): # _xinstanceof(Frechet6Tuple, other=other) # return self if self.fd < other.fd else other # PYCHOK .fd=[0] class Frechet(_Named): '''Frechet base class, requires method L{Frechet.distance} to be overloaded. ''' _adjust = None # not applicable _datum = None # not applicable _f1 = 1 _n1 = 0 _ps1 = None _units = NN _wrap = None # not applicable def __init__(self, points, fraction=None, name=NN, units=NN, **wrap_adjust): '''New C{Frechet...} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @kwarg units: Optional distance units (C{str}). @kwarg wrap_adjust: Optionally, C{wrap} and unroll longitudes, iff applicable (C{bool}) and C{adjust} wrapped, unrolled longitudinal delta by the cosine of the mean latitude, iff applicable. @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}} or B{{wrap}} or B{C{ajust}} not applicable. ''' self._n1, self._ps1 = self._points2(points) if fraction: self.fraction = fraction if name: self.name = name if units and not self.units: self.units = units if wrap_adjust: _bkwds(self, Error=FrechetError, **wrap_adjust) @property_RO def adjust(self): '''Get the adjust setting (C{bool} or C{None} if not applicable). ''' return self._adjust @property_RO def datum(self): '''Get the datum (L{Datum} or C{None} if not applicable). ''' return self._datum def _datum_setter(self, datum): '''(INTERNAL) Set the datum. ''' d = datum or getattr(self._ps1[0], _datum_, datum) if d and d != self.datum: # PYCHOK no cover _xinstanceof(Datum, datum=d) self._datum = d def discrete(self, points, fraction=None): '''Compute the C{forward, discrete Fréchet} distance. @arg points: Second set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)}. @raise FrechetError: Insufficient number of B{C{points}} or an invalid B{C{point}} or B{C{fraction}}. @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit() <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}. ''' n2, ps2 = self._points2(points) f2 = _fraction(fraction, n2) p2 = self.points_fraction if f2 < EPS1 else self.points_ # PYCHOK expected f1 = self.fraction p1 = self.points_fraction if f1 < EPS1 else self.points_ # PYCHOK expected def dF(fi1, fi2): return self.distance(p1(self._ps1, fi1), p2(ps2, fi2)) try: return _frechet_(self._n1, f1, n2, f2, dF, self.units) except TypeError as x: t = _dot_(self.classname, self.discrete.__name__) raise FrechetError(t, txt=str(x)) def distance(self, point1, point2): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}. ''' notOverloaded(self, self.distance, point1, point2) @property_doc_(''' the index fraction (C{float}).''') def fraction(self): '''Get the index fraction (C{float} or C{1}). ''' return self._f1 @fraction.setter # PYCHOK setter! def fraction(self, fraction): '''Set the the index fraction (C{float} or C{1}). @arg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @raise FrechetError: Invalid B{C{fraction}}. ''' self._f1 = _fraction(fraction, self._n1) def point(self, point): '''Convert a point for the C{.distance} method. @arg point: The point to convert ((C{LatLon}, L{Numpy2LatLon}, L{Tuple2LatLon} or C{other}). @return: The converted B{C{point}}. ''' return point # pass thru def points_(self, points, i): '''Get and convert a point for the C{.distance} method. @arg points: The orignal B{C{points}} to convert ((C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg i: The B{C{points}} index (C{int}). @return: The converted B{C{points[i]}}. ''' return self.point(points[i]) def _points2(self, points): '''(INTERNAL) Check a set of points. ''' return _points2(points, closed=False, Error=FrechetError) def points_fraction(self, points, fi): '''Get and convert a I{fractional} point for the C{.distance} method. @arg points: The orignal B{C{points}} to convert ((C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg fi: The I{fractional} index in B{C{points}} (C{float} or C{int}). @return: The interpolated, converted, intermediate B{C{points[fi]}}. ''' return self.point(_fractional(points, fi)) @property_doc_(''' the distance units (C{str}).''') def units(self): '''Get the distance units (C{str} or C{""}). ''' return self._units @units.setter # PYCHOK setter! def units(self, units): '''Set the distance units. @arg units: New units name (C{str}). ''' self._units = str(units or NN) @property_RO def wrap(self): '''Get the wrap setting (C{bool} or C{None} if not applicable). ''' return self._wrap class FrechetDegrees(Frechet): '''L{Frechet} base class for distances in C{degrees} from C{LatLon} points in C{degrees}. ''' _units = _degrees_ if _FOR_DOCS: __init__ = Frechet.__init__ discrete = Frechet.discrete class FrechetRadians(Frechet): '''L{Frechet} base class for distances in C{radians} or C{radians squared} from C{LatLon} points converted from C{degrees} to C{radians}. ''' _units = _radians_ if _FOR_DOCS: __init__ = Frechet.__init__ discrete = Frechet.discrete def point(self, point): '''Convert C{(lat, lon)} point in degrees to C{(a, b)} in radians. @return: An L{PhiLam2Tuple}C{(phi, lam)}. ''' try: return point.philam except AttributeError: # PYCHOK no cover return PhiLam2Tuple(radians(point.lat), radians(point.lon)) class FrechetCosineAndoyerLambert(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{cosineAndoyerLambert_}. @see: L{FrechetCosineForsytheAndoyerLambert}, L{FrechetDistanceTo}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetThomas} and L{FrechetKarney}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, points, datum=None, wrap=False, fraction=None, name=NN): '''New L{FrechetCosineAndoyerLambert} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{points}}' datum (L{Datum}). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}) @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. @raise TypeError: Invalid B{C{datum}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) self._datum_setter(datum) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{cosineAndoyerLambert_} distance in C{radians}. ''' r, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return cosineAndoyerLambert_(p2.phi, p1.phi, r, datum=self._datum) class FrechetCosineForsytheAndoyerLambert(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{cosineForsytheAndoyerLambert_}. @see: L{FrechetCosineAndoyerLambert}, L{FrechetDistanceTo}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetThomas} and L{FrechetKarney}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, points, datum=None, wrap=False, fraction=None, name=NN): '''New L{FrechetCosineForsytheAndoyerLambert} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{points}}' datum (L{Datum}). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}) @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. @raise TypeError: Invalid B{C{datum}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) self._datum_setter(datum) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{cosineForsytheAndoyerLambert_} distance in C{radians}. ''' r, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return cosineForsytheAndoyerLambert_(p2.phi, p1.phi, r, datum=self._datum) class FrechetCosineLaw(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{cosineLaw_}. @see: L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetFlatPolar}, L{FrechetHaversine} and L{FrechetVincentys}. @note: See note at function L{vincentys_}. ''' _wrap = False def __init__(self, points, wrap=False, fraction=None, name=NN): '''New L{FrechetCosineLaw} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{cosineLaw_} distance in C{radians}. ''' r, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return cosineLaw_(p2.phi, p1.phi, r) class FrechetDistanceTo(Frechet): '''Compute the C{Frechet} distance based on the distance from the points' C{LatLon.distanceTo} method, conventionally in C{meter}. @see: L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetThomas} and L{FrechetKarney}. ''' _distanceTo_kwds = {} _units = _meter_ def __init__(self, points, fraction=None, name=NN, **distanceTo_kwds): '''New L{FrechetDistanceTo} calculator/interpolator. @arg points: First set of points (C{LatLon}[]). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @kwarg distanceTo_kwds: Optional keyword arguments for the B{C{points}}' C{LatLon.distanceTo} method. @raise FrechetError: Insufficient number of B{C{points}} or an invalid B{C{point}} or B{C{fraction}}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} missing iff B{C{points}} are L{ellipsoidalKarney.LatLon}s. @note: All B{C{points}} I{must} be instances of the same ellipsoidal or spherical C{LatLon} class. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name) if distanceTo_kwds: self._distanceTo_kwds = distanceTo_kwds if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the distance in C{meter}. ''' return p1.distanceTo(p2, **self._distanceTo_kwds) def _points2(self, points): '''(INTERNAL) Check a set of points. ''' np, ps = Frechet._points2(self, points) for i, p in enumerate(ps): if not callable(getattr(p, _distanceTo_, None)): raise FrechetError(_item_sq(_points_, i), p, txt=_distanceTo_) return np, ps class FrechetEquirectangular(FrechetRadians): '''Compute the C{Frechet} distance based on the C{equirectangular} distance in C{radians squared} like function L{equirectangular_}. @see: L{FrechetCosineLaw}, L{FrechetEuclidean}, L{FrechetFlatPolar}, L{FrechetHaversine} and L{FrechetVincentys}. ''' _adjust = True _units = _radians2_ _wrap = False def __init__(self, points, adjust=True, wrap=False, fraction=None, name=NN): '''New L{FrechetEquirectangular} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{adjust}} or B{C{seed}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, adjust=adjust, wrap=wrap) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{equirectangular_} distance in C{radians squared}. ''' r, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) if self._adjust: r *= _scale_rad(p1.phi, p2.phi) return hypot2(r, p2.phi - p1.phi) # like equirectangular_ d2 class FrechetEuclidean(FrechetRadians): '''Compute the C{Frechet} distance based on the C{Euclidean} distance in C{radians} from function L{euclidean_}. @see: L{FrechetCosineLaw}, L{FrechetEquirectangular}, L{FrechetFlatPolar}, L{FrechetHaversine} and L{FrechetVincentys}. ''' _adjust = True _wrap = True # fixed def __init__(self, points, adjust=True, fraction=None, name=NN): '''New L{FrechetEuclidean} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, adjust=adjust) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{euclidean_} distance in C{radians}. ''' return euclidean_(p2.phi, p1.phi, p2.lam - p1.lam, adjust=self._adjust) class FrechetFlatLocal(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians squared} like function L{flatLocal_}/L{hubeny_}. @see: L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, L{FrechetDistanceTo}, L{FrechetHubeny}, L{FrechetKarney} and L{FrechetThomas}. ''' _datum = Datums.WGS84 _hubeny2_ = None _units = _radians2_ _wrap = False def __init__(self, points, datum=None, wrap=False, fraction=None, name=NN): '''New L{FrechetFlatLocal}/L{FrechetHubeny} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{points}}' datum (L{Datum}). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}) @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. @raise TypeError: Invalid B{C{datum}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) self._datum_setter(datum) self._hubeny2_ = self.datum.ellipsoid._hubeny2_ if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{flatLocal_}/L{hubeny_} distance in C{radians squared}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return self._hubeny2_(p2.phi, p1.phi, d) class FrechetFlatPolar(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{flatPolar_}. @see: L{FrechetCosineLaw}, L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetHaversine} and L{FrechetVincentys}. ''' _wrap = False def __init__(self, points, wrap=False, fraction=None, name=NN): '''New L{FrechetFlatPolar} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{flatPolar_} distance in C{radians}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return flatPolar_(p2.phi, p1.phi, d) class FrechetHaversine(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{haversine_}. @see: L{FrechetCosineLaw}, L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetFlatPolar} and L{FrechetVincentys}. @note: See note at function L{vincentys_}. ''' _wrap = False def __init__(self, points, wrap=False, fraction=None, name=NN): '''New L{FrechetHaversine} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{haversine_} distance in C{radians}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return haversine_(p2.phi, p1.phi, d) class FrechetHubeny(FrechetFlatLocal): # for Karl Hubeny if _FOR_DOCS: __doc__ = FrechetFlatLocal.__doc__ __init__ = FrechetFlatLocal.__init__ discrete = FrechetFlatLocal.discrete distance = FrechetFlatLocal.discrete class FrechetKarney(FrechetDegrees): '''Compute the C{Frechet} distance based on the I{angular} distance in C{degrees} from I{Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>} U{Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>} Inverse method. @see: L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, L{FrechetDistanceTo}, L{FrechetFlatLocal}, L{FrechetHubeny} and L{FrechetThomas}. ''' _datum = Datums.WGS84 _Inverse1 = None _wrap = False def __init__(self, points, datum=None, wrap=False, fraction=None, name=NN): '''New L{FrechetKarney} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{points}}' datum (L{Datum}). @kwarg wrap: Wrap and L{unroll180} longitudes (C{bool}) @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} missing. @raise TypeError: Invalid B{C{datum}}. ''' FrechetDegrees.__init__(self, points, fraction=fraction, name=name, wrap=wrap) self._datum_setter(datum) self._Inverse1 = self.datum.ellipsoid.geodesic.Inverse1 if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the non-negative I{angular} distance in C{degrees}. ''' return self._Inverse1(p1.lat, p1.lon, p2.lat, p2.lon, wrap=self._wrap) class FrechetThomas(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{thomas_}. @see: L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, L{FrechetDistanceTo}, L{FrechetFlatLocal}, L{FrechetHubeny} and L{FrechetKarney}. ''' _datum = Datums.WGS84 _wrap = False def __init__(self, points, datum=None, wrap=False, fraction=None, name=NN): '''New L{FrechetThomas} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg datum: Optional datum overriding the default C{Datums.WGS84} and first B{C{points}}' datum (L{Datum}). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}) @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no L{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. @raise TypeError: Invalid B{C{datum}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) self._datum_setter(datum) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{thomas_} distance in C{radians}. ''' r, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return thomas_(p2.phi, p1.phi, r, datum=self._datum) class FrechetVincentys(FrechetRadians): '''Compute the C{Frechet} distance based on the I{angular} distance in C{radians} from function L{vincentys_}. @see: L{FrechetCosineLaw}, L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetFlatPolar} and L{FrechetHaversine}. @note: See note at function L{vincentys_}. ''' _wrap = False def __init__(self, points, wrap=False, fraction=None, name=NN): '''New L{FrechetVincentys} calculator/interpolator. @arg points: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg wrap: Wrap and L{unrollPI} longitudes (C{bool}). @kwarg fraction: Index fraction (C{float} in L{EPS}..L{EPS1}) to interpolate intermediate B{C{points}} or use C{None}, C{0} or C{1} for no intermediate B{C{points}} and no I{fractional} indices. @kwarg name: Optional calculator/interpolator name (C{str}). @raise FrechetError: Insufficient number of B{C{points}} or invalid B{C{fraction}}. ''' FrechetRadians.__init__(self, points, fraction=fraction, name=name, wrap=wrap) if _FOR_DOCS: discrete = Frechet.discrete def distance(self, p1, p2): '''Return the L{vincentys_} distance in C{radians}. ''' d, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) return vincentys_(p2.phi, p1.phi, d) def _fractional(points, fi): '''(INTERNAL) Compute point at L{fractional} index. ''' i = int(fi) p = points[i] f = fi - float(i) if f > EPS: if f < EPS1: q = points[i + 1] p = LatLon2Tuple(favg(p.lat, q.lat, f=f), favg(p.lon, q.lon, f=f)) else: p = points[i + 1] return p def fractional(points, fi, LatLon=None, **LatLon_kwds): '''Return the point at a given I{fractional} index. @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg fi: The fractional index (C{float} or C{int}). @kwarg LatLon: Optional class to return the I{intermediate}, I{fractional} point (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional B{C{LatLon}} keyword arguments, ignored of B{C{LatLon=None}}. @return: A B{C{LatLon}} or if B{C{LatLon}} is C{None}, a L{LatLon2Tuple}C{(lat, lon)} for B{C{points[fi]}} if I{fractional} index B{C{fi}} is C{int}, otherwise the intermediate point between B{C{points[int(fi)]}} and B{C{points[int(fi) + 1]}} for C{float} I{fractional} index B{C{fi}}. @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}} not subscriptable. ''' try: if not (isscalar(fi) and 0 <= fi < len(points)): raise IndexError p = _fractional(points, fi) except (IndexError, TypeError): raise _IndexError(fractional.__name__, fi) if LatLon and isinstance(p, LatLon2Tuple): p = LatLon(*p, **LatLon_kwds) return p def _frechet_(ni, fi, nj, fj, dF, units): # MCCABE 14 '''(INTERNAL) Recursive core of function L{frechet_} and method C{discrete} of C{Frechet...} classes. ''' iFs = {} def iF(i): # cache index, depth ints and floats return iFs.setdefault(i, i) cF = defaultdict(dict) def rF(i, j, r): # recursive Fréchet i = iF(i) j = iF(j) try: t = cF[i][j] except KeyError: r = iF(r + 1) try: if i > 0: if j > 0: t = min(rF(i - fi, j, r), rF(i - fi, j - fj, r), rF(i, j - fj, r)) elif j < 0: raise IndexError else: # j == 0 t = rF(i - fi, 0, r) elif i < 0: raise IndexError elif j > 0: # i == 0 t = rF(0, j - fj, r) elif j < 0: # i == 0 raise IndexError else: # i == j == 0 t = (-INF, i, j, r) d = dF(i, j) if d > t[0]: t = (d, i, j, r) except IndexError: t = (INF, i, j, r) cF[i][j] = t return t t = rF(ni - 1, nj - 1, 0) t += (sum(map(len, cF.values())), units) # del cF, iFs return Frechet6Tuple(*t) def frechet_(points1, points2, distance=None, units=NN): '''Compute the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} distance between two paths given as sets of points. @arg points1: First set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @arg points2: Second set of points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[] or C{other}[]). @kwarg distance: Callable returning the distance between a B{C{points1}} and a B{C{points2}} point (signature C{(point1, point2)}). @kwarg units: Optional, name of the distance units (C{str}). @return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)} where C{fi1} and C{fi2} are type C{int} indices into B{C{points1}} respectively B{C{points2}}. @raise FrechetError: Insufficient number of B{C{points1}} or B{C{points2}}. @raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit() <https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}. @raise TypeError: If B{C{distance}} is not a callable. @note: Function L{frechet_} does not support I{fractional} indices for intermediate B{C{points1}} and B{C{points2}}. ''' if not callable(distance): raise _IsnotError(callable.__name__, distance=distance) n1, ps1 = _points2(points1, closed=False, Error=FrechetError) n2, ps2 = _points2(points2, closed=False, Error=FrechetError) def dF(i1, i2): return distance(ps1[i1], ps2[i2]) return _frechet_(n1, 1, n2, 1, dF, units) __all__ += _ALL_DOCS(Frechet6Tuple) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.