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# -*- coding: utf-8 -*- 

 

u'''Classes L{Frechet}, L{FrechetDegrees}, L{FrechetRadians}, 

L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetHaversine}, 

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

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

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

 

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.fmath import EPS, EPS1, favg, INF, isscalar, _IsNotError 

from pygeodesy.formy import euclidean_, haversine_, points2 as _points2, \ 

_scaler, vincentys_ 

from pygeodesy.lazily import _ALL_LAZY, _ALL_DOCS 

from pygeodesy.named import LatLon2Tuple, _Named, _NamedTuple, PhiLam2Tuple 

from pygeodesy.utily import unrollPI 

 

from collections import defaultdict 

from math import radians 

 

__all__ = _ALL_LAZY.frechet + _ALL_DOCS('Frechet6Tuple') 

__version__ = '19.10.31' 

 

 

class FrechetError(ValueError): 

'''Fréchet issue. 

''' 

pass 

 

 

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('%s invalid: %r' % ('fraction', fraction)) 

elif fraction < EPS1: 

f = float(fraction) 

return f 

 

 

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}[C{fi1}] and 

C{points2}[C{fi2}]. For type C{float} indices, the distance is 

between an intermediate point along C{points1}[C{int(fi1)}] and 

C{points1}[C{int(fi1)+1}] respectively an intermediate point 

along C{points2}[C{int(fi2)}] and C{points2}[C{int(fi2)+1}]. 

 

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

index. 

''' 

_Names_ = ('fd', 'fi1', 'fi2', 'r', 'n', 'units') 

 

# def __gt__(self, other): 

# _TypeError(Frechet6Tuple, other=other) 

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

# 

# def __lt__(self, other): 

# _TypeError(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 = False 

_f1 = 1 

_n1 = 0 

_ps1 = None 

_units = '' 

_warp = False 

 

def __init__(self, points, fraction=None, name='', units=''): 

'''New L{Frechet} calculator/interpolator. 

 

@param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

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

interpolate intermediate B{C{points}} or C{None} 

or C{1} for no intermediate B{C{points}} and no 

I{fractional} indices. 

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

@keyword units: Optional, distance units (C{str}). 

 

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

invalid B{C{fraction}}. 

''' 

self._n1, self._ps1 = _points2(points, closed=False, Error=FrechetError) 

if fraction: 

self.fraction = fraction 

if name: 

self.name = name 

if units: 

self.units = units 

 

def discrete(self, points, fraction=None): 

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

 

@param points: Second set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

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

interpolate intermediate B{C{points}} or C{None} 

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 

invalid B{C{fraction}}. 

 

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

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

''' 

n2, ps2 = _points2(points, closed=False, Error=FrechetError) 

 

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)) 

 

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

 

def distance(self, point1, point2): 

'''Distance between 2 points from C{.point}. 

 

@note: This method I{must be overloaded}. 

 

@raise AssertionError: Not overloaded. 

''' 

self._notOverloaded(self.distance.__name__, point1, point2) 

 

@property 

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}). 

 

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

interpolate intermediate B{C{points}} or C{None} 

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. 

 

@param point: The point to convert ((C{LatLon}, C{Numpy2LatLon}, 

C{Tuple2LatLon} or C{other}). 

 

@return: The converted B{C{point}}. 

''' 

return point # pass thru 

 

def points_(self, points, i): 

'''Get and convert B{C{points}}[B{C{i}}] for the C{.distance} method. 

 

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

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

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

 

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

''' 

return self.point(points[i]) 

 

def points_fraction(self, points, fi): 

'''Get and convert I{fractional} B{C{points}}[B{C{fi}}] for the C{.distance} method. 

 

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

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

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

 

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

''' 

return self.point(_fractional(points, fi)) 

 

@property 

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. 

 

@param units: New units name (C{str}). 

''' 

self._units = str(units or "") 

 

 

class FrechetDegrees(Frechet): 

'''L{Frechet} base class for distances in C{degrees} from 

C{LatLon} points in C{degrees}. 

''' 

_units = 'degrees' 

 

discrete = Frechet.discrete # for __doc__ 

 

 

class FrechetRadians(Frechet): 

'''L{Frechet} base class for distances in C{radians} from 

C{LatLon} points converted from C{degrees} to C{radians}. 

''' 

_units = 'radians' 

 

discrete = Frechet.discrete # for __doc__ 

 

def point(self, point): 

'''Convert C{(lat, lon)} point in degrees to C{(a, b)} 

in radians. 

 

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

''' 

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

 

 

class FrechetEquirectangular(FrechetRadians): 

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

distance (in radians squared) like function L{equirectangular_}. 

 

@see: L{FrechetEuclidean}, L{FrechetHaversine} and L{FrechetVincentys}. 

''' 

_adjust = True 

_wrap = False 

 

def __init__(self, points, adjust=True, wrap=False, fraction=None, name=''): 

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

 

@param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal 

delta by the cosine of the mean latitude (C{bool}). 

@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). 

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

interpolate intermediate B{C{points}} or C{None} 

or C{1} for no intermediate B{C{points}} and no 

I{fractional} indices. 

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

 

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

invalid B{C{adjust}} or B{C{seed}}. 

''' 

if not adjust: 

self._adjust = False 

if wrap: 

self._wrap = True 

super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) # distance**2 

 

def distance(self, p1, p2): 

'''Return the L{equirectangular_} distance in C{radians squared}. 

''' 

d, _ = unrollPI(p1.lam, p2.lam, wrap=self._wrap) 

if self._adjust: 

d *= _scaler(p1.phi, p2.phi) 

return d**2 + (p2.phi - p1.phi)**2 # like equirectangular_ d2 

 

discrete = Frechet.discrete # for __doc__ 

 

 

class FrechetEuclidean(FrechetRadians): 

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

distance (in radians) from function L{euclidean_}. 

 

@see: L{FrechetEquirectangular}, L{FrechetHaversine} and L{FrechetVincentys}. 

''' 

_adjust = True 

 

def __init__(self, points, adjust=True, fraction=None, name=''): 

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

 

@param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@keyword adjust: Adjust the wrapped, unrolled longitudinal 

delta by the cosine of the mean latitude (C{bool}). 

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

interpolate intermediate B{C{points}} or C{None} 

or C{1} for no intermediate B{C{points}} and no 

I{fractional} indices. 

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

 

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

invalid B{C{fraction}}. 

''' 

if not adjust: 

self._adjust = False 

super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) 

 

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) 

 

discrete = Frechet.discrete # for __doc__ 

 

 

class FrechetHaversine(FrechetRadians): 

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

C{Haversine} distance (in radians) from function L{haversine_}. 

 

@note: See note under L{FrechetVincentys}. 

 

@see: L{FrechetEquirectangular}, L{FrechetEuclidean} and L{FrechetVincentys}. 

''' 

_wrap = False 

 

def __init__(self, points, wrap=False, fraction=None, name=''): 

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

 

@param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). 

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

interpolate intermediate B{C{points}} or C{None} 

or C{1} for no intermediate B{C{points}} and no 

I{fractional} indices. 

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

 

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

invalid B{C{fraction}}. 

''' 

if wrap: 

self._wrap = True 

super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) 

 

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) 

 

discrete = Frechet.discrete # for __doc__ 

 

 

class FrechetVincentys(FrechetRadians): 

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

C{Vincenty} distance (in radians) from function L{vincentys_}. 

 

@note: See note under L{vincentys_}. 

 

@see: L{FrechetEquirectangular}, L{FrechetEuclidean} and L{FrechetHaversine}. 

''' 

_wrap = False 

 

def __init__(self, points, wrap=False, fraction=None, name=''): 

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

 

@param points: First set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). 

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

interpolate intermediate B{C{points}} or C{None} 

or C{1} for no intermediate B{C{points}} and no 

I{fractional} indices. 

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

 

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

invalid B{C{fraction}}. 

''' 

if wrap: 

self._wrap = True 

super(FrechetRadians, self).__init__(points, fraction=fraction, name=name) 

 

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) 

 

discrete = Frechet.discrete # for __doc__ 

 

 

def _fractional(points, fi): 

'''(INTERNAL) Compute point at I{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): 

'''Return the point at a given I{fractional} index. 

 

@param points: The points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@param fi: The fractional index (C{float} or C{int}). 

@keyword LatLon: Optional (sub-)class to return the 

I{intermediate} point (C{LatLon}) or 

C{None}. 

 

@return: A B{C{LatLon}} or a L{LatLon2Tuple}C{(lat, lon)} if 

B{C{LatLon}} is C{None} with B{C{points}}[B{C{fi}}] 

if I{fractional} index B{C{fi}} is C{int}, otherwise 

the intermediate point between B{C{points}}[C{int(B{fi})}] 

and B{C{points}}[C{int(B{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('%s invalid: %r' % ('fractional', fi)) 

 

if LatLon and isinstance(p, LatLon2Tuple): 

p = LatLon(*p) 

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) 

 

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 

 

cF = defaultdict(dict) 

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=''): 

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

distance between two paths given as sets of points. 

 

@param points1: First set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@param points2: Second set of points (C{LatLon}[], C{Numpy2LatLon}[], 

C{Tuple2LatLon}[] or C{other}[]). 

@keyword distance: Callable returning the distance between a B{C{points1}} 

and a B{C{points2}} point (signature C{(point1, point2)}). 

@keyword 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: Keyword C{fraction}, intermediate B{C{points1}} and B{C{points2}} 

and I{fractional} indices are I{not} supported in this L{frechet_} 

function. 

''' 

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) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

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

# 

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

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

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