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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | [![Build Status](https://travis-ci.org/spiros/discrete_frechet.svg?branch=master)](https://travis-ci.org/spiros/discrete_frechet) 2 | 3 | [![DOI](https://zenodo.org/badge/118257492.svg)](https://zenodo.org/badge/latestdoi/118257492) 4 | 5 | Discrete Fréchet distance 6 | ========================= 7 | 8 | Computes the discrete Fréchet distance between 9 | two curves. The Fréchet distance between two curves in a 10 | metric space is a measure of the similarity between the curves. 11 | The discrete Fréchet distance may be used for approximately computing 12 | the Fréchet distance between two arbitrary curves, 13 | as an alternative to using the exact Fréchet distance between a polygonal 14 | approximation of the curves or an approximation of this value. 15 | 16 | This is a Python 3.* implementation of the algorithm produced 17 | in *Eiter, T. and Mannila, H., 1994. [Computing discrete Fréchet distance](http://www.kr.tuwien.ac.at/staff/eiter/et-archive/cdtr9464.pdf). Tech. 18 | Report CD-TR 94/64, Information Systems Department, Technical University 19 | of Vienna.* 20 | 21 | 22 | ``` 23 | Function dF(P, Q): real; 24 | input: polygonal curves P = (u1, . . . , up) and Q = (v1, . . . , vq). 25 | return: δdF (P, Q) 26 | ca : array [1..p, 1..q] of real; 27 | function c(i, j): real; 28 | begin 29 | if ca(i, j) > −1 then return ca(i, j) 30 | elsif i = 1 and j = 1 then ca(i, j) := d(u1, v1) 31 | elsif i > 1 and j = 1 then ca(i, j) := max{ c(i − 1, 1), d(ui, v1) } 32 | elsif i = 1 and j > 1 then ca(i, j) := max{ c(1, j − 1), d(u1, vj ) } 33 | elsif i > 1 and j > 1 then ca(i, j) := 34 | max{ min(c(i − 1, j), c(i − 1, j − 1), c(i, j − 1)), d(ui, vj ) } 35 | else ca(i, j) = ∞ 36 | return ca(i, j); 37 | end; /* function c */ 38 | 39 | begin 40 | for i = 1 to p do for j = 1 to q do ca(i, j) := −1.0; 41 | return c(p, q); 42 | end. 43 | ``` 44 | 45 | Parameters 46 | ---------- 47 | P : Input curve - two dimensional array of points 48 | Q : Input curve - two dimensional array of points 49 | 50 | Returns 51 | ------- 52 | dist: float64 53 | The discrete Frechet distance between curves `P` and `Q`. 54 | 55 | Examples 56 | -------- 57 | ``` 58 | >>> from frechetdist import frdist 59 | >>> P=[[1,1], [2,1], [2,2]] 60 | >>> Q=[[2,2], [0,1], [2,4]] 61 | >>> frdist(P,Q) 62 | >>> 2.0 63 | >>> P=[[1,1], [2,1], [2,2]] 64 | >>> Q=[[1,1], [2,1], [2,2]] 65 | >>> frdist(P,Q) 66 | >>> 0 67 | ``` 68 | -------------------------------------------------------------------------------- /frechetdist.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | 4 | import numpy as np 5 | 6 | __all__ = ['frdist'] 7 | 8 | 9 | def _c(ca, i, j, p, q): 10 | 11 | if ca[i, j] > -1: 12 | return ca[i, j] 13 | elif i == 0 and j == 0: 14 | ca[i, j] = np.linalg.norm(p[i]-q[j]) 15 | elif i > 0 and j == 0: 16 | ca[i, j] = max(_c(ca, i-1, 0, p, q), np.linalg.norm(p[i]-q[j])) 17 | elif i == 0 and j > 0: 18 | ca[i, j] = max(_c(ca, 0, j-1, p, q), np.linalg.norm(p[i]-q[j])) 19 | elif i > 0 and j > 0: 20 | ca[i, j] = max( 21 | min( 22 | _c(ca, i-1, j, p, q), 23 | _c(ca, i-1, j-1, p, q), 24 | _c(ca, i, j-1, p, q) 25 | ), 26 | np.linalg.norm(p[i]-q[j]) 27 | ) 28 | else: 29 | ca[i, j] = float('inf') 30 | 31 | return ca[i, j] 32 | 33 | 34 | def frdist(p, q): 35 | """ 36 | Computes the discrete Fréchet distance between 37 | two curves. The Fréchet distance between two curves in a 38 | metric space is a measure of the similarity between the curves. 39 | The discrete Fréchet distance may be used for approximately computing 40 | the Fréchet distance between two arbitrary curves, 41 | as an alternative to using the exact Fréchet distance between a polygonal 42 | approximation of the curves or an approximation of this value. 43 | 44 | This is a Python 3.* implementation of the algorithm produced 45 | in Eiter, T. and Mannila, H., 1994. Computing discrete Fréchet distance. 46 | Tech. Report CD-TR 94/64, Information Systems Department, Technical 47 | University of Vienna. 48 | http://www.kr.tuwien.ac.at/staff/eiter/et-archive/cdtr9464.pdf 49 | 50 | Function dF(P, Q): real; 51 | input: polygonal curves P = (u1, . . . , up) and Q = (v1, . . . , vq). 52 | return: δdF (P, Q) 53 | ca : array [1..p, 1..q] of real; 54 | function c(i, j): real; 55 | begin 56 | if ca(i, j) > −1 then return ca(i, j) 57 | elsif i = 1 and j = 1 then ca(i, j) := d(u1, v1) 58 | elsif i > 1 and j = 1 then ca(i, j) := max{ c(i − 1, 1), d(ui, v1) } 59 | elsif i = 1 and j > 1 then ca(i, j) := max{ c(1, j − 1), d(u1, vj) } 60 | elsif i > 1 and j > 1 then ca(i, j) := 61 | max{ min(c(i − 1, j), c(i − 1, j − 1), c(i, j − 1)), d(ui, vj ) } 62 | else ca(i, j) = ∞ 63 | return ca(i, j); 64 | end; /* function c */ 65 | 66 | begin 67 | for i = 1 to p do for j = 1 to q do ca(i, j) := −1.0; 68 | return c(p, q); 69 | end. 70 | 71 | Parameters 72 | ---------- 73 | P : Input curve - two dimensional array of points 74 | Q : Input curve - two dimensional array of points 75 | 76 | Returns 77 | ------- 78 | dist: float64 79 | The discrete Fréchet distance between curves `P` and `Q`. 80 | 81 | Examples 82 | -------- 83 | >>> from frechetdist import frdist 84 | >>> P=[[1,1], [2,1], [2,2]] 85 | >>> Q=[[2,2], [0,1], [2,4]] 86 | >>> frdist(P,Q) 87 | >>> 2.0 88 | >>> P=[[1,1], [2,1], [2,2]] 89 | >>> Q=[[1,1], [2,1], [2,2]] 90 | >>> frdist(P,Q) 91 | >>> 0 92 | """ 93 | p = np.array(p, np.float64) 94 | q = np.array(q, np.float64) 95 | 96 | len_p = len(p) 97 | len_q = len(q) 98 | 99 | if len_p == 0 or len_q == 0: 100 | raise ValueError('Input curves are empty.') 101 | 102 | ca = (np.ones((len_p, len_q), dtype=np.float64) * -1) 103 | 104 | dist = _c(ca, len_p-1, len_q-1, p, q) 105 | return dist 106 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | setuptools==65.5.1 2 | numpy==1.22.0 3 | pytest==3.3.2 4 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | import setuptools 2 | 3 | with open("README.md", "r") as fh: 4 | long_description = fh.read() 5 | 6 | setuptools.setup( 7 | name='frechetdist', 8 | version='0.6', 9 | description='Calculate discrete Frechet distance', 10 | url='https://github.com/spiros/discrete_frechet', 11 | author='Spiros Denaxas', 12 | author_email='s.denaxas@gmail.com', 13 | long_description=long_description, 14 | long_description_content_type="text/markdown", 15 | license='Apache License 2.0', 16 | py_modules=['frechetdist'], 17 | install_requires=[ 18 | 'numpy>1.0', 19 | ], 20 | zip_safe=False, 21 | classifiers=[ 22 | "Programming Language :: Python :: 3", 23 | "Operating System :: OS Independent" 24 | ] 25 | ) 26 | -------------------------------------------------------------------------------- /test_all.py: -------------------------------------------------------------------------------- 1 | 2 | import sys 3 | import os 4 | import numpy as np 5 | import pytest 6 | 7 | from frechetdist import frdist 8 | 9 | TEST_CASES = [ 10 | 11 | { 12 | 'P': [[1, 1], [2, 1], [2, 2]], 13 | 'Q': [[2, 2], [0, 1], [2, 4]], 14 | 'expected': 2.0 15 | }, 16 | 17 | { 18 | 'P': np.array((np.linspace(0.0, 1.0, 100), np.ones(100))).T, 19 | 'Q': np.array((np.linspace(0.0, 1.0, 100), np.ones(100))).T, 20 | 'expected': 0 21 | }, 22 | 23 | { 24 | 'P': [[-1, 0], [0, 1], [1, 0], [0, -1]], 25 | 'Q': [[-2, 0], [0, 2], [2, 0], [0, -2]], 26 | 'expected': 1.0 27 | }, 28 | 29 | { 30 | 'P': np.array((np.linspace(0.0, 1.0, 100), np.ones(100)*2)).T, 31 | 'Q': np.array((np.linspace(0.0, 1.0, 100), np.ones(100))).T, 32 | 'expected': 1.0 33 | } 34 | 35 | ] 36 | 37 | 38 | def test_main(): 39 | for test_case in TEST_CASES: 40 | P = test_case['P'] 41 | Q = test_case['Q'] 42 | eo = test_case['expected'] 43 | 44 | assert frdist(P, Q) == eo 45 | 46 | 47 | def test_errors(): 48 | 49 | P = [] 50 | Q = [[2, 2], [0, 1], [2, 4]] 51 | 52 | with pytest.raises(ValueError): 53 | assert frdist(P, Q) == 2.0 54 | --------------------------------------------------------------------------------