# Coverage for pygeodesy/frechet.py : 97%

## 261 statements 253 run 8 missing 50 excluded

Hot-keys on this page

r m x p toggle line displays

j k next/prev highlighted chunk

0 (zero) top of page

1 (one) first highlighted chunk

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 | # -*- coding: utf-8 -*- u'''Fréchet distances. Classes L{Frechet}, L{FrechetDegrees}, L{FrechetRadians}, L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, L{FrechetCosineLaw}, L{FrechetDistanceTo}< L{FrechetEquirectangular}, L{FrechetEuclidean}, L{FrechetExact}, L{FrechetFlatLocal}, L{FrechetFlatPolar}, L{FrechetHaversine}, L{FrechetHubeny}, L{FrechetKarney}, L{FrechetThomas} 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. 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 isscalar, _xinstanceof from pygeodesy.datums import Datum, _WGS84 from pygeodesy.errors import _IsnotError, PointsError from pygeodesy.fmath import hypot2 from pygeodesy.formy import cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, \ cosineLaw_, euclidean_, flatPolar_, haversine_, \ thomas_, vincentys_, _scale_rad from pygeodesy.interns import EPS, EPS1, INF, NN, _datum_, _distanceTo_, _DOT_, \ _n_, _points_, _units_ from pygeodesy.iters import points2 as _points2 from pygeodesy.lazily import _ALL_LAZY, _FOR_DOCS from pygeodesy.named import _Named, _NamedTuple, notOverloaded, _Pass from pygeodesy.namedTuples import PhiLam2Tuple from pygeodesy.points import _fractional from pygeodesy.props import Property_RO, property_doc_ from pygeodesy.streprs import _boolkwds, Fmt from pygeodesy.units import FIx, Float, Number_, _Str_degrees, _Str_meter, \ _Str_NN, _Str_radians, _Str_radians2, _xUnit, _xUnits from pygeodesy.utily import unrollPI from collections import defaultdict as _defaultdict from math import radians __all__ = _ALL_LAZY.frechet __version__ = '21.06.01' 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 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 = _Str_NN # XXX Str to _Pass and for backward compatibility _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, the distance units (C{Unit} or 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{C{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: _boolkwds(self, **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}, see function C{notOverloaded}. ''' notOverloaded(self, 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 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{Unit} or C{str}).''') def units(self): '''Get the distance units (C{Unit} or C{str}). ''' return self._units @units.setter # PYCHOK setter! def units(self, units): '''Set the distance units. @arg units: New units (C{Unit} or C{str}). @raise TypeError: Invalid B{C{units}}. ''' self._units = _xUnits(units, Base=Float) @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 = _Str_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 = _Str_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{FrechetExact}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetThomas} and L{FrechetKarney}. ''' _datum = _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{FrechetExact}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetThomas} and L{FrechetKarney}. ''' _datum = _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{FrechetExact}, 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{FrechetExact}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetThomas} and L{FrechetKarney}. ''' _distanceTo_kwds = {} _units = _Str_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)): i = Fmt.SQUARE(_points_, i) raise FrechetError(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{FrechetExact}, L{FrechetFlatPolar}, L{FrechetHaversine} and L{FrechetVincentys}. ''' _adjust = True _units = _Str_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{FrechetExact}, 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 FrechetExact(FrechetDegrees): '''Compute the C{Frechet} distance based on the I{angular} distance in C{degrees} from method L{GeodesicExact}C{.Inverse}. @see: L{FrechetCosineAndoyerLambert}, L{FrechetCosineForsytheAndoyerLambert}, L{FrechetDistanceTo}, L{FrechetFlatLocal}, L{FrechetHubeny}, L{FrechetKarney} and L{FrechetThomas}. ''' _datum = _WGS84 _Inverse1 = None _wrap = False def __init__(self, points, datum=None, wrap=False, fraction=None, name=NN): '''New L{FrechetExact} 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 TypeError: Invalid B{C{datum}}. ''' FrechetDegrees.__init__(self, points, fraction=fraction, name=name, wrap=wrap) self._datum_setter(datum) self._Inverse1 = self.datum.ellipsoid.geodesicx.Inverse1 # note -x 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 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{FrechetExact}, L{FrechetHubeny}, L{FrechetKarney} and L{FrechetThomas}. ''' _datum = _WGS84 _hubeny2_ = None _units = _Str_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{FrechetExact}, 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{FrechetExact}, 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(FrechetExact): '''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{FrechetExact}, L{FrechetFlatLocal}, L{FrechetHubeny} and L{FrechetThomas}. ''' 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 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{FrechetExact}, L{FrechetFlatLocal}, L{FrechetHubeny} and L{FrechetKarney}. ''' _datum = _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{FrechetExact}, 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 _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, the distance units (C{Unit} or 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) 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} as C{FIx}, the recursion depth C{r}, the number of distances computed C{n} and the L{units} class or class or name of the distance C{units}. If I{fractional} indices C{fi1} and C{fi2} are C{int}, the returned C{fd} is the distance between C{points1[fi1]} and C{points2[fi2]}. For 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_) _Units_ = (_Pass, FIx, FIx, Number_, Number_, _Pass) def toUnits(self, **Error): # PYCHOK expected '''Overloaded C{_NamedTuple.toUnits} for C{fd} units. ''' U = _xUnit(self.units, Float) # PYCHOK expected self._Units_ = (U,) + Frechet6Tuple._Units_[1:] return _NamedTuple.toUnits(self, **Error) # 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] # **) MIT License # # Copyright (C) 2016-2021 -- 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.