# Coverage for pygeodesy/points.py : 96%

## 554 statements 531 run 23 missing 95 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 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 | # -*- coding: utf-8 -*- u'''Utilities for point lists, tuples, etc. Functions to handle collections and sequences of C{LatLon} points specified as 2-d U{NumPy<https://www.NumPy.org>}, C{arrays} or tuples as C{LatLon} or as C{pseudo-x/-y} pairs. C{NumPy} arrays are assumed to contain rows of points with a lat-, a longitude -and possibly other- values in different columns. While iterating over the array rows, create an instance of a given C{LatLon} class "on-the-fly" for each row with the row's lat- and longitude. The original C{NumPy} array is read-accessed only and never duplicated, except to return a I{subset} of the original array. For example, to process a C{NumPy} array, wrap the array by instantiating class L{Numpy2LatLon} and specifying the column index for the lat- and longitude in each row. Then, pass the L{Numpy2LatLon} instance to any L{pygeodesy} function or method accepting a I{points} argument. Similarly, class L{Tuple2LatLon} is used to instantiate a C{LatLon} from each 2+tuple in a sequence of such 2+tuples using the C{ilat} lat- and C{ilon} longitude index in each 2+tuple. ''' from pygeodesy.basics import isclass, isint, isscalar, issequence, \ issubclassof, map1, _Sequence, _xcopy, \ _xdup, _xinstanceof from pygeodesy.constants import EPS, EPS1, PI_2, R_M, isnear0, isnear1, \ _umod_360, _0_0, _0_5, _1_0, _3_0, _90_0, \ _N_90_0, _180_0, _360_0 # from pygeodesy.datums import _spherical_datum # from .formy from pygeodesy.dms import F_D, latDMS, lonDMS, parseDMS2, S_DEG, S_DMS, \ S_MIN, S_SEC, S_SEP from pygeodesy.errors import CrossError, crosserrors, _IndexError, \ _IsnotError, _TypeError, _ValueError, \ _xkwds, _xkwds_pop from pygeodesy.fmath import favg, fdot, Fsum, fsum, hypot # from pygeodesy.fsums import Fsum, fsum # from .fmath from pygeodesy.formy import _bearingTo2, equirectangular_, latlon2n_xyz, \ _spherical_datum from pygeodesy.interns import NN, _colinear_, _COMMASPACE_, _DEQUALSPACED_, \ _ELLIPSIS_, _height_, _immutable_, _lat_, _lon_, \ _near_, _not_, _point_, _SPACE_, _UNDER_, \ _valid_, _tolerance_ # PYCHOK used! from pygeodesy.iters import LatLon2PsxyIter, PointsIter, points2 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS from pygeodesy.named import classname, nameof, notImplemented, notOverloaded, \ _NamedTuple, _xnamed, _xother3, _xotherError from pygeodesy.namedTuples import Bounds2Tuple, Bounds4Tuple, \ LatLon2Tuple, NearestOn3Tuple, \ NearestOn5Tuple, PhiLam2Tuple, \ Point3Tuple, Vector3Tuple, Vector4Tuple from pygeodesy.nvectorBase import NvectorBase, _N_vector_ from pygeodesy.props import deprecated_method, Property_RO, property_doc_, \ property_RO from pygeodesy.streprs import Fmt, hstr, instr, pairs from pygeodesy.units import Number_, Radius, Scalar, Scalar_ from pygeodesy.utily import atan2b, degrees90, degrees180, degrees2m, \ unroll180, unrollPI, wrap90, wrap180 from math import cos, fmod, radians, sin __all__ = _ALL_LAZY.points __version__ = '22.09.24' _fin_ = 'fin' _ilat_ = 'ilat' _ilon_ = 'ilon' _ncols_ = 'ncols' _nrows_ = 'nrows' class LatLon_(object): # XXX in heights._HeightBase.height '''Low-overhead C{LatLon} class for L{Numpy2LatLon} and L{Tuple2LatLon}. ''' # __slots__ efficiency is voided if the __slots__ class attribute # is used in a subclass of a class with the traditional __dict__, # see <https://docs.Python.org/2/reference/datamodel.html#slots> # and __slots__ must be repeated in sub-classes, see "Problems # with __slots__" in Luciano Ramalho, "Fluent Python", page # 276+, O'Reilly, 2016, also at <https://Books.Google.ie/ # books?id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg= # PT364#v=onepage&q=“Problems%20with%20__slots__”&f=false> # # __slots__ = (_lat_, _lon_, _height_, _datum_, _name_) # Property_RO = property_RO # no __dict__ with __slots__! # # However, sys.getsizeof(LatLon_(1, 2)) is 72-88 with __slots__ # but only 48-64 bytes without in Python 2.7.18+ and Python 3+. def __init__(self, lat, lon, name=NN, height=0, datum=None): '''Creat a new, mininal, low-overhead L{LatLon_} instance, without height and datum. @arg lat: Latitude (C{degrees}). @arg lon: Longitude (C{degrees}). @kwarg name: Optional name (C{str}). @kwarg height: Optional height (C{float} or C{int}). @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or I{scalar} radius) or C{None}. @raise TypeError: Invalid B{C{datum}}. @note: The lat- and longitude are taken as-given, un-clipped and un-validated . ''' try: # most common use case self.lat, self.lon = float(lat), float(lon) # Lat(lat), Lon(lon) except (TypeError, ValueError): self.lat, self.lon = parseDMS2(lat, lon, clipLat=0, clipLon=0) # PYCHOK LatLon2Tuple self.name = str(name) if name else NN self.height = height self.datum = datum if datum is None else \ _spherical_datum(datum, name=self.name) def __eq__(self, other): return isinstance(other, LatLon_) and \ other.lat == self.lat and \ other.lon == self.lon def __ne__(self, other): return not self.__eq__(other) def __repr__(self): return self.toRepr() def __str__(self): return self.toStr() def classof(self, *args, **kwds): '''Instantiate this very class. @arg args: Optional, positional arguments. @kwarg kwds: Optional, keyword arguments. @return: New instance (C{self.__class__}). ''' return _xnamed(self.__class__(*args, **kwds), self.name) def copy(self, deep=False): '''Make a shallow or deep copy of this instance. @kwarg deep: If C{True} make a deep, otherwise a shallow copy (C{bool}). @return: The copy (C{This} (sub-)class). ''' return _xcopy(self, deep=deep) def dup(self, **items): '''Duplicate this instance, replacing some items. @kwarg items: Attributes to be changed (C{any}). @return: The duplicate (C{This} (sub-)class). @raise AttributeError: Some B{C{items}} invalid. ''' return _xdup(self, **items) def heightStr(self, prec=-2): '''Return a string for the height B{C{height}}. @kwarg prec: Number of (decimal) digits, unstripped (C{int}). @see: Function L{pygeodesy.hstr}. ''' return hstr(self.height, prec=prec) def intermediateTo(self, other, fraction, height=None, wrap=False): '''Locate the point at a given fraction between (or along) this and an other point. @arg other: The other point (C{LatLon}). @arg fraction: Fraction between both points (C{float}, 0.0 for this and 1.0 for the other point). @kwarg height: Optional height (C{meter}), overriding the intermediate height. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Intermediate point (this C{LatLon}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' f = Scalar(fraction=fraction) if isnear0(f): r = self elif isnear1(f) and not wrap: r = self.others(other) else: r = self.others(other) h = favg(self.height, r.height, f=f) if height is None else height _, lon = unroll180(self.lon, r.lon, wrap=wrap) r = self.classof(favg(self.lat, r.lat, f=f), favg(self.lon, lon, f=f), height=h, datum=self.datum, name=self.intermediateTo.__name__) return r @Property_RO # PYCHOK no cover def isEllipsoidal(self): '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown). ''' return self.datum.isEllipsoidal if self.datum else None @Property_RO # PYCHOK no cover def isEllipsoidalLatLon(self): '''Get C{LatLon} base. ''' return False def isequalTo(self, other, eps=None): '''Compare this point with an other point, I{ignoring} height. @arg other: The other point (C{LatLon}). @kwarg eps: Tolerance for equality (C{degrees}). @return: C{True} if both points are identical, I{ignoring} height, C{False} otherwise. @raise UnitError: Invalid B{C{eps}}. ''' self.others(other) if eps: return max(abs(self.lat - other.lat), abs(self.lon - other.lon)) < Scalar_(eps=eps) else: return self.lat == other.lat and \ self.lon == other.lon @Property_RO def isSpherical(self): # PYCHOK no cover '''Check whether this point is spherical (C{bool} or C{None} if unknown). ''' return self.datum.isSpherical if self.datum else None @Property_RO def latlon(self): '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self.lat, self.lon, name=self.name) @Property_RO def latlonheight(self): '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @Property_RO def _N_vector(self): '''(INTERNAL) Get the minimal, low-overhead (C{nvectorBase._N_vector_}) ''' return _N_vector_(*latlon2n_xyz(self.lat, self.lon), h=self.height, name=self.name) def others(self, *other, **name_other_up): # see .named._namedBase.others '''Refined class comparison. @arg other: The other instance (any C{type}). @kwarg name_other_up: Overriding C{name=other} and C{up=1} keyword arguments. @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' other, name, up = _xother3(self, other, **name_other_up) if isinstance(other, self.__class__) or (hasattr(other, _lat_) and hasattr(other, _lon_)): return other raise _xotherError(self, other, name=name, up=up + 1) @Property_RO def philam(self): '''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name) @Property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.height) @deprecated_method def points(self, points, closed=False, base=None): # PYCHOK no cover '''DEPRECATED, use method C{points2}.''' return points2(points, closed=closed, base=base) def points2(self, points, closed=False, base=None): '''Check a path or polygon represented by points. @arg points: The path or polygon points (C{LatLon}[]) @kwarg closed: Optionally, consider the polygon closed, ignoring any duplicate or closing final B{C{points}} (C{bool}). @kwarg base: Optionally, check all B{C{points}} against this base class, if C{None} don't check. @return: A L{Points2Tuple}C{(number, points)} with the number of points and the points C{list} or C{tuple}. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not B{C{base}}. ''' return points2(points, closed=closed, base=base) def PointsIter(self, points, loop=0, dedup=False): '''Return a points iterator. @arg points: The path or polygon points (C{LatLon}[]) @kwarg loop: Number of loop-back points (non-negative C{int}). @kwarg dedup: Skip duplicate points (C{bool}). @return: A new C{PointsIter} iterator. @raise PointsError: Insufficient number of B{C{points}}. ''' return PointsIter(points, loop=loop, base=self, dedup=dedup) @deprecated_method def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property L{philam}.''' return self.philam def toNvector(self, h=None, Nvector=NvectorBase, **Nvector_kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{including height}. @kwarg h: Optional height, overriding this point's height (C{meter}). @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) or C{None}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} is None}. @return: The C{n-vector} components B{C{Nvector}} or if B{C{Nvector}} is C{None}, a L{Vector4Tuple}C{(x, y, z, h)}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}} argument. ''' x, y, z = latlon2n_xyz(self.lat, self.lon) r = Vector4Tuple(x, y, z, self.height if h is None else h) if Nvector is not None: r = Nvector(x, y, z, **_xkwds(Nvector_kwds, h=r.h, ll=self)) return _xnamed(r, self.name) def toRepr(self, **kwds): '''This L{LatLon_} as a string "class(<degrees>, ...)". @kwarg kwds: Optional, keyword arguments. @return: Class instance (C{str}). ''' _ = _xkwds_pop(kwds, std=None) # PYCHOK std unused return Fmt.PAREN(classname(self), self.toStr(**kwds)) def toStr(self, form=F_D, joined=_COMMASPACE_, **prec_sep_s_D_M_S_kwds): '''Convert this point to a "lat, lon[, height][, name][, ...]" string, formatted in the given C{B{form}at}. @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. @kwarg joined: Separator to join the lat-, longitude, heigth, name and other strings (C{str} or C{None} or C{NN} for non-joined). @kwarg prec_sep_s_D_M_S_kwds: Optional C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}}, B{C{s_DMS}} and possibly other keyword arguments, see functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}. @return: This point in the specified C{B{form}at}, etc. (C{str} or a 2- or 3+tuple C{(lat_str, lon_str[, height_str][, name_str][, ...])} if C{B{joined}=NN} or C{B{joined}=None} and with the C{height_str} and C{name_str} only included if non-zero respectively non-empty). @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more details about keyword arguments C{B{form}at}, C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}. ''' def _t3(prec=None, sep=S_SEP, s_D=S_DEG, s_M=S_MIN, s_S=S_SEC, s_DMS=S_DMS, **kwds): return dict(prec=prec, sep=sep, s_D=s_D, s_M=s_M, s_S=s_S, s_DMS=s_DMS), kwds, prec prec_sep_s_D_M_S, kwds, prec = _t3(**prec_sep_s_D_M_S_kwds) t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S), lonDMS(self.lon, form=form, **prec_sep_s_D_M_S)) if self.height: t += (self.heightStr(),) if self.name: t += (repr(self.name),) if kwds: t += pairs(kwds) if prec is None else pairs(kwds, prec=prec) return joined.join(t) if joined else t @deprecated_method def toStr2(self, **kwds): # PYCHOK no cover '''DEPRECATED, used method L{toRepr}.''' return self.toRepr(**kwds) def _isLatLon(inst): '''(INTERNAL) Check a C{LatLon} or C{LatLon_} instance. ''' return isinstance(inst, (LatLon_, _MODS.latlonBase.LatLonBase)) def _isLatLon_(LL): '''(INTERNAL) Check a (sub-)class of C{LatLon_}. ''' return issubclassof(LL, LatLon_) or (isclass(LL) and all(hasattr(LL, a) for a in _ALL_ATTRS_)) # get all pseudo-slots for class C{LatLon_} _ALL_ATTRS_ = tuple(LatLon_(0, 0).__dict__.keys()) class _Basequence(_Sequence): # immutable, on purpose '''(INTERNAL) Base class. ''' _array = [] _epsilon = EPS _itemname = _point_ def _contains(self, point): '''(INTERNAL) Check for a matching point. ''' return any(self._findall(point, ())) def copy(self, deep=False): # PYCHOK no cover '''Make a shallow or deep copy of this instance. @kwarg deep: If C{True} make a deep, otherwise a shallow copy (C{bool}). @return: The copy (C{This class} or subclass thereof). ''' return _xcopy(self, deep=deep) def _count(self, point): '''(INTERNAL) Count the number of matching points. ''' return sum(1 for _ in self._findall(point, ())) # NOT len()! def dup(self, **items): # PYCHOK no cover '''Duplicate this instance, I{without replacing items}. @kwarg items: No attributes (I{not allowed}). @return: The duplicate (C{This} (sub-)class). @raise TypeError: Any B{C{items}} invalid. ''' if items: t = _SPACE_(classname(self), _immutable_) raise _TypeError(txt=t, this=self, **items) return _xdup(self) @property_doc_(''' the equality tolerance (C{float}).''') def epsilon(self): '''Get the tolerance for equality tests (C{float}). ''' return self._epsilon @epsilon.setter # PYCHOK setter! def epsilon(self, tol): '''Set the tolerance for equality tests (C{scalar}). @raise TypeError: Non-scalar B{C{tol}}. @raise ValueError: Out-of-bounds B{C{tol}}. ''' self._epsilon = Scalar_(tol, name=_tolerance_) def _find(self, point, start_end): '''(INTERNAL) Find the first matching point index. ''' for i in self._findall(point, start_end): return i return -1 def _findall(self, point, start_end): # PYCHOK no cover '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, point, start_end) def _getitem(self, index): '''(INTERNAL) Return point [index] or return a slice. ''' # Luciano Ramalho, "Fluent Python", page 290+, O'Reilly, 2016 if isinstance(index, slice): # XXX an numpy.[nd]array slice is a view, not a copy return self.__class__(self._array[index], **self._slicekwds()) else: return self.point(self._array[index]) def _index(self, point, start_end): '''(INTERNAL) Find the first matching point index. ''' for i in self._findall(point, start_end): return i raise _IndexError(self._itemname, point, txt=_not_('found')) @property_RO def isNumpy2(self): # PYCHOK no cover '''Is this a Numpy2 wrapper? ''' return False # isinstance(self, (Numpy2LatLon, ...)) @property_RO def isPoints2(self): # PYCHOK no cover '''Is this a LatLon2 wrapper/converter? ''' return False # isinstance(self, (LatLon2psxy, ...)) @property_RO def isTuple2(self): # PYCHOK no cover '''Is this a Tuple2 wrapper? ''' return False # isinstance(self, (Tuple2LatLon, ...)) def _iter(self): '''(INTERNAL) Yield all points. ''' _array, point = self._array, self.point for i in range(len(self)): yield point(_array[i]) def point(self, *attrs): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. @arg attrs: Optional arguments. ''' notOverloaded(self, *attrs) def _range(self, start=None, end=None, step=1): '''(INTERNAL) Return the range. ''' if step > 0: if start is None: start = 0 if end is None: end = len(self) elif step < 0: if start is None: start = len(self) - 1 if end is None: end = -1 else: raise _ValueError(step=step) return range(start, end, step) def _repr(self): '''(INTERNAL) Return a string representation. ''' # XXX use Python 3+ reprlib.repr t = repr(self._array[:1]) # only first row t = _SPACE_(t[:-1], _ELLIPSIS_, Fmt.SQUARE(t[-1:], len(self))) t = _SPACE_.join(t.split()) # coalesce spaces return instr(self, t, **self._slicekwds()) def _reversed(self): # PYCHOK false '''(INTERNAL) Yield all points in reverse order. ''' _array, point = self._array, self.point for i in range(len(self) - 1, -1, -1): yield point(_array[i]) def _rfind(self, point, start_end): '''(INTERNAL) Find the last matching point index. ''' def _r3(start=None, end=None, step=-1): return (start, end, step) # PYCHOK returns for i in self._findall(point, _r3(*start_end)): return i return -1 def _slicekwds(self): # PYCHOK no cover '''(INTERNAL) I{Should be overloaded}. ''' return {} class _Array2LatLon(_Basequence): # immutable, on purpose '''(INTERNAL) Base class for Numpy2LatLon or Tuple2LatLon. ''' _array = () _ilat = 0 # row column index _ilon = 0 # row column index _LatLon = LatLon_ # default _shape = () def __init__(self, array, ilat=0, ilon=1, LatLon=None, shape=()): '''Handle a C{NumPy} or C{Tuple} array as a sequence of C{LatLon} points. ''' ais = (_ilat_, ilat), (_ilon_, ilon) if len(shape) != 2 or shape[0] < 1 or shape[1] < len(ais): raise _IndexError('array.shape', shape) self._array = array self._shape = Shape2Tuple(shape) # *shape if LatLon: # check the point class if not _isLatLon_(LatLon): raise _IsnotError(_valid_, LatLon=LatLon) self._LatLon = LatLon # check the attr indices for n, (ai, i) in enumerate(ais): if not isint(i): raise _IsnotError(int.__name__, **{ai: i}) i = int(i) if not 0 <= i < shape[1]: raise _ValueError(ai, i) for aj, j in ais[:n]: if int(j) == i: raise _ValueError(_DEQUALSPACED_(ai, aj, i)) setattr(self, NN(_UNDER_, ai), i) def __contains__(self, latlon): '''Check for a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @return: C{True} if B{C{latlon}} is present, C{False} otherwise. @raise TypeError: Invalid B{C{latlon}}. ''' return self._contains(latlon) def __getitem__(self, index): '''Return row[index] as C{LatLon} or return a L{Numpy2LatLon} slice. ''' return self._getitem(index) def __iter__(self): '''Yield rows as C{LatLon}. ''' return self._iter() def __len__(self): '''Return the number of rows. ''' return self._shape[0] def __repr__(self): '''Return a string representation. ''' return self._repr() def __reversed__(self): # PYCHOK false '''Yield rows as C{LatLon} in reverse order. ''' return self._reversed() __str__ = __repr__ def count(self, latlon): '''Count the number of rows with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @return: Count (C{int}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._count(latlon) def find(self, latlon, *start_end): '''Find the first row with a specific lat-/longitude. @arg latlon: Point (C{LatLon}) or 2-tuple (lat, lon). @arg start_end: Optional C{[start[, end]]} index (integers). @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._find(latlon, start_end) def _findall(self, latlon, start_end): '''(INTERNAL) Yield indices of all matching rows. ''' try: lat, lon = latlon.lat, latlon.lon except AttributeError: try: lat, lon = latlon except (TypeError, ValueError): raise _IsnotError(_valid_, latlon=latlon) _ilat, _ilon = self._ilat, self._ilon _array, _eps = self._array, self._epsilon for i in self._range(*start_end): row = _array[i] if abs(row[_ilat] - lat) <= _eps and \ abs(row[_ilon] - lon) <= _eps: yield i def findall(self, latlon, *start_end): '''Yield indices of all rows with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Indices (C{iterable}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._findall(latlon, start_end) def index(self, latlon, *start_end): # PYCHOK Python 2- issue '''Find index of the first row with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index (C{int}). @raise IndexError: Point not found. @raise TypeError: Invalid B{C{latlon}}. ''' return self._index(latlon, start_end) @Property_RO def ilat(self): '''Get the latitudes column index (C{int}). ''' return self._ilat @Property_RO def ilon(self): '''Get the longitudes column index (C{int}). ''' return self._ilon # next = __iter__ def point(self, row): # PYCHOK *attrs '''Instantiate a point C{LatLon}. @arg row: Array row (numpy.array). @return: Point (C{LatLon}). ''' return self._LatLon(row[self._ilat], row[self._ilon]) def rfind(self, latlon, *start_end): '''Find the last row with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @note: Keyword order, first stop, then start. @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._rfind(latlon, start_end) def _slicekwds(self): '''(INTERNAL) Slice kwds. ''' return dict(ilat=self._ilat, ilon=self._ilon) @Property_RO def shape(self): '''Get the shape of the C{NumPy} array or the C{Tuples} as L{Shape2Tuple}C{(nrows, ncols)}. ''' return self._shape def _subset(self, indices): # PYCHOK no cover '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, indices) def subset(self, indices): '''Return a subset of the C{NumPy} array. @arg indices: Row indices (C{range} or C{int}[]). @note: A C{subset} is different from a C{slice} in 2 ways: (a) the C{subset} is typically specified as a list of (un-)ordered indices and (b) the C{subset} allocates a new, separate C{NumPy} array while a C{slice} is just an other C{view} of the original C{NumPy} array. @return: Sub-array (C{numpy.array}). @raise IndexError: Out-of-range B{C{indices}} value. @raise TypeError: If B{C{indices}} is not a C{range} nor an C{int}[]. ''' if not issequence(indices, tuple): # NO tuple, only list # and range work properly to get Numpy array sub-sets raise _IsnotError(_valid_, indices=type(indices)) n = len(self) for i, v in enumerate(indices): if not isint(v): raise _TypeError(Fmt.SQUARE(indices=i), v) elif not 0 <= v < n: raise _IndexError(Fmt.SQUARE(indices=i), v) return self._subset(indices) class LatLon2psxy(_Basequence): '''Wrapper for C{LatLon} points as "on-the-fly" pseudo-xy coordinates. ''' _closed = False _len = 0 _deg2m = None # default, keep degrees _radius = None _wrap = True def __init__(self, latlons, closed=False, radius=None, wrap=True): '''Handle C{LatLon} points as pseudo-xy coordinates. @note: The C{LatLon} latitude is considered the I{pseudo-y} and longitude the I{pseudo-x} coordinate, likewise for L{LatLon2Tuple}. However, 2-tuples C{(x, y)} are considered as I{(longitude, latitude)}. @arg latlons: Points C{list}, C{sequence}, C{set}, C{tuple}, etc. (C{LatLon[]}). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat- and longitudes (C{bool}). @raise PointsError: Insufficient number of B{C{latlons}}. @raise TypeError: Some B{C{points}} are not B{C{base}}. ''' self._closed = closed self._len, self._array = points2(latlons, closed=closed) if radius: self._radius = r = Radius(radius) self._deg2m = degrees2m(_1_0, r) self._wrap = wrap def __contains__(self, xy): '''Check for a matching point. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @return: C{True} if B{C{xy}} is present, C{False} otherwise. @raise TypeError: Invalid B{C{xy}}. ''' return self._contains(xy) def __getitem__(self, index): '''Return the pseudo-xy or return a L{LatLon2psxy} slice. ''' return self._getitem(index) def __iter__(self): '''Yield all pseudo-xy's. ''' return self._iter() def __len__(self): '''Return the number of pseudo-xy's. ''' return self._len def __repr__(self): '''Return a string representation. ''' return self._repr() def __reversed__(self): # PYCHOK false '''Yield all pseudo-xy's in reverse order. ''' return self._reversed() __str__ = __repr__ def count(self, xy): '''Count the number of matching points. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @return: Count (C{int}). @raise TypeError: Invalid B{C{xy}}. ''' return self._count(xy) def find(self, xy, *start_end): '''Find the first matching point. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{xy}}. ''' return self._find(xy, start_end) def _findall(self, xy, start_end): '''(INTERNAL) Yield indices of all matching points. ''' try: x, y = xy.lon, xy.lat def _x_y_ll3(ll): # match LatLon return ll.lon, ll.lat, ll except AttributeError: try: x, y = xy[:2] except (IndexError, TypeError, ValueError): raise _IsnotError(_valid_, xy=xy) _x_y_ll3 = self.point # PYCHOK expected _array, _eps = self._array, self._epsilon for i in self._range(*start_end): xi, yi, _ = _x_y_ll3(_array[i]) if abs(xi - x) <= _eps and \ abs(yi - y) <= _eps: yield i def findall(self, xy, *start_end): '''Yield indices of all matching points. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Indices (C{iterator}). @raise TypeError: Invalid B{C{xy}}. ''' return self._findall(xy, start_end) def index(self, xy, *start_end): # PYCHOK Python 2- issue '''Find the first matching point. @arg xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index (C{int}). @raise IndexError: Point not found. @raise TypeError: Invalid B{C{xy}}. ''' return self._index(xy, start_end) @property_RO def isPoints2(self): '''Is this a LatLon2 wrapper/converter? ''' return True # isinstance(self, (LatLon2psxy, ...)) def point(self, ll): # PYCHOK *attrs '''Create a pseudo-xy. @arg ll: Point (C{LatLon}). @return: An L{Point3Tuple}C{(x, y, ll)}. ''' x, y = ll.lon, ll.lat # note, x, y = lon, lat if self._wrap: x, y = wrap180(x), wrap90(y) d = self._deg2m if d: # convert degrees to meter (or radians) x *= d y *= d return Point3Tuple(x, y, ll) def rfind(self, xy, *start_end): '''Find the last matching point. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{xy}}. ''' return self._rfind(xy, start_end) def _slicekwds(self): '''(INTERNAL) Slice kwds. ''' return dict(closed=self._closed, radius=self._radius, wrap=self._wrap) class Numpy2LatLon(_Array2LatLon): # immutable, on purpose '''Wrapper for C{NumPy} arrays as "on-the-fly" C{LatLon} points. ''' def __init__(self, array, ilat=0, ilon=1, LatLon=None): '''Handle a C{NumPy} array as a sequence of C{LatLon} points. @arg array: C{NumPy} array (C{numpy.array}). @kwarg ilat: Optional index of the latitudes column (C{int}). @kwarg ilon: Optional index of the longitudes column (C{int}). @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). @raise IndexError: If B{C{array.shape}} is not (1+, 2+). @raise TypeError: If B{C{array}} is not a C{NumPy} array or C{LatLon} is not a class with C{lat} and C{lon} attributes. @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values are the same or out of range. @example: >>> type(array) <type 'numpy.ndarray'> # <class ...> in Python 3+ >>> points = Numpy2LatLon(array, lat=0, lon=1) >>> simply = simplifyRDP(points, ...) >>> type(simply) <type 'numpy.ndarray'> # <class ...> in Python 3+ >>> sliced = points[1:-1] >>> type(sliced) <class '...Numpy2LatLon'> ''' try: # get shape and check some other numpy.array attrs s, _, _ = array.shape, array.nbytes, array.ndim # PYCHOK expected except AttributeError: raise _IsnotError('NumPy', array=type(array)) _Array2LatLon.__init__(self, array, ilat=ilat, ilon=ilon, LatLon=LatLon, shape=s) @property_RO def isNumpy2(self): '''Is this a Numpy2 wrapper? ''' return True # isinstance(self, (Numpy2LatLon, ...)) def _subset(self, indices): return self._array[indices] # NumPy special class Shape2Tuple(_NamedTuple): '''2-Tuple C{(nrows, ncols)}, the number of rows and columns, both C{int}. ''' _Names_ = (_nrows_, _ncols_) _Units_ = ( Number_, Number_) class Tuple2LatLon(_Array2LatLon): '''Wrapper for tuple sequences as "on-the-fly" C{LatLon} points. ''' def __init__(self, tuples, ilat=0, ilon=1, LatLon=None): '''Handle a list of tuples, each containing a lat- and longitude and perhaps other values as a sequence of C{LatLon} points. @arg tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]). @kwarg ilat: Optional index of the latitudes value (C{int}). @kwarg ilon: Optional index of the longitudes value (C{int}). @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). @raise IndexError: If C{(len(B{tuples}), min(len(t) for t in B{tuples}))} is not (1+, 2+). @raise TypeError: If B{C{tuples}} is not a C{list}, C{tuple} or C{sequence} or if B{C{LatLon}} is not a C{LatLon} with C{lat}, C{lon} and C{name} attributes. @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values are the same or out of range. @example: >>> tuples = [(0, 1), (2, 3), (4, 5)] >>> type(tuples) <type 'list'> # <class ...> in Python 3+ >>> points = Tuple2LatLon(tuples, lat=0, lon=1) >>> simply = simplifyRW(points, 0.5, ...) >>> type(simply) <type 'list'> # <class ...> in Python 3+ >>> simply [(0, 1), (4, 5)] >>> sliced = points[1:-1] >>> type(sliced) <class '...Tuple2LatLon'> >>> sliced ...Tuple2LatLon([(2, 3), ...][1], ilat=0, ilon=1) >>> closest, _ = nearestOn2(LatLon_(2, 1), points, adjust=False) >>> closest LatLon_(lat=1.0, lon=2.0) >>> closest, _ = nearestOn2(LatLon_(3, 2), points) >>> closest LatLon_(lat=2.001162, lon=3.001162) ''' _xinstanceof(list, tuple, tuples=tuples) s = len(tuples), min(len(_) for _ in tuples) _Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon, LatLon=LatLon, shape=s) @property_RO def isTuple2(self): '''Is this a Tuple2 wrapper? ''' return True # isinstance(self, (Tuple2LatLon, ...)) def _subset(self, indices): return type(self._array)(self._array[i] for i in indices) def _area2(points, adjust, wrap): '''(INTERNAL) Approximate the area in radians squared, I{signed}. ''' if adjust: # approximate trapezoid by a rectangle, adjusting # the top width by the cosine of the latitudinal # average and bottom width by some fudge factor def _adjust(w, h): c = cos(h) if abs(h) < PI_2 else _0_0 return w * h * (c + 1.2876) * _0_5 else: def _adjust(w, h): # PYCHOK expected return w * h # setting radius=1 converts degrees to radians Ps = LatLon2PsxyIter(points, wrap=wrap, radius=_1_0, loop=1) x1, y1, ll = Ps[0] pts = [ll] A2 = Fsum() # trapezoidal area in radians**2 for i, p in Ps.enumerate(closed=True): x2, y2, ll = p if 0 < i < 4: pts.append(ll) w, x2 = unrollPI(x1, x2, wrap=wrap if i else False) A2 += _adjust(w, (y2 + y1) * _0_5) x1, y1 = x2, y2 return A2.fsum(), tuple(pts) def _areaError(pts, near_=NN): # imported by .ellipsoidalKarney '''(INTERNAL) Area issue. ''' t = _ELLIPSIS_(pts[:3], NN) return _ValueError(NN(near_, 'zero or polar area'), txt=t) def areaOf(points, adjust=True, radius=R_M, wrap=True): '''Approximate the area of a polygon. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg radius: Mean earth radius (C{meter}) or C{None}. @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate area (I{square} C{meter}, same units as B{C{radius}} or C{radians} I{squared} if B{C{radius}} is C{None}). @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @note: This area approximation has limited accuracy and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. @see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf}, L{ellipsoidalExact.areaOf} and L{ellipsoidalKarney.areaOf}. ''' a, _ = _area2(points, adjust, wrap) return abs(a) if radius is None else (abs(a) * Radius(radius)**2) def boundsOf(points, wrap=True, LatLon=None): '''Determine the lower-left SW and upper-right NE corners of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat- and longitudes (C{bool}). @kwarg LatLon: Optional class to return the C{bounds} corners (C{LatLon}) or C{None}. @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as B{C{LatLon}}s if B{C{LatLon}} is C{None} a L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @see: Function L{quadOf}. @example: >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) >>> boundsOf(b) # False >>> 45.0, 1.0, 46.0, 2.0 ''' Ps = LatLon2PsxyIter(points, wrap=wrap, loop=1) lox, loy, _ = hix, hiy, _ = Ps[0] for x, y, _ in Ps.iterate(closed=False): # [1:] if lox > x: lox = x elif hix < x: hix = x if loy > y: loy = y elif hiy < y: hiy = y return Bounds4Tuple(loy, lox, hiy, hix) if LatLon is None else \ Bounds2Tuple(LatLon(loy, lox), LatLon(hiy, hix)) # PYCHOK inconsistent def centroidOf(points, wrap=True, LatLon=None): '''Determine the centroid of a polygon. @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @kwarg LatLon: Optional class to return the centroid (C{LatLon}) or C{None}. @return: Centroid (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)} if C{B{LatLon} is None}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: The B{C{points}} enclose a pole or near-zero area. @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and Paul Bourke's U{Calculating The Area And Centroid Of A Polygon <https://www.SEAS.UPenn.edu/~ese502/lab-content/extra_materials/ Polygon%20Area%20and%20Centroid.pdf>}, 1988. ''' A, X, Y = Fsum(), Fsum(), Fsum() # setting radius=1 converts degrees to radians Ps = LatLon2PsxyIter(points, wrap=wrap, radius=_1_0, loop=1) x1, y1, ll = Ps[0] pts = [ll] # for _areaError for i, p in Ps.enumerate(closed=True): x2, y2, ll = p if 0 < i < 4: pts.append(ll) if wrap and i != 0: _, x2 = unrollPI(x1, x2, wrap=wrap) t = x1 * y2 - x2 * y1 A += t X += t * (x1 + x2) Y += t * (y1 + y2) # XXX more elaborately: # t1, t2 = x1 * y2, -(x2 * y1) # A.fadd_(t1, t2) # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2) # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2) x1, y1 = x2, y2 A = A.fmul(_3_0).fsum() # 6.0 / 2.0 if isnear0(A): raise _areaError(pts, near_=_near_) Y, X = degrees90(Y.fdiv(A).fsum()), degrees180(X.fdiv(A).fsum()) return LatLon2Tuple(Y, X) if LatLon is None else LatLon(Y, X) def fractional(points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds): '''Return the point at a given I{fractional} index. @arg points: The points (C{LatLon}[], L{Numpy2LatLon}[], L{Tuple2LatLon}[], C{Cartesian}[], C{Vector3d}[], L{Vector3Tuple}[]). @arg fi: The fractional index (L{FIx}, C{float} or C{int}). @kwarg j: Optionally, index of the other point (C{int}). @kwarg wrap: Wrap and unroll longitudes (C{bool}) or C{None} for backward compatible L{LatLon2Tuple} or B{C{LatLon}} with averaged lat- and longitudes. Use C{True} or C{False} to get the I{fractional} point computed method C{points[fi].intermediateTo}. @kwarg LatLon: Optional class to return the I{intermediate}, I{fractional} point (C{LatLon}) or C{None}. @kwarg Vector: Optional class to return the I{intermediate}, I{fractional} point (C{Cartesian}, C{Vector3d}) or C{None}. @kwarg kwds: Optional, additional B{C{LatLon}} I{or} B{C{Vector}} keyword arguments, ignored if both C{B{LatLon}} and C{B{Vector}} are C{None}. @return: A L{LatLon2Tuple}C{(lat, lon)} if B{C{wrap}}, B{C{LatLon}} and B{C{Vector}} all are C{None}, the defaults. An instance of B{C{LatLon}} if not C{None} I{or} an instance of B{C{Vector}} if not C{None}. Otherwise with B{C{wrap}} either C{True} or C{False} and B{C{LatLon}} and B{C{Vector}} both C{None}, an instance of B{C{points}}' (sub-)class C{intermediateTo} I{fractional}. Summarized as follows: >>> wrap | LatLon | Vector | returned type/value # -------+--------+--------+--------------+------ # | | | LatLon2Tuple | favg # None | None | None | or** | # | | | Vector3Tuple | favg # None | LatLon | None | LatLon | favg # None | None | Vector | Vector | favg # -------+--------+--------+--------------+------ # True | None | None | points' | .iTo # True | LatLon | None | LatLon | .iTo # True | None | Vector | Vector | .iTo # -------+--------+--------+--------------+------ # False | None | None | points' | .iTo # False | LatLon | None | LatLon | .iTo # False | None | Vector | Vector | .iTo # _____ # favg) averaged lat, lon or x, y, z values # .iTo) value from points[fi].intermediateTo # **) depends on base class of points[fi] @raise IndexError: Fractional index B{C{fi}} invalid or B{C{points}} not subscriptable or not closed. @raise TypeError: Invalid B{C{LatLon}}, B{C{Vector}} or B{C{kwds}} argument. @see: Class L{FIx} and method L{FIx.fractional}. ''' if LatLon and Vector: # PYCHOK no cover kwds = _xkwds(kwds, fi=fi, LatLon=LatLon, Vector=Vector) raise _TypeError(txt=fractional.__name__, **kwds) try: if not isscalar(fi) or fi < 0: raise IndexError n = getattr(fi, _fin_, 0) w = wrap if Vector is None else False # intermediateTo p = _fractional(points, fi, j, fin=n, wrap=w) # see .units.FIx if LatLon: p = LatLon(p.lat, p.lon, **kwds) elif Vector: p = Vector(p.x, p.y, p.z, **kwds) except (IndexError, TypeError): raise _IndexError(fi=fi, points=points, wrap=wrap, txt=fractional.__name__) return p def _fractional(points, fi, j, fin=None, wrap=None): # in .frechet.py '''(INTERNAL) Compute point at L{fractional} index C{fi} and C{j}. ''' i = int(fi) p = points[i] r = fi - float(i) if r > EPS: # EPS0? if j is None: j = i + 1 if fin: j %= fin q = points[j] if r >= EPS1: # PYCHOK no cover p = q elif wrap is not None: # in (True, False) p = p.intermediateTo(q, r, wrap=wrap) elif _isLatLon(p): # backward compatible default p = LatLon2Tuple(favg(p.lat, q.lat, f=r), favg(p.lon, q.lon, f=r), name=fractional.__name__) else: # assume p and q are cartesian or vectorial z = p.z if p.z is q.z else favg(p.z, q.z, f=r) p = Vector3Tuple(favg(p.x, q.x, f=r), favg(p.y, q.y, f=r), z, name=fractional.__name__) return p def isclockwise(points, adjust=False, wrap=True): '''Determine the direction of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{points}} are clockwise, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: The B{C{points}} enclose a pole or zero area. @example: >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) >>> isclockwise(f) # False >>> isclockwise(reversed(f)) # True ''' a, pts = _area2(points, adjust, wrap) if a > 0: # opposite of ellipsoidalExact and -Karney return True elif a < 0: return False # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> raise _areaError(pts) def isconvex(points, adjust=False, wrap=True): '''Determine whether a polygon is convex. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{points}} are convex, C{False} otherwise. @raise CrossError: Some B{C{points}} are colinear. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @example: >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) >>> isconvex(t) # True >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) >>> isconvex(f) # False ''' return bool(isconvex_(points, adjust=adjust, wrap=wrap)) def isconvex_(points, adjust=False, wrap=True): '''Determine whether a polygon is convex I{and clockwise}. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{+1} if B{C{points}} are convex clockwise, C{-1} for convex counter-clockwise B{C{points}}, C{0} otherwise. @raise CrossError: Some B{C{points}} are colinear. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @example: >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) >>> isconvex_(t) # +1 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) >>> isconvex_(f) # 0 ''' def _unroll2(x1, y1, x2, y2, a, w): x21, x2 = unroll180(x1, x2, wrap=w) if a: y = radians(y1 + y2) * _0_5 x21 *= cos(y) if abs(y) < PI_2 else _0_0 return x21, x2 c, s = crosserrors(), 0 Ps = LatLon2PsxyIter(points, wrap=wrap, loop=2) x1, y1, _ = Ps[0] x2, y2, _ = Ps[1] x21, x2 = _unroll2(x1, y1, x2, y2, adjust, False) for i, p in Ps.enumerate(closed=True): x3, y3, ll = p x32, x3 = _unroll2(x2, y2, x3, y3, adjust, (wrap if i > 1 else False)) # get the sign of the distance from point # x3, y3 to the line from x1, y1 to x2, y2 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line> s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2) if s3 > 0: # x3, y3 on the right if s < 0: # non-convex return 0 s = +1 elif s3 < 0: # x3, y3 on the left if s > 0: # non-convex return 0 s = -1 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # PYCHOK no cover # colinear u-turn: x3, y3 not on the # opposite side of x2, y2 as x1, y1 t = Fmt.SQUARE(points=i) raise CrossError(t, ll, txt=_colinear_) x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32 return s # all points on the same side def isenclosedBy(point, points, wrap=False): # MCCABE 15 '''Determine whether a point is enclosed by a polygon. @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}). @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{point}} is inside the polygon, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{point}}, lat- or longitude. @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy} and L{pygeodesy.ispolar} especially if the B{C{points}} may enclose a pole or wrap around the earth longitudinally, methods L{sphericalNvector.LatLon.isenclosedBy}, L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et al. 2009, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>} and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/JTECH-D-11-00019.1>}). ''' try: y0, x0 = point.lat, point.lon except AttributeError: try: y0, x0 = map1(float, *point[:2]) except (IndexError, TypeError, ValueError) as x: raise _ValueError(point=point, cause=x) if wrap: x0, y0 = wrap180(x0), wrap90(y0) def _dxy3(x1, x2, y2, w): dx, x2 = unroll180(x1, x2, wrap=w) return dx, x2, y2 else: x0 = fmod(x0, _360_0) # not x0 % 360! x0_180_ = x0 - _180_0 x0_180 = x0 + _180_0 def _dxy3(x1, x, y, unused): # PYCHOK expected x = _umod_360(float(x)) if x < x0_180_: x += _360_0 elif x >= x0_180: x -= _360_0 return (x - x1), x, y Ps = LatLon2PsxyIter(points, wrap=wrap, loop=1) p = Ps[0] e = m = False S = Fsum() _, x1, y1 = _dxy3(x0, p.x, p.y, False) for i, p in Ps.enumerate(closed=True): dx, x2, y2 = _dxy3(x1, p.x, p.y, (wrap if i else False)) # ignore duplicate and near-duplicate pts if max(abs(dx), abs(y2 - y1)) > EPS: # determine if polygon edge (x1, y1)..(x2, y2) straddles # point (lat, lon) or is on boundary, but do not count # edges on boundary as more than one crossing if abs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1): m = not m dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0): e = not e S += sin(radians(y2)) x1, y1 = x2, y2 # An odd number of meridian crossings means, the polygon # contains a pole. Assume it is the pole on the hemisphere # containing the polygon mean point and if the polygon does # contain the North Pole, flip the result. if m and S.fsum() > 0: e = not e return e def ispolar(points, wrap=False): '''Check whether a polygon encloses a pole. @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: C{True} if the polygon encloses a pole, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon} or don't have C{bearingTo2}, C{initialBearingTo} and C{finalBearingTo} methods. ''' def _cds(points, wrap): # iterate over course deltas Ps = PointsIter(points, loop=2) p2, p1 = Ps[0:2] b1, _ = _bearingTo2(p2, p1, wrap=wrap) for p2 in Ps.iterate(closed=True): if not p2.isequalTo(p1, EPS): b, b2 = _bearingTo2(p1, p2, wrap=wrap) yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180 p1, b1 = p2, b2 # summation of course deltas around pole is 0° rather than normally ±360° # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> s = fsum(_cds(points, wrap)) # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90) return abs(s) < 90 # "zero-ish" def luneOf(lon1, lon2, closed=False, LatLon=LatLon_, **LatLon_kwds): '''Generate an ellipsoidal or spherical U{lune <https://WikiPedia.org/wiki/Spherical_lune>}-shaped path or polygon. @arg lon1: Left longitude (C{degrees90}). @arg lon2: Right longitude (C{degrees90}). @kwarg closed: Optionally, close the path (C{bool}). @kwarg LatLon: Class to use (L{LatLon_}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments. @return: A tuple of 4 or 5 B{C{LatLon}} instances outlining the lune shape. @see: U{Latitude-longitude quadrangle <https://www.MathWorks.com/help/map/ref/areaquad.html>}. ''' t = (LatLon( _0_0, lon1, **LatLon_kwds), LatLon( _90_0, lon1, **LatLon_kwds), LatLon( _0_0, lon2, **LatLon_kwds), LatLon(_N_90_0, lon2, **LatLon_kwds)) if closed: t += t[:1] return t def nearestOn5(point, points, closed=False, wrap=False, LatLon=None, **options): '''Locate the point on a path or polygon closest to a reference point. The closest point is either on and within the extent of a polygon edge or the nearest of that edge's end points. @arg point: Reference point (C{LatLon}). @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes and longitudinal delta (C{bool}) in function L{pygeodesy.equirectangular_}. @kwarg LatLon: Optional class to return the closest point (C{LatLon}) or C{None}. @kwarg options: Other keyword arguments for function L{pygeodesy.equirectangular_}. @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the {closest} point (B{C{LatLon}}) or if C{B{LatLon} is None}, a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}. The C{distance} is the L{pygeodesy.equirectangular} distance between the C{closest} and reference B{C{point}} in C{degrees}. The C{angle} from the reference B{C{point}} to the C{closest} is in compass C{degrees360}, like function L{pygeodesy.compassAngle}. @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}}, see function L{pygeodesy.equirectangular_}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @note: Distances are I{approximated} using function L{pygeodesy.equirectangular_}, subject to the supplied B{C{options}}. Method C{LatLon.nearestOn6} measures distances more accurately. @see: Function L{pygeodesy.nearestOn6} for cartesian points. Use function L{pygeodesy.degrees2m} to convert C{degrees} to C{meter}. ''' def _d2yx(p2, p1, u, w): # w = wrap if (not closed or w < (n - 1)) else False # equirectangular_ returns a Distance4Tuple(distance # in degrees squared, delta lat, delta lon, p2.lon # unroll/wrap); the previous p2.lon unroll/wrap # is also applied to the next edge's p1.lon return equirectangular_(p1.lat, p1.lon + u, p2.lat, p2.lon, wrap=w, **options) def _h(p): # get height or default 0 return getattr(p, _height_, 0) or 0 # 3-D version used in .vector3d._nearestOn2 # # point (x, y) on axis rotated ccw by angle a: # x' = y * sin(a) + x * cos(a) # y' = y * cos(a) - x * sin(a) # # distance (w) along and perpendicular (h) to # a line thru point (dx, dy) and the origin: # w = (y * dy + x * dx) / hypot(dx, dy) # h = (y * dx - x * dy) / hypot(dx, dy) # # closest point on that line thru (dx, dy): # xc = dx * w / hypot(dx, dy) # yc = dy * w / hypot(dx, dy) # or # xc = dx * f # yc = dy * f # with # f = w / hypot(dx, dy) # or # f = (y * dy + x * dx) / hypot2(dx, dy) # # i.e. no need for sqrt or hypot Ps = PointsIter(points, loop=1) p1 = c = Ps[0] u1 = u = _0_0 d, dy, dx, _ = _d2yx(p1, point, u1, False) for i, p2 in Ps.enumerate(closed=closed): # iff wrapped, unroll lon1 (actually previous # lon2) like function unroll180/-PI would've w = False if closed and i == 0 else wrap d21, y21, x21, u2 = _d2yx(p2, p1, u1, w) if d21 > EPS: # distance point to p1, y01 and x01 inverted d2, y01, x01, _ = _d2yx(point, p1, u1, closed) if d2 > EPS: w2 = y01 * y21 + x01 * x21 if w2 > 0: if w2 < d21: # closest is between p1 and p2, use # original delta's, not y21 and x21 f = w2 / d21 p1 = LatLon_(favg(p1.lat, p2.lat, f=f), favg(p1.lon, p2.lon + u2, f=f), height=favg(_h(p1), _h(p2), f=f)) u1 = _0_0 else: # p2 is closest p1, u1 = p2, u2 d2, y01, x01, _ = _d2yx(point, p1, u1, closed) if d2 < d: # p1 is closer, y01 and x01 negated c, u, d, dy, dx = p1, u1, d2, -y01, -x01 p1, u1 = p2, u2 d, a, h = hypot(dx, dy), atan2b(dx, dy), _h(c) if LatLon is None: r = NearestOn5Tuple(c.lat, c.lon + u, d, a, h) else: r = LatLon(c.lat, c.lon + u, height=h) r = NearestOn3Tuple(r, d, a) return _xnamed(r, nameof(point)) def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True): '''Approximate the perimeter of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate perimeter (C{meter}, same units as B{C{radius}}). @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @note: This perimeter is based on the L{pygeodesy.equirectangular_} distance approximation and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. @see: Functions L{sphericalTrigonometry.perimeterOf} and L{ellipsoidalKarney.perimeterOf}. ''' def _degs(points, closed, wrap): # angular edge lengths in degrees Ps = LatLon2PsxyIter(points, wrap=wrap, loop=1) p1, u = Ps[0], _0_0 # previous x2's unroll/wrap for i, p2 in Ps.enumerate(closed=closed): w = False if closed and i == 0 else wrap # apply previous x2's unroll/wrap to new x1 _, dy, dx, u = equirectangular_(p1.y, p1.x + u, p2.y, p2.x, adjust=adjust, limit=None, wrap=w) # PYCHOK non-sequence yield hypot(dx, dy) p1 = p2 d = fsum(_degs(points, closed, wrap)) return degrees2m(d, radius=radius) def quadOf(latS, lonW, latN, lonE, closed=False, LatLon=LatLon_, **LatLon_kwds): '''Generate a quadrilateral path or polygon from two points. @arg latS: Southernmost latitude (C{degrees90}). @arg lonW: Westernmost longitude (C{degrees180}). @arg latN: Northernmost latitude (C{degrees90}). @arg lonE: Easternmost longitude (C{degrees180}). @kwarg closed: Optionally, close the path (C{bool}). @kwarg LatLon: Class to use (L{LatLon_}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments. @return: Return a tuple of 4 or 5 B{C{LatLon}} instances outlining the quadrilateral. @see: Function L{boundsOf}. ''' t = (LatLon(latS, lonW, **LatLon_kwds), LatLon(latN, lonW, **LatLon_kwds), LatLon(latN, lonE, **LatLon_kwds), LatLon(latS, lonE, **LatLon_kwds)) if closed: t += t[:1] return t __all__ += _ALL_DOCS(_Array2LatLon, _Basequence) # **) MIT License # # Copyright (C) 2016-2022 -- 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.