# Coverage for pygeodesy/azimuthal.py : 95%

## 332 statements 316 run 16 missing 33 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 | # -*- coding: utf-8 -*- u'''Equidistant, Equal-Area, and other Azimuthal projections. Classes L{Equidistant}, L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney}, L{Gnomonic}, L{GnomonicExact}, L{GnomonicKarney}, L{LambertEqualArea}, L{Orthographic} and L{Stereographic}, classes L{AzimuthalError}, L{Azimuthal7Tuple} and functions L{equidistant} and L{gnomonic}. L{EquidistantExact} and L{GnomonicExact} are based on exact geodesic L{GeodesicExact} and L{GeodesicLineExact}, Python versions of I{Karney}'s C++ original U{GeodesicExact<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1GeodesicExact.html>}, respectively U{GeodesicLineExact <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1GeodesicLineExact.html>}. Using L{EquidistantGeodSolve} requires I{Karney}'s utility U{GeodSolve <https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} to be available and set in env variable C{PYGEODESY_GEODSOLVE}, see module L{geodsolve} for more details. L{EquidistantKarney} and L{GnomonicKarney} require I{Charles Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib/>} package to be installed. Other azimuthal classes implement only (**) U{Snyder's FORMULAS FOR THE SPHERE <https://Pubs.USGS.gov/pp/1395/report.pdf>} and use those for any datum, spherical and ellipsoidal. The radius used for the latter is the ellipsoid's I{mean radius of curvature} at the latitude of the projection center point. For further justification, see the first paragraph under U{Snyder's FORMULAS FOR THE ELLIPSOID, page 197<https://Pubs.USGS.gov/pp/1395/report.pdf>}. Page numbers in C{Snyder} references apply to U{John P. Snyder, "Map Projections -- A Working Manual", 1987<https://Pubs.USGS.gov/pp/1395/report.pdf>}. See also U{here<https://WikiPedia.org/wiki/Azimuthal_equidistant_projection>}, especially the U{Comparison of the Azimuthal equidistant projection and some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii<https://WikiPedia.org/wiki/Azimuthal_equidistant_projection #/media/File:Comparison_azimuthal_projections.svg>}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division from pygeodesy.basics import copysign0, isnon0, _xinstanceof from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB from pygeodesy.datums import _spherical_datum, _WGS84 from pygeodesy.errors import _datum_datum, _ValueError, _xkwds from pygeodesy.fmath import euclid, Fsum, hypot from pygeodesy.interns import EPS, EPS0, EPS1, _EPStol, NAN, NN, \ _azimuth_, _datum_, _lat_, _lon_, \ _no_, _scale_, _SPACE_, _x_, _y_, \ _0_0, _0_1, _0_5, _1_0, _2_0, _360_0 from pygeodesy.karney import _norm180 from pygeodesy.latlonBase import LatLonBase as _LLB from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass from pygeodesy.namedTuples import LatLon2Tuple, LatLon4Tuple from pygeodesy.props import deprecated_Property_RO, Property_RO, \ property_doc_, property_RO from pygeodesy.streprs import Fmt, _fstrLL0 from pygeodesy.units import Bearing, Easting, Lat_, Lon_, \ Northing, Scalar, Scalar_ from pygeodesy.utily import asin1, atan2b, atan2d, sincos2, sincos2d from math import acos, atan, atan2, degrees, sin, sqrt __all__ = _ALL_LAZY.azimuthal __version__ = '21.07.03' _EPS_K = _EPStol * _0_1 # Karney's eps_ or _EPSmin * _0_1? _over_horizon_ = 'over horizon' _TRIPS = 21 # numit, 4 sufficient class _AzimuthalBase(_NamedBase): '''(INTERNAL) Base class for azimuthal projections. @see: I{Karney}'s C++ class U{AzimuthalEquidistant<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1AzimuthalEquidistant.html>} and U{Gnomonic <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>} or the Python versions L{EquidistantKarney}, respectively L{GnomonicKarney}. ''' _datum = _WGS84 # L{Datum} _iteration = None # iteration number for L{GnomonicKarney} _latlon0 = LatLon2Tuple(_0_0, _0_0) # lat0, lon0 (L{LatLon2Tuple}) _sc0 = (_0_0, _1_0) # 2-Tuple C{sincos2d(lat0)} def __init__(self, lat0, lon0, datum=None, name=NN): '''New azimuthal projection. @arg lat0: Latitude of the center point (C{degrees90}). @arg lon0: Longitude of the center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or (spherical) B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' if datum not in (None, self._datum): self._datum = _spherical_datum(datum, name=name) if name: self.name = name if lat0 or lon0: # often both 0 self.reset(lat0, lon0) @Property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @Property_RO def equatoradius(self): '''Get the geodesic's equatorial radius, semi-axis (C{meter}). ''' return self.datum.ellipsoid.a @property_RO def iteration(self): '''Get the iteration number (C{int}) or C{None} if not available/applicable. ''' return self._iteration @Property_RO def flattening(self): '''Get the geodesic's flattening (C{float}). ''' return self.datum.ellipsoid.f def forward(self, lat, lon, name=NN): '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, lat, lon, name=name) def _forward(self, lat, lon, name, _k_t_2): '''(INTERNAL) Azimuthal (spherical) forward C{lat, lon} to C{x, y}. ''' lat, lon = Lat_(lat), Lon_(lon) sa, ca, sb, cb = sincos2d(lat, lon - self.lon0) s0, c0 = self._sc0 k, t = _k_t_2(s0 * sa + c0 * ca * cb) if t: r = k * self.radius x = Easting(x=r * ca * sb) y = Northing(y=r * (c0 * sa - s0 * ca * cb)) z = atan2b(x, y) # (x, y) for azimuth from true North else: # 0 or 180 x = y = z = _0_0 t = Azimuthal7Tuple(x, y, lat, lon, z, k, self.datum, name=name or self.name) return t @Property_RO def lat0(self): '''Get the center latitude (C{degrees90}). ''' return self._latlon0.lat @property def latlon0(self): '''Get the center lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}) in (C{degrees90}, C{degrees180}). ''' return self._latlon0 @latlon0.setter # PYCHOK setter! def latlon0(self, latlon0): '''Set the center lat- and longitude (C{LatLon}, L{LatLon2Tuple} or L{LatLon4Tuple}). @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or ellipsoidal mismatch of B{C{latlon0}} and this projection. ''' B = _LLEB if self.datum.isEllipsoidal else _LLB _xinstanceof(B, LatLon2Tuple, LatLon4Tuple, latlon0=latlon0) if hasattr(latlon0, _datum_): _datum_datum(self.datum, latlon0.datum, Error=AzimuthalError) self.reset(latlon0.lat, latlon0.lon) @Property_RO def lon0(self): '''Get the center longitude (C{degrees180}). ''' return self._latlon0.lon @deprecated_Property_RO def majoradius(self): # PYCHOK no cover '''DEPRECATED, use property C{equatoradius}.''' return self.equatoradius @Property_RO def radius(self): '''Get this projection's mean radius of curvature (C{meter}). ''' return self.datum.ellipsoid.rocMean(self.lat0) def reset(self, lat0, lon0): '''Set or reset the center point of this azimuthal projection. @arg lat0: Center point latitude (C{degrees90}). @arg lon0: Center point longitude (C{degrees180}). @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' self._update(True) # force reset self._latlon0 = LatLon2Tuple(Lat_(lat0=lat0, Error=AzimuthalError), Lon_(lon0=lon0, Error=AzimuthalError)) self._sc0 = tuple(sincos2d(self.lat0)) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, x, y, name=name, LatLon=LatLon, **LatLon_kwds) def _reverse(self, x, y, name, LatLon, LatLon_kwds, _c_t, lea): '''(INTERNAL) Azimuthal (spherical) reverse C{x, y} to C{lat, lon}. ''' x = Easting(x=x) y = Northing(y=y) r = hypot(x, y) c, t = _c_t(r / self.radius) if t: s0, c0 = self._sc0 sc, cc = sincos2(c) k = c / sc z = atan2b(x, y) # (x, y) for azimuth from true North t = s0 * cc if r > EPS0: t += c0 * sc * (y / r) lat = degrees(asin1(t)) if lea or abs(c0) > EPS: lon = atan2d(x * sc, c0 * cc * r - s0 * sc * y) else: lon = atan2d(x, (y if s0 < 0 else -y)) lon = _norm180(self.lon0 + lon) else: k, z = _1_0, _0_0 lat, lon = self.latlon0 r = Azimuthal7Tuple(x, y, lat, lon, z, k, self.datum, name=name or self.name) if LatLon is None else \ self._toLatLon(lat, lon, LatLon, LatLon_kwds, name) return r def _reverse2(self, x, y): '''(INTERNAL) See iterating functions .ellipsoidalBaseDI._intersect3, .ellipsoidalBaseDI._intersects2 and .ellipsoidalBaseDI._nearestOne. ''' t = self.reverse(x, y) # LatLon=None d = euclid(t.lat - self.lat0, t.lon - self.lon0) return t, d def _toLatLon(self, lat, lon, LatLon, LatLon_kwds, name): '''(INTERNAL) Check B{C{LatLon}} and return an instance. ''' kwds = _xkwds(LatLon_kwds, datum=self.datum) r = self._xnamed(LatLon(lat, lon, **kwds), name=name) # handle .classof B = _LLEB if self.datum.isEllipsoidal else _LLB _xinstanceof(B, LatLon=r) return r def toRepr(self, prec=6, **unused): # PYCHOK expected '''Return a string representation of this projection. @kwarg prec: Optional number of decimals, unstripped (C{int}). @return: This projection as C{"<classname>(lat0, lon0, ...)"} (C{str}). ''' return _fstrLL0(self, prec, True) def toStr(self, prec=6, sep=_SPACE_, **unused): # PYCHOK expected '''Return a string representation of this projection. @kwarg prec: Optional number of decimal, unstripped (C{int}). @kwarg sep: Optional separator to join (C{str}). @return: This projection as C{"lat0 lon0"} (C{str}). ''' t = _fstrLL0(self, prec, False) return t if sep is None else sep.join(t) class AzimuthalError(_ValueError): '''An azimuthal L{Equidistant}, L{EquidistantKarney}, L{Gnomonic}, L{LambertEqualArea}, L{Orthographic}, L{Stereographic} or L{Azimuthal7Tuple} issue. ''' pass class Azimuthal7Tuple(_NamedTuple): '''7-Tuple C{(x, y, lat, lon, azimuth, scale, datum)}, in C{meter}, C{meter}, C{degrees90}, C{degrees180}, compass C{degrees}, C{scalar} and C{Datum} where C{(x, y)} is the easting and northing of a projected point, C{(lat, lon)} the geodetic location, C{azimuth} the azimuth, clockwise from true North and C{scale} is the projection scale, either C{1 / reciprocal} or C{1} or C{-1} in the L{Equidistant} case. ''' _Names_ = (_x_, _y_, _lat_, _lon_, _azimuth_, _scale_, _datum_) _Units_ = ( Easting, Northing, Lat_, Lon_, Bearing, Scalar, _Pass) class Equidistant(_AzimuthalBase): '''Azimuthal equidistant projection for the sphere**, see U{Snyder, pp 195-197 <https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/AzimuthalEquidistantProjection.html>}. @note: Results from this L{Equidistant} and an L{EquidistantExact}, L{EquidistantGeodSolve} or L{EquidistantKarney} projection C{may differ} by 10% or more. For an example, see method C{testDiscrepancies} in module C{testAzimuthal.py}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal equidistant east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. @note: The C{scale} will be C{-1} if B{C{(lat, lon)}} is antipodal to the projection center C{(lat0, lon0)}. ''' def _k_t(c): t = abs(c) < EPS1 if t: c = acos(c) k = c / sin(c) else: k = copysign0(_1_0, c) return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal equidistant location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): return c, (c > EPS) return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) def equidistant(lat0, lon0, datum=_WGS84, exact=False, geodsolve=False, name=NN): '''Return an L{EquidistantExact}, L{EquidistantGeodSolve} or (if I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} package is installed) an L{EquidistantKarney}, otherwise an L{Equidistant} instance. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg exact: Return an L{EquidistantExact} instance. @kwarg geodsolve: Return an L{EquidistantGeodSolve} instance. @kwarg name: Optional name for the projection (C{str}). @return: An L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} or L{Equidistant} instance. @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or (spherical) B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' if exact: return EquidistantExact(lat0, lon0, datum=datum, name=name) elif geodsolve: return EquidistantGeodSolve(lat0, lon0, datum=datum, name=name) # PYCHOK types try: return EquidistantKarney(lat0, lon0, datum=datum, name=name) # PYCHOK types except ImportError: return Equidistant(lat0, lon0, datum=datum, name=name) # PYCHOK types class _AzimuthalGeodesic(_AzimuthalBase): '''(INTERNAL) Base class for azimuthal projections using U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>} or exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. ''' _mask = 0 @Property_RO def geodesic(self): '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self) def _7Tuple(self, x, y, r, M=None, name=NN): '''(INTERNAL) Return an C{Azimuthal7Tuple}. ''' s = M if M is not None else ( # reciprocal, azimuthal scale (r.m12 / r.s12) if r.a12 > _EPS_K else _1_0) z = (r.azi2 + _360_0) % _360_0 # -180 <= r.azi2 < 180 return Azimuthal7Tuple(x, y, r.lat2, r.lon2, z, s, self.datum, name=name or self.name) class _EquidistantBase(_AzimuthalGeodesic): '''(INTERNAL) Base for classes L{EquidistantExact}, L{EquidistantGeodSolve} and L{EquidistantKarney}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{EquidistantExact}, L{EquidistantGeodSolve} or L{EquidistantKarney} projection. ''' _AzimuthalGeodesic.__init__(self, lat0, lon0, datum=datum, name=name) g = self.geodesic # g.STANDARD = g.AZIMUTH | g.DISTANCE | g.LATITUDE | g.LONGITUDE self._mask = g.REDUCEDLENGTH | g.STANDARD # | g.LONG_UNROLL def forward(self, lat, lon, name=NN): '''Convert an (ellipsoidal) geodetic location to azimuthal equidistant east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. @note: A call to C{.forward} followed by a call to C{.reverse} will return the original C{lat, lon} to within roundoff. ''' r = self.geodesic.Inverse(self.lat0, self.lon0, Lat_(lat), Lon_(lon), self._mask) x, y = sincos2d(r.azi1) return self._7Tuple(x * r.s12, y * r.s12, r, name=name) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal equidistant location to (ellipsoidal) geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The scale of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' x = Easting(x=x) y = Northing(y=y) z = atan2d(x, y) # (x, y) for azimuth from true North s = hypot( x, y) r = self.geodesic.Direct(self.lat0, self.lon0, z, s, self._mask) return self._7Tuple(x, y, r, name=name) if LatLon is None else \ self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds, name) class EquidistantExact(_EquidistantBase): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. An azimuthal equidistant projection is centered at an arbitrary position on the ellipsoid. For a point in projected space C{(x, y)}, the geodesic distance from the center position is C{hypot(x, y)} and the C{azimuth} of the geodesic from the center point is C{atan2(x, y)}, clockwise from true North. The C{.forward} and C{.reverse} methods also return the C{azimuth} of the geodesic at C{(x, y)} and the C{scale} in the azimuthal direction which, together with the basic properties of the projection, serve to specify completely the local affine transformation between geographic and projected coordinates. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{EquidistantExact} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. ''' _EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _EquidistantBase.forward reverse = _EquidistantBase.reverse @Property_RO def geodesic(self): '''Get this projection's exact geodesic (L{GeodesicExact}). ''' return self.datum.ellipsoid.geodesicx class EquidistantGeodSolve(_EquidistantBase): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, based on (exact) geodesic I{wrappers} L{GeodesicSolve} and L{GeodesicLineSolve} and intended I{for testing purposes only}. @see: L{EquidistantExact} and module L{geodsolve}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{EquidistantGeodSolve} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. ''' _EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _EquidistantBase.forward reverse = _EquidistantBase.reverse @Property_RO def geodesic(self): '''Get this projection's (exact) geodesic (L{GeodesicSolve}). ''' return self.datum.ellipsoid.geodsolve class EquidistantKarney(_EquidistantBase): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. @see: L{EquidistantExact}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{EquidistantKarney} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise ImportError: Package U{geographiclib<https://PyPI.org/project/geographiclib>} not installed or not found. @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. ''' _EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _EquidistantBase.forward reverse = _EquidistantBase.reverse @Property_RO def geodesic(self): '''Get this projection's I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>}, provided package U{geographiclib <https://PyPI.org/project/geographiclib>} is installed. ''' return self.datum.ellipsoid.geodesic _Equidistants = (Equidistant, EquidistantExact, EquidistantGeodSolve, EquidistantKarney) # PYCHOK in .ellipsoidalBaseDI class Gnomonic(_AzimuthalBase): '''Azimuthal gnomonic projection for the sphere**, see U{Snyder, pp 164-168 <https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/GnomonicProjection.html>}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal equidistant east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): t = c > EPS k = (_1_0 / c) if t else _1_0 return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal equidistant location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): return atan(c), (c > EPS) return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) def gnomonic(lat0, lon0, datum=_WGS84, exact=False, geodsolve=False, name=NN): '''Return a L{GnomonicExact} or (if I{Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed) a L{GnomonicKarney}, otherwise a L{Gnomonic} instance. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg exact: Return a L{GnomonicExact} instance. @kwarg geodsolve: Return an L{GnomonicGeodSolve} instance. @kwarg name: Optional name for the projection (C{str}). @return: A L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} or L{Gnomonic} instance. @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or (spherical) B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' if exact: return GnomonicExact(lat0, lon0, datum=datum, name=name) elif geodsolve: return GnomonicGeodSolve(lat0, lon0, datum=datum, name=name) # PYCHOK types try: return GnomonicKarney(lat0, lon0, datum=datum, name=name) # PYCHOK types except ImportError: return Gnomonic(lat0, lon0, datum=datum, name=name) # PYCHOK types class _GnomonicBase(_AzimuthalGeodesic): '''(INTERNAL) Base for classes L{GnomonicExact} and L{GnomonicKarney}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicExact} or L{GnomonicKarney} projection. ''' _AzimuthalGeodesic.__init__(self, lat0, lon0, datum=datum, name=name) g = self.geodesic self._mask = g.ALL # | g.LONG_UNROLL def forward(self, lat, lon, name=NN, raiser=True): # PYCHOK signature '''Convert an (ellipsoidal) geodetic location to azimuthal gnomonic east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @kwarg raiser: Do or don't throw an error (C{bool}) if the location lies over the horizon. @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1 / reciprocal**2} in I{radial} direction and C{1 / reciprocal} in the direction perpendicular to this. Both C{x} and C{y} will be C{NAN} if the (geodetic) location lies over the horizon and C{B{raiser}=False}. @raise AzimuthalError: Invalid B{C{lat}}, B{C{lon}} or the location lies over the horizon and C{B{raiser}=True}. ''' self._iteration = 0 r = self.geodesic.Inverse(self.lat0, self.lon0, Lat_(lat), Lon_(lon), self._mask) M = r.M21 if M > EPS0: q = r.m12 / M # .M12 x, y = sincos2d(r.azi1) x *= q y *= q elif raiser: raise AzimuthalError(lat=lat, lon=lon, txt=_over_horizon_) else: x = y = NAN t = self._7Tuple(x, y, r, M=M, name=name) t._iteraton = self._iteration # = 0 return t def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal gnomonic location to (ellipsoidal) geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @raise AzimuthalError: No convergence. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{azimuth} is clockwise from true North. The scale is C{1 / reciprocal**2} in C{radial} direction and C{1 / reciprocal} in the direction perpendicular to this. ''' x = Easting(x=x) y = Northing(y=y) z = atan2d(x, y) # (x, y) for azimuth from true North q = hypot( x, y) d = e = self.equatoradius s = e * atan(q / e) if q > e: def _d(r, q): return (r.M12 - q * r.m12) * r.m12 # negated q = _1_0 / q else: # little == True def _d(r, q): # PYCHOK _d return (q * r.M12 - r.m12) * r.M12 # negated e *= _EPS_K m = self._mask g = self.geodesic._Line(self.lat0, self.lon0, z, m) P = g.Position S = Fsum(s) for self._iteration in range(1, _TRIPS): r = P(s, m) if abs(d) < e: break s, d = S.fsum2_(_d(r, q)) else: raise AzimuthalError(x=x, y=y, txt=_no_(Fmt.convergence(e))) t = self._7Tuple(x, y, r, M=r.M12, name=name) if LatLon is None else \ self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds, name) t._iteration = self._iteration return t class GnomonicExact(_GnomonicBase): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. @see: I{Karney}'s U{Detailed Description<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Gnomonic.html>}, especially the B{Warning}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicExact} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _GnomonicBase.forward reverse = _GnomonicBase.reverse @Property_RO def geodesic(self): '''Get this projection's exact geodesic (L{GeodesicExact}). ''' return self.datum.ellipsoid.geodesicx class GnomonicGeodSolve(_GnomonicBase): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, based on (exact) geodesic I{wrappers} L{GeodesicSolve} and L{GeodesicLineSolve} and intended I{for testing purposes only}. @see: L{GnomonicExact} and module L{geodsolve}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicGeodSolve} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _GnomonicBase.forward reverse = _GnomonicBase.reverse @Property_RO def geodesic(self): '''Get this projection's (exact) geodesic (L{GeodesicSolve}). ''' return self.datum.ellipsoid.geodsolve class GnomonicKarney(_GnomonicBase): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. @see: L{GnomonicExact}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicKarney} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise ImportError: Package U{geographiclib<https://PyPI.org/project/geographiclib>} not installed or not found. @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _GnomonicBase.forward reverse = _GnomonicBase.reverse @Property_RO def geodesic(self): '''Get this projection's I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>}, provided package U{geographiclib <https://PyPI.org/project/geographiclib>} is installed. ''' return self.datum.ellipsoid.geodesic class LambertEqualArea(_AzimuthalBase): '''Lambert-equal-area projection for the sphere** (aka U{Lambert zenithal equal-area projection<https://WikiPedia.org/wiki/Lambert_azimuthal_equal-area_projection>}, see U{Snyder, pp 185-187<https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/LambertAzimuthalEqual-AreaProjection.html>}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal Lambert-equal-area east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): c = c + _1_0 t = c > EPS0 k = sqrt(_2_0 / c) if t else _1_0 return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal Lambert-equal-area location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): c = c * _0_5 t = c > EPS if t: c = _2_0 * asin1(c) return c, t return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, True) class Orthographic(_AzimuthalBase): '''Orthographic projection for the sphere**, see U{Snyder, pp 148-153 <https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/OrthographicProjection.html>}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal orthographic east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): return _1_0, (c >= 0) return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal orthographic location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): t = c > EPS if t: c = asin1(c) return c, t return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) class Stereographic(_AzimuthalBase): '''Stereographic projection for the sphere**, see U{Snyder, pp 157-160 <https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/StereographicProjection.html>}. ''' _k0 = _1_0 # central scale factor (C{scalar}) if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal stereographic east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing C{y} of point in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): c = c + _1_0 t = isnon0(c) k = (_2_0 * self._k0 / c) if t else _1_0 return k, t return self._forward(lat, lon, name, _k_t) @property_doc_('''optional, central scale factor (C{scalar}).''') def k0(self): '''Get the central scale factor (C{scalar}). ''' return self._k0 @k0.setter # PYCHOK setter! def k0(self, factor): '''Set the central scale factor (C{scalar}). ''' n = Stereographic.k0.fget.__name__ self._k0 = Scalar_(factor, name=n, low=EPS, high=2) # XXX high=1, 2, other? def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal stereographic location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): t = c > EPS if t: c = _2_0 * atan2(c, 2 * self._k0) return c, t return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) __all__ += _ALL_DOCS(_AzimuthalBase) # **) 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.