# Coverage for pygeodesy/karney.py : 94%

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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 | # -*- coding: utf-8 -*- u'''I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} C{geodesic}, wrapped. Wrapper around I{Karney}'s Python classes C{Geodesic} and C{GeodesicLine} and several C{Math} functions from I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}, provided that package is installed. The I{wrapped} class methods return a L{GDict} instance providing access to the C{dict} items by C{key} or by C{attribute} name. I{Karney}-based functionality ============================= 1. The following classes and functions in C{pygeodesy} - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4}, L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} -- U{AlbersEqualArea<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1AlbersEqualArea.html>} - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1CassiniSoldner.html>} - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Geocentric.html>} - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1EllipticFunction.html>} - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>} - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1TransverseMercatorExact.html>} - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1PolygonAreaT.html>} - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1GeodesicLineExact.html>} - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/html/geoid.html>} - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Georef.html>} - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>} - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1LocalCartesian.html>} - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1PolarStereographic.html>} - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1TransverseMercator.html>} - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1UTMUPS.html>} - L{atand}, L{atan2d}, L{sincos2}, L{sincos2d}-- U{Math<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html>} are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/html/annotated.html>}. 2. These C{pygeodesy} modules and classes - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney} - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve}, L{GnomonicKarney}, L{HeightIDWkarney} are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} C{geodesic} or C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/html/utilities.html>}. 3. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections and trilaterations - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn}, L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2}, L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5} - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn}, L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2}, L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5} - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn}, L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2}, L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5} are implementations of I{Karney}'s solution posted under U{The B{ellipsoidal} case <https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 4. Spherical functions - L{excessKarney_}, L{sphericalTrigonometry.areaOf} in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon <http://OSGeo-org.1560.x6.Nabble.com/Area-of-a-spherical-polygon-td3841625.html>}. ''' from pygeodesy.basics import copysign0, _xImportError, _xversion from pygeodesy.datums import _ellipsoidal_datum, _WGS84 # PYCHOK used! from pygeodesy.ellipsoids import Ellipsoid2 from pygeodesy.errors import _ValueError, _xkwds # PYCHOK shared from pygeodesy.interns import MAX as _MAX, NAN, NN, _lat1_, \ _lat2_, _lon2_, _0_0, _1_0, _2_0, \ _16_0, _180_0, _360_0 from pygeodesy.iters import PointsIter from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import _Dict, _NamedTuple, _Pass from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple from pygeodesy.props import Property, Property_RO from pygeodesy.units import Degrees as _Deg, Meter as _M, \ Meter2 as _M2, _1mm as _TOL_M # PYCHOK shared from pygeodesy.utily import atan2d, unroll180, wrap360 from math import fmod __all__ = _ALL_LAZY.karney __version__ = '21.08.12' _16th = _1_0 / _16_0 _a12_ = 'a12' _azi1_ = 'azi1' _azi2_ = 'azi2' _lon1_ = 'lon1' _m12_ = 'm12' _M12_ = 'M12' _M21_ = 'M21' _s12_ = 's12' _S12_ = 'S12' class _GTuple(_NamedTuple): # in .testNamedTuples '''(INTERNAL) Helper. ''' def toGDict(self, **updates): '''Convert this C{*Tuple} to a L{GDict}. @kwarg updates: Optional updates to apply (C{nam=value} pairs) ''' r = GDict(zip(self._Names_, self)) if updates: r.update(updates) return r class Direct9Tuple(_GTuple): '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in C{meter} I{squared}. ''' _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_) _Units_ = (_Deg, _Deg, _Deg, _Deg, _M, _Pass, _Pass, _Pass, _M2) class GDict(_Dict): '''Basic C{dict} with both key I{and} attribute access to the C{dict} items. Results of all C{geodesic} methods are returned as a L{GDict} instance. ''' def toDirect9Tuple(self, dflt=NAN): '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method C{geographiclib.geodesic.Geodesic._GenDirect}. @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} ''' def _9Tuple(a12=dflt, lat2=dflt, lon2=dflt, azi2=dflt, s12=dflt, m12=dflt, M12=dflt, M21=dflt, S12=dflt, **unused): return Direct9Tuple(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12) return _9Tuple(**self) def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} result. @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)}. ''' def _12Tuple(lat1=dflt, lon1=dflt, azi1=dflt, lat2=dflt, lon2=dflt, azi2=dflt, s12=dflt, a12=dflt, m12=dflt, M12=dflt, M21=dflt, S12=dflt, **unused): return GeodSolve12Tuple(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12) return _12Tuple(**self) def toInverse10Tuple(self, dflt=NAN): '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s method C{geographiclib.geodesic.Geodesic._GenInverse}. @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)}. ''' def _10Tuple(a12=dflt, s12=dflt, salp1=dflt, calp1=dflt, salp2=dflt, calp2=dflt, m12=dflt, M12=dflt, M21=dflt, S12=dflt, **unused): return Inverse10Tuple(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12) return _10Tuple(**self) class GeodesicError(_ValueError): # PYCHOK exported '''Error raised for I{geodesicx}'s methods for lack of convergence or other issues. ''' pass class GeodSolve12Tuple(_GTuple): '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic scales C{M12} and C{M21} C{scalar}, see U{GeodSolve <https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>}. ''' # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_) _Units_ = (_Deg, _Deg, _Deg, _Deg, _Deg, _Deg, _M, _Deg, _Pass, _Pass, _Pass, _M2) class Inverse10Tuple(_GTuple): '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and sines and cosines of initial and final (forward) azimuths. ''' _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_) _Units_ = (_Deg, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2) class _Wrapped(object): ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>} classes. ''' _geographiclib = None @Property_RO # MCCABE 14 def Geodesic(self): '''Get the I{wrapped} C{Geodesic} class, provided the U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed, otherwise an C{ImportError}. ''' self._xgeographiclib(_Wrapped.Geodesic) from geographiclib.geodesic import Geodesic as _Geodesic class Geodesic(_Geodesic): '''I{Karney}'s U{Geodesic<https://GeographicLib.SourceForge.io/html/ python/code.html#geographiclib.geodesic.Geodesic>} wrapper. ''' def __init__(self, a_ellipsoid, f=None, name=NN): # PYCHOK signature '''New C{Geodesic} instance. @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum (L{datum}) or the equatorial radius of the ellipsoid (C{meter}). @arg f: The flattening of the ellipsoid (C{scalar}) if B{C{a_ellipsoid}) is specified as C{meter}. @kwarg name: Optional name (C{str}). ''' if f is None: self._E = _ellipsoidal_datum(a_ellipsoid, name=name).ellipsoid else: self._E = Ellipsoid2(a_ellipsoid, f, name=name) _Geodesic.__init__(self, self.ellipsoid.a, self.ellipsoid.f) Area = _Geodesic.Polygon # like GeodesicExact.Area _debug = 0 # like .geodesicx.bases._GeodesicBase @Property def debug(self): '''Get the C{debug} option (C{bool}). ''' return bool(self._debug) @debug.setter # PYCHOK setter! def debug(self, debug): '''Set the C{debug} option. @arg debug: Include more details in results (C{bool}). ''' from pygeodesy.geodesicx.gxbases import Caps self._debug = Caps._DEBUG_ALL if debug else 0 def Direct(self, lat1, lon1, azi1, s12, *outmask): '''Return the C{Direct} result. ''' d = _Geodesic.Direct(self, lat1, lon1, azi1, s12, *outmask) return GDict(d) def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask '''Return the destination lat, lon and reverse azimuth (final bearing) in C{degrees}. @return: L{Destination3Tuple}C{(lat, lon, final)}. ''' m = self.AZIMUTH | self.LATITUDE | self.LONGITUDE d = self.Direct(lat1, lon1, azi1, s12, m) return Destination3Tuple(d.lat2, d.lon2, d.azi2) @Property_RO def ellipsoid(self): '''Get this geodesic's ellipsoid (C{Ellipsoid[2]}). ''' return self._E def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12, outmask=_Geodesic.STANDARD): '''(INTERNAL) Get C{._GenDirect} result as C{GDict}. ''' def _toGdict(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12): return GDict(a12=a12, lat2=lat2, lon2=lon2, azi2=azi2, s12=s12, m12=m12, M12=M12, M21=M21, S12=S12) t = _Geodesic._GenDirect(self, lat, lon, azi, arcmode, s12_a12, outmask) return _toGdict(*t) def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=_Geodesic.STANDARD): '''(INTERNAL) Get C{._GenInverse} result as C{GDict}. ''' def _toGdict(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12): return GDict(a12=a12, s12=s12, salp1=salp1, calp1=calp1, azi1=atan2d(salp1, calp1), salp2=salp2, calp2=calp2, azi2=atan2d(salp2, calp2), m12=m12, M12=M12, M21=M21, S12=S12, lon1=lon1) t =_Geodesic._GenInverse(self, lat1, lon1, lat2, lon2, outmask) return _toGdict(*t) def Inverse(self, lat1, lon1, lat2, lon2, *outmask): '''Return the C{Inverse} result. ''' d = _Geodesic.Inverse(self, lat1, lon1, lat2, lon2, *outmask) return GDict(d) def Inverse1(self, lat1, lon1, lat2, lon2, wrap=False): '''Return the non-negative, I{angular} distance in C{degrees}. ''' # see .FrechetKarney.distance, .HausdorffKarney._distance # and .HeightIDWkarney._distances _, lon2 = unroll180(lon1, lon2, wrap=wrap) # self.LONG_UNROLL d = self.Inverse(lat1, lon1, lat2, lon2) # XXX self.DISTANCE needed for 'a12'? return abs(d.a12) def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask '''Return the distance in C{meter} and the forward and reverse azimuths (initial and final bearing) in C{degrees}. @return: L{Distance3Tuple}C{(distance, initial, final)}. ''' m = self.DISTANCE | self.AZIMUTH d = self.Inverse(lat1, lon1, lat2, lon2, m) return Distance3Tuple(d.s12, wrap360(d.azi1), wrap360(d.azi2)) def Line(self, lat1, lon1, azi1, *caps): return _wrapped.GeodesicLine(self, lat1, lon1, azi1, *caps) _Line = Line # for .azimuthal._GnomonicBase.reverse, matching # PYCHOK .geodesicx.GeodesictExact._Line and -._GDictDirect # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__ # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__ # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__ return Geodesic @Property_RO def GeodesicLine(self): '''Get the I{wrapped} C{GeodesicLine} class, provided the U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed, otherwise an C{ImportError}. ''' self._xgeographiclib(_Wrapped.GeodesicLine) from geographiclib.geodesicline import GeodesicLine as _GeodesicLine class GeodesicLine(_GeodesicLine): '''I{Karney}'s U{GeodesicLine <https://GeographicLib.SourceForge.io/html/ python/code.html#geographiclib.geodesicline.GeodesicLine>} wrapper. ''' def ArcPosition(self, a12, *outmask): d = _GeodesicLine.ArcPosition(self, a12, *outmask) return GDict(d) def Position(self, s12, *outmask): d = _GeodesicLine.Position(self, s12, *outmask) return GDict(d) # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__ # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__ return GeodesicLine @Property_RO def Geodesic_WGS84(self): '''Get the I{wrapped} C{Geodesic.WGS84} I{instance} provided the U{geographiclib<https://PyPI.org/project/geographiclib>} package is installed, otherwise an C{ImportError}. ''' return _WGS84.ellipsoid.geodesic @Property_RO def geographiclib(self): '''Get the imported C{geographiclib}, provided the U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed, otherwise an C{ImportError}. ''' return self._xgeographiclib(_Wrapped.geographiclib) @Property_RO def Math(self): '''Get the C{Math} class, provided the U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed, otherwise C{None}. ''' try: self._xgeographiclib(_Wrapped.Math) from geographiclib.geomath import Math # replace karney. with Math. functions from pygeodesy import karney karney._around = Math.AngRound karney._diff182 = Math.AngDiff karney._fix90 = Math.LatFix karney._isfinite = Math.isfinite karney._norm180 = Math.AngNormalize karney._sum2 = Math.sum try: # geographiclib 1.49 karney._remainder = Math.remainder except AttributeError: pass except ImportError: Math = None return Math def _xgeographiclib(self, where): '''(INTERNAL) Import C{geographiclib}. ''' if self._geographiclib is None: try: import geographiclib as g except ImportError as x: raise _xImportError(x, where) self._geographiclib = _xversion(g, _Wrapped, 1, 49, name=where.name) return self._geographiclib _wrapped = _Wrapped() # PYCHOK singleton, .datum def _around(x): '''Coarsen a scalar to zero. @return: Coarsened value (C{float}). ''' M = _wrapped.Math if M: return M.AngRound(x) if x: y = abs(x) if y < _16th: y = _16th - y x = copysign0(_16th - y, x) else: x = _0_0 # -0 to 0 return x def _diff182(deg0, deg): # mimick Math.AngDiff '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately. @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}. ''' M = _wrapped.Math if M: return M.AngDiff(deg0, deg) d, t = _sum2(_norm180(-deg0), _norm180(deg)) d = _norm180(d) if t > 0 and d == _180_0: d = -_180_0 return _sum2(d, t) # def _Equidistant(equidistant, exact=False, geodsolve=False): # # (INTERNAL) Get the C{EquidistantExact}, C{-GeodSolve} or # # C{-Karney} class if B{C{equidistant}} in not callable. # if equidistant is None or not callable(equidistant): # if exact: # from pygeodesy.azimuthal import EquidistantExact as equidistant # elif geodsolve: # from pygeodesy.azimuthal import EquidistantGeodSolve as equidistant # else: # from pygeodesy.azimuthal import EquidistantKarney as equidistant # return equidistant def _fix90(deg): # mimick Math.LatFix '''Replace angle in C{degrees} outside [-90,90] by NAN. @return: Angle C{degrees} or NAN. ''' M = _wrapped.Math if M: return M.LatFix(deg) return NAN if abs(deg) > 90 else deg def _fsum2_(*vs): # see .test/testKarney.py '''Cascaded summation, like C{.fmath.fsum_}. @arg vs: Values to be added (C{scalar}[]). @return: 2-Tuple C{(sum_of_vs, residual)}. @note: NOT "error-free", see .test/testKarney.py. @see: U{Algorithm 4.1<http://www.ti3.TUHH.De/paper/rump/OgRuOi05.pdf>}. ''' s = t = _0_0 for v in vs: s, t = _3sum2(s, t, v) return _sum2(s, t) def _isfinite(x): # mimick Math.AngNormalize '''Check finitenessof C{x}. @return: True if finite. ''' M = _wrapped.Math if M: return M.isfinite(x) return abs(x) <= _MAX def _norm180(deg): # mimick Math.AngNormalize '''Reduce angle in C{degrees} to (-180,180]. @return: Reduced angle C{degrees}. ''' M = _wrapped.Math if M: return M.AngNormalize(deg) # with Python 2.7.16 and 3.7.3 on macOS 10.13.6 # fmod( 0, 360) == 0.0 # fmod( 360, 360) == 0.0 # fmod(-0, 360) == 0.0 # fmod(-0.0, 360) == -0.0 # fmod(-360, 360) == -0.0 # however, using the % operator ... # 0 % 360 == 0 # 360 % 360 == 0 # 360.0 % 360 == 0.0 # -0 % 360 == 0 # -360 % 360 == 0 # -0.0 % 360 == 0.0 # -360.0 % 360 == 0.0 # On Windows 32-bit with Python 2.7, math.fmod(-0.0, 360) # == +0.0. This fixes this bug. See also Math::AngNormalize # in the C++ library, Math::sincosd has a similar fix. d = (fmod(deg, _360_0) if _isfinite(deg) else NAN) if deg else deg return (d + _360_0) if d < -_180_0 else (d # XXX was <= twice if d < _180_0 else (d - _360_0)) def _polygon(geodesic, points, closed, line, wrap): '''(INTERNAL) Compute the area or perimeter of a polygon, using a L{GeodesicExact}, L{GeodesicSolve} or (if the C{geographiclib} package is installed) a C{Geodesic} or C{_wrapped.Geodesic} instance. ''' if not wrap: # capability LONG_UNROLL can't be off raise _ValueError(wrap=wrap) gP = geodesic.Polygon(line) p_ = gP.AddPoint Ps = PointsIter(points, loop=1) # base=LatLonEllipsoidalBase(0, 0) p0 = Ps[0] # note, lon deltas are unrolled, by default p_(p0.lat, p0.lon) for p in Ps.iterate(closed=closed): p_(p.lat, p.lon) if closed and line and p != p0: p_(p0.lat, p0.lon) # gP.Compute returns (number_of_points, perimeter, signed area) return gP.Compute(False, True)[1 if line else 2] def _remainder(x, y): '''Remainder of C{x / y}. @return: Remainder in the range M{[-y / 2, y / 2]}. ''' M = _wrapped.Math if M: try: # geographiclib 1.49 return M.remainder(x, y) except AttributeError: pass z = (fmod(x, y) if _isfinite(x) else NAN) if x else x # On Windows 32-bit with python 2.7, math.fmod(-0.0, 360) # == +0.0. This fixes this bug. See also Math::AngNormalize # in the C++ library, Math.sincosd has a similar fix. h = y / _2_0 return (z + y) if z < -h else (z if z < h else (z - y)) def _sum2(u, v): # mimick Math::sum, actually sum2 '''Error-free summation like C{Math::sum}. @return: 2-Tuple C{(sum_u_plus_v, residual)}. @note: The C{residual} can be the same as B{C{u}} or B{C{v}}. @see: U{Algorithm 3.1<http://www.ti3.TUHH.De/paper/rump/OgRuOi05.pdf>}. ''' M = _wrapped.Math if M: return M.sum(u, v) s = u + v r = s - v t = s - r # if True: # Algorithm 3.1 t = (u - r) + (v - t) # else: # in Math C/C++ # r -= u # t -= v # t = -(r + t) # u + v = s + t # = round(u + v) + t return s, t def _3sum2(s, t, x): '''Accumulate B{C{x}} into C{_sum2(s, t)}. @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/ html/Accumulator_8hpp_source.html>} comments for more details. ''' if x: t, u = _sum2(t, x) # start at least- s, t = _sum2(s, t) # significant end if s: t += u # accumulate u to t else: s = u # result is u return s, t def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}. @return: 2-Tuple C{(lon2 - lon1, lon2)} with B{C{lon2}} unrolled if B{C{wrap}} is C{True}, normalized otherwise. ''' if wrap: d, t = _diff182(lon1, lon2) lon2 = (lon1 + d) + t # _fsum2_(lon1, d, t) else: lon2 = _norm180(lon2) return (lon2 - lon1), lon2 # **) 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.