Coverage for pygeodesy/karney.py: 89%
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2# -*- coding: utf-8 -*-
4u'''I{Charles F.F. Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} C{geodesic}, wrapped.
6Wrapper around Python classes C{Geodesic} and C{GeodesicLine} and several C{Math} functions from
7I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}, provided
8that package is installed.
10The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items either
11by C{key} or by C{attribute} name.
13With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module and
14L{pygeodesy.geodesicx} will use U{GeographicLib 2.0<https://GeographicLib.SourceForge.io/C++/doc/>}
15transcoding, otherwise C{1.52} or older.
17Karney-based functionality
18==========================
201. The following classes and functions in C{pygeodesy}
22 - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4},
23 L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} --
24 U{AlbersEqualArea<https://GeographicLib.SourceForge.io/C++/doc/
25 classGeographicLib_1_1AlbersEqualArea.html>}
27 - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/
28 classGeographicLib_1_1CassiniSoldner.html>}
30 - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/
31 classGeographicLib_1_1Geocentric.html>}
33 - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/
34 classGeographicLib_1_1EllipticFunction.html>}
36 - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant
37 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}
39 - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact
40 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}
42 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/
43 html/classGeographicLib_1_1PolygonAreaT.html>}
45 - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/
46 classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/
47 classGeographicLib_1_1GeodesicLineExact.html>}
49 - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>}
51 - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/
52 classGeographicLib_1_1Georef.html>}
54 - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic
55 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}
57 - L{JacobiConformal} -- U{JacobiConformal
58 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1JacobiConformal.html#details>}
60 - L{KTransverseMercator} - U{TransverseMercator
61 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
63 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
64 classGeographicLib_1_1LocalCartesian.html>}
66 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}.
68 - L{Rhumb}, L{RhumbLine} -- U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},
69 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>},
70 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
72 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/
73 classGeographicLib_1_1PolarStereographic.html>}
75 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/
76 classGeographicLib_1_1TransverseMercator.html>}
78 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/
79 classGeographicLib_1_1UTMUPS.html>}
81 - L{pygeodesy.atand}, L{pygeodesy.atan2d}, L{pygeodesy.sincos2}, L{pygeodesy.sincos2d}, L{pygeodesy.tand} -- U{
82 Math<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
84are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}.
862. These C{pygeodesy} modules and classes
88 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumbsolve}
89 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve},
90 L{GnomonicKarney}, L{HeightIDWkarney}
92are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>}
93C{geodesic}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or
94C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}.
963. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations
98 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn},
99 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2},
100 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5}
102 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn},
103 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2},
104 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5}
106 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn},
107 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2},
108 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5}
110 - L{RhumbLine.intersection2}, L{RhumbLine.nearestOn4}
112are iterative implementations of I{Karney}'s solution posted here under U{The B{ellipsoidal} case
113<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics
114on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}).
1164. Spherical functions
118 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf}
120in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon
121<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer.
122'''
124from pygeodesy.basics import _copysign, neg, unsigned0, _xgeographiclib, \
125 _xImportError, _xversion_info, _xinstanceof, \
126 _zip, isodd # PYCHOK shared
127from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, _1_16th, \
128 _180_0, _N_180_0, _360_0
129from pygeodesy.datums import _a_ellipsoid, _WGS84
130from pygeodesy.errors import _ValueError, _xkwds, _xkwds_get
131from pygeodesy.fmath import cbrt, fremainder, norm2, hypot as _hypot, unstr # PYCHOK shared
132from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi2_, _composite_, _DOT_, \
133 _lat2_, _lon2_, _m12_, _M12_, _M21_, _number_, _s12_, \
134 _S12_, _UNDER
135from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
136from pygeodesy.named import callername, classname, _Dict, _NamedBase, \
137 _NamedTuple, _Pass
138from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple
139from pygeodesy.props import deprecated_method, Property, Property_RO, property_RO
140# from pygeodesy.streps import unstr # from .fmath
141from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \
142 Meter as _M, Meter2 as _M2, Number_, \
143 Precision_, _1mm as _TOL_M # PYCHOK shared
144from pygeodesy.utily import atan2d, fabs, sincos2d, tand, unroll180, wrap360
146# from math import fabs # from .utily
148__all__ = _ALL_LAZY.karney
149__version__ = '23.03.30'
151_EWGS84 = _WGS84.ellipsoid # PYCHOK in .geodesicx.gx, .ktm, .rhumbx, .solveBase
152_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
153_perimeter_ = 'perimeter'
156class _GTuple(_NamedTuple): # in .testNamedTuples
157 '''(INTERNAL) Helper.
158 '''
159 def toGDict(self, **updates):
160 '''Convert this C{*Tuple} to a L{GDict}.
162 @kwarg updates: Optional items to apply (C{nam=value} pairs)
163 '''
164 r = GDict(_zip(self._Names_, self)) # strict=True
165 if updates:
166 r.update(updates)
167 if self._iteration is not None:
168 r._iteration = self._iteration
169 return r
172class _Lat(Lat):
173 '''(INTERNAL) Latitude B{C{lat}}.
174 '''
175 def __init__(self, *lat, **Error_name):
176 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
177 Lat.__new__(_Lat, *lat, **kwds)
180class _Lon(Lon):
181 '''(INTERNAL) Longitude B{C{lon}}.
182 '''
183 def __init__(self, *lon, **Error_name):
184 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
185 Lon.__new__(_Lon, *lon, **kwds)
188class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
189 '''3-Tuple C{(number, perimeter, area)} with the C{number}
190 of points on the polygon or polyline, the C{perimeter} in
191 C{meter} and the C{area} in C{meter} I{squared}.
192 '''
193 _Names_ = (_number_, _perimeter_, _area_)
194 _Units_ = ( Number_, _M, _M2)
197class Caps(object): # PYCHOK
198 '''(INTERNAL) Overriden by C{Caps} below.
199 '''
200 EMPTY = 0 # formerly aka NONE
201 LATITUDE = 1 << 7 # compute latitude C{lat2}
202 LONGITUDE = 1 << 8 # compute longitude C{lon2}
203 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
204 DISTANCE = 1 << 10 # compute distance C{s12}
205 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct
206 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12}
207 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21}
208 AREA = 1 << 14 # compute area C{S12}
210 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE
211 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
213 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb
214 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position
215 REVERSE2 = 1 << 17 # reverse C{azi2}
217 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
218 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
220 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
221 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
223 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only
224 _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
226 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
227 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
228 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
229 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
230 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
231 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs
232 _OUT_ALL = ALL
233 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
235 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
236 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
237 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK
238 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL
239 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
240# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
242Caps = Caps() # PYCHOK singleton
243'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
244rhumb capabilities (C{caps}) and expected results (C{outmask}).
246C{AREA} - compute area C{S12},
248C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
250C{DISTANCE} - compute distance C{s12},
252C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
254C{EMPTY} - nothing, formerly aka C{NONE},
256C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
258C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
260C{LATITUDE} - compute latitude C{lat2},
262C{LONGITUDE} - compute longitude C{lon2},
264C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
266C{REDUCEDLENGTH} - compute reduced length C{m12},
268C{REVERSE2} - reverse C{azi2},
270and C{ALL} - all of the above.
272C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
275class _CapsBase(_NamedBase): # in .geodesicx.gxbases, .rhumbx
276 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
277 '''
278 ALL = Caps.ALL
279 AREA = Caps.AREA
280 AZIMUTH = Caps.AZIMUTH
281 DISTANCE = Caps.DISTANCE
282 DISTANCE_IN = Caps.DISTANCE_IN
283 EMPTY = Caps.EMPTY # aka NONE
284 GEODESICSCALE = Caps.GEODESICSCALE
285 LATITUDE = Caps.LATITUDE
286 LINE_OFF = Caps.LINE_OFF
287 LONGITUDE = Caps.LONGITUDE
288 LONG_UNROLL = Caps.LONG_UNROLL
289 REDUCEDLENGTH = Caps.REDUCEDLENGTH
290 STANDARD = Caps.STANDARD
292 _caps = 0 # None
293 _debug = 0 # or Caps._DEBUG_...
295 @Property_RO
296 def caps(self):
297 '''Get the capabilities (bit-or'ed C{Caps}).
298 '''
299 return self._caps
301 def caps_(self, caps):
302 '''Check the available capabilities.
304 @arg caps: Bit-or'ed combination of L{Caps} values
305 for all capabilities to be checked.
307 @return: C{True} if I{all} B{C{caps}} are available,
308 C{False} otherwise (C{bool}).
309 '''
310 caps &= Caps._OUT_ALL
311 return (self.caps & caps) == caps
313 @property
314 def debug(self):
315 '''Get the C{debug} option (C{bool}).
316 '''
317 return bool(self._debug)
319 @debug.setter # PYCHOK setter!
320 def debug(self, debug):
321 '''Set the C{debug} option (C{bool}) to include
322 more details in L{GDict} results.
323 '''
324 self._debug = Caps._DEBUG_ALL if debug else 0
326 def _iter2tion(self, r, s):
327 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
328 '''
329 i = _xkwds_get(s, iter=None)
330 if i is not None:
331 self._iteration = r._iteration = i
332 return r
335class Direct9Tuple(_GTuple):
336 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
337 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
338 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
339 C{meter} I{squared}.
340 '''
341 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
342 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
345class GDict(_Dict): # XXX _NamedDict
346 '''Basic C{dict} with both key I{and} attribute access
347 to the C{dict} items.
349 Results of all C{geodesic} methods are returned as a
350 L{GDict} instance.
351 '''
352 _iteration = None # Iteration number (C{int}) or C{None}
354 @property_RO
355 def iteration(self): # see .named._NamedBase
356 '''Get the iteration number (C{int}) or
357 C{None} if not available/applicable.
358 '''
359 return self._iteration
361 def toDirect9Tuple(self, dflt=NAN):
362 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s
363 method C{geographiclib.geodesic.Geodesic._GenDirect}.
365 @kwarg dflt: Default value for missing items (C{any}).
367 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
368 s12, m12, M12, M21, S12)}
369 '''
370 return self._toTuple(Direct9Tuple, dflt)
372 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
373 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
374 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
375 result.
377 @kwarg dflt: Default value for missing items (C{any}).
379 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
380 s12, a12, m12, M12, M21, S12)}.
381 '''
382 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
384 def toInverse10Tuple(self, dflt=NAN):
385 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
386 method C{geographiclib.geodesic.Geodesic._GenInverse}.
388 @kwarg dflt: Default value for missing items (C{any}).
390 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
391 salp2, calp2, m12, M12, M21, S12)}.
392 '''
393 return self._toTuple(Inverse10Tuple, dflt)
395 @deprecated_method
396 def toRhumb7Tuple(self, dflt=NAN):
397 '''DEPRECATED, used method C{toRhumb8Tuple}.
399 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
400 '''
401 return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt)
403 def toRhumb8Tuple(self, dflt=NAN):
404 '''Convert this L{GDict} result to a 8-tuple.
406 @kwarg dflt: Default value for missing items (C{any}).
408 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
409 azi12, s12, S12, a12)}.
410 '''
411 return self._toTuple(_MODS.rhumbx.Rhumb8Tuple, dflt)
413 def toRhumbSolve7Tuple(self, dflt=NAN):
414 '''Convert this L{GDict} result to a 8-tuple.
416 @kwarg dflt: Default value for missing items (C{any}).
418 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
419 azi12, s12, S12)}.
420 '''
421 return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt)
423 def _toTuple(self, nTuple, dflt):
424 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
425 '''
426 _g = getattr
427 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
428 return nTuple(t, iteration=self._iteration)
431class GeodesicError(_ValueError):
432 '''Error raised for L{pygeodesy.geodesicx} lack of convergence
433 or other L{pygeodesy.geodesicx} or L{pygeodesy.karney} issues.
434 '''
435 pass
438class Inverse10Tuple(_GTuple):
439 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
440 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
441 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
442 C{calp2} of the initial C{1} and final C{2} foward azimuths.
443 '''
444 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
445 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
447 def toGDict(self, **updates):
448 '''Convert this C{Inverse10Tuple} to a L{GDict}.
450 @kwarg updates: Optional items to apply (C{nam=value} pairs)
451 '''
452 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple
453 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
454 **updates) # PYCHOK indent
457class _Wrapped(object):
458 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
459 <https://PyPI.org/project/geographiclib>} classes.
460 '''
462 @Property_RO # MCCABE 24
463 def Geodesic(self):
464 '''Get the I{wrapped} C{Geodesic} class, provided the U{geographiclib
465 <https://PyPI.org/project/geographiclib>} package is installed,
466 otherwise an C{ImportError}.
467 '''
468 _Geodesic = self.geographiclib.Geodesic
469 _DIRECT3 = _Geodesic.AZIMUTH | _Geodesic.LATITUDE | _Geodesic.LONGITUDE
470 _INVERSE3 = _Geodesic.AZIMUTH | _Geodesic.DISTANCE
472 class Geodesic(_Geodesic):
473 '''I{Karney}'s U{Geodesic<https://GeographicLib.SourceForge.io/C++/doc/
474 python/code.html#geographiclib.geodesic.Geodesic>} wrapper.
475 '''
476 _debug = 0 # like .geodesicx.bases._GeodesicBase
477 _E = _EWGS84
478 LINE_OFF = 0 # in .azimuthal._GnomonicBase and .css.CassiniSoldner
480 def __init__(self, a_ellipsoid=_EWGS84, f=None, name=NN): # PYCHOK signature
481 '''New C{Geodesic} instance.
483 @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum
484 (L{Datum}) or the equatorial radius
485 of the ellipsoid (C{meter}).
486 @arg f: The flattening of the ellipsoid (C{scalar}) if
487 B{C{a_ellipsoid}) is specified as C{meter}.
488 @kwarg name: Optional name (C{str}).
489 '''
490 if a_ellipsoid not in (Geodesic._E, None): # spherical OK
491 self._E = _a_ellipsoid(a_ellipsoid, f, name=name) # raiser=NN
492 try:
493 _Geodesic.__init__(self, *self.ellipsoid.a_f)
494 except (TypeError, ValueError) as x:
495 _raiseX(self, x, *self.ellipsoid.a_f)
497 Area = _Geodesic.Polygon # like GeodesicExact.Area
499 @Property
500 def debug(self):
501 '''Get the C{debug} option (C{bool}).
502 '''
503 return bool(self._debug)
505 @debug.setter # PYCHOK setter!
506 def debug(self, debug):
507 '''Set the C{debug} option (C{bool}) to include
508 more details in L{GDict} results.
509 '''
510 self._debug = _MODS.geodesicx.Caps._DEBUG_ALL if debug else 0
512 def Direct(self, lat1, lon1, azi1, s12, *outmask):
513 '''Return the C{Direct} result.
514 '''
515 try:
516 d = _Geodesic.Direct(self, lat1, lon1, azi1, s12, *outmask)
517 except (TypeError, ValueError) as x:
518 _raiseX(self, x, lat1, lon1, azi1, s12, *outmask)
519 return GDict(d)
521 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask
522 '''Return the destination lat, lon and reverse azimuth
523 (final bearing) in C{degrees}.
525 @return: L{Destination3Tuple}C{(lat, lon, final)}.
526 '''
527 d = self.Direct(lat1, lon1, azi1, s12, _DIRECT3)
528 return Destination3Tuple(d.lat2, d.lon2, d.azi2)
530 @Property_RO
531 def ellipsoid(self):
532 '''Get this geodesic's ellipsoid (C{Ellipsoid[2]}).
533 '''
534 return self._E
536 @Property_RO
537 def f1(self): # in .css.CassiniSoldner.reset
538 '''Get the geodesic's ellipsoid I{1 - flattening} (C{float}).
539 '''
540 return getattr(self, _UNDER(Geodesic.f1.name), self.ellipsoid.f1)
542 def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12,
543 outmask=_Geodesic.STANDARD):
544 '''(INTERNAL) Get C{._GenDirect} result as C{GDict}.
545 '''
546 try:
547 t = _Geodesic._GenDirect(self, lat, lon, azi, arcmode, s12_a12, outmask)
548 except (TypeError, ValueError) as x:
549 _raiseX(self, x, lat, lon, azi, arcmode, s12_a12, outmask)
550 return Direct9Tuple(t).toGDict() # *t
552 def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=_Geodesic.STANDARD):
553 '''(INTERNAL) Get C{._GenInverse} result as C{GDict}.
554 '''
555 try:
556 t = _Geodesic._GenInverse(self, lat1, lon1, lat2, lon2, outmask)
557 except (TypeError, ValueError) as x:
558 _raiseX(self, x, lat1, lon1, lat2, lon2, outmask)
559 return Inverse10Tuple(t).toGDict(lon1=lon1, lon2=lon2) # *t
561 def Inverse(self, lat1, lon1, lat2, lon2, *outmask):
562 '''Return the C{Inverse} result.
563 '''
564 try:
565 d = _Geodesic.Inverse(self, lat1, lon1, lat2, lon2, *outmask)
566 except (TypeError, ValueError) as x:
567 _raiseX(self, x, lat1, lon1, lat2, lon2, *outmask)
568 return GDict(d)
570 def Inverse1(self, lat1, lon1, lat2, lon2, wrap=False):
571 '''Return the non-negative, I{angular} distance in C{degrees}.
572 '''
573 # see .FrechetKarney.distance, .HausdorffKarney._distance
574 # and .HeightIDWkarney._distances
575 _, lon2 = unroll180(lon1, lon2, wrap=wrap) # self.LONG_UNROLL
576 r = self.Inverse(lat1, lon1, lat2, lon2)
577 # XXX self.DISTANCE needed for 'a12'?
578 return fabs(r.a12)
580 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
581 '''Return the distance in C{meter} and the forward and
582 reverse azimuths (initial and final bearing) in C{degrees}.
584 @return: L{Distance3Tuple}C{(distance, initial, final)}.
585 '''
586 r = self.Inverse(lat1, lon1, lat2, lon2, _INVERSE3)
587 return Distance3Tuple(r.s12, wrap360(r.azi1), wrap360(r.azi2))
589 def Line(self, lat1, lon1, azi1, *caps):
590 '''Set up a L{GeodesicLine} to compute several points on a
591 single geodesic.
592 '''
593 return _wrapped.GeodesicLine(self, lat1, lon1, azi1, *caps)
595 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__
596 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__
597 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__
598 return Geodesic
600 @Property_RO # MCCABE 16
601 def GeodesicLine(self):
602 '''Get the I{wrapped} C{GeodesicLine} class, provided the U{geographiclib
603 <https://PyPI.org/project/geographiclib>} package is installed,
604 otherwise an C{ImportError}.
605 '''
606 _GeodesicLine = self.geographiclib.GeodesicLine
608 class GeodesicLine(_GeodesicLine):
609 '''I{Karney}'s U{GeodesicLine <https://GeographicLib.SourceForge.io/C++/doc/
610 python/code.html#geographiclib.geodesicline.GeodesicLine>} wrapper.
611 '''
612 def __init__(self, lat1, lon1, azi1, *caps):
613 try:
614 _GeodesicLine.__init__(self, lat1, lon1, azi1, *caps)
615 except (TypeError, ValueError) as x:
616 _raiseX(self, x, lat1, lon1, azi1, *caps)
618 @Property_RO
619 def a1(self):
620 '''Get the I{equatorial arc} (C{degrees}), the arc length between
621 the northward equatorial crossing and point C{(lat1, lon1)}.
623 @see: U{EquatorialArc<https://GeographicLib.SourceForge.io/
624 C++/doc/classGeographicLib_1_1GeodesicLine.html>}
625 '''
626 try:
627 return _atan2d(self._ssig1, self._csig1)
628 except AttributeError:
629 return NAN # see .geodesicx.gxline._GeodesicLineExact
631 equatorarc = a1
633 def ArcPosition(self, a12, *outmask):
634 try:
635 d = _GeodesicLine.ArcPosition(self, a12, *outmask)
636 except (TypeError, ValueError) as x:
637 _raiseX(self, x, a12, *outmask)
638 return GDict(d)
640 @Property_RO
641 def azi0(self): # see .css.CassiniSoldner.forward4
642 '''Get the I{equatorial azimuth} (C{degrees}), the azimuth of the
643 geodesic line as it crosses the equator in a northward direction.
645 @see: U{EquatorialAzimuth<https://GeographicLib.SourceForge.io/
646 C++/doc/classGeographicLib_1_1GeodesicLine.html>}
647 '''
648 try:
649 return _atan2d(self._salp0, self._calp0)
650 except AttributeError:
651 return NAN # see .geodesicx.gxline._GeodesicLineExact
653 equatorazimuth = azi0
655 def Position(self, s12, *outmask):
656 try:
657 d = _GeodesicLine.Position(self, s12, *outmask)
658 except (TypeError, ValueError) as x:
659 _raiseX(self, x, s12, *outmask)
660 return GDict(d)
662 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__
663 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__
664 return GeodesicLine
666 @Property_RO
667 def Geodesic_WGS84(self):
668 '''Get the I{wrapped} C{Geodesic.WGS84} I{instance} provided the
669 U{geographiclib<https://PyPI.org/project/geographiclib>} package
670 is installed, otherwise an C{ImportError}.
671 '''
672 return _EWGS84.geodesic
674 @Property_RO
675 def geographiclib(self):
676 '''Get the imported C{geographiclib}, provided the U{geographiclib
677 <https://PyPI.org/project/geographiclib>} package is installed,
678 otherwise an C{ImportError}.
679 '''
680 g = _xgeographiclib(self.__class__, 1, 49)
681 from geographiclib.geodesic import Geodesic
682 g.Geodesic = Geodesic
683 from geographiclib.geodesicline import GeodesicLine
684 g.GeodesicLine = GeodesicLine
685 from geographiclib.geomath import Math
686 g.Math = Math
687 return g
689 @Property_RO # MCCABE 13
690 def Math(self):
691 '''Get the C{Math} class, provided the U{geographiclib
692 <https://PyPI.org/project/geographiclib>} package is
693 installed, otherwise C{None}.
694 '''
695 try:
696 g = self.geographiclib
697 M = g.Math
698 if _xversion_info(g) < (2,):
699 if _K_2_0:
700 M = None
701# elif not _K_2_0: # XXX set 2.0?
702# _K_2_0 = True
703 except (AttributeError, ImportError):
704 M = None
705 return M
707_wrapped = _Wrapped() # PYCHOK singleton, .datum, .test/base.py
710def _around(x): # in .utily.sincos2d
711 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
713 @return: Coarsened value (C{float}).
715 @see: I{Karney}'s U{Math.AngRound<https://SourceForge.net/p/
716 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
717 '''
718 try:
719 return _wrapped.Math.AngRound(x)
720 except AttributeError:
721 pass
722 if x:
723 y = _1_16th - fabs(x)
724 if y > 0: # fabs(x) < _1_16th
725 x = _copysign(_1_16th - y, x)
726 else:
727 x = _0_0 # -0 to 0
728 return x
731def _atan2d(y, x):
732 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
733 '''
734 try:
735 return _wrapped.Math.atan2d(y, x)
736 except AttributeError:
737 return atan2d(y, x)
740def _cbrt(x):
741 '''Return C{cubic root(B{x})}.
742 '''
743 try:
744 return _wrapped.Math.cbrt(x)
745 except AttributeError:
746 return cbrt(x)
749def _copyBit(x, y):
750 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
751 '''
752 return (-x) if _signBit(y) else x
755def _diff182(deg0, deg):
756 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
758 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
759 '''
760 try:
761 return _wrapped.Math.AngDiff(deg0, deg)
762 except AttributeError:
763 pass
764 if _K_2_0: # geographiclib 2.0
765 d, t = _sum2(fremainder(-deg0, _360_0),
766 fremainder( deg, _360_0))
767 d, t = _sum2(fremainder( d, _360_0), t)
768 if d in (_0_0, _180_0, _N_180_0):
769 d = _copysign(d, -t if t else (deg - deg0))
770 else:
771 d, t = _sum2(_norm180(-deg0), _norm180(deg))
772 d = _norm180(d)
773 if t > 0 and d == _180_0:
774 d = _N_180_0
775 d, t = _sum2(d, t)
776 return d, t
779# def _Equidistant(equidistant, exact=False, geodsolve=False):
780# # (INTERNAL) Get the C{EquidistantExact}, C{-GeodSolve} or
781# # C{-Karney} class if B{C{equidistant}} in not callable.
782# if equidistant is None or not callable(equidistant):
783# if exact:
784# equidistant = _MODS.azimuthal.EquidistantExact
785# elif geodsolve:
786# equidistant = _MODS.azimuthal.EquidistantGeodSolve
787# else:
788# equidistant = _MODS.azimuthal.EquidistantKarney
789# return equidistant
792def _fix90(deg): # mimick Math.LatFix
793 '''Replace angle in C{degrees} outside [-90,90] by NAN.
795 @return: Angle C{degrees} or NAN.
796 '''
797 try:
798 return _wrapped.Math.LatFix(deg)
799 except AttributeError:
800 return NAN if fabs(deg) > 90 else deg
803def _isfinite(x): # mimick Math.AngNormalize
804 '''Check finiteness of C{x}.
806 @return: C{True} if finite.
807 '''
808 try:
809 return _wrapped.Math.isfinite(x)
810 except AttributeError:
811 return _math_isfinite(x) # and fabs(x) <= _MAX
814def _norm2(x, y): # mimick Math.norm
815 '''Normalize C{B{x}} and C{B{y}}.
817 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
818 '''
819 try:
820 return _wrapped.Math.norm(x, y)
821 except AttributeError:
822 return norm2(x, y)
825def _norm180(deg): # mimick Math.AngNormalize
826 '''Reduce angle in C{degrees} to (-180,180].
828 @return: Reduced angle C{degrees}.
829 '''
830 try:
831 return _wrapped.Math.AngNormalize(deg)
832 except AttributeError:
833 pass
834 d = fremainder(deg, _360_0)
835 if d in (_180_0, -_180_0):
836 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
837 return d
840def _polygon(geodesic, points, closed, line, wrap):
841 '''(INTERNAL) Compute the area or perimeter of a polygon,
842 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
843 C{geographiclib} package is installed) a C{Geodesic}
844 or C{_wrapped.Geodesic} instance.
845 '''
846 if not wrap: # capability LONG_UNROLL can't be off
847 raise _ValueError(wrap=wrap)
849 if _MODS.booleans.isBoolean(points):
850 # recursive call for each boolean clip
852 def _a_p(clip, *args, **unused):
853 return _polygon(geodesic, clip, *args)
855 if not closed: # closed only
856 raise _ValueError(closed=closed, points=_composite_)
858 return points._sum1(_a_p, closed, line, wrap)
860 gP = geodesic.Polygon(line)
861 _A = gP.AddPoint
863 Ps = _MODS.iters.PointsIter(points, loop=1) # base=LatLonEllipsoidalBase(0, 0)
864 p0 = Ps[0]
866 # note, lon deltas are unrolled, by default
867 _A(p0.lat, p0.lon)
868 for p in Ps.iterate(closed=closed):
869 _A(p.lat, p.lon)
870 if closed and line and p != p0:
871 _A(p0.lat, p0.lon)
873 # gP.Compute returns (number_of_points, perimeter, signed area)
874 return gP.Compute(False, True)[1 if line else 2]
877def _polynomial(x, cs, i, j): # PYCHOK shared
878 '''(INTERNAL) Like C{GeographicLib.Math.hpp.polyval} but with a
879 different signature and cascaded summation as C{karney._sum2_}.
881 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
882 '''
883 s, t = cs[i], _0_0
884 _s2_ = _sum2_
885 for c in cs[i+1:j]:
886 s, t = _s2_(s * x, t * x, c)
887 return s # + t
890def _raiseX(inst, x, *args): # PYCHOK no cover
891 '''(INTERNAL) Throw a C{GeodesicError} for C{geographiclib} issue B{C{x}} .
892 '''
893 n = _DOT_(classname(inst), callername(up=2, underOK=True))
894 raise GeodesicError(unstr(n, *args), cause=x)
897def _remainder(x, y):
898 '''Remainder of C{x / y}.
900 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
901 '''
902 try:
903 return _wrapped.Math.remainder(x, y)
904 except AttributeError:
905 return fremainder(x, y)
908if _K_2_0:
909 from pygeodesy.basics import signBit as _signBit
910 from math import cos as _cos, sin as _sin
912 def _sincos2(rad):
913 return _sin(rad), _cos(rad)
915else:
916 from pygeodesy.utily import sincos2 as _sincos2 # PYCHOK shared
918 def _signBit(x):
919 '''(INTERNAL) GeographicLin 1.52-.
920 '''
921 return x < 0
924def _sincos2d(deg):
925 '''Return sine and cosine of an angle in C{degrees}.
927 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
928 '''
929 try:
930 return _wrapped.Math.sincosd(deg)
931 except AttributeError:
932 return sincos2d(deg)
935def _sincos2de(deg, t):
936 '''Return sine and cosine of a corrected angle in C{degrees}.
938 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
939 '''
940 try:
941 return _wrapped.Math.sincosde(deg, t)
942 except AttributeError:
943 return sincos2d(deg, adeg=t)
946def _sum2(u, v): # mimick Math::sum, actually sum2
947 '''Error-free summation like C{Math::sum}.
949 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
951 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
953 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
954 '''
955 try:
956 return _wrapped.Math.sum(u, v)
957 except AttributeError:
958 pass
959 s = u + v
960 r = s - v
961 t = s - r
962 # if Algorithm_3_1:
963 # t = (u - t) + (v + r)
964 # elif C_CPP: # Math::sum C/C++
965 # r -= u
966 # t -= v
967 # t += r
968 # t = -t
969 # else:
970 t = (u - r) + (v - t)
971 return s, t
974def _sum2_(s, t, *vs):
975 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
977 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
979 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
980 html/Accumulator_8hpp_source.html>} comments for more details and
981 function C{_sum2} above.
983 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
984 '''
985 _s2, _u0 = _sum2, unsigned0
986 for v in vs:
987 if v:
988 t, u = _s2(t, v) # start at the least-
989 if s:
990 s, t = _s2(s, t) # significant end
991 if s:
992 t += u # accumulate u into t
993# elif t: # s == 0 implies t == 0
994# raise _AssertionError(t=t, txt=_not_(_0_))
995 else:
996 s = _u0(u) # result is u, t = 0
997 else:
998 s, t = _u0(t), u
999 return s, t
1002def _tand(x):
1003 '''Return C{tan(B{x})} in C{degrees}.
1004 '''
1005 try:
1006 return _wrapped.Math.tand(x)
1007 except AttributeError:
1008 return tand(x)
1011def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
1012 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
1014 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
1015 unrolled if B{C{wrap}} is C{True}, normalized otherwise.
1016 '''
1017 if wrap:
1018 d, t = _diff182(lon1, lon2)
1019 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
1020 else:
1021 lon2 = _norm180(lon2)
1022 return (lon2 - lon1), lon2
1025def _unsigned2(x):
1026 '''(INTERNAL) Unsign B{C{x}}.
1027 '''
1028 return (neg(x), True) if _signBit(x) else (x, False)
1031__all__ += _ALL_DOCS(_CapsBase)
1033# **) MIT License
1034#
1035# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1036#
1037# Permission is hereby granted, free of charge, to any person obtaining a
1038# copy of this software and associated documentation files (the "Software"),
1039# to deal in the Software without restriction, including without limitation
1040# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1041# and/or sell copies of the Software, and to permit persons to whom the
1042# Software is furnished to do so, subject to the following conditions:
1043#
1044# The above copyright notice and this permission notice shall be included
1045# in all copies or substantial portions of the Software.
1046#
1047# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1048# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1049# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1050# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1051# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1052# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1053# OTHER DEALINGS IN THE SOFTWARE.