Coverage for pygeodesy/karney.py: 92%
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2# -*- coding: utf-8 -*-
4u'''Wrapper around several C{geomath.Math} functions from I{Karney}'s Python package U{geographiclib
5<https://PyPI.org/project/geographiclib>}, provided that package is installed.
7Methods of the I{wrapped} L{Geodesic<geodesicw.Geodesic>} and L{GeodesicLine<geodesicw.GeodesicLine>}
8classes return a L{GDict} instance offering access to the C{dict} items either by C{key} or by
9C{attribute} name.
11With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, modules L{geodesicw},
12L{geodesicx} and this module will use U{GeographicLib 2.0+<https://GeographicLib.SourceForge.io/C++/doc/>}
13and newer transcoding, otherwise C{1.52} or older. Set C{PYGEODESY_GEOGRAPHICLIB=2.4} to default to the
14C{Jacobi amplitude} instead of C{Bulirsch}' function in methods L{ExactTransverseMercator.forward
15<pygeodesy.ExactTransverseMercator.forward>} and L{reverse <pygeodesy.ExactTransverseMercator.reverse>}.
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/classGeographicLib_1_1AlbersEqualArea.html>}
26 - L{AuxAngle}, L{AuxDST}, L{AuxDLat}, L{AuxLat} -- U{AuxAngle
27 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>},
28 U{DST<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DST.html>},
29 U{DAuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>},
30 U{AuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxLatitude.html>} in I{GeographicLib 2.2+}
32 - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/
33 classGeographicLib_1_1CassiniSoldner.html>}
35 - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}
37 - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/
38 classGeographicLib_1_1EllipticFunction.html>}
40 - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant
41 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}
43 - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact
44 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}
46 - L{Geodesic}, L{GeodesicLine} -- I{wrapped} U{geodesic.Geodesic<https://PyPI.org/project/geographiclib>},
47 I{wrapped} U{geodesicline.GeodesicLine<https://PyPI.org/project/geographiclib>}
49 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/C++/doc/
50 classGeographicLib_1_1PolygonAreaT.html>}
52 - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/
53 classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/
54 classGeographicLib_1_1GeodesicLineExact.html>}
56 - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>}
58 - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Georef.html>}
60 - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic
61 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}
63 - L{Intersector} -- U{Intersect
64 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} from I{GeographicLib 2.3+}
66 - L{JacobiConformal} -- U{JacobiConformal
67 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1experimental_1_1JacobiConformal.html>}
69 - L{KTransverseMercator} - U{TransverseMercator
70 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
72 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
73 classGeographicLib_1_1LocalCartesian.html>}
75 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}
77 - L{rhumb.aux_}, L{RhumbAux}, L{RhumbLineAux} -- U{Rhumb
78 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine
79 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} from I{GeographicLib 2.2+}
81 - L{rhumb.ekx}, L{Rhumb}, L{RhumbLine} -- U{Rhumb
82 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},
83 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>},
84 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
85 from I{GeographicLib 2.0}
87 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>}
89 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
91 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>}
93 - L{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{tand} -- U{geomath.Math
94 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
96are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}.
982. These C{pygeodesy} modules and classes
100 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodesici}, L{geodsolve}, L{karney}, L{rhumb.solve}
101 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve},
102 L{GnomonicKarney}, L{HeightIDWkarney}, L{Intersectool}
104are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} or
105C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>},
106U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} or
107U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}.
1093. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations
111 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn},
112 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2},
113 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5}
115 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn},
116 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2},
117 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5}
119 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn},
120 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2},
121 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5}
123 - L{RhumbLineAux.Intersection} and L{RhumbLine.Intersection}
125are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case
126<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics
127on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}).
1294. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points
131 - L{RhumbLineAux.Intersecant2}, L{RhumbLineAux.PlumbTo}, L{RhumbLine.Intersecant2} and L{RhumbLine.PlumbTo}
133are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept
134<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
1365. Spherical functions
138 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf}
140in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon
141<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer.
142'''
143# make sure int/int division yields float quotient, see .basics
144from __future__ import division as _; del _ # noqa: E702 ;
146from pygeodesy.basics import _copysign, _isin, isint, neg, unsigned0, \
147 _xgeographiclib, _zip
148from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \
149 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0
150from pygeodesy.errors import GeodesicError, _ValueError, _xkwds
151from pygeodesy.fmath import cbrt, fremainder, norm2 # Fhorner, Fsum
152from pygeodesy.internals import _getenv, _popen2, _PYGEODESY_ENV, typename, \
153 _version_info
154from pygeodesy.interns import NN, _a12_, _area_, _azi1_, _azi2_, _azi12_, \
155 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \
156 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \
157 _SPACE_, _UNDER_, _X_, _1_, _2_, _BAR_ # PYCHOK used!
158from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _FOR_DOCS
159from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass
160from pygeodesy.props import deprecated_method, Property_RO, property_RO, \
161 property_ROnce
162from pygeodesy.units import Azimuth as _Azi, Degrees as _Deg, Lat, Lon, \
163 Meter as _M, Meter2 as _M2, Number_
164from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
166# from math import fabs # from .utily
168__all__ = _ALL_LAZY.karney
169__version__ = '25.05.28'
171_2_4_ = '2.4'
172_K_2_0 = _getenv(_PYGEODESY_ENV(typename(_xgeographiclib)[2:]), _2_)
173_K_2_4 = _K_2_0 == _2_4_
174_K_2_0 = _K_2_4 or (_K_2_0 == _2_)
175_perimeter_ = 'perimeter'
178class _GTuple(_NamedTuple): # in .testNamedTuples
179 '''(INTERNAL) Helper.
180 '''
181 def toGDict(self, **updates): # NO name=NN
182 '''Convert this C{*Tuple} to a L{GDict}.
184 @kwarg updates: Optional items to apply (C{name=value} pairs)
185 '''
186 r = GDict(_zip(self._Names_, self)) # strict=True
187 if updates:
188 r.update(updates)
189 if self._iteration is not None:
190 r._iteration = self._iteration
191 return r
194class _Lat(Lat):
195 '''(INTERNAL) Latitude B{C{lat}}.
196 '''
197 def __init__(self, *lat, **Error_name):
198 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
199 Lat.__new__(_Lat, *lat, **kwds)
202class _Lon(Lon):
203 '''(INTERNAL) Longitude B{C{lon}}.
204 '''
205 def __init__(self, *lon, **Error_name):
206 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
207 Lon.__new__(_Lon, *lon, **kwds)
210class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
211 '''3-Tuple C{(number, perimeter, area)} with the C{number}
212 of points of the polygon or polyline, the C{perimeter} in
213 C{meter} and the C{area} in C{meter} I{squared}.
214 '''
215 _Names_ = (_number_, _perimeter_, _area_)
216 _Units_ = ( Number_, _M, _M2)
219class Caps(object):
220 '''I{Enum}-style masks to be bit-C{or}'ed to specify C{geodesic}, C{rhumb}
221 or C{-lines} capabilities (C{caps}) and method results (C{outmask}).
223 C{AREA} - compute the area C{S12},
225 C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
227 C{DISTANCE} - compute distance C{s12} and angular distance C{a12},
229 C{DISTANCE_IN} - allow distance C{s12} in method C{.Direct},
231 C{EMPTY} - nothing, formerly aka C{NONE},
233 C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
235 C{LATITUDE} - compute latitude C{lat2},
237 C{LINE_OFF} - Line without updates from parent C{geodesic} or C{rhumb}.
239 C{LONGITUDE} - compute longitude C{lon2},
241 C{LONG_UNROLL} - unroll C{lon2} in method C{.Direct},
243 C{NONFINITONAN} - set all C{GDict} items to C{NAN} iff any argument is C{non-finite}.
245 C{REDUCEDLENGTH} - compute the reduced length C{m12},
247 C{REVERSE2} - reverse azimuth C{azi2} by 180 degrees,
249 and C{ALL} - all of the above.
251 C{STANDARD} = C{AZIMUTH | DISTANCE | LATITUDE | LONGITUDE}
253 C{LINE_CAPS} = C{STANDARD | DISTANCE_IN | REDUCEDLENGTH | GEODESICSCALE}
254 '''
255 EMPTY = 0 # formerly aka NONE
256 _CAP_1 = 1 << 0 # for goedesici/-w
257 _CAP_1p = 1 << 1 # for goedesici/-w
258 _CAP_2 = 1 << 2
259 _CAP_3 = 1 << 3 # for goedesici/-w
260 _CAP_4 = 1 << 4 # for goedesicw
261# = 1 << 5 # unused
262# = 1 << 6 # unused
263 _CAP_ALL = 0x1F
264# _CAP_MASK = _CAP_ALL
265 LATITUDE = 1 << 7 # compute latitude C{lat2}
266 LONGITUDE = 1 << 8 | _CAP_3 # compute longitude C{lon2}
267 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
268 DISTANCE = 1 << 10 | _CAP_1 # compute distance C{s12}
269 DISTANCE_IN = 1 << 11 | _CAP_1 | _CAP_1p # allow distance C{s12} in Direct
270 REDUCEDLENGTH = 1 << 12 | _CAP_1 | _CAP_2 # compute reduced length C{m12}
271 GEODESICSCALE = 1 << 13 | _CAP_1 | _CAP_2 # compute geodesic scales C{M12} and C{M21}
272 AREA = 1 << 14 | _CAP_4 # compute area C{S12}
274 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE
275 STANDARD_LINE = STANDARD | DISTANCE_IN # for goedesici/-w
277 LINE_CAPS = STANDARD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only
278 LONG_UNROLL = 1 << 15 # unroll C{lon2} in .Direct and .Position
279 NONFINITONAN = 1 << 16 # see method GDict._toNAN
280 LINE_OFF = 1 << 17 # Line without updates from parent geodesic or rhumb
281 REVERSE2 = 1 << 18 # reverse C{azi2}
282 ALL = 0x7F80 | _CAP_ALL # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
284 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
285 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
287 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
288 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
290 _SALP_CALPs_ = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
292 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
293 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
294 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
295 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
296 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
297 _DEBUG_LINE | _SALP_CALPs_
299 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE # for goedesicw only
300 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only
302 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py
303 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
305 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
306 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL
307 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
308# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline
309 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
310# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
312 def items(self):
313 '''Yield all I{public} C{Caps} as 2-tuple C{(NAME, mask)}.
314 '''
315 for n, C in type(self).__dict__.items():
316 if isint(C) and not n.startswith(_UNDER_) \
317 and n.replace(_UNDER_, NN).isupper():
318 yield n, C
320 def toStr(self, Cask, sep=_BAR_):
321 '''Return C{Caps} or an C{outmask} as C{str} or tuple of C{str}s.
322 '''
323 s = (n for n, C in sorted(Caps.items())
324 if C and (Cask & C) == C) # and int1s(C) <= 3
325 return sep.join(s) if sep else tuple(s)
327if _FOR_DOCS: # PYCHOK force ...
328 pass # ... CAPS.__doc__ into epydoc
329else:
330 Caps = Caps() # PYCHOK singleton
332_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._toNAN, -._unCaps
333 azi1=Caps.AZIMUTH,
334 azi2=Caps.AZIMUTH,
335 lat1=Caps.LATITUDE,
336 lat2=Caps.LATITUDE,
337 lon1=Caps.LONGITUDE,
338 lon2=Caps.LONGITUDE,
339 m12 =Caps.REDUCEDLENGTH,
340 M12 =Caps.GEODESICSCALE,
341 M21 =Caps.GEODESICSCALE,
342 s12 =Caps.DISTANCE,
343 S12 =Caps.AREA)
346class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
347 '''(INTERNAL) Base class for C{Geodesic*}, C{Geodesic*Exact}, C{Intersectool} and C{Rhumb*Base}.
348 '''
349 ALL = Caps.ALL
350 AREA = Caps.AREA
351 AZIMUTH = Caps.AZIMUTH
352 DISTANCE = Caps.DISTANCE
353 DISTANCE_IN = Caps.DISTANCE_IN
354 EMPTY = Caps.EMPTY # aka NONE
355 GEODESICSCALE = Caps.GEODESICSCALE
356 LATITUDE = Caps.LATITUDE
357 LINE_CAPS = Caps.LINE_CAPS
358 LINE_OFF = Caps.LINE_OFF
359 LONGITUDE = Caps.LONGITUDE
360 LONG_UNROLL = Caps.LONG_UNROLL
361 NONFINITONAN = Caps.NONFINITONAN
362 REDUCEDLENGTH = Caps.REDUCEDLENGTH
363 STANDARD = Caps.STANDARD
364 STANDARD_LINE = Caps.STANDARD_LINE # for geodesici
366 _caps = 0 # None
367 _debug = 0 # or Caps._DEBUG_...
369 @Property_RO
370 def caps(self):
371 '''Get the capabilities (bit-or'ed C{Caps}).
372 '''
373 return self._caps
375 def caps_(self, caps):
376 '''Check the available capabilities.
378 @arg caps: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}
379 values for all capabilities to be checked.
381 @return: C{True} if I{all} B{C{caps}} are available, C{False}
382 otherwise (C{bool}).
383 '''
384 caps &= Caps._OUT_ALL
385 return (self.caps & caps) == caps
387 @property
388 def debug(self):
389 '''Get the C{debug} option (C{bool}).
390 '''
391 return bool(self._debug)
393 @debug.setter # PYCHOK setter!
394 def debug(self, debug):
395 '''Set the C{debug} option (C{bool}) to include
396 more details in L{GDict} results.
397 '''
398 self._debug = Caps._DEBUG_ALL if debug else 0
400 def _iter2tion(self, r, iter=None, **unused):
401 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
402 '''
403 if iter is not None:
404 self._iteration = r._iteration = iter
405 return r
408class Direct9Tuple(_GTuple):
409 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
410 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
411 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
412 C{meter} I{squared}.
413 '''
414 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
415 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
418class GDict(ADict): # XXX _NamedDict
419 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items.
421 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are
422 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}.
423 '''
424 def toDirect9Tuple(self, dflt=NAN):
425 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method
426 C{geographiclib.geodesic.Geodesic._GenDirect}.
428 @kwarg dflt: Default value for missing items (C{any}).
430 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
431 s12, m12, M12, M21, S12)}
432 '''
433 return self._toTuple(Direct9Tuple, dflt)
435 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
436 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
437 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
438 result.
440 @kwarg dflt: Default value for missing items (C{any}).
442 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
443 s12, a12, m12, M12, M21, S12)}.
444 '''
445 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
447 def toInverse10Tuple(self, dflt=NAN):
448 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
449 method C{geographiclib.geodesic.Geodesic._GenInverse}.
451 @kwarg dflt: Default value for missing items (C{any}).
453 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
454 salp2, calp2, m12, M12, M21, S12)}.
455 '''
456 return self._toTuple(Inverse10Tuple, dflt)
458 def _toNAN(self, outmask): # .GeodesicExact._GDistInverse, .GeodesicLineExact._GenPosition
459 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s.
460 '''
461 if (outmask & Caps.NONFINITONAN):
462 d = dict((k, NAN) for k, C in _key2Caps.items()
463 if (outmask & C) == C)
464 self.set_(**d)
465 return self
467 @deprecated_method
468 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
469 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}.
471 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
472 '''
473 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt)
475 def toRhumb8Tuple(self, dflt=NAN):
476 '''Convert this L{GDict} result to a 8-tuple.
478 @kwarg dflt: Default value for missing items (C{any}).
480 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
481 azi12, s12, S12, a12)}.
482 '''
483 return self._toTuple(Rhumb8Tuple, dflt)
485 def toRhumbSolve7Tuple(self, dflt=NAN):
486 '''Convert this L{GDict} result to a 8-tuple.
488 @kwarg dflt: Default value for missing items (C{any}).
490 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
491 azi12, s12, S12)}.
492 '''
493 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt)
495 def _toTuple(self, nTuple, dflt):
496 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
497 '''
498 _g = getattr
499 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
500 return nTuple(t, iteration=self._iteration)
502 def _2X(self, gl, _2X=_X_): # .Intersectool, .Intersector
503 '''(INTERNAL) Rename C{-2} attr to C{-X} or C{-M}.
504 '''
505 X = GDict(self)
506 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_):
507 if n in X: # X._X = X._2
508 X[n[:-1] + _2X] = X.pop(n)
509 v = getattr(gl, n, X)
510 if v is not X: # X._2 = gl._2
511 X[n] = v
512 return X
514 def _unCaps(self, outmask): # in .geodsolve
515 '''(INTERNAL) Remove superfluous items.
516 '''
517 for k, C in _key2Caps.items():
518 if k in self and (outmask & C) != C:
519 self.pop(k) # delattr(self, k)
520 return self
523class GeodSolve12Tuple(_GTuple):
524 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with
525 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in
526 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and
527 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic
528 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve
529 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}.
530 '''
531 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12
532 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_)
533 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2)
536class Inverse10Tuple(_GTuple):
537 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
538 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
539 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
540 C{calp2} of the initial C{1} and final C{2} (forward) azimuths.
541 '''
542 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
543 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
545 def toGDict(self, **updates):
546 '''Convert this C{Inverse10Tuple} to a L{GDict}.
548 @kwarg updates: Optional items to apply (C{nam=value} pairs)
549 '''
550 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK namedTuple
551 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
552 **updates) # PYCHOK indent
555class _kWrapped(_CapsBase): # in .geodesicw
556 '''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
557 <https://PyPI.org/project/geographiclib>} classes.
558 '''
560 @property_ROnce
561 def geographiclib(self):
562 '''Lazily import C{geographiclib}, provided the U{geographiclib
563 <https://PyPI.org/project/geographiclib>} package is installed,
564 otherwise raise a C{LazyImportError}.
565 '''
566 g = _xgeographiclib(type(self), 1, 49)
567 from geographiclib.geodesic import Geodesic
568 g.Geodesic = Geodesic
569 from geographiclib.geodesicline import GeodesicLine
570 g.GeodesicLine = GeodesicLine
571 from geographiclib.geomath import Math
572 g.Math = Math
573# from geographiclib.polygonarea import PolygonArea
574# g.PolygonArea = PolygonArea # see below
575 return g
577 @property_ROnce
578 def Math(self):
579 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
580 <https://PyPI.org/project/geographiclib>} package is installed,
581 otherwise C{None}.
582 '''
583 try:
584 g = self.geographiclib
585 M = g.Math
586 if _version_info(g) < (2,):
587 if _K_2_0:
588 M = None
589# elif not _K_2_0: # XXX set 2.0?
590# _K_2_0 = True
591 except (AttributeError, ImportError):
592 M = None
593 return M
595 @property_RO
596 def Math_K_2(self):
597 return (_2_4_ if _K_2_4 else
598 (_2_ if _K_2_0 else _1_)) if self.Math else NN
600 @property_ROnce
601 def _PolygonArea(self): # lazy import
602 from geographiclib.polygonarea import PolygonArea
603 return PolygonArea
605_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
608class Rhumb8Tuple(_GTuple):
609 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
610 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
611 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
612 line and the angular distance C{a12} between both points.
613 '''
614 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
615 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
617 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
618 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
619 method C{geographiclib.geodesic.Geodesic._GenDirect}.
621 @kwarg dflt: Default value for missing items (C{any}).
622 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
623 to specify or override L{Inverse10Tuple} items.
625 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
626 m12, M12, M21, S12)}
627 '''
628 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
629 azi2=self.azi12, M21=_1_0) # PYCHOK attr
630 if a12_azi1_azi2_m12_M12_M21:
631 d.update(a12_azi1_azi2_m12_M12_M21)
632 return self._toTuple(Direct9Tuple, dflt, d)
634 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
635 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
636 method C{geographiclib.geodesic.Geodesic._GenInverse}.
638 @kwarg dflt: Default value for missing items (C{any}).
639 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
640 arguments to specify or override L{Inverse10Tuple} items.
642 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
643 m12, M12, M21, S12)}.
644 '''
645 s, c = sincos2d(self.azi12) # PYCHOK attr
646 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
647 salp2=s, calp2=c, M21=_1_0)
648 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
649 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
650 return self._toTuple(Inverse10Tuple, dflt, d)
652 def _toTuple(self, nTuple, dflt, updates={}):
653 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
654 '''
655 _g = self.toGDict(**updates).get
656 t = tuple(_g(n, dflt) for n in nTuple._Names_)
657 return nTuple(t, name=self.name)
659 @deprecated_method
660 def _to7Tuple(self):
661 '''DEPRECATED, do not use!'''
662 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1])
665class _Xables(object):
666 '''(INTERNAL) Get I{Karney}'s executable paths from/and env vars.
667 '''
668 bin_ = '/opt/local/bin/' # '/opt/local/Cellar/geographiclib/2.3/bin/' # HomeBrew on macOS
669 ENV = NN
671 def GeoConvert(self, *dir_):
672 return self._path(self.GeoConvert, *dir_)
674 def GeodSolve(self, *dir_):
675 return self._path(self.GeodSolve, *dir_)
677 def IntersectTool(self, *dir_):
678 return self._path(self.IntersectTool, *dir_)
680 def RhumbSolve(self, *dir_):
681 return self._path(self.RhumbSolve, *dir_)
683 def name_version(self, path, base=True):
684 # return C{(path + ' ' + version)} of an executable
685 if path:
686 try:
687 r, s = _popen2((path, '--version'))
688 if base:
689 path = _MODS.os.path.basename(path)
690 r = _SPACE_(path, r.split()[-1])
691 else:
692 r = _MODS.streprs.Fmt.PARENSPACED(r, s)
693 return r
694 except (IndexError, IOError, OSError):
695 pass
696 return NN
698 def _path(self, which, *dir_):
699 n = typename(which, which)
700 self.ENV = E = _PYGEODESY_ENV(n)
701 return _getenv(E, NN) or (NN(dir_[0], n) if dir_ else E)
703 def X_not(self, path):
704 return 'env %s=%r not executable' % (self.ENV, path)
706 def X_OK(self, path): # is C{path} an executable?
707 os = _MODS.os # import os
708 return os.access(path, os.X_OK) if path else False
710_Xables = _Xables() # PYCHOK singleton
713def _around(x): # in .utily.sincos2d
714 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
716 @return: Coarsened value (C{float}).
718 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
719 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
720 '''
721 try:
722 return _wrapped.Math.AngRound(x)
723 except AttributeError:
724 if x:
725 y = _1_16th - fabs(x)
726 if y > 0: # fabs(x) < _1_16th
727 x = _copysign(_1_16th - y, x)
728 else:
729 x = _0_0 # -0 to 0
730 return x
733def _atan2d(y, x):
734 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
735 '''
736 try:
737 return _wrapped.Math.atan2d(y, x)
738 except AttributeError:
739 return atan2d(y, x)
742def _cbrt(x):
743 '''Return C{cubic root(B{x})}.
744 '''
745 try:
746 return _wrapped.Math.cbrt(x)
747 except AttributeError:
748 return cbrt(x)
751def _copyBit(x, y):
752 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
753 '''
754 return (-x) if _signBit(y) else x
757def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
758 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
759 '''
760 r = cx - sx
761 if r:
762 r *= (cx + sx) * _2_0
763 return r
766def _diff182(deg0, deg, K_2_0=False):
767 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
769 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
770 '''
771 try:
772 return _wrapped.Math.AngDiff(deg0, deg)
773 except AttributeError:
774 if K_2_0 or _K_2_0: # geographiclib 2.0
775 _r, _360 = fremainder, _360_0
776 d, t = _sum2(_r(-deg0, _360),
777 _r( deg, _360))
778 d, t = _sum2(_r( d, _360), t)
779 if _isin(d, _0_0, _180_0, _N_180_0):
780 d = _copysign(d, -t if t else (deg - deg0))
781 else:
782 _n = _norm180
783 d, t = _sum2(_n(-deg0), _n(deg))
784 d = _n(d)
785 if t > 0 and d == _180_0:
786 d = _N_180_0
787 d, t = _sum2(d, t)
788 return d, t
791def _fix90(deg): # mimick Math.LatFix
792 '''Replace angle in C{degrees} outside [-90,90] by NAN.
794 @return: Angle C{degrees} or NAN.
795 '''
796 try:
797 return _wrapped.Math.LatFix(deg)
798 except AttributeError:
799 return NAN if fabs(deg) > 90 else deg
802def _isfinite(x): # mimick geomath.Math.isfinite
803 '''Check finiteness of C{x}.
805 @return: C{True} if finite.
806 '''
807 try:
808 return _wrapped.Math.isfinite(x)
809 except AttributeError:
810 return _math_isfinite(x) # and fabs(x) <= _MAX
813def _llz2gl(gl, **llz2): # see .geodesici._llz2G
814 '''(INTERNAL) Set C{gl.lat2, .lon2, .azi2} from C{llz2}.
815 '''
816 if llz2:
817 for n in (_lat2_, _lon2_, _azi2_): # _lat1_, _lon1_, _azi1_
818 v = llz2.get(n, None)
819 if v is not None:
820 setattr(gl, n, v)
821 return gl
824def _norm2(x, y): # mimick geomath.Math.norm
825 '''Normalize C{B{x}} and C{B{y}}.
827 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
828 '''
829 try:
830 return _wrapped.Math.norm(x, y)
831 except AttributeError:
832 return norm2(x, y)
835def _norm180(deg): # mimick geomath.Math.AngNormalize
836 '''Reduce angle in C{degrees} to (-180,180].
838 @return: Reduced angle C{degrees}.
839 '''
840 try:
841 return _wrapped.Math.AngNormalize(deg)
842 except AttributeError:
843 d = fremainder(deg, _360_0)
844 if _isin(d, _180_0, _N_180_0):
845 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
846 return d
849def _polygon(geodesic, points, closed, line, wrap, polar):
850 '''(INTERNAL) Compute the area or perimeter of a polygon,
851 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
852 C{geographiclib} package is installed) a C{Geodesic}
853 or C{geodesicw.Geodesic} instance.
854 '''
855 if not wrap: # capability LONG_UNROLL can't be off
856 notImplemented(None, wrap=wrap, up=3)
858 if _MODS.booleans.isBoolean(points):
859 # recursive call for each boolean clip
861 def _a_p(clip, *args, **unused):
862 return _polygon(geodesic, clip, *args)
864 if not closed: # closed only
865 raise _ValueError(closed=closed, points=_composite_)
867 return points._sum1(_a_p, closed, line, wrap, polar)
869 gP = geodesic.Polygon(line)
870 _A = gP.AddPoint
872 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
873 p1 = p0 = Ps[0]
875 # note, lon deltas are unrolled, by default
876 _A(p1.lat, p1.lon)
877 for p2 in Ps.iterate(closed=closed):
878 if wrap and not Ps.looped:
879 p2 = _unrollon(p1, p2)
880 _A(p2.lat, p2.lon)
881 p1 = p2
882 if closed and line and p1 != p0:
883 _A(p0.lat, p0.lon)
885 # gP.Compute returns (number_of_points, perimeter, signed area)
886 return gP.Compute(reverse=False, sign=True, polar=polar)[1 if line else 2]
889try:
890 from math import fma as _fma # since 3.13
892 def _poly_fma(x, s, *cs):
893 for c in cs:
894 s = _fma(s, x, c)
895 return s
897except ImportError: # Python 3.12-
899 def _poly_fma(x, s, *cs): # PYCHOK redef
900 t = _0_0
901 for c in cs:
902 s, t, _ = _sum3(s * x, t * x, c)
903 return s + t
905# def _poly_fma(x, s, *cs):
906# S = Fhorner(x, *cs, incx=False)
907# S += s
908# return float(S)
910def _polynomial(x, cs, i, j): # PYCHOK shared
911 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
912 signature and cascaded summation different from C{karney._sum3}.
914 @return: M{sum(x**(j - k - 1) * cs[k] for k in range(i, j)}
915 '''
916 if (i + 1) < j <= len(cs): # load _Rtuple._tuple
917 try:
918 r = _wrapped.Math.polyval(j - i - 1, cs, i, x)
919 except AttributeError: # no .Math
920 r = _poly_fma(x, _0_0, *cs[i:j])
921 else:
922 r = cs[i]
923 return float(r)
926def _remainder(x, y):
927 '''Remainder of C{x / y}.
929 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
930 '''
931 try:
932 return _wrapped.Math.remainder(x, y)
933 except AttributeError:
934 return fremainder(x, y)
937if _K_2_0:
938 from math import cos as _cos, sin as _sin
940 def _sincos2(rad):
941 return _sin(rad), _cos(rad)
943 _signBit = _MODS.basics.signBit
944else:
945 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
947 def _signBit(x):
948 '''(INTERNAL) GeographicLib 1.52-.
949 '''
950 return x < 0
953def _sincos2d(deg):
954 '''Return sine and cosine of an angle in C{degrees}.
956 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
957 '''
958 try:
959 return _wrapped.Math.sincosd(deg)
960 except AttributeError:
961 return sincos2d(deg)
964def _sincos2de(deg, t):
965 '''Return sine and cosine of a corrected angle in C{degrees}.
967 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
968 '''
969 try:
970 return _wrapped.Math.sincosde(deg, t)
971 except AttributeError:
972 return sincos2d(deg, adeg=t)
975def _sum2(a, b): # mimick geomath.Math.sum, actually sum2
976 '''Error-free summation like C{geomath.Math.sum}.
978 @return: 2-Tuple C{(B{a} + B{b}, residual)}.
980 @note: The C{residual} can be the same as B{C{a}} or B{C{b}}.
982 @see: U{TwoSum<https://accurate-algorithms.readthedocs.io/en/latest/ch04summation.html>}
983 and I{Knuth}'s U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
984 '''
985 try:
986 return _wrapped.Math.sum(a, b)
987 except AttributeError:
988 # if Algorithm_3_1:
989 s = a + b
990 r = s - b
991 t = s - r
992 # elif C_CPP: # Math::sum C/C++
993 # r -= a; t -= b; t += r; t = -t
994 # else:
995 t = (a - r) + (b - t)
996 # assert fabs(s) >= fabs(t)
997 return s, t
1000def _sum3(s, t, *xs):
1001 '''Accumulate any B{C{xs}} into a previous C{_sum2(s, t)}.
1003 @return: 3-Tuple C{(s, t, n)} where C{s} is the sum of B{s}, B{t} and all
1004 B{xs}, C{t} the residual and C{n} the number of zero C{xs}.
1006 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
1007 C++/doc/Accumulator_8hpp_source.html>} comments for more details and
1008 function C{_sum2} above.
1010 @note: Not "error-free", see C{pygeodesy.test/testKarney.py}.
1011 '''
1012 z = 0
1013 for x in xs:
1014 if x:
1015 t, r = _sum2(t, x) # start at the least-
1016 if s:
1017 s, t = _sum2(s, t) # -significant end
1018 if s:
1019 t += r # accumulate r into t
1020 else:
1021 # assert t == 0 # s == 0 implies t == 0
1022 s = unsigned0(r) # result is r, t = 0
1023 else:
1024 s, t = unsigned0(t), r
1025 else:
1026 z += 1
1027 # assert fabs(s) >= fabs(t)
1028 return s, t, z
1031def _tand(x):
1032 '''Return C{tan(B{x})} in C{degrees}.
1033 '''
1034 try:
1035 return _wrapped.Math.tand(x)
1036 except AttributeError:
1037 return tand(x) # Error=None
1040def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
1041 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
1043 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
1044 unrolled if C{B{wrap} is True}, normalized otherwise.
1045 '''
1046 if wrap:
1047 d, t = _diff182(lon1, lon2)
1048 lon2, t, _ = _sum3(d, t, lon1) # (lon1 + d) + t
1049 lon2 += t
1050 else:
1051 lon2 = _norm180(lon2)
1052 return (lon2 - lon1), lon2
1055def _unsigned2(x):
1056 '''(INTERNAL) Unsign B{C{x}}.
1057 '''
1058 return (neg(x), True) if _signBit(x) else (x, False)
1061__all__ += _ALL_DOCS(Caps, _CapsBase)
1063# **) MIT License
1064#
1065# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1066#
1067# Permission is hereby granted, free of charge, to any person obtaining a
1068# copy of this software and associated documentation files (the "Software"),
1069# to deal in the Software without restriction, including without limitation
1070# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1071# and/or sell copies of the Software, and to permit persons to whom the
1072# Software is furnished to do so, subject to the following conditions:
1073#
1074# The above copyright notice and this permission notice shall be included
1075# in all copies or substantial portions of the Software.
1076#
1077# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1078# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1079# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1080# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1081# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1082# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1083# OTHER DEALINGS IN THE SOFTWARE.