Coverage for pygeodesy/karney.py: 93%
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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 _ # PYCHOK semicolon
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__ = '25.04.14'
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{REDUCEDLENGTH} - compute the reduced length C{m12},
245 C{REVERSE2} - reverse azimuth C{azi2} by 180 degrees,
247 and C{ALL} - all of the above.
249 C{STANDARD} = C{AZIMUTH | DISTANCE | LATITUDE | LONGITUDE}
251 C{LINE_CAPS} = C{STANDARD | DISTANCE_IN | REDUCEDLENGTH | GEODESICSCALE}
252 '''
253 EMPTY = 0 # formerly aka NONE
254 _CAP_1 = 1 << 0 # for goedesici/-w
255 _CAP_1p = 1 << 1 # for goedesici/-w
256 _CAP_2 = 1 << 2
257 _CAP_3 = 1 << 3 # for goedesici/-w
258 _CAP_4 = 1 << 4 # for goedesicw
259# = 1 << 5 # unused
260# = 1 << 6 # unused
261 _CAP_ALL = 0x1F
262# _CAP_MASK = _CAP_ALL
263 LATITUDE = 1 << 7 # compute latitude C{lat2}
264 LONGITUDE = 1 << 8 | _CAP_3 # compute longitude C{lon2}
265 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
266 DISTANCE = 1 << 10 | _CAP_1 # compute distance C{s12}
267 DISTANCE_IN = 1 << 11 | _CAP_1 | _CAP_1p # allow distance C{s12} in Direct
268 REDUCEDLENGTH = 1 << 12 | _CAP_1 | _CAP_2 # compute reduced length C{m12}
269 GEODESICSCALE = 1 << 13 | _CAP_1 | _CAP_2 # compute geodesic scales C{M12} and C{M21}
270 AREA = 1 << 14 | _CAP_4 # compute area C{S12}
272 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE
273 STANDARD_LINE = STANDARD | DISTANCE_IN # for goedesici/-w
275 LINE_CAPS = STANDARD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only
276 LONG_UNROLL = 1 << 15 # unroll C{lon2} in .Direct and .Position
277# = 1 << 16 # unused
278 LINE_OFF = 1 << 17 # Line without updates from parent geodesic or rhumb
279 REVERSE2 = 1 << 18 # reverse C{azi2}
280 ALL = 0x7F80 | _CAP_ALL # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
282 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
283 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
285 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
286 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
288 _SALP_CALPs_ = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
290 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
291 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
292 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
293 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
294 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
295 _DEBUG_LINE | _SALP_CALPs_
297 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE # for goedesicw only
298 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only
300 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py
301 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
303 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
304 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL
305 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
306# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline
307 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
308# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
310 def items(self):
311 '''Yield all I{public} C{Caps} as 2-tuple C{(NAME, mask)}.
312 '''
313 for n, C in type(self).__dict__.items():
314 if isint(C) and not n.startswith(_UNDER_) \
315 and n.replace(_UNDER_, NN).isupper():
316 yield n, C
318 def toStr(self, Cask, sep=_BAR_):
319 '''Return C{Caps} or an C{outmask} as C{str} or tuple of C{str}s.
320 '''
321 s = (n for n, C in sorted(Caps.items())
322 if C and (Cask & C) == C) # and int1s(C) <= 3
323 return sep.join(s) if sep else tuple(s)
325if _FOR_DOCS: # PYCHOK force ...
326 pass # ... CAPS.__doc__ into epydoc
327else:
328 Caps = Caps() # PYCHOK singleton
330_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._unCaps
331 azi2=Caps.AZIMUTH,
332 lat2=Caps.LATITUDE,
333 lon2=Caps.LONGITUDE,
334 m12 =Caps.REDUCEDLENGTH,
335 M12 =Caps.GEODESICSCALE,
336 M21 =Caps.GEODESICSCALE,
337 s12 =Caps.DISTANCE,
338 S12 =Caps.AREA)
341class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
342 '''(INTERNAL) Base class for C{Geodesic*}, C{Geodesic*Exact}, C{Intersectool} and C{Rhumb*Base}.
343 '''
344 ALL = Caps.ALL
345 AREA = Caps.AREA
346 AZIMUTH = Caps.AZIMUTH
347 DISTANCE = Caps.DISTANCE
348 DISTANCE_IN = Caps.DISTANCE_IN
349 EMPTY = Caps.EMPTY # aka NONE
350 GEODESICSCALE = Caps.GEODESICSCALE
351 LATITUDE = Caps.LATITUDE
352 LINE_CAPS = Caps.LINE_CAPS
353 LINE_OFF = Caps.LINE_OFF
354 LONGITUDE = Caps.LONGITUDE
355 LONG_UNROLL = Caps.LONG_UNROLL
356 REDUCEDLENGTH = Caps.REDUCEDLENGTH
357 STANDARD = Caps.STANDARD
358 STANDARD_LINE = Caps.STANDARD_LINE # for geodesici
360 _caps = 0 # None
361 _debug = 0 # or Caps._DEBUG_...
363 @Property_RO
364 def caps(self):
365 '''Get the capabilities (bit-or'ed C{Caps}).
366 '''
367 return self._caps
369 def caps_(self, caps):
370 '''Check the available capabilities.
372 @arg caps: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}
373 values for all capabilities to be checked.
375 @return: C{True} if I{all} B{C{caps}} are available, C{False}
376 otherwise (C{bool}).
377 '''
378 caps &= Caps._OUT_ALL
379 return (self.caps & caps) == caps
381 @property
382 def debug(self):
383 '''Get the C{debug} option (C{bool}).
384 '''
385 return bool(self._debug)
387 @debug.setter # PYCHOK setter!
388 def debug(self, debug):
389 '''Set the C{debug} option (C{bool}) to include
390 more details in L{GDict} results.
391 '''
392 self._debug = Caps._DEBUG_ALL if debug else 0
394 def _iter2tion(self, r, iter=None, **unused):
395 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
396 '''
397 if iter is not None:
398 self._iteration = r._iteration = iter
399 return r
402class Direct9Tuple(_GTuple):
403 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
404 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
405 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
406 C{meter} I{squared}.
407 '''
408 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
409 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
412class GDict(ADict): # XXX _NamedDict
413 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items.
415 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are
416 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}.
417 '''
418 def toDirect9Tuple(self, dflt=NAN):
419 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method
420 C{geographiclib.geodesic.Geodesic._GenDirect}.
422 @kwarg dflt: Default value for missing items (C{any}).
424 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
425 s12, m12, M12, M21, S12)}
426 '''
427 return self._toTuple(Direct9Tuple, dflt)
429 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
430 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
431 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
432 result.
434 @kwarg dflt: Default value for missing items (C{any}).
436 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
437 s12, a12, m12, M12, M21, S12)}.
438 '''
439 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
441 def toInverse10Tuple(self, dflt=NAN):
442 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
443 method C{geographiclib.geodesic.Geodesic._GenInverse}.
445 @kwarg dflt: Default value for missing items (C{any}).
447 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
448 salp2, calp2, m12, M12, M21, S12)}.
449 '''
450 return self._toTuple(Inverse10Tuple, dflt)
452 def _toNAN(self, outmask): # .GeodesicLineExact._GenPosition
453 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s.
454 '''
455 d = dict((n, NAN) for n in GeodSolve12Tuple._Names_)
456 return self.set_(**d)._unCaps(outmask)
458 @deprecated_method
459 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
460 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}.
462 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
463 '''
464 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt)
466 def toRhumb8Tuple(self, dflt=NAN):
467 '''Convert this L{GDict} result to a 8-tuple.
469 @kwarg dflt: Default value for missing items (C{any}).
471 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
472 azi12, s12, S12, a12)}.
473 '''
474 return self._toTuple(Rhumb8Tuple, dflt)
476 def toRhumbSolve7Tuple(self, dflt=NAN):
477 '''Convert this L{GDict} result to a 8-tuple.
479 @kwarg dflt: Default value for missing items (C{any}).
481 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
482 azi12, s12, S12)}.
483 '''
484 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt)
486 def _toTuple(self, nTuple, dflt):
487 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
488 '''
489 _g = getattr
490 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
491 return nTuple(t, iteration=self._iteration)
493 def _2X(self, gl, _2X=_X_): # .Intersectool, .Intersector
494 '''(INTERNAL) Rename C{-2} attr to C{-X} or C{-M}.
495 '''
496 X = GDict(self)
497 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_):
498 if n in X: # X._X = X._2
499 X[n[:-1] + _2X] = X.pop(n)
500 v = getattr(gl, n, X)
501 if v is not X: # X._2 = gl._2
502 X[n] = v
503 return X
505 def _unCaps(self, outmask): # in .geodsolve
506 '''(INTERNAL) Remove superfluous items.
507 '''
508 for k, C in _key2Caps.items():
509 if k in self and (outmask & C) != C:
510 self.pop(k) # delattr(self, k)
511 return self
514class GeodSolve12Tuple(_GTuple):
515 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with
516 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in
517 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and
518 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic
519 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve
520 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}.
521 '''
522 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12
523 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_)
524 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2)
527class Inverse10Tuple(_GTuple):
528 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
529 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
530 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
531 C{calp2} of the initial C{1} and final C{2} (forward) azimuths.
532 '''
533 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
534 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
536 def toGDict(self, **updates):
537 '''Convert this C{Inverse10Tuple} to a L{GDict}.
539 @kwarg updates: Optional items to apply (C{nam=value} pairs)
540 '''
541 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK namedTuple
542 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
543 **updates) # PYCHOK indent
546class _kWrapped(object): # in .geodesicw
547 '''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
548 <https://PyPI.org/project/geographiclib>} classes.
549 '''
551 @property_ROnce
552 def geographiclib(self):
553 '''Lazily import C{geographiclib}, provided the U{geographiclib
554 <https://PyPI.org/project/geographiclib>} package is installed,
555 otherwise raise a C{LazyImportError}.
556 '''
557 g = _xgeographiclib(type(self).__module__, 1, 49)
558 from geographiclib.geodesic import Geodesic
559 g.Geodesic = Geodesic
560 from geographiclib.geodesicline import GeodesicLine
561 g.GeodesicLine = GeodesicLine
562 from geographiclib.geomath import Math
563 g.Math = Math
564 return g
566 @property_ROnce
567 def Math(self):
568 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
569 <https://PyPI.org/project/geographiclib>} package is installed,
570 otherwise C{None}.
571 '''
572 try:
573 g = self.geographiclib
574 M = g.Math
575 if _version_info(g) < (2,):
576 if _K_2_0:
577 M = None
578# elif not _K_2_0: # XXX set 2.0?
579# _K_2_0 = True
580 except (AttributeError, ImportError):
581 M = None
582 return M
584 @property_RO
585 def Math_K_2(self):
586 return (_2_4_ if _K_2_4 else
587 (_2_ if _K_2_0 else _1_)) if self.Math else NN
589_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
592class Rhumb8Tuple(_GTuple):
593 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
594 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
595 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
596 line and the angular distance C{a12} between both points.
597 '''
598 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
599 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
601 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
602 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
603 method C{geographiclib.geodesic.Geodesic._GenDirect}.
605 @kwarg dflt: Default value for missing items (C{any}).
606 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
607 to specify or override L{Inverse10Tuple} items.
609 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
610 m12, M12, M21, S12)}
611 '''
612 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
613 azi2=self.azi12, M21=_1_0) # PYCHOK attr
614 if a12_azi1_azi2_m12_M12_M21:
615 d.update(a12_azi1_azi2_m12_M12_M21)
616 return self._toTuple(Direct9Tuple, dflt, d)
618 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
619 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
620 method C{geographiclib.geodesic.Geodesic._GenInverse}.
622 @kwarg dflt: Default value for missing items (C{any}).
623 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
624 arguments to specify or override L{Inverse10Tuple} items.
626 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
627 m12, M12, M21, S12)}.
628 '''
629 s, c = sincos2d(self.azi12) # PYCHOK attr
630 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
631 salp2=s, calp2=c, M21=_1_0)
632 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
633 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
634 return self._toTuple(Inverse10Tuple, dflt, d)
636 def _toTuple(self, nTuple, dflt, updates={}):
637 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
638 '''
639 _g = self.toGDict(**updates).get
640 t = tuple(_g(n, dflt) for n in nTuple._Names_)
641 return nTuple(t, name=self.name)
643 @deprecated_method
644 def _to7Tuple(self):
645 '''DEPRECATED, do not use!'''
646 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1])
649class _Xables(object):
650 '''(INTERNAL) Get I{Karney}'s executable paths from/and env vars.
651 '''
652 bin_ = '/opt/local/bin/' # '/opt/local/Cellar/geographiclib/2.3/bin/' # HomeBrew on macOS
653 ENV = NN
655 def GeoConvert(self, *dir_):
656 return self._path(self.GeoConvert, *dir_)
658 def GeodSolve(self, *dir_):
659 return self._path(self.GeodSolve, *dir_)
661 def IntersectTool(self, *dir_):
662 return self._path(self.IntersectTool, *dir_)
664 def RhumbSolve(self, *dir_):
665 return self._path(self.RhumbSolve, *dir_)
667 def name_version(self, path, base=True):
668 # return C{(path + ' ' + version)} of an executable
669 if path:
670 try:
671 r, s = _popen2((path, '--version'))
672 if base:
673 path = _MODS.os.path.basename(path)
674 r = _SPACE_(path, r.split()[-1])
675 else:
676 r = _MODS.streprs.Fmt.PARENSPACED(r, s)
677 return r
678 except (IndexError, IOError, OSError):
679 pass
680 return NN
682 def _path(self, which, *dir_):
683 n = typename(which, which)
684 self.ENV = E = _PYGEODESY_ENV(n)
685 return _getenv(E, NN) or (NN(dir_[0], n) if dir_ else E)
687 def X_not(self, path):
688 return 'env %s=%r not executable' % (self.ENV, path)
690 def X_OK(self, path): # is C{path} an executable?
691 os = _MODS.os # import os
692 return os.access(path, os.X_OK) if path else False
694_Xables = _Xables() # PYCHOK singleton
697def _around(x): # in .utily.sincos2d
698 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
700 @return: Coarsened value (C{float}).
702 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
703 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
704 '''
705 try:
706 return _wrapped.Math.AngRound(x)
707 except AttributeError:
708 if x:
709 y = _1_16th - fabs(x)
710 if y > 0: # fabs(x) < _1_16th
711 x = _copysign(_1_16th - y, x)
712 else:
713 x = _0_0 # -0 to 0
714 return x
717def _atan2d(y, x):
718 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
719 '''
720 try:
721 return _wrapped.Math.atan2d(y, x)
722 except AttributeError:
723 return atan2d(y, x)
726def _cbrt(x):
727 '''Return C{cubic root(B{x})}.
728 '''
729 try:
730 return _wrapped.Math.cbrt(x)
731 except AttributeError:
732 return cbrt(x)
735def _copyBit(x, y):
736 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
737 '''
738 return (-x) if _signBit(y) else x
741def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
742 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
743 '''
744 r = cx - sx
745 if r:
746 r *= (cx + sx) * _2_0
747 return r
750def _diff182(deg0, deg, K_2_0=False):
751 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
753 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
754 '''
755 try:
756 return _wrapped.Math.AngDiff(deg0, deg)
757 except AttributeError:
758 if K_2_0 or _K_2_0: # geographiclib 2.0
759 _r, _360 = fremainder, _360_0
760 d, t = _sum2(_r(-deg0, _360),
761 _r( deg, _360))
762 d, t = _sum2(_r( d, _360), t)
763 if _isin(d, _0_0, _180_0, _N_180_0):
764 d = _copysign(d, -t if t else (deg - deg0))
765 else:
766 _n = _norm180
767 d, t = _sum2(_n(-deg0), _n(deg))
768 d = _n(d)
769 if t > 0 and d == _180_0:
770 d = _N_180_0
771 d, t = _sum2(d, t)
772 return d, t
775def _fix90(deg): # mimick Math.LatFix
776 '''Replace angle in C{degrees} outside [-90,90] by NAN.
778 @return: Angle C{degrees} or NAN.
779 '''
780 try:
781 return _wrapped.Math.LatFix(deg)
782 except AttributeError:
783 return NAN if fabs(deg) > 90 else deg
786def _isfinite(x): # mimick geomath.Math.isfinite
787 '''Check finiteness of C{x}.
789 @return: C{True} if finite.
790 '''
791 try:
792 return _wrapped.Math.isfinite(x)
793 except AttributeError:
794 return _math_isfinite(x) # and fabs(x) <= _MAX
797def _llz2gl(gl, **llz2): # see .geodesici._llz2G
798 '''(INTERNAL) Set C{gl.lat2, .lon2, .azi2} from C{llz2}.
799 '''
800 if llz2:
801 for n in (_lat2_, _lon2_, _azi2_): # _lat1_, _lon1_, _azi1_
802 v = llz2.get(n, None)
803 if v is not None:
804 setattr(gl, n, v)
805 return gl
808def _norm2(x, y): # mimick geomath.Math.norm
809 '''Normalize C{B{x}} and C{B{y}}.
811 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
812 '''
813 try:
814 return _wrapped.Math.norm(x, y)
815 except AttributeError:
816 return norm2(x, y)
819def _norm180(deg): # mimick geomath.Math.AngNormalize
820 '''Reduce angle in C{degrees} to (-180,180].
822 @return: Reduced angle C{degrees}.
823 '''
824 try:
825 return _wrapped.Math.AngNormalize(deg)
826 except AttributeError:
827 d = fremainder(deg, _360_0)
828 if _isin(d, _180_0, _N_180_0):
829 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
830 return d
833def _polygon(geodesic, points, closed, line, wrap):
834 '''(INTERNAL) Compute the area or perimeter of a polygon,
835 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
836 C{geographiclib} package is installed) a C{Geodesic}
837 or C{geodesicw.Geodesic} instance.
838 '''
839 if not wrap: # capability LONG_UNROLL can't be off
840 notImplemented(None, wrap=wrap, up=3)
842 if _MODS.booleans.isBoolean(points):
843 # recursive call for each boolean clip
845 def _a_p(clip, *args, **unused):
846 return _polygon(geodesic, clip, *args)
848 if not closed: # closed only
849 raise _ValueError(closed=closed, points=_composite_)
851 return points._sum1(_a_p, closed, line, wrap)
853 gP = geodesic.Polygon(line)
854 _A = gP.AddPoint
856 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
857 p1 = p0 = Ps[0]
859 # note, lon deltas are unrolled, by default
860 _A(p1.lat, p1.lon)
861 for p2 in Ps.iterate(closed=closed):
862 if wrap and not Ps.looped:
863 p2 = _unrollon(p1, p2)
864 _A(p2.lat, p2.lon)
865 p1 = p2
866 if closed and line and p1 != p0:
867 _A(p0.lat, p0.lon)
869 # gP.Compute returns (number_of_points, perimeter, signed area)
870 return gP.Compute(False, True)[1 if line else 2]
873try:
874 from math import fma as _fma # since 3.13
876 def _poly_fma(x, s, *cs):
877 for c in cs:
878 s = _fma(s, x, c)
879 return s
881except ImportError: # Python 3.12-
883 def _poly_fma(x, s, *cs): # PYCHOK redef
884 t = _0_0
885 for c in cs:
886 s, t, _ = _sum3(s * x, t * x, c)
887 return s + t
889# def _poly_fma(x, s, *cs):
890# S = Fhorner(x, *cs, incx=False)
891# S += s
892# return float(S)
894def _polynomial(x, cs, i, j): # PYCHOK shared
895 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
896 signature and cascaded summation different from C{karney._sum3}.
898 @return: M{sum(x**(j - k - 1) * cs[k] for k in range(i, j)}
899 '''
900 if (i + 1) < j <= len(cs): # load _Rtuple._tuple
901 try:
902 r = _wrapped.Math.polyval(j - i - 1, cs, i, x)
903 except AttributeError: # no .Math
904 r = _poly_fma(x, _0_0, *cs[i:j])
905 else:
906 r = cs[i]
907 return float(r)
910def _remainder(x, y):
911 '''Remainder of C{x / y}.
913 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
914 '''
915 try:
916 return _wrapped.Math.remainder(x, y)
917 except AttributeError:
918 return fremainder(x, y)
921if _K_2_0:
922 from math import cos as _cos, sin as _sin
924 def _sincos2(rad):
925 return _sin(rad), _cos(rad)
927 _signBit = _MODS.basics.signBit
928else:
929 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
931 def _signBit(x):
932 '''(INTERNAL) GeographicLib 1.52-.
933 '''
934 return x < 0
937def _sincos2d(deg):
938 '''Return sine and cosine of an angle in C{degrees}.
940 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
941 '''
942 try:
943 return _wrapped.Math.sincosd(deg)
944 except AttributeError:
945 return sincos2d(deg)
948def _sincos2de(deg, t):
949 '''Return sine and cosine of a corrected angle in C{degrees}.
951 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
952 '''
953 try:
954 return _wrapped.Math.sincosde(deg, t)
955 except AttributeError:
956 return sincos2d(deg, adeg=t)
959def _sum2(a, b): # mimick geomath.Math.sum, actually sum2
960 '''Error-free summation like C{geomath.Math.sum}.
962 @return: 2-Tuple C{(B{a} + B{b}, residual)}.
964 @note: The C{residual} can be the same as B{C{a}} or B{C{b}}.
966 @see: U{TwoSum<https://accurate-algorithms.readthedocs.io/en/latest/ch04summation.html>}
967 and I{Knuth}'s U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
968 '''
969 try:
970 return _wrapped.Math.sum(a, b)
971 except AttributeError:
972 # if Algorithm_3_1:
973 s = a + b
974 r = s - b
975 t = s - r
976 # elif C_CPP: # Math::sum C/C++
977 # r -= a; t -= b; t += r; t = -t
978 # else:
979 t = (a - r) + (b - t)
980 # assert fabs(s) >= fabs(t)
981 return s, t
984def _sum3(s, t, *xs):
985 '''Accumulate any B{C{xs}} into a previous C{_sum2(s, t)}.
987 @return: 3-Tuple C{(s, t, n)} where C{s} is the sum of B{s}, B{t} and all
988 B{xs}, C{t} the residual and C{n} the number of zero C{xs}.
990 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
991 C++/doc/Accumulator_8hpp_source.html>} comments for more details and
992 function C{_sum2} above.
994 @note: Not "error-free", see C{pygeodesy.test/testKarney.py}.
995 '''
996 z = 0
997 for x in xs:
998 if x:
999 t, r = _sum2(t, x) # start at the least-
1000 if s:
1001 s, t = _sum2(s, t) # -significant end
1002 if s:
1003 t += r # accumulate r into t
1004 else:
1005 # assert t == 0 # s == 0 implies t == 0
1006 s = unsigned0(r) # result is r, t = 0
1007 else:
1008 s, t = unsigned0(t), r
1009 else:
1010 z += 1
1011 # assert fabs(s) >= fabs(t)
1012 return s, t, z
1015def _tand(x):
1016 '''Return C{tan(B{x})} in C{degrees}.
1017 '''
1018 try:
1019 return _wrapped.Math.tand(x)
1020 except AttributeError:
1021 return tand(x) # Error=None
1024def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
1025 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
1027 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
1028 unrolled if C{B{wrap} is True}, normalized otherwise.
1029 '''
1030 if wrap:
1031 d, t = _diff182(lon1, lon2)
1032 lon2, t, _ = _sum3(d, t, lon1) # (lon1 + d) + t
1033 lon2 += t
1034 else:
1035 lon2 = _norm180(lon2)
1036 return (lon2 - lon1), lon2
1039def _unsigned2(x):
1040 '''(INTERNAL) Unsign B{C{x}}.
1041 '''
1042 return (neg(x), True) if _signBit(x) else (x, False)
1045__all__ += _ALL_DOCS(Caps, _CapsBase)
1047# **) MIT License
1048#
1049# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1050#
1051# Permission is hereby granted, free of charge, to any person obtaining a
1052# copy of this software and associated documentation files (the "Software"),
1053# to deal in the Software without restriction, including without limitation
1054# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1055# and/or sell copies of the Software, and to permit persons to whom the
1056# Software is furnished to do so, subject to the following conditions:
1057#
1058# The above copyright notice and this permission notice shall be included
1059# in all copies or substantial portions of the Software.
1060#
1061# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1062# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1063# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1064# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1065# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1066# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1067# OTHER DEALINGS IN THE SOFTWARE.