Coverage for pygeodesy/karney.py: 94%
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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.
15Karney-based functionality
16==========================
181. The following classes and functions in C{pygeodesy}
20 - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4},
21 L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} --
22 U{AlbersEqualArea<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AlbersEqualArea.html>}
24 - L{AuxAngle}, L{AuxDST}, L{AuxDLat}, L{AuxLat} -- U{AuxAngle
25 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>},
26 U{DST<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DST.html>},
27 U{DAuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>},
28 U{AuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxLatitude.html>} in I{GeographicLib 2.2+}
30 - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/
31 classGeographicLib_1_1CassiniSoldner.html>}
33 - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}
35 - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/
36 classGeographicLib_1_1EllipticFunction.html>}
38 - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant
39 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}
41 - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact
42 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}
44 - L{Geodesic}, L{GeodesicLine} -- I{wrapped} U{geodesic.Geodesic<https://PyPI.org/project/geographiclib>},
45 I{wrapped} U{geodesicline.GeodesicLine<https://PyPI.org/project/geographiclib>}
47 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/C++/doc/
48 classGeographicLib_1_1PolygonAreaT.html>}
50 - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/
51 classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/
52 classGeographicLib_1_1GeodesicLineExact.html>}
54 - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>}
56 - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Georef.html>}
58 - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic
59 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}
61 - L{Intersector} -- U{Intersect
62 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} from I{GeographicLib 2.3+}
64 - L{JacobiConformal} -- U{JacobiConformal
65 <https://geographiclib.sourceforge.io/C++/doc/classGeographicLib_1_1experimental_1_1JacobiConformal.html>}
67 - L{KTransverseMercator} - U{TransverseMercator
68 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
70 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
71 classGeographicLib_1_1LocalCartesian.html>}
73 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}
75 - L{rhumb.aux_}, L{RhumbAux}, L{RhumbLineAux} -- U{Rhumb
76 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine
77 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} from I{GeographicLib 2.2+}
79 - L{rhumb.ekx}, L{Rhumb}, L{RhumbLine} -- U{Rhumb
80 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},
81 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>},
82 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
83 from I{GeographicLib 2.0}
85 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>}
87 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
89 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>}
91 - L{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{tand} -- U{geomath.Math
92 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
94are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}.
962. These C{pygeodesy} modules and classes
98 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodesici}, L{geodsolve}, L{karney}, L{rhumb.solve}
99 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve},
100 L{GnomonicKarney}, L{HeightIDWkarney}, L{Intersectool}
102are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} or
103C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>},
104U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} or
105U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}.
1073. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations
109 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn},
110 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2},
111 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5}
113 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn},
114 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2},
115 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5}
117 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn},
118 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2},
119 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5}
121 - L{RhumbLineAux.Intersection} and L{RhumbLine.Intersection}
123are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case
124<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics
125on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}).
1274. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points
129 - L{RhumbLineAux.Intersecant2}, L{RhumbLineAux.PlumbTo}, L{RhumbLine.Intersecant2} and L{RhumbLine.PlumbTo}
131are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept
132<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
1345. Spherical functions
136 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf}
138in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon
139<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer.
140'''
141# make sure int/int division yields float quotient, see .basics
142from __future__ import division as _; del _ # PYCHOK semicolon
144from pygeodesy.basics import _copysign, isint, neg, unsigned0, _xgeographiclib, \
145 _zip, _version_info
146from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \
147 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0
148from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get1
149from pygeodesy.fmath import cbrt, fremainder, norm2
150# from pygeodesy.internals import _version_info # from .basics
151from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi1_, _azi2_, _azi12_, \
152 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \
153 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \
154 _UNDER_, _X_, _BAR_ # PYCHOK used!
155from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
156from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass
157from pygeodesy.props import deprecated_method, Property_RO, property_ROnce
158from pygeodesy.units import Azimuth as _Azi, Degrees as _Deg, Lat, Lon, \
159 Meter as _M, Meter2 as _M2, Number_
160from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
162# from math import fabs # from .utily
164__all__ = _ALL_LAZY.karney
165__version__ = '24.07.25'
167_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
168_perimeter_ = 'perimeter'
171class _GTuple(_NamedTuple): # in .testNamedTuples
172 '''(INTERNAL) Helper.
173 '''
174 def toGDict(self, **updates): # NO name=NN
175 '''Convert this C{*Tuple} to a L{GDict}.
177 @kwarg updates: Optional items to apply (C{name=value} pairs)
178 '''
179 r = GDict(_zip(self._Names_, self)) # strict=True
180 if updates:
181 r.update(updates)
182 if self._iteration is not None:
183 r._iteration = self._iteration
184 return r
187class _Lat(Lat):
188 '''(INTERNAL) Latitude B{C{lat}}.
189 '''
190 def __init__(self, *lat, **Error_name):
191 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
192 Lat.__new__(_Lat, *lat, **kwds)
195class _Lon(Lon):
196 '''(INTERNAL) Longitude B{C{lon}}.
197 '''
198 def __init__(self, *lon, **Error_name):
199 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
200 Lon.__new__(_Lon, *lon, **kwds)
203class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
204 '''3-Tuple C{(number, perimeter, area)} with the C{number}
205 of points of the polygon or polyline, the C{perimeter} in
206 C{meter} and the C{area} in C{meter} I{squared}.
207 '''
208 _Names_ = (_number_, _perimeter_, _area_)
209 _Units_ = ( Number_, _M, _M2)
212class Caps(object):
213 '''(INTERNAL) Overriden by C{Caps} below.
214 '''
215 EMPTY = 0 # formerly aka NONE
216 _CAP_1 = 1 << 0 # for goedesici/-w
217 _CAP_1p = 1 << 1 # for goedesici/-w
218 _CAP_2 = 1 << 2
219 _CAP_3 = 1 << 3 # for goedesici/-w
220 _CAP_4 = 1 << 4 # for goedesicw
221 _CAP_ALL = 0x1F
222# _CAP_MASK = _CAP_ALL
223 LATITUDE = 1 << 7 # compute latitude C{lat2}
224 LONGITUDE = 1 << 8 | _CAP_3 # compute longitude C{lon2}
225 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
226 DISTANCE = 1 << 10 | _CAP_1 # compute distance C{s12}
227 DISTANCE_IN = 1 << 11 | _CAP_1 | _CAP_1p # allow distance C{s12} in Direct
228 REDUCEDLENGTH = 1 << 12 | _CAP_1 | _CAP_2 # compute reduced length C{m12}
229 GEODESICSCALE = 1 << 13 | _CAP_1 | _CAP_2 # compute geodesic scales C{M12} and C{M21}
230 AREA = 1 << 14 | _CAP_4 # compute area C{S12}
232 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE
234 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE # for goedesicw only
235 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only
236 _STD = STANDARD # for goedesicw only
237 _STD_LINE = _STD | DISTANCE_IN # for goedesici/-w
239 LINE_CAPS = _STD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only
240 LONG_UNROLL = 1 << 15 # unroll C{lon2} in .Direct and .Position
241# = 1 << 16 # unused
242 LINE_OFF = 1 << 17 # Line without updates from parent geodesic or rhumb
243 REVERSE2 = 1 << 18 # reverse C{azi2}
244 ALL = 0x7F80 | _CAP_ALL # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
246 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
247 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
249 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
250 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
252 _SALP_CALPs_ = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
254 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
255 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
256 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
257 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
258 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
259 _DEBUG_LINE | _SALP_CALPs_
261 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py
262 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
264 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
265 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL
266 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
267# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline
268 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
269# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
271 def items(self):
272 '''Yield all I{public} C{Caps} as 2-tuple C{(NAME, mask)}.
273 '''
274 for n, C in Caps.__class__.__dict__.items():
275 if isint(C) and not n.startswith(_UNDER_) \
276 and n.replace(_UNDER_, NN).isupper():
277 yield n, C
279 def toStr(self, Cask, sep=_BAR_):
280 '''Return C{Caps} or an C{outmask} as C{str} or tuple of C{str}s.
281 '''
282 s = (n for n, C in sorted(Caps.items())
283 if C and (Cask & C) == C) # and int1s(C) <= 3
284 return sep.join(s) if sep else tuple(s)
286Caps = Caps() # PYCHOK singleton
287'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
288rhumb capabilities (C{caps}) and expected results (C{outmask}).
290C{AREA} - compute area C{S12},
292C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
294C{DISTANCE} - compute distance C{s12} and angular distance C{a12},
296C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
298C{EMPTY} - nothing, formerly aka C{NONE},
300C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
302C{LATITUDE} - compute latitude C{lat2},
304C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
306C{LONGITUDE} - compute longitude C{lon2},
308C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
310C{REDUCEDLENGTH} - compute reduced length C{m12},
312C{REVERSE2} - reverse C{azi2},
314and C{ALL} - all of the above.
316C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
318_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._unCaps
319 azi2=Caps.AZIMUTH,
320 lat2=Caps.LATITUDE,
321 lon2=Caps.LONGITUDE,
322 m12 =Caps.REDUCEDLENGTH,
323 M12 =Caps.GEODESICSCALE,
324 M21 =Caps.GEODESICSCALE,
325 s12 =Caps.DISTANCE,
326 S12 =Caps.AREA)
329class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
330 '''(INTERNAL) Base class for C{Geodesic*}, C{Geodesic*Exact}, C{Intersectool} and C{Rhumb*Base}.
331 '''
332 ALL = Caps.ALL
333 AREA = Caps.AREA
334 AZIMUTH = Caps.AZIMUTH
335 DISTANCE = Caps.DISTANCE
336 DISTANCE_IN = Caps.DISTANCE_IN
337 EMPTY = Caps.EMPTY # aka NONE
338 GEODESICSCALE = Caps.GEODESICSCALE
339 LATITUDE = Caps.LATITUDE
340 LINE_CAPS = Caps.LINE_CAPS
341 LINE_OFF = Caps.LINE_OFF
342 LONGITUDE = Caps.LONGITUDE
343 LONG_UNROLL = Caps.LONG_UNROLL
344 REDUCEDLENGTH = Caps.REDUCEDLENGTH
345 STANDARD = Caps.STANDARD
346 _STD_LINE = Caps._STD_LINE # for geodesici
348 _caps = 0 # None
349 _debug = 0 # or Caps._DEBUG_...
351 @Property_RO
352 def caps(self):
353 '''Get the capabilities (bit-or'ed C{Caps}).
354 '''
355 return self._caps
357 def caps_(self, caps):
358 '''Check the available capabilities.
360 @arg caps: Bit-or'ed combination of L{Caps} values
361 for all capabilities to be checked.
363 @return: C{True} if I{all} B{C{caps}} are available,
364 C{False} otherwise (C{bool}).
365 '''
366 caps &= Caps._OUT_ALL
367 return (self.caps & caps) == caps
369 @property
370 def debug(self):
371 '''Get the C{debug} option (C{bool}).
372 '''
373 return bool(self._debug)
375 @debug.setter # PYCHOK setter!
376 def debug(self, debug):
377 '''Set the C{debug} option (C{bool}) to include
378 more details in L{GDict} results.
379 '''
380 self._debug = Caps._DEBUG_ALL if debug else 0
382 def _iter2tion(self, r, iter=None, **unused):
383 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
384 '''
385 if iter is not None:
386 self._iteration = r._iteration = iter
387 return r
390class Direct9Tuple(_GTuple):
391 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
392 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
393 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
394 C{meter} I{squared}.
395 '''
396 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
397 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
400class GDict(ADict): # XXX _NamedDict
401 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items.
403 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are
404 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}.
405 '''
406 def toDirect9Tuple(self, dflt=NAN):
407 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method
408 C{geographiclib.geodesic.Geodesic._GenDirect}.
410 @kwarg dflt: Default value for missing items (C{any}).
412 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
413 s12, m12, M12, M21, S12)}
414 '''
415 return self._toTuple(Direct9Tuple, dflt)
417 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
418 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
419 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
420 result.
422 @kwarg dflt: Default value for missing items (C{any}).
424 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
425 s12, a12, m12, M12, M21, S12)}.
426 '''
427 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
429 def toInverse10Tuple(self, dflt=NAN):
430 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
431 method C{geographiclib.geodesic.Geodesic._GenInverse}.
433 @kwarg dflt: Default value for missing items (C{any}).
435 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
436 salp2, calp2, m12, M12, M21, S12)}.
437 '''
438 return self._toTuple(Inverse10Tuple, dflt)
440 def _toNAN(self, outmask): # .GeodesicLineExact._GenPosition
441 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s.
442 '''
443 d = dict((n, NAN) for n in GeodSolve12Tuple._Names_)
444 return self.set_(**d)._unCaps(outmask)
446 @deprecated_method
447 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
448 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}.
450 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
451 '''
452 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt)
454 def toRhumb8Tuple(self, dflt=NAN):
455 '''Convert this L{GDict} result to a 8-tuple.
457 @kwarg dflt: Default value for missing items (C{any}).
459 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
460 azi12, s12, S12, a12)}.
461 '''
462 return self._toTuple(Rhumb8Tuple, dflt)
464 def toRhumbSolve7Tuple(self, dflt=NAN):
465 '''Convert this L{GDict} result to a 8-tuple.
467 @kwarg dflt: Default value for missing items (C{any}).
469 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
470 azi12, s12, S12)}.
471 '''
472 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt)
474 def _toTuple(self, nTuple, dflt):
475 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
476 '''
477 _g = getattr
478 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
479 return nTuple(t, iteration=self._iteration)
481 def _2X(self, gl, _2X=_X_): # .Intersectool, .Intersector
482 '''(INTERNAL) Rename C{-2} attr to C{-X} or C{-M}.
483 '''
484 X = GDict(self)
485 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_):
486 if n in X: # X._X = X._2
487 X[n[:-1] + _2X] = X.pop(n)
488 v = getattr(gl, n, X)
489 if v is not X: # X._2 = gl._2
490 X[n] = v
491 return X
493 def _unCaps(self, outmask): # in .geodsolve
494 '''(INTERNAL) Remove superfluous items.
495 '''
496 for k, C in _key2Caps.items():
497 if k in self and (outmask & C) != C:
498 self.pop(k) # delattr(self, k)
499 return self
502class GeodSolve12Tuple(_GTuple):
503 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with
504 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in
505 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and
506 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic
507 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve
508 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}.
509 '''
510 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12
511 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_)
512 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2)
515class Inverse10Tuple(_GTuple):
516 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
517 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
518 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
519 C{calp2} of the initial C{1} and final C{2} (forward) azimuths.
520 '''
521 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
522 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
524 def toGDict(self, **updates):
525 '''Convert this C{Inverse10Tuple} to a L{GDict}.
527 @kwarg updates: Optional items to apply (C{nam=value} pairs)
528 '''
529 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK namedTuple
530 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
531 **updates) # PYCHOK indent
534class _kWrapped(object): # in .geodesicw
535 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
536 <https://PyPI.org/project/geographiclib>} classes.
537 '''
539 @property_ROnce
540 def geographiclib(self):
541 '''Lazily import C{geographiclib}, provided the U{geographiclib
542 <https://PyPI.org/project/geographiclib>} package is installed,
543 otherwise raise a C{LazyImportError}.
544 '''
545 g = _xgeographiclib(self.__class__.__module__, 1, 49)
546 from geographiclib.geodesic import Geodesic
547 g.Geodesic = Geodesic
548 from geographiclib.geodesicline import GeodesicLine
549 g.GeodesicLine = GeodesicLine
550 from geographiclib.geomath import Math
551 g.Math = Math
552 return g
554 @property_ROnce
555 def Math(self):
556 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
557 <https://PyPI.org/project/geographiclib>} package is installed,
558 otherwise C{None}.
559 '''
560 try:
561 g = self.geographiclib
562 M = g.Math
563 if _version_info(g) < (2,):
564 if _K_2_0:
565 M = None
566# elif not _K_2_0: # XXX set 2.0?
567# _K_2_0 = True
568 except (AttributeError, ImportError):
569 M = None
570 return M
572_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
575class Rhumb8Tuple(_GTuple):
576 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
577 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
578 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
579 line and the angular distance C{a12} between both points.
580 '''
581 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
582 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
584 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
585 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
586 method C{geographiclib.geodesic.Geodesic._GenDirect}.
588 @kwarg dflt: Default value for missing items (C{any}).
589 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
590 to specify or override L{Inverse10Tuple} items.
592 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
593 m12, M12, M21, S12)}
594 '''
595 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
596 azi2=self.azi12, M21=_1_0) # PYCHOK attr
597 if a12_azi1_azi2_m12_M12_M21:
598 d.update(a12_azi1_azi2_m12_M12_M21)
599 return self._toTuple(Direct9Tuple, dflt, d)
601 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
602 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
603 method C{geographiclib.geodesic.Geodesic._GenInverse}.
605 @kwarg dflt: Default value for missing items (C{any}).
606 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
607 arguments to specify or override L{Inverse10Tuple} items.
609 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
610 m12, M12, M21, S12)}.
611 '''
612 s, c = sincos2d(self.azi12) # PYCHOK attr
613 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
614 salp2=s, calp2=c, M21=_1_0)
615 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
616 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
617 return self._toTuple(Inverse10Tuple, dflt, d)
619 def _toTuple(self, nTuple, dflt, updates={}):
620 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
621 '''
622 _g = self.toGDict(**updates).get
623 t = tuple(_g(n, dflt) for n in nTuple._Names_)
624 return nTuple(t, name=self.name)
626 @deprecated_method
627 def _to7Tuple(self):
628 '''DEPRECATED, do not use!'''
629 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1])
632def _around(x): # in .utily.sincos2d
633 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
635 @return: Coarsened value (C{float}).
637 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
638 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
639 '''
640 try:
641 return _wrapped.Math.AngRound(x)
642 except AttributeError:
643 if x:
644 y = _1_16th - fabs(x)
645 if y > 0: # fabs(x) < _1_16th
646 x = _copysign(_1_16th - y, x)
647 else:
648 x = _0_0 # -0 to 0
649 return x
652def _atan2d(y, x):
653 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
654 '''
655 try:
656 return _wrapped.Math.atan2d(y, x)
657 except AttributeError:
658 return atan2d(y, x)
661def _cbrt(x):
662 '''Return C{cubic root(B{x})}.
663 '''
664 try:
665 return _wrapped.Math.cbrt(x)
666 except AttributeError:
667 return cbrt(x)
670def _copyBit(x, y):
671 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
672 '''
673 return (-x) if _signBit(y) else x
676def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
677 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
678 '''
679 r = cx - sx
680 if r:
681 r *= (cx + sx) * _2_0
682 return r
685def _diff182(deg0, deg, K_2_0=False):
686 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
688 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
689 '''
690 try:
691 return _wrapped.Math.AngDiff(deg0, deg)
692 except AttributeError:
693 if K_2_0 or _K_2_0: # geographiclib 2.0
694 _r, _360 = fremainder, _360_0
695 d, t = _sum2(_r(-deg0, _360),
696 _r( deg, _360))
697 d, t = _sum2(_r( d, _360), t)
698 if d in (_0_0, _180_0, _N_180_0):
699 d = _copysign(d, -t if t else (deg - deg0))
700 else:
701 _n = _norm180
702 d, t = _sum2(_n(-deg0), _n(deg))
703 d = _n(d)
704 if t > 0 and d == _180_0:
705 d = _N_180_0
706 d, t = _sum2(d, t)
707 return d, t
710def _fix90(deg): # mimick Math.LatFix
711 '''Replace angle in C{degrees} outside [-90,90] by NAN.
713 @return: Angle C{degrees} or NAN.
714 '''
715 try:
716 return _wrapped.Math.LatFix(deg)
717 except AttributeError:
718 return NAN if fabs(deg) > 90 else deg
721def _isfinite(x): # mimick geomath.Math.isfinite
722 '''Check finiteness of C{x}.
724 @return: C{True} if finite.
725 '''
726 try:
727 return _wrapped.Math.isfinite(x)
728 except AttributeError:
729 return _math_isfinite(x) # and fabs(x) <= _MAX
732def _llz2gl(gl, **llz2): # see .geodesici._llz2G
733 '''(INTERNAL) Set C{gl.lat2, .lon2, .azi2} from C{llz2}.
734 '''
735 if llz2:
736 for n in (_lat2_, _lon2_, _azi2_): # _lat1_, _lon1_, _azi1_
737 v = llz2.get(n, None)
738 if v is not None:
739 setattr(gl, n, v)
740 return gl
743def _norm2(x, y): # mimick geomath.Math.norm
744 '''Normalize C{B{x}} and C{B{y}}.
746 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
747 '''
748 try:
749 return _wrapped.Math.norm(x, y)
750 except AttributeError:
751 return norm2(x, y)
754def _norm180(deg): # mimick geomath.Math.AngNormalize
755 '''Reduce angle in C{degrees} to (-180,180].
757 @return: Reduced angle C{degrees}.
758 '''
759 try:
760 return _wrapped.Math.AngNormalize(deg)
761 except AttributeError:
762 d = fremainder(deg, _360_0)
763 if d in (_180_0, _N_180_0):
764 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
765 return d
768def _polygon(geodesic, points, closed, line, wrap):
769 '''(INTERNAL) Compute the area or perimeter of a polygon,
770 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
771 C{geographiclib} package is installed) a C{Geodesic}
772 or C{geodesicw.Geodesic} instance.
773 '''
774 if not wrap: # capability LONG_UNROLL can't be off
775 notImplemented(None, wrap=wrap, up=3)
777 if _MODS.booleans.isBoolean(points):
778 # recursive call for each boolean clip
780 def _a_p(clip, *args, **unused):
781 return _polygon(geodesic, clip, *args)
783 if not closed: # closed only
784 raise _ValueError(closed=closed, points=_composite_)
786 return points._sum1(_a_p, closed, line, wrap)
788 gP = geodesic.Polygon(line)
789 _A = gP.AddPoint
791 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
792 p1 = p0 = Ps[0]
794 # note, lon deltas are unrolled, by default
795 _A(p1.lat, p1.lon)
796 for p2 in Ps.iterate(closed=closed):
797 if wrap and not Ps.looped:
798 p2 = _unrollon(p1, p2)
799 _A(p2.lat, p2.lon)
800 p1 = p2
801 if closed and line and p1 != p0:
802 _A(p0.lat, p0.lon)
804 # gP.Compute returns (number_of_points, perimeter, signed area)
805 return gP.Compute(False, True)[1 if line else 2]
808def _polynomial(x, cs, i, j): # PYCHOK shared
809 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
810 different signature and cascaded summation as C{karney._sum2_}.
812 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
813 '''
814 # assert 0 <= i <= j <= len(cs)
815# try:
816# return _wrapped.Math.polyval(j - i - 1, cs, i, x)
817# except AttributeError:
818# s, t = cs[i], _0_0
819# for c in cs[i+1:j]:
820# s, t = _sum2_(s * x, t * x, c)
821# return s # + t
822 s = cs[i]
823 i += 1
824 if x and i < j:
825 s, _ = _sum2_(s, _0_0, x=x, *cs[i:j])
826 return s # + t
829def _remainder(x, y):
830 '''Remainder of C{x / y}.
832 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
833 '''
834 try:
835 return _wrapped.Math.remainder(x, y)
836 except AttributeError:
837 return fremainder(x, y)
840if _K_2_0:
841 from math import cos as _cos, sin as _sin
843 def _sincos2(rad):
844 return _sin(rad), _cos(rad)
846 _signBit = _MODS.basics.signBit
847else:
848 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
850 def _signBit(x):
851 '''(INTERNAL) GeographicLib 1.52-.
852 '''
853 return x < 0
856def _sincos2d(deg):
857 '''Return sine and cosine of an angle in C{degrees}.
859 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
860 '''
861 try:
862 return _wrapped.Math.sincosd(deg)
863 except AttributeError:
864 return sincos2d(deg)
867def _sincos2de(deg, t):
868 '''Return sine and cosine of a corrected angle in C{degrees}.
870 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
871 '''
872 try:
873 return _wrapped.Math.sincosde(deg, t)
874 except AttributeError:
875 return sincos2d(deg, adeg=t)
878def _sum2(u, v): # mimick geomath.Math.sum, actually sum2
879 '''Error-free summation like C{geomath.Math.sum}.
881 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
883 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
885 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
886 '''
887 try:
888 return _wrapped.Math.sum(u, v)
889 except AttributeError:
890 s = u + v
891 r = s - v
892 t = s - r
893 # if Algorithm_3_1:
894 # t = (u - t) + (v + r)
895 # elif C_CPP: # Math::sum C/C++
896 # r -= u
897 # t -= v
898 # t += r
899 # t = -t
900 # else:
901 t = (u - r) + (v - t)
902 return s, t
905def _sum2_(s, t, *vs, **x):
906 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
908 @kwarg x: Optional polynomial C{B{x}=1} (C{scalar}).
910 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
912 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
913 C++/doc/Accumulator_8hpp_source.html>} comments for more details and
914 function C{_sum2} above.
916 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
917 '''
918 x = _xkwds_get1(x, x=_1_0)
919 p = x != _1_0
921 _s2, _u0 = _sum2, unsigned0
922 for v in vs:
923 if p:
924 s *= x
925 t *= x
926 if v:
927 t, u = _s2(t, v) # start at the least-
928 if s:
929 s, t = _s2(s, t) # significant end
930 if s:
931 t += u # accumulate u into t
932# elif t: # s == 0 implies t == 0
933# raise _AssertionError(t=t, txt_not_=_0_)
934 else:
935 s = _u0(u) # result is u, t = 0
936 else:
937 s, t = _u0(t), u
938 return s, t
941def _tand(x):
942 '''Return C{tan(B{x})} in C{degrees}.
943 '''
944 try:
945 return _wrapped.Math.tand(x)
946 except AttributeError:
947 return tand(x)
950def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
951 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
953 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
954 unrolled if C{B{wrap} is True}, normalized otherwise.
955 '''
956 if wrap:
957 d, t = _diff182(lon1, lon2)
958 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
959 else:
960 lon2 = _norm180(lon2)
961 return (lon2 - lon1), lon2
964def _unsigned2(x):
965 '''(INTERNAL) Unsign B{C{x}}.
966 '''
967 return (neg(x), True) if _signBit(x) else (x, False)
970__all__ += _ALL_DOCS(_CapsBase)
972# **) MIT License
973#
974# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
975#
976# Permission is hereby granted, free of charge, to any person obtaining a
977# copy of this software and associated documentation files (the "Software"),
978# to deal in the Software without restriction, including without limitation
979# the rights to use, copy, modify, merge, publish, distribute, sublicense,
980# and/or sell copies of the Software, and to permit persons to whom the
981# Software is furnished to do so, subject to the following conditions:
982#
983# The above copyright notice and this permission notice shall be included
984# in all copies or substantial portions of the Software.
985#
986# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
987# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
988# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
989# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
990# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
991# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
992# OTHER DEALINGS IN THE SOFTWARE.