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.
7The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items
8either by C{key} or by C{attribute} name.
9All methods of the I{wrapped} L{Geodesic<geodesicw.Geodesic>} and L{GeodesicLine<geodesicw.GeodesicLine>}
10classes return a L{GDict} instance offering access to the C{dict} items either by C{key} or by
11C{attribute} name.
13With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, modules L{geodesicx},
14L{geodesicw} and this module will use U{GeographicLib 2.0<https://GeographicLib.SourceForge.io/C++/doc/>}
15and newer transcoding, otherwise C{1.52} or older.
17Karney-based functionality
18==========================
201. The following classes and functions in C{pygeodesy}
22 - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4},
23 L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} --
24 U{AlbersEqualArea<https://GeographicLib.SourceForge.io/C++/doc/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{JacobiConformal} -- U{JacobiConformal
64 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1JacobiConformal.html#details>}
66 - L{KTransverseMercator} - U{TransverseMercator
67 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
69 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
70 classGeographicLib_1_1LocalCartesian.html>}
72 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}
74 - L{rhumb.aux_}, L{RhumbAux}, L{RhumbLineAux} -- U{Rhumb
75 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine
76 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} from I{GeographicLib 2.2+}
78 - L{rhumb.ekx}, L{Rhumb}, L{RhumbLine} -- U{Rhumb
79 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},
80 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>},
81 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
82 from I{GeographicLib 2.0}
84 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>}
86 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
88 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>}
90 - L{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{tand} -- U{geomath.Math
91 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
93are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}.
952. These C{pygeodesy} modules and classes
97 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumb.solve}
98 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve},
99 L{GnomonicKarney}, L{HeightIDWkarney}
101are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>}
102C{geodesic}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or
103C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}.
1053. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations
107 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn},
108 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2},
109 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5}
111 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn},
112 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2},
113 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5}
115 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn},
116 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2},
117 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5}
119 - L{RhumbLineAux.Intersection} and L{RhumbLine.Intersection}
121are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case
122<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics
123on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}).
1254. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points
127 - L{RhumbLineAux.Intersecant2}, L{RhumbLineAux.PlumbTo}, L{RhumbLine.Intersecant2} and L{RhumbLine.PlumbTo}
129are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept
130<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
1325. Spherical functions
134 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf}
136in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon
137<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer.
138'''
139# make sure int/int division yields float quotient, see .basics
140from __future__ import division as _; del _ # PYCHOK semicolon
142from pygeodesy.basics import _copysign, int1s, isint, itemsorted, neg, unsigned0, \
143 _xgeographiclib, _zip, _version_info
144from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \
145 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0
146from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get1, \
147 _xkwds_kwds, _xkwds_not
148from pygeodesy.fmath import cbrt, fremainder, norm2
149# from pygeodesy.internals import _version_info # from .basics
150from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi1_, _azi2_, _azi12_, \
151 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \
152 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \
153 _UNDER_, _X_, _BAR_ # PYCHOK used!
154from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
155from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass
156from pygeodesy.props import deprecated_method, Property_RO
157from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \
158 Meter as _M, Meter2 as _M2, Number_
159from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
161# from math import fabs # from .utily
163__all__ = _ALL_LAZY.karney
164__version__ = '24.07.09'
166_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
167_perimeter_ = 'perimeter'
170class _GTuple(_NamedTuple): # in .testNamedTuples
171 '''(INTERNAL) Helper.
172 '''
173 def toGDict(self, **updates): # NO name=NN
174 '''Convert this C{*Tuple} to a L{GDict}.
176 @kwarg updates: Optional items to apply (C{name=value} pairs)
177 '''
178 r = GDict(_zip(self._Names_, self)) # strict=True
179 if updates:
180 r.update(updates)
181 if self._iteration is not None:
182 r._iteration = self._iteration
183 return r
186class _Lat(Lat):
187 '''(INTERNAL) Latitude B{C{lat}}.
188 '''
189 def __init__(self, *lat, **Error_name):
190 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
191 Lat.__new__(_Lat, *lat, **kwds)
194class _Lon(Lon):
195 '''(INTERNAL) Longitude B{C{lon}}.
196 '''
197 def __init__(self, *lon, **Error_name):
198 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
199 Lon.__new__(_Lon, *lon, **kwds)
202class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
203 '''3-Tuple C{(number, perimeter, area)} with the C{number}
204 of points of the polygon or polyline, the C{perimeter} in
205 C{meter} and the C{area} in C{meter} I{squared}.
206 '''
207 _Names_ = (_number_, _perimeter_, _area_)
208 _Units_ = ( Number_, _M, _M2)
211class Caps(object): # PYCHOK
212 '''(INTERNAL) Overriden by C{Caps} below.
213 '''
214 EMPTY = 0 # formerly aka NONE
215 _CAP_1 = 1 << 0 # for goedesici/-w
216 _CAP_1p = 1 << 1 # for goedesici/-w
217 _CAP_2 = 1 << 2
218 _CAP_3 = 1 << 3 # for goedesici/-w
219# _CAP_4 = 1 << 4
220# _CAP_ALL = 0x1F
221# _CAP_MASK = _CAP_ALL
222 LATITUDE = 1 << 7 # compute latitude C{lat2}
223 LONGITUDE = 1 << 8 # compute longitude C{lon2} _CAP_3
224 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
225 DISTANCE = 1 << 10 # compute distance C{s12} _CAP_1
226 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct _CAP_1 | _CAP_1p
227 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} _CAP_1 | _CAP_2
228 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} _CAP_1 | _CAP_2
229 AREA = 1 << 14 # compute area C{S12} _CAP_4
231 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE
232 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
234 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE | _CAP_3 # for goedesicw only
235 _INVERSE3 = AZIMUTH | DISTANCE | _CAP_1 # for goedesicw only
236 _STD = STANDARD | _CAP_3 | _CAP_1 # for goedesicw only
237 _STD_LINE = _STD | _CAP_2 | _CAP_1p # for goedesici/-w
239 LINE_CAPS = _STD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only
241 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb
242 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position
243 REVERSE2 = 1 << 17 # reverse C{azi2}
245 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
246 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
248 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
249 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
251 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only
252 _S_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 | _ANGLE_ONLY | _S_CALPs_
261 _OUT_ALL = ALL
262 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
264 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
265 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
266# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline
267 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL
268 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
269# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
271 def toStr(self, Csk, sep=_BAR_):
272 '''Return a C{Caps} or C{outmask} as C{str} or tuple of C{str}s.
273 '''
274 s = []
275 for c, C in itemsorted(self.__class__.__dict__):
276 if isint(C) and (Csk & C) and int1s(C) == 1 \
277 and (C in (Caps.REVERSE2, Caps._S_CALPs_)
278 or c.replace(_UNDER_, NN).isupper()):
279 s.append(c)
280 return sep.join(s) if sep else tuple(s)
282Caps = Caps() # PYCHOK singleton
283'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
284rhumb capabilities (C{caps}) and expected results (C{outmask}).
286C{AREA} - compute area C{S12},
288C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
290C{DISTANCE} - compute distance C{s12},
292C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
294C{EMPTY} - nothing, formerly aka C{NONE},
296C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
298C{LATITUDE} - compute latitude C{lat2},
300C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
302C{LONGITUDE} - compute longitude C{lon2},
304C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
306C{REDUCEDLENGTH} - compute reduced length C{m12},
308C{REVERSE2} - reverse C{azi2},
310and C{ALL} - all of the above.
312C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
314_KEY2Caps = dict(azi2=Caps.AZIMUTH, # see GDict._unCaps
315 lat2=Caps.LATITUDE,
316 lon2=Caps.LONGITUDE,
317 m12 =Caps.REDUCEDLENGTH,
318 M12 =Caps.GEODESICSCALE,
319 M21 =Caps.GEODESICSCALE,
320 s12 =Caps.DISTANCE,
321 S12 =Caps.AREA)
324class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
325 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
326 '''
327 ALL = Caps.ALL
328 AREA = Caps.AREA
329 AZIMUTH = Caps.AZIMUTH
330 DISTANCE = Caps.DISTANCE
331 DISTANCE_IN = Caps.DISTANCE_IN
332 EMPTY = Caps.EMPTY # aka NONE
333 GEODESICSCALE = Caps.GEODESICSCALE
334 LATITUDE = Caps.LATITUDE
335 LINE_CAPS = Caps.LINE_CAPS
336 LINE_OFF = Caps.LINE_OFF
337 LONGITUDE = Caps.LONGITUDE
338 LONG_UNROLL = Caps.LONG_UNROLL
339 REDUCEDLENGTH = Caps.REDUCEDLENGTH
340 STANDARD = Caps.STANDARD
341 _STD_LINE = Caps._STD_LINE # for geodesici
343 _caps = 0 # None
344 _debug = 0 # or Caps._DEBUG_...
346 @Property_RO
347 def caps(self):
348 '''Get the capabilities (bit-or'ed C{Caps}).
349 '''
350 return self._caps
352 def caps_(self, caps):
353 '''Check the available capabilities.
355 @arg caps: Bit-or'ed combination of L{Caps} values
356 for all capabilities to be checked.
358 @return: C{True} if I{all} B{C{caps}} are available,
359 C{False} otherwise (C{bool}).
360 '''
361 caps &= Caps._OUT_ALL
362 return (self.caps & caps) == caps
364 @property
365 def debug(self):
366 '''Get the C{debug} option (C{bool}).
367 '''
368 return bool(self._debug)
370 @debug.setter # PYCHOK setter!
371 def debug(self, debug):
372 '''Set the C{debug} option (C{bool}) to include
373 more details in L{GDict} results.
374 '''
375 self._debug = Caps._DEBUG_ALL if debug else 0
377 def _iter2tion(self, r, iter=None, **unused):
378 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
379 '''
380 if iter is not None:
381 self._iteration = r._iteration = iter
382 return r
385class Direct9Tuple(_GTuple):
386 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
387 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
388 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
389 C{meter} I{squared}.
390 '''
391 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
392 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
395class GDict(ADict): # XXX _NamedDict
396 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items.
398 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are
399 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}.
400 '''
401 def toDirect9Tuple(self, dflt=NAN):
402 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method
403 C{geographiclib.geodesic.Geodesic._GenDirect}.
405 @kwarg dflt: Default value for missing items (C{any}).
407 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
408 s12, m12, M12, M21, S12)}
409 '''
410 return self._toTuple(Direct9Tuple, dflt)
412 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
413 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
414 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
415 result.
417 @kwarg dflt: Default value for missing items (C{any}).
419 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
420 s12, a12, m12, M12, M21, S12)}.
421 '''
422 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
424 def toInverse10Tuple(self, dflt=NAN):
425 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
426 method C{geographiclib.geodesic.Geodesic._GenInverse}.
428 @kwarg dflt: Default value for missing items (C{any}).
430 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
431 salp2, calp2, m12, M12, M21, S12)}.
432 '''
433 return self._toTuple(Inverse10Tuple, dflt)
435 def _toNAN(self, outmask): # .GeodesicLineExact._GenPosition
436 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s.
437 '''
438 d = dict((n, NAN) for n in GeodSolve12Tuple._Names_)
439 return self.set_(**d)._unCaps(outmask)
441 @deprecated_method
442 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
443 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}.
445 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
446 '''
447 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt)
449 def toRhumb8Tuple(self, dflt=NAN):
450 '''Convert this L{GDict} result to a 8-tuple.
452 @kwarg dflt: Default value for missing items (C{any}).
454 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
455 azi12, s12, S12, a12)}.
456 '''
457 return self._toTuple(Rhumb8Tuple, dflt)
459 def toRhumbSolve7Tuple(self, dflt=NAN):
460 '''Convert this L{GDict} result to a 8-tuple.
462 @kwarg dflt: Default value for missing items (C{any}).
464 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
465 azi12, s12, S12)}.
466 '''
467 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt)
469 def _toTuple(self, nTuple, dflt):
470 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
471 '''
472 _g = getattr
473 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
474 return nTuple(t, iteration=self._iteration)
476 def _2X(self, gl, _2X=_X_): # .Intesectool, .Intersector
477 '''(INTERNAL) Rename attr tail from C{-2} to C{-X} or C{-M}.
478 '''
479 X = GDict(self)
480 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_):
481 if n in X: # X._X = X._2
482 X[n[:-1] + _2X] = X.pop(n)
483 v = getattr(gl, n, X)
484 if v is not X: # X._2 = gl._2
485 X[n] = v
486 return X
488 def _unCaps(self, outmask): # in .geodsolve
489 '''(INTERNAL) Remove superfluous items.
490 '''
491 for k, m in _KEY2Caps.items():
492 if k in self and not (outmask & m):
493 self.pop(k) # delattr(self, k)
494 return self
497class GeodSolve12Tuple(_GTuple):
498 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with
499 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in
500 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and
501 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic
502 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve
503 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}.
504 '''
505 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12
506 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_)
507 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2)
510class Inverse10Tuple(_GTuple):
511 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
512 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
513 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
514 C{calp2} of the initial C{1} and final C{2} (forward) azimuths.
515 '''
516 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
517 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
519 def toGDict(self, **updates):
520 '''Convert this C{Inverse10Tuple} to a L{GDict}.
522 @kwarg updates: Optional items to apply (C{nam=value} pairs)
523 '''
524 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK namedTuple
525 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
526 **updates) # PYCHOK indent
529class _kWrapped(object): # in .geodesicw
530 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
531 <https://PyPI.org/project/geographiclib>} classes.
532 '''
534 @Property_RO
535 def geographiclib(self):
536 '''Lazily import C{geographiclib}, provided the U{geographiclib
537 <https://PyPI.org/project/geographiclib>} package is installed,
538 otherwise raise a C{LazyImportError}.
539 '''
540 g = _xgeographiclib(self.__class__, 1, 49)
541 from geographiclib.geodesic import Geodesic
542 g.Geodesic = Geodesic
543 from geographiclib.geodesicline import GeodesicLine
544 g.GeodesicLine = GeodesicLine
545 from geographiclib.geomath import Math
546 g.Math = Math
547 return g
549 @Property_RO
550 def Math(self):
551 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
552 <https://PyPI.org/project/geographiclib>} package is installed,
553 otherwise C{None}.
554 '''
555 try:
556 g = self.geographiclib
557 M = g.Math
558 if _version_info(g) < (2,):
559 if _K_2_0:
560 M = None
561# elif not _K_2_0: # XXX set 2.0?
562# _K_2_0 = True
563 except (AttributeError, ImportError):
564 M = None
565 return M
567_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
570class Rhumb8Tuple(_GTuple):
571 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
572 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
573 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
574 line and the angular distance C{a12} between both points.
575 '''
576 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
577 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
579 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
580 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
581 method C{geographiclib.geodesic.Geodesic._GenDirect}.
583 @kwarg dflt: Default value for missing items (C{any}).
584 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
585 to specify or override L{Inverse10Tuple} items.
587 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
588 m12, M12, M21, S12)}
589 '''
590 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
591 azi2=self.azi12, M21=_1_0) # PYCHOK attr
592 if a12_azi1_azi2_m12_M12_M21:
593 d.update(a12_azi1_azi2_m12_M12_M21)
594 return self._toTuple(Direct9Tuple, dflt, d)
596 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
597 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
598 method C{geographiclib.geodesic.Geodesic._GenInverse}.
600 @kwarg dflt: Default value for missing items (C{any}).
601 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
602 arguments to specify or override L{Inverse10Tuple} items.
604 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
605 m12, M12, M21, S12)}.
606 '''
607 s, c = sincos2d(self.azi12) # PYCHOK attr
608 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
609 salp2=s, calp2=c, M21=_1_0)
610 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
611 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
612 return self._toTuple(Inverse10Tuple, dflt, d)
614 def _toTuple(self, nTuple, dflt, updates={}):
615 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
616 '''
617 _g = self.toGDict(**updates).get
618 t = tuple(_g(n, dflt) for n in nTuple._Names_)
619 return nTuple(t, name=self.name)
621 @deprecated_method
622 def _to7Tuple(self):
623 '''DEPRECATED, do not use!'''
624 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1])
627def _around(x): # in .utily.sincos2d
628 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
630 @return: Coarsened value (C{float}).
632 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
633 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
634 '''
635 try:
636 return _wrapped.Math.AngRound(x)
637 except AttributeError:
638 if x:
639 y = _1_16th - fabs(x)
640 if y > 0: # fabs(x) < _1_16th
641 x = _copysign(_1_16th - y, x)
642 else:
643 x = _0_0 # -0 to 0
644 return x
647def _atan2d(y, x):
648 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
649 '''
650 try:
651 return _wrapped.Math.atan2d(y, x)
652 except AttributeError:
653 return atan2d(y, x)
656def _cbrt(x):
657 '''Return C{cubic root(B{x})}.
658 '''
659 try:
660 return _wrapped.Math.cbrt(x)
661 except AttributeError:
662 return cbrt(x)
665def _copyBit(x, y):
666 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
667 '''
668 return (-x) if _signBit(y) else x
671def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
672 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
673 '''
674 r = cx - sx
675 if r:
676 r *= (cx + sx) * _2_0
677 return r
680def _diff182(deg0, deg, K_2_0=False):
681 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
683 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
684 '''
685 try:
686 return _wrapped.Math.AngDiff(deg0, deg)
687 except AttributeError:
688 if K_2_0 or _K_2_0: # geographiclib 2.0
689 _r, _360 = fremainder, _360_0
690 d, t = _sum2(_r(-deg0, _360),
691 _r( deg, _360))
692 d, t = _sum2(_r( d, _360), t)
693 if d in (_0_0, _180_0, _N_180_0):
694 d = _copysign(d, -t if t else (deg - deg0))
695 else:
696 _n = _norm180
697 d, t = _sum2(_n(-deg0), _n(deg))
698 d = _n(d)
699 if t > 0 and d == _180_0:
700 d = _N_180_0
701 d, t = _sum2(d, t)
702 return d, t
705def _fix90(deg): # mimick Math.LatFix
706 '''Replace angle in C{degrees} outside [-90,90] by NAN.
708 @return: Angle C{degrees} or NAN.
709 '''
710 try:
711 return _wrapped.Math.LatFix(deg)
712 except AttributeError:
713 return NAN if fabs(deg) > 90 else deg
716def _isfinite(x): # mimick geomath.Math.isfinite
717 '''Check finiteness of C{x}.
719 @return: C{True} if finite.
720 '''
721 try:
722 return _wrapped.Math.isfinite(x)
723 except AttributeError:
724 return _math_isfinite(x) # and fabs(x) <= _MAX
727def _llz2line(line, **llz2):
728 '''(INTERNAL) Set C{line.lat2, .lon2, .azi2} from C{llz2}.
729 '''
730 if llz2:
731 llz2 = _xkwds_not(None, **_xkwds_kwds(llz2, lat2=None, lon2=None, azi2=None))
732 if llz2:
733 line.__dict__.update(llz2)
734 return line
737def _norm2(x, y): # mimick geomath.Math.norm
738 '''Normalize C{B{x}} and C{B{y}}.
740 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
741 '''
742 try:
743 return _wrapped.Math.norm(x, y)
744 except AttributeError:
745 return norm2(x, y)
748def _norm180(deg): # mimick geomath.Math.AngNormalize
749 '''Reduce angle in C{degrees} to (-180,180].
751 @return: Reduced angle C{degrees}.
752 '''
753 try:
754 return _wrapped.Math.AngNormalize(deg)
755 except AttributeError:
756 d = fremainder(deg, _360_0)
757 if d in (_180_0, _N_180_0):
758 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
759 return d
762def _polygon(geodesic, points, closed, line, wrap):
763 '''(INTERNAL) Compute the area or perimeter of a polygon,
764 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
765 C{geographiclib} package is installed) a C{Geodesic}
766 or C{geodesicw.Geodesic} instance.
767 '''
768 if not wrap: # capability LONG_UNROLL can't be off
769 notImplemented(None, wrap=wrap, up=3)
771 if _MODS.booleans.isBoolean(points):
772 # recursive call for each boolean clip
774 def _a_p(clip, *args, **unused):
775 return _polygon(geodesic, clip, *args)
777 if not closed: # closed only
778 raise _ValueError(closed=closed, points=_composite_)
780 return points._sum1(_a_p, closed, line, wrap)
782 gP = geodesic.Polygon(line)
783 _A = gP.AddPoint
785 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
786 p1 = p0 = Ps[0]
788 # note, lon deltas are unrolled, by default
789 _A(p1.lat, p1.lon)
790 for p2 in Ps.iterate(closed=closed):
791 if wrap and not Ps.looped:
792 p2 = _unrollon(p1, p2)
793 _A(p2.lat, p2.lon)
794 p1 = p2
795 if closed and line and p1 != p0:
796 _A(p0.lat, p0.lon)
798 # gP.Compute returns (number_of_points, perimeter, signed area)
799 return gP.Compute(False, True)[1 if line else 2]
802def _polynomial(x, cs, i, j): # PYCHOK shared
803 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
804 different signature and cascaded summation as C{karney._sum2_}.
806 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
807 '''
808 # assert 0 <= i <= j <= len(cs)
809# try:
810# return _wrapped.Math.polyval(j - i - 1, cs, i, x)
811# except AttributeError:
812# s, t = cs[i], _0_0
813# for c in cs[i+1:j]:
814# s, t = _sum2_(s * x, t * x, c)
815# return s # + t
816 s = cs[i]
817 i += 1
818 if x and i < j:
819 s, _ = _sum2_(s, _0_0, x=x, *cs[i:j])
820 return s # + t
823def _remainder(x, y):
824 '''Remainder of C{x / y}.
826 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
827 '''
828 try:
829 return _wrapped.Math.remainder(x, y)
830 except AttributeError:
831 return fremainder(x, y)
834if _K_2_0:
835 from math import cos as _cos, sin as _sin
837 def _sincos2(rad):
838 return _sin(rad), _cos(rad)
840 _signBit = _MODS.basics.signBit
841else:
842 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
844 def _signBit(x):
845 '''(INTERNAL) GeographicLib 1.52-.
846 '''
847 return x < 0
850def _sincos2d(deg):
851 '''Return sine and cosine of an angle in C{degrees}.
853 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
854 '''
855 try:
856 return _wrapped.Math.sincosd(deg)
857 except AttributeError:
858 return sincos2d(deg)
861def _sincos2de(deg, t):
862 '''Return sine and cosine of a corrected angle in C{degrees}.
864 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
865 '''
866 try:
867 return _wrapped.Math.sincosde(deg, t)
868 except AttributeError:
869 return sincos2d(deg, adeg=t)
872def _sum2(u, v): # mimick geomath.Math.sum, actually sum2
873 '''Error-free summation like C{geomath.Math.sum}.
875 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
877 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
879 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
880 '''
881 try:
882 return _wrapped.Math.sum(u, v)
883 except AttributeError:
884 s = u + v
885 r = s - v
886 t = s - r
887 # if Algorithm_3_1:
888 # t = (u - t) + (v + r)
889 # elif C_CPP: # Math::sum C/C++
890 # r -= u
891 # t -= v
892 # t += r
893 # t = -t
894 # else:
895 t = (u - r) + (v - t)
896 return s, t
899def _sum2_(s, t, *vs, **x):
900 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
902 @kwarg x: Optional polynomial C{B{x}=1} (C{scalar}).
904 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
906 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
907 C++/doc/Accumulator_8hpp_source.html>} comments for more details and
908 function C{_sum2} above.
910 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
911 '''
912 x = _xkwds_get1(x, x=_1_0)
913 p = x != _1_0
915 _s2, _u0 = _sum2, unsigned0
916 for v in vs:
917 if p:
918 s *= x
919 t *= x
920 if v:
921 t, u = _s2(t, v) # start at the least-
922 if s:
923 s, t = _s2(s, t) # significant end
924 if s:
925 t += u # accumulate u into t
926# elif t: # s == 0 implies t == 0
927# raise _AssertionError(t=t, txt_not_=_0_)
928 else:
929 s = _u0(u) # result is u, t = 0
930 else:
931 s, t = _u0(t), u
932 return s, t
935def _tand(x):
936 '''Return C{tan(B{x})} in C{degrees}.
937 '''
938 try:
939 return _wrapped.Math.tand(x)
940 except AttributeError:
941 return tand(x)
944def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
945 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
947 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
948 unrolled if C{B{wrap} is True}, normalized otherwise.
949 '''
950 if wrap:
951 d, t = _diff182(lon1, lon2)
952 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
953 else:
954 lon2 = _norm180(lon2)
955 return (lon2 - lon1), lon2
958def _unsigned2(x):
959 '''(INTERNAL) Unsign B{C{x}}.
960 '''
961 return (neg(x), True) if _signBit(x) else (x, False)
964__all__ += _ALL_DOCS(_CapsBase)
966# **) MIT License
967#
968# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
969#
970# Permission is hereby granted, free of charge, to any person obtaining a
971# copy of this software and associated documentation files (the "Software"),
972# to deal in the Software without restriction, including without limitation
973# the rights to use, copy, modify, merge, publish, distribute, sublicense,
974# and/or sell copies of the Software, and to permit persons to whom the
975# Software is furnished to do so, subject to the following conditions:
976#
977# The above copyright notice and this permission notice shall be included
978# in all copies or substantial portions of the Software.
979#
980# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
981# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
982# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
983# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
984# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
985# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
986# OTHER DEALINGS IN THE SOFTWARE.