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, neg, unsigned0, \
143 _xgeographiclib, _xImportError, _xversion_info, \
144 _xinstanceof, _zip, isodd # PYCHOK shared
145from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \
146 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0
147from pygeodesy.errors import GeodesicError, itemsorted, _ValueError, _xkwds, \
148 _xkwds_get
149from pygeodesy.fmath import cbrt, fremainder, hypot as _hypot, norm2, \
150 euclid, Fsum, unstr # PYCHOK shared
151# from pygeodesy.fsums import Fsum # from .fmath
152from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi2_, _azi12_, \
153 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \
154 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \
155 _UNDER_, _BAR_ # PYCHOK used!
156from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
157from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass
158from pygeodesy.props import deprecated_method, Property_RO, property_RO # PYCHOK shared
159# from pygeodesy.streps import unstr # from .fmath
160from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \
161 Meter as _M, Meter2 as _M2, Number_, \
162 Precision_, _1mm as _TOL_M # PYCHOK shared
163from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
165# from math import fabs # from .utily
167__all__ = _ALL_LAZY.karney
168__version__ = '23.12.18'
170_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
171_perimeter_ = 'perimeter'
174class _GTuple(_NamedTuple): # in .testNamedTuples
175 '''(INTERNAL) Helper.
176 '''
177 def toGDict(self, **updates):
178 '''Convert this C{*Tuple} to a L{GDict}.
180 @kwarg updates: Optional items to apply (C{nam=value} pairs)
181 '''
182 r = GDict(_zip(self._Names_, self)) # strict=True
183 if updates:
184 r.update(updates)
185 if self._iteration is not None:
186 r._iteration = self._iteration
187 return r
190class _Lat(Lat):
191 '''(INTERNAL) Latitude B{C{lat}}.
192 '''
193 def __init__(self, *lat, **Error_name):
194 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
195 Lat.__new__(_Lat, *lat, **kwds)
198class _Lon(Lon):
199 '''(INTERNAL) Longitude B{C{lon}}.
200 '''
201 def __init__(self, *lon, **Error_name):
202 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
203 Lon.__new__(_Lon, *lon, **kwds)
206class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
207 '''3-Tuple C{(number, perimeter, area)} with the C{number}
208 of points of the polygon or polyline, the C{perimeter} in
209 C{meter} and the C{area} in C{meter} I{squared}.
210 '''
211 _Names_ = (_number_, _perimeter_, _area_)
212 _Units_ = ( Number_, _M, _M2)
215class Caps(object): # PYCHOK
216 '''(INTERNAL) Overriden by C{Caps} below.
217 '''
218 EMPTY = 0 # formerly aka NONE
219 _CAP_1 = 1 << 0 # for goedesicw only
220 _CAP_1p = 1 << 1 # for goedesicw only
221# _CAP_2 = 1 << 2
222 _CAP_3 = 1 << 3 # for goedesicw only
223# _CAP_4 = 1 << 4
224# _CAP_ALL = 0x1F
225# _CAP_MASK = _CAP_ALL
226 LATITUDE = 1 << 7 # compute latitude C{lat2}
227 LONGITUDE = 1 << 8 # compute longitude C{lon2} _CAP_3
228 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
229 DISTANCE = 1 << 10 # compute distance C{s12} _CAP_1
230 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct _CAP_1 | _CAP_1p
231 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} _CAP_1 | _CAP_2
232 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} _CAP_1 | _CAP_2
233 AREA = 1 << 14 # compute area C{S12} _CAP_4
235 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE
236 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
238 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE | _CAP_3 # for goedesicw only
239 _INVERSE3 = AZIMUTH | DISTANCE | _CAP_1 # for goedesicw only
240 _STD = STANDARD | _CAP_3 | _CAP_1 # for goedesicw only
241 _STD_LINE = _STD | _CAP_1p # for goedesicw only
243 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb
244 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position
245 REVERSE2 = 1 << 17 # reverse C{azi2}
247 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
248 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
250 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
251 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
253 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only
254 _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
256 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
257 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
258 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
259 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
260 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
261 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs
263 _OUT_ALL = ALL
264 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
266 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
267 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
268# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline
269 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL
270 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
271# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
273 def toStr(self, Csk, sep=_BAR_):
274 '''Return a C{Caps} or C{outmask} as C{str} or tuple of C{str}s.
275 '''
276 s = []
277 for c, C in itemsorted(self.__class__.__dict__):
278 if isint(C) and (Csk & C) and int1s(C) == 1 \
279 and (C in (Caps.REVERSE2, Caps._SALPs_CALPs)
280 or c.replace(_UNDER_, NN).isupper()):
281 s.append(c)
282 return sep.join(s) if sep else tuple(s)
284Caps = Caps() # PYCHOK singleton
285'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
286rhumb capabilities (C{caps}) and expected results (C{outmask}).
288C{AREA} - compute area C{S12},
290C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
292C{DISTANCE} - compute distance C{s12},
294C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
296C{EMPTY} - nothing, formerly aka C{NONE},
298C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
300C{LATITUDE} - compute latitude C{lat2},
302C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
304C{LONGITUDE} - compute longitude C{lon2},
306C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
308C{REDUCEDLENGTH} - compute reduced length C{m12},
310C{REVERSE2} - reverse C{azi2},
312and C{ALL} - all of the above.
314C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
317class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
318 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
319 '''
320 ALL = Caps.ALL
321 AREA = Caps.AREA
322 AZIMUTH = Caps.AZIMUTH
323 DISTANCE = Caps.DISTANCE
324 DISTANCE_IN = Caps.DISTANCE_IN
325 EMPTY = Caps.EMPTY # aka NONE
326 GEODESICSCALE = Caps.GEODESICSCALE
327 LATITUDE = Caps.LATITUDE
328 LINE_OFF = Caps.LINE_OFF
329 LONGITUDE = Caps.LONGITUDE
330 LONG_UNROLL = Caps.LONG_UNROLL
331 REDUCEDLENGTH = Caps.REDUCEDLENGTH
332 STANDARD = Caps.STANDARD
334 _caps = 0 # None
335 _debug = 0 # or Caps._DEBUG_...
337 @Property_RO
338 def caps(self):
339 '''Get the capabilities (bit-or'ed C{Caps}).
340 '''
341 return self._caps
343 def caps_(self, caps):
344 '''Check the available capabilities.
346 @arg caps: Bit-or'ed combination of L{Caps} values
347 for all capabilities to be checked.
349 @return: C{True} if I{all} B{C{caps}} are available,
350 C{False} otherwise (C{bool}).
351 '''
352 caps &= Caps._OUT_ALL
353 return (self.caps & caps) == caps
355 @property
356 def debug(self):
357 '''Get the C{debug} option (C{bool}).
358 '''
359 return bool(self._debug)
361 @debug.setter # PYCHOK setter!
362 def debug(self, debug):
363 '''Set the C{debug} option (C{bool}) to include
364 more details in L{GDict} results.
365 '''
366 self._debug = Caps._DEBUG_ALL if debug else 0
368 def _iter2tion(self, r, s):
369 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
370 '''
371 i = _xkwds_get(s, iter=None)
372 if i is not None:
373 self._iteration = r._iteration = i
374 return r
377class Direct9Tuple(_GTuple):
378 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
379 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
380 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
381 C{meter} I{squared}.
382 '''
383 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
384 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
387class GDict(_Dict): # XXX _NamedDict
388 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items.
390 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are
391 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}.
392 '''
393 def toDirect9Tuple(self, dflt=NAN):
394 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method
395 C{geographiclib.geodesic.Geodesic._GenDirect}.
397 @kwarg dflt: Default value for missing items (C{any}).
399 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
400 s12, m12, M12, M21, S12)}
401 '''
402 return self._toTuple(Direct9Tuple, dflt)
404 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
405 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
406 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
407 result.
409 @kwarg dflt: Default value for missing items (C{any}).
411 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
412 s12, a12, m12, M12, M21, S12)}.
413 '''
414 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
416 def toInverse10Tuple(self, dflt=NAN):
417 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
418 method C{geographiclib.geodesic.Geodesic._GenInverse}.
420 @kwarg dflt: Default value for missing items (C{any}).
422 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
423 salp2, calp2, m12, M12, M21, S12)}.
424 '''
425 return self._toTuple(Inverse10Tuple, dflt)
427 @deprecated_method
428 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
429 '''DEPRECATED, used method C{toRhumb8Tuple}.
431 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
432 '''
433 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt)
435 def toRhumb8Tuple(self, dflt=NAN):
436 '''Convert this L{GDict} result to a 8-tuple.
438 @kwarg dflt: Default value for missing items (C{any}).
440 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
441 azi12, s12, S12, a12)}.
442 '''
443 return self._toTuple(Rhumb8Tuple, dflt)
445 def toRhumbSolve7Tuple(self, dflt=NAN):
446 '''Convert this L{GDict} result to a 8-tuple.
448 @kwarg dflt: Default value for missing items (C{any}).
450 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
451 azi12, s12, S12)}.
452 '''
453 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt)
455 def _toTuple(self, nTuple, dflt):
456 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
457 '''
458 _g = getattr
459 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
460 return nTuple(t, iteration=self._iteration)
463class Inverse10Tuple(_GTuple):
464 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
465 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
466 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
467 C{calp2} of the initial C{1} and final C{2} (forward) azimuths.
468 '''
469 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
470 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
472 def toGDict(self, **updates):
473 '''Convert this C{Inverse10Tuple} to a L{GDict}.
475 @kwarg updates: Optional items to apply (C{nam=value} pairs)
476 '''
477 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple
478 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
479 **updates) # PYCHOK indent
482class _kWrapped(object): # in .geodesicw
483 ''''(INTERNAL) Wrapper around I{Karney}'s U{geographiclib
484 <https://PyPI.org/project/geographiclib>}.
485 '''
487 @Property_RO
488 def geographiclib(self):
489 '''Lazily import C{geographiclib}, provided the U{geographiclib
490 <https://PyPI.org/project/geographiclib>} package is installed,
491 otherwise a C{LazyImportError}.
492 '''
493 g = _xgeographiclib(self.__class__, 1, 49)
494 from geographiclib.geodesic import Geodesic
495 g.Geodesic = Geodesic
496 from geographiclib.geodesicline import GeodesicLine
497 g.GeodesicLine = GeodesicLine
498 from geographiclib.geomath import Math
499 g.Math = Math
500 return g
502 @Property_RO
503 def Math(self):
504 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
505 <https://PyPI.org/project/geographiclib>} package is installed,
506 otherwise C{None}.
507 '''
508 try:
509 g = self.geographiclib
510 M = g.Math
511 if _xversion_info(g) < (2,):
512 if _K_2_0:
513 M = None
514# elif not _K_2_0: # XXX set 2.0?
515# _K_2_0 = True
516 except (AttributeError, ImportError):
517 M = None
518 return M
520_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
523class Rhumb8Tuple(_GTuple):
524 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
525 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
526 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
527 line and the angular distance C{a12} between both points.
528 '''
529 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
530 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
532 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
533 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
534 method C{geographiclib.geodesic.Geodesic._GenDirect}.
536 @kwarg dflt: Default value for missing items (C{any}).
537 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
538 to specify or override L{Inverse10Tuple} items.
540 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
541 m12, M12, M21, S12)}
542 '''
543 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
544 azi2=self.azi12, M21=_1_0) # PYCHOK attr
545 if a12_azi1_azi2_m12_M12_M21:
546 d.update(a12_azi1_azi2_m12_M12_M21)
547 return self._toTuple(Direct9Tuple, dflt, d)
549 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
550 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
551 method C{geographiclib.geodesic.Geodesic._GenInverse}.
553 @kwarg dflt: Default value for missing items (C{any}).
554 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
555 arguments to specify or override L{Inverse10Tuple} items.
557 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
558 m12, M12, M21, S12)}.
559 '''
560 s, c = sincos2d(self.azi12) # PYCHOK attr
561 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
562 salp2=s, calp2=c, M21=_1_0)
563 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
564 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
565 return self._toTuple(Inverse10Tuple, dflt, d)
567 def _toTuple(self, nTuple, dflt, updates={}):
568 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
569 '''
570 _g = self.toGDict(**updates).get
571 t = tuple(_g(n, dflt) for n in nTuple._Names_)
572 return nTuple(t, name=self.name)
574 @deprecated_method
575 def _to7Tuple(self):
576 '''DEPRECATED, do not use!'''
577 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1])
580def _around(x): # in .utily.sincos2d
581 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
583 @return: Coarsened value (C{float}).
585 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
586 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
587 '''
588 try:
589 return _wrapped.Math.AngRound(x)
590 except AttributeError:
591 if x:
592 y = _1_16th - fabs(x)
593 if y > 0: # fabs(x) < _1_16th
594 x = _copysign(_1_16th - y, x)
595 else:
596 x = _0_0 # -0 to 0
597 return x
600def _atan2d(y, x):
601 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
602 '''
603 try:
604 return _wrapped.Math.atan2d(y, x)
605 except AttributeError:
606 return atan2d(y, x)
609def _cbrt(x):
610 '''Return C{cubic root(B{x})}.
611 '''
612 try:
613 return _wrapped.Math.cbrt(x)
614 except AttributeError:
615 return cbrt(x)
618def _copyBit(x, y):
619 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
620 '''
621 return (-x) if _signBit(y) else x
624def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
625 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
626 '''
627 r = cx - sx
628 if r:
629 r *= (cx + sx) * _2_0
630 return r
633def _diff182(deg0, deg, K_2_0=False):
634 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
636 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
637 '''
638 try:
639 return _wrapped.Math.AngDiff(deg0, deg)
640 except AttributeError:
641 if K_2_0 or _K_2_0: # geographiclib 2.0
642 _r, _360 = fremainder, _360_0
643 d, t = _sum2(_r(-deg0, _360),
644 _r( deg, _360))
645 d, t = _sum2(_r( d, _360), t)
646 if d in (_0_0, _180_0, _N_180_0):
647 d = _copysign(d, -t if t else (deg - deg0))
648 else:
649 _n = _norm180
650 d, t = _sum2(_n(-deg0), _n(deg))
651 d = _n(d)
652 if t > 0 and d == _180_0:
653 d = _N_180_0
654 d, t = _sum2(d, t)
655 return d, t
658def _fix90(deg): # mimick Math.LatFix
659 '''Replace angle in C{degrees} outside [-90,90] by NAN.
661 @return: Angle C{degrees} or NAN.
662 '''
663 try:
664 return _wrapped.Math.LatFix(deg)
665 except AttributeError:
666 return NAN if fabs(deg) > 90 else deg
669def _isfinite(x): # mimick geomath.Math.isfinite
670 '''Check finiteness of C{x}.
672 @return: C{True} if finite.
673 '''
674 try:
675 return _wrapped.Math.isfinite(x)
676 except AttributeError:
677 return _math_isfinite(x) # and fabs(x) <= _MAX
680def _norm2(x, y): # mimick geomath.Math.norm
681 '''Normalize C{B{x}} and C{B{y}}.
683 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
684 '''
685 try:
686 return _wrapped.Math.norm(x, y)
687 except AttributeError:
688 return norm2(x, y)
691def _norm180(deg): # mimick geomath.Math.AngNormalize
692 '''Reduce angle in C{degrees} to (-180,180].
694 @return: Reduced angle C{degrees}.
695 '''
696 try:
697 return _wrapped.Math.AngNormalize(deg)
698 except AttributeError:
699 d = fremainder(deg, _360_0)
700 if d in (_180_0, _N_180_0):
701 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
702 return d
705def _polygon(geodesic, points, closed, line, wrap):
706 '''(INTERNAL) Compute the area or perimeter of a polygon,
707 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
708 C{geographiclib} package is installed) a C{Geodesic}
709 or C{geodesicw.Geodesic} instance.
710 '''
711 if not wrap: # capability LONG_UNROLL can't be off
712 notImplemented(None, wrap=wrap, up=3)
714 if _MODS.booleans.isBoolean(points):
715 # recursive call for each boolean clip
717 def _a_p(clip, *args, **unused):
718 return _polygon(geodesic, clip, *args)
720 if not closed: # closed only
721 raise _ValueError(closed=closed, points=_composite_)
723 return points._sum1(_a_p, closed, line, wrap)
725 gP = geodesic.Polygon(line)
726 _A = gP.AddPoint
728 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
729 p1 = p0 = Ps[0]
731 # note, lon deltas are unrolled, by default
732 _A(p1.lat, p1.lon)
733 for p2 in Ps.iterate(closed=closed):
734 if wrap and not Ps.looped:
735 p2 = _unrollon(p1, p2)
736 _A(p2.lat, p2.lon)
737 p1 = p2
738 if closed and line and p1 != p0:
739 _A(p0.lat, p0.lon)
741 # gP.Compute returns (number_of_points, perimeter, signed area)
742 return gP.Compute(False, True)[1 if line else 2]
745def _polynomial(x, cs, i, j): # PYCHOK shared
746 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
747 different signature and cascaded summation as C{karney._sum2_}.
749 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
750 '''
751 # assert 0 <= i <= j <= len(cs)
752# try:
753# return _wrapped.Math.polyval(j - i - 1, cs, i, x)
754# except AttributeError:
755# s, t = cs[i], _0_0
756# for c in cs[i+1:j]:
757# s, t = _sum2_(s * x, t * x, c)
758# return s # + t
759 s, _ = _sum2_(cs[i], _0_0, x=x, *cs[i+1:j])
760 return s # + t
763def _remainder(x, y):
764 '''Remainder of C{x / y}.
766 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
767 '''
768 try:
769 return _wrapped.Math.remainder(x, y)
770 except AttributeError:
771 return fremainder(x, y)
774if _K_2_0:
775 from math import cos as _cos, sin as _sin
777 def _sincos2(rad):
778 return _sin(rad), _cos(rad)
780 _signBit = _MODS.basics.signBit
781else:
782 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
784 def _signBit(x):
785 '''(INTERNAL) GeographicLib 1.52-.
786 '''
787 return x < 0
790def _sincos2d(deg):
791 '''Return sine and cosine of an angle in C{degrees}.
793 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
794 '''
795 try:
796 return _wrapped.Math.sincosd(deg)
797 except AttributeError:
798 return sincos2d(deg)
801def _sincos2de(deg, t):
802 '''Return sine and cosine of a corrected angle in C{degrees}.
804 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
805 '''
806 try:
807 return _wrapped.Math.sincosde(deg, t)
808 except AttributeError:
809 return sincos2d(deg, adeg=t)
812def _sum2(u, v): # mimick geomath.Math.sum, actually sum2
813 '''Error-free summation like C{geomath.Math.sum}.
815 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
817 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
819 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
820 '''
821 try:
822 return _wrapped.Math.sum(u, v)
823 except AttributeError:
824 s = u + v
825 r = s - v
826 t = s - r
827 # if Algorithm_3_1:
828 # t = (u - t) + (v + r)
829 # elif C_CPP: # Math::sum C/C++
830 # r -= u
831 # t -= v
832 # t += r
833 # t = -t
834 # else:
835 t = (u - r) + (v - t)
836 return s, t
839def _sum2_(s, t, *vs, **x):
840 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
842 @kwarg x: Optional polynomial C{B{x}=1} (C{scalar}).
844 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
846 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
847 html/Accumulator_8hpp_source.html>} comments for more details and
848 function C{_sum2} above.
850 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
851 '''
852 x = _xkwds_get(x, x=0)
854 _s2, _u0 = _sum2, unsigned0
855 for v in vs:
856 if x:
857 s *= x
858 t *= x
859 if v:
860 t, u = _s2(t, v) # start at the least-
861 if s:
862 s, t = _s2(s, t) # significant end
863 if s:
864 t += u # accumulate u into t
865# elif t: # s == 0 implies t == 0
866# raise _AssertionError(t=t, txt=_not_(_0_))
867 else:
868 s = _u0(u) # result is u, t = 0
869 else:
870 s, t = _u0(t), u
871 return s, t
874def _tand(x):
875 '''Return C{tan(B{x})} in C{degrees}.
876 '''
877 try:
878 return _wrapped.Math.tand(x)
879 except AttributeError:
880 return tand(x)
883def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
884 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
886 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
887 unrolled if B{C{wrap}} is C{True}, normalized otherwise.
888 '''
889 if wrap:
890 d, t = _diff182(lon1, lon2)
891 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
892 else:
893 lon2 = _norm180(lon2)
894 return (lon2 - lon1), lon2
897def _unsigned2(x):
898 '''(INTERNAL) Unsign B{C{x}}.
899 '''
900 return (neg(x), True) if _signBit(x) else (x, False)
903__all__ += _ALL_DOCS(_CapsBase)
905# **) MIT License
906#
907# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
908#
909# Permission is hereby granted, free of charge, to any person obtaining a
910# copy of this software and associated documentation files (the "Software"),
911# to deal in the Software without restriction, including without limitation
912# the rights to use, copy, modify, merge, publish, distribute, sublicense,
913# and/or sell copies of the Software, and to permit persons to whom the
914# Software is furnished to do so, subject to the following conditions:
915#
916# The above copyright notice and this permission notice shall be included
917# in all copies or substantial portions of the Software.
918#
919# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
920# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
921# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
922# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
923# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
924# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
925# OTHER DEALINGS IN THE SOFTWARE.