Coverage for pygeodesy/karney.py: 94%
282 statements
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2# -*- coding: utf-8 -*-
4u'''Wrapper around several C{geomath.Math} functions from I{Karney}'s Python package
5U{geographiclib<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.
10With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module,
11L{pygeodesy.geodesicw} and L{pygeodesy.geodesicx} will use U{GeographicLib 2.0
12<https://GeographicLib.SourceForge.io/C++/doc/>} and newer transcoding, otherwise C{1.52}
13or 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{JacobiConformal} -- U{JacobiConformal
62 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1JacobiConformal.html#details>}
64 - L{KTransverseMercator} - U{TransverseMercator
65 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
67 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
68 classGeographicLib_1_1LocalCartesian.html>}
70 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}
72 - L{rhumbaux} C{RhumbAux}, C{RhumbLineAux} -- U{Rhumb
73 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine
74 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} in I{GeographicLib 2.2+}
76 - L{rhumbx} C{Rhumb}, C{RhumbLine} -- U{Rhumb
77 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},
78 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>},
79 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
80 in I{GeographicLib 2.0}
82 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>}
84 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}
86 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>}
88 - L{pygeodesy.atand}, L{pygeodesy.atan2d}, L{pygeodesy.sincos2}, L{pygeodesy.sincos2d}, L{pygeodesy.tand} -- U{geomath.Math
89 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}
91are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}.
932. These C{pygeodesy} modules and classes
95 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumbsolve}
96 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve},
97 L{GnomonicKarney}, L{HeightIDWkarney}
99are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>}
100C{geodesic}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or
101C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}.
1033. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations
105 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn},
106 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2},
107 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5}
109 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn},
110 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2},
111 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5}
113 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn},
114 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2},
115 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5}
117 - L{RhumbLineAux.intersection2} and L{RhumbLineAux.nearestOn4} C{(exact=None)} in L{rhumbaux} and
118 L{RhumbLine.intersection2} and L{RhumbLine.nearestOn4} C{(exact=None)} in L{rhumbx}
120are iterative implementations of I{Karney}'s solution posted here under U{The B{ellipsoidal} case
121<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics
122on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}).
1244. Spherical functions
126 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf}
128in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon
129<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer.
130'''
131# make sure int/int division yields float quotient, see .basics
132from __future__ import division as _; del _ # PYCHOK semicolon
134from pygeodesy.basics import _copysign, neg, unsigned0, _xgeographiclib, \
135 _xImportError, _xversion_info, _xinstanceof, \
136 _zip, isodd # PYCHOK shared
137from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, _1_16th, \
138 _1_0, _2_0, _180_0, _N_180_0, _360_0
139from pygeodesy.datums import _a_ellipsoid, _EWGS84, _WGS84 # PYCHOK shared
140# from pygeodesy.ellipsoids import _EWGS84 # from .datums
141from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get
142from pygeodesy.fmath import cbrt, fremainder, norm2, unstr, \
143 Fsum, hypot as _hypot # PYCHOK shared
144from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \
145 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, _M12_, _M21_, \
146 _number_, _s12_, _S12_
147from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
148from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass
149from pygeodesy.props import deprecated_method, Property_RO, property_RO
150# from pygeodesy.streps import unstr # from .fmath
151from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \
152 Meter as _M, Meter2 as _M2, Number_, \
153 Precision_, _1mm as _TOL_M # PYCHOK shared
154from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
156# from math import fabs # from .utily
158__all__ = _ALL_LAZY.karney
159__version__ = '23.08.20'
161_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
162_perimeter_ = 'perimeter'
165class _GTuple(_NamedTuple): # in .testNamedTuples
166 '''(INTERNAL) Helper.
167 '''
168 def toGDict(self, **updates):
169 '''Convert this C{*Tuple} to a L{GDict}.
171 @kwarg updates: Optional items to apply (C{nam=value} pairs)
172 '''
173 r = GDict(_zip(self._Names_, self)) # strict=True
174 if updates:
175 r.update(updates)
176 if self._iteration is not None:
177 r._iteration = self._iteration
178 return r
181class _Lat(Lat):
182 '''(INTERNAL) Latitude B{C{lat}}.
183 '''
184 def __init__(self, *lat, **Error_name):
185 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
186 Lat.__new__(_Lat, *lat, **kwds)
189class _Lon(Lon):
190 '''(INTERNAL) Longitude B{C{lon}}.
191 '''
192 def __init__(self, *lon, **Error_name):
193 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
194 Lon.__new__(_Lon, *lon, **kwds)
197class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
198 '''3-Tuple C{(number, perimeter, area)} with the C{number}
199 of points on the polygon or polyline, the C{perimeter} in
200 C{meter} and the C{area} in C{meter} I{squared}.
201 '''
202 _Names_ = (_number_, _perimeter_, _area_)
203 _Units_ = ( Number_, _M, _M2)
206class Caps(object): # PYCHOK
207 '''(INTERNAL) Overriden by C{Caps} below.
208 '''
209 EMPTY = 0 # formerly aka NONE
210 _CAP_1 = 1 << 0 # for goedesicw only
211 _CAP_1p = 1 << 1 # for goedesicw only
212# _CAP_2 = 1 << 2
213 _CAP_3 = 1 << 3 # for goedesicw only
214# _CAP_4 = 1 << 4
215# _CAP_ALL = 0x1F
216# _CAP_MASK = _CAP_ALL
217 LATITUDE = 1 << 7 # compute latitude C{lat2}
218 LONGITUDE = 1 << 8 # compute longitude C{lon2} _CAP_3
219 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
220 DISTANCE = 1 << 10 # compute distance C{s12} _CAP_1
221 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct _CAP_1 | _CAP_1p
222 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} _CAP_1 | _CAP_2
223 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} _CAP_1 | _CAP_2
224 AREA = 1 << 14 # compute area C{S12} _CAP_4
226 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE
227 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
229 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE | _CAP_3 # for goedesicw only
230 _INVERSE3 = AZIMUTH | DISTANCE | _CAP_1 # for goedesicw only
231 _STD = STANDARD | _CAP_3 | _CAP_1 # for goedesicw only
232 _STD_LINE = _STD | _CAP_1p # for goedesicw only
234 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb
235 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position
236 REVERSE2 = 1 << 17 # reverse C{azi2}
238 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
239 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
241 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
242 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
244 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only
245 _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
247 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
248 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
249 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
250 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
251 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
252 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs
253 _OUT_ALL = ALL
254 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
256 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
257 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
258 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK
259 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL
260 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
261# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
263Caps = Caps() # PYCHOK singleton
264'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
265rhumb capabilities (C{caps}) and expected results (C{outmask}).
267C{AREA} - compute area C{S12},
269C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
271C{DISTANCE} - compute distance C{s12},
273C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
275C{EMPTY} - nothing, formerly aka C{NONE},
277C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
279C{LATITUDE} - compute latitude C{lat2},
281C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
283C{LONGITUDE} - compute longitude C{lon2},
285C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
287C{REDUCEDLENGTH} - compute reduced length C{m12},
289C{REVERSE2} - reverse C{azi2},
291and C{ALL} - all of the above.
293C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
296class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
297 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
298 '''
299 ALL = Caps.ALL
300 AREA = Caps.AREA
301 AZIMUTH = Caps.AZIMUTH
302 DISTANCE = Caps.DISTANCE
303 DISTANCE_IN = Caps.DISTANCE_IN
304 EMPTY = Caps.EMPTY # aka NONE
305 GEODESICSCALE = Caps.GEODESICSCALE
306 LATITUDE = Caps.LATITUDE
307 LINE_OFF = Caps.LINE_OFF
308 LONGITUDE = Caps.LONGITUDE
309 LONG_UNROLL = Caps.LONG_UNROLL
310 REDUCEDLENGTH = Caps.REDUCEDLENGTH
311 STANDARD = Caps.STANDARD
313 _caps = 0 # None
314 _debug = 0 # or Caps._DEBUG_...
316 @Property_RO
317 def caps(self):
318 '''Get the capabilities (bit-or'ed C{Caps}).
319 '''
320 return self._caps
322 def caps_(self, caps):
323 '''Check the available capabilities.
325 @arg caps: Bit-or'ed combination of L{Caps} values
326 for all capabilities to be checked.
328 @return: C{True} if I{all} B{C{caps}} are available,
329 C{False} otherwise (C{bool}).
330 '''
331 caps &= Caps._OUT_ALL
332 return (self.caps & caps) == caps
334 @property
335 def debug(self):
336 '''Get the C{debug} option (C{bool}).
337 '''
338 return bool(self._debug)
340 @debug.setter # PYCHOK setter!
341 def debug(self, debug):
342 '''Set the C{debug} option (C{bool}) to include
343 more details in L{GDict} results.
344 '''
345 self._debug = Caps._DEBUG_ALL if debug else 0
347 def _iter2tion(self, r, s):
348 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
349 '''
350 i = _xkwds_get(s, iter=None)
351 if i is not None:
352 self._iteration = r._iteration = i
353 return r
356class Direct9Tuple(_GTuple):
357 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
358 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
359 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
360 C{meter} I{squared}.
361 '''
362 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
363 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
366class GDict(_Dict): # XXX _NamedDict
367 '''Basic C{dict} with both key I{and} attribute access
368 to the C{dict} items.
370 Results of all C{geodesic} methods are returned as a
371 L{GDict} instance.
372 '''
373 _iteration = None # Iteration number (C{int}) or C{None}
375 @property_RO
376 def iteration(self): # see .named._NamedBase
377 '''Get the iteration number (C{int}) or
378 C{None} if not available/applicable.
379 '''
380 return self._iteration
382 def toDirect9Tuple(self, dflt=NAN):
383 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s
384 method C{geographiclib.geodesic.Geodesic._GenDirect}.
386 @kwarg dflt: Default value for missing items (C{any}).
388 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
389 s12, m12, M12, M21, S12)}
390 '''
391 return self._toTuple(Direct9Tuple, dflt)
393 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
394 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
395 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
396 result.
398 @kwarg dflt: Default value for missing items (C{any}).
400 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
401 s12, a12, m12, M12, M21, S12)}.
402 '''
403 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
405 def toInverse10Tuple(self, dflt=NAN):
406 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
407 method C{geographiclib.geodesic.Geodesic._GenInverse}.
409 @kwarg dflt: Default value for missing items (C{any}).
411 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
412 salp2, calp2, m12, M12, M21, S12)}.
413 '''
414 return self._toTuple(Inverse10Tuple, dflt)
416 @deprecated_method
417 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
418 '''DEPRECATED, used method C{toRhumb8Tuple}.
420 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
421 '''
422 return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt)
424 def toRhumb8Tuple(self, dflt=NAN):
425 '''Convert this L{GDict} result to a 8-tuple.
427 @kwarg dflt: Default value for missing items (C{any}).
429 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
430 azi12, s12, S12, a12)}.
431 '''
432 return self._toTuple(Rhumb8Tuple, dflt)
434 def toRhumbSolve7Tuple(self, dflt=NAN):
435 '''Convert this L{GDict} result to a 8-tuple.
437 @kwarg dflt: Default value for missing items (C{any}).
439 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
440 azi12, s12, S12)}.
441 '''
442 return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt)
444 def _toTuple(self, nTuple, dflt):
445 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
446 '''
447 _g = getattr
448 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
449 return nTuple(t, iteration=self._iteration)
452class Inverse10Tuple(_GTuple):
453 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
454 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
455 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
456 C{calp2} of the initial C{1} and final C{2} foward azimuths.
457 '''
458 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
459 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
461 def toGDict(self, **updates):
462 '''Convert this C{Inverse10Tuple} to a L{GDict}.
464 @kwarg updates: Optional items to apply (C{nam=value} pairs)
465 '''
466 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple
467 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
468 **updates) # PYCHOK indent
471class _kWrapped(object): # in .geodesicw
472 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
473 <https://PyPI.org/project/geographiclib>} classes.
474 '''
476 @Property_RO
477 def geographiclib(self):
478 '''Get the imported C{geographiclib}, provided the U{geographiclib
479 <https://PyPI.org/project/geographiclib>} package is installed,
480 otherwise an C{ImportError}.
481 '''
482 g = _xgeographiclib(self.__class__, 1, 49)
483 from geographiclib.geodesic import Geodesic
484 g.Geodesic = Geodesic
485 from geographiclib.geodesicline import GeodesicLine
486 g.GeodesicLine = GeodesicLine
487 from geographiclib.geomath import Math
488 g.Math = Math
489 return g
491 @Property_RO # MCCABE 13
492 def Math(self):
493 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
494 <https://PyPI.org/project/geographiclib>} package is installed,
495 otherwise C{None}.
496 '''
497 try:
498 g = self.geographiclib
499 M = g.Math
500 if _xversion_info(g) < (2,):
501 if _K_2_0:
502 M = None
503# elif not _K_2_0: # XXX set 2.0?
504# _K_2_0 = True
505 except (AttributeError, ImportError):
506 M = None
507 return M
509_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
512class Rhumb8Tuple(_GTuple):
513 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
514 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
515 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
516 line and the angular distance C{a12} between both points.
517 '''
518 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
519 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
521 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
522 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
523 method C{geographiclib.geodesic.Geodesic._GenDirect}.
525 @kwarg dflt: Default value for missing items (C{any}).
526 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
527 to specify or override L{Inverse10Tuple} items.
529 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
530 m12, M12, M21, S12)}
531 '''
532 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
533 azi2=self.azi12, M21=_1_0) # PYCHOK attr
534 if a12_azi1_azi2_m12_M12_M21:
535 d.update(a12_azi1_azi2_m12_M12_M21)
536 return self._toTuple(Direct9Tuple, dflt, d)
538 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
539 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
540 method C{geographiclib.geodesic.Geodesic._GenInverse}.
542 @kwarg dflt: Default value for missing items (C{any}).
543 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
544 arguments to specify or override L{Inverse10Tuple} items.
546 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
547 m12, M12, M21, S12)}.
548 '''
549 s, c = sincos2d(self.azi12) # PYCHOK attr
550 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
551 salp2=s, calp2=c, M21=_1_0)
552 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
553 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
554 return self._toTuple(Inverse10Tuple, dflt, d)
556 def _toTuple(self, nTuple, dflt, updates={}):
557 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
558 '''
559 _g = self.toGDict(**updates).get
560 t = tuple(_g(n, dflt) for n in nTuple._Names_)
561 return nTuple(t, name=self.name)
563 @deprecated_method
564 def _to7Tuple(self):
565 '''DEPRECATED, do not use!'''
566 return _MODS.deprecated.Rhumb7Tuple(self[:-1])
569def _around(x): # in .utily.sincos2d
570 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
572 @return: Coarsened value (C{float}).
574 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
575 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
576 '''
577 try:
578 return _wrapped.Math.AngRound(x)
579 except AttributeError:
580 if x:
581 y = _1_16th - fabs(x)
582 if y > 0: # fabs(x) < _1_16th
583 x = _copysign(_1_16th - y, x)
584 else:
585 x = _0_0 # -0 to 0
586 return x
589def _atan2d(y, x):
590 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
591 '''
592 try:
593 return _wrapped.Math.atan2d(y, x)
594 except AttributeError:
595 return atan2d(y, x)
598def _cbrt(x):
599 '''Return C{cubic root(B{x})}.
600 '''
601 try:
602 return _wrapped.Math.cbrt(x)
603 except AttributeError:
604 return cbrt(x)
607def _copyBit(x, y):
608 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
609 '''
610 return (-x) if _signBit(y) else x
613def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
614 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
615 '''
616 r = cx - sx
617 if r:
618 r *= (cx + sx) * _2_0
619 return r
622def _diff182(deg0, deg, K_2_0=False):
623 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
625 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
626 '''
627 try:
628 return _wrapped.Math.AngDiff(deg0, deg)
629 except AttributeError:
630 if K_2_0 or _K_2_0: # geographiclib 2.0
631 _r, _360 = fremainder, _360_0
632 d, t = _sum2(_r(-deg0, _360),
633 _r( deg, _360))
634 d, t = _sum2(_r( d, _360), t)
635 if d in (_0_0, _180_0, _N_180_0):
636 d = _copysign(d, -t if t else (deg - deg0))
637 else:
638 _n = _norm180
639 d, t = _sum2(_n(-deg0), _n(deg))
640 d = _n(d)
641 if t > 0 and d == _180_0:
642 d = _N_180_0
643 d, t = _sum2(d, t)
644 return d, t
647def _fix90(deg): # mimick Math.LatFix
648 '''Replace angle in C{degrees} outside [-90,90] by NAN.
650 @return: Angle C{degrees} or NAN.
651 '''
652 try:
653 return _wrapped.Math.LatFix(deg)
654 except AttributeError:
655 return NAN if fabs(deg) > 90 else deg
658def _isfinite(x): # mimick geomath.Math.isfinite
659 '''Check finiteness of C{x}.
661 @return: C{True} if finite.
662 '''
663 try:
664 return _wrapped.Math.isfinite(x)
665 except AttributeError:
666 return _math_isfinite(x) # and fabs(x) <= _MAX
669def _norm2(x, y): # mimick geomath.Math.norm
670 '''Normalize C{B{x}} and C{B{y}}.
672 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
673 '''
674 try:
675 return _wrapped.Math.norm(x, y)
676 except AttributeError:
677 return norm2(x, y)
680def _norm180(deg): # mimick geomath.Math.AngNormalize
681 '''Reduce angle in C{degrees} to (-180,180].
683 @return: Reduced angle C{degrees}.
684 '''
685 try:
686 return _wrapped.Math.AngNormalize(deg)
687 except AttributeError:
688 d = fremainder(deg, _360_0)
689 if d in (_180_0, _N_180_0):
690 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
691 return d
694def _polygon(geodesic, points, closed, line, wrap):
695 '''(INTERNAL) Compute the area or perimeter of a polygon,
696 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
697 C{geographiclib} package is installed) a C{Geodesic}
698 or C{geodesicw.Geodesic} instance.
699 '''
700 if not wrap: # capability LONG_UNROLL can't be off
701 notImplemented(None, wrap=wrap, up=3)
703 if _MODS.booleans.isBoolean(points):
704 # recursive call for each boolean clip
706 def _a_p(clip, *args, **unused):
707 return _polygon(geodesic, clip, *args)
709 if not closed: # closed only
710 raise _ValueError(closed=closed, points=_composite_)
712 return points._sum1(_a_p, closed, line, wrap)
714 gP = geodesic.Polygon(line)
715 _A = gP.AddPoint
717 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
718 p1 = p0 = Ps[0]
720 # note, lon deltas are unrolled, by default
721 _A(p1.lat, p1.lon)
722 for p2 in Ps.iterate(closed=closed):
723 if wrap and not Ps.looped:
724 p2 = _unrollon(p1, p2)
725 _A(p2.lat, p2.lon)
726 p1 = p2
727 if closed and line and p1 != p0:
728 _A(p0.lat, p0.lon)
730 # gP.Compute returns (number_of_points, perimeter, signed area)
731 return gP.Compute(False, True)[1 if line else 2]
734def _polynomial(x, cs, i, j): # PYCHOK shared
735 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
736 different signature and cascaded summation as C{karney._sum2_}.
738 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
739 '''
740 # assert 0 <= i <= j <= len(cs)
741# try:
742# return _wrapped.Math.polyval(j - i - 1, cs, i, x)
743# except AttributeError:
744# pass
745 s, t = cs[i], _0_0
746 for c in cs[i+1:j]:
747 s, t = _sum2_(s * x, t * x, c)
748 return s # + t
751def _remainder(x, y):
752 '''Remainder of C{x / y}.
754 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
755 '''
756 try:
757 return _wrapped.Math.remainder(x, y)
758 except AttributeError:
759 return fremainder(x, y)
762if _K_2_0:
763 from math import cos as _cos, sin as _sin
765 def _sincos2(rad):
766 return _sin(rad), _cos(rad)
768 _signBit = _MODS.basics.signBit
769else:
770 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
772 def _signBit(x):
773 '''(INTERNAL) GeographicLib 1.52-.
774 '''
775 return x < 0
778def _sincos2d(deg):
779 '''Return sine and cosine of an angle in C{degrees}.
781 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
782 '''
783 try:
784 return _wrapped.Math.sincosd(deg)
785 except AttributeError:
786 return sincos2d(deg)
789def _sincos2de(deg, t):
790 '''Return sine and cosine of a corrected angle in C{degrees}.
792 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
793 '''
794 try:
795 return _wrapped.Math.sincosde(deg, t)
796 except AttributeError:
797 return sincos2d(deg, adeg=t)
800def _sum2(u, v): # mimick geomath.Math.sum, actually sum2
801 '''Error-free summation like C{geomath.Math.sum}.
803 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
805 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
807 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
808 '''
809 try:
810 return _wrapped.Math.sum(u, v)
811 except AttributeError:
812 s = u + v
813 r = s - v
814 t = s - r
815 # if Algorithm_3_1:
816 # t = (u - t) + (v + r)
817 # elif C_CPP: # Math::sum C/C++
818 # r -= u
819 # t -= v
820 # t += r
821 # t = -t
822 # else:
823 t = (u - r) + (v - t)
824 return s, t
827def _sum2_(s, t, *vs):
828 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
830 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
832 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
833 html/Accumulator_8hpp_source.html>} comments for more details and
834 function C{_sum2} above.
836 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
837 '''
838 _s2, _u0 = _sum2, unsigned0
839 for v in vs:
840 if v:
841 t, u = _s2(t, v) # start at the least-
842 if s:
843 s, t = _s2(s, t) # significant end
844 if s:
845 t += u # accumulate u into t
846# elif t: # s == 0 implies t == 0
847# raise _AssertionError(t=t, txt=_not_(_0_))
848 else:
849 s = _u0(u) # result is u, t = 0
850 else:
851 s, t = _u0(t), u
852 return s, t
855def _tand(x):
856 '''Return C{tan(B{x})} in C{degrees}.
857 '''
858 try:
859 return _wrapped.Math.tand(x)
860 except AttributeError:
861 return tand(x)
864def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
865 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
867 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
868 unrolled if B{C{wrap}} is C{True}, normalized otherwise.
869 '''
870 if wrap:
871 d, t = _diff182(lon1, lon2)
872 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
873 else:
874 lon2 = _norm180(lon2)
875 return (lon2 - lon1), lon2
878def _unsigned2(x):
879 '''(INTERNAL) Unsign B{C{x}}.
880 '''
881 return (neg(x), True) if _signBit(x) else (x, False)
884__all__ += _ALL_DOCS(_CapsBase)
886# **) MIT License
887#
888# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
889#
890# Permission is hereby granted, free of charge, to any person obtaining a
891# copy of this software and associated documentation files (the "Software"),
892# to deal in the Software without restriction, including without limitation
893# the rights to use, copy, modify, merge, publish, distribute, sublicense,
894# and/or sell copies of the Software, and to permit persons to whom the
895# Software is furnished to do so, subject to the following conditions:
896#
897# The above copyright notice and this permission notice shall be included
898# in all copies or substantial portions of the Software.
899#
900# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
901# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
902# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
903# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
904# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
905# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
906# OTHER DEALINGS IN THE SOFTWARE.