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
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_0, \
138 _1_16th, _180_0, _N_180_0, _360_0
139from pygeodesy.datums import _WGS84, _a_ellipsoid # PYCHOK shared
140from pygeodesy.errors import GeodesicError, _ValueError, _xkwds, _xkwds_get
141from pygeodesy.fmath import cbrt, fremainder, norm2, hypot as _hypot, unstr # PYCHOK shared
142from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \
143 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, _M12_, _M21_, \
144 _number_, _s12_, _S12_
145from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
146from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass
147from pygeodesy.props import deprecated_method, Property_RO, property_RO
148# from pygeodesy.streps import unstr # from .fmath
149from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \
150 Meter as _M, Meter2 as _M2, Number_, \
151 Precision_, _1mm as _TOL_M # PYCHOK shared
152from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
154# from math import fabs # from .utily
156__all__ = _ALL_LAZY.karney
157__version__ = '23.08.09'
159_EWGS84 = _WGS84.ellipsoid # PYCHOK in .auxilats, .geodesicx.gx, .ktm, .solveBase
160_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
161_perimeter_ = 'perimeter'
164class _GTuple(_NamedTuple): # in .testNamedTuples
165 '''(INTERNAL) Helper.
166 '''
167 def toGDict(self, **updates):
168 '''Convert this C{*Tuple} to a L{GDict}.
170 @kwarg updates: Optional items to apply (C{nam=value} pairs)
171 '''
172 r = GDict(_zip(self._Names_, self)) # strict=True
173 if updates:
174 r.update(updates)
175 if self._iteration is not None:
176 r._iteration = self._iteration
177 return r
180class _Lat(Lat):
181 '''(INTERNAL) Latitude B{C{lat}}.
182 '''
183 def __init__(self, *lat, **Error_name):
184 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
185 Lat.__new__(_Lat, *lat, **kwds)
188class _Lon(Lon):
189 '''(INTERNAL) Longitude B{C{lon}}.
190 '''
191 def __init__(self, *lon, **Error_name):
192 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
193 Lon.__new__(_Lon, *lon, **kwds)
196class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
197 '''3-Tuple C{(number, perimeter, area)} with the C{number}
198 of points on the polygon or polyline, the C{perimeter} in
199 C{meter} and the C{area} in C{meter} I{squared}.
200 '''
201 _Names_ = (_number_, _perimeter_, _area_)
202 _Units_ = ( Number_, _M, _M2)
205class Caps(object): # PYCHOK
206 '''(INTERNAL) Overriden by C{Caps} below.
207 '''
208 EMPTY = 0 # formerly aka NONE
209 _CAP_1 = 1 << 0 # for goedesicw only
210 _CAP_1p = 1 << 1 # for goedesicw only
211# _CAP_2 = 1 << 2
212 _CAP_3 = 1 << 3 # for goedesicw only
213# _CAP_4 = 1 << 4
214# _CAP_ALL = 0x1F
215# _CAP_MASK = _CAP_ALL
216 LATITUDE = 1 << 7 # compute latitude C{lat2}
217 LONGITUDE = 1 << 8 # compute longitude C{lon2} _CAP_3
218 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
219 DISTANCE = 1 << 10 # compute distance C{s12} _CAP_1
220 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct _CAP_1 | _CAP_1p
221 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} _CAP_1 | _CAP_2
222 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} _CAP_1 | _CAP_2
223 AREA = 1 << 14 # compute area C{S12} _CAP_4
225 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE
226 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
228 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE | _CAP_3 # for goedesicw only
229 _INVERSE3 = AZIMUTH | DISTANCE | _CAP_1 # for goedesicw only
230 _STD = STANDARD | _CAP_3 | _CAP_1 # for goedesicw only
231 _STD_LINE = _STD | _CAP_1p # for goedesicw only
233 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb
234 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position
235 REVERSE2 = 1 << 17 # reverse C{azi2}
237 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
238 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
240 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
241 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
243 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only
244 _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
246 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
247 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
248 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
249 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
250 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
251 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs
252 _OUT_ALL = ALL
253 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
255 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
256 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
257 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK
258 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL
259 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
260# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
262Caps = Caps() # PYCHOK singleton
263'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
264rhumb capabilities (C{caps}) and expected results (C{outmask}).
266C{AREA} - compute area C{S12},
268C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
270C{DISTANCE} - compute distance C{s12},
272C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
274C{EMPTY} - nothing, formerly aka C{NONE},
276C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
278C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
280C{LATITUDE} - compute latitude C{lat2},
282C{LONGITUDE} - compute longitude C{lon2},
284C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
286C{REDUCEDLENGTH} - compute reduced length C{m12},
288C{REVERSE2} - reverse C{azi2},
290and C{ALL} - all of the above.
292C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
295class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
296 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
297 '''
298 ALL = Caps.ALL
299 AREA = Caps.AREA
300 AZIMUTH = Caps.AZIMUTH
301 DISTANCE = Caps.DISTANCE
302 DISTANCE_IN = Caps.DISTANCE_IN
303 EMPTY = Caps.EMPTY # aka NONE
304 GEODESICSCALE = Caps.GEODESICSCALE
305 LATITUDE = Caps.LATITUDE
306 LINE_OFF = Caps.LINE_OFF
307 LONGITUDE = Caps.LONGITUDE
308 LONG_UNROLL = Caps.LONG_UNROLL
309 REDUCEDLENGTH = Caps.REDUCEDLENGTH
310 STANDARD = Caps.STANDARD
312 _caps = 0 # None
313 _debug = 0 # or Caps._DEBUG_...
315 @Property_RO
316 def caps(self):
317 '''Get the capabilities (bit-or'ed C{Caps}).
318 '''
319 return self._caps
321 def caps_(self, caps):
322 '''Check the available capabilities.
324 @arg caps: Bit-or'ed combination of L{Caps} values
325 for all capabilities to be checked.
327 @return: C{True} if I{all} B{C{caps}} are available,
328 C{False} otherwise (C{bool}).
329 '''
330 caps &= Caps._OUT_ALL
331 return (self.caps & caps) == caps
333 @property
334 def debug(self):
335 '''Get the C{debug} option (C{bool}).
336 '''
337 return bool(self._debug)
339 @debug.setter # PYCHOK setter!
340 def debug(self, debug):
341 '''Set the C{debug} option (C{bool}) to include
342 more details in L{GDict} results.
343 '''
344 self._debug = Caps._DEBUG_ALL if debug else 0
346 def _iter2tion(self, r, s):
347 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
348 '''
349 i = _xkwds_get(s, iter=None)
350 if i is not None:
351 self._iteration = r._iteration = i
352 return r
355class Direct9Tuple(_GTuple):
356 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
357 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
358 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
359 C{meter} I{squared}.
360 '''
361 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
362 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
365class GDict(_Dict): # XXX _NamedDict
366 '''Basic C{dict} with both key I{and} attribute access
367 to the C{dict} items.
369 Results of all C{geodesic} methods are returned as a
370 L{GDict} instance.
371 '''
372 _iteration = None # Iteration number (C{int}) or C{None}
374 @property_RO
375 def iteration(self): # see .named._NamedBase
376 '''Get the iteration number (C{int}) or
377 C{None} if not available/applicable.
378 '''
379 return self._iteration
381 def toDirect9Tuple(self, dflt=NAN):
382 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s
383 method C{geographiclib.geodesic.Geodesic._GenDirect}.
385 @kwarg dflt: Default value for missing items (C{any}).
387 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
388 s12, m12, M12, M21, S12)}
389 '''
390 return self._toTuple(Direct9Tuple, dflt)
392 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
393 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
394 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
395 result.
397 @kwarg dflt: Default value for missing items (C{any}).
399 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
400 s12, a12, m12, M12, M21, S12)}.
401 '''
402 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
404 def toInverse10Tuple(self, dflt=NAN):
405 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
406 method C{geographiclib.geodesic.Geodesic._GenInverse}.
408 @kwarg dflt: Default value for missing items (C{any}).
410 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
411 salp2, calp2, m12, M12, M21, S12)}.
412 '''
413 return self._toTuple(Inverse10Tuple, dflt)
415 @deprecated_method
416 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
417 '''DEPRECATED, used method C{toRhumb8Tuple}.
419 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
420 '''
421 return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt)
423 def toRhumb8Tuple(self, dflt=NAN):
424 '''Convert this L{GDict} result to a 8-tuple.
426 @kwarg dflt: Default value for missing items (C{any}).
428 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
429 azi12, s12, S12, a12)}.
430 '''
431 return self._toTuple(Rhumb8Tuple, dflt)
433 def toRhumbSolve7Tuple(self, dflt=NAN):
434 '''Convert this L{GDict} result to a 8-tuple.
436 @kwarg dflt: Default value for missing items (C{any}).
438 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
439 azi12, s12, S12)}.
440 '''
441 return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt)
443 def _toTuple(self, nTuple, dflt):
444 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
445 '''
446 _g = getattr
447 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
448 return nTuple(t, iteration=self._iteration)
451class Inverse10Tuple(_GTuple):
452 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
453 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
454 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
455 C{calp2} of the initial C{1} and final C{2} foward azimuths.
456 '''
457 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
458 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
460 def toGDict(self, **updates):
461 '''Convert this C{Inverse10Tuple} to a L{GDict}.
463 @kwarg updates: Optional items to apply (C{nam=value} pairs)
464 '''
465 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple
466 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
467 **updates) # PYCHOK indent
470class _kWrapped(object):
471 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
472 <https://PyPI.org/project/geographiclib>} classes.
473 '''
475 @Property_RO
476 def geographiclib(self):
477 '''Get the imported C{geographiclib}, provided the U{geographiclib
478 <https://PyPI.org/project/geographiclib>} package is installed,
479 otherwise an C{ImportError}.
480 '''
481 g = _xgeographiclib(self.__class__, 1, 49)
482 from geographiclib.geodesic import Geodesic
483 g.Geodesic = Geodesic
484 from geographiclib.geodesicline import GeodesicLine
485 g.GeodesicLine = GeodesicLine
486 from geographiclib.geomath import Math
487 g.Math = Math
488 return g
490 @Property_RO # MCCABE 13
491 def Math(self):
492 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
493 <https://PyPI.org/project/geographiclib>} package is installed,
494 otherwise C{None}.
495 '''
496 try:
497 g = self.geographiclib
498 M = g.Math
499 if _xversion_info(g) < (2,):
500 if _K_2_0:
501 M = None
502# elif not _K_2_0: # XXX set 2.0?
503# _K_2_0 = True
504 except (AttributeError, ImportError):
505 M = None
506 return M
508_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
511class Rhumb8Tuple(_GTuple):
512 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
513 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
514 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
515 line and the angular distance C{a12} between both points.
516 '''
517 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
518 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
520 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
521 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
522 method C{geographiclib.geodesic.Geodesic._GenDirect}.
524 @kwarg dflt: Default value for missing items (C{any}).
525 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
526 to specify or override L{Inverse10Tuple} items.
528 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
529 m12, M12, M21, S12)}
530 '''
531 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
532 azi2=self.azi12, M21=_1_0) # PYCHOK attr
533 if a12_azi1_azi2_m12_M12_M21:
534 d.update(a12_azi1_azi2_m12_M12_M21)
535 return self._toTuple(Direct9Tuple, dflt, d)
537 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
538 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
539 method C{geographiclib.geodesic.Geodesic._GenInverse}.
541 @kwarg dflt: Default value for missing items (C{any}).
542 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
543 arguments to specify or override L{Inverse10Tuple} items.
545 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
546 m12, M12, M21, S12)}.
547 '''
548 s, c = sincos2d(self.azi12) # PYCHOK attr
549 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
550 salp2=s, calp2=c, M21=_1_0)
551 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
552 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
553 return self._toTuple(Inverse10Tuple, dflt, d)
555 def _toTuple(self, nTuple, dflt, updates={}):
556 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
557 '''
558 _g = self.toGDict(**updates).get
559 t = tuple(_g(n, dflt) for n in nTuple._Names_)
560 return nTuple(t, name=self.name)
562 @deprecated_method
563 def _to7Tuple(self):
564 '''DEPRECATED, do not use!'''
565 return _MODS.deprecated.Rhumb7Tuple(self[:-1])
568def _around(x): # in .utily.sincos2d
569 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
571 @return: Coarsened value (C{float}).
573 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
574 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
575 '''
576 try:
577 return _wrapped.Math.AngRound(x)
578 except AttributeError:
579 if x:
580 y = _1_16th - fabs(x)
581 if y > 0: # fabs(x) < _1_16th
582 x = _copysign(_1_16th - y, x)
583 else:
584 x = _0_0 # -0 to 0
585 return x
588def _atan2d(y, x):
589 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
590 '''
591 try:
592 return _wrapped.Math.atan2d(y, x)
593 except AttributeError:
594 return atan2d(y, x)
597def _cbrt(x):
598 '''Return C{cubic root(B{x})}.
599 '''
600 try:
601 return _wrapped.Math.cbrt(x)
602 except AttributeError:
603 return cbrt(x)
606def _copyBit(x, y):
607 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
608 '''
609 return (-x) if _signBit(y) else x
612def _diff182(deg0, deg, K_2_0=False):
613 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
615 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
616 '''
617 try:
618 return _wrapped.Math.AngDiff(deg0, deg)
619 except AttributeError:
620 if K_2_0 or _K_2_0: # geographiclib 2.0
621 _r, _360 = fremainder, _360_0
622 d, t = _sum2(_r(-deg0, _360),
623 _r( deg, _360))
624 d, t = _sum2(_r( d, _360), t)
625 if d in (_0_0, _180_0, _N_180_0):
626 d = _copysign(d, -t if t else (deg - deg0))
627 else:
628 _n = _norm180
629 d, t = _sum2(_n(-deg0), _n(deg))
630 d = _n(d)
631 if t > 0 and d == _180_0:
632 d = _N_180_0
633 d, t = _sum2(d, t)
634 return d, t
637def _fix90(deg): # mimick Math.LatFix
638 '''Replace angle in C{degrees} outside [-90,90] by NAN.
640 @return: Angle C{degrees} or NAN.
641 '''
642 try:
643 return _wrapped.Math.LatFix(deg)
644 except AttributeError:
645 return NAN if fabs(deg) > 90 else deg
648def _isfinite(x): # mimick geomath.Math.AngNormalize
649 '''Check finiteness of C{x}.
651 @return: C{True} if finite.
652 '''
653 try:
654 return _wrapped.Math.isfinite(x)
655 except AttributeError:
656 return _math_isfinite(x) # and fabs(x) <= _MAX
659def _norm2(x, y): # mimick geomath.Math.norm
660 '''Normalize C{B{x}} and C{B{y}}.
662 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
663 '''
664 try:
665 return _wrapped.Math.norm(x, y)
666 except AttributeError:
667 return norm2(x, y)
670def _norm180(deg): # mimick geomath.Math.AngNormalize
671 '''Reduce angle in C{degrees} to (-180,180].
673 @return: Reduced angle C{degrees}.
674 '''
675 try:
676 return _wrapped.Math.AngNormalize(deg)
677 except AttributeError:
678 d = fremainder(deg, _360_0)
679 if d in (_180_0, _N_180_0):
680 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
681 return d
684def _polygon(geodesic, points, closed, line, wrap):
685 '''(INTERNAL) Compute the area or perimeter of a polygon,
686 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
687 C{geographiclib} package is installed) a C{Geodesic}
688 or C{geodesicw.Geodesic} instance.
689 '''
690 if not wrap: # capability LONG_UNROLL can't be off
691 notImplemented(None, wrap=wrap, up=3)
693 if _MODS.booleans.isBoolean(points):
694 # recursive call for each boolean clip
696 def _a_p(clip, *args, **unused):
697 return _polygon(geodesic, clip, *args)
699 if not closed: # closed only
700 raise _ValueError(closed=closed, points=_composite_)
702 return points._sum1(_a_p, closed, line, wrap)
704 gP = geodesic.Polygon(line)
705 _A = gP.AddPoint
707 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
708 p1 = p0 = Ps[0]
710 # note, lon deltas are unrolled, by default
711 _A(p1.lat, p1.lon)
712 for p2 in Ps.iterate(closed=closed):
713 if wrap and not Ps.looped:
714 p2 = _unrollon(p1, p2)
715 _A(p2.lat, p2.lon)
716 p1 = p2
717 if closed and line and p1 != p0:
718 _A(p0.lat, p0.lon)
720 # gP.Compute returns (number_of_points, perimeter, signed area)
721 return gP.Compute(False, True)[1 if line else 2]
724def _polynomial(x, cs, i, j): # PYCHOK shared
725 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
726 different signature and cascaded summation as C{karney._sum2_}.
728 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
729 '''
730 # assert 0 <= i <= j <= len(cs)
731# try:
732# return _wrapped.Math.polyval(j - i - 1, cs, i, x)
733# except AttributeError:
734# pass
735 s, t = cs[i], _0_0
736 for c in cs[i+1:j]:
737 s, t = _sum2_(s * x, t * x, c)
738 return s # + t
741def _remainder(x, y):
742 '''Remainder of C{x / y}.
744 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
745 '''
746 try:
747 return _wrapped.Math.remainder(x, y)
748 except AttributeError:
749 return fremainder(x, y)
752if _K_2_0:
753 from pygeodesy.basics import signBit as _signBit
754 from math import cos as _cos, sin as _sin
756 def _sincos2(rad):
757 return _sin(rad), _cos(rad)
759else:
760 from pygeodesy.utily import sincos2 as _sincos2 # PYCHOK shared
762 def _signBit(x):
763 '''(INTERNAL) GeographicLin 1.52-.
764 '''
765 return x < 0
768def _sincos2d(deg):
769 '''Return sine and cosine of an angle in C{degrees}.
771 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
772 '''
773 try:
774 return _wrapped.Math.sincosd(deg)
775 except AttributeError:
776 return sincos2d(deg)
779def _sincos2de(deg, t):
780 '''Return sine and cosine of a corrected angle in C{degrees}.
782 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
783 '''
784 try:
785 return _wrapped.Math.sincosde(deg, t)
786 except AttributeError:
787 return sincos2d(deg, adeg=t)
790def _sum2(u, v): # mimick geomath.Math.sum, actually sum2
791 '''Error-free summation like C{geomath.Math.sum}.
793 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
795 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
797 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
798 '''
799 try:
800 return _wrapped.Math.sum(u, v)
801 except AttributeError:
802 s = u + v
803 r = s - v
804 t = s - r
805 # if Algorithm_3_1:
806 # t = (u - t) + (v + r)
807 # elif C_CPP: # Math::sum C/C++
808 # r -= u
809 # t -= v
810 # t += r
811 # t = -t
812 # else:
813 t = (u - r) + (v - t)
814 return s, t
817def _sum2_(s, t, *vs):
818 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
820 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
822 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
823 html/Accumulator_8hpp_source.html>} comments for more details and
824 function C{_sum2} above.
826 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
827 '''
828 _s2, _u0 = _sum2, unsigned0
829 for v in vs:
830 if v:
831 t, u = _s2(t, v) # start at the least-
832 if s:
833 s, t = _s2(s, t) # significant end
834 if s:
835 t += u # accumulate u into t
836# elif t: # s == 0 implies t == 0
837# raise _AssertionError(t=t, txt=_not_(_0_))
838 else:
839 s = _u0(u) # result is u, t = 0
840 else:
841 s, t = _u0(t), u
842 return s, t
845def _tand(x):
846 '''Return C{tan(B{x})} in C{degrees}.
847 '''
848 try:
849 return _wrapped.Math.tand(x)
850 except AttributeError:
851 return tand(x)
854def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
855 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
857 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
858 unrolled if B{C{wrap}} is C{True}, normalized otherwise.
859 '''
860 if wrap:
861 d, t = _diff182(lon1, lon2)
862 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
863 else:
864 lon2 = _norm180(lon2)
865 return (lon2 - lon1), lon2
868def _unsigned2(x):
869 '''(INTERNAL) Unsign B{C{x}}.
870 '''
871 return (neg(x), True) if _signBit(x) else (x, False)
874__all__ += _ALL_DOCS(_CapsBase)
876# **) MIT License
877#
878# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
879#
880# Permission is hereby granted, free of charge, to any person obtaining a
881# copy of this software and associated documentation files (the "Software"),
882# to deal in the Software without restriction, including without limitation
883# the rights to use, copy, modify, merge, publish, distribute, sublicense,
884# and/or sell copies of the Software, and to permit persons to whom the
885# Software is furnished to do so, subject to the following conditions:
886#
887# The above copyright notice and this permission notice shall be included
888# in all copies or substantial portions of the Software.
889#
890# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
891# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
892# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
893# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
894# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
895# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
896# OTHER DEALINGS IN THE SOFTWARE.