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}, L{RhumbAux}, L{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>} from I{GeographicLib 2.2+}
76 - L{rhumbx}, L{Rhumb}, L{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 from 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 implementations of I{Karney}'s iterative solution posted 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, hypot as _hypot, norm2, \
143 Fsum, unstr # PYCHOK shared
144# from pygeodesy.fsums import Fsum # from .fmath
145from pygeodesy.interns import _2_, _a12_, _area_, _azi2_, _azi12_, _composite_, \
146 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, _M12_, _M21_, \
147 _number_, _s12_, _S12_
148from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv
149from pygeodesy.named import _Dict, _NamedBase, _NamedTuple, notImplemented, _Pass
150from pygeodesy.props import deprecated_method, Property_RO, property_RO
151# from pygeodesy.streps import unstr # from .fmath
152from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \
153 Meter as _M, Meter2 as _M2, Number_, \
154 Precision_, _1mm as _TOL_M # PYCHOK shared
155from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs
157# from math import fabs # from .utily
159__all__ = _ALL_LAZY.karney
160__version__ = '23.09.15'
162_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_
163_perimeter_ = 'perimeter'
166class _GTuple(_NamedTuple): # in .testNamedTuples
167 '''(INTERNAL) Helper.
168 '''
169 def toGDict(self, **updates):
170 '''Convert this C{*Tuple} to a L{GDict}.
172 @kwarg updates: Optional items to apply (C{nam=value} pairs)
173 '''
174 r = GDict(_zip(self._Names_, self)) # strict=True
175 if updates:
176 r.update(updates)
177 if self._iteration is not None:
178 r._iteration = self._iteration
179 return r
182class _Lat(Lat):
183 '''(INTERNAL) Latitude B{C{lat}}.
184 '''
185 def __init__(self, *lat, **Error_name):
186 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
187 Lat.__new__(_Lat, *lat, **kwds)
190class _Lon(Lon):
191 '''(INTERNAL) Longitude B{C{lon}}.
192 '''
193 def __init__(self, *lon, **Error_name):
194 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)
195 Lon.__new__(_Lon, *lon, **kwds)
198class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea
199 '''3-Tuple C{(number, perimeter, area)} with the C{number}
200 of points on the polygon or polyline, the C{perimeter} in
201 C{meter} and the C{area} in C{meter} I{squared}.
202 '''
203 _Names_ = (_number_, _perimeter_, _area_)
204 _Units_ = ( Number_, _M, _M2)
207class Caps(object): # PYCHOK
208 '''(INTERNAL) Overriden by C{Caps} below.
209 '''
210 EMPTY = 0 # formerly aka NONE
211 _CAP_1 = 1 << 0 # for goedesicw only
212 _CAP_1p = 1 << 1 # for goedesicw only
213# _CAP_2 = 1 << 2
214 _CAP_3 = 1 << 3 # for goedesicw only
215# _CAP_4 = 1 << 4
216# _CAP_ALL = 0x1F
217# _CAP_MASK = _CAP_ALL
218 LATITUDE = 1 << 7 # compute latitude C{lat2}
219 LONGITUDE = 1 << 8 # compute longitude C{lon2} _CAP_3
220 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}
221 DISTANCE = 1 << 10 # compute distance C{s12} _CAP_1
222 DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct _CAP_1 | _CAP_1p
223 REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} _CAP_1 | _CAP_2
224 GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} _CAP_1 | _CAP_2
225 AREA = 1 << 14 # compute area C{S12} _CAP_4
227 STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE
228 ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*
230 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE | _CAP_3 # for goedesicw only
231 _INVERSE3 = AZIMUTH | DISTANCE | _CAP_1 # for goedesicw only
232 _STD = STANDARD | _CAP_3 | _CAP_1 # for goedesicw only
233 _STD_LINE = _STD | _CAP_1p # for goedesicw only
235 LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb
236 LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position
237 REVERSE2 = 1 << 17 # reverse C{azi2}
239 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE
240 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA
242 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE
243 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA
245 _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only
246 _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse
248 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details
249 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details
250 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details
251 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details
252 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \
253 _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs
254 _OUT_ALL = ALL
255 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL
257 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE
258 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE
259 _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK
260 _LINE = AZIMUTH | LATITUDE | LONG_UNROLL
261 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE
262# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE
264Caps = Caps() # PYCHOK singleton
265'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or
266rhumb capabilities (C{caps}) and expected results (C{outmask}).
268C{AREA} - compute area C{S12},
270C{AZIMUTH} - include azimuths C{azi1} and C{azi2},
272C{DISTANCE} - compute distance C{s12},
274C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},
276C{EMPTY} - nothing, formerly aka C{NONE},
278C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},
280C{LATITUDE} - compute latitude C{lat2},
282C{LINE_OFF} - Line without updates from parent geodesic or rhumb.
284C{LONGITUDE} - compute longitude C{lon2},
286C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},
288C{REDUCEDLENGTH} - compute reduced length C{m12},
290C{REVERSE2} - reverse C{azi2},
292and C{ALL} - all of the above.
294C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''
297class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases
298 '''(INTERNAL) Base class for C{[_]Geodesic*Exact}.
299 '''
300 ALL = Caps.ALL
301 AREA = Caps.AREA
302 AZIMUTH = Caps.AZIMUTH
303 DISTANCE = Caps.DISTANCE
304 DISTANCE_IN = Caps.DISTANCE_IN
305 EMPTY = Caps.EMPTY # aka NONE
306 GEODESICSCALE = Caps.GEODESICSCALE
307 LATITUDE = Caps.LATITUDE
308 LINE_OFF = Caps.LINE_OFF
309 LONGITUDE = Caps.LONGITUDE
310 LONG_UNROLL = Caps.LONG_UNROLL
311 REDUCEDLENGTH = Caps.REDUCEDLENGTH
312 STANDARD = Caps.STANDARD
314 _caps = 0 # None
315 _debug = 0 # or Caps._DEBUG_...
317 @Property_RO
318 def caps(self):
319 '''Get the capabilities (bit-or'ed C{Caps}).
320 '''
321 return self._caps
323 def caps_(self, caps):
324 '''Check the available capabilities.
326 @arg caps: Bit-or'ed combination of L{Caps} values
327 for all capabilities to be checked.
329 @return: C{True} if I{all} B{C{caps}} are available,
330 C{False} otherwise (C{bool}).
331 '''
332 caps &= Caps._OUT_ALL
333 return (self.caps & caps) == caps
335 @property
336 def debug(self):
337 '''Get the C{debug} option (C{bool}).
338 '''
339 return bool(self._debug)
341 @debug.setter # PYCHOK setter!
342 def debug(self, debug):
343 '''Set the C{debug} option (C{bool}) to include
344 more details in L{GDict} results.
345 '''
346 self._debug = Caps._DEBUG_ALL if debug else 0
348 def _iter2tion(self, r, s):
349 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.
350 '''
351 i = _xkwds_get(s, iter=None)
352 if i is not None:
353 self._iteration = r._iteration = i
354 return r
357class Direct9Tuple(_GTuple):
358 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc
359 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},
360 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in
361 C{meter} I{squared}.
362 '''
363 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)
364 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)
367class GDict(_Dict): # XXX _NamedDict
368 '''Basic C{dict} with both key I{and} attribute access
369 to the C{dict} items.
371 Results of all C{geodesic} methods are returned as a
372 L{GDict} instance.
373 '''
374 _iteration = None # Iteration number (C{int}) or C{None}
376 @property_RO
377 def iteration(self): # see .named._NamedBase
378 '''Get the iteration number (C{int}) or
379 C{None} if not available/applicable.
380 '''
381 return self._iteration
383 def toDirect9Tuple(self, dflt=NAN):
384 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s
385 method C{geographiclib.geodesic.Geodesic._GenDirect}.
387 @kwarg dflt: Default value for missing items (C{any}).
389 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
390 s12, m12, M12, M21, S12)}
391 '''
392 return self._toTuple(Direct9Tuple, dflt)
394 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args
395 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s
396 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
397 result.
399 @kwarg dflt: Default value for missing items (C{any}).
401 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,
402 s12, a12, m12, M12, M21, S12)}.
403 '''
404 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)
406 def toInverse10Tuple(self, dflt=NAN):
407 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s
408 method C{geographiclib.geodesic.Geodesic._GenInverse}.
410 @kwarg dflt: Default value for missing items (C{any}).
412 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,
413 salp2, calp2, m12, M12, M21, S12)}.
414 '''
415 return self._toTuple(Inverse10Tuple, dflt)
417 @deprecated_method
418 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover
419 '''DEPRECATED, used method C{toRhumb8Tuple}.
421 @return: A I{DEPRECATED} L{Rhumb7Tuple}.
422 '''
423 return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt)
425 def toRhumb8Tuple(self, dflt=NAN):
426 '''Convert this L{GDict} result to a 8-tuple.
428 @kwarg dflt: Default value for missing items (C{any}).
430 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,
431 azi12, s12, S12, a12)}.
432 '''
433 return self._toTuple(Rhumb8Tuple, dflt)
435 def toRhumbSolve7Tuple(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{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,
441 azi12, s12, S12)}.
442 '''
443 return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt)
445 def _toTuple(self, nTuple, dflt):
446 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.
447 '''
448 _g = getattr
449 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)
450 return nTuple(t, iteration=self._iteration)
453class Inverse10Tuple(_GTuple):
454 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length
455 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area
456 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},
457 C{calp2} of the initial C{1} and final C{2} foward azimuths.
458 '''
459 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)
460 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)
462 def toGDict(self, **updates):
463 '''Convert this C{Inverse10Tuple} to a L{GDict}.
465 @kwarg updates: Optional items to apply (C{nam=value} pairs)
466 '''
467 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple
468 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple
469 **updates) # PYCHOK indent
472class _kWrapped(object): # in .geodesicw
473 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
474 <https://PyPI.org/project/geographiclib>} classes.
475 '''
477 @Property_RO
478 def geographiclib(self):
479 '''Get the imported C{geographiclib}, provided the U{geographiclib
480 <https://PyPI.org/project/geographiclib>} package is installed,
481 otherwise an C{ImportError}.
482 '''
483 g = _xgeographiclib(self.__class__, 1, 49)
484 from geographiclib.geodesic import Geodesic
485 g.Geodesic = Geodesic
486 from geographiclib.geodesicline import GeodesicLine
487 g.GeodesicLine = GeodesicLine
488 from geographiclib.geomath import Math
489 g.Math = Math
490 return g
492 @Property_RO # MCCABE 13
493 def Math(self):
494 '''Wrap the C{geomath.Math} class, provided the U{geographiclib
495 <https://PyPI.org/project/geographiclib>} package is installed,
496 otherwise C{None}.
497 '''
498 try:
499 g = self.geographiclib
500 M = g.Math
501 if _xversion_info(g) < (2,):
502 if _K_2_0:
503 M = None
504# elif not _K_2_0: # XXX set 2.0?
505# _K_2_0 = True
506 except (AttributeError, ImportError):
507 M = None
508 return M
510_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py
513class Rhumb8Tuple(_GTuple):
514 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},
515 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the
516 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb
517 line and the angular distance C{a12} between both points.
518 '''
519 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)
520 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)
522 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):
523 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s
524 method C{geographiclib.geodesic.Geodesic._GenDirect}.
526 @kwarg dflt: Default value for missing items (C{any}).
527 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments
528 to specify or override L{Inverse10Tuple} items.
530 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,
531 m12, M12, M21, S12)}
532 '''
533 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr
534 azi2=self.azi12, M21=_1_0) # PYCHOK attr
535 if a12_azi1_azi2_m12_M12_M21:
536 d.update(a12_azi1_azi2_m12_M12_M21)
537 return self._toTuple(Direct9Tuple, dflt, d)
539 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):
540 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s
541 method C{geographiclib.geodesic.Geodesic._GenInverse}.
543 @kwarg dflt: Default value for missing items (C{any}).
544 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword
545 arguments to specify or override L{Inverse10Tuple} items.
547 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,
548 m12, M12, M21, S12)}.
549 '''
550 s, c = sincos2d(self.azi12) # PYCHOK attr
551 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr
552 salp2=s, calp2=c, M21=_1_0)
553 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:
554 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)
555 return self._toTuple(Inverse10Tuple, dflt, d)
557 def _toTuple(self, nTuple, dflt, updates={}):
558 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.
559 '''
560 _g = self.toGDict(**updates).get
561 t = tuple(_g(n, dflt) for n in nTuple._Names_)
562 return nTuple(t, name=self.name)
564 @deprecated_method
565 def _to7Tuple(self):
566 '''DEPRECATED, do not use!'''
567 return _MODS.deprecated.Rhumb7Tuple(self[:-1])
570def _around(x): # in .utily.sincos2d
571 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.
573 @return: Coarsened value (C{float}).
575 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/
576 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}
577 '''
578 try:
579 return _wrapped.Math.AngRound(x)
580 except AttributeError:
581 if x:
582 y = _1_16th - fabs(x)
583 if y > 0: # fabs(x) < _1_16th
584 x = _copysign(_1_16th - y, x)
585 else:
586 x = _0_0 # -0 to 0
587 return x
590def _atan2d(y, x):
591 '''Return C{atan2(B{y}, B{x})} in C{degrees}.
592 '''
593 try:
594 return _wrapped.Math.atan2d(y, x)
595 except AttributeError:
596 return atan2d(y, x)
599def _cbrt(x):
600 '''Return C{cubic root(B{x})}.
601 '''
602 try:
603 return _wrapped.Math.cbrt(x)
604 except AttributeError:
605 return cbrt(x)
608def _copyBit(x, y):
609 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.
610 '''
611 return (-x) if _signBit(y) else x
614def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases
615 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).
616 '''
617 r = cx - sx
618 if r:
619 r *= (cx + sx) * _2_0
620 return r
623def _diff182(deg0, deg, K_2_0=False):
624 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.
626 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.
627 '''
628 try:
629 return _wrapped.Math.AngDiff(deg0, deg)
630 except AttributeError:
631 if K_2_0 or _K_2_0: # geographiclib 2.0
632 _r, _360 = fremainder, _360_0
633 d, t = _sum2(_r(-deg0, _360),
634 _r( deg, _360))
635 d, t = _sum2(_r( d, _360), t)
636 if d in (_0_0, _180_0, _N_180_0):
637 d = _copysign(d, -t if t else (deg - deg0))
638 else:
639 _n = _norm180
640 d, t = _sum2(_n(-deg0), _n(deg))
641 d = _n(d)
642 if t > 0 and d == _180_0:
643 d = _N_180_0
644 d, t = _sum2(d, t)
645 return d, t
648def _fix90(deg): # mimick Math.LatFix
649 '''Replace angle in C{degrees} outside [-90,90] by NAN.
651 @return: Angle C{degrees} or NAN.
652 '''
653 try:
654 return _wrapped.Math.LatFix(deg)
655 except AttributeError:
656 return NAN if fabs(deg) > 90 else deg
659def _isfinite(x): # mimick geomath.Math.isfinite
660 '''Check finiteness of C{x}.
662 @return: C{True} if finite.
663 '''
664 try:
665 return _wrapped.Math.isfinite(x)
666 except AttributeError:
667 return _math_isfinite(x) # and fabs(x) <= _MAX
670def _norm2(x, y): # mimick geomath.Math.norm
671 '''Normalize C{B{x}} and C{B{y}}.
673 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.
674 '''
675 try:
676 return _wrapped.Math.norm(x, y)
677 except AttributeError:
678 return norm2(x, y)
681def _norm180(deg): # mimick geomath.Math.AngNormalize
682 '''Reduce angle in C{degrees} to (-180,180].
684 @return: Reduced angle C{degrees}.
685 '''
686 try:
687 return _wrapped.Math.AngNormalize(deg)
688 except AttributeError:
689 d = fremainder(deg, _360_0)
690 if d in (_180_0, _N_180_0):
691 d = _copysign(_180_0, deg) if _K_2_0 else _180_0
692 return d
695def _polygon(geodesic, points, closed, line, wrap):
696 '''(INTERNAL) Compute the area or perimeter of a polygon,
697 using a L{GeodesicExact}, L{GeodesicSolve} or (if the
698 C{geographiclib} package is installed) a C{Geodesic}
699 or C{geodesicw.Geodesic} instance.
700 '''
701 if not wrap: # capability LONG_UNROLL can't be off
702 notImplemented(None, wrap=wrap, up=3)
704 if _MODS.booleans.isBoolean(points):
705 # recursive call for each boolean clip
707 def _a_p(clip, *args, **unused):
708 return _polygon(geodesic, clip, *args)
710 if not closed: # closed only
711 raise _ValueError(closed=closed, points=_composite_)
713 return points._sum1(_a_p, closed, line, wrap)
715 gP = geodesic.Polygon(line)
716 _A = gP.AddPoint
718 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)
719 p1 = p0 = Ps[0]
721 # note, lon deltas are unrolled, by default
722 _A(p1.lat, p1.lon)
723 for p2 in Ps.iterate(closed=closed):
724 if wrap and not Ps.looped:
725 p2 = _unrollon(p1, p2)
726 _A(p2.lat, p2.lon)
727 p1 = p2
728 if closed and line and p1 != p0:
729 _A(p0.lat, p0.lon)
731 # gP.Compute returns (number_of_points, perimeter, signed area)
732 return gP.Compute(False, True)[1 if line else 2]
735def _polynomial(x, cs, i, j): # PYCHOK shared
736 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a
737 different signature and cascaded summation as C{karney._sum2_}.
739 @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)}
740 '''
741 # assert 0 <= i <= j <= len(cs)
742# try:
743# return _wrapped.Math.polyval(j - i - 1, cs, i, x)
744# except AttributeError:
745# pass
746 s, t = cs[i], _0_0
747 for c in cs[i+1:j]:
748 s, t = _sum2_(s * x, t * x, c)
749 return s # + t
752def _remainder(x, y):
753 '''Remainder of C{x / y}.
755 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.
756 '''
757 try:
758 return _wrapped.Math.remainder(x, y)
759 except AttributeError:
760 return fremainder(x, y)
763if _K_2_0:
764 from math import cos as _cos, sin as _sin
766 def _sincos2(rad):
767 return _sin(rad), _cos(rad)
769 _signBit = _MODS.basics.signBit
770else:
771 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared
773 def _signBit(x):
774 '''(INTERNAL) GeographicLib 1.52-.
775 '''
776 return x < 0
779def _sincos2d(deg):
780 '''Return sine and cosine of an angle in C{degrees}.
782 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
783 '''
784 try:
785 return _wrapped.Math.sincosd(deg)
786 except AttributeError:
787 return sincos2d(deg)
790def _sincos2de(deg, t):
791 '''Return sine and cosine of a corrected angle in C{degrees}.
793 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.
794 '''
795 try:
796 return _wrapped.Math.sincosde(deg, t)
797 except AttributeError:
798 return sincos2d(deg, adeg=t)
801def _sum2(u, v): # mimick geomath.Math.sum, actually sum2
802 '''Error-free summation like C{geomath.Math.sum}.
804 @return: 2-Tuple C{(B{u} + B{v}, residual)}.
806 @note: The C{residual} can be the same as B{C{u}} or B{C{v}}.
808 @see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.
809 '''
810 try:
811 return _wrapped.Math.sum(u, v)
812 except AttributeError:
813 s = u + v
814 r = s - v
815 t = s - r
816 # if Algorithm_3_1:
817 # t = (u - t) + (v + r)
818 # elif C_CPP: # Math::sum C/C++
819 # r -= u
820 # t -= v
821 # t += r
822 # t = -t
823 # else:
824 t = (u - r) + (v - t)
825 return s, t
828def _sum2_(s, t, *vs):
829 '''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}.
831 @return: 2-Tuple C{(B{s} + B{t} + sum(B{vs}), residual)}.
833 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/
834 html/Accumulator_8hpp_source.html>} comments for more details and
835 function C{_sum2} above.
837 @note: NOT "error-free", see C{pygeodesy.test/testKarney.py}.
838 '''
839 _s2, _u0 = _sum2, unsigned0
840 for v in vs:
841 if v:
842 t, u = _s2(t, v) # start at the least-
843 if s:
844 s, t = _s2(s, t) # significant end
845 if s:
846 t += u # accumulate u into t
847# elif t: # s == 0 implies t == 0
848# raise _AssertionError(t=t, txt=_not_(_0_))
849 else:
850 s = _u0(u) # result is u, t = 0
851 else:
852 s, t = _u0(t), u
853 return s, t
856def _tand(x):
857 '''Return C{tan(B{x})} in C{degrees}.
858 '''
859 try:
860 return _wrapped.Math.tand(x)
861 except AttributeError:
862 return tand(x)
865def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2
866 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.
868 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}
869 unrolled if B{C{wrap}} is C{True}, normalized otherwise.
870 '''
871 if wrap:
872 d, t = _diff182(lon1, lon2)
873 lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t
874 else:
875 lon2 = _norm180(lon2)
876 return (lon2 - lon1), lon2
879def _unsigned2(x):
880 '''(INTERNAL) Unsign B{C{x}}.
881 '''
882 return (neg(x), True) if _signBit(x) else (x, False)
885__all__ += _ALL_DOCS(_CapsBase)
887# **) MIT License
888#
889# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
890#
891# Permission is hereby granted, free of charge, to any person obtaining a
892# copy of this software and associated documentation files (the "Software"),
893# to deal in the Software without restriction, including without limitation
894# the rights to use, copy, modify, merge, publish, distribute, sublicense,
895# and/or sell copies of the Software, and to permit persons to whom the
896# Software is furnished to do so, subject to the following conditions:
897#
898# The above copyright notice and this permission notice shall be included
899# in all copies or substantial portions of the Software.
900#
901# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
902# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
903# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
904# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
905# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
906# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
907# OTHER DEALINGS IN THE SOFTWARE.