1

2# -*- coding: utf-8 -*-

3

4 u'''Wrapper around several C{geomath.Math} functions from I{Karney}'s Python package U{geographiclib

5<https://PyPI.org/project/geographiclib>}, provided that package is installed.

6

7 Methods of the I{wrapped} L{Geodesic<geodesicw.Geodesic>} and L{GeodesicLine<geodesicw.GeodesicLine>}

8 classes return a L{GDict} instance offering access to the C{dict} items either by C{key} or by

9 C{attribute} name.

10

11 With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, modules L{geodesicw},

12 L{geodesicx} and this module will use U{GeographicLib 2.0+<https://GeographicLib.SourceForge.io/C++/doc/>}

13 and newer transcoding, otherwise C{1.52} or older. Set C{PYGEODESY_GEOGRAPHICLIB=2.4} to default to the

14 C{Jacobi amplitude} instead of C{Bulirsch}' function in methods L{ExactTransverseMercator.forward

15<pygeodesy.ExactTransverseMercator.forward>} and L{reverse <pygeodesy.ExactTransverseMercator.reverse>}.

16

17 Karney-based functionality

18==========================

19

20 1. The following classes and functions in C{pygeodesy}

21

22 - L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4},

23 L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} --

24 U{AlbersEqualArea<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AlbersEqualArea.html>}

25

26 - L{AuxAngle}, L{AuxDST}, L{AuxDLat}, L{AuxLat} -- U{AuxAngle

27 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxAngle.html>},

28 U{DST<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DST.html>},

29 U{DAuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1DAuxLatitude.html>},

30 U{AuxLatitude<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AuxLatitude.html>} in I{GeographicLib 2.2+}

31

32 - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/

33 classGeographicLib_1_1CassiniSoldner.html>}

34

35 - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}

36

37 - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/

38 classGeographicLib_1_1EllipticFunction.html>}

39

40 - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant

41 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}

42

43 - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact

44 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}

45

46 - L{Geodesic}, L{GeodesicLine} -- I{wrapped} U{geodesic.Geodesic<https://PyPI.org/project/geographiclib>},

47 I{wrapped} U{geodesicline.GeodesicLine<https://PyPI.org/project/geographiclib>}

48

49 - L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/C++/doc/

50 classGeographicLib_1_1PolygonAreaT.html>}

51

52 - L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/

53 classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/

54 classGeographicLib_1_1GeodesicLineExact.html>}

55

56 - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>}

57

58 - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Georef.html>}

59

60 - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic

61 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}

62

63 - L{Intersector} -- U{Intersect

64 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} from I{GeographicLib 2.3+}

65

66 - L{JacobiConformal} -- U{JacobiConformal

67 <https://geographiclib.sourceforge.io/C++/doc/classGeographicLib_1_1experimental_1_1JacobiConformal.html>}

68

69 - L{KTransverseMercator} - U{TransverseMercator

70 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}

71

72 - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/

73 classGeographicLib_1_1LocalCartesian.html>}

74

75 - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}

76

77 - L{rhumb.aux_}, L{RhumbAux}, L{RhumbLineAux} -- U{Rhumb

78 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and U{RhumbLine

79 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} from I{GeographicLib 2.2+}

80

81 - L{rhumb.ekx}, L{Rhumb}, L{RhumbLine} -- U{Rhumb

82 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>},

83 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>},

84 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}

85 from I{GeographicLib 2.0}

86

87 - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1PolarStereographic.html>}

88

89 - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>}

90

91 - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1UTMUPS.html>}

92

93 - L{atan1d}, L{atan2d}, L{sincos2}, L{sincos2d}, L{tand} -- U{geomath.Math

94 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}

95

96 are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}.

97

98 2. These C{pygeodesy} modules and classes

99

100 - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodesici}, L{geodsolve}, L{karney}, L{rhumb.solve}

101 - L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve},

102 L{GnomonicKarney}, L{HeightIDWkarney}, L{Intersectool}

103

104 are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} or

105 C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>},

106 U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} or

107 U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}.

108

109 3. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections, nearest points and trilaterations

110

111 - L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn},

112 L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2},

113 L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5}

114

115 - L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn},

116 L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2},

117 L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5}

118

119 - L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn},

120 L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2},

121 L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5}

122

123 - L{RhumbLineAux.Intersection} and L{RhumbLine.Intersection}

124

125 are implementations of I{Karney}'s iterative solution posted under U{The B{ellipsoidal} case

126<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics

127 on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}).

128

129 4. The C{pygeodesy} methods to compute I{ellipsoidal} intersections and nearest points

130

131 - L{RhumbLineAux.Intersecant2}, L{RhumbLineAux.PlumbTo}, L{RhumbLine.Intersecant2} and L{RhumbLine.PlumbTo}

132

133 are I{transcoded} of I{Karney}'s iterative C++ function U{rhumb-intercept

134<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.

135

136 5. Spherical functions

137

138 - L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf}

139

140 in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon

141<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer.

142'''

143# make sure int/int division yields float quotient, see .basics

144 from __future__ import division as _; del _ # PYCHOK semicolon

145

146 from pygeodesy.basics import _copysign, isint, neg, unsigned0, _xgeographiclib, \

147 _zip, _version_info

148 from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, \

149 _1_16th, _1_0, _2_0, _180_0, _N_180_0, _360_0

150 from pygeodesy.errors import GeodesicError, _ValueError, _xkwds

151 from pygeodesy.fmath import cbrt, fremainder, norm2 # Fhorner, Fsum

152# from pygeodesy.internals import _version_info # from .basics

153 from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi1_, _azi2_, _azi12_, \

154 _composite_, _lat1_, _lat2_, _lon1_, _lon2_, \

155 _m12_, _M12_, _M21_, _number_, _s12_, _S12_, \

156 _UNDER_, _X_, _BAR_ # PYCHOK used!

157 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv

158 from pygeodesy.named import ADict, _NamedBase, _NamedTuple, notImplemented, _Pass

159 from pygeodesy.props import deprecated_method, Property_RO, property_RO, \

160 property_ROnce

161 from pygeodesy.units import Azimuth as _Azi, Degrees as _Deg, Lat, Lon, \

162 Meter as _M, Meter2 as _M2, Number_

163 from pygeodesy.utily import atan2d, sincos2d, tand, _unrollon, fabs

164

165# from math import fabs # from .utily

166

167__all__ = _ALL_LAZY.karney

168__version__ = '24.09.13'

169

170_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_)

171_K_2_4 = _K_2_0 == '2.4'

172_K_2_0 = _K_2_0 == _2_ or _K_2_4

173_perimeter_ = 'perimeter'

174

175

176 class _GTuple(_NamedTuple): # in .testNamedTuples

177 '''(INTERNAL) Helper.

178 '''

179 def toGDict(self, **updates): # NO name=NN

180 '''Convert this C{*Tuple} to a L{GDict}.

181

182 @kwarg updates: Optional items to apply (C{name=value} pairs)

183 '''

184 r = GDict(_zip(self._Names_, self)) # strict=True

185 if updates:

186 r.update(updates)

187 if self._iteration is not None:

188 r._iteration = self._iteration

189 return r

190

191

192 class _Lat(Lat):

193 '''(INTERNAL) Latitude B{C{lat}}.

194 '''

195 def __init__(self, *lat, **Error_name):

196 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)

197 Lat.__new__(_Lat, *lat, **kwds)

198

199

200 class _Lon(Lon):

201 '''(INTERNAL) Longitude B{C{lon}}.

202 '''

203 def __init__(self, *lon, **Error_name):

204 kwds = _xkwds(Error_name, clip=0, Error=GeodesicError)

205 Lon.__new__(_Lon, *lon, **kwds)

206

207

208 class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea

209 '''3-Tuple C{(number, perimeter, area)} with the C{number}

210 of points of the polygon or polyline, the C{perimeter} in

211 C{meter} and the C{area} in C{meter} I{squared}.

212 '''

213 _Names_ = (_number_, _perimeter_, _area_)

214 _Units_ = ( Number_, _M, _M2)

215

216

217 class Caps(object):

218 '''(INTERNAL) Overriden by C{Caps} below.

219 '''

220 EMPTY = 0 # formerly aka NONE

221 _CAP_1 = 1 << 0 # for goedesici/-w

222 _CAP_1p = 1 << 1 # for goedesici/-w

223 _CAP_2 = 1 << 2

224 _CAP_3 = 1 << 3 # for goedesici/-w

225 _CAP_4 = 1 << 4 # for goedesicw

226 _CAP_ALL = 0x1F

227# _CAP_MASK = _CAP_ALL

228 LATITUDE = 1 << 7 # compute latitude C{lat2}

229 LONGITUDE = 1 << 8 | _CAP_3 # compute longitude C{lon2}

230 AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2}

231 DISTANCE = 1 << 10 | _CAP_1 # compute distance C{s12}

232 DISTANCE_IN = 1 << 11 | _CAP_1 | _CAP_1p # allow distance C{s12} in Direct

233 REDUCEDLENGTH = 1 << 12 | _CAP_1 | _CAP_2 # compute reduced length C{m12}

234 GEODESICSCALE = 1 << 13 | _CAP_1 | _CAP_2 # compute geodesic scales C{M12} and C{M21}

235 AREA = 1 << 14 | _CAP_4 # compute area C{S12}

236

237 STANDARD = AZIMUTH | DISTANCE | LATITUDE | LONGITUDE

238

239 _DIRECT3 = AZIMUTH | LATITUDE | LONGITUDE # for goedesicw only

240 _INVERSE3 = AZIMUTH | DISTANCE # for goedesicw only

241 _STD = STANDARD # for goedesicw only

242 _STD_LINE = _STD | DISTANCE_IN # for goedesici/-w

243

244 LINE_CAPS = _STD_LINE | REDUCEDLENGTH | GEODESICSCALE # .geodesici only

245 LONG_UNROLL = 1 << 15 # unroll C{lon2} in .Direct and .Position

246# = 1 << 16 # unused

247 LINE_OFF = 1 << 17 # Line without updates from parent geodesic or rhumb

248 REVERSE2 = 1 << 18 # reverse C{azi2}

249 ALL = 0x7F80 | _CAP_ALL # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_*

250

251 LATITUDE_LONGITUDE = LATITUDE | LONGITUDE

252 LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA

253

254 AZIMUTH_DISTANCE = AZIMUTH | DISTANCE

255 AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA

256

257 _SALP_CALPs_ = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse

258

259 _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details

260 _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details

261 _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details

262 _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details

263 _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \

264 _DEBUG_LINE | _SALP_CALPs_

265

266 _OUT_ALL = ALL # see geographiclib.geodesiccapabilities.py

267 _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL

268

269 _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE

270 _AZIMUTH_LATITUDE_LONG_UNROLL = AZIMUTH | LATITUDE | LONG_UNROLL

271 _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE

272# _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK # == DISTANCE_IN in .gx, .gxline

273 _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE

274# _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE

275

276 def items(self):

277 '''Yield all I{public} C{Caps} as 2-tuple C{(NAME, mask)}.

278 '''

279 for n, C in Caps.__class__.__dict__.items():

280 if isint(C) and not n.startswith(_UNDER_) \

281 and n.replace(_UNDER_, NN).isupper():

282 yield n, C

283

284 def toStr(self, Cask, sep=_BAR_):

285 '''Return C{Caps} or an C{outmask} as C{str} or tuple of C{str}s.

286 '''

287 s = (n for n, C in sorted(Caps.items())

288 if C and (Cask & C) == C) # and int1s(C) <= 3

289 return sep.join(s) if sep else tuple(s)

290

291 Caps = Caps() # PYCHOK singleton

292'''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or

293 rhumb capabilities (C{caps}) and results (C{outmask}).

294

295 C{AREA} - compute area C{S12},

296

297 C{AZIMUTH} - include azimuths C{azi1} and C{azi2},

298

299 C{DISTANCE} - compute distance C{s12} and angular distance C{a12},

300

301 C{DISTANCE_IN} - allow distance C{s12} in C{.Direct},

302

303 C{EMPTY} - nothing, formerly aka C{NONE},

304

305 C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21},

306

307 C{LATITUDE} - compute latitude C{lat2},

308

309 C{LINE_OFF} - Line without updates from parent geodesic or rhumb.

310

311 C{LONGITUDE} - compute longitude C{lon2},

312

313 C{LONG_UNROLL} - unroll C{lon2} in C{.Direct},

314

315 C{REDUCEDLENGTH} - compute reduced length C{m12},

316

317 C{REVERSE2} - reverse C{azi2},

318

319 and C{ALL} - all of the above.

320

321 C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}'''

322

323_key2Caps = dict(a12 =Caps.DISTANCE, # in GDict._unCaps

324 azi2=Caps.AZIMUTH,

325 lat2=Caps.LATITUDE,

326 lon2=Caps.LONGITUDE,

327 m12 =Caps.REDUCEDLENGTH,

328 M12 =Caps.GEODESICSCALE,

329 M21 =Caps.GEODESICSCALE,

330 s12 =Caps.DISTANCE,

331 S12 =Caps.AREA)

332

333

334 class _CapsBase(_NamedBase): # in .auxilats, .geodesicx.gxbases

335 '''(INTERNAL) Base class for C{Geodesic*}, C{Geodesic*Exact}, C{Intersectool} and C{Rhumb*Base}.

336 '''

337 ALL = Caps.ALL

338 AREA = Caps.AREA

339 AZIMUTH = Caps.AZIMUTH

340 DISTANCE = Caps.DISTANCE

341 DISTANCE_IN = Caps.DISTANCE_IN

342 EMPTY = Caps.EMPTY # aka NONE

343 GEODESICSCALE = Caps.GEODESICSCALE

344 LATITUDE = Caps.LATITUDE

345 LINE_CAPS = Caps.LINE_CAPS

346 LINE_OFF = Caps.LINE_OFF

347 LONGITUDE = Caps.LONGITUDE

348 LONG_UNROLL = Caps.LONG_UNROLL

349 REDUCEDLENGTH = Caps.REDUCEDLENGTH

350 STANDARD = Caps.STANDARD

351 _STD_LINE = Caps._STD_LINE # for geodesici

352

353 _caps = 0 # None

354 _debug = 0 # or Caps._DEBUG_...

355

356 @Property_RO

357 def caps(self):

358 '''Get the capabilities (bit-or'ed C{Caps}).

359 '''

360 return self._caps

361

362 def caps_(self, caps):

363 '''Check the available capabilities.

364

365 @arg caps: Bit-or'ed combination of L{Caps} values

366 for all capabilities to be checked.

367

368 @return: C{True} if I{all} B{C{caps}} are available,

369 C{False} otherwise (C{bool}).

370 '''

371 caps &= Caps._OUT_ALL

372 return (self.caps & caps) == caps

373

374 @property

375 def debug(self):

376 '''Get the C{debug} option (C{bool}).

377 '''

378 return bool(self._debug)

379

380 @debug.setter # PYCHOK setter!

381 def debug(self, debug):

382 '''Set the C{debug} option (C{bool}) to include

383 more details in L{GDict} results.

384 '''

385 self._debug = Caps._DEBUG_ALL if debug else 0

386

387 def _iter2tion(self, r, iter=None, **unused):

388 '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}.

389 '''

390 if iter is not None:

391 self._iteration = r._iteration = iter

392 return r

393

394

395 class Direct9Tuple(_GTuple):

396 '''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc

397 length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees},

398 distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in

399 C{meter} I{squared}.

400 '''

401 _Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_)

402 _Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2)

403

404

405 class GDict(ADict): # XXX _NamedDict

406 '''A C{dict} with both C{key} I{and} C{attribute} access to the C{dict} items.

407

408 Results of all C{geodesic} and C{rhumb} methods (with capitalized named) are

409 returned as L{GDict} instances, see for example L{GeodesicExact} and L{RhumbAux}.

410 '''

411 def toDirect9Tuple(self, dflt=NAN):

412 '''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s method

413 C{geographiclib.geodesic.Geodesic._GenDirect}.

414

415 @kwarg dflt: Default value for missing items (C{any}).

416

417 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,

418 s12, m12, M12, M21, S12)}

419 '''

420 return self._toTuple(Direct9Tuple, dflt)

421

422 def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args

423 '''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s

424 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}

425 result.

426

427 @kwarg dflt: Default value for missing items (C{any}).

428

429 @return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2,

430 s12, a12, m12, M12, M21, S12)}.

431 '''

432 return self._toTuple(_MODS.geodsolve.GeodSolve12Tuple, dflt)

433

434 def toInverse10Tuple(self, dflt=NAN):

435 '''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s

436 method C{geographiclib.geodesic.Geodesic._GenInverse}.

437

438 @kwarg dflt: Default value for missing items (C{any}).

439

440 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1,

441 salp2, calp2, m12, M12, M21, S12)}.

442 '''

443 return self._toTuple(Inverse10Tuple, dflt)

444

445 def _toNAN(self, outmask): # .GeodesicLineExact._GenPosition

446 '''(INTERNAL) Convert this C{GDict} to all C{NAN}s.

447 '''

448 d = dict((n, NAN) for n in GeodSolve12Tuple._Names_)

449 return self.set_(**d)._unCaps(outmask)

450

451 @deprecated_method

452 def toRhumb7Tuple(self, dflt=NAN): # PYCHOK no cover

453 '''DEPRECATED on 23.12.07, use method C{toRhumb8Tuple}.

454

455 @return: A I{DEPRECATED} L{Rhumb7Tuple}.

456 '''

457 return self._toTuple(_MODS.deprecated.classes.Rhumb7Tuple, dflt)

458

459 def toRhumb8Tuple(self, dflt=NAN):

460 '''Convert this L{GDict} result to a 8-tuple.

461

462 @kwarg dflt: Default value for missing items (C{any}).

463

464 @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2,

465 azi12, s12, S12, a12)}.

466 '''

467 return self._toTuple(Rhumb8Tuple, dflt)

468

469 def toRhumbSolve7Tuple(self, dflt=NAN):

470 '''Convert this L{GDict} result to a 8-tuple.

471

472 @kwarg dflt: Default value for missing items (C{any}).

473

474 @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2,

475 azi12, s12, S12)}.

476 '''

477 return self._toTuple(_MODS.rhumb.solve.RhumbSolve7Tuple, dflt)

478

479 def _toTuple(self, nTuple, dflt):

480 '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}.

481 '''

482 _g = getattr

483 t = tuple(_g(self, n, dflt) for n in nTuple._Names_)

484 return nTuple(t, iteration=self._iteration)

485

486 def _2X(self, gl, _2X=_X_): # .Intersectool, .Intersector

487 '''(INTERNAL) Rename C{-2} attr to C{-X} or C{-M}.

488 '''

489 X = GDict(self)

490 for n in (_lat2_, _lon2_, _azi2_, _s12_, _a12_):

491 if n in X: # X._X = X._2

492 X[n[:-1] + _2X] = X.pop(n)

493 v = getattr(gl, n, X)

494 if v is not X: # X._2 = gl._2

495 X[n] = v

496 return X

497

498 def _unCaps(self, outmask): # in .geodsolve

499 '''(INTERNAL) Remove superfluous items.

500 '''

501 for k, C in _key2Caps.items():

502 if k in self and (outmask & C) != C:

503 self.pop(k) # delattr(self, k)

504 return self

505

506

507 class GeodSolve12Tuple(_GTuple):

508 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with

509 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in

510 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and

511 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic

512 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve

513 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}.

514 '''

515 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12

516 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_)

517 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2)

518

519

520 class Inverse10Tuple(_GTuple):

521 '''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length

522 C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area

523 C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1},

524 C{calp2} of the initial C{1} and final C{2} (forward) azimuths.

525 '''

526 _Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_)

527 _Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2)

528

529 def toGDict(self, **updates):

530 '''Convert this C{Inverse10Tuple} to a L{GDict}.

531

532 @kwarg updates: Optional items to apply (C{nam=value} pairs)

533 '''

534 return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK namedTuple

535 azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple

536 **updates) # PYCHOK indent

537

538

539 class _kWrapped(object): # in .geodesicw

540 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib

541 <https://PyPI.org/project/geographiclib>} classes.

542 '''

543

544 @property_ROnce

545 def geographiclib(self):

546 '''Lazily import C{geographiclib}, provided the U{geographiclib

547 <https://PyPI.org/project/geographiclib>} package is installed,

548 otherwise raise a C{LazyImportError}.

549 '''

550 g = _xgeographiclib(self.__class__.__module__, 1, 49)

551 from geographiclib.geodesic import Geodesic

552 g.Geodesic = Geodesic

553 from geographiclib.geodesicline import GeodesicLine

554 g.GeodesicLine = GeodesicLine

555 from geographiclib.geomath import Math

556 g.Math = Math

557 return g

558

559 @property_ROnce

560 def Math(self):

561 '''Wrap the C{geomath.Math} class, provided the U{geographiclib

562 <https://PyPI.org/project/geographiclib>} package is installed,

563 otherwise C{None}.

564 '''

565 try:

566 g = self.geographiclib

567 M = g.Math

568 if _version_info(g) < (2,):

569 if _K_2_0:

570 M = None

571# elif not _K_2_0: # XXX set 2.0?

572# _K_2_0 = True

573 except (AttributeError, ImportError):

574 M = None

575 return M

576

577 @property_RO

578 def Math_K_2(self):

579 return ('_K_2_4' if _K_2_4 else

580 ('_K_2_0' if _K_2_0 else '_K_1_0')) if self.Math else NN

581

582_wrapped = _kWrapped() # PYCHOK singleton, .datum, .test/base.py

583

584

585 class Rhumb8Tuple(_GTuple):

586 '''8-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)} with lat- C{lat1},

587 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of the

588 rhumb line C{azi12}, the distance C{s12}, the area C{S12} under the rhumb

589 line and the angular distance C{a12} between both points.

590 '''

591 _Names_ = (_lat1_, _lon1_, _lat2_, _lon2_, _azi12_, _s12_, _S12_, _a12_)

592 _Units_ = ( Lat, Lon, Lat, Lon, _Azi, _M, _M2, _Deg)

593

594 def toDirect9Tuple(self, dflt=NAN, **a12_azi1_azi2_m12_M12_M21):

595 '''Convert this L{Rhumb8Tuple} result to a 9-tuple, like I{Karney}'s

596 method C{geographiclib.geodesic.Geodesic._GenDirect}.

597

598 @kwarg dflt: Default value for missing items (C{any}).

599 @kwarg a12_azi1_azi2_m12_M12_M21: Optional keyword arguments

600 to specify or override L{Inverse10Tuple} items.

601

602 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, s12,

603 m12, M12, M21, S12)}

604 '''

605 d = dict(azi1=self.azi12, M12=_1_0, m12=self.s12, # PYCHOK attr

606 azi2=self.azi12, M21=_1_0) # PYCHOK attr

607 if a12_azi1_azi2_m12_M12_M21:

608 d.update(a12_azi1_azi2_m12_M12_M21)

609 return self._toTuple(Direct9Tuple, dflt, d)

610

611 def toInverse10Tuple(self, dflt=NAN, **a12_m12_M12_M21_salp1_calp1_salp2_calp2):

612 '''Convert this L{Rhumb8Tuple} to a 10-tuple, like I{Karney}'s

613 method C{geographiclib.geodesic.Geodesic._GenInverse}.

614

615 @kwarg dflt: Default value for missing items (C{any}).

616 @kwarg a12_m12_M12_M21_salp1_calp1_salp2_calp2: Optional keyword

617 arguments to specify or override L{Inverse10Tuple} items.

618

619 @return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, salp2, calp2,

620 m12, M12, M21, S12)}.

621 '''

622 s, c = sincos2d(self.azi12) # PYCHOK attr

623 d = dict(salp1=s, calp1=c, M12=_1_0, m12=self.s12, # PYCHOK attr

624 salp2=s, calp2=c, M21=_1_0)

625 if a12_m12_M12_M21_salp1_calp1_salp2_calp2:

626 d.update(a12_m12_M12_M21_salp1_calp1_salp2_calp2)

627 return self._toTuple(Inverse10Tuple, dflt, d)

628

629 def _toTuple(self, nTuple, dflt, updates={}):

630 '''(INTERNAL) Convert this C{Rhumb8Tuple} to an B{C{nTuple}}.

631 '''

632 _g = self.toGDict(**updates).get

633 t = tuple(_g(n, dflt) for n in nTuple._Names_)

634 return nTuple(t, name=self.name)

635

636 @deprecated_method

637 def _to7Tuple(self):

638 '''DEPRECATED, do not use!'''

639 return _MODS.deprecated.classes.Rhumb7Tuple(self[:-1])

640

641

642 def _around(x): # in .utily.sincos2d

643 '''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}.

644

645 @return: Coarsened value (C{float}).

646

647 @see: I{Karney}'s U{geomath.Math.AngRound<https://SourceForge.net/p/

648 geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>}

649 '''

650 try:

651 return _wrapped.Math.AngRound(x)

652 except AttributeError:

653 if x:

654 y = _1_16th - fabs(x)

655 if y > 0: # fabs(x) < _1_16th

656 x = _copysign(_1_16th - y, x)

657 else:

658 x = _0_0 # -0 to 0

659 return x

660

661

662 def _atan2d(y, x):

663 '''Return C{atan2(B{y}, B{x})} in C{degrees}.

664 '''

665 try:

666 return _wrapped.Math.atan2d(y, x)

667 except AttributeError:

668 return atan2d(y, x)

669

670

671 def _cbrt(x):

672 '''Return C{cubic root(B{x})}.

673 '''

674 try:

675 return _wrapped.Math.cbrt(x)

676 except AttributeError:

677 return cbrt(x)

678

679

680 def _copyBit(x, y):

681 '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}.

682 '''

683 return (-x) if _signBit(y) else x

684

685

686 def _2cos2x(cx, sx): # in .auxDST, .auxLat, .gxbases

687 '''Return M{2 * cos(2 * x)} from cos(x) and sin(x).

688 '''

689 r = cx - sx

690 if r:

691 r *= (cx + sx) * _2_0

692 return r

693

694

695 def _diff182(deg0, deg, K_2_0=False):

696 '''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately.

697

698 @return: 2-Tuple C{(delta_angle, residual)} in C{degrees}.

699 '''

700 try:

701 return _wrapped.Math.AngDiff(deg0, deg)

702 except AttributeError:

703 if K_2_0 or _K_2_0: # geographiclib 2.0

704 _r, _360 = fremainder, _360_0

705 d, t = _sum2(_r(-deg0, _360),

706 _r( deg, _360))

707 d, t = _sum2(_r( d, _360), t)

708 if d in (_0_0, _180_0, _N_180_0):

709 d = _copysign(d, -t if t else (deg - deg0))

710 else:

711 _n = _norm180

712 d, t = _sum2(_n(-deg0), _n(deg))

713 d = _n(d)

714 if t > 0 and d == _180_0:

715 d = _N_180_0

716 d, t = _sum2(d, t)

717 return d, t

718

719

720 def _fix90(deg): # mimick Math.LatFix

721 '''Replace angle in C{degrees} outside [-90,90] by NAN.

722

723 @return: Angle C{degrees} or NAN.

724 '''

725 try:

726 return _wrapped.Math.LatFix(deg)

727 except AttributeError:

728 return NAN if fabs(deg) > 90 else deg

729

730

731 def _isfinite(x): # mimick geomath.Math.isfinite

732 '''Check finiteness of C{x}.

733

734 @return: C{True} if finite.

735 '''

736 try:

737 return _wrapped.Math.isfinite(x)

738 except AttributeError:

739 return _math_isfinite(x) # and fabs(x) <= _MAX

740

741

742 def _llz2gl(gl, **llz2): # see .geodesici._llz2G

743 '''(INTERNAL) Set C{gl.lat2, .lon2, .azi2} from C{llz2}.

744 '''

745 if llz2:

746 for n in (_lat2_, _lon2_, _azi2_): # _lat1_, _lon1_, _azi1_

747 v = llz2.get(n, None)

748 if v is not None:

749 setattr(gl, n, v)

750 return gl

751

752

753 def _norm2(x, y): # mimick geomath.Math.norm

754 '''Normalize C{B{x}} and C{B{y}}.

755

756 @return: 2-Tuple of C{(B{x}, B{y})}, normalized.

757 '''

758 try:

759 return _wrapped.Math.norm(x, y)

760 except AttributeError:

761 return norm2(x, y)

762

763

764 def _norm180(deg): # mimick geomath.Math.AngNormalize

765 '''Reduce angle in C{degrees} to (-180,180].

766

767 @return: Reduced angle C{degrees}.

768 '''

769 try:

770 return _wrapped.Math.AngNormalize(deg)

771 except AttributeError:

772 d = fremainder(deg, _360_0)

773 if d in (_180_0, _N_180_0):

774 d = _copysign(_180_0, deg) if _K_2_0 else _180_0

775 return d

776

777

778 def _polygon(geodesic, points, closed, line, wrap):

779 '''(INTERNAL) Compute the area or perimeter of a polygon,

780 using a L{GeodesicExact}, L{GeodesicSolve} or (if the

781 C{geographiclib} package is installed) a C{Geodesic}

782 or C{geodesicw.Geodesic} instance.

783 '''

784 if not wrap: # capability LONG_UNROLL can't be off

785 notImplemented(None, wrap=wrap, up=3)

786

787 if _MODS.booleans.isBoolean(points):

788 # recursive call for each boolean clip

789

790 def _a_p(clip, *args, **unused):

791 return _polygon(geodesic, clip, *args)

792

793 if not closed: # closed only

794 raise _ValueError(closed=closed, points=_composite_)

795

796 return points._sum1(_a_p, closed, line, wrap)

797

798 gP = geodesic.Polygon(line)

799 _A = gP.AddPoint

800

801 Ps = _MODS.iters.PointsIter(points, loop=1, wrap=wrap) # base=LatLonEllipsoidalBase(0, 0)

802 p1 = p0 = Ps[0]

803

804 # note, lon deltas are unrolled, by default

805 _A(p1.lat, p1.lon)

806 for p2 in Ps.iterate(closed=closed):

807 if wrap and not Ps.looped:

808 p2 = _unrollon(p1, p2)

809 _A(p2.lat, p2.lon)

810 p1 = p2

811 if closed and line and p1 != p0:

812 _A(p0.lat, p0.lon)

813

814 # gP.Compute returns (number_of_points, perimeter, signed area)

815 return gP.Compute(False, True)[1 if line else 2]

816

817

818 try:

819 from math import fma as _fma # since 3.13

820

821 def _poly_fma(x, s, *cs):

822 for c in cs:

823 s = _fma(s, x, c)

824 return s

825

826 except ImportError: # Python 3.12-

827

828 def _poly_fma(x, s, *cs): # PYCHOK redef

829 t = _0_0

830 for c in cs:

831 s, t, _ = _sum3(s * x, t * x, c)

832 return s + t

833

834# def _poly_fma(x, *cs):

835# S = Fhorner(x, *cs, incx=False)

836# return float(S)

837

838 def _polynomial(x, cs, i, j): # PYCHOK shared

839 '''(INTERNAL) Like C++ C{GeographicLib.Math.hpp.polyval} but with a

840 signature and cascaded summation different from C{karney._sum3}.

841

842 @return: M{sum(x**(j - k - 1) * cs[k] for k in range(i, j)}

843 '''

844 if (i + 1) < j <= len(cs): # load _Rtuple._tuple

845 try:

846 r = _wrapped.Math.polyval(j - i - 1, cs, i, x)

847 except AttributeError:

848 r = _poly_fma(x, *cs[i:j])

849 else:

850 r = cs[i]

851 return float(r)

852

853

854 def _remainder(x, y):

855 '''Remainder of C{x / y}.

856

857 @return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0.

858 '''

859 try:

860 return _wrapped.Math.remainder(x, y)

861 except AttributeError:

862 return fremainder(x, y)

863

864

865 if _K_2_0:

866 from math import cos as _cos, sin as _sin

867

868 def _sincos2(rad):

869 return _sin(rad), _cos(rad)

870

871 _signBit = _MODS.basics.signBit

872 else:

873 _sincos2 = _MODS.utily.sincos2 # PYCHOK shared

874

875 def _signBit(x):

876 '''(INTERNAL) GeographicLib 1.52-.

877 '''

878 return x < 0

879

880

881 def _sincos2d(deg):

882 '''Return sine and cosine of an angle in C{degrees}.

883

884 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.

885 '''

886 try:

887 return _wrapped.Math.sincosd(deg)

888 except AttributeError:

889 return sincos2d(deg)

890

891

892 def _sincos2de(deg, t):

893 '''Return sine and cosine of a corrected angle in C{degrees}.

894

895 @return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}.

896 '''

897 try:

898 return _wrapped.Math.sincosde(deg, t)

899 except AttributeError:

900 return sincos2d(deg, adeg=t)

901

902

903 def _sum2(a, b): # mimick geomath.Math.sum, actually sum2

904 '''Error-free summation like C{geomath.Math.sum}.

905

906 @return: 2-Tuple C{(B{a} + B{b}, residual)}.

907

908 @note: The C{residual} can be the same as B{C{a}} or B{C{b}}.

909

910 @see: U{TwoSum<https://accurate-algorithms.readthedocs.io/en/latest/ch04summation.html>}

911 and I{Knuth}'s U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}.

912 '''

913 try:

914 return _wrapped.Math.sum(a, b)

915 except AttributeError:

916 # if Algorithm_3_1:

917 s = a + b

918 r = s - b

919 t = s - r

920 # elif C_CPP: # Math::sum C/C++

921 # r -= a; t -= b; t += r; t = -t

922 # else:

923 t = (a - r) + (b - t)

924 # assert fabs(s) >= fabs(t)

925 return s, t

926

927

928 def _sum3(s, t, *xs):

929 '''Accumulate any B{C{xs}} into a previous C{_sum2(s, t)}.

930

931 @return: 3-Tuple C{(s, t, n)} where C{s} is the sum of B{s}, B{t} and all

932 B{xs}, C{t} the residual and C{n} the number of zero C{xs}.

933

934 @see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/

935 C++/doc/Accumulator_8hpp_source.html>} comments for more details and

936 function C{_sum2} above.

937

938 @note: Not "error-free", see C{pygeodesy.test/testKarney.py}.

939 '''

940 z = 0

941 for x in xs:

942 if x:

943 t, r = _sum2(t, x) # start at the least-

944 if s:

945 s, t = _sum2(s, t) # -significant end

946 if s:

947 t += r # accumulate r into t

948 else:

949 # assert t == 0 # s == 0 implies t == 0

950 s = unsigned0(r) # result is r, t = 0

951 else:

952 s, t = unsigned0(t), r

953 else:

954 z += 1

955 # assert fabs(s) >= fabs(t)

956 return s, t, z

957

958

959 def _tand(x):

960 '''Return C{tan(B{x})} in C{degrees}.

961 '''

962 try:

963 return _wrapped.Math.tand(x)

964 except AttributeError:

965 return tand(x)

966

967

968 def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2

969 '''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}.

970

971 @return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}}

972 unrolled if C{B{wrap} is True}, normalized otherwise.

973 '''

974 if wrap:

975 d, t = _diff182(lon1, lon2)

976 lon2, t, _ = _sum3(d, t, lon1) # (lon1 + d) + t

977 lon2 += t

978 else:

979 lon2 = _norm180(lon2)

980 return (lon2 - lon1), lon2

981

982

983 def _unsigned2(x):

984 '''(INTERNAL) Unsign B{C{x}}.

985 '''

986 return (neg(x), True) if _signBit(x) else (x, False)

987

988

989__all__ += _ALL_DOCS(_CapsBase)

990

991# **) MIT License

992#

993# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

994#

995# Permission is hereby granted, free of charge, to any person obtaining a

996# copy of this software and associated documentation files (the "Software"),

997# to deal in the Software without restriction, including without limitation

998# the rights to use, copy, modify, merge, publish, distribute, sublicense,

999# and/or sell copies of the Software, and to permit persons to whom the

1000# Software is furnished to do so, subject to the following conditions:

1001#

1002# The above copyright notice and this permission notice shall be included

1003# in all copies or substantial portions of the Software.

1004#

1005# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1006# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1007# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1008# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1009# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1010# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1011# OTHER DEALINGS IN THE SOFTWARE.