1

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

3

4 u'''A pure Python implementation of geodesy tools for various ellipsoidal and spherical earth models

5 using precision exact, elliptic, trigonometric, vector-based, iterative and approximate methods for

6 geodetic (lat-/longitude), geocentric (U{ECEF<https://WikiPedia.org/wiki/ECEF>} cartesian), local (U{LTP

7<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>) and certain U{triaxial ellipsoidal

8<https://GeographicLib.SourceForge.io/1.44/triaxial.html>} coordinates.

9

10 Transcoded in part from U{JavaScript originals<https://GitHub.com/ChrisVeness/geodesy>} by I{Chris Veness (C)

11 2005-2024} and from several U{C++ classes<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>} by I{Charles

12 F. F. Karney (C) 2008-2024} and published under the same U{MIT License<https://OpenSource.org/licenses/MIT>}**.

13

14 There are four modules for ellipsoidal earth models, C{ellipsoidalExact}, C{-Karney}, C{-Vincenty} and C{-Nvector}

15 and two for spherical ones, C{sphericalTrigonometry} and C{-Nvector}. Each module provides a geodetic B{C{LatLon}}

16 and a geocentric B{C{Cartesian}} class with methods and functions to compute distance, surface area, perimeter,

17 forward and reverse azimuth, initial and final bearing, intermediate and nearest points, intersections of geodesic,

18 great circle and rhumb lines, circle intersections and secants, U{3-point resections

19<https://WikiPedia.org/wiki/Position_resection_and_intersection>}, triangulation, trilateration (by intersection,

20 by overlap and in 3-D), conversions and unrolling, among other things.

21

22 Also included are modules for conversions to and from U{Cassini-Soldner

23<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1CassiniSoldner.html>},

24 U{ECEF<https://WikiPedia.org/wiki/ECEF>} (Earth-Centered, Earth-Fixed cartesian), U{UTM

25<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} (Universal Transverse Mercator

26 and U{Exact<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}),

27 U{UPS<https://WikiPedia.org/wiki/Universal_polar_stereographic_coordinate_system>} (Universal Polar

28 Stereographic) and U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>} (Pseudo-Mercator) coordinates,

29 U{MGRS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1MGRS.html>} (Military Grid Reference

30 System, UTM I{and} UPS) and U{OSGR<https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} (British

31 Ordinance Survery Grid Reference) grid references, U{TRF<http://ITRF.ENSG.IGN.Fr>} (Terrestrial Reference

32 Frames) and modules to encode and decode U{EPSG<https://EPSG.org>}, U{Geohashes

33<https://www.Movable-Type.co.UK/scripts/geohash.html>}, U{Georefs (WGRS)

34<https://WikiPedia.org/wiki/World_Geographic_Reference_System>} and U{Garefs (GARS)

35<https://WikiPedia.org/wiki/Global_Area_Reference_System>}.

36

37 Other modules provide U{Albers equal-area

38<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AlbersEqualArea.html>} projections, U{equidistant

39<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>} and other I{azimuthal}

40 projections, Lambert I{conformal conic} projections and positions, functions to clip paths or polygons of C{LatLon}

41 points using the U{Cohen-Sutherland<https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>},

42 U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/article/pii/S259014861930007X>},

43 U{Greiner-Hormann<http://www.inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>},

44 U{Liang-Barsky<https://www.CS.Helsinki.FI/group/goa/viewing/leikkaus/intro.html>} and

45 U{Sutherland-Hodgman<https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} methods,

46 functions to U{simplify<https://Bost.Ocks.org/mike/simplify>} or linearize a path of C{LatLon}

47 points (or a U{NumPy array<https://docs.SciPy.org/doc/numpy/reference/generated/numpy.array.html>}),

48 including implementations of the U{Ramer-Douglas-Peucker<https://WikiPedia.org/wiki/

49 Ramer-Douglas-Peucker_algorithm>}, the U{Visvalingam-Whyatt<https://hydra.Hull.ac.UK/

50 resources/hull:8338>} and the U{Reumann-Witkam<https://psimpl.SourceForge.net/reumann-witkam.html>}

51 algorithms and modified versions of the former.

52

53 Plus modules and classes to U{interpolate<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} the

54 L{height<pygeodesy.heights>} of C{LatLon} points and L{Geoid<pygeodesy.geoids>} models, compute various U{Fréchet

55<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/wiki/Hausdorff_distance>}

56 distances or perform I{boolean} operations between (composite) polygons.

57

58 For further details see the U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}, the descriptions of

59 U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}, U{Vincenty

60<https://www.Movable-Type.co.UK/scripts/latlong-vincenty.html>} and U{Vector-based

61<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>} geodesy, the original U{JavaScript source

62<https://GitHub.com/ChrisVeness/geodesy>} or U{docs<https://www.Movable-Type.co.UK/scripts/geodesy/docs>}

63 and I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} and C++ U{GeographicLib

64<https://GeographicLib.SourceForge.io/C++/doc/index.html>}.

65

66 Installation

67============

68

69 To install C{pygeodesy}, type C{python[3] -m pip install pygeodesy} or C{python[3] -m easy_install

70 pygeodesy} in a terminal or command window.

71

72 If the wheel C{pygeodesy-yy.m.d-py2.py3-none-any.whl} is missing in U{PyPI Download files<https://

73 PyPI.org/project/pygeodesy/#files>}, download the file from U{GitHub/dist<https://GitHub.com/mrJean1/

74 PyGeodesy/tree/master/dist>}. Install that with C{python[3] -m pip install <path-to-downloaded-wheel>}

75 and verify with C{python[3] -m pygeodesy}.

76

77 Alternatively, download C{pygeodesy-yy.m.d.tar.gz} from U{PyPI<https://PyPI.org/project/pygeodesy>}

78 or U{GitHub<https://GitHub.com/mrJean1/PyGeodesy>}, C{unzip} the downloaded file, C{cd} to

79 directory C{pygeodesy-yy.m.d} and type C{python[3] setup.py install}.

80

81 To run all C{pygeodesy} tests, type C{python[3] test/run.py} or type C{python[3] test/unitTestSuite.py}

82 before or after installation.

83

84 Dependencies

85============

86

87 Installation of I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}

88 is optional, but required for module L{ellipsoidalKarney}, L{azimuthal} classes L{EquidistantKarney}

89 and L{GnomonicKarney} and the L{HeightIDWkarney} interpolator.

90

91 Both U{numpy<https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>} must be

92 installed for most L{Geoid...<pygeodesy.geoids>} and L{Height...<pygeodesy.heights>} interpolators,

93 except L{GeoidKarney} and the L{HeightIDW...<pygeodesy.heights>} ones.

94

95 Functions and C{LatLon} methods L{circin6}, L{circum3}, L{circum4_} and L{soddy4} and functions

96 L{triaxum5} and L{trilaterate3d2} require U{numpy<https://PyPI.org/project/numpy>} to be installed,

97 modules L{auxilats} and L{rhumb} may need U{numpy<https://PyPI.org/project/numpy>}.

98

99 Modules L{ellipsoidalGeodSolve} and L{geodsolve} and L{azimuthal} classes L{EquidistantGeodSolve}

100 and L{GnomonicGeodSolve} depend on I{Karney}'s C++ utility U{GeodSolve

101<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} to be executable and set with

102 env variable C{PYGEODESY_GEODSOLVE} or with property L{Ellipsoid.geodsolve}.

103

104 Class L{Intersectool} in module L{geodesici} needs I{Karney}'s C++ utility U{IntersectTool

105<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} to be executable and set with

106 env variable C{PYGEODESY_INTERSECTTOOL}.

107

108 To compare C{MGRS} results from modules L{mgrs} and C{testMgrs} with I{Karney}'s C++ utility

109 U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html>}, the latter must

110 be executable and set with env variable C{PYGEODESY_GEOCONVERT}.

111

112 Module L{rhumb.solve} needs I{Karney}'s C++ utility U{RhumbSolve

113<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} to be executable and set with

114 env variable C{PYGEODESY_RHUMBSOLVE} or with property L{Ellipsoid.rhumbsolve}.

115

116 Documentation

117=============

118

119 In addition to the C{pygeodesy} package, the U{pygeodesy<https://PyPI.org/project/pygeodesy>}

120 U{distribution files<https://GitHub.com/mrJean1/PyGeodesy/tree/master/dist>} contain the tests,

121 the test results (on macOS only) and the complete U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}

122(generated by U{Epydoc<https://PyPI.org/project/epydoc>} using command line:

123 C{epydoc --html --no-private --no-source --name=pygeodesy --url=... -v pygeodesy}).

124

125 Tests

126=====

127

128 The tests ran with Python 3.13.3 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0),

129 Python 3.12.7 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0,

130 U{numpy<https://PyPI.org/project/numpy>} 2.1.0, U{scipy<https://PyPI.org/project/scipy>} 1.14.1,

131 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3,

132 U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3 and

133 U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3),

134 Python 3.11.5 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0,

135 U{numpy<https://PyPI.org/project/numpy>} 1.24.2 and U{scipy<https://PyPI.org/project/scipy>} 1.10.1),

136 Python 3.10.8 (with U{geographiclib <https://PyPI.org/project/geographiclib>} 2.0,

137 U{numpy<https://PyPI.org/project/numpy>} 1.23.3, U{scipy<https://PyPI.org/project/scipy>} 1.9.1,

138 U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3,

139 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3) and

140 Python 2.7.18 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50,

141 U{numpy<https://PyPI.org/project/numpy>} 1.16.6, U{scipy<https://PyPI.org/project/scipy>} 1.2.2,

142 U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3,

143 U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3,

144 U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3 and

145 U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.3), all in 64-bit on

146 macOS 15.4.1 Sequoia.

147

148 All tests ran with and without C{lazy import} for Python 3 and with command line option C{-W default} and

149 env variable C{PYGEODESY_WARNINGS=on} for all Python versions. The results of those tests are included in

150 the distribution files.

151

152 Test coverage has been measured with U{coverage<https://PyPI.org/project/coverage>} 7.6.1 using Python

153 3.13.3, 3.12.7, 3.11.5 and 3.10.8. The complete coverage report in HTML and a PDF summary are included in

154 the distribution files.

155

156 Python 3.13.3, 3.12.7, 3.11.5 and 3.10.8 run on Apple M4 Si (C{arm64}), I{natively}. Python 2.7.18 runs

157 on Intel (C{x86_64}) or Intel I{emulation} ("C{arm64_x86_64}", see function L{machine<pygeodesy.machine>}).

158

159 The tests also ran with Python 3.13.3 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on

160 U{Debian 12<https://Cirrus-CI.com/github/mrJean1/PyGeodesy/master>} in 64-bit only, with Python 3.12.5 (and

161 U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on U{Windows 2019Server

162<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64-bit only and with Python 2.7.18 (and U{geographiclib

163<https://PyPI.org/project/geographiclib>} 1.52) on U{Windows 10<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>}

164 in 64- and 32-bit.

165

166 A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller

167<https://PyPI.org/project/pyinstaller>} 3.4 and 64-bit Python 3.7.3 on macOS 10.13.6 High Sierra.

168

169 Previously, the tests were run with Python 3.13.0-2, 3.12.0-6, 3.11.2-4, 3.10.1-7, 3.9.6, 3.9.1, 3.8.7, 3.7.1, 2.7.15,

170 U{PyPy<https://PyPy.org>} 7.3.12 (Python 3.10.12), 7.3.1 (Python 3.6.9) and U{PyPy<https://PyPy.org>} 7.1.1 (Python

171 2.7.13) (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.52, U{numpy<https://PyPI.org/project/numpy>}

172 1.16.3, 1.16.4, 1.16.6, 1.19.0, 1.19.4, 1.19.5 or 1.22.4 and U{scipy<https://PyPI.org/project/scipy>} 1.2.1, 1.4.1,

173 1.5.2 or 1.8.1) on U{Ubuntu 16.04<https://Travis-CI.com/mrJean1/PyGeodesy>}, with Python 3.10.0-1, 3.9.0-5, 3.8.0-6,

174 3.7.2-6, 3.7.0, 3.6.2-5, 3.5.3, 2.7.13-17, 2.7.10 and 2.6.9 (and U{numpy<https://PyPI.org/project/numpy>} 1.19.0,

175 1.16.5, 1.16.2, 1.15.2, 1.14.0, 1.13.1, 1.8.0rc1 or 1.6.2 and U{scipy<https://PyPI.org/project/scipy>} 1.5.0), U{PyPy

176<https://PyPy.org>} 7.3.0 (Python 2.7.13 and 3.6.9), U{PyPy<https://PyPy.org>} 6.0.0 (Python 2.7.13 and 3.5.3)

177 and U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy

178<https://PyPI.org/project/numpy>} 1.11.3) on macOS 14.0-6.1 Sonoma, 13.0-5.2 Ventura, 12.1-6 Monterey, 11.0-5.2-6.1

179 Big Sur (aka 10.16), 10.15.3, 10.15.5-7 Catalina, 10.14 Mojave, 10.13.6 High Sierra and 10.12 Sierra, MacOS X

180 10.11 El Capitan and/or MacOS X 10.10 Yosemite, with U{Pythonista<https://OMZ-Software.com/pythonista>}3.2 (with

181 geographiclib 1.50 or 1.49 and numpy 1.8.0) on iOS 14.4.2, 11.4.1, 12.0-3 on iPad4, iPhone6, iPhone10 and/or

182 iPhone12, with U{Pythonista<https://OMZ-Software.com/pythonista>} 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3

183 on iPad4, all in 64-bit only and with 32-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with

184 32-bit Python 2.6.6 on Windows XP SP3.

185

186 Notes

187=====

188

189 All Python source code has been statically U{checked<https://GitHub.com/ActiveState/code/tree/master/recipes/

190 Python/546532_PyChecker_postprocessor>} with U{PyChecker<https://PyPI.org/project/pychecker>}, U{PyFlakes

191<https://PyPI.org/project/pyflakes>}, U{PyCodeStyle<https://PyPI.org/project/pycodestyle>} (formerly Pep8) and

192 U{McCabe<https://PyPI.org/project/mccabe>} using Python 2.7.18 and with U{Flake8<https://PyPI.org/project/flake8>}

193 using Python 3.11.5, both in 64-bit on macOS 15.4.1 Sequoia.

194

195 For a summary of all I{Karney}-based functionality in C{pygeodesy}, see module U{karney

196<https://mrJean1.GitHub.io/PyGeodesy/docs/pygeodesy.karney-module.html>}.

197

198 In Python 2, symbols L{S_DEG}, L{S_MIN}, L{S_SEC}, L{S_RAD} and L{S_SEP} may be multi-byte, non-ascii

199 characters and if so, I{not} C{unicode}.

200

201 Env variables

202=============

203

204 The following environment variables are observed by C{pygeodesy}:

205

206 - C{PYGEODESY_EXCEPTION_CHAINING} - see module L{errors<pygeodesy.errors>}.

207 - C{PYGEODESY_FMT_FORM} - see module L{dms<pygeodesy.dms>}.

208 - C{PYGEODESY_FSUM_F2PRODUCT} - see module L{fsums<pygeodesy.fsums>} and method L{f2product<pygeodesy.Fsum.f2product>}.

209 - C{PYGEODESY_FSUM_NONFINITES} - see module L{fsums<pygeodesy.fsums>} and method L{nonfinites<pygeodesy.Fsum.nonfinites>}.

210 - C{PYGEODESY_FSUM_RESIDUAL} - see module L{fsums<pygeodesy.fsums>} and method L{RESIDUAL<pygeodesy.Fsum.RESIDUAL>}.

211 - C{PYGEODESY_GEOCONVERT} - see module L{mgrs<pygeodesy.mgrs>}.

212 - C{PYGEODESY_GEODSOLVE} - see module L{geodsolve<pygeodesy.geodsolve>}.

213 - C{PYGEODESY_INTERSECTTOOL} - see module L{geodesici<pygeodesy.geodesici>}.

214 - C{PYGEODESY_LAZY_IMPORT} - see module L{lazily<pygeodesy.lazily>} and variable L{isLazy<pygeodesy.isLazy>}.

215 - C{PYGEODESY_NOTIMPLEMENTED} - C{__special__} methods return C{NotImplemented} if set to "std".

216 - C{PYGEODESY_RHUMBSOLVE} - see module L{rhumb.solve<pygeodesy.rhumb.solve>}.

217 - C{PYGEODESY_UPS_POLES} - see modules L{ups<pygeodesy.ups>} and L{mgrs<pygeodesy.mgrs>}.

218

219 and these to specify standard or I{named} C{repr}esentations:

220

221 - C{PYGEODESY_AZIMUTH_STD_REPR} - see method L{Azimuth<pygeodesy.Azimuth>}C{.__repr__}.

222 - C{PYGEODESY_BEARING_STD_REPR} - see method L{Bearing<pygeodesy.Bearing>}C{.__repr__}.

223 - C{PYGEODESY_BOOL_STD_REPR} - see method L{Bool<pygeodesy.Bool>}C{.__repr__}.

224 - C{PYGEODESY_DEGREES_STD_REPR} - see method L{Degrees<pygeodesy.Degrees>}C{.__repr__}.

225 - C{PYGEODESY_EPOCH_STD_REPR} - see method L{Float<pygeodesy.Epoch>}C{.__repr__}.

226 - C{PYGEODESY_FLOAT_STD_REPR} - see method L{Float<pygeodesy.Float>}C{.__repr__}.

227 - C{PYGEODESY_INT_STD_REPR} - see method L{Int<pygeodesy.Int>}C{.__repr__}.

228 - C{PYGEODESY_METER_STD_REPR} - see method L{Meter<pygeodesy.Meter>}C{.__repr__}.

229 - C{PYGEODESY_RADIANS_STD_REPR} - see method L{Radians<pygeodesy.Radians>}C{.__repr__}.

230 - C{PYGEODESY_STR_STD_REPR} - see method L{Str<pygeodesy.Str>}C{.__repr__}.

231

232 plus during development:

233

234 - C{PYGEODESY_FOR_DOCS} - for extended documentation by C{epydoc}.

235 - C{PYGEODESY_GEOGRAPHICLIB} - see module L{karney<pygeodesy.karney>}.

236 - C{PYGEODESY_WARNINGS} - see module L{props<pygeodesy.props>} and function L{DeprecationWarnings<pygeodesy.DeprecationWarnings>}.

237 - C{PYGEODESY_XPACKAGES} - see module L{basics<pygeodesy.basics>}.

238 - C{PYTHONDEVMODE} - see modules L{errors<pygeodesy.errors>} and L{props<pygeodesy.props>}.

239

240 and:

241

242 - C{PYGEODESY_INIT__ALL__} - Set env variable C{PYGEODESY_INIT__ALL__} to anything other than C{"__all__"} to avoid

243 importing all C{pygeodesy} modules unnecessarily (in Python 2 or with C{PYGEODESY_LAZY_IMPORT} turned off in Python

244 3). However, to import a C{pygeodesy} item, the item name must be qualified with the C{module} name, for example

245 C{ from pygeodesy.ellipsoidalExact import LatLon } or C{ from pygeodesy.deprecated import collins }

246

247 License

248=======

249

250**) U{Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.<https://OpenSource.org/licenses/MIT>}

251

252 C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software

253 and associated documentation files (the "Software"), to deal in the Software without restriction,

254 including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense,

255 and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so,

256 subject to the following conditions:}

257

258 C{The above copyright notice and this permission notice shall be included in all copies or substantial

259 portions of the Software.}

260

261 C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT

262 NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.

263 IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,

264 WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE

265 SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.}

266

267@newfield example: Example, Examples

268

269@var EPS: System's M{epsilon} ≈ 2.22044604925e-16 (C{float}).

270@var EPS0: M{EPS**2} ≈ 4.9e-32 for near-zero comparison

271@var EPS02: M{EPS**4} ≈ 2.4e-63 for near-zero squared comparison

272@var EPS1: M{1 - EPS} ≈ 0.9999999999999998 (C{float}).

273@var EPS2: M{EPS * 2} ≈ 4.440892098501e-16 (C{float}).

274@var EPS_2: M{EPS / 2} ≈ 1.110223024625e-16 (C{float}).

275@var EPS4: M{EPS * 4} ≈ 8.881784197001e-16 (C{float}).

276

277@var F_D: Format degrees as unsigned "deg°" with symbol, plus compass point suffix C{N, S, E} or C{W} (C{str}).

278@var F_DM: Format degrees as unsigned "deg°min′" with symbols, plus suffix (C{str}).

279@var F_DMS: Format degrees as unsigned "deg°min′sec″" with symbols, plus suffix (C{str}).

280@var F_DEG: Format degrees as unsigned "[D]DD" I{without} symbol, plus suffix (C{str}).

281@var F_MIN: Format degrees as unsigned "[D]DDMM" I{without} symbols, plus suffix (C{str}).

282@var F_SEC: Format degrees as unsigned "[D]DDMMSS" I{without} symbols, plus suffix (C{str}).

283@var F_D60: Format degrees as unsigned "[D]DD.MMSS" C{sexagecimal} I{without} symbols, plus suffix (C{str}).

284@var F__E: Format degrees as unsigned "%E" I{without} symbols, plus suffix (C{str}).

285@var F__F: Format degrees as unsigned "%F" I{without} symbols, plus suffix (C{str}).

286@var F__G: Format degrees as unsigned "%G" I{without} symbols, plus suffix (C{str}).

287@var F_RAD: Convert degrees to radians and format as unsigned "RR" with symbol, plus suffix (C{str}).

288

289@var F_D_: Format degrees as signed "-/deg°" with symbol, I{without} suffix (C{str}).

290@var F_DM_: Format degrees as signed "-/deg°min′" with symbols, I{without} suffix (C{str}).

291@var F_DMS_: Format degrees as signed "-/deg°min′sec″" with symbols, I{without} suffix (C{str}).

292@var F_DEG_: Format degrees as signed "-/[D]DD" I{without} symbol, I{without} suffix (C{str}).

293@var F_MIN_: Format degrees as signed "-/[D]DDMM" I{without} symbols, I{without} suffix (C{str}).

294@var F_SEC_: Format degrees as signed "-/[D]DDMMSS" I{without} symbols, I{without} suffix (C{str}).

295@var F_D60_: Format degrees as signed "-/[D]DD.MMSS" C{sexagecimal} I{without} symbols, I{without} suffix (C{str}).

296@var F__E_: Format degrees as signed "-/%E" I{without} symbols, I{without} suffix (C{str}).

297@var F__F_: Format degrees as signed "-/%F" I{without} symbols, I{without} suffix (C{str}).

298@var F__G_: Format degrees as signed "-/%G" I{without} symbols, I{without} suffix (C{str}).

299@var F_RAD_: Convert degrees to radians and format as signed "-/RR" I{without} symbol, I{without} suffix (C{str}).

300

301@var F_D__: Format degrees as signed "-/+deg°" with symbol, I{without} suffix (C{str}).

302@var F_DM__: Format degrees as signed "-/+deg°min′" with symbols, I{without} suffix (C{str}).

303@var F_DMS__: Format degrees as signed "-/+deg°min′sec″" with symbols, I{without} suffix (C{str}).

304@var F_DEG__: Format degrees as signed "-/+[D]DD" I{without} symbol, I{without} suffix (C{str}).

305@var F_MIN__: Format degrees as signed "-/+[D]DDMM" I{without} symbols, without suffix (C{str}).

306@var F_SEC__: Format degrees as signed "-/+[D]DDMMSS" I{without} symbols, I{without} suffix (C{str}).

307@var F_D60__: Format degrees as signed "-/+[D]DD.MMSS" C{sexagecimal} I{without} symbols, I{without} suffix (C{str}).

308@var F__E__: Format degrees as signed "-/+%E" I{without} symbols, I{without} suffix (C{str}).

309@var F__F__: Format degrees as signed "-/+%F" I{without} symbols, I{without} suffix (C{str}).

310@var F__G__: Format degrees as signed "-/+%G" I{without} symbols, I{without} suffix (C{str}).

311@var F_RAD__: Convert degrees to radians and format as signed "-/+RR" I{without} symbol, I{without} suffix (C{str}).

312

313@var DIG: System's M{float decimal digits} = 15 (C{int}).

314@var INF: Infinity (C{float}), see functions L{isinf<pygeodesy.isinf>} and L{isfinite<pygeodesy.isfinite>} and C{NINF}.

315@var INT0: C{int(0)}, missing Z-components, C{if B{z}=B{INT0}}, see functions L{isint0<pygeodesy.isint0>}, L{meeus2<pygeodesy.meeus2>}

316@var MANT_DIG: System's M{float mantissa bits} = 53 (C{int}).

317@var MAX: System's M{float max} ≈ 1.798e+308 (C{float}).

318@var MIN: System's M{float min} ≈ 2.225e-308 (C{float}).

319@var NAN: Not-A-Number (C{float}), see function L{isnan<pygeodesy.isnan>}.

320@var NEG0: Negative 0.0 (C{float}), see function L{isneg0<pygeodesy.isneg0>}.

321@var NINF: Negative infinity (C{float}), see function L{isninf<pygeodesy.isninf>} and C{INF}.

322@var NN: Empty (C{str}), U{I{Nomen Nescio}<https://Wiktionary.org/wiki/N.N.>}.

323

324@var PI: Constant M{math.pi} (C{float}).

325@var PI2: Two PI, M{PI * 2}, aka I{Tau} (C{float}).

326@var PI_2: Half PI, M{PI / 2} (C{float}).

327@var PI3: Three PI, M{PI * 3} (C{float}).

328@var PI3_2: One and a half PI, M{PI * 3 / 2} (C{float}).

329@var PI_3: One third PI, M{PI / 3} (C{float}).

330@var PI4: Four PI, M{PI * 4} (C{float}).

331@var PI_4: Quarter PI, M{PI / 4} (C{float}).

332

333@var R_MA: Equatorial earth radius (C{meter}), WGS84, EPSG:3785.

334@var R_MB: Polar earth radius (C{meter}), WGS84, EPSG:3785.

335@var R_M: Mean (spherical) earth radius (C{meter}).

336@var R_KM: Mean (spherical) earth radius (C{Km}, kilometer).

337@var R_NM: Mean (spherical) earth radius (C{NM}, nautical miles).

338@var R_SM: Mean (spherical) earth radius (C{SM}, statute miles).

339@var R_FM: Former FAI-Sphere earth radius (C{meter}).

340@var R_GM: Average earth radius, distance to geoid surface (C{meter})

341@var R_QM: Earth' (triaxial) quadratic mean radius (C{meter})

342@var R_VM: Aviation/Navigation earth radius (C{meter}).

343

344@var S_DEG: Degrees symbol, default C{"°"}

345@var S_MIN: Minutes symbol, default C{"′"} aka I{PRIME}

346@var S_SEC: Seconds symbol, default C{"″"} aka I{DOUBLE_PRIME}

347@var S_RAD: Radians symbol, default C{""} aka L{NN<pygeodesy.NN>}

348@var S_DMS: If C{True}, include, otherwise cancel all DMS symbols, default C{True}.

349@var S_SEP: Separator between C{deg°|min′|sec″|suffix}, default C{""} aka L{NN<pygeodesy.NN>}

350

351@var Conics: Registered, predefined conics (C{enum-like}).

352@var Datums: Registered, predefined datums (C{enum-like}).

353@var Ellipsoids: Registered, predefined ellipsoids (C{enum-like}).

354@var RefFrames: Registered, predefined reference frames (C{enum-like}).

355@var Transforms: Registered, predefined transforms (C{enum-like}).

356@var Triaxials: Registered, predefined triaxial ellipsoids (C{enum-like}).

357

358@var isLazy: Lazy import setting (C{int} 0, 1, 2 or 3+) from C{env} variable C{PYGEODESY_LAZY_IMPORT}, or C{None} if C{lazy import} is not supported or not enabled, or C{False} if initializing C{lazy import} failed.

359

360@var pygeodesy_abspath: Fully qualified C{pygeodesy} directory name (C{str}).

361

362@var version: Normalized C{pygeodesy} version (C{str}).

363'''

364

365 import os.path as _os_path

366 import sys as _sys

367

368_init__all__ = True

369# <https://PyInstaller.ReadTheDocs.io/en/stable/runtime-information.html>

370_isfrozen = getattr(_sys, 'frozen', False)

371 pygeodesy_abspath = _os_path.dirname(_os_path.abspath(__file__)) # _sys._MEIPASS + '/pygeodesy'

372_pygeodesy_ = __package__ or _os_path.basename(pygeodesy_abspath)

373

374 if _isfrozen: # avoid lazy import

375 _lazy_import2 = None

376 else:

377 # setting __path__ should ...

378 __path__ = [pygeodesy_abspath]

379 try: # ... make this import work, ...

380 import pygeodesy.lazily as _

381 except ImportError: # ... if it doesn't, extend _sys.path to include

382 # this very directory such that all public and private sub-modules

383 # can be imported (by epydoc, checked by PyChecker, etc.)

384 _sys.path.insert(0, pygeodesy_abspath) # XXX __path__[0]

385

386 try: # lazily requires Python 3.7+, see lazily.__doc__

387 from pygeodesy.lazily import _init__all__, _lazy_import2 # PYCHOK expected

388 _, __getattr__ = _lazy_import2(_pygeodesy_) # PYCHOK expected

389

390 except (ImportError, NotImplementedError): # LazyImportError

391 _lazy_import2 = None

392

393 if _init__all__ and not _lazy_import2: # import and set __all__

394

395 # import all public modules and export as such

396 import pygeodesy.albers as albers # PYCHOK exported

397 import pygeodesy.auxilats as auxilats # PYCHOK exported

398 import pygeodesy.azimuthal as azimuthal # PYCHOK exported

399 import pygeodesy.basics as basics # PYCHOK exported

400 import pygeodesy.booleans as booleans # PYCHOK exported

401 import pygeodesy.cartesianBase as cartesianBase # PYCHOK INTERNAL

402 import pygeodesy.clipy as clipy # PYCHOK exported

403 import pygeodesy.constants as constants # PYCHOK exported

404 import pygeodesy.css as css # PYCHOK exported

405 import pygeodesy.datums as datums # PYCHOK exported

406 import pygeodesy.deprecated as deprecated # PYCHOK exported

407 import pygeodesy.dms as dms # PYCHOK exported

408 import pygeodesy.ecef as ecef # PYCHOK exported

409 import pygeodesy.ecefLocals as ecefLocals # PYCHOK exported

410 import pygeodesy.elevations as elevations # PYCHOK exported

411 import pygeodesy.ellipsoidalBase as ellipsoidalBase # PYCHOK INTERNAL

412 import pygeodesy.ellipsoidalBaseDI as ellipsoidalBaseDI # PYCHOK INTERNAL

413 import pygeodesy.ellipsoidalExact as ellipsoidalExact # PYCHOK exported

414 import pygeodesy.ellipsoidalGeodSolve as ellipsoidalGeodSolve # PYCHOK exported

415 import pygeodesy.ellipsoidalKarney as ellipsoidalKarney # PYCHOK exported

416 import pygeodesy.ellipsoidalNvector as ellipsoidalNvector # PYCHOK exported

417 import pygeodesy.ellipsoidalVincenty as ellipsoidalVincenty # PYCHOK exported

418 import pygeodesy.ellipsoids as ellipsoids # PYCHOK exported

419 import pygeodesy.elliptic as elliptic # PYCHOK exported

420 import pygeodesy.epsg as epsg # PYCHOK exported

421 import pygeodesy.etm as etm # PYCHOK exported

422 import pygeodesy.errors as errors # PYCHOK exported

423 import pygeodesy.fmath as fmath # PYCHOK exported

424 import pygeodesy.formy as formy # PYCHOK exported

425 import pygeodesy.frechet as frechet # PYCHOK exported

426 import pygeodesy.fstats as fstats # PYCHOK exported

427 import pygeodesy.fsums as fsums # PYCHOK exported

428 import pygeodesy.gars as gars # PYCHOK exported

429 import pygeodesy.geodesici as geodesici # PYCHOK exported

430 import pygeodesy.geodesicw as geodesicw # PYCHOK exported

431 import pygeodesy.geodesicx as geodesicx # PYCHOK exported

432 import pygeodesy.geodsolve as geodsolve # PYCHOK exported

433 import pygeodesy.geohash as geohash # PYCHOK exported

434 import pygeodesy.geoids as geoids # PYCHOK exported

435 import pygeodesy.hausdorff as hausdorff # PYCHOK exported

436 import pygeodesy.heights as heights # PYCHOK exported

437 import pygeodesy.internals as internals # PYCHOK exported

438 import pygeodesy.interns as interns # PYCHOK exported

439 import pygeodesy.iters as iters # PYCHOK exported

440 import pygeodesy.karney as karney # PYCHOK exported

441 import pygeodesy.ktm as ktm # PYCHOK exported

442 import pygeodesy.latlonBase as latlonBase # PYCHOK INTERNAL

443 import pygeodesy.lazily as lazily # PYCHOK exported

444 import pygeodesy.lcc as lcc # PYCHOK exported

445 import pygeodesy.ltp as ltp # PYCHOK exported

446 import pygeodesy.ltpTuples as ltpTuples # PYCHOK exported

447 import pygeodesy.mgrs as mgrs # PYCHOK exported

448 import pygeodesy.named as named # PYCHOK exported

449 import pygeodesy.namedTuples as namedTuples # PYCHOK exported

450 import pygeodesy.nvectorBase as nvectorBase # PYCHOK INTERNAL

451 import pygeodesy.osgr as osgr # PYCHOK exported

452 import pygeodesy.points as points # PYCHOK exported

453 import pygeodesy.props as props # PYCHOK exported

454 import pygeodesy.resections as resections # PYCHOK exported

455 import pygeodesy.rhumb as rhumb # PYCHOK exported

456 import pygeodesy.simplify as simplify # PYCHOK exported

457 import pygeodesy.sphericalBase as sphericalBase # PYCHOK INTERNAL

458 import pygeodesy.sphericalNvector as sphericalNvector # PYCHOK exported

459 import pygeodesy.sphericalTrigonometry as sphericalTrigonometry # PYCHOK exported

460 import pygeodesy.solveBase as solveBase # PYCHOK exported

461 import pygeodesy.streprs as streprs # PYCHOK exported

462 import pygeodesy.trf as trf # PYCHOK exported

463 import pygeodesy.triaxials as triaxials # PYCHOK exported

464 import pygeodesy.units as units # PYCHOK exported

465 import pygeodesy.unitsBase as unitsBase # PYCHOK INTERNAL

466 import pygeodesy.ups as ups # PYCHOK exported

467 import pygeodesy.utily as utily # PYCHOK exported

468 import pygeodesy.utm as utm # PYCHOK exported

469 import pygeodesy.utmups as utmups # PYCHOK exported

470 import pygeodesy.utmupsBase as utmupsBase # PYCHOK INTERNAL

471 import pygeodesy.vector2d as vector2d # PYCHOK exported

472 import pygeodesy.vector3d as vector3d # PYCHOK exported

473 import pygeodesy.vector3dBase as vector3dBase # PYCHOK INTERNAL

474 import pygeodesy.webmercator as webmercator # PYCHOK exported

475 import pygeodesy.wgrs as wgrs # PYCHOK exported

476

477 # lift all public classes, constants, functions, etc. but ONLY

478 # from the following modules ... (see also David Beazley's

479 # talk <https://DaBeaz.com/modulepackage/index.html>) ... BUT

480 # NOT modules ellipsoidal*, epsg, gars, geohash, spherical*,

481 # vector and wgrs ... in order keep those as modules ONLY

482 from pygeodesy.albers import * # PYCHOK __all__

483 from pygeodesy.azimuthal import * # PYCHOK __all__

484# from pygeodesy.auxilats import * # PYCHOK __(_)__

485 from pygeodesy.basics import * # PYCHOK __all__

486 from pygeodesy.booleans import * # PYCHOK __all__

487 from pygeodesy.cartesianBase import * # PYCHOK __(_)__ INTERNAL

488 from pygeodesy.clipy import * # PYCHOK __all__

489 from pygeodesy.constants import * # PYCHOK __all__

490 from pygeodesy.css import * # PYCHOK __all__

491 from pygeodesy.datums import * # PYCHOK __all__

492 from pygeodesy.deprecated import * # PYCHOK __all__ DEPRECATED

493 from pygeodesy.dms import * # PYCHOK __all__

494 from pygeodesy.ecef import * # PYCHOK __all__

495# from pygeodesy.ecefLocals import * # PYCHOK __all__

496 from pygeodesy.elevations import * # PYCHOK __all__

497# from pygeodesy.ellipsoidalBase import * # PYCHOK __(_)__ INTERNAL

498# from pygeodesy.ellipsoidalBaseDI import * # PYCHOK __(_)__ INTERNAL

499# from pygeodesy.ellipsoidalExact import * # PYCHOK __(_)__

500# from pygeodesy.ellipsoidalGeodSolve import * # PYCHOK __(_)__

501# from pygeodesy.ellipsoidalKarney import * # PYCHOK __(_)__

502# from pygeodesy.ellipsoidalNvector import * # PYCHOK __(_)__

503 from pygeodesy.ellipsoidalVincenty import * # PYCHOK __(_)__

504 from pygeodesy.ellipsoids import * # PYCHOK __all__

505 from pygeodesy.elliptic import * # PYCHOK __all__

506 from pygeodesy.epsg import * # PYCHOK __all__

507 from pygeodesy.etm import * # PYCHOK __all__

508 from pygeodesy.errors import * # PYCHOK __all__

509 from pygeodesy.fmath import * # PYCHOK __all__

510 from pygeodesy.formy import * # PYCHOK __all__

511 from pygeodesy.frechet import * # PYCHOK __all__

512 from pygeodesy.fstats import * # PYCHOK __all__

513 from pygeodesy.fsums import * # PYCHOK __all__

514 from pygeodesy.gars import * # PYCHOK __all__

515 from pygeodesy.geodesici import * # PYCHOK __all__

516 from pygeodesy.geodesicw import * # PYCHOK __all__

517 from pygeodesy.geodesicx import * # PYCHOK __all__

518 from pygeodesy.geodsolve import * # PYCHOK __all__

519 from pygeodesy.geohash import * # PYCHOK __all__

520 from pygeodesy.geoids import * # PYCHOK __all__

521 from pygeodesy.hausdorff import * # PYCHOK __all__

522 from pygeodesy.heights import * # PYCHOK __all__

523 from pygeodesy.internals import * # PYCHOK __all__

524 from pygeodesy.interns import * # PYCHOK __all__

525 from pygeodesy.iters import * # PYCHOK __all__

526 from pygeodesy.karney import * # PYCHOK __all__

527 from pygeodesy.ktm import * # PYCHOK __all__

528 from pygeodesy.latlonBase import * # PYCHOK __(_)__ INTERNAL

529 from pygeodesy.lazily import * # PYCHOK __all__

530 from pygeodesy.lcc import * # PYCHOK __all__

531 from pygeodesy.ltp import * # PYCHOK __all__

532 from pygeodesy.ltpTuples import * # PYCHOK __all__

533 from pygeodesy.mgrs import * # PYCHOK __all__

534 from pygeodesy.named import * # PYCHOK __all__

535 from pygeodesy.namedTuples import * # PYCHOK __all__

536 from pygeodesy.nvectorBase import * # PYCHOK __(_)__ INTERNAL

537 from pygeodesy.osgr import * # PYCHOK __all__

538 from pygeodesy.points import * # PYCHOK __all__

539 from pygeodesy.props import * # PYCHOK __all__

540 from pygeodesy.resections import * # PYCHOK __all__

541 from pygeodesy.rhumb import * # PYCHOK __all__

542 from pygeodesy.simplify import * # PYCHOK __all__

543# from pygeodesy.sphericalBase import * # PYCHOK __(_)__ INTERNAL

544# from pygeodesy.sphericalNvector import * # PYCHOK __(_)__

545# from pygeodesy.sphericalTrigonometry import * # PYCHOK __(_)__

546# from pygeodesy.solveBase import * # PYCHOK __(_)__ INTERNAL

547 from pygeodesy.streprs import * # PYCHOK __all__

548 from pygeodesy.trf import * # PYCHOK __all__

549 from pygeodesy.triaxials import * # PYCHOK __all__

550 from pygeodesy.units import * # PYCHOK __all__

551 from pygeodesy.unitsBase import * # PYCHOK __all__ Float, ...

552 from pygeodesy.ups import * # PYCHOK __all__

553 from pygeodesy.utily import * # PYCHOK __all__

554 from pygeodesy.utm import * # PYCHOK __all__

555 from pygeodesy.utmups import * # PYCHOK __all__

556# from pygeodesy.utmupsBase import * # PYCHOK __(_)__ INTERNAL

557 from pygeodesy.vector2d import * # PYCHOK __all__

558 from pygeodesy.vector3d import * # PYCHOK __all__

559 from pygeodesy.vector3dBase import * # PYCHOK __(_)__ INTERNAL

560 from pygeodesy.webmercator import * # PYCHOK __all__

561 from pygeodesy.wgrs import * # PYCHOK __all__

562

563 def _all(globalocals):

564 from pygeodesy.internals import _headof, _DOT_ # PYCHOK expected

565 from pygeodesy.interns import NN as _NN, _attribute_, _COMMASPACE_, \

566 _module_, _s_, _UNDER_ # PYCHOK expected

567 from pygeodesy.streprs import Fmt as _Fmt # PYCHOK expected

568 # collect all public module and attribute names and check

569 # that modules are imported from this package, 'pygeodesy'

570 # (but the latter only when not bundled with PyInstaller or

571 # Py2Exe, since the file-layout is different. Courtesy of

572 # GilderGeek<https://GitHub.com/mrJean1/PyGeodesy/issues/31>)

573 ns = list(lazily._ALL_INIT)

574# XXX ps = () if _isfrozen else set([_pygeodesy_] + __name__.split(_DOT_))

575 for mod, attrs in lazily._all_enums():

576 mod = _headof(_headof(mod))

577 if mod not in globalocals:

578 t = _DOT_(_pygeodesy_, mod)

579 raise ImportError('missing %s%s: %s' % (_module_, _NN, t))

580 ns.append(mod)

581 # check that all other public attrs do exist

582 if attrs and isinstance(attrs, tuple):

583 attrs = lazily._ALL_ATTRS(attrs)

584 t = tuple(a for a in attrs if a not in globalocals)

585 if t:

586 s = _Fmt.SQUARE(_s_, len(t)) if len(t) > 1 else _NN

587 t = _COMMASPACE_.join(_DOT_(_pygeodesy_, mod, a) for a in t)

588 raise ImportError('missing %s%s: %s' % (_attribute_, s, t))

589 ns.extend(attrs)

590# XXX if ps: # check that mod is a _pygeodesy_ module

591# XXX m = globalocals[mod] # assert(typename(m) == mod)

592# XXX f = getattr(m, _dunder_file_, _NN)

593# XXX d = _os_path.dirname(_os_path.abspath(f)) if f else pygeodesy_abspath

594# XXX p = getattr(m, _dunder_package_, _NN) or _pygeodesy_

595# XXX if p not in ps or d != pygeodesy_abspath:

596# XXX t = '%s from %r' % (_DOT_(p, mod), f or p)

597# XXX raise ImportError('foreign %s: %s' % (_module_, t))

598 return tuple(set(ns)) # remove duplicates

599

600 __all__ = _all(globals()) # or locals()

601 else:

602 __all__ = ()

603 _init__all__ = False

604

605 from pygeodesy.internals import _version2, _DOT_ # PYCHOK import

606# from pygeodesy.interns import _DOT_ # from .internals

607__version__ = '25.05.05'

608# see setup.py for similar logic

609 version = _DOT_(*_version2(__version__, n=3))

610

611 del _DOT_, _lazy_import2, _os_path, _sys, _version2

612

613# **) MIT License

614#

615# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

616#

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

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

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

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

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

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

623#

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

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

626#

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

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

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

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

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

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

633# OTHER DEALINGS IN THE SOFTWARE.