Coverage for pygeodesy/__init__.py: 98%

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1 

2# -*- coding: utf-8 -*- 

3 

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

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

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

7cartesian) and certain U{triaxial ellipsoidal<https://GeographicLib.SourceForge.io/1.44/triaxial.html>} 

8coordinates. 

9 

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

11(C) 2005-2022} and from several U{C++ classes<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>} 

12by I{Charles F. F. Karney (C) 2008-2023} and published under the same U{MIT License 

13<https://OpenSource.org/licenses/MIT>}**. 

14 

15There are four modules for ellipsoidal earth models, C{ellipsoidalExact}, C{-Karney}, 

16C{-Vincenty} and C{-Nvector} and two for spherical ones, C{sphericalTrigonometry} 

17and C{-Nvector}. Each module provides a geodetic B{C{LatLon}} and a geocentric 

18B{C{Cartesian}} class with methods and functions to compute distance, surface area, 

19perimeter, initial and final bearing, intermediate and nearest points, circle intersections 

20and secants, path intersections, U{3-point resections<https://WikiPedia.org/wiki/ 

21Position_resection_and_intersection>}, rhumb and rhumb lines, triangulation, trilateration 

22(by intersection, by overlap and in 3d), conversions and unrolling, among other things. For 

23more information and further details see the U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}, 

24the descriptions of U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}, 

25U{Vincenty<https://www.Movable-Type.co.UK/scripts/latlong-vincenty.html>} and U{Vector-based 

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

27source<https://GitHub.com/ChrisVeness/geodesy>} or U{docs<https://www.Movable-Type.co.UK/scripts/geodesy/docs>} 

28and I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} and U{C++ GeographicLib 

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

30 

31Also included are modules for conversions to and from U{Cassini-Soldner 

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

33U{ECEF<https://WikiPedia.org/wiki/ECEF>} (Earth-Centered, Earth-Fixed cartesian), U{UTM 

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

35and U{Exact<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>}), 

36U{UPS<https://WikiPedia.org/wiki/Universal_polar_stereographic_coordinate_system>} (Universal Polar 

37Stereographic) and U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>} (Pseudo-Mercator) coordinates, 

38U{MGRS<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1MGRS.html>} (Military Grid Reference 

39System, UTM I{and} UPS) and U{OSGR<https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} (British 

40Ordinance Survery Grid Reference) grid references, U{TRF<http://ITRF.ENSG.IGN.Fr>} (Terrestrial Reference 

41Frames) and modules to encode and decode U{EPSG<https://EPSG.org>}, U{Geohashes 

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

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

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

45 

46Other modules provide U{Albers equal-area<https://GeographicLib.SourceForge.io/ 

47C++/doc/classGeographicLib_1_1AlbersEqualArea.html>} projections, U{equidistant 

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

49and other I{azimuthal} projections, Lambert I{conformal conic} projections and 

50positions, functions to clip paths or polygons of C{LatLon} points using the 

51U{Cohen-Sutherland<https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>}, 

52U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/article/pii/S259014861930007X>}, 

53U{Greiner-Hormann<http://www.inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}, 

54U{Liang-Barsky<https://www.CS.Helsinki.FI/group/goa/viewing/leikkaus/intro.html>} and 

55U{Sutherland-Hodgman<https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} methods, 

56functions to U{simplify<https://Bost.Ocks.org/mike/simplify>} or linearize a path of C{LatLon} 

57points (or a U{NumPy array<https://docs.SciPy.org/doc/numpy/reference/generated/numpy.array.html>}), 

58including implementations of the U{Ramer-Douglas-Peucker<https://WikiPedia.org/wiki/ 

59Ramer-Douglas-Peucker_algorithm>}, the U{Visvalingam-Whyatt<https://hydra.Hull.ac.UK/ 

60resources/hull:8338>} and the U{Reumann-Witkam<https://psimpl.SourceForge.net/reumann-witkam.html>} 

61algorithms and modified versions of the former. Other classes provide I{boolean} operations between 

62(composite) polygons or U{interpolate <https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} 

63the L{height<pygeodesy.heights>} of C{LatLon} points and L{Geoid<pygeodesy.geoids>} models, compute 

64various U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/ 

65wiki/Hausdorff_distance>} distances. 

66 

67Installation 

68============ 

69 

70To install PyGeodesy, type C{python[3] -m pip install PyGeodesy} or C{python[3] -m easy_install 

71PyGeodesy} in a terminal or command window. 

72 

73If the wheel C{PyGeodesy-yy.m.d-py2.py3-none-any.whl} is missing in U{PyPI Download files<https:// 

74PyPI.org/project/PyGeodesy/#files>}, download the file from U{GitHub/dist<https://GitHub.com/mrJean1/ 

75PyGeodesy/tree/master/dist>}. Install that with C{python[3] -m pip install <path-to-downloaded-wheel>} 

76and verify with C{python[3] -m pygeodesy}. 

77 

78Alternatively, download C{PyGeodesy-yy.m.d.zip} from U{PyPI<https://PyPI.org/project/PyGeodesy>} 

79or U{GitHub<https://GitHub.com/mrJean1/PyGeodesy>}, C{unzip} the downloaded file, C{cd} to 

80directory C{Pygeodesy-yy.m.d} and type C{python[3] setup.py install}. 

81 

82To run all PyGeodesy tests, type C{python[3] test/run.py} or type C{python[3] test/unitTestSuite.py} 

83before or after installation. 

84 

85Dependencies 

86============ 

87 

88Installation of I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>} 

89is optional, but required to use modules L{ellipsoidalKarney} and L{css}, L{azimuthal} classes 

90L{EquidistantKarney} and L{GnomonicKarney} and the L{HeightIDWkarney} interpolator. 

91 

92Both U{numpy<https://PyPI.org/project/numpy>} and U{scipy<https://PyPI.org/project/scipy>} must be 

93installed for most L{Geoid...<pygeodesy.geoids>} and L{Height...<pygeodesy.heights>} interpolators, 

94except L{GeoidKarney} and the L{HeightIDW...<pygeodesy.heights>} ones. 

95 

96Functions and C{LatLon} methods L{circin6}, L{circum3}, L{circum4_}, L{soddy4}, L{trilaterate3d2} do and 

97C{trilaterate5} and modules L{auxilats} and L{rhumb} may require U{numpy<https://PyPI.org/project/numpy>}. 

98 

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

100and 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 

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

103 

104To compare C{MGRS} results from modules L{mgrs} and C{testMgrs} with I{Karney}'s C++ utility 

105U{GeoConvert<https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html>}, the latter must 

106be executable and set with env variable C{PYGEODESY_GEOCONVERT}. 

107 

108Module L{rhumb.solve} needs I{Karney}'s C++ utility U{RhumbSolve 

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

110env variable C{PYGEODESY_RHUMBSOLVE} or with property L{Ellipsoid.rhumbsolve}. 

111 

112Documentation 

113============= 

114 

115In addition to the C{pygeodesy} package, the U{PyGeodesy<https://PyPI.org/project/PyGeodesy>} 

116U{distribution files<https://GitHub.com/mrJean1/PyGeodesy/tree/master/dist>} contain the tests, 

117the test results (on macOS only) and the complete U{documentation<https://mrJean1.GitHub.io/PyGeodesy>} 

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

119C{epydoc --html --no-private --no-source --name=PyGeodesy --url=... -v pygeodesy}). 

120 

121Tests 

122===== 

123 

124The tests ran with Python 3.12.3 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, 

125Python 3.11.5 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0, U{numpy 

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

1273.10.8 (with U{geographiclib <https://PyPI.org/project/geographiclib>} 2.0, U{numpy 

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

129<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.2, U{GeodSolve 

130<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.2 and U{RhumbSolve 

131<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.2), Python 3.9.6 and Python 2.7.18 (with 

132U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50, U{numpy<https://PyPI.org/project/numpy>} 

1331.16.6, U{scipy<https://PyPI.org/project/scipy>} 1.2.2, U{GeoConvert 

134<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.2, U{GeodSolve 

135<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.2 and U{RhumbSolve 

136<https://GeographicLib.SourceForge.io/C++/doc/utilities.html>} 2.2), all on macOS 14.5 Sonoma and 

137in 64-bit only. 

138 

139All tests ran with and without C{lazy import} for Python 3 and with command line option C{-W default} and 

140env variable C{PYGEODESY_WARNINGS=on} for all Python versions. The results of those tests are included in 

141the distribution files. 

142 

143Test coverage has been measured with U{coverage<https://PyPI.org/project/coverage>} 7.2.2 using only Python 

1443.11.5 and 3.10.8. The complete coverage report in HTML and a PDF summary are included in the distribution files. 

145 

146PyPy 7.3.12 (Python 3.10.12), Python 3.11.5, 3.10.8 and 3.9.6 ran on Apple M1 Silicon (C{arm64}), I{natively}. 

147Python 3.8.10 and 2.7.18 ran on Intel (C{x86_64}) or Intel I{emulation} ("C{arm64_x86_64}", see function 

148L{pygeodesy.machine}). 

149 

150The tests also ran with Python 3.11.5 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 2.0) on 

151U{Debian 11<https://Cirrus-CI.com/github/mrJean1/PyGeodesy/master>} in 64-bit only and with Python 3.11.5, 

1523.10.10 and 2.7.18 (all with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.52) on U{Windows 10 

153<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} in 64- and/or 32-bit. 

154 

155A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller 

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

157 

158Previously, the tests were run with Python 3.12.0-2, 3.11.2-4, 3.10.1-7, 3.9.1, 3.8.7, 3.7.1, 2.7.15, U{PyPy 

159<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 

1602.7.13) (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.52, U{numpy<https://PyPI.org/project/numpy>} 

1611.16.3, 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, 

1621.5.2 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, 

1633.7.2-6, 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, 

1641.16.5, 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 

165<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) 

166and U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy 

167<https://PyPI.org/project/numpy>} 1.11.3) on macOS 14.0-4.1 Sonoma, 13.0-5.2 Ventura, 12.1-6 Monterey, 11.0-5.2-6.1 

168Big 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 

16910.11 El Capitan and/or MacOS X 10.10 Yosemite, with U{Pythonista<https://OMZ-Software.com/pythonista>}3.2 (with 

170geographiclib 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 

171iPhone12, with U{Pythonista<https://OMZ-Software.com/pythonista>} 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 

172on iPad4, all in 64-bit only and with 32-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with 

17332-bit Python 2.6.6 on Windows XP SP3. 

174 

175Notes 

176===== 

177 

178All Python source code has been statically U{checked<https://GitHub.com/ActiveState/code/tree/master/recipes/ 

179Python/546532_PyChecker_postprocessor>} with U{PyChecker<https://PyPI.org/project/pychecker>}, U{PyFlakes 

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

181U{McCabe<https://PyPI.org/project/mccabe>} using Python 2.7.18 and with U{Flake8<https://PyPI.org/project/flake8>} 

182using Python 3.11.5, both in 64-bit on macOS 14.5 Sonoma. 

183 

184For a summary of all I{Karney}-based functionality in C{pygeodesy}, see module U{karney 

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

186 

187In 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 

188characters and if so, I{not} C{unicode}. 

189 

190Env variables 

191============= 

192 

193The following environment variables are observed by C{PyGeodesy}: 

194 

195 - C{PYGEODESY_EXCEPTION_CHAINING} - see module L{pygeodesy.errors}. 

196 - C{PYGEODESY_FMT_FORM} - see module L{pygeodesy.dms}. 

197 - C{PYGEODESY_FSUM_RESIDUAL} - see module L{pygeodesy.fsums} and class L{pygeodesy.Fsum}. 

198 - C{PYGEODESY_GEOCONVERT} - see module L{pygeodesy.mgrs}. 

199 - C{PYGEODESY_GEODSOLVE} - see module L{pygeodesy.geodsolve}. 

200 - C{PYGEODESY_LAZY_IMPORT} - see module L{pygeodesy.lazily} and variable L{pygeodesy.isLazy}. 

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

202 - C{PYGEODESY_RHUMBSOLVE} - see module L{pygeodesy.rhumb.solve}. 

203 - C{PYGEODESY_UPS_POLES} - see modules L{pygeodesy.ups} and L{pygeodesy.mgrs}. 

204 

205and these to control standard or I{named} C{repr}esentations: 

206 

207 - C{PYGEODESY_BEARING_STD_REPR} - see method L{pygeodesy.Bearing}C{.__repr__}. 

208 - C{PYGEODESY_BOOL_STD_REPR} - see method L{pygeodesy.Bool}C{.__repr__}. 

209 - C{PYGEODESY_DEGREES_STD_REPR} - see method L{pygeodesy.Degrees}C{.__repr__}. 

210 - C{PYGEODESY_FLOAT_STD_REPR} - see method L{pygeodesy.Float}C{.__repr__}. 

211 - C{PYGEODESY_INT_STD_REPR} - see method L{pygeodesy.Int}C{.__repr__}. 

212 - C{PYGEODESY_METER_STD_REPR} - see method L{pygeodesy.Meter}C{.__repr__}. 

213 - C{PYGEODESY_RADIANS_STD_REPR} - see method L{pygeodesy.Radians}C{.__repr__}. 

214 - C{PYGEODESY_STR_STD_REPR} - see method L{pygeodesy.Str}C{.__repr__}. 

215 

216plus during development: 

217 

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

219 - C{PYGEODESY_GEOGRAPHICLIB} - see module L{pygeodesy.karney}. 

220 - C{PYGEODESY_WARNINGS} - see module L{pygeodesy.props} and function L{pygeodesy.DeprecationWarnings}. 

221 - C{PYGEODESY_XPACKAGES} - see module L{pygeodesy.basics}. 

222 - C{PYTHONDEVMODE} - see modules L{pygeodesy.errors} and L{pygeodesy.props}. 

223 

224and: 

225 

226 - C{PYGEODESY_INIT__ALL__} - Set env variable C{PYGEODESY_INIT__ALL__} to anything 

227 other than C{"__all__"} to avoid importing all C{pygeodesy} modules unnecessarily 

228 (in Python 2 or with C{PYGEODESY_LAZY_IMPORT} turned off in Python 3). However, 

229 to import a C{pygeodesy} item, the item name must be qualified with the C{module} 

230 name, for example C{ from pygeodesy.ellipsoidalExact import LatLon } or C{ from 

231 pygeodesy.deprecated import collins } 

232 

233License 

234======= 

235 

236**) U{Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

237<https://OpenSource.org/licenses/MIT>} 

238 

239C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software 

240and associated documentation files (the "Software"), to deal in the Software without restriction, 

241including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 

242and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, 

243subject to the following conditions:} 

244 

245C{The above copyright notice and this permission notice shall be included in all copies or substantial 

246portions of the Software.} 

247 

248C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT 

249NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 

250IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 

251WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 

252SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.} 

253 

254@newfield example: Example, Examples 

255 

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

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

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

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

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

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

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

263 

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

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

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

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

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

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

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

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

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

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

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

275 

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

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

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

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

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

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

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

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

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

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

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

287 

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

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

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

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

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

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

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

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

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

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

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

299 

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

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

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

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

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

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

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

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

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

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

310 

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

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

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

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

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

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

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

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

319 

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

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

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

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

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

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

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

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

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

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

330 

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

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

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

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

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

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

337 

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

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

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

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

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

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

344 

345@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. 

346 

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

348 

349@var version: Normalized C{PyGeodesy} version (C{str}). 

350''' 

351 

352import os.path as _os_path 

353import sys as _sys 

354 

355_init__all__ = True 

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

357_isfrozen = getattr(_sys, 'frozen', False) 

358pygeodesy_abspath = _os_path.dirname(_os_path.abspath(__file__)) # _sys._MEIPASS + '/pygeodesy' 

359_pygeodesy_ = __package__ or _os_path.basename(pygeodesy_abspath) 

360 

361if _isfrozen: # avoid lazy import 

362 _lazy_import2 = None 

363else: 

364 # setting __path__ should ... 

365 __path__ = [pygeodesy_abspath] 

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

367 import pygeodesy.lazily as _ 

368 except ImportError: # ... if it doesn't, extend 

369 # _sys.path to include this very directory such 

370 # that all public and private sub-modules can 

371 # be imported (and checked by PyChecker, etc.) 

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

373 

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

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

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

377 

378 except (ImportError, NotImplementedError): # LazyImportError 

379 _lazy_import2 = None 

380 

381if _init__all__ and not _lazy_import2: # import and set __all__ 

382 

383 # import all public modules and export as such 

384 import pygeodesy.albers as albers # PYCHOK exported 

385 import pygeodesy.auxilats as auxilats # PYCHOK exported 

386 import pygeodesy.azimuthal as azimuthal # PYCHOK exported 

387 import pygeodesy.basics as basics # PYCHOK exported 

388 import pygeodesy.booleans as booleans # PYCHOK exported 

389 import pygeodesy.cartesianBase as cartesianBase # PYCHOK INTERNAL 

390 import pygeodesy.clipy as clipy # PYCHOK exported 

391 import pygeodesy.constants as constants # PYCHOK exported 

392 import pygeodesy.css as css # PYCHOK exported 

393 import pygeodesy.datums as datums # PYCHOK exported 

394 import pygeodesy.deprecated as deprecated # PYCHOK exported 

395 import pygeodesy.dms as dms # PYCHOK exported 

396 import pygeodesy.ecef as ecef # PYCHOK exported 

397 import pygeodesy.elevations as elevations # PYCHOK exported 

398 import pygeodesy.ellipsoidalBase as ellipsoidalBase # PYCHOK INTERNAL 

399 import pygeodesy.ellipsoidalBaseDI as ellipsoidalBaseDI # PYCHOK INTERNAL 

400 import pygeodesy.ellipsoidalExact as ellipsoidalExact # PYCHOK exported 

401 import pygeodesy.ellipsoidalGeodSolve as ellipsoidalGeodSolve # PYCHOK exported 

402 import pygeodesy.ellipsoidalKarney as ellipsoidalKarney # PYCHOK exported 

403 import pygeodesy.ellipsoidalNvector as ellipsoidalNvector # PYCHOK exported 

404 import pygeodesy.ellipsoidalVincenty as ellipsoidalVincenty # PYCHOK exported 

405 import pygeodesy.ellipsoids as ellipsoids # PYCHOK exported 

406 import pygeodesy.elliptic as elliptic # PYCHOK exported 

407 import pygeodesy.epsg as epsg # PYCHOK exported 

408 import pygeodesy.etm as etm # PYCHOK exported 

409 import pygeodesy.errors as errors # PYCHOK exported 

410 import pygeodesy.fmath as fmath # PYCHOK exported 

411 import pygeodesy.formy as formy # PYCHOK exported 

412 import pygeodesy.frechet as frechet # PYCHOK exported 

413 import pygeodesy.fstats as fstats # PYCHOK exported 

414 import pygeodesy.fsums as fsums # PYCHOK exported 

415 import pygeodesy.gars as gars # PYCHOK exported 

416 import pygeodesy.geodesicw as geodesicw # PYCHOK exported 

417 import pygeodesy.geodesicx as geodesicx # PYCHOK exported 

418 import pygeodesy.geodsolve as geodsolve # PYCHOK exported 

419 import pygeodesy.geohash as geohash # PYCHOK exported 

420 import pygeodesy.geoids as geoids # PYCHOK exported 

421 import pygeodesy.hausdorff as hausdorff # PYCHOK exported 

422 import pygeodesy.heights as heights # PYCHOK exported 

423 import pygeodesy.internals as internals # PYCHOK exported 

424 import pygeodesy.interns as interns # PYCHOK exported 

425 import pygeodesy.iters as iters # PYCHOK exported 

426 import pygeodesy.karney as karney # PYCHOK exported 

427 import pygeodesy.ktm as ktm # PYCHOK exported 

428 import pygeodesy.latlonBase as latlonBase # PYCHOK INTERNAL 

429 import pygeodesy.lazily as lazily # PYCHOK exported 

430 import pygeodesy.lcc as lcc # PYCHOK exported 

431 import pygeodesy.ltp as ltp # PYCHOK exported 

432 import pygeodesy.ltpTuples as ltpTuples # PYCHOK exported 

433 import pygeodesy.mgrs as mgrs # PYCHOK exported 

434 import pygeodesy.named as named # PYCHOK exported 

435 import pygeodesy.namedTuples as namedTuples # PYCHOK exported 

436 import pygeodesy.nvectorBase as nvectorBase # PYCHOK INTERNAL 

437 import pygeodesy.osgr as osgr # PYCHOK exported 

438 import pygeodesy.points as points # PYCHOK exported 

439 import pygeodesy.props as props # PYCHOK exported 

440 import pygeodesy.resections as resections # PYCHOK exported 

441 import pygeodesy.rhumb as rhumb # PYCHOK exported 

442 import pygeodesy.simplify as simplify # PYCHOK exported 

443 import pygeodesy.sphericalBase as sphericalBase # PYCHOK INTERNAL 

444 import pygeodesy.sphericalNvector as sphericalNvector # PYCHOK exported 

445 import pygeodesy.sphericalTrigonometry as sphericalTrigonometry # PYCHOK exported 

446 import pygeodesy.solveBase as solveBase # PYCHOK exported 

447 import pygeodesy.streprs as streprs # PYCHOK exported 

448 import pygeodesy.trf as trf # PYCHOK exported 

449 import pygeodesy.triaxials as triaxials # PYCHOK exported 

450 import pygeodesy.units as units # PYCHOK exported 

451 import pygeodesy.unitsBase as unitsBase # PYCHOK INTERNAL 

452 import pygeodesy.ups as ups # PYCHOK exported 

453 import pygeodesy.utily as utily # PYCHOK exported 

454 import pygeodesy.utm as utm # PYCHOK exported 

455 import pygeodesy.utmups as utmups # PYCHOK exported 

456 import pygeodesy.utmupsBase as utmupsBase # PYCHOK INTERNAL 

457 import pygeodesy.vector2d as vector2d # PYCHOK exported 

458 import pygeodesy.vector3d as vector3d # PYCHOK exported 

459 import pygeodesy.vector3dBase as vector3dBase # PYCHOK INTERNAL 

460 import pygeodesy.webmercator as webmercator # PYCHOK exported 

461 import pygeodesy.wgrs as wgrs # PYCHOK exported 

462 

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

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

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

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

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

468 from pygeodesy.albers import * # PYCHOK __all__ 

469 from pygeodesy.azimuthal import * # PYCHOK __all__ 

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

471 from pygeodesy.basics import * # PYCHOK __all__ 

472 from pygeodesy.booleans import * # PYCHOK __all__ 

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

474 from pygeodesy.clipy import * # PYCHOK __all__ 

475 from pygeodesy.constants import * # PYCHOK __all__ 

476 from pygeodesy.css import * # PYCHOK __all__ 

477 from pygeodesy.datums import * # PYCHOK __all__ 

478 from pygeodesy.deprecated import * # PYCHOK __all__ DEPRECATED 

479 from pygeodesy.dms import * # PYCHOK __all__ 

480 from pygeodesy.ecef import * # PYCHOK __all__ 

481 from pygeodesy.elevations import * # PYCHOK __all__ 

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

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

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

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

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

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

488 from pygeodesy.ellipsoidalVincenty import VincentyError # PYCHOK lazily 

489 from pygeodesy.ellipsoids import * # PYCHOK __all__ 

490 from pygeodesy.elliptic import * # PYCHOK __all__ 

491 from pygeodesy.epsg import Epsg, EPSGError # PYCHOK lazily 

492 from pygeodesy.etm import * # PYCHOK __all__ 

493 from pygeodesy.errors import * # PYCHOK __all__ 

494 from pygeodesy.fmath import * # PYCHOK __all__ 

495 from pygeodesy.formy import * # PYCHOK __all__ 

496 from pygeodesy.frechet import * # PYCHOK __all__ 

497 from pygeodesy.fstats import * # PYCHOK __all__ 

498 from pygeodesy.fsums import * # PYCHOK __all__ 

499 from pygeodesy.gars import Garef, GARSError # PYCHOK lazily 

500 from pygeodesy.geodesicw import * # PYCHOK __all__ 

501 from pygeodesy.geodesicx import * # PYCHOK __all__ 

502 from pygeodesy.geodsolve import * # PYCHOK __all__ 

503 from pygeodesy.geohash import Geohash, GeohashError, \ 

504 Neighbors8Dict, Resolutions2Tuple # PYCHOK lazily 

505 from pygeodesy.geoids import * # PYCHOK __all__ 

506 from pygeodesy.hausdorff import * # PYCHOK __all__ 

507 from pygeodesy.heights import * # PYCHOK __all__ 

508 from pygeodesy.internals import * # PYCHOK __all__ 

509 from pygeodesy.interns import * # PYCHOK __all__ 

510 from pygeodesy.iters import * # PYCHOK __all__ 

511 from pygeodesy.karney import * # PYCHOK __all__ 

512 from pygeodesy.ktm import * # PYCHOK __all__ 

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

514 from pygeodesy.lazily import * # PYCHOK __all__ 

515 from pygeodesy.lcc import * # PYCHOK __all__ 

516 from pygeodesy.ltp import * # PYCHOK __all__ 

517 from pygeodesy.ltpTuples import * # PYCHOK __all__ 

518 from pygeodesy.mgrs import * # PYCHOK __all__ 

519 from pygeodesy.named import * # PYCHOK __all__ 

520 from pygeodesy.namedTuples import * # PYCHOK __all__ 

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

522 from pygeodesy.osgr import * # PYCHOK __all__ 

523 from pygeodesy.points import * # PYCHOK __all__ 

524 from pygeodesy.props import * # PYCHOK __all__ 

525 from pygeodesy.resections import * # PYCHOK __all__ 

526 from pygeodesy.rhumb import * # PYCHOK __all__ 

527 from pygeodesy.simplify import * # PYCHOK __all__ 

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

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

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

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

532 from pygeodesy.streprs import * # PYCHOK __all__ 

533 from pygeodesy.trf import * # PYCHOK __all__ 

534 from pygeodesy.triaxials import * # PYCHOK __all__ 

535 from pygeodesy.units import * # PYCHOK __all__ 

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

537 from pygeodesy.ups import * # PYCHOK __all__ 

538 from pygeodesy.utily import * # PYCHOK __all__ 

539 from pygeodesy.utm import * # PYCHOK __all__ 

540 from pygeodesy.utmups import * # PYCHOK __all__ 

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

542 from pygeodesy.vector2d import * # PYCHOK __all__ 

543 from pygeodesy.vector3d import * # PYCHOK __all__ 

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

545 from pygeodesy.webmercator import * # PYCHOK __all__ 

546 from pygeodesy.wgrs import Georef, WGRSError # PYCHOK lazily 

547 

548 def _all(globalocals): 

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

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

551 _module_, _s_, _UNDER_ # PYCHOK expected 

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

553 # collect all public module and attribute names and check 

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

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

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

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

558 ns = list(lazily._ALL_INIT) 

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

560 for mod, attrs in lazily._ALL_LAZY.enums(): 

561 mod = _headof(_headof(mod)) 

562 if mod not in globalocals: 

563 t = _DOT_(_pygeodesy_, mod) 

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

565 ns.append(mod) 

566 # check that all other public attrs do exist 

567 if attrs and isinstance(attrs, tuple): 

568 attrs = lazily._ALL_ATTRS(attrs) 

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

570 if t: 

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

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

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

574 ns.extend(attrs) 

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

576# XXX m = globalocals[mod] # assert(_dunder_nameof(m) == mod) 

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

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

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

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

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

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

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

584 

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

586else: 

587 __all__ = () 

588 _init__all__ = False 

589 

590from pygeodesy.internals import _version2, _DOT_ # PYCHOK import 

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

592__version__ = '24.06.01' 

593# see setup.py for similar logic 

594version = _DOT_(*_version2(__version__, n=3)) 

595 

596del _DOT_, _lazy_import2, _os_path, _sys, _version2 

597 

598# **) MIT License 

599# 

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

601# 

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

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

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

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

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

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

608# 

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

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

611# 

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

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

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

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

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

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

618# OTHER DEALINGS IN THE SOFTWARE.