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# -*- coding: utf-8 -*-
and spherical earth models using precision trigonometric, vector-based, elliptic and approximate methods for geodetic (lat-/longitude) and geocentric (U{ECEF<https://WikiPedia.org/wiki/ECEF>} cartesian) coordinates.
Transcribed from U{JavaScript originals<https://GitHub.com/ChrisVeness/geodesy>} by I{Chris Veness (C) 2005-2016} and several U{C++ classes <https://GeographicLib.SourceForge.io/html/annotated.html>} by I{Charles Karney (C) 2008-2019} and published under the same U{MIT License <https://OpenSource.org/licenses/MIT>}**.
There are three modules for ellipsoidal earth models, I{ellipsoidalKarney}, I{-Vincenty} and I{-Nvector} and two for spherical ones, I{sphericalTrigonometry} and I{-Nvector}. Each module provides a geodetic I{LatLon} and a geocentric I{Cartesian} class with methods and functions to compute distance, initial and final bearing, intermediate and nearest points, area, perimeter, conversions and unrolling, among other things. For more information and further details see the U{documentation<https://mrJean1.GitHub.io/PyGeodesy>}, the descriptions of U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}, U{Vincenty<https://www.Movable-Type.co.UK/scripts/latlong-vincenty.html>} and U{Vector-based<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>} geodesy, the original U{JavaScript source<https://GitHub.com/ChrisVeness/geodesy>} or U{docs<https://www.Movable-Type.co.UK/scripts/geodesy/docs>} and the Python U{GeographicLib<https://PyPI.org/project/geographiclib>}.
Also included are modules for conversions to and from U{Cassini-Soldner <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1CassiniSoldner.html>}, U{ECEF<https://WikiPedia.org/wiki/ECEF>} (Earth-Centered, Earth-Fixed cartesian), U{UPS<https://WikiPedia.org/wiki/Universal_polar_stereographic_coordinate_system>} (Universal Polar Stereographic), U{UTM <https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} (U{Exact <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1TransverseMercatorExact.html>} and Universal Transverse Mercator) and U{Web Mercator <https://WikiPedia.org/wiki/Web_Mercator>} (Pseudo-Mercator) coordinates, U{MGRS<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} (NATO Military Grid Reference System) and U{OSGR <https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} (British Ordinance Survery Grid Reference) grid references, U{TRF <http://ITRF.ENSG.IGN.FR>} (Terrestrial Reference Frames) and modules to encode and decode U{EPSG<https://www.EPSG-Registry.org>}, U{Geohashes <https://www.Movable-Type.co.UK/scripts/geohash.html>}, U{Georefs (WGRS) <https://WikiPedia.org/wiki/World_Geographic_Reference_System>} and U{Garefs (GARS)<https://WikiPedia.org/wiki/Global_Area_Reference_System>}.
Other modules provide Lambert conformal conic projections and positions (from U{John P. Snyder, "Map Projections -- A Working Manual", 1987, pp 107-109 <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>}), functions to clip a path or polygon of C{LatLon} points using the U{Cohen–Sutherland <https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>} and the U{Sutherland-Hodgman<https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} methods, functions to U{simplify<https://Bost.Ocks.org/mike/simplify>} or linearize a path of C{LatLon} points (or a U{NumPy array <https://docs.SciPy.org/doc/numpy/reference/generated/numpy.array.html>}), including implementations of the U{Ramer-Douglas-Peucker <https://WikiPedia.org/wiki/Ramer-Douglas-Peucker_algorithm>} the U{Visvalingam-Whyatt<https://hydra.Hull.ac.UK/resources/hull:8338>} and U{Reumann-Witkam<https://psimpl.SourceForge.net/reumann-witkam.html>} the algorithms and modified versions of the former. Other classes U{interpolate<https://docs.SciPy.org/doc/scipy/reference/interpolate.html>} the height of C{LatLon} points and several C{Geoid} models or compute various U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>} or U{Hausdorff<https://WikiPedia.org/wiki/Hausdorff_distance>} distances.
Installation ============
To install PyGeodesy, type C{pip install PyGeodesy} or C{easy_install PyGeodesy} in a terminal or command window. Alternatively, download C{PyGeodesy-yy.m.d.zip} from U{PyPI<https://PyPI.org/project/PyGeodesy>} or U{GitHub<https://GitHub.com/mrJean1/PyGeodesy>}, C{unzip} the downloaded file, C{cd} to directory C{Pygeodesy-yy.m.d} and type C{python setup.py install}. To run all PyGeodesy tests, type C{python setup.py test} before installation.
Installation of U{GeographicLib<https://PyPI.org/project/geographiclib>}, U{NumPy<https://www.NumPy.org>} and U{SciPy<https://SciPy.org>} is optional. However, the former is required for classes L{CassiniSoldner} and L{Css} and function L{toCss}, for module L{ellipsoidalKarney} classes C{LatLon} and C{Cartesian} and functions C{areaOf} and C{perimeterOf} and for the L{HeightIDWkarney} interpolator. The latter are needed for the C{Geoid...} and C{Height...} interpolator classes, except the L{GeoidKarney} and all C{HeightIDW...} classes.
Documentation =============
In addition to the C{pygeodesy} package, the U{PyGeodesy <https://PyPI.org/project/PyGeodesy>} distribution files contain the tests, the test results (on macOS only) and the complete U{documentation <https://mrJean1.GitHub.io/PyGeodesy>} (generated by U{Epydoc <https://PyPI.org/project/epydoc>} using command line: C{epydoc --html --no-private --no-source --name=PyGeodesy --url=... -v pygeodesy}).
Tests =====
The tests have been run with Python 3.7.5 and 2.7.17 (both with U{geographiclib <https://PyPI.org/project/geographiclib>} 1.50, U{numpy <https://PyPI.org/project/numpy>} 1.17.2 respectively 1.16.5 and U{scipy <https://SciPy.org/scipylib/download.html>} 1.3.1 respectively 1.2.2), with Python 3.8.1 and with U{PyPy<https://PyPy.org>} 6.0.0 (Python 2.7.13 and 3.5.3), all on macOS 10.13.6 High Sierra and I{all in 64-bit only}. The results of those tests are included in the distribution files.
Test coverage has been measured with U{coverage <https://PyPI.org/project/coverage>} 4.5.4 using Python 3.7.5 (with U{geographiclib<https://PyPI.org/project/geographiclib>} 1.50, U{numpy <https://PyPI.org/project/numpy>} 1.17.2 and U{scipy <https://SciPy.org/scipylib/download.html>} 1.3.1) and Python 3.8.1. An HMTL report is included in the distribution files.
With Python 3.7 and 3.8, the tests run I{with and without} C{lazy import}.
The tests also ran with Python 2.7.14, 3.5.6 and 3.6.3 (and U{geographiclib <https://PyPI.org/project/geographiclib>} 1.49 or 1.50) on U{Ubuntu 14.04 <https://Travis-CI.org/mrJean1/PyGeodesy>} and with Python 3.7.3 (and U{geographiclib<https://PyPI.org/project/geographiclib>} 1.49 or 1.50) on U{Debian 9<https://Cirrus-CI.com/github/mrJean1/PyGeodesy/master>} I{all in 64-bit only} and with Python 2.7.15, 3.6.8 and 3.7.2 (all with U{geographiclib <https://PyPI.org/project/geographiclib>} 1.49 or 1.50) on U{Windows Server 2012R2<https://CI.AppVeyor.com/project/mrJean1/pygeodesy>} I{in both 32- and 64-bit}.
A single-File and single-Directory application with C{pygeodesy} has been bundled using U{PyInstaller<https://www.PyInstaller.org>} 3.4 and 64-bit Python 3.7.3 on macOS 10.13.6 High Sierra.
Previously, the tests were run with Python 2.6.9 (and numpy 1.6.2), 2.7.10 (and numpy 1.8.0rc1), 2.7.13, 2.7.14, 2.7.15, 2.7.16 (and numpy 1.13.1, 1.14.0, 1.15.2 or 1.16.2), 3.5.3, 3.6.2, 3.6.3, 3.6.4, 3.6.5, 3.7.0, 3.7.2, 3.7.3, 3.7.4, 3.8 and U{Intel-Python<https://software.Intel.com/en-us/distribution-for-python>} 3.5.3 (and U{numpy<https://PyPI.org/project/numpy>} 1.11.3) on MacOS X 10.10 Yosemite, MacOS X 10.11 El Capitan, macOS 10.12 Sierra, macOS 10.13.5 High Sierra and macOS 10.14 Mojave, with U{Pythonista 3.1<https://OMZ-Software.com/pythonista>} on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 on iPad4, with U{Pythonista 3.2 <https://OMZ-Software.com/pythonista>} (with geographiclib 1.49 or 1.50 and numpy 1.8.0) on iOS 11.4.1, 12.0, 12.2 and 12.3 on iPad4, iPhone6 and/or iPhone10, all in 64-bit only and with 32-bit Python 2.6.6 on Windows XP SP3 and with 32-bit Python 2.7.14 on Windows 10 Pro.
Notes =====
All Python source code has been statically U{checked <https://GitHub.com/ActiveState/code/tree/master/recipes/Python/546532_PyChecker_postprocessor>} with U{PyChecker<https://PyPI.org/project/pychecker>}, U{PyFlakes <https://PyPI.org/project/pyflakes>}, U{PyCodeStyle <https://PyPI.org/project/pycodestyle>} (formerly Pep8) and U{McCabe <https://PyPI.org/project/mccabe>} using Python 2.7.17 and with U{Flake8 <https://PyPI.org/project/flake8>} using Python 3.8.1, both in 64-bit on macOS 10.13.6 High Sierra.
Some function and method names differ from the JavaScript version. In such cases documentation tag B{JS name:} shows the original JavaScript name.
License =======
**) U{Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. <https://OpenSource.org/licenses/MIT>}
C{Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:}
C{The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.}
C{THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.}
@newfield example: Example, Examples @newfield JSname: JS name, JS names
@var EPS: System's M{epsilon} ≈2.22e-16 (C{float}). @var EPS_2: Half system's M{epsilon} ≈1.11e-16 (C{float}). @var EPS1: M{1 - EPS} ≈0.9999999999999998 (C{float}). @var EPS1_2: M{1 - EPS_2} ≈0.9999999999999999 (C{float}).
@var F_D: Format degrees as unsigned "deg°" plus suffix (C{str}). @var F_DM: Format degrees as unsigned "deg°min′" plus suffix (C{str}). @var F_DMS: Format degrees as unsigned "deg°min′sec″" plus suffix (C{str}). @var F_DEG: Format degrees as unsigned "[D]DD" plus suffix without symbol (C{str}). @var F_MIN: Format degrees as unsigned "[D]DDMM" plus suffix without symbols (C{str}). @var F_SEC: Format degrees as unsigned "[D]DDMMSS" plus suffix without symbols (C{str}). @var F_RAD: Convert degrees to radians and format as unsigned "RR" plus suffix (C{str}).
@var F_D_: Format degrees as signed "-/deg°" without suffix (C{str}). @var F_DM_: Format degrees as signed "-/deg°min′" without suffix (C{str}). @var F_DMS_: Format degrees as signed "-/deg°min′sec″" without suffix (C{str}). @var F_DEG_: Format degrees as signed "-/[D]DD" without suffix and symbol (C{str}). @var F_MIN_: Format degrees as signed "-/[D]DDMM" without suffix and symbols (C{str}). @var F_SEC_: Format degrees as signed "-/[D]DDMMSS" without suffix and symbols (C{str}). @var F_RAD_: Convert degrees to radians and format as signed "-/RR" without suffix (C{str}).
@var F_D__: Format degrees as signed "-/+deg°" without suffix (C{str}). @var F_DM__: Format degrees as signed "-/+deg°min′" without suffix (C{str}). @var F_DMS__: Format degrees as signed "-/+deg°min′sec″" without suffix (C{str}). @var F_DEG__: Format degrees as signed "-/+[D]DD" without suffix and symbol (C{str}). @var F_MIN__: Format degrees as signed "-/+[D]DDMM" without suffix and symbols (C{str}). @var F_SEC__: Format degrees as signed "-/+[D]DDMMSS" without suffix and symbols (C{str}). @var F_RAD__: Convert degrees to radians and format as signed "-/+RR" without suffix (C{str}).
@var INF: Infinity (C{float}), see C{isinf}, C{isfinite}. @var MANTIS: System's M{mantissa bits} ≈53 (C{int}). @var MAX: System's M{float max} ≈1.798e+308 (C{float}). @var MIN: System's M{float min} ≈2.225e-308 (C{float}). @var NAN: Not-A-Number (C{float}), see C{isnan}. @var NEG0: Negative 0.0 (C{float}), see C{isneg0}.
@var OK: Unique OK object (C{str}).
@var PI: Constant M{math.pi} (C{float}). @var PI2: Two PI, M{math.pi * 2} (C{float}). @var PI_2: Half PI, M{math.pi / 2} (C{float}). @var PI_4: Quarter PI, M{PI / 4} (C{float}).
@var R_M: Mean (spherical) earth radius (C{meter}). @var R_MA: Major (equatorial) earth radius (C{meter}) WGS84, EPSG:3785. @var R_MB: Minor (polar) earth radius (C{meter}) WGS84, EPSG:3785. @var R_KM: Mean (spherical) earth radius (C{km}, kilometer). @var R_NM: Mean (spherical) earth radius (C{NM}, nautical miles). @var R_SM: Mean (spherical) earth radius (C{SM}, statute miles). @var R_FM: Former FAI Sphere earth radius (C{meter}). @var R_VM: Aviation/Navigation earth radius (C{meter}).
@var S_DEG: Degrees symbol "°" (C{str}). @var S_MIN: Minutes symbol "′" (C{str}). @var S_SEC: Seconds symbol "″" (C{str}). @var S_RAD: Radians symbol "" (C{str}). @var S_SEP: Separator between deg°, min′ and sec″ "" (C{str}).
@var Conics: Registered conics (C{enum-like}). @var Datums: Registered datums (C{enum-like}). @var Ellipsoids: Registered ellipsoids (C{enum-like}). @var RefFrames: Registered reference frames (C{enum-like}). @var Transforms: Registered transforms (C{enum-like}).
@var pygeodesy_abspath: Fully qualified C{pygeodesy} directory name (C{str}).
@var version: Normalized C{PyGeodesy} version (C{str}).
'''
# <https://PyInstaller.ReadTheDocs.io/en/stable/runtime-information.html>
# see setup.py for similar logic
_lazy_import2 = None else: # setting __path__ should ... except ImportError: # ... if it doesn't, extend # sys.path to include this very directory such # that all public and private sub-modules can # be imported (and checked by PyChecker, etc.) sys.path.insert(0, pygeodesy_abspath) # XXX __path__[0]
# lazily requires Python 3.7+, see lazily.__doc__
# import all public modules and export as such
# lift all public classes, constants, functions, etc. but ONLY # from the following modules ... (see also David Beazley's # talk <https://DaBeaz.com/modulepackage/index.html>) ... BUT # NOT modules ellipsoidal*, epsg, gars, geohash, spherical*, # vector and wgrs ... in order keep those as modules ONLY # from pygeodesy.bases import * # PYCHOK __all__ # from pygeodesy.ellipsoidalKarney import - # MODULE O_N_L_Y # from pygeodesy.ellipsoidalNvector import - # MODULE O_N_L_Y # from pygeodesy.nvector import - # MODULE O_N_L_Y # from pygeodesy.sphericalNvector import - # MODULE O_N_L_Y # from pygeodesy.sphericalTrigonometry import - # MODULE O_N_L_Y
# collect all public module and attribute names and check # that modules are imported from this package, 'pygeodesy' # (but the latter only when not bundled with PyInstaller or # Py2Exe, since the file-layout is different. Courtesy of # GilderGeek <https://GitHub.com/mrJean1/PyGeodesy/issues/31>) # XXX ps = () if _isfrozen else set([_pygeodesy] + __name__.split('.')) raise ImportError('missing %s: %s.%s' % ('module', _pygeodesy, mod)) # check that all other public attributes do exist raise ImportError('missing %s: %s.%s' % ('attribute', mod, a)) # XXX if ps: # check that mod is a _pygeodesy module # XXX m = globalocals[mod] # assert(m.__name__ == mod) # XXX f = getattr(m, '__file__', '') # XXX d = dirname(abspath(f)) if f else pygeodesy_abspath # XXX p = getattr(m, '__package__', '') or _pygeodesy # XXX if p not in ps or d != pygeodesy_abspath: # XXX raise ImportError('foreign module: %s.%s from %r' % (p, mod, f or p))
# XXX del ellipsoidalBase, sphericalBase # PYCHOK expected
# **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE. |