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# Package pygeodesy

A pure Python implementation of geodesy tools for various ellipsoidal and spherical earth models using precision trigonometric, vector-based, exact, elliptic, iterative and approximate methods for geodetic (lat-/longitude), geocentric (ECEF cartesian) and certain triaxial ellipsoidal coordinates.

Transcoded from JavaScript originals by Chris Veness (C) 2005-2022 and from several C++ classes by Charles F. F. Karney (C) 2008-2023 and published under the same MIT License**.

There are four modules for ellipsoidal earth models, `ellipsoidalExact`, `-Karney`, `-Vincenty` and `-Nvector` and two for spherical ones, `sphericalTrigonometry` and `-Nvector`. Each module provides a geodetic `LatLon` and a geocentric `Cartesian` class with methods and functions to compute distance, surface area, perimeter, forward and reverse azimuth, initial and final bearing, intermediate and nearest points, intersections of geodesic, great circle and rhumb lines, circle intersections and secants, 3-point resections, triangulation, trilateration (by intersection, by overlap and in 3d), conversions and unrolling, among other things. For more information and further details see the documentation, the descriptions of Latitude/Longitude, Vincenty and Vector-based geodesy, the original JavaScript source or docs and Karney's Python geographiclib and C++ GeographicLib.

Also included are modules for conversions to and from Cassini-Soldner, ECEF (Earth-Centered, Earth-Fixed cartesian), UTM (Universal Transverse Mercator and Exact), UPS (Universal Polar Stereographic) and Web Mercator (Pseudo-Mercator) coordinates, MGRS (Military Grid Reference System, UTM and UPS) and OSGR (British Ordinance Survery Grid Reference) grid references, TRF (Terrestrial Reference Frames) and modules to encode and decode EPSG, Geohashes, Georefs (WGRS) and Garefs (GARS).

Other modules provide Albers equal-area projections, equidistant and other azimuthal projections, Lambert conformal conic projections and positions, functions to clip paths or polygons of `LatLon` points using the Cohen-Sutherland, Forster-Hormann-Popa, Greiner-Hormann, Liang-Barsky and Sutherland-Hodgman methods, functions to simplify or linearize a path of `LatLon` points (or a NumPy array), including implementations of the Ramer-Douglas-Peucker, the Visvalingam-Whyatt and the Reumann-Witkam algorithms and modified versions of the former. Other classes provide boolean operations between (composite) polygons or interpolate the height of `LatLon` points and Geoid models, compute various Fréchet or Hausdorff distances.

# Installation

To install PyGeodesy, type `python[3] -m pip install PyGeodesy` or `python[3] -m easy_install PyGeodesy` in a terminal or command window.

If the wheel `PyGeodesy-yy.m.d-py2.py3-none-any.whl` is missing in PyPI Download files, download the file from GitHub/dist. Install that with `python[3] -m pip install <path-to-downloaded-wheel>` and verify with `python[3] -m pygeodesy`.

Alternatively, download `PyGeodesy-yy.m.d.zip` from PyPI or GitHub, `unzip` the downloaded file, `cd` to directory `Pygeodesy-yy.m.d` and type `python[3] setup.py install`.

To run all PyGeodesy tests, type `python[3] test/run.py` or type `python[3] test/unitTestSuite.py` before or after installation.

# Dependencies

Installation of Karney's Python package geographiclib is optional, but required to use modules ellipsoidalKarney and css, azimuthal classes EquidistantKarney and GnomonicKarney and the HeightIDWkarney interpolator.

Both numpy and scipy must be installed for most Geoid... and Height... interpolators, except GeoidKarney and the HeightIDW... ones.

Functions and `LatLon` methods circin6, circum3, circum4_, soddy4, trilaterate3d2 do and `trilaterate5` and modules auxilats and rhumb may require numpy.

Modules ellipsoidalGeodSolve and geodsolve and azimuthal classes EquidistantGeodSolve and GnomonicGeodSolve depend on Karney's C++ utility GeodSolve to be executable and set with env variable `PYGEODESY_GEODSOLVE` or with property Ellipsoid.geodsolve.

Class Intersectool and module geodesici need Karney's C++ utility IntersectTool to be executable and set with env variable `PYGEODESY_INTERSECTTOOL`.

To compare `MGRS` results from modules mgrs and `testMgrs` with Karney's C++ utility GeoConvert, the latter must be executable and set with env variable `PYGEODESY_GEOCONVERT`.

Module rhumb.solve needs Karney's C++ utility RhumbSolve to be executable and set with env variable `PYGEODESY_RHUMBSOLVE` or with property Ellipsoid.rhumbsolve.

# Documentation

In addition to the `pygeodesy` package, the PyGeodesy distribution files contain the tests, the test results (on macOS only) and the complete documentation (generated by Epydoc using command line: `epydoc --html --no-private --no-source --name=PyGeodesy --url=... -v pygeodesy`).

# Tests

The tests ran with Python 3.13.0b4, Python 3.12.4 (with geographiclib 2.0, GeodSolve 2.3, IntersectTool 2.3 and RhumbSolve 2.3), Python 3.11.5 (with geographiclib 2.0, numpy 1.24.2 and scipy 1.10.1), Python 3.10.8 (with geographiclib 2.0, numpy 1.23.3, scipy 1.9.1, GeoConvert 2.3, GeodSolve 2.3) and Python 2.7.18 (with geographiclib 1.50, numpy 1.16.6, scipy 1.2.2, GeoConvert 2.3, GeodSolve 2.3, IntersectTool 2.3 and RhumbSolve 2.3), all in 64-bit on macOS 14.5 Sonoma.

All tests ran with and without `lazy import` for Python 3 and with command line option `-W default` and env variable `PYGEODESY_WARNINGS=on` for all Python versions. The results of those tests are included in the distribution files.

Test coverage has been measured with coverage 7.6.0 using Python 3.12.4, 3.11.5 and 3.10.8. The complete coverage report in HTML and a PDF summary are included in the distribution files.

Python 3.13.0b4, 3.12.4, 3.11.5 and 3.10.8 run on Apple M1 Silicon (`arm64`), natively. Python 2.7.18 runs on Intel (`x86_64`) or Intel emulation ("`arm64_x86_64`", see function machine).

The tests also ran with Python 3.12.4 (and geographiclib 2.0) on Debian 12 in 64-bit only, with Python 3.12.3 (and geographiclib 2.0) on Windows 2019Server in 64-bit only and with Python 2.7.18 (and geographiclib 1.52) on Windows 10 in 64- and 32-bit.

A single-File and single-Directory application with `pygeodesy` has been bundled using PyInstaller 3.4 and 64-bit Python 3.7.3 on macOS 10.13.6 High Sierra.

Previously, the tests were run with Python 3.12.0-3, 3.11.2-4, 3.10.1-7, 3.9.6, 3.9.1, 3.8.7, 3.7.1, 2.7.15, PyPy 7.3.12 (Python 3.10.12), 7.3.1 (Python 3.6.9) and PyPy 7.1.1 (Python 2.7.13) (and geographiclib 1.52, numpy 1.16.3, 1.16.4, 1.16.6, 1.19.0, 1.19.4, 1.19.5 or 1.22.4 and scipy 1.2.1, 1.4.1, 1.5.2 or 1.8.1) on Ubuntu 16.04, with Python 3.10.0-1, 3.9.0-5, 3.8.0-6, 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 numpy 1.19.0, 1.16.5, 1.16.2, 1.15.2, 1.14.0, 1.13.1, 1.8.0rc1 or 1.6.2 and scipy 1.5.0), PyPy 7.3.0 (Python 2.7.13 and 3.6.9), PyPy 6.0.0 (Python 2.7.13 and 3.5.3) and Intel-Python 3.5.3 (and 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 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 10.11 El Capitan and/or MacOS X 10.10 Yosemite, with Pythonista3.2 (with 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 iPhone12, with Pythonista 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 on iPad4, all in 64-bit only and with 32-bit Python 2.7.14 on Windows Server 2012R2, Windows 10 Pro and with 32-bit Python 2.6.6 on Windows XP SP3.

# Notes

All Python source code has been statically checked with PyChecker, PyFlakes, PyCodeStyle (formerly Pep8) and McCabe using Python 2.7.18 and with Flake8 using Python 3.11.5, both in 64-bit on macOS 14.5 Sonoma.

For a summary of all Karney-based functionality in `pygeodesy`, see module karney.

In Python 2, symbols S_DEG, S_MIN, S_SEC, S_RAD and S_SEP may be multi-byte, non-ascii characters and if so, not `unicode`.

# Env variables

The following environment variables are observed by `PyGeodesy`:

- `PYGEODESY_EXCEPTION_CHAINING` - see module errors.
- `PYGEODESY_FMT_FORM` - see module dms.
- `PYGEODESY_FSUM_RESIDUAL` - see module fsums and class Fsum.
- `PYGEODESY_GEOCONVERT` - see module mgrs.
- `PYGEODESY_GEODSOLVE` - see module geodsolve.
- `PYGEODESY_INTERSECTTOOL` - see module geodesici.
- `PYGEODESY_LAZY_IMPORT` - see module lazily and variable isLazy.
- `PYGEODESY_NOTIMPLEMENTED` - `__special__` methods return `NotImplemented` if set to "std".
- `PYGEODESY_RHUMBSOLVE` - see module rhumb.solve.
- `PYGEODESY_UPS_POLES` - see modules ups and mgrs.

and these to control standard or named `repr`esentations:

- `PYGEODESY_BEARING_STD_REPR` - see method Bearing`.__repr__`.
- `PYGEODESY_BOOL_STD_REPR` - see method Bool`.__repr__`.
- `PYGEODESY_DEGREES_STD_REPR` - see method Degrees`.__repr__`.
- `PYGEODESY_FLOAT_STD_REPR` - see method Float`.__repr__`.
- `PYGEODESY_INT_STD_REPR` - see method Int`.__repr__`.
- `PYGEODESY_METER_STD_REPR` - see method Meter`.__repr__`.
- `PYGEODESY_RADIANS_STD_REPR` - see method Radians`.__repr__`.
- `PYGEODESY_STR_STD_REPR` - see method Str`.__repr__`.

plus during development:

- `PYGEODESY_FOR_DOCS` - for extended documentation by `epydoc`.
- `PYGEODESY_GEOGRAPHICLIB` - see module karney.
- `PYGEODESY_WARNINGS` - see module props and function DeprecationWarnings.
- `PYGEODESY_XPACKAGES` - see module basics.
- `PYTHONDEVMODE` - see modules errors and props.

and:

- `PYGEODESY_INIT__ALL__` - Set env variable `PYGEODESY_INIT__ALL__` to anything other than `"__all__"` to avoid importing all `pygeodesy` modules unnecessarily (in Python 2 or with `PYGEODESY_LAZY_IMPORT` turned off in Python 3). However, to import a `pygeodesy` item, the item name must be qualified with the `module` name, for example `from pygeodesy.ellipsoidalExact import LatLon` or `from pygeodesy.deprecated import collins`

# License

**) Copyright (C) 2016-2024 -- 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.`

Version: 24.07.24

Submodules
pygeodesy.__main__: Print pygeodesy version, etc. pygeodesy.albers: Albers Equal-Area projections. pygeodesy.auxilats: Classes AuxAngle, AuxDLat, AuxDST and AuxLat transcoded to Python from Karney's C++ class AuxAngle, DAuxLatitude, DST, repectively AuxLatitude all in GeographicLib version 2.2+. pygeodesy.auxilats._CX_4: Coeficients for `_AUXLATITUDE_ORDER` 4 from Karney's C++ class AuxLatitude trancoded to a double, uniquified Python `dict[auxout][auxin]`. pygeodesy.auxilats._CX_6: Coeficients for `_AUXLATITUDE_ORDER` 6 from Karney's C++ class AuxLatitude trancoded to a double, uniquified Python `dict[auxout][auxin]`. pygeodesy.auxilats._CX_8: Coeficients for `_AUXLATITUDE_ORDER` 8 from Karney's C++ class AuxLatitude trancoded to a double, uniquified Python `dict[auxout][auxin]`. pygeodesy.auxilats.__main__: Print auxilats version, etc. pygeodesy.auxilats.auxAngle: (INTERNAL) Auxiliary latitudes' base classes, constants and functions. pygeodesy.auxilats.auxDLat: Class AuxDLat transcoded to Python from Karney's C++ class DAuxLatitude in GeographicLib version 2.2+. pygeodesy.auxilats.auxDST: Discrete Sine Transforms (AuxDST) in Python, transcoded from Karney's C++ class DST in GeographicLib version 2.2+. pygeodesy.auxilats.auxLat: Class AuxLat transcoded to Python from Karney's C++ class AuxLatitude in GeographicLib version 2.2+. pygeodesy.auxilats.auxily: (INTERNAL) Auxiliary latitudes' classes, constants and functions. pygeodesy.azimuthal: Equidistant, Equal-Area, and other Azimuthal projections. pygeodesy.basics: Some, basic definitions, functions and dependencies. pygeodesy.booleans: Boolean operations on composite polygons and clips. pygeodesy.cartesianBase: (INTERNAL) Private `CartesianBase` class for elliposiodal, spherical and N-/vectorial `Cartesian`s and public functions rtp2xyz, rtp2xyz_, xyz2rtp and xyz2rtp_. pygeodesy.clipy: Clip a path or polygon of `LatLon` points against a rectangular box or an arbitrary (convex) region. pygeodesy.constants: Single-instance `float` and `int` constants across `pygeodesy` modules and related functions pygeodesy.float_, pygeodesy.isclose, pygeodesy.isfinite, pygeodesy.isinf, pygeodesy.isint0, pygeodesy.isnan, pygeodesy.isnear0, pygeodesy.isnear1, pygeodesy.isnear90, pygeodesy.isneg0, pygeodesy.isninf, pygeodesy.isnon0 and pygeodesy.remainder. pygeodesy.css: Cassini-Soldner (CSS) projection. pygeodesy.datums: Datums and transformations thereof. pygeodesy.deprecated: DEPRECATED classes, constants, functions, interns, methods, etc. pygeodesy.deprecated.bases: DEPRECATED on 2021.02.10, use (INTERNAL) module pygeodesy.latlonBase instead. pygeodesy.deprecated.classes: DEPRECATED classes kept for backward compatibility. pygeodesy.deprecated.consterns: DEPRECATED constants and interns kept for backward compatibility. pygeodesy.deprecated.datum: DEPRECATED on 2022.09.12, use module pygeodesy.datums or pygeodesy.ellipsoids instead. pygeodesy.deprecated.functions: DEPRECATED functions kept for backward compatibility. pygeodesy.deprecated.nvector: DEPRECATED on 2021.05.20, use (INTERNAL) module pygeodesy.nvectorBase instead. pygeodesy.deprecated.rhumbBase: DEPRECATED on 2023.11.26, use module pygeodesy.rhumb.bases instead. pygeodesy.deprecated.rhumbaux: DEPRECATED on 2023.11.26, use module pygeodesy.rhumb.aux_ instead. pygeodesy.deprecated.rhumbsolve: DEPRECATED on 2023.11.26, use module pygeodesy.rhumb.solve instead. pygeodesy.deprecated.rhumbx: DEPRECATED on 2023.11.26, use module pygeodesy.rhumb.ekx instead. pygeodesy.dms: Parsers and formatters of angles in degrees, minutes and seconds or radians. pygeodesy.ecef: Geocentric Earth-Centered, Earth-Fixed (ECEF) coordinates. pygeodesy.elevations: Web-services-based elevations and `CONUS` geoid heights. pygeodesy.ellipsoidalBase: (INTERNAL) Private ellipsoidal base classes `CartesianEllipsoidalBase` and `LatLonEllipsoidalBase`. pygeodesy.ellipsoidalBaseDI: (INTERNAL) Private, ellipsoidal Direct/Inverse geodesy base class `LatLonEllipsoidalBaseDI` and functions. pygeodesy.ellipsoidalExact: Exact ellipsoidal geodesy using Karney's Exact Geodesic. pygeodesy.ellipsoidalGeodSolve: Exact ellipsoidal geodesy, intended for testing purposes only. pygeodesy.ellipsoidalKarney: Ellipsoidal, Karney-based geodesy. pygeodesy.ellipsoidalNvector: Ellipsoidal, `N-vector`-based geodesy. pygeodesy.ellipsoidalVincenty: Ellipsoidal, Vincenty-based geodesy. pygeodesy.ellipsoids: Ellipsoidal and spherical earth models. pygeodesy.elliptic: Karney's elliptic functions and integrals. pygeodesy.epsg: European Petroleum Survey Group (EPSG) en-/decoding. pygeodesy.errors: Errors, exceptions, exception formatting and exception chaining. pygeodesy.etm: A pure Python version of Karney's `Exact Transverse Mercator` (ETM) projection. pygeodesy.fmath: Utilities using precision floating point summation. pygeodesy.formy: Formulary of basic geodesy functions and approximations. pygeodesy.frechet: Fréchet distances. pygeodesy.fstats: Classes for running statistics and regressions based on pygeodesy.Fsum, precision floating point summation. pygeodesy.fsums: Class Fsum for precision floating point summation and running summation based on, respectively similar to Python's `math.fsum`. pygeodesy.gars: Global Area Reference System (GARS) en-/decoding. pygeodesy.geodesici: Classes Intersectool and Intersector to find the intersections of two geodesic lines or line segments. pygeodesy.geodesicw: Wrapper around Python classes `geodesic.Geodesic` and `geodesicline.GeodesicLine` from Karney's Python package geographiclib, provided that package is installed. pygeodesy.geodesicx: A pure Python version of Karney's C++ classes GeodesicExact and GeodesicLineExact. pygeodesy.geodesicx._C4_24: A Python version of part of Karney's C++ module GeodesicExactC4. pygeodesy.geodesicx._C4_27: A Python version of part of Karney's C++ module GeodesicExactC4. pygeodesy.geodesicx._C4_30: A Python version of part of Karney's C++ module GeodesicExactC4. pygeodesy.geodesicx.__main__: Print geodesicx version, etc. pygeodesy.geodesicx.gx: A pure Python version of Karney's C++ class GeodesicExact. pygeodesy.geodesicx.gxarea: Slightly enhanced versions of classes PolygonArea and `Accumulator` from Karney's Python geographiclib. pygeodesy.geodesicx.gxbases: (INTERNAL) Private geodesicx base class, functions and constants. pygeodesy.geodesicx.gxline: A pure Python version of Karney's C++ class GeodesicLineExact. pygeodesy.geodsolve: Wrapper to invoke Karney's GeodSolve utility as an (exact) geodesic, but intended for testing purposes only. pygeodesy.geohash: Geohash en-/decoding. pygeodesy.geoids: Geoid models and geoid height interpolations. pygeodesy.hausdorff: Hausdorff distances. pygeodesy.heights: Height interpolations at `LatLon` points from known `knots`. pygeodesy.internals: Mostly INTERNAL functions, except machine, print_ and printf. pygeodesy.interns: Single `str`ing constants, `intern`'ed across `pygeodesy` modules and function pygeodesy.machine. pygeodesy.iters: Iterators with options. pygeodesy.karney: Wrapper around several `geomath.Math` functions from Karney's Python package geographiclib, provided that package is installed. pygeodesy.ktm: A pure Python version of Karney's C++ class TransverseMercator based on Krüger series. pygeodesy.latlonBase: (INTERNAL) Base class LatLonBase for all elliposiodal, spherical and N-vectorial `LatLon` classes. pygeodesy.lazily: Lazily import `pygeodesy` modules and attributes, based on lazy_import from Brett Cannon's modutil. pygeodesy.lcc: Lambert Conformal Conic (LCC) projection. pygeodesy.ltp: Local Tangent Plane (LTP) and local cartesian coordinates. pygeodesy.ltpTuples: Named, Local Tangent Plane (LTP) tuples. pygeodesy.mgrs: Military Grid Reference System (MGRS/NATO) references. pygeodesy.named: (INTERNAL) Nameable class instances. pygeodesy.namedTuples: Named tuples. pygeodesy.nvectorBase: (INTERNAL) Private elliposiodal and spherical `Nvector` base classes LatLonNvectorBase and NvectorBase and function sumOf. pygeodesy.osgr: Ordnance Survey Grid References (OSGR) references on the UK National Grid. pygeodesy.points: Utilities for point lists, tuples, etc. pygeodesy.props: Mutable, immutable and caching/memoizing properties and deprecation decorators. pygeodesy.resections: 3-Point resection functions cassini, collins5, pierlot, pierlotx and tienstra7, survey functions snellius3 and wildberger3 and triangle functions triAngle, triAngle5, triSide, triSide2 and triSide4. pygeodesy.rhumb: Package of lazily imported `rhumb` modules rhumb.aux_, rhumb.ekx and rhumb.solve. pygeodesy.rhumb.aux_: A pure Python version of Karney's Auxiliary Latitudes, C++ classes Rhumb and RhumbLine from GeographicLib version 2.2+ renamed to RhumbAux respectively RhumbLineAux. pygeodesy.rhumb.bases: (INTERNAL) base classes `RhumbBase` and `RhumbLineBase`, pure Python version of Karney's C++ classes Rhumb and RhumbLine from GeographicLib versions 2.0 and 2.2 and Karney's C++ example Rhumb intersect. pygeodesy.rhumb.ekx: A pure Python version of Karney's elliptic functions, Krüger series expansion, C++ classes Rhumb and and RhumbLine from GeographicLib version 2.0, kept for backward compatibility. pygeodesy.rhumb.solve: Wrapper to invoke Karney's RhumbSolve utility as an (exact) rhumb or rhumb line from either GeographicLib 2.0 or 2.2+. pygeodesy.simplify: Simplify or linearize a path. pygeodesy.solveBase: (INTERNAL) Private base classes for pygeodesy.geodsolve and pygeodesy.rhumb.solve. pygeodesy.sphericalBase: (INTERNAL) Private spherical base classes `CartesianSphericalBase` and `LatLonSphericalBase` for sphericalNvector and sphericalTrigonometry. pygeodesy.sphericalNvector: Spherical, `N-vector`-based geodesy. pygeodesy.sphericalTrigonometry: Spherical, `trigonometry`-based geodesy. pygeodesy.streprs: Floating point and other formatting utilities. pygeodesy.trf: Veness' Terrestrial Reference Frames (TRF). pygeodesy.triaxials: Triaxal ellipsoid classes ordered Triaxial and unordered Triaxial_ and Jacobi conformal projections JacobiConformal and JacobiConformalSpherical, transcoded from Charles Karney's C++ class JacobiConformal to pure Python and miscellaneous classes BetaOmega2Tuple, BetaOmega3Tuple, Jacobi2Tuple and TriaxialError. pygeodesy.units: Various named units, all sub-classes of `Float`, `Int` or `Str` from basic `float`, `int` respectively `str` to named units as Degrees, Feet, Meter, Radians, etc. pygeodesy.unitsBase: Basic `Float`, `Int` and `Str`ing units classes. pygeodesy.ups: Karney's Universal Polar Stereographic (UPS) projection. pygeodesy.utily: Various utility functions. pygeodesy.utm: Veness' Universal Transverse Mercator (UTM) projection. pygeodesy.utmups: Karney's UTM and UPS utilities. pygeodesy.utmupsBase: (INTERNAL) Private class `UtmUpsBase`, functions and constants for modules epsg, etm, mgrs, ups and utm. pygeodesy.vector2d: 2- or 3-D vectorial functions circin6, circum3, circum4_, iscolinearWith, meeus2, nearestOn, radii11 and soddy4. pygeodesy.vector3d: Extended 3-D vector class Vector3d and functions. pygeodesy.vector3dBase: (INTERNAL) Private, 3-D vector base class `Vector3dBase`. pygeodesy.webmercator: Web Mercator (WM) projection. pygeodesy.wgrs: World Geographic Reference System (WGRS) en-/decoding.

Classes
| VincentyError Error raised by Vincenty's `Direct` and `Inverse` methods for coincident points or lack of convergence.
| Epsg EPSG class, a named `int`.
| EPSGError EPSG encode, decode or other Epsg issue.
| Garef Garef class, a named `str`.
| GARSError Global Area Reference System (GARS) encode, decode or other Garef issue.
| Geohash Geohash class, a named `str`.
| GeohashError Geohash encode, decode or other Geohash issue.
| Neighbors8Dict 8-Dict `(N, NE, E, SE, S, SW, W, NW)` of Geohashes, providing key and attribute access to the items.
| Resolutions2Tuple 2-Tuple `(res1, res2)` with the primary (longitudinal) and secondary (latitudinal) resolution, both in `degrees`.
| Georef Georef class, a named `str`.
| WGRSError World Geographic Reference System (WGRS) encode, decode or other Georef issue.
| ADict A `dict` with both key and attribute access to the `dict` items.
| Aer Local `Azimuth-Elevation-Range` (AER) in a local tangent plane.
| Aer4Tuple 4-Tuple `(azimuth, elevation, slantrange, ltp)`, all in `meter` except `ltp`.
| Albers7Tuple 7-Tuple `(x, y, lat, lon, gamma, scale, datum)`, in `meter`, `meter`, `degrees90`, `degrees180`, `degrees360`, `scalar` and `Datum` where `(x, y)` is the projected, `(lat, lon)` the geodetic location, `gamma` the meridian convergence at point, the bearing of the y-axis measured clockwise from true North and `scale` is the azimuthal scale of the projection at point.
| AlbersEqualArea An Albers equal-area (authalic) projection with a single standard parallel.
| AlbersEqualArea2 An Albers equal-area (authalic) projection with two standard parallels.
| AlbersEqualArea4 An Albers equal-area (authalic) projection specified by the `sin` and `cos` of both standard parallels.
| AlbersEqualAreaCylindrical An AlbersEqualArea projection at `lat=0` and `k0=1` degenerating to the cylindrical-equal-area projection.
| AlbersEqualAreaNorth An azimuthal AlbersEqualArea projection at `lat=90` and `k0=1` degenerating to the azimuthal LambertEqualArea projection.
| AlbersEqualAreaSouth An azimuthal AlbersEqualArea projection at `lat=-90` and `k0=1` degenerating to the azimuthal LambertEqualArea projection.
| AlbersError An AlbersEqualArea, AlbersEqualArea2, AlbersEqualArea4, AlbersEqualAreaCylindrical, AlbersEqualAreaNorth, AlbersEqualAreaSouth or Albers7Tuple issue.
| Area3Tuple 3-Tuple `(number, perimeter, area)` with the `number` of points of the polygon or polyline, the `perimeter` in `meter` and the `area` in `meter` squared.
| Attitude The pose of a plane or camera in space.
| Attitude4Tuple 4-Tuple `(alt, tilt, yaw, roll)` with `altitude` in (positive) `meter` and `tilt`, `yaw` and `roll` in `degrees` representing the attitude of a plane or camera.
| AttitudeError An Attitude or Attitude4Tuple issue.
| AuxError Error raised for a rhumb.aux_, `Aux`, `AuxDLat` or `AuxLat` issue.
| Azimuthal7Tuple 7-Tuple `(x, y, lat, lon, azimuth, scale, datum)`, in `meter`, `meter`, `degrees90`, `degrees180`, compass `degrees`, `scalar` and `Datum` where `(x, y)` is the easting and northing of a projected point, `(lat, lon)` the geodetic location, `azimuth` the azimuth, clockwise from true North and `scale` is the projection scale, either `1 / reciprocal` or `1` or `-1` in the Equidistant case.
| AzimuthalError An azimuthal Equidistant, EquidistantKarney, Gnomonic, LambertEqualArea, Orthographic, Stereographic or Azimuthal7Tuple issue.
| Band Named `str` representing a UTM/UPS band letter, unchecked.
| Bearing Named `float` representing a bearing in compass `degrees` from (true) North.
| Bearing2Tuple 2-Tuple `(initial, final)` bearings, both in compass `degrees360`.
| Bearing_ Named `float` representing a bearing in `radians` from compass `degrees` from (true) North.
| BetaOmega2Tuple 2-Tuple `(beta, omega)` with ellipsoidal lat- and longitude `beta` and `omega` both in Radians (or Degrees).
| BetaOmega3Tuple 3-Tuple `(beta, omega, height)` with ellipsoidal lat- and longitude `beta` and `omega` both in Radians (or Degrees) and the `height`, rather the (signed) distance to the triaxial's surface (measured along the radial line to the triaxial's center) in `meter`, conventionally.
| Bool Named `bool`, a sub-class of `int` like Python's `bool`.
| BooleanFHP Composite class providing boolean operations between two composites using Forster-Hormann-Popa's C++ implementation, transcoded to pure Python.
| BooleanGH Composite class providing boolean operations between two composites using the Greiner-Hormann algorithm and Correia's implementation, modified and extended.
| Bounds2Tuple 2-Tuple `(latlonSW, latlonNE)` with the bounds' lower-left and upper-right corner as `LatLon` instance.
| Bounds4Tuple 4-Tuple `(latS, lonW, latN, lonE)` with the bounds' lower-left `(LatS, LowW)` and upper-right `(latN, lonE)` corner lat- and longitudes.
| CSSError Cassini-Soldner (CSS) conversion or other Css issue.
| CassiniSoldner Cassini-Soldner projection, a Python version of Karney's C++ class CassiniSoldner.
| ChLV Conversion between WGS84 geodetic and Swiss projection coordinates using pygeodesy.EcefKarney's Earth-Centered, Earth-Fixed (ECEF) methods.
| ChLV9Tuple 9-Tuple `(Y, X, h_, lat, lon, height, ltp, ecef, M)` with unfalsed Swiss (Y, X, h_) coordinates and height, all in `meter`, `ltp` either a ChLV, ChLVa or ChLVe instance and `ecef` (EcefKarney at Bern, Ch), otherwise like Local9Tuple.
| ChLVEN2Tuple 2-Tuple `(E_LV95, N_LV95)` with falsed Swiss LV95 easting and norting in `meter (2_600_000, 1_200_000)` and origin at `Bern, Ch`.
| ChLVYX2Tuple 2-Tuple `(Y, X)` with unfalsed Swiss LV95 easting and norting in `meter`.
| ChLVa Conversion between WGS84 geodetic and Swiss projection coordinates using the Approximate formulas, page 13.
| ChLVe Conversion between WGS84 geodetic and Swiss projection coordinates using the Ellipsoidal approximate formulas, pp 10-11 and Bolliger, J. pp 148-151 (also GGGS).
| ChLVyx2Tuple 2-Tuple `(y_LV03, x_LV03)` with falsed Swiss LV03 easting and norting in `meter (600_000, 200_000)` and origin at `Bern, Ch`.
| Circin6Tuple 6-Tuple `(radius, center, deltas, cA, cB, cC)` with the `radius`, the trilaterated `center` and contact points of the inscribed aka In- circle of a triangle.
| Circle4Tuple 4-Tuple `(radius, height, lat, beta)` of the `radius` and `height`, both conventionally in `meter` of a parallel circle of latitude at (geodetic) latitude `lat` and the parametric (or reduced) auxiliary latitude `beta`, both in `degrees90`.
| Circum3Tuple 3-Tuple `(radius, center, deltas)` with the `circumradius` and trilaterated `circumcenter` of the `circumcircle` through 3 points (aka {Meeus}' Type II circle) or the `radius` and `center` of the smallest Meeus' Type I circle.
| Circum4Tuple 4-Tuple `(radius, center, rank, residuals)` with `radius` and `center` of a sphere least-squares fitted through given points and the `rank` and `residuals` -if any- from numpy.linalg.lstsq.
| ClipCS4Tuple 4-Tuple `(start, end, i, j)` for each edge of a clipped path with the `start` and `end` points (`LatLon`) of the portion of the edge inside or on the clip box and the indices `i` and `j` (`int`) of the edge start and end points in the original path.
| ClipError Clip box or clip region issue.
| ClipFHP4Tuple 4-Tuple `(lat, lon, height, clipid)` for each point of the clipFHP4 result with the `lat`-, `lon`gitude, `height` and `clipid` of the polygon or clip.
| ClipGH4Tuple 4-Tuple `(lat, lon, height, clipid)` for each point of the clipGH4 result with the `lat`-, `lon`gitude, `height` and `clipid` of the polygon or clip.
| ClipLB6Tuple 6-Tuple `(start, end, i, fi, fj, j)` for each edge of the clipped path with the `start` and `end` points (`LatLon`) of the portion of the edge inside or on the clip box, indices `i` and `j` (both `int`) of the original path edge start and end points and fractional indices `fi` and `fj` (both FIx) of the `start` and `end` points along the edge of the original path.
| ClipSH3Tuple 3-Tuple `(start, end, original)` for each edge of a clipped polygon, the `start` and `end` points (`LatLon`) of the portion of the edge inside or on the clip region and `original` indicates whether the edge is part of the original polygon or part of the clip region (`bool`).
| Collins5Tuple 5-Tuple `(pointP, pointH, a, b, c)` with survey `pointP`, auxiliary `pointH`, each an instance of `pointA`'s (sub-)class and triangle sides `a`, `b` and `c` in `meter`, conventionally.
| Conic Lambert conformal conic projection (1- or 2-SP).
| CrossError Error raised for zero or near-zero vectorial cross products, occurring for coincident or colinear points, lines or bearings.
| Css Cassini-Soldner East-/Northing location.
| Curvature2Tuple 2-Tuple `(meridional, prime_vertical)` of radii of curvature, both in `meter`, conventionally.
| Datum Ellipsoid and transform parameters for an earth model.
| Degrees Named `float` representing a coordinate in `degrees`, optionally clipped.
| Degrees2 Named `float` representing a distance in `degrees squared`.
| Degrees_ Named `Degrees` representing a coordinate in `degrees` with optional limits `low` and `high`.
| Destination2Tuple 2-Tuple `(destination, final)`, `destination` in `LatLon` and `final` bearing in compass `degrees360`.
| Destination3Tuple 3-Tuple `(lat, lon, final)`, destination `lat`, `lon` in `degrees90` respectively `degrees180` and `final` bearing in compass `degrees360`.
| Direct9Tuple 9-Tuple `(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)` with arc length `a12`, angles `lat2`, `lon2` and azimuth `azi2` in `degrees`, distance `s12` and reduced length `m12` in `meter` and area `S12` in `meter` squared.
| Distance Named `float` representing a distance, conventionally in `meter`.
| Distance2Tuple 2-Tuple `(distance, initial)`, `distance` in `meter` and `initial` bearing in compass `degrees360`.
| Distance3Tuple 3-Tuple `(distance, initial, final)`, `distance` in `meter` and `initial` and `final` bearing, both in compass `degrees360`.
| Distance4Tuple 4-Tuple `(distance2, delta_lat, delta_lon, unroll_lon2)` with the distance in `degrees squared`, the latitudinal `delta_lat = lat2 - lat1`, the wrapped, unrolled and adjusted longitudinal `delta_lon = lon2 - lon1` and `unroll_lon2`, the unrolled or original `lon2`.
| Distance_ Named `float` with optional `low` and `high` limits representing a distance, conventionally in `meter`.
| DivMod2Tuple 2-Tuple `(div, mod)` with the quotient `div` and remainder `mod` results of a `divmod` operation.
| ETMError Exact Transverse Mercator (ETM) parse, projection or other Etm issue or ExactTransverseMercator conversion failure.
| EasNor2Tuple 2-Tuple `(easting, northing)`, both in `meter`, conventionally.
| EasNor3Tuple 3-Tuple `(easting, northing, height)`, all in `meter`, conventionally.
| EasNorAziRk4Tuple 4-Tuple `(easting, northing, azimuth, reciprocal)` for the Cassini-Soldner location with `easting` and `northing` in `meters` and the `azimuth` of easting direction and `reciprocal` of azimuthal northing scale, both in `degrees`.
| EasNorAziRkEqu6Tuple 6-Tuple `(easting, northing, azimuth, reciprocal, equatorarc, equatorazimuth)` for the Cassini-Soldner location with `easting` and `northing` in `meters` and the `azimuth` of easting direction, `reciprocal` of azimuthal northing scale, `equatorarc` and `equatorazimuth`, all in `degrees`.
| EasNorRadius3Tuple 3-Tuple `(easting, northing, radius)`, all in `meter`.
| Easting Named `float` representing an easting, conventionally in `meter`.
| Ecef9Tuple 9-Tuple `(x, y, z, lat, lon, height, C, M, datum)` with geocentric `x`, `y` and `z` plus geodetic `lat`, `lon` and `height`, case `C` (see the `Ecef*.reverse` methods) and optionally, the rotation matrix `M` (EcefMatrix) and `datum`, with `lat` and `lon` in `degrees` and `x`, `y`, `z` and `height` in `meter`, conventionally.
| EcefError An ECEF or `Ecef*` related issue.
| EcefFarrell21 Conversion between geodetic and geocentric, Earth-Centered, Earth-Fixed (ECEF) coordinates based on Jay A. Farrell's Table 2.1, page 29.
| EcefFarrell22 Conversion between geodetic and geocentric, Earth-Centered, Earth-Fixed (ECEF) coordinates based on Jay A. Farrell's Table 2.2, page 30.
| EcefKarney Conversion between geodetic and geocentric, Earth-Centered, Earth-Fixed (ECEF) coordinates transcoded from Karney's C++ Geocentric methods.
| EcefMatrix A rotation matrix known as East-North-Up (ENU) to ECEF.
| EcefSudano Conversion between geodetic and geocentric, Earth-Centered, Earth-Fixed (ECEF) coordinates based on John J. Sudano's paper.
| EcefVeness Conversion between geodetic and geocentric, Earth-Centered, Earth-Fixed (ECEF) coordinates transcoded from Chris Veness' JavaScript classes LatLonEllipsoidal, Cartesian.
| EcefYou Conversion between geodetic and geocentric, Earth-Centered, Earth-Fixed (ECEF) coordinates using Rey-Jer You's transformation for non-prolate ellipsoids.
| Elevation2Tuple 2-Tuple `(elevation, data_source)` in `meter` and `str`.
| Ellipsoid Ellipsoid with equatorial and polar radii, flattening, inverse flattening and other, often used, cached attributes, supporting oblate and prolate ellipsoidal and spherical earth models.
| Ellipsoid2 An Ellipsoid specified by equatorial radius and flattening.
| Elliptic Elliptic integrals and functions.
| Elliptic3Tuple 3-Tuple `(sn, cn, dn)` all `scalar`.
| EllipticError Elliptic function, integral, convergence or other Elliptic issue.
| Enu Local `Eeast-North-Up` (ENU) location in a local tangent plane.
| Enu4Tuple 4-Tuple `(east, north, up, ltp)`, in `meter` except `ltp`.
| Epoch Named `epoch` with optional `low` and `high` limits representing a fractional calendar year.
| Equidistant Azimuthal equidistant projection for the sphere***, see Snyder, pp 195-197 and MathWorld-Wolfram.
| EquidistantExact Azimuthal equidistant projection, a Python version of Karney's C++ class AzimuthalEquidistant, based on exact geodesic classes GeodesicExact and GeodesicLineExact.
| EquidistantGeodSolve Azimuthal equidistant projection, a Python version of Karney's C++ class AzimuthalEquidistant, based on (exact) geodesic wrappers GeodesicSolve and GeodesicLineSolve and intended for testing purposes only.
| EquidistantKarney Azimuthal equidistant projection, a Python version of Karney's C++ class AzimuthalEquidistant, requiring package geographiclib to be installed.
| Etm Exact Transverse Mercator (ETM) coordinate, a sub-class of Utm, a Universal Transverse Mercator (UTM) coordinate using the ExactTransverseMercator projection for highest accuracy.
| ExactTransverseMercator Pure Python version of Karney's C++ class TransverseMercatorExact, a numerically exact transverse Mercator projection, further referred to as `TMExact`.
| FIx A named Fractional Index, an `int` or `float` index into a `list` or `tuple` of `points`, typically.
| Fcbrt Cubic root of a precision summation.
| Fcook Cook's `RunningStats` computing the running mean, median and (sample) kurtosis, skewness, variance, standard deviation and Jarque-Bera normality.
| Fdot Precision dot product.
| Feet Named `float` representing a distance or length in `feet`.
| Fhorner Precision polynomial evaluation using the Horner form.
| Fhypot Precision summation and hypotenuse, default `root=2`.
| Flinear Cook's `RunningRegression` computing the running slope, intercept and correlation of a linear regression.
| Float Named `float`.
| Float_ Named `float` with optional `low` and `high` limit.
| Footprint5Tuple 5-Tuple `(center, upperleft, upperight, loweright, lowerleft)` with the `center` and 4 corners of the local projection of a `Frustum`, each an Xyz4Tuple, XyzLocal, `LatLon`, etc.
| Forward4Tuple 4-Tuple `(easting, northing, gamma, scale)` in `meter`, `meter`, meridian convergence `gamma` at point in `degrees` and the `scale` of projection at point `scalar`.
| Fpolynomial Precision polynomial evaluation.
| Fpowers Precision summation of powers, optimized for `power=2, 3 and 4`.
| Frechet Frechet base class, requires method Frechet.distance to be overloaded.
| Frechet6Tuple 6-Tuple `(fd, fi1, fi2, r, n, units)` with the discrete Fréchet distance `fd`, fractional indices `fi1` and `fi2` as `FIx`, the recursion depth `r`, the number of distances computed `n` and the units class or class or name of the distance `units`.
| FrechetCosineAndoyerLambert Compute the `Frechet` distance based on the angular distance in `radians` from function pygeodesy.cosineAndoyerLambert.
| FrechetCosineForsytheAndoyerLambert Compute the `Frechet` distance based on the angular distance in `radians` from function pygeodesy.cosineForsytheAndoyerLambert.
| FrechetCosineLaw Compute the `Frechet` distance based on the angular distance in `radians` from function pygeodesy.cosineLaw.
| FrechetDegrees DEPRECATED, use an other `Frechet*` class.
| FrechetDistanceTo Compute the `Frechet` distance based on the distance from the point1s' `LatLon.distanceTo` method, conventionally in `meter`.
| FrechetEquirectangular Compute the `Frechet` distance based on the equirectangular distance in `radians squared` like function pygeodesy.equirectangular.
| FrechetError Fréchet issue.
| FrechetEuclidean Compute the `Frechet` distance based on the Euclidean distance in `radians` from function pygeodesy.euclidean.
| FrechetExact Compute the `Frechet` distance based on the angular distance in `degrees` from method GeodesicExact`.Inverse`.
| FrechetFlatLocal Compute the `Frechet` distance based on the angular distance in `radians squared` like function pygeodesy.flatLocal_/pygeodesy.hubeny.
| FrechetFlatPolar Compute the `Frechet` distance based on the angular distance in `radians` from function flatPolar_.
| FrechetHaversine Compute the `Frechet` distance based on the angular distance in `radians` from function pygeodesy.haversine_.
| FrechetHubeny Compute the `Frechet` distance based on the angular distance in `radians squared` like function pygeodesy.flatLocal_/pygeodesy.hubeny.
| FrechetKarney Compute the `Frechet` distance based on the angular distance in `degrees` from Karney's geographiclib geodesic.Geodesic `Inverse` method.
| FrechetRadians DEPRECATED, use an other `Frechet*` class.
| FrechetThomas Compute the `Frechet` distance based on the angular distance in `radians` from function pygeodesy.thomas_.
| FrechetVincentys Compute the `Frechet` distance based on the angular distance in `radians` from function pygeodesy.vincentys_.
| Froot The root of a precision summation.
| Frustum A rectangular pyramid, typically representing a camera's field-of-view (fov) and the intersection with (or projection to) a local tangent plane.
| Fsqrt Square root of a precision summation.
| Fsum Precision floating point summation and running summation.
| Fsum2Tuple 2-Tuple `(fsum, residual)` with the precision running `fsum` and the `residual`, the sum of the remaining partials.
| Fwelford Welford's accumulator computing the running mean, (sample) variance and standard deviation.
| GDict A `dict` with both `key` and `attribute` access to the `dict` items.
| GeodSolve12Tuple 12-Tuple `(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)` with angles `lat1`, `lon1`, `azi1`, `lat2`, `lon2` and `azi2` and arc `a12` all in `degrees`, initial `azi1` and final `azi2` forward azimuths, distance `s12` and reduced length `m12` in `meter`, area `S12` in `meter` squared and geodesic scale factors `M12` and `M21`, both `scalar`, see GeodSolve.
| Geodesic Wrapper around Karney's class geographiclib.geodesic.Geodesic.
| GeodesicAreaExact Area and perimeter of a geodesic polygon, an enhanced version of Karney's Python class PolygonArea using the more accurate surface area.
| GeodesicError Error raised for convergence or other issues in geodesicx, geodesicw or karney.
| GeodesicExact A pure Python version of Karney's C++ class GeodesicExact, modeled after Karney's Python class geodesic.Geodesic.
| GeodesicLine Wrapper around Karney's class geographiclib.geodesicline.GeodesicLine.
| GeodesicLineExact A pure Python version of Karney's C++ class GeodesicLineExact, modeled after Karney's Python class geodesicline.GeodesicLine.
| GeodesicLineSolve Wrapper to invoke Karney's GeodSolve as an `Exact` version of Karney's Python class GeodesicLine.
| GeodesicSolve Wrapper to invoke Karney's GeodSolve as an `Exact` version of Karney's Python class Geodesic.
| GeoidError Geoid interpolator `Geoid...` or interpolation issue.
| GeoidG2012B Geoid height interpolator for GEOID12B Model grids CONUS, Alaska, Hawaii, Guam and Northern Mariana Islands, Puerto Rico and U.S. Virgin Islands and American Samoa based on `SciPy` RectBivariateSpline or interp2d interpolation.
| GeoidHeight2Tuple 2-Tuple `(height, model_name)`, geoid `height` in `meter` and `model_name` as `str`.
| GeoidHeight5Tuple 5-Tuple `(lat, lon, egm84, egm96, egm2008)` for GeoidHeights.dat tests with the heights for 3 different EGM grids at `degrees90` and `degrees180` degrees (after converting `lon` from original `0 <= EasterLon <= 360`).
| GeoidKarney Geoid height interpolator for Karney's GeographicLib Earth Gravitational Model (EGM) geoid egm*.pgm datasets using bilinear or cubic interpolation and caching in pure Python, transcoded from Karney's C++ class Geoid.
| GeoidPGM Geoid height interpolator for Karney's GeographicLib Earth Gravitational Model (EGM) geoid egm*.pgm datasets but based on `SciPy` RectBivariateSpline or interp2d interpolation.
| Gnomonic Azimuthal gnomonic projection for the sphere***, see Snyder, pp 164-168 and MathWorld-Wolfram.
| GnomonicExact Azimuthal gnomonic projection, a Python version of Karney's C++ class Gnomonic, based on exact geodesic classes GeodesicExact and GeodesicLineExact.
| GnomonicGeodSolve Azimuthal gnomonic projection, a Python version of Karney's C++ class Gnomonic, based on (exact) geodesic wrappers GeodesicSolve and GeodesicLineSolve and intended for testing purposes only.
| GnomonicKarney Azimuthal gnomonic projection, a Python version of Karney's C++ class Gnomonic, requiring package geographiclib to be installed.
| Hausdorff Hausdorff base class, requires method Hausdorff.distance to be overloaded.
| Hausdorff6Tuple 6-Tuple `(hd, i, j, mn, md, units)` with the Hausdorff distance `hd`, indices `i` and `j`, the total count `mn`, the `mean Hausdorff` distance `md` and the class or name of both distance `units`.
| HausdorffCosineAndoyerLambert Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.cosineAndoyerLambert.
| HausdorffCosineForsytheAndoyerLambert Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.cosineForsytheAndoyerLambert.
| HausdorffCosineLaw Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.cosineLaw_.
| HausdorffDegrees Hausdorff base class for distances from `LatLon` points in `degrees`.
| HausdorffDistanceTo Compute the `Hausdorff` distance based on the distance from the points' `LatLon.distanceTo` method, conventionally in `meter`.
| HausdorffEquirectangular Compute the `Hausdorff` distance based on the `equirectangular` distance in `radians squared` like function pygeodesy.equirectangular.
| HausdorffError Hausdorff issue.
| HausdorffEuclidean Compute the `Hausdorff` distance based on the `Euclidean` distance in `radians` from function pygeodesy.euclidean_.
| HausdorffExact Compute the `Hausdorff` distance based on the angular distance in `degrees` from method GeodesicExact`.Inverse`.
| HausdorffFlatLocal Compute the `Hausdorff` distance based on the angular distance in `radians squared` like function pygeodesy.flatLocal_/pygeodesy.hubeny_.
| HausdorffFlatPolar Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.flatPolar_.
| HausdorffHaversine Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.haversine_.
| HausdorffHubeny Compute the `Hausdorff` distance based on the angular distance in `radians squared` like function pygeodesy.flatLocal_/pygeodesy.hubeny_.
| HausdorffKarney Compute the `Hausdorff` distance based on the angular distance in `degrees` from Karney's geographiclib Geodesic Inverse method.
| HausdorffRadians Hausdorff base class for distances from `LatLon` points converted from `degrees` to `radians`.
| HausdorffThomas Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.thomas_.
| HausdorffVincentys Compute the `Hausdorff` distance based on the angular distance in `radians` from function pygeodesy.vincentys_.
| Height Named `float` representing a height, conventionally in `meter`.
| HeightCubic Height interpolator based on `SciPy` interp2d `kind='cubic'`.
| HeightError Height interpolator `Height...` or interpolation issue.
| HeightIDWcosineAndoyerLambert Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.cosineAndoyerLambert_.
| HeightIDWcosineForsytheAndoyerLambert Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.cosineForsytheAndoyerLambert_.
| HeightIDWcosineLaw Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.cosineLaw_.
| HeightIDWdistanceTo Height interpolator using Inverse Distance Weighting (IDW) and the distance from the points' `LatLon.distanceTo` method, conventionally in `meter`.
| HeightIDWequirectangular Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians squared` like function pygeodesy.equirectangular4.
| HeightIDWeuclidean Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.euclidean_.
| HeightIDWexact Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `degrees` from method GeodesicExact.Inverse.
| HeightIDWflatLocal Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians squared` like function pygeodesy.flatLocal_/pygeodesy.hubeny_.
| HeightIDWflatPolar Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.flatPolar_.
| HeightIDWhaversine Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.haversine_.
| HeightIDWhubeny Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians squared` like function pygeodesy.flatLocal_/pygeodesy.hubeny_.
| HeightIDWkarney Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `degrees` from Karney's geographiclib method Geodesic.Inverse.
| HeightIDWthomas Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.thomas_.
| HeightIDWvincentys Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function pygeodesy.vincentys_.
| HeightLSQBiSpline Height interpolator using `SciPy` LSQSphereBivariateSpline.
| HeightLinear Height interpolator based on `SciPy` interp2d `kind='linear'`.
| HeightSmoothBiSpline Height interpolator using `SciPy` SmoothSphereBivariateSpline.
| HeightX Like Height, used to distinguish the interpolated height from an original Height at a clip intersection.
| Height_ Named `float` with optional `low` and `high` limits representing a height, conventionally in `meter`.
| Int Named `int`.
| Int_ Named `int` with optional limits `low` and `high`.
| Intersect7Tuple 7-Tuple `(A, B, sAB, aAB, c, kA, kB)` with `A` and `B` each a `LatLon` or LatLon4Tuple`(lat, lon, height, datum)` of the intersection on each geodesic line, the distance `sAB` in in `meter` and angular distance `aAB` in `degrees` between `A` and `B`, coincidence indicator `c` and segment indicators `kA` and `kB` all `int`, see XDict and method intersect7.
| Intersection3Tuple 3-Tuple `(point, outside1, outside2)` of an intersection `point` and `outside1`, the position of the `point`, `-1` if before the start, `+1` if after the end and `0` if on or between the start and end point of the first line.
| IntersectionError Error raised for line or circle intersection issues.
| Intersectool Wrapper to invoke Karney's utility IntersectTool similar to class Intersector.
| Intersectool5Tuple 5-Tuple `(A, B, sAB, aAB, c)` with `A` and `B` the `Position` of the intersection on each geodesic line, the distance `sAB` between `A` and `B` in `meter`, the angular distance `aAB` in `degrees` and coincidence indicator `c` (`int`), see XDict.
| Intersector Finder of intersections between two goedesic lines, each an instance of GeodesicLineExact, wrapped GeodesicLine or GeodesicLineSolve.
| Intersector5Tuple 5-Tuple `(A, B, sAB, aAB, c)` with `A` and `B` the `Position` of the intersection on each geodesic line, the distance `sAB` between `A` and `B` in `meter`, angular distance `aAB` in `degrees` and coincidence indicator `c` (`int`), see XDict.
| Inverse10Tuple 10-Tuple `(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)` with arc length `a12` in `degrees`, distance `s12` and reduced length `m12` in `meter`, area `S12` in `meter` squared and the sines `salp1`, `salp2` and cosines `calp1`, `calp2` of the initial `1` and final `2` (forward) azimuths.
| Jacobi2Tuple 2-Tuple `(x, y)` with a Jacobi Conformal `x` and `y` projection, both in Radians (or Degrees).
| JacobiConformal This is a conformal projection of a triaxial ellipsoid to a plane in which the `X` and `Y` grid lines are straight.
| JacobiConformalSpherical An alternate, spherical JacobiConformal projection.
| KTMError Error raised for KTransverseMercator and KTransverseMercator.forward issues.
| KTransverseMercator Karney's C++ class TransverseMercator transcoded to pure Python, following is a partial copy of Karney's documentation.
| LCCError Lambert Conformal Conic `LCC` or other Lcc issue.
| Lam Named `float` representing a longitude in `radians`.
| LambertEqualArea Lambert-equal-area projection for the sphere*** (aka Lambert zenithal equal-area projection, see Snyder, pp 185-187 and MathWorld-Wolfram.
| Lamd Named `float` representing a longitude in `radians` converted from `degrees`.
| Lat Named `float` representing a latitude in `degrees`.
| LatLon2PsxyIter Iterate and convert for `points` with optional loop-back and copies.
| LatLon2Tuple 2-Tuple `(lat, lon)` in `degrees90` and `degrees180`.
| LatLon2psxy Wrapper for `LatLon` points as "on-the-fly" pseudo-xy coordinates.
| LatLon3Tuple 3-Tuple `(lat, lon, height)` in `degrees90`, `degrees180` and `meter`, conventionally.
| LatLon4Tuple 4-Tuple `(lat, lon, height, datum)` in `degrees90`, `degrees180`, `meter` and Datum.
| LatLonAziRk4Tuple 4-Tuple `(lat, lon, azimuth, reciprocal)`, all in `degrees` where `azimuth` is the azimuth of easting direction and `reciprocal` the reciprocal of azimuthal northing scale.
| LatLonDatum3Tuple 3-Tuple `(lat, lon, datum)` in `degrees90`, `degrees180` and Datum.
| LatLonDatum5Tuple 5-Tuple `(lat, lon, datum, gamma, scale)` in `degrees90`, `degrees180`, Datum, `degrees` and `float`.
| LatLonFHP A point or intersection in a BooleanFHP clip or composite.
| LatLonGH A point or intersection in a BooleanGH clip or composite.
| LatLonPrec3Tuple 3-Tuple `(lat, lon, precision)` in `degrees`, `degrees` and `int`.
| LatLonPrec5Tuple 5-Tuple `(lat, lon, precision, height, radius)` in `degrees`, `degrees`, `int` and `height` or `radius` in `meter` (or `None` if missing).
| LatLon_ Low-overhead `LatLon` class, mainly for Numpy2LatLon and Tuple2LatLon.
| Lat_ Named `float` representing a latitude in `degrees` within limits `low` and `high`.
| LazyAttributeError Raised if a `lazily imported` attribute is missing or invalid.
| LazyImportError Raised if `lazy import` is not supported, disabled or failed some other way.
| Lcc Lambert conformal conic East-/Northing location.
| LenError Error raised for mis-matching `len` values.
| LimitError Error raised for lat- or longitudinal values or deltas exceeding the given `limit` in functions equirectangular, equirectangular4, `nearestOn*` and `simplify*` or methods with `limit` or `options` keyword arguments.
| Local9Tuple 9-Tuple `(x, y, z, lat, lon, height, ltp, ecef, M)` with local `x`, `y`, `z` all in `meter`, geodetic `lat`, `lon`, `height`, local tangent plane `ltp` (Ltp), `ecef` (Ecef9Tuple) with geocentric `x`, `y`, `z`, geodetic `lat`, `lon`, `height` and concatenated rotation matrix `M` (EcefMatrix) or `None`.
| LocalCartesian Conversion between geodetic `(lat, lon, height)` and local cartesian `(x, y, z)` coordinates with geodetic origin `(lat0, lon0, height0)`, transcoded from Karney's C++ class LocalCartesian.
| LocalError A LocalCartesian or Ltp related issue.
| Lon Named `float` representing a longitude in `degrees`.
| Lon_ Named `float` representing a longitude in `degrees` within limits `low` and `high`.
| Los A Line-Of-Sight (LOS) from a `LatLon` or `Cartesian` location.
| Ltp A local tangent plan (LTP), a sub-class of `LocalCartesian` with (re-)configurable ECEF converter.
| MGRSError Military Grid Reference System (MGRS) parse or other Mgrs issue.
| Meeus2Tuple 2-Tuple `(radius, Type)` with `radius` and Meeus' `Type` of the smallest circle containing 3 points.
| Meter Named `float` representing a distance or length in `meter`.
| Meter2 Named `float` representing an area in `meter squared`.
| Meter3 Named `float` representing a volume in `meter cubed`.
| Meter_ Named `float` representing a distance or length in `meter`.
| Mgrs Military Grid Reference System (MGRS/NATO) references, with method to convert to UTM coordinates.
| Mgrs4Tuple 4-Tuple `(zone, EN, easting, northing)`, `zone` and grid tile `EN` as `str`, `easting` and `northing` in `meter`.
| Mgrs6Tuple 6-Tuple `(zone, EN, easting, northing, band, datum)`, with `zone`, grid tile `EN` and `band` as `str`, `easting` and `northing` in `meter` and `datum` a Datum.
| Middle5Tuple 5-Tuple `(A, B, sMM, aMM, c)` with `A` and `B` the line segments including the mid-point location in `latM`, `lonM`, distance `s1M` in `meter` and angular distance `a1M` in `degrees`, the distance between both mid-points `sMM` in `meter` and angular distance `aMM` in `degrees` and coincidence indicator `c` (`int`).
| NearestOn2Tuple 2-Tuple `(closest, fraction)` of the `closest` point on and `fraction` along a line (segment) between two points.
| NearestOn3Tuple 3-Tuple `(closest, distance, angle)` of the `closest` point on the polygon, either a `LatLon` instance or a LatLon3Tuple`(lat, lon, height)` and the `distance` and `angle` to the `closest` point are in `meter` respectively compass `degrees360`.
| NearestOn6Tuple 6-Tuple `(closest, distance, fi, j, start, end)` with the `closest` point, the `distance` in `meter`, conventionally and the `start` and `end` point of the path or polygon edge.
| NearestOn8Tuple 8-Tuple `(closest, distance, fi, j, start, end, initial, final)`, like NearestOn6Tuple but extended with the `initial` and the `final` bearing at the reference respectively the `closest` point, both in compass `degrees`.
| Ned Local `North-Eeast-Down` (NED) location in a local tangent plane.
| Ned4Tuple 4-Tuple `(north, east, down, ltp)`, all in `meter` except `ltp`.
| Northing Named `float` representing a northing, conventionally in `meter`.
| NumPyError Error raised for `NumPy` issues.
| Number_ Named `int` representing a non-negative number.
| Numpy2LatLon Wrapper for `NumPy` arrays as "on-the-fly" `LatLon` points.
| OSGRError Error raised for a parseOSGR, Osgr or other OSGR issue.
| Orthographic Orthographic projection for the sphere***, see Snyder, pp 148-153 and MathWorld-Wolfram.
| Osgr Ordnance Survey Grid References (OSGR) coordinates on the National Grid.
| PGMError Issue parsing or cropping an `egm*.pgm` geoid dataset.
| ParseError Error parsing degrees, radians or several other formats.
| Phi Named `float` representing a latitude in `radians`.
| PhiLam2Tuple 2-Tuple `(phi, lam)` with latitude `phi` in `radians[PI_2]` and longitude `lam` in `radians[PI]`.
| PhiLam3Tuple 3-Tuple `(phi, lam, height)` with latitude `phi` in `radians[PI_2]`, longitude `lam` in `radians[PI]` and `height` in `meter`.
| PhiLam4Tuple 4-Tuple `(phi, lam, height, datum)` with latitude `phi` in `radians[PI_2]`, longitude `lam` in `radians[PI]`, `height` in `meter` and Datum.
| Phid Named `float` representing a latitude in `radians` converted from `degrees`.
| Point3Tuple 3-Tuple `(x, y, ll)` in `meter`, `meter` and `LatLon`.
| Points2Tuple 2-Tuple `(number, points)` with the `number` of points and -possible reduced- `list` or `tuple` of `points`.
| PointsError Error for an insufficient number of points.
| PointsIter Iterator for `points` with optional loop-back and copies.
| PolygonArea For `geographiclib` compatibility, sub-class of GeodesicAreaExact.
| Precision_ Named `int` with optional `low` and `high` limits representing a precision.
| Property
| Property_RO
| Radians Named `float` representing a coordinate in `radians`, optionally clipped.
| Radians2 Named `float` representing a distance in `radians squared`.
| Radians_ Named `float` representing a coordinate in `radians` with optional limits `low` and `high`.
| Radical2Tuple 2-Tuple `(ratio, xline)` of the radical `ratio` and radical `xline`, both `scalar` and `0.0 <= ratio <= 1.0`
| Radii11Tuple 11-Tuple `(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)` with the `Tangent` circle radii `rA`, `rB` and `rC`, the `circumradius` `cR`, the `Incircle` radius `rIn` aka `inradius`, the inner and outer Soddy circle radii `riS` and `roS`, the sides `a`, `b` and `c` and semi-perimeter `s` of a triangle, all in `meter` conventionally.
| Radius Named `float` representing a radius, conventionally in `meter`.
| RadiusThetaPhi3Tuple 3-Tuple `(r, theta, phi)` with radial distance `r` in `meter`, inclination `theta` (with respect to the positive z-axis) and azimuthal angle `phi` in Degrees or Radians representing a spherical, polar position.
| Radius_ Named `float` with optional `low` and `high` limits representing a radius, conventionally in `meter`.
| RangeError Error raised for lat- or longitude values outside the `clip`, `clipLat`, `clipLon` in functions parse3llh, parseDMS, parseDMS2 and parseRad or the `limit` set with functions clipDegrees and clipRadians.
| RefFrame Terrestrial Reference Frame (TRF) parameters.
| ResectionError Error raised for issues in pygeodesy.resections.
| ResidualError Error raised for a division, power or root operation of an Fsum instance with a `residual` ratio exceeding the RESIDUAL threshold.
| Reverse4Tuple 4-Tuple `(lat, lon, gamma, scale)` with `lat`- and `lon`gitude in `degrees`, meridian convergence `gamma` at point in `degrees` and the `scale` of projection at point `scalar`.
| Rhumb Class to solve the direct and inverse rhumb problems, based on elliptic functions or Krüger series expansion
| Rhumb8Tuple 8-Tuple `(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)` with lat- `lat1`, `lat2` and longitudes `lon1`, `lon2` of both points, the azimuth of the rhumb line `azi12`, the distance `s12`, the area `S12` under the rhumb line and the angular distance `a12` between both points.
| RhumbAux Class to solve the direct and inverse rhumb problems, based on Auxiliary Latitudes for accuracy near the poles.
| RhumbError Error raised for a rhumb aux_, ekx or solve issue.
| RhumbLine Compute one or several points on a single rhumb line.
| RhumbLineAux Compute one or several points on a single rhumb line.
| RhumbLineSolve Wrapper to invoke Karney's RhumbSolve like a class, similar to pygeodesy.RhumbLine and pygeodesy.RhumbLineAux.
| RhumbSolve Wrapper to invoke Karney's RhumbSolve like a class, similar to pygeodesy.Rhumb and pygeodesy.RhumbAux.
| RhumbSolve7Tuple 7-Tuple `(lat1, lon1, lat2, lon2, azi12, s12, S12)` with lat- `lat1`, `lat2` and longitudes `lon1`, `lon2` of both points, the azimuth of the rhumb line `azi12`, the distance `s12` and the area `S12` under the rhumb line between both points.
| Scalar Named `float` representing a factor, fraction, scale, etc.
| Scalar_ Named `float` with optional `low` and `high` limits representing a factor, fraction, scale, etc.
| SciPyError Error raised for `SciPy` issues.
| SciPyWarning Error thrown for `SciPy` warnings.
| Shape2Tuple 2-Tuple `(nrows, ncols)`, the number of rows and columns, both `int`.
| Soddy4Tuple 4-Tuple `(radius, center, deltas, outer)` with `radius` and (trilaterated) `center` of the inner Soddy circle and the radius of the `outer` Soddy circle.
| Stereographic Stereographic projection for the sphere***, see Snyder, pp 157-160 and MathWorld-Wolfram.
| Str Named, callable `str`.
| Str_ Extended, callable `str` class, not nameable.
| Survey3Tuple 3-Tuple `(PA, PB, PC)` with distance from survey point `P` to each of the triangle corners `A`, `B` and `C` in `meter`, conventionally.
| TRFError Terrestrial Reference Frame (TRF), Epoch, RefFrame or RefFrame conversion issue.
| TRFXform A Terrestrial Reference Frame (TRF) converter between two reference frames observed at an `epoch`.
| TRFXform7Tuple 7-Tuple `(tx, ty, tz, s, sx, sy, sz)` of conversion parameters with translations `tx`, `ty` and `tz` in `milli-meter`, scale `s` in `ppB` and rotations `sx`, `sy` and `sz` in `milli-arc-seconds`.
| Tienstra7Tuple 7-Tuple `(pointP, A, B, C, a, b, c)` with survey `pointP`, interior triangle angles `A`, `B` and `C` in `degrees` and triangle sides `a`, `b` and `c` in `meter`, conventionally.
| Transform Helmert datum transformation.
| TransformXform Helmert transformation, extended with an `Xform` TRF converter.
| TriAngle5Tuple 5-Tuple `(radA, radB, radC, rIn, area)` with the interior angles at triangle corners `A`, `B` and `C` in `radians`, the `InCircle` radius `rIn` aka `inradius` in `meter` and the triangle `area` in `meter` squared, conventionally.
| TriSide2Tuple 2-Tuple `(a, radA)` with triangle side `a` in `meter`, conventionally and angle `radA` at the opposite triangle corner in `radians`.
| TriSide4Tuple 4-Tuple `(a, b, radC, d)` with interior angle `radC` at triangle corner `C` in `radians`with the length of triangle sides `a` and `b` and with triangle height `d` perpendicular to triangle side `c`, in the same units as triangle sides `a` and `b`.
| Triangle7Tuple 7-Tuple `(A, a, B, b, C, c, area)` with interior angles `A`, `B` and `C` in `degrees`, spherical sides `a`, `b` and `c` in `meter` conventionally and the `area` of a (spherical) triangle in square `meter` conventionally.
| Triangle8Tuple 8-Tuple `(A, a, B, b, C, c, D, E)` with interior angles `A`, `B` and `C`, spherical sides `a`, `b` and `c`, the spherical deficit `D` and the spherical excess `E` of a (spherical) triangle, all in `radians`.
| TriangleError Error raised for triangle, intersection or resection issues.
| Triaxial Ordered triaxial ellipsoid.
| TriaxialError Raised for Triaxial issues.
| Triaxial_ Unordered triaxial ellipsoid and base class.
| Trilaterate5Tuple 5-Tuple `(min, minPoint, max, maxPoint, n)` with `min` and `max` in `meter`, the corresponding trilaterated `minPoint` and `maxPoint` as `LatLon` and the number `n`.
| Tuple2LatLon Wrapper for tuple sequences as "on-the-fly" `LatLon` points.
| UPSError Universal Polar Stereographic (UPS) parse or other Ups issue.
| UTMError Universal Transverse Mercator (UTM parse or other Utm issue.
| UTMUPSError Universal Transverse Mercator/Universal Polar Stereographic (UTM/UPS) parse, validate or other issue.
| UnitError Default exception for units issues for a value exceeding the `low` or `high` limit.
| Ups Universal Polar Stereographic (UPS) coordinate.
| Utm Universal Transverse Mercator (UTM) coordinate.
| UtmUps2Tuple 2-Tuple `(zone, hemipole)` as `int` and `str`, where `zone` is `1..60` for UTM or `0` for UPS and `hemipole` `'N'|'S'` is the UTM hemisphere or the UPS pole.
| UtmUps5Tuple 5-Tuple `(zone, hemipole, easting, northing, band)` as `int`, `str`, `meter`, `meter` and `band` letter, where `zone` is `1..60` for UTM or `0` for UPS, `hemipole` `'N'|'S'` is the UTM hemisphere or the UPS pole and `band` is `""` or the longitudinal UTM band `'C'|'D'|..|'W'|'X'` or polar UPS band `'A'|'B'|'Y'|'Z'`.
| UtmUps8Tuple 8-Tuple `(zone, hemipole, easting, northing, band, datum, gamma, scale)` as `int`, `str`, `meter`, `meter`, `band` letter, `Datum`, `degrees` and `scalar`, where `zone` is `1..60` for UTM or `0` for UPS, `hemipole` `'N'|'S'` is the UTM hemisphere or the UPS pole and `band` is `""` or the longitudinal UTM band `'C'|'D'|..|'W'|'X'` or polar UPS band `'A'|'B'|'Y'|'Z'`.
| UtmUpsLatLon5Tuple 5-Tuple `(zone, band, hemipole, lat, lon)` as `int`, `str`, `str`, `degrees90` and `degrees180`, where `zone` is `1..60` for UTM or `0` for UPS, `band` is `""` or the longitudinal UTM band `'C'|'D'|..|'W'|'X'` or polar UPS band `'A'|'B'|'Y'|'Z'` and `hemipole` `'N'|'S'` is the UTM hemisphere or the UPS pole.
| Uvw 3-D `u-v-w` (UVW) components.
| Uvw3Tuple 3-Tuple `(u, v, w)`, in `meter`.
| Vector2Tuple 2-Tuple `(x, y)` of (geocentric) components, each in `meter` or the same `units`.
| Vector3Tuple 3-Tuple `(x, y, z)` of (geocentric) components, all in `meter` or the same `units`.
| Vector3d Extended 3-D vector.
| Vector4Tuple 4-Tuple `(x, y, z, h)` of (geocentric) components, all in `meter` or the same `units`.
| VectorError Vector3d, `Cartesian*` or `*Nvector` issues.
| WebMercatorError Web Mercator (WM) parser or Wm issue.
| Wm Web Mercator (WM) coordinate.
| XDict 4+Item result from Intersectool and Intersector methods `All`, `Closest`, `Next` and `Segment` with the intersection offsets `sA`, `sB` and `sX0` in `meter` and the coincidence indicator `c`, an `int`, +1 for parallel, -1 for anti-parallel or 0 otherwise.
| Xyz4Tuple 4-Tuple `(x, y, z, ltp)`, all in `meter` except `ltp`.
| XyzLocal Local `(x, y, z)` in a local tangent plane (LTP), also base class for local Enu.
| Zone Named `int` representing a UTM/UPS zone number.
| a_f2Tuple 2-Tuple `(a, f)` specifying an ellipsoid by equatorial radius `a` in `meter` and scalar flattening `f`.
| property_RO
| property_ROnce
| property_ROver

Functions
Geodesic_WGS84() Get the wrapped Geodesic`(WGS84)` singleton, provided geographiclib is installed, otherwise an `ImportError`. |
NM2m(nm) Convert nautical miles to meter (m). |
SM2m(sm) Convert statute miles to meter (m). |
SinCos2(x) Get `sin` and `cos` of typed angle. |
UtmUps(zone, hemipole, easting, northing, band='', datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, falsed=True, **name) Class-like function to create a UTM/UPS coordinate. |
a_b2e(a, b) Return `e`, the 1st eccentricity for a given equatorial and polar radius. |
a_b2e2(a, b) Return `e2`, the 1st eccentricity squared for a given equatorial and polar radius. |
a_b2e22(a, b) Return `e22`, the 2nd eccentricity squared for a given equatorial and polar radius. |
a_b2e32(a, b) Return `e32`, the 3rd eccentricity squared for a given equatorial and polar radius. |
a_b2f(a, b) Return `f`, the flattening for a given equatorial and polar radius. |
a_b2f2(a, b) Return `f2`, the 2nd flattening for a given equatorial and polar radius. |
a_b2f_(a, b) Return `f_`, the inverse flattening for a given equatorial and polar radius. |
a_b2n(a, b) Return `n`, the 3rd flattening for a given equatorial and polar radius. |
a_f2b(a, f) Return `b`, the polar radius for a given equatorial radius and flattening. |
a_f_2b(a, f_) Return `b`, the polar radius for a given equatorial radius and inverse flattening. |
acos1(x) Return `math.acos(max(-1, min(1, x)))`. |
acre2ha(acres) Convert acres to hectare. |
acre2m2(acres) Convert acres to square meter. |
anstr(name, OKd=`'``._-``'`, sub='_') Make a valid name of alphanumeric and OKd characters. |
antipode(lat, lon, **name) Return the antipode, the point diametrically opposite to a given point in `degrees`. |
antipode_(phi, lam, **name) Return the antipode, the point diametrically opposite to a given point in `radians`. |
areaOf(points, adjust=True, radius=6371008.771415, wrap=True) Approximate the area of a polygon or composite. |
asin1(x) Return `math.asin(max(-1, min(1, x)))`. |
atan1(y, x=1.0) Return `atan(y / x)` angle in `radians` [-PI/2..+PI/2] using `atan2` for consistency and to avoid `ZeroDivisionError`. |
atan1d(y, x=1.0) Return `atan(y / x)` angle in `degrees` [-90..+90] using `atan2d` for consistency and to avoid `ZeroDivisionError`. |
atan2b(y, x) Return `atan2(y, x)` in degrees [0..+360]. |
atan2d(y, x, reverse=False) Return `atan2(y, x)` in degrees [-180..+180], optionally reversed (by 180 degrees for `azimuth`s). |
attrs(inst, *names, **Nones_True__pairs_kwds) Get instance attributes as name=value strings, with `float`s formatted by function fstr. |
b_f2a(b, f) Return `a`, the equatorial radius for a given polar radius and flattening. |
b_f_2a(b, f_) Return `a`, the equatorial radius for a given polar radius and inverse flattening. |
bearing(lat1, lon1, lat2, lon2, **final_wrap) Compute the initial or final bearing (forward or reverse azimuth) between two (spherical) points. |
bearingDMS(bearing, form=`'``d``'`, prec=None, sep='', **s_D_M_S) Convert bearing to a string (without compass point suffix). |
bearing_(phi1, lam1, phi2, lam2, final=False, wrap=False) Compute the initial or final bearing (forward or reverse azimuth) between two (spherical) points. |
boundsOf(points, wrap=False, LatLon=None) Determine the bottom-left SW and top-right NE corners of a path or polygon. |
bqrt(x) Return the 4-th, bi-quadratic or quartic root, x**(1 / 4), preserving `type(x)`. |
callername(up=1, dflt='', source=False, underOK=False) Get the name of the invoking callable. |
cassini(pointA, pointB, pointC, alpha, beta, useZ=False, **Clas_and_kwds) 3-Point resection using Cassini's method. |
cbrt(x) Compute the cube root x**(1/3), preserving `type(x)`. |
cbrt2(x) Compute the cube root squared x**(2/3), preserving `type(x)`. |
centroidOf(points, wrap=False, LatLon=None) Determine the centroid of a polygon. |
chain2m(chains) Convert UK chains to meter. |
circin6(point1, point2, point3, eps=8.881784197001252e-16, useZ=True) Return the radius and center of the inscribed aka Incircle of a (2- or 3-D) triangle. |
circle4(earth, lat) Get the equatorial or a parallel circle of latitude. |
circum3(point1, point2, point3, circum=True, eps=8.881784197001252e-16, useZ=True) Return the radius and center of the smallest circle through or containing three (2- or 3-D) points. |
circum4_(*points, **useZ_Vector_and_kwds) Best-fit a sphere through three or more (3-D) points. |
classname(inst, prefixed=None) Return the instance' class name optionally prefixed with the module name. |
classnaming(prefixed=None) Get/set the default class naming for `[module.]class` names. |
clipCS4(points, lowerleft, upperight, closed=False, inull=False) Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm. |
clipDegrees(deg, limit) Clip a lat- or longitude to the given range. |
clipFHP4(points, corners, closed=False, inull=False, raiser=False, eps=2.220446049250313e-16) Clip one or more polygons against a clip region or box using Forster-Hormann-Popa's C++ implementation transcoded to pure Python. |
clipGH4(points, corners, closed=False, inull=False, raiser=True, xtend=False, eps=2.220446049250313e-16) Clip one or more polygons against a clip region or box using the Greiner-Hormann algorithm, Correia's implementation modified and extended. |
clipLB6(points, lowerleft, upperight, closed=False, inull=False) Clip a path against a rectangular clip box using the Liang-Barsky algorithm. |
clipRadians(rad, limit) Clip a lat- or longitude to the given range. |
clipSH(points, corners, closed=False, inull=False) Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm. |
clipSH3(points, corners, closed=False, inull=False) Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm. |
clips(sb, limit=50, white='', length=False) Clip a string to the given length limit. |
collins5(pointA, pointB, pointC, alpha, beta, useZ=False, **Clas_and_kwds) 3-Point resection using Collins' method. |
compassAngle(lat1, lon1, lat2, lon2, adjust=True, wrap=False) Return the angle from North for the direction vector (lon2 - lon1, lat2 - lat1) between two points. |
compassDMS(bearing, form=`'``d``'`, prec=None, sep='', **s_D_M_S) Convert bearing to a string suffixed with compass point. |
compassPoint(bearing, prec=3) Convert a `bearing` from North to a compass point. |
copysign0(x, y) Like `math.copysign(x, y)` except `zero`, unsigned. |
copytype(x, y) Return the value of x as `type` of `y`. |
cosineAndoyerLambert(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=False) Compute the distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines formula. |
cosineAndoyerLambert_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`) Compute the angular distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines formula. |
cosineForsytheAndoyerLambert(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=False) Compute the distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula. |
cosineForsytheAndoyerLambert_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`) Compute the angular distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula. |
cosineLaw(lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) Compute the distance between two points using the spherical Law of Cosines formula. |
cosineLaw_(phi2, phi1, lam21) Compute the angular distance between two points using the spherical Law of Cosines formula. |
cot(rad, **error_kwds) Return the `cotangent` of an angle in `radians`. |
cot_(*rads, **error_kwds) Return the `cotangent` of angle(s) in `radiansresection`. |
cotd(deg, **error_kwds) Return the `cotangent` of an angle in `degrees`. |
cotd_(*degs, **error_kwds) Return the `cotangent` of angle(s) in `degrees`. |
crosserrors(raiser=None) Report or ignore vectorial cross product errors. |
date2epoch(year, month, day) Return the `epoch` for a calendar day. |
degDMS(deg, prec=6, s_D=`'``°``'`, s_M=`'``\xe2\x80\xb2``'`, s_S=`'``″``'`, neg='-', pos='') Convert degrees to a string in degrees, minutes or seconds. |
degrees(x) Convert angle x from radians to degrees. |
degrees180(rad) Convert radians to degrees and wrap [-180..+180). |
degrees2grades(deg) Convert degrees to grades (aka gons or gradians). |
degrees2m(deg, radius=6371008.771415, lat=0) Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. |
degrees360(rad) Convert radians to degrees and wrap [0..+360). |
degrees90(rad) Convert radians to degrees and wrap [-90..+90). |
deprecated_Property_RO(method) Decorator for a DEPRECATED Property_RO. |
deprecated_class(cls_or_class) Use inside __new__ or __init__ of a DEPRECATED class. |
deprecated_function(call) Decorator for a DEPRECATED function. |
deprecated_method(call) Decorator for a DEPRECATED method. |
deprecated_property_RO(method) Decorator for a DEPRECATED property_RO. |
e22f(e2) Return `f`, the flattening for a given 1st eccentricity squared. |
e2f(e) Return `f`, the flattening for a given 1st eccentricity. |
egmGeoidHeights(GeoidHeights_dat) Generate geoid egm*.pgm height tests from GeoidHeights.dat Test data for Geoids. |
elevation2(lat, lon, timeout=2.0) Get the geoid elevation at an `NAD83` to `NAVD88` location. |
enstr2(easting, northing, prec, *extras, **wide_dot) Return an MGRS/OSGR easting, northing string representations. |
epoch2date(epoch) Return the date for a reference frame `epoch`. |
equidistant(lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, exact=False, geodsolve=False, **name) Return an EquidistantExact, EquidistantGeodSolve or (if Karney's geographiclib package is installed) an EquidistantKarney, otherwise an Equidistant instance. |
equirectangular(lat1, lon1, lat2, lon2, radius=6371008.771415, **adjust_limit_wrap) Compute the distance between two points using the Equirectangular Approximation / Projection. |
equirectangular4(lat1, lon1, lat2, lon2, adjust=True, limit=45, wrap=False) Compute the distance between two points using the Equirectangular Approximation / Projection. |
euclid(x, y) Appoximate the norm sqrt(x**2 + y**2) by max(abs(x), abs(y)) + min(abs(x), abs(y)) * 0.4142.... |
euclid_(*xs) Appoximate the norm sqrt(sum(x**2 for x in xs)) by cascaded euclid. |
euclidean(lat1, lon1, lat2, lon2, radius=6371008.771415, adjust=True, wrap=False) Approximate the `Euclidean` distance between two (spherical) points. |
euclidean_(phi2, phi1, lam21, adjust=True) Approximate the angular `Euclidean` distance between two (spherical) points. |
exception_chaining(exc=None) Get an error's cause or the exception chaining setting. |
excessAbc_(A, b, c) Compute the spherical excess `E` of a (spherical) triangle from two sides and the included (small) angle. |
excessCagnoli_(a, b, c) Compute the spherical excess `E` of a (spherical) triangle using Cagnoli's (D.34) formula. |
excessGirard_(A, B, C) Compute the spherical excess `E` of a (spherical) triangle using Girard's formula. |
excessKarney(lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) Compute the surface area of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator using Karney's method. |
excessKarney_(phi2, phi1, lam21) Compute the spherical excess `E` of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator using Karney's method. |
excessLHuilier_(a, b, c) Compute the spherical excess `E` of a (spherical) triangle using L'Huilier's's Theorem. |
excessQuad(lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) Compute the surface area of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator. |
excessQuad_(phi2, phi1, lam21) Compute the spherical excess `E` of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator. |
f2e2(f) Return `e2`, the 1st eccentricity squared for a given flattening. |
f2e22(f) Return `e22`, the 2nd eccentricity squared for a given flattening. |
f2e32(f) Return `e32`, the 3rd eccentricity squared for a given flattening. |
f2f2(f) Return `f2`, the 2nd flattening for a given flattening. |
f2f_(f) Return `f_`, the inverse flattening for a given flattening. |
f2n(f) Return `n`, the 3rd flattening for a given flattening. |
f_2f(f_) Return `f`, the flattening for a given inverse flattening. |
facos1(x) Fast approximation of pygeodesy.acos1`(x)`. |
fasin1(x) Fast approximation of pygeodesy.asin1`(x)`. |
fatan(x) Fast approximation of `atan(x)`. |
fatan1(x) Fast approximation of `atan(x)` for `0 <= x < 1`, unchecked. |
fatan2(y, x) Fast approximation of `atan2(y, x)`. |
fathom2m(fathoms) Convert Imperial fathom to meter. |
favg(a, b, f=0.5) Return the precision average of two values. |
fdot(a, *b) Return the precision dot product sum(a[i] * b[i] for i=0..len(a)). |
fdot3(xs, ys, zs, start=0) Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)-1). |
fhorner(x, *cs) Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)-1) using the Horner form. |
fidw(xs, ds, beta=2) Interpolate using Inverse Distance Weighting (IDW). |
flatLocal(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True, wrap=False) Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. |
flatLocal_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True) Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. |
flatPolar(lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) Compute the distance between two (spherical) points using the polar coordinate flat-Earth formula. |
flatPolar_(phi2, phi1, lam21) Compute the angular distance between two (spherical) points using the polar coordinate flat-Earth formula. |
float0_(*xs) Yield `xs` as a non-NEG0 `float`. |
float_(*fs, **sets) Get scalars as `float` or intern'ed `float`. |
fmean(xs) Compute the accurate mean sum(xs) / len(xs). |
fmean_(*xs) Compute the accurate mean sum(xs) / len(xs). |
fpolynomial(x, *cs, **over) Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) [/ over]. |
fpowers(x, n, alts=0) Return a series of powers [x**i for i=1..n]. |
fprod(xs, start=1) Iterable product, like `math.prod` or `numpy.prod`. |
fractional(points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds) Return the point at a given fractional index. |
frandoms(n, seeded=None) Generate `n` (long) lists of random `floats`. |
frange(start, number, step=1) Generate a range of `float`s. |
frechet_(point1s, point2s, distance=None, units='') Compute the discrete Fréchet distance between two paths, each given as a set of points. |
value |
freduce(function, sequence, initial=...) Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. |
fremainder(x, y) Remainder in range `[-y / 2, y / 2]`. |
fstr(floats, prec=6, fmt='F', ints=False, sep=', ', strepr=None, force=True) Convert one or more floats to string, optionally stripped of trailing zero decimals. |
fstrzs(efstr, ap1z=False) Strip trailing zero decimals from a `float` string. |
fsum(xs, floats=False) Precision floating point summation based on/like Python's `math.fsum`. |
fsum1(xs, floats=False) Precision floating point summation, 1-primed. |
fsum1_(*xs, **floats) Precision floating point summation, 1-primed of all positional items. |
fsum1f_(*xs) Precision floating point summation iff all `xs` items are known to be scalar. |
fsum_(*xs, **floats) Precision floating point summation of all positional items. |
fsumf_(*xs) Precision floating point summation iff all `xs` items are known to be scalar. |
ft2m(feet, usurvey=False, pied=False, fuss=False) Convert International, US Survey, French or German `feet` to `meter`. |
furlong2m(furlongs) Convert a furlong to meter. |
geoidHeight2(lat, lon, model=0, timeout=2.0) Get the `NAVD88` geoid height at an `NAD83` location. |
gnomonic(lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, exact=False, geodsolve=False, **name) Return a GnomonicExact or (if Karney's geographiclib package is installed) a GnomonicKarney, otherwise a Gnomonic instance. |
grades(rad) Convert radians to grades (aka gons or gradians). |
grades2degrees(gon) Convert grades (aka gons or gradians) to `degrees`. |
grades2radians(gon) Convert grades (aka gons or gradians) to `radians`. |
grades400(rad) Convert radians to grades (aka gons or gradians) and wrap [0..+400). |
halfs2(str2) Split a string in 2 halfs. |
hartzell(pov, los=False, earth=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, **name_LatLon_and_kwds) Compute the intersection of the earth's surface and a Line-Of-Sight from a Point-Of-View in space. |
hartzell4(pov, los=False, tri_biax=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, **name) Compute the intersection of a tri-/biaxial ellipsoid and a Line-Of-Sight from a Point-Of-View outside. |
hausdorff_(model, target, both=False, early=True, seed=None, units='', distance=None, point=<function _point at 0x7fbe888d7bd0>) Compute the `directed` or `symmetric` Hausdorff distance between 2 sets of points with or without early breaking and random sampling. |
haversine(lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) Compute the distance between two (spherical) points using the Haversine formula. |
haversine_(phi2, phi1, lam21) Compute the angular distance between two (spherical) points using the Haversine formula. |
heightOf(angle, distance, radius=6371008.771415) Determine the height above the (spherical) earth' surface after traveling along a straight line at a given tilt. |
heightOrthometric(h_ll, N) Get the orthometric height H, the height above the geoid, earth surface. |
horizon(height, radius=6371008.771415, refraction=False) Determine the distance to the horizon from a given altitude above the (spherical) earth. |
hstr(height, prec=2, fmt='%+.*f', ints=False, m='') Return a string for the height value. |
hubeny(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True, wrap=False) Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. |
hubeny_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True) Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. |
hypot(x, y) Return the Euclidean distance, sqrt(x*x + y*y). |
hypot1(x) Compute the norm sqrt(1 + x**2). |
hypot2(x, y) Compute the squared norm x**2 + y**2. |
hypot2_(*xs) Compute the squared norm `fsum(x**2 for x in xs)`. |
hypot_(*xs) Compute the norm sqrt(sum(x**2 for x in xs)). |
instr(inst, *args, **kwds) Return the string representation of an instantiation. |
int1s(x) Count the number of 1-bits in an `int`, unsigned. |
intersection2(lat1, lon1, bearing1, lat2, lon2, bearing2, datum=None, wrap=False, small=100000.0) Conveniently compute the intersection of two lines each defined by a (geodetic) point and a bearing from North, using either ... |
intersection3d3(start1, end1, start2, end2, eps=2.220446049250313e-16, useZ=True, **Vector_and_kwds) Compute the intersection point of two (2- or 3-D) lines, each defined by two points or by a point and a bearing. |
intersections2(center1, radius1, center2, radius2, sphere=True, **Vector_and_kwds) Compute the intersection of two spheres or circles, each defined by a (3-D) center point and a radius. |
isBoolean(obj) Check for `Boolean` composites. |
isCartesian(obj, ellipsoidal=None) Is `obj`ect some `Cartesian`? |
isDEPRECATED(obj) Is `obj`ect a `DEPRECATED` class, method or function? |
isError(exc) Check a (caught) exception. |
isLatLon(obj, ellipsoidal=None) Is `obj`ect some `LatLon`? |
isNumpy2(obj) Check for a `Numpy2LatLon` points wrapper. |
isNvector(obj, ellipsoidal=None) Is `obj`ect some `Nvector`? |
isPoints2(obj) Check for a `LatLon2psxy` points wrapper. |
isTuple2(obj) Check for a `Tuple2LatLon` points wrapper. |
isantipode(lat1, lon1, lat2, lon2, eps=2.220446049250313e-16) Check whether two points are antipodal, on diametrically opposite sides of the earth. |
isantipode_(phi1, lam1, phi2, lam2, eps=2.220446049250313e-16) Check whether two points are antipodal, on diametrically opposite sides of the earth. |
isbool(obj) Is `obj`ect a `bool`ean? |
isclass(obj) Is `obj`ect a `Class` or `type`? |
isclockwise(points, adjust=False, wrap=True) Determine the direction of a path or polygon. |
isclose(a, b, rel_tol=1e-12, abs_tol=4.930380657631324e-32) Like `math.isclose`, but with defaults such that `isclose(0, EPS0)` is `True` by default. |
iscolinearWith(point, point1, point2, eps=2.220446049250313e-16, useZ=True) Check whether a point is colinear with two other (2- or 3-D) points. |
iscomplex(obj, both=False) Is `obj`ect a `complex` or complex literal `str`? |
isconvex(points, adjust=False, wrap=False) Determine whether a polygon is convex. |
isconvex_(points, adjust=False, wrap=False) Determine whether a polygon is convex and clockwise. |
isenclosedBy(point, points, wrap=False) Determine whether a point is enclosed by a polygon or composite. |
isfinite(obj) Check a finite `scalar` or `complex` value. |
isfloat(obj, both=False) Is `obj`ect a `float` or float literal `str`? |
isidentifier(obj) Is `obj`ect a Python identifier? |
bool |
isinf(x) Check if float x is infinite (positive or negative). |
isinstanceof(obj, *Classes) Is `obj`ect an instance of one of the `Classes`? |
isint(obj, both=False) Is `obj`ect an `int` or integer `float` value? |
isint0(obj, both=False) Check for INT0 or `int(0)` value. |
isiterable(obj) Is `obj`ect `iterable`? |
isiterablen(obj) Is `obj`ect `iterable` and has `len`gth? |
iskeyword(x, y) y in x. |
islistuple(obj, minum=0) Is `obj`ect a `list` or `tuple` with non-zero length? |
bool |
isnan(x) Check if float x is not a number (NaN). |
isnear0(x, eps0=4.930380657631324e-32) Is `x` near zero within a tolerance? |
isnear1(x, eps1=4.930380657631324e-32) Is `x` near one within a tolerance? |
isnear90(x, eps90=4.930380657631324e-32) Is `x` near 90 within a tolerance? |
isneg0(x) Check for NEG0, negative `0.0`. |
isninf(x) Check for NINF, negative `INF`. |
isnon0(x, eps0=4.930380657631324e-32) Is `x` non-zero with a tolerance? |
isnormal(lat, lon, eps=0) Check whether `lat` and `lon` are within their respective normal range in `degrees`. |
isnormal_(phi, lam, eps=0) Check whether `phi` and `lam` are within their respective normal range in `radians`. |
isodd(x) Is `x` odd? |
ispolar(points, wrap=False) Check whether a polygon encloses a pole. |
isscalar(obj, both=False) Is `obj`ect an `int` or integer `float` value? |
issequence(obj, *excls) Is `obj`ect some sequence type? |
isstr(obj) Is `obj`ect some string type? |
issubclassof(Sub, *Supers) Is `Sub` a class and sub-class of some other class(es)? |
itemsorted(adict, *items_args, **asorted_reverse) Return the items of `adict` sorted alphabetically, case-insensitively and in ascending order. |
iterNumpy2(obj) Iterate over Numpy2 wrappers or other sequences exceeding the threshold. |
iterNumpy2over(n=None) Get or set the iterNumpy2 threshold. |
km2m(km) Convert kilo meter to meter (m). |
latDMS(deg, form=`'``dms``'`, prec=None, sep='', **s_D_M_S) Convert latitude to a string, optionally suffixed with N or S. |
latlon2n_xyz(lat, lon, **name) Convert lat-, longitude to `n-vector` (normal to the earth's surface) X, Y and Z components. |
latlonDMS(lls, **m_form_prec_sep_s_D_M_S) Convert one or more `LatLon` instances to strings. |
latlonDMS_(*lls, **m_form_prec_sep_s_D_M_S) Convert one or more `LatLon` instances to strings. |
len2(items) Make built-in function `len` work for generators, iterators, etc. |
limiterrors(raiser=None) Get/set the throwing of LimitErrors. |
lonDMS(deg, form=`'``dms``'`, prec=None, sep='', **s_D_M_S) Convert longitude to a string, optionally suffixed with E or W. |
lrstrip(txt, lrpairs=`{``'``(``'``:` `'``)``'``,` `'``<``'``:` `'``>``'``,` `'``[``'``:` `'``]``'``,` `'``{``'``:` `'``}``'``}`) Left- and right-strip parentheses, brackets, etc. |
luneOf(lon1, lon2, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds) Generate an ellipsoidal or spherical lune-shaped path or polygon. |
m2NM(meter) Convert meter to nautical miles (NM). |
m2SM(meter) Convert meter to statute miles (SM). |
m2chain(meter) Convert meter to UK chains. |
m2degrees(distance, radius=6371008.771415, lat=0) Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. |
m2fathom(meter) Convert meter to Imperial fathoms. |
m2ft(meter, usurvey=False, pied=False, fuss=False) Convert meter to International, US Survey, French or or German feet (`ft`). |
m2furlong(meter) Convert meter to furlongs. |
m2km(meter) Convert meter to kilo meter (Km). |
m2radians(distance, radius=6371008.771415, lat=0) Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. |
m2toise(meter) Convert meter to French toises. |
m2yard(meter) Convert meter to UK yards. |
machine() Return standard `platform.machine`, but distinguishing Intel native from Intel emulation on Apple Silicon (on macOS only). |
map1(fun1, *xs) Call a single-argument function to each `xs` and return a `tuple` of results. |
map2(fun, *xs) Like Python's `map` but returning a `tuple` of results. |
meeus2(point1, point2, point3, circum=False, useZ=True) Return the radius and Meeus' Type of the smallest circle through or containing three (2- or 3-D) points. |
modulename(clas, prefixed=None) Return the class name optionally prefixed with the module name. |
n2e2(n) Return `e2`, the 1st eccentricity squared for a given 3rd flattening. |
n2f(n) Return `f`, the flattening for a given 3rd flattening. |
n2f_(n) Return `f_`, the inverse flattening for a given 3rd flattening. |
n_xyz2latlon(x, y, z, **name) Convert `n-vector` components to lat- and longitude in `degrees`. |
n_xyz2philam(x, y, z, **name) Convert `n-vector` components to lat- and longitude in `radians`. |
nameof(inst) Get the name of an instance. |
nearestOn(point, point1, point2, within=True, useZ=True, Vector=None, **Vector_kwds) Locate the point between two points closest to a reference (2- or 3-D). |
nearestOn5(point, points, closed=False, wrap=False, adjust=True, limit=9, **LatLon_and_kwds) Locate the point on a path or polygon closest to a reference point. |
nearestOn6(point, points, closed=False, useZ=True, **Vector_and_kwds) Locate the point on a path or polygon closest to a reference point. |
neg(x, neg0=None) Negate `x` and optionally, negate `0.0` and `-0.0`. |
neg_(*xs) Negate all `xs` with neg. |
norm2(x, y) Normalize a 2-dimensional vector. |
normDMS(strDMS, norm=None, **s_D_M_S) Normalize all degrees, minutes and seconds (DMS) symbols in a string to the default symbols S_DEG, S_MIN, S_SEC. |
norm_(*xs) Normalize all n-dimensional vector components. |
normal(lat, lon, **name) Normalize a lat- and longitude pair in `degrees`. |
normal_(phi, lam, **name) Normalize a lat- and longitude pair in `radians`. |
notImplemented(inst, *args, **kwds) Raise a `NotImplementedError` for a missing instance method or property or for a missing caller feature. |
notOverloaded(inst, *args, **kwds) Raise an `AssertionError` for a method or property not overloaded. |
opposing(bearing1, bearing2, margin=90.0) Compare the direction of two bearings given in `degrees`. |
opposing_(radians1, radians2, margin=1.5707963267948966) Compare the direction of two bearings given in `radians`. |
pairs(items, prec=6, fmt='F', ints=False, sep='=') Convert items to name=value strings, with `float`s handled like fstr. |
parse3d(str3d, sep=',', Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds) Parse an `"x, y, z"` string. |
parse3llh(strllh, height=0, sep=',', clipLat=90, clipLon=180, wrap=False, **s_D_M_S) Parse a string `"lat, lon [, h]"` representing lat-, longitude in `degrees` and optional height in `meter`. |
parseDDDMMSS(strDDDMMSS, suffix=`'``NSEW``'`, sep='', clip=0, sexagecimal=False) Parse a lat- or longitude represention forms as [D]DDMMSS in degrees. |
parseDMS(strDMS, suffix=`'``NSEW``'`, sep='', clip=0, **s_D_M_S) Parse a lat- or longitude representation in `degrees`. |
parseDMS2(strLat, strLon, sep='', clipLat=90, clipLon=180, wrap=False, **s_D_M_S) Parse a lat- and a longitude representions `"lat, lon"` in `degrees`. |
parseETM5(strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, **name) Parse a string representing a UTM coordinate, consisting of `"zone[band] hemisphere easting northing"`. |
parseMGRS(strMGRS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, **name) Parse a string representing a MGRS grid reference, consisting of `"[zone]Band, EN, easting, northing"`. |
parseOSGR(strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, **name_Osgr_kwds) Parse a string representing an OS Grid Reference, consisting of `"[GD] easting northing"`. |
parseRad(strRad, suffix=`'``NSEW``'`, clip=0) Parse a string representing angle in `radians`. |
parseUPS5(strUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Ups=<class 'pygeodesy.ups.Ups'>, falsed=True, **name) Parse a string representing a UPS coordinate, consisting of `"[zone][band] pole easting northing"` where `zone` is pseudo zone `"00"|"0"|""` and `band` is `'A'|'B'|'Y'|'Z'|''`. |
parseUTM5(strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, **name) Parse a string representing a UTM coordinate, consisting of `"zone[band] hemisphere easting northing"`. |
parseUTMUPS5(strUTMUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, **name) Parse a string representing a UTM or UPS coordinate, consisting of `"zone[band] hemisphere/pole easting northing"`. |
parseWM(strWM, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, **name) Parse a string `"e n [r]"` representing a WM coordinate, consisting of easting, northing and an optional radius. |
perimeterOf(points, closed=False, adjust=True, radius=6371008.771415, wrap=True) Approximate the perimeter of a path, polygon. |
philam2n_xyz(phi, lam, **name) Convert lat-, longitude to `n-vector` (normal to the earth's surface) X, Y and Z components. |
pierlot(point1, point2, point3, alpha12, alpha23, useZ=False, eps=2.220446049250313e-16, **Clas_and_kwds) 3-Point resection using Pierlot's method `ToTal` with approximate limits for the (pseudo-)singularities. |
pierlotx(point1, point2, point3, alpha1, alpha2, alpha3, useZ=False, **Clas_and_kwds) 3-Point resection using Pierlot's method `ToTal` with exact limits for the (pseudo-)singularities. |
points2(points, closed=True, base=None, Error=<class 'pygeodesy.errors.PointsError'>) Check a path or polygon represented by points. |
precision(form, prec=None) Set the default precison for a given F_ form. |
print_(*args, **nl_nt_prec_prefix__end_file_flush_sep__kwds) Python 3+ `print`-like formatting and printing. |
printf(fmt, *args, **nl_nt_prec_prefix__end_file_flush_sep__kwds) `Printf-style` and Python 3+ `print`-like formatting and printing. |
property_doc_(doc) Decorator for a standard `property` with basic documentation. |
quadOf(latS, lonW, latN, lonE, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds) Generate a quadrilateral path or polygon from two points. |
radians(x) Convert angle x from degrees to radians. |
radians2m(rad, radius=6371008.771415, lat=0) Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. |
radiansPI(deg) Convert and wrap degrees to radians [-PI..+PI]. |
radiansPI2(deg) Convert and wrap degrees to radians [0..+2PI). |
radiansPI_2(deg) Convert and wrap degrees to radians [-3PI/2..+PI/2]. |
radical2(distance, radius1, radius2, **name) Compute the radical ratio and radical line of two intersecting circles. |
radii11(point1, point2, point3, useZ=True) Return the radii of the `In-`, Soddy and `Tangent` circles of a (2- or 3-D) triangle. |
randomrangenerator(seed) Return a `seed`ed random range function generator. |
rangerrors(raiser=None) Get/set the throwing of RangeErrors. |
remainder(x, y) Mimick Python 3.7+ `math.remainder`. |
reprs(objs, prec=6, fmt='F', ints=False) Convert objects to `repr` strings, with `float`s handled like fstr. |
rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds) Convert spherical, polar `(r, theta, phi)` to cartesian `(x, y, z)` coordinates. |
rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds) Convert spherical, polar `(r, theta, phi)` to cartesian `(x, y, z)` coordinates. |
signBit(x) Return `signbit(x)`, like C++. |
signOf(x) Return sign of `x` as `int`. |
simplify1(points, distance=0.001, radius=6371008.771415, indices=False, **options) Basic simplification of a path of `LatLon` points. |
simplifyRDP(points, distance=0.001, radius=6371008.771415, shortest=False, indices=False, **options) Ramer-Douglas-Peucker (RDP) simplification of a path of `LatLon` points. |
simplifyRDPm(points, distance=0.001, radius=6371008.771415, shortest=False, indices=False, **options) Modified Ramer-Douglas-Peucker (RDPm) simplification of a path of `LatLon` points. |
simplifyRW(points, pipe=0.001, radius=6371008.771415, shortest=False, indices=False, **options) Reumann-Witkam (RW) simplification of a path of `LatLon` points. |
simplifyVW(points, area=0.001, radius=6371008.771415, attr=None, indices=False, **options) Visvalingam-Whyatt (VW) simplification of a path of `LatLon` points. |
simplifyVWm(points, area=0.001, radius=6371008.771415, attr=None, indices=False, **options) Modified Visvalingam-Whyatt (VWm) simplification of a path of `LatLon` points. |
sincos2(rad) Return the `sine` and `cosine` of an angle in `radians`. |
sincos2_(*rads) Return the `sine` and `cosine` of angle(s) in `radians`. |
sincos2d(deg, **adeg) Return the `sine` and `cosine` of an angle in `degrees`. |
sincos2d_(*degs) Return the `sine` and `cosine` of angle(s) in `degrees`. |
sincostan3(rad) Return the `sine`, `cosine` and `tangent` of an angle in `radians`. |
snellius3(a, b, degC, alpha, beta) Snellius' surveying using Snellius Pothenot. |
soddy4(point1, point2, point3, eps=8.881784197001252e-16, useZ=True) Return the radius and center of the `inner` Soddy circle of a (2- or 3-D) triangle. |
splice(iterable, n=2, **fill) Split an iterable into `n` slices. |
sqrt0(x, Error=None) Return the square root `sqrt(x)` iff `x >` EPS02, preserving `type(x)`. |
sqrt3(x) Return the square root, cubed sqrt(x)**3 or sqrt(x**3), preserving `type(x)`. |
sqrt_a(h, b) Compute `a` side of a right-angled triangle from `sqrt(h**2 - b**2)`. |
str2ub(arg) (INTERNAL) Helper, no-op. |
strs(objs, prec=6, fmt='F', ints=False) Convert objects to `str` strings, with `float`s handled like fstr. |
tanPI_2_2(rad) Compute the tangent of half angle, 90 degrees rotated. |
tan_2(rad, **semi) Compute the tangent of half angle. |
tand(deg, **error_kwds) Return the `tangent` of an angle in `degrees`. |
tand_(*degs, **error_kwds) Return the `tangent` of angle(s) in `degrees`. |
thomas(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=False) Compute the distance between two (ellipsoidal) points using Thomas' formula. |
thomas_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`) Compute the angular distance between two (ellipsoidal) points using Thomas' formula. |
tienstra7(pointA, pointB, pointC, alpha, beta=None, gamma=None, useZ=False, **Clas_and_kwds) 3-Point resection using Tienstra's formula. |
toCss(latlon, cs0=None, height=None, Css=<class 'pygeodesy.css.Css'>, **name) Convert an (ellipsoidal) geodetic point to a Cassini-Soldner location. |
toDMS(deg, form=`'``dms``'`, prec=2, sep='', ddd=2, neg='-', pos='+', **s_D_M_S) Convert signed `degrees` to string, without suffix. |
toEtm8(latlon, lon=None, datum=None, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, strict=True, zone=None, **name_cmoff) Convert a geodetic lat-/longitude to an ETM coordinate. |
toLcc(latlon, conic=Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0`...`, height=None, Lcc=<class 'pygeodesy.lcc.Lcc'>, **name_Lcc_kwds) Convert an (ellipsoidal) geodetic point to a Lambert location. |
toMgrs(utmups, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, **name_Mgrs_kwds) Convert a UTM or UPS coordinate to an MGRS grid reference. |
toOsgr(latlon, lon=None, kTM=False, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Osgr=<class 'pygeodesy.osgr.Osgr'>, **prec_name_Osgr_kwds) Convert a lat-/longitude point to an OSGR coordinate. |
toUps8(latlon, lon=None, datum=None, Ups=<class 'pygeodesy.ups.Ups'>, pole='', falsed=True, strict=True, **name) Convert a lat-/longitude point to a UPS coordinate. |
toUtm8(latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, strict=True, zone=None, **name_cmoff) Convert a lat-/longitude point to a UTM coordinate. |
toUtmUps8(latlon, lon=None, datum=None, falsed=True, Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, pole='', **name_cmoff) Convert a lat-/longitude point to a UTM or UPS coordinate. |
toWm(latlon, lon=None, earth=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, **name_Wm_kwds_radius) Convert a lat-/longitude point to a WM coordinate. |
toise2m(toises) Convert French toises to meter. |
trfTransform0(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False) Get a Helmert transform to convert one `reframe` observed at `epoch` to an other `reframe2` at observed at `epoch2 or epoch`. |
trfTransforms(reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False) Yield all Helmert transform to convert one `reframe` observed at `epoch` to an other `reframe2` at observed at `epoch2 or epoch`. |
trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True) Define a new Terrestrial Reference Frame (TRF) converter or get an existing one. |
triAngle(a, b, c) Compute one angle of a triangle. |
triAngle5(a, b, c) Compute the angles of a triangle. |
triArea(a, b, c) Compute the area of a triangle using Heron's `stable` formula. |
triSide(a, b, radC) Compute one side of a triangle. |
triSide2(b, c, radB) Compute a side and its opposite angle of a triangle. |
triSide4(radA, radB, c) Compute two sides and the height of a triangle. |
trilaterate2d2(x1, y1, radius1, x2, y2, radius2, x3, y3, radius3, eps=None, **Vector_and_kwds) Trilaterate three circles, each given as a (2-D) center and a radius. |
trilaterate3d2(center1, radius1, center2, radius2, center3, radius3, eps=2.220446049250313e-16, **Vector_and_kwds) Trilaterate three spheres, each given as a (3-D) center and a radius. |
truncate(x, ndigits=None) Truncate to the given number of digits. |
tyr3d(tilt=0, yaw=0, roll=0, Vector=<class 'pygeodesy.vector3d.Vector3d'>, **name_Vector_kwds) Convert an attitude pose into a (3-D) direction vector. |
ub2str(arg) (INTERNAL) Helper, no-op. |
unroll180(lon1, lon2, wrap=True) Unroll longitudinal delta and wrap longitude in degrees. |
unrollPI(rad1, rad2, wrap=True) Unroll longitudinal delta and wrap longitude in radians. |
unsigned0(x) Unsign if `0.0`. |
unstr(where, *args, **kwds) Return the string representation of an invokation. |
upsZoneBand5(lat, lon, strict=True, **name) Return the UTM/UPS zone number, polar Band letter, pole and clipped lat- and longitude for a given location. |
utmZoneBand5(lat, lon, cmoff=False, **name) Return the UTM zone number, Band letter, hemisphere and (clipped) lat- and longitude for a given location. |
utmupsValidate(coord, falsed=False, MGRS=False, Error=<class 'pygeodesy.utmups.UTMUPSError'>) Check a UTM or UPS coordinate. |
utmupsValidateOK(coord, falsed=False, ok=True) Check a UTM or UPS coordinate. |
utmupsZoneBand5(lat, lon, cmoff=False, **name) Return the UTM/UPS zone number, Band letter, hemisphere/pole and clipped lat- and longitude for a given location. |
vincentys(lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) Compute the distance between two (spherical) points using Vincenty's spherical formula. |
vincentys_(phi2, phi1, lam21) Compute the angular distance between two (spherical) points using Vincenty's spherical formula. |
wildberger3(a, b, c, alpha, beta, R3=<built-in function min>) Snellius' surveying using Rational Trigonometry. |
wrap180(deg) Wrap degrees to [-180..+180]. |
wrap360(deg) Wrap degrees to [0..+360). |
wrap90(deg) Wrap degrees to [-90..+90]. |
wrapPI(rad) Wrap radians to [-PI..+PI]. |
wrapPI2(rad) Wrap radians to [0..+2PI). |
wrapPI_2(rad) Wrap radians to [-PI/2..+PI/2]. |
wrap_normal(*normal) Define the operation for the keyword argument `wrap=True`, across pygeodesy: wrap, normalize or no-op. |
xyz2rtp(x_xyz, y=0, z=0, **name) Convert cartesian `(x, y, z)` to spherical, polar `(r, theta, phi)` coordinates. |
xyz2rtp_(x_xyz, y=0, z=0, **name) Convert cartesian `(x, y, z)` to spherical, polar `(r, theta, phi)` coordinates. |
yard2m(yards) Convert UK yards to meter. |
zcrt(x) Return the 6-th, zenzi-cubic root, x**(1 / 6), preserving `type(x)`. |
zqrt(x) Return the 8-th, zenzi-quartic or squared-quartic root, x**(1 / 8), preserving `type(x)`. |

Variables
| pygeodesy_abspath = ``'``/Users/jean/Library/CloudStorage/Dropbox/``...`` Fully qualified `pygeodesy` directory name (`str`).
| version = `'24.7.24'` Normalized `PyGeodesy` version (`str`).
| Caps = `Caps()`
| Conics = `Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97`...`` Registered, predefined conics (`enum-like`).
| DIG = `15` System's float decimal digits = 15 (`int`).
| Datums = `Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipso`...`` Registered, predefined datums (`enum-like`).
| DeprecationWarnings = `DeprecationWarnings()`
| EPS = `2.220446049250313e-16` System's epsilon ≈ 2.22044604925e-16 (`float`).
| EPS0 = `4.930380657631324e-32` EPS**2 ≈ 4.9e-32 for near-zero comparison
| EPS02 = `2.4308653429145085e-63` EPS**4 ≈ 2.4e-63 for near-zero squared comparison
| EPS1 = `0.9999999999999998` 1 - EPS ≈ 0.9999999999999998 (`float`).
| EPS2 = `4.440892098500626e-16` EPS * 2 ≈ 4.440892098501e-16 (`float`).
| EPS4 = `8.881784197001252e-16` EPS * 4 ≈ 8.881784197001e-16 (`float`).
| EPS_2 = `1.1102230246251565e-16` EPS / 2 ≈ 1.110223024625e-16 (`float`).
| Ellipsoids = `Ellipsoids.Sphere: Ellipsoid(name='Sphere', a=637`...`` Registered, predefined ellipsoids (`enum-like`).
| F_D = ``'``d``'`` Format degrees as unsigned "deg°" with symbol, plus compass point suffix `N, S, E` or `W` (`str`).
| F_D60 = ``'``d60``'`` Format degrees as unsigned "[D]DD.MMSS" `sexagecimal` without symbols, plus suffix (`str`).
| F_D60_ = `'-d60'` Format degrees as signed "-/[D]DD.MMSS" `sexagecimal` without symbols, without suffix (`str`).
| F_D60__ = `'+d60'` Format degrees as signed "-/+[D]DD.MMSS" `sexagecimal` without symbols, without suffix (`str`).
| F_DEG = ``'``deg``'`` Format degrees as unsigned "[D]DD" without symbol, plus suffix (`str`).
| F_DEG_ = `'-deg'` Format degrees as signed "-/[D]DD" without symbol, without suffix (`str`).
| F_DEG__ = `'+deg'` Format degrees as signed "-/+[D]DD" without symbol, without suffix (`str`).
| F_DM = ``'``dm``'`` Format degrees as unsigned "deg°min′" with symbols, plus suffix (`str`).
| F_DMS = ``'``dms``'`` Format degrees as unsigned "deg°min′sec″" with symbols, plus suffix (`str`).
| F_DMS_ = `'-dms'` Format degrees as signed "-/deg°min′sec″" with symbols, without suffix (`str`).
| F_DMS__ = `'+dms'` Format degrees as signed "-/+deg°min′sec″" with symbols, without suffix (`str`).
| F_DM_ = `'-dm'` Format degrees as signed "-/deg°min′" with symbols, without suffix (`str`).
| F_DM__ = `'+dm'` Format degrees as signed "-/+deg°min′" with symbols, without suffix (`str`).
| F_D_ = `'-d'` Format degrees as signed "-/deg°" with symbol, without suffix (`str`).
| F_D__ = `'+d'` Format degrees as signed "-/+deg°" with symbol, without suffix (`str`).
| F_MIN = ``'``min``'`` Format degrees as unsigned "[D]DDMM" without symbols, plus suffix (`str`).
| F_MIN_ = `'-min'` Format degrees as signed "-/[D]DDMM" without symbols, without suffix (`str`).
| F_MIN__ = `'+min'` Format degrees as signed "-/+[D]DDMM" without symbols, without suffix (`str`).
| F_RAD = ``'``rad``'`` Convert degrees to radians and format as unsigned "RR" with symbol, plus suffix (`str`).
| F_RAD_ = `'-rad'` Convert degrees to radians and format as signed "-/RR" without symbol, without suffix (`str`).
| F_RAD__ = `'+rad'` Convert degrees to radians and format as signed "-/+RR" without symbol, without suffix (`str`).
| F_SEC = ``'``sec``'`` Format degrees as unsigned "[D]DDMMSS" without symbols, plus suffix (`str`).
| F_SEC_ = `'-sec'` Format degrees as signed "-/[D]DDMMSS" without symbols, without suffix (`str`).
| F_SEC__ = `'+sec'` Format degrees as signed "-/+[D]DDMMSS" without symbols, without suffix (`str`).
| F__E = ``'``e``'`` Format degrees as unsigned "%E" without symbols, plus suffix (`str`).
| F__E_ = `'-e'` Format degrees as signed "-/%E" without symbols, without suffix (`str`).
| F__E__ = `'+e'` Format degrees as signed "-/+%E" without symbols, without suffix (`str`).
| F__F = ``'``f``'`` Format degrees as unsigned "%F" without symbols, plus suffix (`str`).
| F__F_ = `'-f'` Format degrees as signed "-/%F" without symbols, without suffix (`str`).
| F__F__ = `'+f'` Format degrees as signed "-/+%F" without symbols, without suffix (`str`).
| F__G = ``'``g``'`` Format degrees as unsigned "%G" without symbols, plus suffix (`str`).
| F__G_ = `'-g'` Format degrees as signed "-/%G" without symbols, without suffix (`str`).
| F__G__ = `'+g'` Format degrees as signed "-/+%G" without symbols, without suffix (`str`).
| INF = `inf` Infinity (`float`), see functions isinf and isfinite and `NINF`.
| INT0 = `0` `int(0)`, missing Z-components, `if z=INT0`, see functions isint0, meeus2
| MANT_DIG = `53` System's float mantissa bits = 53 (`int`).
| MAX = `1.7976931348623157e+308` System's float max ≈ 1.798e+308 (`float`).
| MAX_EXP = `1024`
| MIN = `2.2250738585072014e-308` System's float min ≈ 2.225e-308 (`float`).
| MIN_EXP = `-1021`
| NAN = `nan` Not-A-Number (`float`), see function isnan.
| NEG0 = `-0.0` Negative 0.0 (`float`), see function isneg0.
| NINF = `-inf` Negative infinity (`float`), see function isninf and `INF`.
| NN = `''` Empty (`str`), Nomen Nescio.
| NorthPole = `NvectorBase(0.0, 0.0, 1.0)`
| PI = `3.141592653589793` Constant math.pi (`float`).
| PI2 = `6.283185307179586` Two PI, PI * 2, aka Tau (`float`).
| PI3 = `9.42477796076938` Three PI, PI * 3 (`float`).
| PI3_2 = `4.71238898038469` One and a half PI, PI * 3 / 2 (`float`).
| PI4 = `12.566370614359172` Four PI, PI * 4 (`float`).
| PI_2 = `1.5707963267948966` Half PI, PI / 2 (`float`).
| PI_3 = `1.0471975511965976` One third PI, PI / 3 (`float`).
| PI_4 = `0.7853981633974483` Quarter PI, PI / 4 (`float`).
| R_FM = `6371000.0` Former FAI-Sphere earth radius (`meter`).
| R_GM = `6371230.0` Average earth radius, distance to geoid surface (`meter`)
| R_KM = `6371.0087714149995` Mean (spherical) earth radius (`Km`, kilometer).
| R_M = `6371008.771415` Mean (spherical) earth radius (`meter`).
| R_MA = `6378137.0` Equatorial earth radius (`meter`), WGS84, EPSG:3785.
| R_MB = `6356752.3` Polar earth radius (`meter`), WGS84, EPSG:3785.
| R_NM = `3440.06953100162` Mean (spherical) earth radius (`NM`, nautical miles).
| R_QM = `6372797.560856` Earth' (triaxial) quadratic mean radius (`meter`)
| R_SM = `3958.7613160486508` Mean (spherical) earth radius (`SM`, statute miles).
| R_VM = `6366707.0194937` Aviation/Navigation earth radius (`meter`).
| RefFrames = `RefFrames.ETRF89: RefFrame(name='ETRF89', epoch=19`...`` Registered, predefined reference frames (`enum-like`).
| S_DEG = ``'``°``'`` Degrees symbol, default `"°"`
| S_DMS = `True` If `True` include, otherwise cancel all DMS symbols, default `True`.
| S_MIN = ``'``\xe2\x80\xb2``'`` Minutes symbol, default `"′"` aka PRIME
| S_RAD = `''` Radians symbol, default `""` aka NN
| S_SEC = ``'``″``'`` Seconds symbol, default `"″"` aka DOUBLE_PRIME
| S_SEP = `''` Separator between `deg°|min′|sec″|suffix`, default `""` aka NN
| SouthPole = `NvectorBase(0.0, 0.0, -1.0)`
| Transforms = `Transforms.OSGB36: Transform(name='OSGB36', tx=-4`...`` Registered, predefined transforms (`enum-like`).
| Triaxials = `` Registered, predefined triaxial ellipsoids (`enum-like`).
| isLazy = `None` Lazy import setting (`int` 0, 1, 2 or 3+) from `env` variable `PYGEODESY_LAZY_IMPORT`, or `None` if `lazy import` is not supported or not enabled, or `False` if initializing `lazy import` failed.

Function Details

### NM2m (nm) |
Convert nautical miles to meter (m). Arguments: `nm` - Value in nautical miles (`scalar`). Returns: Value in meter (`float`). Raises: `ValueError` - Invalid `nm`.

### SM2m (sm) |
Convert statute miles to meter (m). Arguments: `sm` - Value in statute miles (`scalar`). Returns: Value in meter (`float`). Raises: `ValueError` - Invalid `sm`.

### SinCos2 (x) |
Get `sin` and `cos` of typed angle. Arguments: `x` - Angle (Degrees, Radians or scalar `radians`). Returns: 2-Tuple (`sin(x)`, `cos(x)`).

### UtmUps (zone, hemipole, easting, northing, band='', datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, falsed=True, **name) |
Class-like function to create a UTM/UPS coordinate. Arguments: `zone` - The UTM zone with/-out longitudinal Band or UPS zone `0` or `"00"` with/-out polar Band (`str` or `int`). `hemipole` - UTM hemisphere or UPS top/center of projection (`str`, `'N[orth]'` or `'S[outh]'`). `easting` - Easting, see `falsed` (`meter`). `northing` - Northing, see `falsed` (`meter`). `band` - Optional, UTM latitudinal `'C'|'D'|..|'W'|'X'` or UPS polar Band letter `'A'|'B'|'Y'|'Z'` Band letter (`str`). `datum` - The coordinate's datum (Datum). `falsed` - If `True`, both `easting` and `northing` are falsed (`bool`). `name` - Optional Utm or Ups `name=NN` (`str`). Returns: New UTM or UPS instance (Utm or Ups). Raises: `TypeError` - Invalid `datum`. `UTMUPSError` - UTM or UPS validation failed. See Also: Classes Utm and Ups and Karney's UTMUPS.

### a_b2e (a, b) |
Return `e`, the 1st eccentricity for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The unsigned, (1st) eccentricity (`float` or `0`), sqrt(1 - (b / a)**2). Note: The result is always non-negative and `0` for near-spherical ellipsoids.

### a_b2e2 (a, b) |
Return `e2`, the 1st eccentricity squared for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The signed, (1st) eccentricity squared (`float` or `0`), 1 - (b / a)**2. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_b2e22 (a, b) |
Return `e22`, the 2nd eccentricity squared for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The signed, 2nd eccentricity squared (`float` or `0`), (a / b)**2 - 1. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_b2e32 (a, b) |
Return `e32`, the 3rd eccentricity squared for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The signed, 3rd eccentricity squared (`float` or `0`), (a**2 - b**2) / (a**2 + b**2). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_b2f (a, b) |
Return `f`, the flattening for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The flattening (`scalar` or `0`), (a - b) / a. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_b2f2 (a, b) |
Return `f2`, the 2nd flattening for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The signed, 2nd flattening (`scalar` or `0`), (a - b) / b. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_b2f_ (a, b) |
Return `f_`, the inverse flattening for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The inverse flattening (`scalar` or `0`), a / (a - b). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_b2n (a, b) |
Return `n`, the 3rd flattening for a given equatorial and polar radius. Arguments: `a` - Equatorial radius (`scalar` > 0). `b` - Polar radius (`scalar` > 0). Returns: The signed, 3rd flattening (`scalar` or `0`), (a - b) / (a + b). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### a_f2b (a, f) |
Return `b`, the polar radius for a given equatorial radius and flattening. Arguments: `a` - Equatorial radius (`scalar` > 0). `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The polar radius (`float`), a * (1 - f).

### a_f_2b (a, f_) |
Return `b`, the polar radius for a given equatorial radius and inverse flattening. Arguments: `a` - Equatorial radius (`scalar` > 0). `f_` - Inverse flattening (`scalar` >>> 1). Returns: The polar radius (`float`), a * (f_ - 1) / f_.

### acre2ha (acres) |
Convert acres to hectare. Arguments: `acres` - Value in acres (`scalar`). Returns: Value in `hectare` (`float`). Raises: `ValueError` - Invalid `acres`.

### acre2m2 (acres) |
Convert acres to square meter. Arguments: `acres` - Value in acres (`scalar`). Returns: Value in `meter^2` (`float`). Raises: `ValueError` - Invalid `acres`.

### anstr (name, OKd=`'``._-``'`, sub='_') |
Make a valid name of alphanumeric and OKd characters. Arguments: `name` - The original name (`str`). `OKd` - Other acceptable characters (`str`). `sub` - Substitute for invalid charactes (`str`). Returns: The modified name (`str`). Note: Leading and trailing whitespace characters are removed, intermediate whitespace characters are coalesced and substituted.

### antipode (lat, lon, **name) |
Return the antipode, the point diametrically opposite to a given point in `degrees`. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `name` - Optional `name=NN` (`str`). Returns: A LatLon2Tuple`(lat, lon)`. See Also: Functions antipode_ and normal and Geosphere.

### antipode_ (phi, lam, **name) |
Return the antipode, the point diametrically opposite to a given point in `radians`. Arguments: `phi` - Latitude (`radians`). `lam` - Longitude (`radians`). `name` - Optional `name=NN` (`str`). Returns: A PhiLam2Tuple`(phi, lam)`. See Also: Functions antipode and normal_ and Geosphere.

### areaOf (points, adjust=True, radius=6371008.771415, wrap=True) |
Approximate the area of a polygon or composite. Arguments: `points` - The polygon points or clips (`LatLon`[], BooleanFHP or BooleanGH). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `radius` - Mean earth radius (`meter`) or `None`. `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: Approximate area (square `meter`, same units as `radius` or `radians` squared if `radius is None`). Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - Invalid `radius`. Note: This area approximation has limited accuracy and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. See Also: sphericalNvector.areaOf, sphericalTrigonometry.areaOf, ellipsoidalExact.areaOf and ellipsoidalKarney.areaOf.

### atan1d (y, x=1.0) |
Return `atan(y / x)` angle in `degrees` [-90..+90] using `atan2d` for consistency and to avoid `ZeroDivisionError`. See Also: Function pygeodesy.atan2d.

### atan2b (y, x) |
Return `atan2(y, x)` in degrees [0..+360]. See Also: Function pygeodesy.atan2d.

### atan2d (y, x, reverse=False) |
Return `atan2(y, x)` in degrees [-180..+180], optionally reversed (by 180 degrees for `azimuth`s). See Also: Karney's C++ function Math.atan2d.

### attrs (inst, *names, **Nones_True__pairs_kwds) |
Get instance attributes as name=value strings, with `float`s formatted by function fstr. Arguments: `inst` - The instance (any `type`). `names` - The attribute names, all other positional (`str`). `Nones_True__pairs_kwds` - Keyword argument for function pairs, except `Nones=True` to in-/exclude missing or `None`-valued attributes. Returns: A `tuple(sep.join(t) for t in zip(names, reprs(values, ...)))` of `str`s.

### b_f2a (b, f) |
Return `a`, the equatorial radius for a given polar radius and flattening. Arguments: `b` - Polar radius (`scalar` > 0). `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The equatorial radius (`float`), b / (1 - f).

### b_f_2a (b, f_) |
Return `a`, the equatorial radius for a given polar radius and inverse flattening. Arguments: `b` - Polar radius (`scalar` > 0). `f_` - Inverse flattening (`scalar` >>> 1). Returns: The equatorial radius (`float`), b * f_ / (f_ - 1).

### bearing (lat1, lon1, lat2, lon2, **final_wrap) |
Compute the initial or final bearing (forward or reverse azimuth) between two (spherical) points. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `final_wrap` - Optional keyword arguments for function pygeodesy.bearing_. Returns: Initial or final bearing (compass `degrees360`) or zero if both points coincide.

### bearingDMS (bearing, form=`'``d``'`, prec=None, sep='', **s_D_M_S) |
Convert bearing to a string (without compass point suffix). Arguments: `bearing` - Bearing from North (compass `degrees360`). `form` - Format specifier for `deg` (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F_D60, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F_D60_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F_D60__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. `sep` - Separator between degrees, minutes, seconds, suffix (`str`). `s_D_M_S` - Optional keyword arguments `s_D=str`, `s_M=str`, `s_S=str` and `s_DMS=True` to override any or cancel all DMS symbols, defaults S_DEG, S_MIN respectively S_SEC. Returns: Compass degrees per the specified `form` (`str`). See Also: Function pygeodesy.toDMS.

### bearing_ (phi1, lam1, phi2, lam2, final=False, wrap=False) |
Compute the initial or final bearing (forward or reverse azimuth) between two (spherical) points. Arguments: `phi1` - Start latitude (`radians`). `lam1` - Start longitude (`radians`). `phi2` - End latitude (`radians`). `lam2` - End longitude (`radians`). `final` - If `True`, return the final, otherwise the initial bearing (`bool`). `wrap` - If `True`, wrap or normalize and unroll `phi2` and `lam2` (`bool`). Returns: Initial or final bearing (compass `radiansPI2`) or zero if both are coincident. See Also: Bearing, Course between two points and Bearing Between Two Points.

### boundsOf (points, wrap=False, LatLon=None) |
Determine the bottom-left SW and top-right NE corners of a path or polygon. Arguments: `points` - The path or polygon points (`LatLon`[]). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). `LatLon` - Optional class to return the `bounds` corners (`LatLon`) or `None`. Returns: A Bounds2Tuple`(latlonSW, latlonNE)`, each a `LatLon` or if `LatLon is None`, a Bounds4Tuple`(latS, lonW, latN, lonE)`. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. See Also: Function quadOf.

### bqrt (x) |
Return the 4-th, bi-quadratic or quartic root, x**(1 / 4), preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). Returns: Quartic root (`float` or an Fsum). Raises: `TypeeError` - Invalid `x`. `ValueError` - Negative `x`. See Also: Functions zcrt and zqrt.

### callername (up=1, dflt='', source=False, underOK=False) |
Get the name of the invoking callable. Arguments: `up` - Number of call stack frames up (`int`). `dflt` - Default return value (`any`). `source` - Include source file name and line number (`bool`). `underOK` - If `True`, private, internal callables are OK, otherwise private callables are skipped (`bool`). Returns: The callable name (`str`) or `dflt` if none found.

### cassini (pointA, pointB, pointC, alpha, beta, useZ=False, **Clas_and_kwds) |
3-Point resection using Cassini's method. Arguments: `pointA` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `pointB` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `pointC` - Center point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `alpha` - Angle subtended by triangle side `pointA` to `pointC` (`degrees`, non-negative). `beta` - Angle subtended by triangle side `pointB` to `pointC` (`degrees`, non-negative). `useZ` - If `True`, use and interpolate the Z component, otherwise force `z=INT0` (`bool`). `Clas_and_kwds` - Optional class `Clas=pointA.classof` to return the survey point with optionally other `Clas` keyword arguments to instantiate the survey point. Returns: The survey point, an instance of `Clas` or `pointA`'s (sub-)class. Raises: `ResectionError` - Near-coincident, -colinear or -concyclic points or negative or invalid `alpha` or `beta`. `TypeError` - Invalid `pointA`, `pointB` or `pointM`. Note: Typically, `pointC` is between `pointA` and `pointB`. See Also: Three Point Resection Problem and functions collins5, pierlot, pierlotx and tienstra7.

### cbrt (x) |
Compute the cube root x**(1/3), preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). Returns: Cubic root (`float` or Fsum). See Also: Functions cbrt2 and sqrt3.

### cbrt2 (x) |
Compute the cube root squared x**(2/3), preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). Returns: Cube root squared (`float` or Fsum). See Also: Functions cbrt and sqrt3.

### centroidOf (points, wrap=False, LatLon=None) |
Determine the centroid of a polygon. Arguments: `points` - The polygon points (`LatLon`[]). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). `LatLon` - Optional class to return the centroid (`LatLon`) or `None`. Returns: Centroid (`LatLon`) or a LatLon2Tuple`(lat, lon)` if `LatLon is None`. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - The `points` enclose a pole or near-zero area. See Also: Centroid and Paul Bourke's Calculating The Area And Centroid Of A Polygon, 1988.

### chain2m (chains) |
Convert UK chains to meter. Arguments: `chains` - Value in chains (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `chains`.

### circin6 (point1, point2, point3, eps=8.881784197001252e-16, useZ=True) |
Return the radius and center of the inscribed aka Incircle of a (2- or 3-D) triangle. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `eps` - Tolerance for function pygeodesy.trilaterate3d2 if `useZ is True` else pygeodesy.trilaterate2d2. `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: Circin6Tuple`(radius, center, deltas, cA, cB, cC)`. The `center` and contact points `cA`, `cB` and `cC`, each an instance of `point1`'s (sub-)class, are co-planar with the three given points. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10 and `useZ is True`. `IntersectionError` - Near-coincident or -colinear points or a trilateration or `numpy` issue. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Functions radii11 and circum3, Contact Triangle and Incircle.

### circle4 (earth, lat) |
Get the equatorial or a parallel circle of latitude. Arguments: `earth` - The earth radius, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Geodetic latitude (`degrees90`, `str`). Returns: A Circle4Tuple`(radius, height, lat, beta)` instance. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `earth`. `ValueError` - `earth` or `lat`.

### circum3 (point1, point2, point3, circum=True, eps=8.881784197001252e-16, useZ=True) |
Return the radius and center of the smallest circle through or containing three (2- or 3-D) points. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `circum` - If `True` return the `circumradius` and `circumcenter` always, ignoring the Meeus' Type I case (`bool`). `eps` - Tolerance for function pygeodesy.trilaterate3d2 if `useZ is True` else pygeodesy.trilaterate2d2. `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: A Circum3Tuple`(radius, center, deltas)`. The `center`, an instance of `point1`'s (sub-)class, is co-planar with the three given points. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10 and `useZ is True`. `IntersectionError` - Near-coincident or -colinear points or a trilateration or `numpy` issue. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Functions pygeodesy.circum4_ and pygeodesy.meeus2 and Meeus, J. Astronomical Algorithms, 2nd Ed. 1998, page 127ff, circumradius and circumcircle.

### circum4_ (*points, **useZ_Vector_and_kwds) |
Best-fit a sphere through three or more (3-D) points. Arguments: `points` - The points (each a `Cartesian`, Vector3d, `Vector3Tuple`, or `Vector4Tuple`). `useZ_Vector_and_kwds` - Keyword arguments `useZ=True` (`bool`) to use the Z components, otherwise force all `z=INT0`, class `Vector=None` to return the center point with optionally, additional n`Vector` keyword arguments, otherwise the first `points`' (sub-)class is used. Returns: Circum4Tuple`(radius, center, rank, residuals)` with `center` an instance of `points[0]`' (sub-)class or `Vector` if specified. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10. `NumPyError` - Some `numpy` issue. `PointsError` - Too few `points`. `TypeError` - One of the `points` is invalid. See Also: Functions pygeodesy.circum3 and pygeodesy.meeus2, Jekel, Charles F. Least Squares Sphere Fit Sep 13, 2015, Appendix A, numpy.linalg.lstsq and Eberly 6.

### classname (inst, prefixed=None) |
Return the instance' class name optionally prefixed with the module name. Arguments: `inst` - The object (any `type`). `prefixed` - Include the module name (`bool`), see function `classnaming`. Returns: The `inst`'s `[module.]class` name (`str`).

### classnaming (prefixed=None) |
Get/set the default class naming for `[module.]class` names. Arguments: `prefixed` - Include the module name (`bool`). Returns: Previous class naming setting (`bool`).

### clipCS4 (points, lowerleft, upperight, closed=False, inull=False) |
Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm. Arguments: `points` - The points (`LatLon`[]). `lowerleft` - Bottom-left corner of the clip box (`LatLon`). `upperight` - Top-right corner of the clip box (`LatLon`). `closed` - Optionally, close the path (`bool`). `inull` - Optionally, retain null edges if inside (`bool`). Returns: Yield a ClipCS4Tuple`(start, end, i, j)` for each edge of the clipped path. Raises: `ClipError` - The `lowerleft` and `upperight` corners specify an invalid clip box. `PointsError` - Insufficient number of `points`.

### clipDegrees (deg, limit) |
Clip a lat- or longitude to the given range. Arguments: `deg` - Unclipped lat- or longitude (`scalar degrees`). `limit` - Valid `-/+limit` range (`degrees`). Returns: Clipped value (`degrees`). Raises: `RangeError` - If `deg` outside the valid `-/+limit` range and rangerrors is `True`.

### clipFHP4 (points, corners, closed=False, inull=False, raiser=False, eps=2.220446049250313e-16) |
Clip one or more polygons against a clip region or box using Forster-Hormann-Popa's C++ implementation transcoded to pure Python. Arguments: `points` - The polygon points and clips (`LatLon`[]). `corners` - Three or more points defining the clip regions (`LatLon`[]) or two points to specify a single, rectangular clip box. `closed` - If `True`, close each result clip (`bool`). `inull` - If `True`, retain null edges in result clips (`bool`). `raiser` - If `True`, throw ClipError exceptions (`bool`). `esp` - Tolerance for eliminating null edges (`degrees`, same units as the `points` and `corners` coordinates). Returns: Yield a ClipFHP4Tuple`(lat, lon, height, clipid)` for each clipped point. The result may consist of several clips, each a (closed) polygon with a unique `clipid`. Raises: `ClipError` - Insufficient `points` or `corners` or an open clip. See Also: Forster, Hormann and Popa, class BooleanFHP and function clipGH4.

### clipGH4 (points, corners, closed=False, inull=False, raiser=True, xtend=False, eps=2.220446049250313e-16) |
Clip one or more polygons against a clip region or box using the Greiner-Hormann algorithm, Correia's implementation modified and extended. Arguments: `points` - The polygon points and clips (`LatLon`[]). `corners` - Three or more points defining the clip regions (`LatLon`[]) or two points to specify a single, rectangular clip box. `closed` - If `True`, close each result clip (`bool`). `inull` - If `True`, retain null edges in result clips (`bool`). `raiser` - If `True`, throw ClipError exceptions (`bool`). `xtend` - If `True`, extend edges of degenerate cases, an attempt to handle the latter (`bool`). `esp` - Tolerance for eliminating null edges (`degrees`, same units as the `points` and `corners` coordinates). Returns: Yield a ClipGH4Tuple`(lat, lon, height, clipid)` for each clipped point. The result may consist of several clips, each a (closed) polygon with a unique `clipid`. Raises: `ClipError` - Insufficient `points` or `corners`, an open clip, a degenerate case or unhandled intersection. Note: To handle degenerate cases like `point-edge` and `point-point` intersections, use function clipFHP4. See Also: Greiner-Hormann, Ionel Daniel Stroe, Correia's univ-polyclip, class BooleanGH and function clipFHP4.

### clipLB6 (points, lowerleft, upperight, closed=False, inull=False) |
Clip a path against a rectangular clip box using the Liang-Barsky algorithm. Arguments: `points` - The points (`LatLon`[]). `lowerleft` - Bottom-left corner of the clip box (`LatLon`). `upperight` - Top-right corner of the clip box (`LatLon`). `closed` - Optionally, close the path (`bool`). `inull` - Optionally, retain null edges if inside (`bool`). Returns: Yield a ClipLB6Tuple`(start, end, i, fi, fj, j)` for each edge of the clipped path. Raises: `ClipError` - The `lowerleft` and `upperight` corners specify an invalid clip box. `PointsError` - Insufficient number of `points`. See Also: Liang-Barsky Line Clipping, Liang-Barsky line clipping algorithm and Liang-Barsky algorithm.

### clipRadians (rad, limit) |
Clip a lat- or longitude to the given range. Arguments: `rad` - Unclipped lat- or longitude (`radians`). `limit` - Valid `-/+limit` range (`radians`). Returns: Clipped value (`radians`). Raises: `RangeError` - If `rad` outside the valid `-/+limit` range and rangerrors is `True`.

### clipSH (points, corners, closed=False, inull=False) |
Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm. Arguments: `points` - The polygon points (`LatLon`[]). `corners` - Three or more points defining a convex clip region (`LatLon`[]) or two points to specify a rectangular clip box. `closed` - Close the clipped points (`bool`). `inull` - Optionally, include null edges (`bool`). Returns: Yield the clipped points (`LatLon`[]). Raises: `ClipError` - The `corners` specify a polar, zero-area, non-convex or otherwise invalid clip box or region. `PointsError` - Insufficient number of `points`.

### clipSH3 (points, corners, closed=False, inull=False) |
Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm. Arguments: `points` - The polygon points (`LatLon`[]). `corners` - Three or more points defining a convex clip region (`LatLon`[]) or two points to specify a rectangular clip box. `closed` - Close the clipped points (`bool`). `inull` - Optionally, include null edges (`bool`). Returns: Yield a ClipSH3Tuple`(start, end, original)` for each edge of the clipped polygon. Raises: `ClipError` - The `corners` specify a polar, zero-area, non-convex or otherwise invalid clip box or region. `PointsError` - Insufficient number of `points` or `corners`.

### clips (sb, limit=50, white='', length=False) |
Clip a string to the given length limit. Arguments: `sb` - String (`str` or `bytes`). `limit` - Length limit (`int`). `white` - Optionally, replace all whitespace (`str`). `len` - IF `True` append the original [length] (`bool`). Returns: The clipped or unclipped `sb`.

### collins5 (pointA, pointB, pointC, alpha, beta, useZ=False, **Clas_and_kwds) |
3-Point resection using Collins' method. Arguments: `pointA` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `pointB` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `pointC` - Center point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `alpha` - Angle subtended by triangle side `b` from `pointA` to `pointC` (`degrees`, non-negative). `beta` - Angle subtended by triangle side `a` from `pointB` to `pointC` (`degrees`, non-negative). `useZ` - If `True`, use and interpolate the Z component, otherwise force `z=INT0` (`bool`). `Clas_and_kwds` - Optional class `Clas=pointA.classof` to return the survey point with optionally other `Clas` keyword arguments to instantiate the survey point. Returns: Collins5Tuple`(pointP, pointH, a, b, c)` with survey `pointP`, auxiliary `pointH`, each an instance of `Clas` or `pointA`'s (sub-)class and triangle sides `a`, `b` and `c` in `meter`, conventionally. Raises: `ResectionError` - Near-coincident, -colinear or -concyclic points or negative or invalid `alpha` or `beta`. `TypeError` - Invalid `pointA`, `pointB` or `pointM`. Note: Typically, `pointC` is between `pointA` and `pointB`. See Also: Collins' methode and functions cassini, pierlot, pierlotx and tienstra7.

### compassAngle (lat1, lon1, lat2, lon2, adjust=True, wrap=False) |
Return the angle from North for the direction vector (lon2 - lon1, lat2 - lat1) between two points. Suitable only for short, not near-polar vectors up to a few hundred Km or Miles. Use function pygeodesy.bearing for longer vectors. Arguments: `lat1` - From latitude (`degrees`). `lon1` - From longitude (`degrees`). `lat2` - To latitude (`degrees`). `lon2` - To longitude (`degrees`). `adjust` - Adjust the longitudinal delta by the cosine of the mean latitude (`bool`). `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Compass angle from North (`degrees360`). Note: Courtesy of Martin Schultz. See Also: Local, flat earth approximation.

### compassDMS (bearing, form=`'``d``'`, prec=None, sep='', **s_D_M_S) |
Convert bearing to a string suffixed with compass point. Arguments: `bearing` - Bearing from North (compass `degrees360`). `form` - Format specifier for `deg` (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F_D60, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F_D60_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F_D60__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. `sep` - Separator between degrees, minutes, seconds, suffix (`str`). `s_D_M_S` - Optional keyword arguments `s_D=str`, `s_M=str` `s_S=str` and `s_DMS=True` to override any or cancel all DMS symbols, defaults S_DEG, S_MIN respectively S_SEC. Returns: Compass degrees and point in the specified form (`str`). See Also: Function pygeodesy.toDMS.

### compassPoint (bearing, prec=3) |
Convert a `bearing` from North to a compass point. Arguments: `bearing` - Bearing (compass `degrees360`). `prec` - Precision, number of compass point characters: 1 for cardinal or basic winds, 2 for intercardinal or ordinal or principal winds, 3 for secondary-intercardinal or half-winds or 4 for quarter-winds). Returns: Compass point (1-, 2-, 3- or 4-letter `str`). Raises: `ValueError` - Invalid `bearing` or `prec`. See Also: Dms.compassPoint and Compass rose.

### copysign0 (x, y) |
Like `math.copysign(x, y)` except `zero`, unsigned. Returns: `math.copysign(x, y)` if `x` else `type(x)(0)`.

### copytype (x, y) |
Return the value of x as `type` of `y`. Returns: `type(y)(x)`.

### cosineAndoyerLambert (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=False) |
Compute the distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as the `datum`'s ellipsoid axes or `radians` if `datum is None`). Raises: `TypeError` - Invalid `datum`. See Also: Functions cosineAndoyerLambert_, cosineForsytheAndoyerLambert, cosineLaw, equirectangular, euclidean, flatLocal/hubeny, flatPolar, haversine, thomas and vincentys and method Ellipsoid.distance2.

### cosineAndoyerLambert_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`) |
Compute the angular distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. Returns: Angular distance (`radians`). Raises: `TypeError` - Invalid `datum`. See Also: Functions cosineAndoyerLambert, cosineForsytheAndoyerLambert_, cosineLaw_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_ and Geodesy-PHP.

### cosineForsytheAndoyerLambert (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=False) |
Compute the distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as the `datum`'s ellipsoid axes or `radians` if `datum is None`). Raises: `TypeError` - Invalid `datum`. See Also: Functions cosineForsytheAndoyerLambert_, cosineAndoyerLambert, cosineLaw, equirectangular, euclidean, flatLocal/hubeny, flatPolar, haversine, thomas and vincentys and method Ellipsoid.distance2.

### cosineForsytheAndoyerLambert_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`) |
Compute the angular distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). `datum` - Datum (Datum) or ellipsoid to use (Ellipsoid, Ellipsoid2 or a_f2Tuple). Returns: Angular distance (`radians`). Raises: `TypeError` - Invalid `datum`. See Also: Functions cosineForsytheAndoyerLambert, cosineAndoyerLambert_, cosineLaw_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_ and Geodesy-PHP.

### cosineLaw (lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) |
Compute the distance between two points using the spherical Law of Cosines formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as `radius` or the ellipsoid or datum axes). Raises: `TypeError` - Invalid `radius`. See Also: Functions cosineLaw_, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, flatLocal/hubeny, flatPolar, haversine, thomas and vincentys and method Ellipsoid.distance2. Note: See note at function vincentys_.

### cosineLaw_ (phi2, phi1, lam21) |
Compute the angular distance between two points using the spherical Law of Cosines formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). Returns: Angular distance (`radians`). See Also: Functions cosineLaw, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_. Note: See note at function vincentys_.

### cot (rad, **error_kwds) |
Return the `cotangent` of an angle in `radians`. Arguments: `rad` - Angle (`radians`). `error_kwds` - Error to raise (`ValueError`). Returns: `cot(rad)`. Raises: `ValueError` - pygeodesy.isnear0`(sin(rad)`.

### cot_ (*rads, **error_kwds) |
Return the `cotangent` of angle(s) in `radiansresection`. Arguments: `rads` - One or more angles (`radians`). `error_kwds` - Error to raise (`ValueError`). Returns: Yield the `cot(rad)` for each angle. Raises: `ValueError` - See pygeodesy.cot.

### cotd (deg, **error_kwds) |
Return the `cotangent` of an angle in `degrees`. Arguments: `deg` - Angle (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: `cot(deg)`. Raises: `ValueError` - pygeodesy.isnear0`(sin(deg)`.

### cotd_ (*degs, **error_kwds) |
Return the `cotangent` of angle(s) in `degrees`. Arguments: `degs` - One or more angles (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: Yield the `cot(deg)` for each angle. Raises: `ValueError` - See pygeodesy.cotd.

### crosserrors (raiser=None) |
Report or ignore vectorial cross product errors. Arguments: `raiser` - Use `True` to throw or `False` to ignore CrossError exceptions. Use `None` to leave the setting unchanged. Returns: Previous setting (`bool`). See Also: Property `Vector3d[Base].crosserrors`.

### date2epoch (year, month, day) |
Return the `epoch` for a calendar day. Arguments: `year` - Year of the date (`scalar`). `month` - Month in the `year` (`scalar`, 1..12). `day` - Day in the `month` (`scalar`, 1..31). Returns: Epoch, the fractional year (`float`). Raises: `TRFError` - Invalid `year`, `month` or `day`. Note: Any `year` is considered a leap year, i.e. having 29 days in February.

### degDMS (deg, prec=6, s_D=`'``°``'`, s_M=`'``\xe2\x80\xb2``'`, s_S=`'``″``'`, neg='-', pos='') |
Convert degrees to a string in degrees, minutes or seconds. Arguments: `deg` - Value in degrees (`scalar degrees`). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. `s_D` - D symbol for degrees (`str`). `s_M` - M symbol for minutes (`str`) or `""`. `s_S` - S symbol for seconds (`str`) or `""`. `neg` - Optional sign for negative (`'-'`). `pos` - Optional sign for positive (`''`). Returns: Either degrees, minutes or seconds (`str`). See Also: Function pygeodesy.toDMS.

### degrees180 (rad) |
Convert radians to degrees and wrap [-180..+180). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`degrees180`).

### degrees2grades (deg) |
Convert degrees to grades (aka gons or gradians). Arguments: `deg` - Angle (`degrees`). Returns: Angle (`grades`).

### degrees2m (deg, radius=6371008.771415, lat=0) |
Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. Arguments: `deg` - The angle (`degrees`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Distance (`meter`, same units as `radius` or equatorial and polar radii) or `0.0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `deg`, `radius` or `lat`. See Also: Function radians2m and m2degrees.

### degrees360 (rad) |
Convert radians to degrees and wrap [0..+360). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`degrees360`).

### degrees90 (rad) |
Convert radians to degrees and wrap [-90..+90). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`degrees90`).

### deprecated_Property_RO (method) |
Decorator for a DEPRECATED Property_RO. Arguments: `method` - The `Property_RO.fget` method (`callable`). Returns: The `method` DEPRECATED.

### deprecated_class (cls_or_class) |
Use inside __new__ or __init__ of a DEPRECATED class. Arguments: `cls_or_class` - The class (`cls` or `Class`). Note: NOT a decorator!

### deprecated_function (call) |
Decorator for a DEPRECATED function. Arguments: `call` - The deprecated function (`callable`). Returns: The `call` DEPRECATED.

### deprecated_method (call) |
Decorator for a DEPRECATED method. Arguments: `call` - The deprecated method (`callable`). Returns: The `call` DEPRECATED.

### deprecated_property_RO (method) |
Decorator for a DEPRECATED property_RO. Arguments: `method` - The `property_RO.fget` method (`callable`). Returns: The `method` DEPRECATED.

### e22f (e2) |
Return `f`, the flattening for a given 1st eccentricity squared. Arguments: `e2` - The (1st) eccentricity squared, signed (NINF < `float` < 1) Returns: The flattening (`float` or `0`), e2 / (sqrt(e2 - 1) + 1).

### e2f (e) |
Return `f`, the flattening for a given 1st eccentricity. Arguments: `e` - The (1st) eccentricity (0 <= `float` < 1) Returns: The flattening (`scalar` or `0`). See Also: Function e22f.

### egmGeoidHeights (GeoidHeights_dat) |
Generate geoid egm*.pgm height tests from GeoidHeights.dat Test data for Geoids. Arguments: `GeoidHeights_dat` - The un-gz-ed `GeoidHeights.dat` file (`str` or `file` handle). Returns: For each test, yield a GeoidHeight5Tuple`(lat, lon, egm84, egm96, egm2008)`. Raises: `GeoidError` - Invalid `GeoidHeights_dat`. Note: Function egmGeoidHeights is used to test the geoids GeoidKarney and GeoidPGM, see PyGeodesy module `test/testGeoids.py`.

### elevation2 (lat, lon, timeout=2.0) |
Get the geoid elevation at an `NAD83` to `NAVD88` location. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `timeout` - Optional, query timeout (seconds). Returns: An Elevation2Tuple`(elevation, data_source)` or (`None, "error"`) in case of errors. Raises: `ValueError` - Invalid `timeout`. Note: The returned `elevation is None` if `lat` or `lon` is invalid or outside the `Conterminous US (CONUS)`, if conversion failed or if the query timed out. The `"error"` is the `HTTP-, IO-, SSL-` or other `-Error` as a string (`str`). See Also: USGS Elevation Point Query Service, the FAQ, geoid.py, module geoids, classes GeoidG2012B, GeoidKarney and GeoidPGM.

### enstr2 (easting, northing, prec, *extras, **wide_dot) |
Return an MGRS/OSGR easting, northing string representations. Arguments: `easting` - Easting from false easting (`meter`). `northing` - Northing from from false northing (`meter`). `prec` - Precision, the number of decimal digits (`int`) or if negative, the number of units to drop, like MGRS PRECISION. `extras` - Optional leading items (`str`s). `wide_dot` - Optional keword argument `wide=5` for the number of unit digits (`int`) and `dot=False` (`bool`) to insert a decimal point. Returns: `extras` + 2-tuple `(str(easting), str(northing))` or + 2-tuple `("", "")` for `prec <= -wide`. Raises: `ValueError` - Invalid `easting`, `northing` or `prec`. Note: The `easting` and `northing` values are truncated, not rounded.

### epoch2date (epoch) |
Return the date for a reference frame `epoch`. Arguments: `epoch` - Fractional year (`scalar`). Returns: 3-Tuple `(year, month, day)`. Raises: `TRFError` - Invalid `epoch`. Note: Any `year` is considered a leap year, i.e. having 29 days in February.

### equidistant (lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, exact=False, geodsolve=False, **name) |
Return an EquidistantExact, EquidistantGeodSolve or (if Karney's geographiclib package is installed) an EquidistantKarney, otherwise an Equidistant instance. Arguments: `lat0` - Latitude of center point (`degrees90`). `lon0` - Longitude of center point (`degrees180`). `datum` - Optional datum or ellipsoid (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple) or scalar earth radius (`meter`). `exact` - Return an EquidistantExact instance. `geodsolve` - Return an EquidistantGeodSolve instance. `name` - Optional `name=NN` for the projection (`str`). Returns: An EquidistantExact, EquidistantGeodSolve, EquidistantKarney or Equidistant instance. Raises: `AzimuthalError` - Invalid `lat0` or `lon0` or (spherical) `datum`. `GeodesicError` - Issue with GeodesicExact, GeodesicSolve or Karney's wrapped `Geodesic`. `TypeError` - Invalid `datum`.

### equirectangular (lat1, lon1, lat2, lon2, radius=6371008.771415, **adjust_limit_wrap) |
Compute the distance between two points using the Equirectangular Approximation / Projection. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple). `adjust_limit_wrap` - Optional keyword arguments for function equirectangular4. Returns: Distance (`meter`, same units as `radius` or the ellipsoid or datum axes). Raises: `TypeError` - Invalid `radius`. See Also: Function equirectangular4 for more details, the available `options`, errors, restrictions and other, approximate or accurate distance functions.

### equirectangular4 (lat1, lon1, lat2, lon2, adjust=True, limit=45, wrap=False) |
Compute the distance between two points using the Equirectangular Approximation / Projection. This approximation is valid for short distance of several hundred Km or Miles, see the `limit` keyword argument and LimitError. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `limit` - Optional limit for lat- and longitudinal deltas (`degrees`) or `None` or `0` for unlimited. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: A Distance4Tuple`(distance2, delta_lat, delta_lon, unroll_lon2)` in `degrees squared`. Raises: `LimitError` - If the lat- and/or longitudinal delta exceeds the `-limit..limit` range and limiterrors is `True`. See Also: Local, flat earth approximation, functions equirectangular, cosineAndoyerLambert, cosineForsytheAndoyerLambert, cosineLaw, euclidean, flatLocal/hubeny, flatPolar, haversine, thomas and vincentys and methods Ellipsoid.distance2, `LatLon.distanceTo*` and `LatLon.equirectangularTo`.

### euclid (x, y) |
Appoximate the norm sqrt(x**2 + y**2) by max(abs(x), abs(y)) + min(abs(x), abs(y)) * 0.4142.... Arguments: `x` - X component (`scalar` or Fsum instance). `y` - Y component (`scalar` or Fsum instance). Returns: Appoximate norm (`float` or Fsum). See Also: Function euclid_.

### euclid_ (*xs) |
Appoximate the norm sqrt(sum(x**2 for x in xs)) by cascaded euclid. Arguments: `xs` - X arguments (each `scalar` or an Fsum instance), all positional. Returns: Appoximate norm (`float` or Fsum). See Also: Function euclid.

### euclidean (lat1, lon1, lat2, lon2, radius=6371008.771415, adjust=True, wrap=False) |
Approximate the `Euclidean` distance between two (spherical) points. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `adjust` - Adjust the longitudinal delta by the cosine of the mean latitude (`bool`). `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as `radius` or the ellipsoid or datum axes). Raises: `TypeError` - Invalid `radius`. See Also: Distance between two (spherical) points, functions euclid, euclidean_, cosineAndoyerLambert, cosineForsytheAndoyerLambert, cosineLaw, equirectangular, flatLocal/hubeny, flatPolar, haversine, thomas and vincentys and methods Ellipsoid.distance2, `LatLon.distanceTo*` and `LatLon.equirectangularTo`.

### euclidean_ (phi2, phi1, lam21, adjust=True) |
Approximate the angular `Euclidean` distance between two (spherical) points. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). `adjust` - Adjust the longitudinal delta by the cosine of the mean latitude (`bool`). Returns: Angular distance (`radians`). See Also: Functions euclid, euclidean, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_.

### exception_chaining (exc=None) |
Get an error's cause or the exception chaining setting. Arguments: `exc` - An error instance (`Exception`) or `None`. Returns: If `exc is None`, return `True` if exception chaining is enabled for PyGeodesy errors, `False` if turned off and `None` if not available. If `exc is not None`, return it's error cause or `None` if there is none. Note: To enable exception chaining for `pygeodesy` errors, set env var `PYGEODESY_EXCEPTION_CHAINING` to any non-empty value prior to `import pygeodesy`.

### excessAbc_ (A, b, c) |
Compute the spherical excess `E` of a (spherical) triangle from two sides and the included (small) angle. Arguments: `A` - An interior triangle angle (`radians`). `b` - Frist adjacent triangle side (`radians`). `c` - Second adjacent triangle side (`radians`). Returns: Spherical excess (`radians`). Raises: `UnitError` - Invalid `A`, `b` or `c`. See Also: Functions excessGirard_, excessLHuilier_ and Spherical trigonometry.

### excessCagnoli_ (a, b, c) |
Compute the spherical excess `E` of a (spherical) triangle using Cagnoli's (D.34) formula. Arguments: `a` - First triangle side (`radians`). `b` - Second triangle side (`radians`). `c` - Third triangle side (`radians`). Returns: Spherical excess (`radians`). Raises: `UnitError` - Invalid `a`, `b` or `c`. See Also: Function excessLHuilier_ and Spherical trigonometry.

### excessGirard_ (A, B, C) |
Compute the spherical excess `E` of a (spherical) triangle using Girard's formula. Arguments: `A` - First interior triangle angle (`radians`). `B` - Second interior triangle angle (`radians`). `C` - Third interior triangle angle (`radians`). Returns: Spherical excess (`radians`). Raises: `UnitError` - Invalid `A`, `B` or `C`. See Also: Function excessLHuilier_ and Spherical trigonometry.

### excessKarney (lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) |
Compute the surface area of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator using Karney's method. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) or `None`. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Surface area, signed (square `meter` or the same units as `radius` squared) or the spherical excess (`radians`) if `radius=0` or `None`. Raises: `TypeError` - Invalid `radius`. `UnitError` - Invalid `lat2` or `lat1`. `ValueError` - Semi-circular longitudinal delta. See Also: Functions excessKarney_ and excessQuad.

### excessKarney_ (phi2, phi1, lam21) |
Compute the spherical excess `E` of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator using Karney's method. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). Returns: Spherical excess, signed (`radians`). Raises: `ValueError` - Semi-circular longitudinal delta `lam21`. See Also: Function excessKarney and Area of a spherical polygon.

### excessLHuilier_ (a, b, c) |
Compute the spherical excess `E` of a (spherical) triangle using L'Huilier's's Theorem. Arguments: `a` - First triangle side (`radians`). `b` - Second triangle side (`radians`). `c` - Third triangle side (`radians`). Returns: Spherical excess (`radians`). Raises: `UnitError` - Invalid `a`, `b` or `c`. See Also: Function excessCagnoli_, excessGirard_ and Spherical trigonometry.

### excessQuad (lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) |
Compute the surface area of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) or `None`. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Surface area, signed (square `meter` or the same units as `radius` squared) or the spherical excess (`radians`) if `radius=0` or `None`. Raises: `TypeError` - Invalid `radius`. `UnitError` - Invalid `lat2` or `lat1`. See Also: Function excessQuad_ and excessKarney.

### excessQuad_ (phi2, phi1, lam21) |
Compute the spherical excess `E` of a (spherical) quadrilateral bounded by a segment of a great circle, two meridians and the equator. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). Returns: Spherical excess, signed (`radians`). See Also: Function excessQuad and Spherical trigonometry.

### f2e2 (f) |
Return `e2`, the 1st eccentricity squared for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The signed, (1st) eccentricity squared (`float` < 1), f * (2 - f). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids. See Also: Eccentricity conversions and Flattening.

### f2e22 (f) |
Return `e22`, the 2nd eccentricity squared for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The signed, 2nd eccentricity squared (`float` > -1 or `INF`), f * (2 - f) / (1 - f)**2. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids. See Also: Eccentricity conversions.

### f2e32 (f) |
Return `e32`, the 3rd eccentricity squared for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The signed, 3rd eccentricity squared (`float`), f * (2 - f) / (1 + (1 - f)**2). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids. See Also: Eccentricity conversions.

### f2f2 (f) |
Return `f2`, the 2nd flattening for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The signed, 2nd flattening (`scalar` or `INF`), f / (1 - f). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids. See Also: Eccentricity conversions and Flattening.

### f2f_ (f) |
Return `f_`, the inverse flattening for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The inverse flattening (`scalar` or `0`), 1 / f. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### f2n (f) |
Return `n`, the 3rd flattening for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The signed, 3rd flattening (-1 <= `float` < 1), f / (2 - f). Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids. See Also: Eccentricity conversions and Flattening.

### f_2f (f_) |
Return `f`, the flattening for a given inverse flattening. Arguments: `f_` - Inverse flattening (`scalar` >>> 1). Returns: The flattening (`scalar` or `0`), 1 / f_. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids.

### facos1 (x) |
Fast approximation of pygeodesy.acos1`(x)`. See Also: ShaderFastLibs.h.

### fasin1 (x) |
Fast approximation of pygeodesy.asin1`(x)`. See Also: facos1.

### fatan1 (x) |
Fast approximation of `atan(x)` for `0 <= x < 1`, unchecked. See Also: ShaderFastLibs.h and Efficient approximations for the arctangent function, IEEE Signal Processing Magazine, 111, May 2006.

### fatan2 (y, x) |
Fast approximation of `atan2(y, x)`. See Also: fastApproximateAtan(x, y) and fatan1.

### fathom2m (fathoms) |
Convert Imperial fathom to meter. Arguments: `fathoms` - Value in fathoms (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `fathoms`. See Also: Function toise2m, Fathom and Klafter.

### favg (a, b, f=0.5) |
Return the precision average of two values. Arguments: `a` - One (`scalar` or an Fsum or Fsum2Tuple). `b` - Other (`scalar` or an Fsum or Fsum2Tuple). `f` - Optional fraction (`float`). Returns: a + f * (b - a) (`float`).

### fdot (a, *b) |
Return the precision dot product sum(a[i] * b[i] for i=0..len(a)). Arguments: `a` - Iterable of values (each `scalar`). `b` - Other values (each `scalar`), all positional. Returns: Dot product (`float`). Raises: `LenError` - Unequal `len(a)` and `len(b)`. See Also: Class Fdot and Algorithm 5.10 DotK.

### fdot3 (xs, ys, zs, start=0) |
Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)-1). Arguments: `xs` - Iterable (each `scalar` or an Fsum or Fsum2Tuple instance). `ys` - Iterable (each `scalar` or an Fsum or Fsum2Tuple instance). `zs` - Iterable (each `scalar` or an Fsum or Fsum2Tuple instance). `start` - Optional bias (`scalar` or an Fsum or Fsum2Tuple). Returns: Dot product (`float`). Raises: `LenError` - Unequal `len(xs)`, `len(ys)` and/or `len(zs)`. `OverflowError` - Partial `2sum` overflow.

### fhorner (x, *cs) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)-1) using the Horner form. Returns: Horner sum (`float`). See Also: Class Fhorner for further details.

### fidw (xs, ds, beta=2) |
Interpolate using Inverse Distance Weighting (IDW). Arguments: `xs` - Known values (each `scalar` or an Fsum or Fsum2Tuple instance). `ds` - Non-negative distances (each `scalar` or an Fsum or Fsum2Tuple instance). `beta` - Inverse distance power (`int`, 0, 1, 2, or 3). Returns: Interpolated value `x` (`float`). Raises: `LenError` - Unequal or zero `len(ds)` and `len(xs)`. `TypeError` - An invalid `ds` or `xs`. `ValueError` - Invalid `beta`, negative `ds` or weighted `ds` below EPS. Note: Using `beta=0` returns the mean of `xs`.

### flatLocal (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True, wrap=False) |
Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `scaled` - Scale prime_vertical by `cos(phi)` (`bool`), see method pygeodesy.Ellipsoid.roc2_. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as the `datum`'s ellipsoid axes). Raises: `TypeError` - Invalid `datum`. Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude. See Also: Functions flatLocal_ or hubeny_, cosineLaw, flatPolar, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, haversine, thomas, vincentys, method Ellipsoid.distance2 and local, flat earth approximation.

### flatLocal_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True) |
Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `scaled` - Scale prime_vertical by `cos(phi)` (`bool`), see method pygeodesy.Ellipsoid.roc2_. Returns: Angular distance (`radians`). Raises: `TypeError` - Invalid `datum`. Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude. See Also: Functions flatLocal or hubeny, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatPolar_, euclidean_, haversine_, thomas_ and vincentys_ and local, flat earth approximation.

### flatPolar (lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) |
Compute the distance between two (spherical) points using the polar coordinate flat-Earth formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as `radius` or the ellipsoid or datum axes). Raises: `TypeError` - Invalid `radius`. See Also: Functions flatPolar_, cosineAndoyerLambert, cosineForsytheAndoyerLambert,cosineLaw, flatLocal/hubeny, equirectangular, euclidean, haversine, thomas and vincentys.

### flatPolar_ (phi2, phi1, lam21) |
Compute the angular distance between two (spherical) points using the polar coordinate flat-Earth formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). Returns: Angular distance (`radians`). See Also: Functions flatPolar, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, euclidean_, flatLocal_/hubeny_, haversine_, thomas_ and vincentys_.

### float_ (*fs, **sets) |
Get scalars as `float` or intern'ed `float`. Arguments: `fs` - One more values (`scalar`), all positional. `sets` - Use `sets=True` to `intern` each `fs`, otherwise don't `intern`. Returns: A single `float` if only one `fs` is given, otherwise a tuple of `float`s. Raises: `TypeError` - Some `fs` is not `scalar`.

### fmean (xs) |
Compute the accurate mean sum(xs) / len(xs). Arguments: `xs` - Values (`scalar` or Fsum instances). Returns: Mean value (`float`). Raises: `LenError` - No `xs` values. `OverflowError` - Partial `2sum` overflow.

### fmean_ (*xs) |
Compute the accurate mean sum(xs) / len(xs). See Also: Function fmean for further details.

### fpolynomial (x, *cs, **over) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) [/ over]. Arguments: `over` - Optional final, non-zero divisor (`scalar`). Returns: Polynomial value (`float`). See Also: Class Fpolynomial for further details.

### fpowers (x, n, alts=0) |
Return a series of powers [x**i for i=1..n]. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). `n` - Highest exponent (`int`). `alts` - Only alternating powers, starting with this exponent (`int`). Returns: Tuple of powers of `x` (each `type(x)`). Raises: `TypeError` - Invalid `x` or `n` not `int`. `ValueError` - Non-finite `x` or invalid `n`.

### fprod (xs, start=1) |
Iterable product, like `math.prod` or `numpy.prod`. Arguments: `xs` - Iterable of values to be multiplied (each `scalar` or an Fsum). `start` - Initial value, also the value returned for an empty `xs` (`scalar`). Returns: The product (`float` or an Fsum). See Also: NumPy.prod.

### fractional (points, fi, j=None, wrap=None, LatLon=None, Vector=None, **kwds) |
  Return the point at a given fractional index. Arguments: `points` - The points (`LatLon`[], Numpy2LatLon[], Tuple2LatLon[], `Cartesian`[], `Vector3d`[], Vector3Tuple[]). `fi` - The fractional index (FIx, `float` or `int`). `j` - Optionally, index of the other point (`int`). `wrap` - If `True`, wrap or normalize and unroll the {points} (`bool`) or `None` for a backward compatible LatLon2Tuple or `LatLon` with averaged lat- and longitudes. Use `True` or `False` to get the fractional point computed by method `points[fi].intermediateTo`. `LatLon` - Optional class to return the intermediate, fractional point (`LatLon`) or `None`. `Vector` - Optional class to return the intermediate, fractional point (`Cartesian`, `Vector3d`) or `None`. `kwds` - Optional, additional `LatLon` or `Vector` keyword arguments, ignored if both `LatLon` and `Vector` are `None`. Returns: A LatLon2Tuple`(lat, lon)` if `wrap`, `LatLon` and `Vector` all are `None`, the defaults. An instance of `LatLon` if not `None` or an instance of `Vector` if not `None`. Otherwise with `wrap` either `True` or `False` and `LatLon` and `Vector` both `None`, an instance of `points`' (sub-)class `intermediateTo` fractional. Summarized as follows:
      >>>  wrap  | LatLon | Vector | returned type/value
      #   -------+--------+--------+--------------+------
      #          |        |        | LatLon2Tuple | favg
      #    None  |  None  |  None  |   or**       |
      #          |        |        | Vector3Tuple | favg
      #    None  | LatLon |  None  | LatLon       | favg
      #    None  |  None  | Vector | Vector       | favg
      #   -------+--------+--------+--------------+------
      #    True  |  None  |  None  | points'      | .iTo
      #    True  | LatLon |  None  | LatLon       | .iTo
      #    True  |  None  | Vector | Vector       | .iTo
      #   -------+--------+--------+--------------+------
      #    False |  None  |  None  | points'      | .iTo
      #    False | LatLon |  None  | LatLon       | .iTo
      #    False |  None  | Vector | Vector       | .iTo
      # _____
      # favg) averaged lat, lon or x, y, z values
      # .iTo) value from points[fi].intermediateTo
      # **) depends on base class of points[fi]
Raises: `IndexError` - Fractional index `fi` invalid or `points` not subscriptable or not closed. `TypeError` - Invalid `LatLon`, `Vector` or `kwds` argument. See Also: Class FIx and method FIx.fractional.

### frandoms (n, seeded=None) |
Generate `n` (long) lists of random `floats`. Arguments: `n` - Number of lists to generate (`int`, non-negative). `seeded` - If `scalar`, use `random.seed(seeded)` or if `True`, seed using today's `year-day`. See Also: Hettinger.

### frange (start, number, step=1) |
Generate a range of `float`s. Arguments: `start` - First value (`float`). `number` - The number of `float`s to generate (`int`). `step` - Increment value (`float`). Returns: A generator (`float`s). See Also: NumPy.prod.

### frechet_ (point1s, point2s, distance=None, units='') |
Compute the discrete Fréchet distance between two paths, each given as a set of points. Arguments: `point1s` - First set of points (`LatLon`[], Numpy2LatLon[], Tuple2LatLon[] or `other`[]). `point2s` - Second set of points (`LatLon`[], Numpy2LatLon[], Tuple2LatLon[] or `other`[]). `distance` - Callable returning the distance between a `point1s` and a `point2s` point (signature `(point1, point2)`). `units` - Optional, the distance units (`Unit` or `str`). Returns: A Frechet6Tuple`(fd, fi1, fi2, r, n, units)` where `fi1` and `fi2` are type `int` indices into `point1s` respectively `point2s`. Raises: `FrechetError` - Insufficient number of `point1s` or `point2s`. `RecursionError` - Recursion depth exceeded, see sys.getrecursionlimit(). `TypeError` - If `distance` is not a callable. Note: Function frechet_ does not support fractional indices for intermediate `point1s` and `point2s`.

### freduce (function, sequence, initial=...) |
Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). If initial is present, it is placed before the items of the sequence in the calculation, and serves as a default when the sequence is empty. Returns: value

### fremainder (x, y) |
Remainder in range `[-y / 2, y / 2]`. Arguments: `x` - Numerator (`scalar`). `y` - Modulus, denominator (`scalar`). Returns: Remainder (`scalar`, preserving signed 0.0) or `NAN` for any non-finite `x`. Raises: `ValueError` - Infinite or near-zero `y`. See Also: Karney's Math.remainder and Python 3.7+ math.remainder.

### fstr (floats, prec=6, fmt='F', ints=False, sep=', ', strepr=None, force=True) |
Convert one or more floats to string, optionally stripped of trailing zero decimals. Arguments: `floats` - Single or a list, sequence, tuple, etc. (`scalar`s). `prec` - The `float` precision, number of decimal digits (0..9). Trailing zero decimals are stripped if `prec` is positive, but kept for negative `prec` values. In addition, trailing decimal zeros are stripped for alternate, form '#'. `fmt` - Optional `float` format (`letter`). `ints` - Optionally, remove the decimal dot for `int` values (`bool`). `sep` - Separator joining the `floats` (`str`). `strepr` - Optional callable to format non-`floats` (typically `repr`, `str`) or `None` to raise a TypeError and used only if `force is not True`. `force` - If `True` format all `floats` using `fmt`, otherwise use `strepr` for non-`floats`. Returns: The `sep.join(strs(floats, ...)` joined (`str`) or single `strs((floats,), ...)` (`str`) if `floats` is `scalar`.

### fstrzs (efstr, ap1z=False) |
Strip trailing zero decimals from a `float` string. Arguments: `efstr` - Float with or without exponent (`str`). `ap1z` - Append the decimal point and one zero decimal if the `efstr` is all digits (`bool`). Returns: Float (`str`).

### fsum (xs, floats=False) |
Precision floating point summation based on/like Python's `math.fsum`. Arguments: `xs` - Iterable of items to add (each `scalar` or an Fsum or Fsum2Tuple instance). `floats` - Use `floats=True` iff all `xs` items are known to be scalar (`bool`). Returns: Precision `fsum` (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar `xs` item. `ValueError` - Invalid or non-finite `xs` item. Note: Exception and non-finite handling may differ if not based on Python's `math.fsum`. See Also: Class Fsum and methods Fsum.fsum and Fsum.fadd.

### fsum1 (xs, floats=False) |
Precision floating point summation, 1-primed. Arguments: `xs` - Iterable of items to add (each `scalar` or an Fsum or Fsum2Tuple instance). `floats` - Use `floats=True` iff all `xs` items are known to be scalar (`bool`). See Also: Function fsum for further details.

### fsum1_ (*xs, **floats) |
Precision floating point summation, 1-primed of all positional items. Arguments: `xs` - Items to add (each `scalar` or an Fsum or Fsum2Tuple instance), all positional. `floats` - Use `floats=True` iff all `xs` items are known to be scalar (`bool`). See Also: Function fsum_ for further details.

### fsum1f_ (*xs) |
Precision floating point summation iff all `xs` items are known to be scalar. See Also: Function fsum_ for further details.

### fsum_ (*xs, **floats) |
Precision floating point summation of all positional items. Arguments: `xs` - Items to add (each `scalar` or an Fsum or Fsum2Tuple instance), all positional. `floats` - Use `floats=True` iff all `xs` items are known to be scalar (`bool`). See Also: Function fsum for further details.

### fsumf_ (*xs) |
Precision floating point summation iff all `xs` items are known to be scalar. See Also: Function fsum_ for further details.

### ft2m (feet, usurvey=False, pied=False, fuss=False) |
Convert International, US Survey, French or German `feet` to `meter`. Arguments: `feet` - Value in feet (`scalar`). `usurvey` - If `True`, convert US Survey foot else ... `pied` - If `True`, convert French pied-du-Roi else ... `fuss` - If `True`, convert German Fuss, otherwise International foot to `meter`. Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `feet`.

### furlong2m (furlongs) |
Convert a furlong to meter. Arguments: `furlongs` - Value in furlongs (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `furlongs`.

### geoidHeight2 (lat, lon, model=0, timeout=2.0) |
Get the `NAVD88` geoid height at an `NAD83` location. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `model` - Optional, geoid model ID (`int`). `timeout` - Optional, query timeout (seconds). Returns: An GeoidHeight2Tuple`(height, model_name)` or `(None, "error"`) in case of errors. Raises: `ValueError` - Invalid `timeout`. Note: The returned `height is None` if `lat` or `lon` is invalid or outside the `Conterminous US (CONUS)`, if the `model` was invalid, if conversion failed or if the query timed out. The `"error"` is the `HTTP-, IO-, SSL-, URL-` or other `-Error` as a string (`str`). See Also: NOAA National Geodetic Survey, Geoid, USGS10mElev.py, module geoids, classes GeoidG2012B, GeoidKarney and GeoidPGM.

### gnomonic (lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, exact=False, geodsolve=False, **name) |
Return a GnomonicExact or (if Karney's geographiclib package is installed) a GnomonicKarney, otherwise a Gnomonic instance. Arguments: `lat0` - Latitude of center point (`degrees90`). `lon0` - Longitude of center point (`degrees180`). `datum` - Optional datum or ellipsoid (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple) or scalar earth radius (`meter`). `exact` - Return a GnomonicExact instance. `geodsolve` - Return a GnomonicGeodSolve instance. `name` - Optional `name=NN` for the projection (`str`). Returns: A GnomonicExact, GnomonicGeodSolve, GnomonicKarney or Gnomonic instance. Raises: `AzimuthalError` - Invalid `lat0` or `lon0` or (spherical) `datum`. `GeodesicError` - Issue with GeodesicExact, GeodesicSolve or Karney's wrapped `Geodesic`. `TypeError` - Invalid `datum`.

### grades (rad) |
Convert radians to grades (aka gons or gradians). Arguments: `rad` - Angle (`radians`). Returns: Angle (`grades`).

### grades2degrees (gon) |
Convert grades (aka gons or gradians) to `degrees`. Arguments: `gon` - Angle (`grades`). Returns: Angle (`degrees`).

### grades2radians (gon) |
Convert grades (aka gons or gradians) to `radians`. Arguments: `gon` - Angle (`grades`). Returns: Angle (`radians`).

### grades400 (rad) |
Convert radians to grades (aka gons or gradians) and wrap [0..+400). Arguments: `rad` - Angle (`radians`). Returns: Angle, wrapped (`grades`).

### halfs2 (str2) |
Split a string in 2 halfs. Arguments: `str2` - String to split (`str`). Returns: 2-Tuple `(_1st, _2nd)` half (`str`). Raises: `ValueError` - Zero or odd `len(str2)`.

### hartzell (pov, los=False, earth=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, **name_LatLon_and_kwds) |
Compute the intersection of the earth's surface and a Line-Of-Sight from a Point-Of-View in space. Arguments: `pov` - Point-Of-View outside the earth (`LatLon`, `Cartesian`, Ecef9Tuple or Vector3d). `los` - Line-Of-Sight, direction to earth (Los, Vector3d), `True` for the normal, plumb onto the surface or `False` or `None` to point to the center of the earth. `earth` - The earth model (Datum, Ellipsoid, Ellipsoid2, a_f2Tuple or a `scalar` earth radius in `meter`). `name_LatLon_and_kwds` - Optional, overriding `name="hartzell"` (`str`), class `LatLon=None` to return the intersection plus additional `LatLon` keyword arguments, include the `datum` if different and to convert from `earth`. Returns: The intersection (Vector3d, `pov`'s `cartesian type` or the given `LatLon` instance) with attribute `heigth` set to the distance to the `pov`. Raises: `IntersectionError` - Invalid `pov` or `pov` inside the earth or invalid `los` or `los` points outside or away from the earth. `TypeError` - Invalid `earth`, `ellipsoid` or `datum`. See Also: Class Los, functions tyr3d and hartzell4 and methods Ellipsoid.hartzell4 and any `Cartesian.hartzell` and `LatLon.hartzell`.

### hartzell4 (pov, los=False, tri_biax=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, **name) |
Compute the intersection of a tri-/biaxial ellipsoid and a Line-Of-Sight from a Point-Of-View outside. Arguments: `pov` - Point-Of-View outside the tri-/biaxial (`Cartesian`, Ecef9Tuple `LatLon` or Vector3d). `los` - Line-Of-Sight, direction to the tri-/biaxial (Los, Vector3d), `True` for the normal, plumb onto the surface or `False` or `None` to point to the center of the tri-/biaxial. `tri_biax` - A triaxial (Triaxial, Triaxial_, JacobiConformal or JacobiConformalSpherical) or biaxial ellipsoid (Datum, Ellipsoid, Ellipsoid2, a_f2Tuple or `scalar` radius, conventionally in `meter`). `name` - Optional, overriding `name="hartzell4"` (`str`). Returns: Vector4Tuple`(x, y, z, h)` on the tri-/biaxial's surface, with `h` the distance from `pov` to `(x, y, z)` along the `los`, all in `meter`, conventionally. Raises: `TriaxialError` - Invalid `pov` or `pov` inside the tri-/biaxial or invalid `los` or `los` points outside or away from the tri-/biaxial. `TypeError` - Invalid `tri_biax`, `ellipsoid` or `datum`. See Also: Class pygeodesy3.Los, functions pygeodesy.tyr3d and pygeodesy.hartzell and lookAtSpheroid and "Satellite Line-of-Sight Intersection with Earth".

### hausdorff_ (model, target, both=False, early=True, seed=None, units='', distance=None, point=<function _point at 0x7fbe888d7bd0>) |
Compute the `directed` or `symmetric` Hausdorff distance between 2 sets of points with or without early breaking and random sampling. Arguments: `model` - First set of points (`LatLon`[], `Numpy2LatLon`[], `Tuple2LatLon`[] or `other`[]). `target` - Second set of points (`LatLon`[], `Numpy2LatLon`[], `Tuple2LatLon`[] or `other`[]). `both` - Return the `directed` (forward only) or the `symmetric` (combined forward and reverse) `Hausdorff` distance (`bool`). `early` - Enable or disable early breaking (`bool`). `seed` - Random sampling seed (`any`) or `None`, `0` or `False` for no random sampling. `units` - Optional, the distance units (`Unit` or `str`). `distance` - Callable returning the distance between a `model` and `target` point (signature `(point1, point2)`). `point` - Callable returning the `model` or `target` point suitable for `distance` (signature `(point)`). Returns: A Hausdorff6Tuple`(hd, i, j, mn, md, units)`. Raises: `HausdorffError` - Insufficient number of `model` or `target` points. `TypeError` - If `distance` or `point` is not callable.

### haversine (lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) |
Compute the distance between two (spherical) points using the Haversine formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as `radius`). Raises: `TypeError` - Invalid `radius`. See Also: Distance between two (spherical) points, functions cosineLaw, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, flatLocal/hubeny, flatPolar, thomas and vincentys and methods Ellipsoid.distance2, `LatLon.distanceTo*` and `LatLon.equirectangularTo`. Note: See note at function vincentys_.

### haversine_ (phi2, phi1, lam21) |
Compute the angular distance between two (spherical) points using the Haversine formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). Returns: Angular distance (`radians`). See Also: Functions haversine, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, euclidean_, flatLocal_/hubeny_, flatPolar_, thomas_ and vincentys_. Note: See note at function vincentys_.

### heightOf (angle, distance, radius=6371008.771415) |
Determine the height above the (spherical) earth' surface after traveling along a straight line at a given tilt. Arguments: `angle` - Tilt angle above horizontal (`degrees`). `distance` - Distance along the line (`meter` or same units as `radius`). `radius` - Optional mean earth radius (`meter`). Returns: Height (`meter`, same units as `distance` and `radius`). Raises: `ValueError` - Invalid `angle`, `distance` or `radius`. See Also: MultiDop geog_lib.GeogBeamHt (Shapiro et al. 2009, JTECH and Potvin et al. 2012, JTECH).

### heightOrthometric (h_ll, N) |
Get the orthometric height H, the height above the geoid, earth surface. Arguments: `h_ll` - The height above the ellipsoid (`meter`) or an ellipsoidal location (`LatLon` with a `height` or `h` attribute). `N` - The geoid height (`meter`), the height of the geoid above the ellipsoid at the same `h_ll` location. Returns: Orthometric height `H = h - N` (`meter`, same units as `h` and `N`). See Also: Ellipsoid, Geoid, and Othometric Heights, page 6 and module pygeodesy.geoids.

### horizon (height, radius=6371008.771415, refraction=False) |
Determine the distance to the horizon from a given altitude above the (spherical) earth. Arguments: `height` - Altitude (`meter` or same units as `radius`). `radius` - Optional mean earth radius (`meter`). `refraction` - Consider atmospheric refraction (`bool`). Returns: Distance (`meter`, same units as `height` and `radius`). Raises: `ValueError` - Invalid `height` or `radius`. See Also: Distance to horizon.

### hstr (height, prec=2, fmt='%+.*f', ints=False, m='') |
Return a string for the height value. Arguments: `height` - Height value (`float`). `prec` - The `float` precision, number of decimal digits (0..9). Trailing zero decimals are stripped if `prec` is positive, but kept for negative `prec` values. `fmt` - Optional `float` format (`letter`). `ints` - Optionally, remove the decimal dot for `int` values (`bool`). `m` - Optional unit of the height (`str`).

### hubeny (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True, wrap=False) |
Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `scaled` - Scale prime_vertical by `cos(phi)` (`bool`), see method pygeodesy.Ellipsoid.roc2_. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as the `datum`'s ellipsoid axes). Raises: `TypeError` - Invalid `datum`. Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude. See Also: Functions flatLocal_ or hubeny_, cosineLaw, flatPolar, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, haversine, thomas, vincentys, method Ellipsoid.distance2 and local, flat earth approximation.

### hubeny_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, scaled=True) |
Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `scaled` - Scale prime_vertical by `cos(phi)` (`bool`), see method pygeodesy.Ellipsoid.roc2_. Returns: Angular distance (`radians`). Raises: `TypeError` - Invalid `datum`. Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude. See Also: Functions flatLocal or hubeny, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatPolar_, euclidean_, haversine_, thomas_ and vincentys_ and local, flat earth approximation.

### hypot1 (x) |
Compute the norm sqrt(1 + x**2). Arguments: `x` - Argument (`scalar` or Fsum or Fsum2Tuple). Returns: Norm (`float`).

### hypot2 (x, y) |
Compute the squared norm x**2 + y**2. Arguments: `x` - X (`scalar` or Fsum or Fsum2Tuple). `y` - Y (`scalar` or Fsum or Fsum2Tuple). Returns: `x**2 + y**2` (`float`).

### hypot2_ (*xs) |
Compute the squared norm `fsum(x**2 for x in xs)`. Arguments: `xs` - Components (each `scalar` or an Fsum or Fsum2Tuple instance), all positional. Returns: Squared norm (`float`). See Also: Class Fpowers for further details.

### hypot_ (*xs) |
Compute the norm sqrt(sum(x**2 for x in xs)). Similar to Python 3.8+ n-dimension math.hypot, but exceptions, `nan` and `infinite` values are handled differently. Arguments: `xs` - X arguments (`scalar`s), all positional. Returns: Norm (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `ValueError` - Invalid or no `xs` values. Note: The Python 3.8+ Euclidian distance math.dist between 2 n-dimensional points p1 and p2 can be computed as hypot_(*((c1 - c2) for c1, c2 in zip(p1, p2))), provided p1 and p2 have the same, non-zero length n.

### instr (inst, *args, **kwds) |
Return the string representation of an instantiation. Arguments: `inst` - The instance (any `type`). `args` - Optional positional arguments. `kwds` - Optional keyword arguments. Returns: Representation (`str`).

### int1s (x) |
Count the number of 1-bits in an `int`, unsigned. Note: `int1s(-x) == int1s(abs(x))`.

### intersection2 (lat1, lon1, bearing1, lat2, lon2, bearing2, datum=None, wrap=False, small=100000.0) |
Conveniently compute the intersection of two lines each defined by a (geodetic) point and a bearing from North, using either ... 1) vector3d.intersection3d3 for `small` distances (below 100 Km or about 0.88 degrees) or if no `datum` is specified, or ... 2) sphericalTrigonometry.intersection for a spherical `datum` or a `scalar datum` representing the earth radius, conventionally in `meter` or ... 3) sphericalNvector.intersection if `datum` is a negative `scalar`, (negative) earth radius, conventionally in `meter` or ... 4) ellipsoidalKarney.intersection3 for an ellipsoidal `datum` and if Karney's geographiclib is installed, otherwise ... 5) ellipsoidalExact.intersection3, provided `datum` is ellipsoidal. Arguments: `lat1` - Latitude of the first point (`degrees`). `lon1` - Longitude of the first point (`degrees`). `bearing1` - Bearing at the first point (compass `degrees`). `lat2` - Latitude of the second point (`degrees`). `lon2` - Longitude of the second point (`degrees`). `bearing2` - Bearing at the second point (compass `degrees`). `datum` - Optional datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) or `scalar` earth radius (`meter`, same units as `radius1` and `radius2`) or `None`. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). `small` - Upper limit for small distances (`meter`). Returns: A LatLon2Tuple`(lat, lon)` with the lat- and longitude of the intersection point. Raises: `IntersectionError` - Ambiguous or infinite intersection or colinear, parallel or otherwise non-intersecting lines. `TypeError` - Invalid `datum`. `UnitError` - Invalid `lat1`, `lon1`, `bearing1`, `lat2`, `lon2` or `bearing2`. See Also: Method RhumbLine.intersection2. Note: The returned intersections may be near-antipodal.

### intersection3d3 (start1, end1, start2, end2, eps=2.220446049250313e-16, useZ=True, **Vector_and_kwds) |
Compute the intersection point of two (2- or 3-D) lines, each defined by two points or by a point and a bearing. Arguments: `start1` - Start point of the first line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `end1` - End point of the first line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`) or the bearing at `start1` (compass `degrees`). `start2` - Start point of the second line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `end2` - End point of the second line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`) or the bearing at `start2` (Ccompass `degrees`). `eps` - Tolerance for skew line distance and length (`EPS`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). `Vector_and_kwds` - Optional class `Vector=None` to return the intersection points and optional, additional `Vector` keyword arguments, otherwise `start1`'s (sub-)class. Returns: An Intersection3Tuple`(point, outside1, outside2)` with `point` an instance of `Vector` or `start1`'s (sub-)class. Raises: `IntersectionError` - Invalid, skew, non-co-planar or otherwise non-intersecting lines. Note: The `outside` values is `0` for lines specified by point and bearing. See Also: Line-line intersection and line-line distance, skew lines and point-line distance.

### intersections2 (center1, radius1, center2, radius2, sphere=True, **Vector_and_kwds) |
Compute the intersection of two spheres or circles, each defined by a (3-D) center point and a radius. Arguments: `center1` - Center of the first sphere or circle (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius1` - Radius of the first sphere or circle (same units as the `center1` coordinates). `center2` - Center of the second sphere or circle (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius2` - Radius of the second sphere or circle (same units as the `center1` and `center2` coordinates). `sphere` - If `True` compute the center and radius of the intersection of two spheres. If `False`, ignore the `z`-component and compute the intersection of two circles (`bool`). `Vector_and_kwds` - Optional class `Vector=None` to return the intersection points and optional, additional `Vector` keyword arguments, otherwise `center1`'s (sub-)class. Returns: If `sphere is True`, a 2-tuple of the `center` and `radius` of the intersection of the spheres. For abutting circles, `radius` is `0.0` and `center` is the radical center. If `sphere is False`, a 2-tuple with the two intersection points of the circles. For abutting circles, both points are the same instance, aka the radical center. Raises: `IntersectionError` - Concentric, invalid or non-intersecting spheres or circles. `TypeError` - Invalid `center1` or `center2`. `UnitError` - Invalid `radius1` or `radius2`. See Also: Sphere-Sphere and Circle-Circle Intersection.

### isBoolean (obj) |
Check for `Boolean` composites. Arguments: `obj` - The object (any `type`). Returns: `True` if `obj` is BooleanFHP, BooleanGH or some other composite, `False` otherwise.

### isCartesian (obj, ellipsoidal=None) |
Is `obj`ect some `Cartesian`? Arguments: `obj` - The object (any `type`). `ellipsoidal` - If `None`, return the type of any `Cartesian`, if `True`, only an ellipsoidal `Cartesian type` or if `False`, only a spherical `Cartesian type`. Returns: `type(obj` if a `Cartesian` of the required type, `False` if a `Cartesian` of an other type or {None} otherwise.

### isDEPRECATED (obj) |
Is `obj`ect a `DEPRECATED` class, method or function? Returns: `True` if `DEPRECATED`, {False} if not or `None` if undetermined.

### isError (exc) |
Check a (caught) exception. Arguments: `exc` - The exception C({Exception}). Returns: `True` if `exc` is a `pygeodesy` error, `False` if `exc` is a standard Python error of `None` if neither.

### isLatLon (obj, ellipsoidal=None) |
Is `obj`ect some `LatLon`? Arguments: `obj` - The object (any `type`). `ellipsoidal` - If `None`, return the type of any `LatLon`, if `True`, only an ellipsoidal `LatLon type` or if `False`, only a spherical `LatLon type`. Returns: `type(obj` if a `LatLon` of the required type, `False` if a `LatLon` of an other type or {None} otherwise.

### isNumpy2 (obj) |
Check for a `Numpy2LatLon` points wrapper. Arguments: `obj` - The object (any `type`). Returns: `True` if `obj` is a `Numpy2LatLon` instance, `False` otherwise.

### isNvector (obj, ellipsoidal=None) |
Is `obj`ect some `Nvector`? Arguments: `obj` - The object (any `type`). `ellipsoidal` - If `None`, return the type of any `Nvector`, if `True`, only an ellipsoidal `Nvector type` or if `False`, only a spherical `Nvector type`. Returns: `type(obj` if an `Nvector` of the required type, `False` if an `Nvector` of an other type or {None} otherwise.

### isPoints2 (obj) |
Check for a `LatLon2psxy` points wrapper. Arguments: `obj` - The object (any `type`). Returns: `True` if `obj` is a `LatLon2psxy` instance, `False` otherwise.

### isTuple2 (obj) |
Check for a `Tuple2LatLon` points wrapper. Arguments: `obj` - The object (any). Returns: `True` if `obj` is a `Tuple2LatLon` instance, `False` otherwise.

### isantipode (lat1, lon1, lat2, lon2, eps=2.220446049250313e-16) |
Check whether two points are antipodal, on diametrically opposite sides of the earth. Arguments: `lat1` - Latitude of one point (`degrees`). `lon1` - Longitude of one point (`degrees`). `lat2` - Latitude of the other point (`degrees`). `lon2` - Longitude of the other point (`degrees`). `eps` - Tolerance for near-equality (`degrees`). Returns: `True` if points are antipodal within the `eps` tolerance, `False` otherwise. See Also: Functions isantipode_ and antipode.

### isantipode_ (phi1, lam1, phi2, lam2, eps=2.220446049250313e-16) |
Check whether two points are antipodal, on diametrically opposite sides of the earth. Arguments: `phi1` - Latitude of one point (`radians`). `lam1` - Longitude of one point (`radians`). `phi2` - Latitude of the other point (`radians`). `lam2` - Longitude of the other point (`radians`). `eps` - Tolerance for near-equality (`radians`). Returns: `True` if points are antipodal within the `eps` tolerance, `False` otherwise. See Also: Functions isantipode and antipode_.

### isbool (obj) |
Is `obj`ect a `bool`ean? Arguments: `obj` - The object (any `type`). Returns: `True` if `bool`ean, `False` otherwise.

### isclockwise (points, adjust=False, wrap=True) |
Determine the direction of a path or polygon. Arguments: `points` - The path or polygon points (`LatLon`[]). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: `True` if `points` are clockwise, `False` otherwise. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - The `points` enclose a pole or zero area.

### iscolinearWith (point, point1, point2, eps=2.220446049250313e-16, useZ=True) |
Check whether a point is colinear with two other (2- or 3-D) points. Arguments: `point` - The point (Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point1` - First point (Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point2` - Second point (Vector3d, `Vector3Tuple` or `Vector4Tuple`). `eps` - Tolerance (`scalar`), same units as `x`, `y` and `z`. `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: `True` if `point` is colinear `point1` and `point2`, `False` otherwise. Raises: `TypeError` - Invalid `point`, `point1` or `point2`. See Also: Function nearestOn.

### iscomplex (obj, both=False) |
Is `obj`ect a `complex` or complex literal `str`? Arguments: `obj` - The object (any `type`). `both` - If `True`, check complex `str` (`bool`). Returns: `True` if `complex`, `False` otherwise.

### isconvex (points, adjust=False, wrap=False) |
Determine whether a polygon is convex. Arguments: `points` - The polygon points (`LatLon`[]). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: `True` if `points` are convex, `False` otherwise. Raises: `CrossError` - Some `points` are colinear. `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`.

### isconvex_ (points, adjust=False, wrap=False) |
Determine whether a polygon is convex and clockwise. Arguments: `points` - The polygon points (`LatLon`[]). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: `+1` if `points` are convex clockwise, `-1` for convex counter-clockwise `points`, `0` otherwise. Raises: `CrossError` - Some `points` are colinear. `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`.

### isenclosedBy (point, points, wrap=False) |
Determine whether a point is enclosed by a polygon or composite. Arguments: `point` - The point (`LatLon` or 2-tuple `(lat, lon)`). `points` - The polygon points or clips (`LatLon`[], BooleanFHP or BooleanGH). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: `True` if the `point` is inside the polygon or composite, `False` otherwise. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - Invalid `point`, lat- or longitude. See Also: Functions pygeodesy.isconvex and pygeodesy.ispolar especially if the `points` may enclose a pole or wrap around the earth longitudinally, methods sphericalNvector.LatLon.isenclosedBy, sphericalTrigonometry.LatLon.isenclosedBy and MultiDop GeogContainPt (Shapiro et.al. 2009, JTECH and Potvin et al. 2012, JTECH).

### isfinite (obj) |
Check a finite `scalar` or `complex` value. Arguments: `obj` - Value (`scalar` or `complex`). Returns: `False` if `obj` is `INF`, `NINF` or `NAN`, `True` otherwise. Raises: `TypeError` - Non-scalar and non-complex `obj`.

### isfloat (obj, both=False) |
Is `obj`ect a `float` or float literal `str`? Arguments: `obj` - The object (any `type`). `both` - If `True`, check float `str` (`bool`). Returns: `True` if `float`, `False` otherwise.

### isinstanceof (obj, *Classes) |
Is `obj`ect an instance of one of the `Classes`? Arguments: `obj` - The object (any `type`). `Classes` - One or more classes (`Class`). Returns: `type(obj` if one of the `Classes`, `None` otherwise.

### isint (obj, both=False) |
Is `obj`ect an `int` or integer `float` value? Arguments: `obj` - The object (any `type`). `both` - If `True`, check `float` and Fsum type and value (`bool`). Returns: `True` if `int` or integer `float` or Fsum, `False` otherwise. Note: Both `isint(True)` and `isint(False)` return `False` (and no longer `True`).

### isint0 (obj, both=False) |
Check for INT0 or `int(0)` value. Arguments: `obj` - The object (any `type`). `both` - If `true`, also check `float(0)` (`bool`). Returns: `True` if `obj` is INT0, `int(0)` or `float(0)`, `False` otherwise.

### isiterable (obj) |
Is `obj`ect `iterable`? Arguments: `obj` - The object (any `type`). Returns: `True` if `iterable`, `False` otherwise.

### isiterablen (obj) |
Is `obj`ect `iterable` and has `len`gth? Arguments: `obj` - The object (any `type`). Returns: `True` if `iterable` with `len`gth, `False` otherwise.

### islistuple (obj, minum=0) |
Is `obj`ect a `list` or `tuple` with non-zero length? Arguments: `obj` - The object (any `type`). `minum` - Minimal `len` required C({int}). Returns: `True` if a `list` or `tuple` with `len` at least `minum`, `False` otherwise.

### isnear0 (x, eps0=4.930380657631324e-32) |
Is `x` near zero within a tolerance? Arguments: `x` - Value (`scalar`). `eps0` - Near-zero tolerance (`EPS0`). Returns: `True` if `abs(x) < eps0`, `False` otherwise. See Also: Function isnon0.

### isnear1 (x, eps1=4.930380657631324e-32) |
Is `x` near one within a tolerance? Arguments: `x` - Value (`scalar`). `eps1` - Near-one tolerance (`EPS0`). Returns: `isnear0(x - 1, eps0=eps1)`. See Also: Function isnear0.

### isnear90 (x, eps90=4.930380657631324e-32) |
Is `x` near 90 within a tolerance? Arguments: `x` - Value (`scalar`). `eps90` - Near-90 tolerance (`EPS0`). Returns: `isnear0(x - 90, eps0=eps90)`. See Also: Function isnear0.

### isneg0 (x) |
Check for NEG0, negative `0.0`. Arguments: `x` - Value (`scalar`). Returns: `True` if `x` is `NEG0` or `-0.0`, `False` otherwise.

### isninf (x) |
Check for NINF, negative `INF`. Arguments: `x` - Value (`scalar`). Returns: `True` if `x` is `NINF` or `-inf`, `False` otherwise.

### isnon0 (x, eps0=4.930380657631324e-32) |
Is `x` non-zero with a tolerance? Arguments: `x` - Value (`scalar`). `eps0` - Non-zero tolerance (`EPS0`). Returns: `True` if `abs(x) > eps0`, `False` otherwise. See Also: Function isnear0.

### isnormal (lat, lon, eps=0) |
Check whether `lat` and `lon` are within their respective normal range in `degrees`. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `eps` - Optional tolerance `degrees`). Returns: `True` if `(abs(lat) + eps) <= 90` and `(abs(lon) + eps) <= 180`, `False` othwerwise. See Also: Functions isnormal_ and normal.

### isnormal_ (phi, lam, eps=0) |
Check whether `phi` and `lam` are within their respective normal range in `radians`. Arguments: `phi` - Latitude (`radians`). `lam` - Longitude (`radians`). `eps` - Optional tolerance `radians`). Returns: `True` if `(abs(phi) + eps) <= PI/2` and `(abs(lam) + eps) <= PI`, `False` othwerwise. See Also: Functions isnormal and normal_.

### isodd (x) |
Is `x` odd? Arguments: `x` - Value (`scalar`). Returns: `True` if odd, `False` otherwise.

### ispolar (points, wrap=False) |
Check whether a polygon encloses a pole. Arguments: `points` - The polygon points (`LatLon`[]). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: `True` if the polygon encloses a pole, `False` otherwise. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon` or don't have `bearingTo2`, `initialBearingTo` and `finalBearingTo` methods.

### isscalar (obj, both=False) |
Is `obj`ect an `int` or integer `float` value? Arguments: `obj` - The object (any `type`). `both` - If `True`, check Fsum. Returns: `True` if `int`, `float` or Fsum with zero residual, `False` otherwise.

### issequence (obj, *excls) |
Is `obj`ect some sequence type? Arguments: `obj` - The object (any `type`). `excls` - Classes to exclude (`type`), all positional. Returns: `True` if a sequence, `False` otherwise. Note: Excluding `tuple` implies excluding `namedtuple`.

### isstr (obj) |
Is `obj`ect some string type? Arguments: `obj` - The object (any `type`). Returns: `True` if a `str`, `bytes`, ..., `False` otherwise.

### issubclassof (Sub, *Supers) |
Is `Sub` a class and sub-class of some other class(es)? Arguments: `Sub` - The sub-class (`Class`). `Supers` - One or more C(super) classes (`Class`). Returns: `True` if a sub-class of any `Supers`, `False` if not (`bool`) or `None` if not a class or if no `Supers` are given or none of those are a class.

### itemsorted (adict, *items_args, **asorted_reverse) |
Return the items of `adict` sorted alphabetically, case-insensitively and in ascending order. Arguments: `items_args` - Optional positional argument(s) for method `adict.items(B*{items_args})`. `asorted_reverse` - Use `asorted=False` for alphabetical, case-sensitive sorting and `reverse=True` for sorting in `descending` order.

### iterNumpy2 (obj) |
Iterate over Numpy2 wrappers or other sequences exceeding the threshold. Arguments: `obj` - Points array, list, sequence, set, etc. (any). Returns: `True` do, `False` don't iterate.

### iterNumpy2over (n=None) |
Get or set the iterNumpy2 threshold. Arguments: `n` - Optional, new threshold (`int`). Returns: Previous threshold (`int`). Raises: `ValueError` - Invalid `n`.

### km2m (km) |
Convert kilo meter to meter (m). Arguments: `km` - Value in kilo meter (`scalar`). Returns: Value in meter (`float`). Raises: `ValueError` - Invalid `km`.

### latDMS (deg, form=`'``dms``'`, prec=None, sep='', **s_D_M_S) |
Convert latitude to a string, optionally suffixed with N or S. Arguments: `deg` - Latitude to be formatted (`scalar degrees`). `form` - Format specifier for `deg` (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F_D60, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F_D60_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F_D60__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. `sep` - Separator between degrees, minutes, seconds, suffix (`str`). `s_D_M_S` - Optional keyword arguments `s_D=str`, `s_M=str` `s_S=str` and `s_DMS=True` to override any or cancel all DMS symbols, defaults S_DEG, S_MIN respectively S_SEC. Returns: Degrees in the specified form (`str`). See Also: Functions pygeodesy.toDMS and pygeodesy.lonDMS.

### latlon2n_xyz (lat, lon, **name) |
Convert lat-, longitude to `n-vector` (normal to the earth's surface) X, Y and Z components. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `name` - Optional `name=NN` (`str`). Returns: A Vector3Tuple`(x, y, z)`. See Also: Function philam2n_xyz. Note: These are `n-vector` x, y and z components, NOT geocentric ECEF x, y and z coordinates!

### latlonDMS (lls, **m_form_prec_sep_s_D_M_S) |
Convert one or more `LatLon` instances to strings. Arguments: `lls` - Single (`LatLon`) or list, sequence, tuple, etc. (`LatLon`s). `m_form_prec_sep_s_D_M_S` - Optional keyword arguments `meter`, `format`, `precision`, `s_D`, `s_M`, `s_S`, `s_DMS` and DEPRECATED `sep=None`, see method `LatLon.toStr` and functions pygeodesy.latDMS and pygeodesy.lonDMS for more details. Returns: A `tuple` of `str`s if `lls` is a list, sequence, tuple, etc. of `LatLon`s or a single `str` if `lls` is a single `LatLon`. See Also: Functions pygeodesy.latlonDMS_, pygeodesy.latDMS, pygeodesy.lonDMS and pygeodesy.toDMS and method `LatLon.toStr`. Note: Keyword argument `sep=None` to join a `str`ing from the returned `tuple` has been DEPRECATED, use `sep.join(latlonDMS_(...))` instead.

### latlonDMS_ (*lls, **m_form_prec_sep_s_D_M_S) |
Convert one or more `LatLon` instances to strings. Arguments: `lls` - The instances (`LatLon`s), all positional arguments. `m_form_prec_sep_s_D_M_S` - Optional keyword arguments `meter`, `format`, `precision`, `s_D`, `s_M`, `s_S`, `s_DMS` and DEPRECATED `sep=None`, see method `LatLon.toStr` and functions pygeodesy.latDMS and pygeodesy.lonDMS for more details. Returns: A `tuple` of `str`s if 2 or more `LatLon` instances or a single `str` if only a single `LatLon` instance is given in `lls`. See Also: Functions pygeodesy.latlonDMS, pygeodesy.latDMS and pygeodesy.lonDMS and pygeodesy.toDMS and method `LatLon.toStr`. Note: Keyword argument `sep=None` to join a `str`ing from the returned `tuple` has been DEPRECATED, use `sep.join(latlonDMS_(...))` instead.

### len2 (items) |
Make built-in function `len` work for generators, iterators, etc. since those can only be started exactly once. Arguments: `items` - Generator, iterator, list, range, tuple, etc. Returns: 2-Tuple `(n, items)` of the number of items (`int`) and the items (`list` or `tuple`).

### limiterrors (raiser=None) |
Get/set the throwing of LimitErrors. Arguments: `raiser` - Choose `True` to raise or `False` to ignore LimitError exceptions. Use `None` to leave the setting unchanged. Returns: Previous setting (`bool`).

### lonDMS (deg, form=`'``dms``'`, prec=None, sep='', **s_D_M_S) |
Convert longitude to a string, optionally suffixed with E or W. Arguments: `deg` - Longitude to be formatted (`scalar degrees`). `form` - Format specifier for `deg` (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F_D60, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F_D60_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F_D60__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. `sep` - Separator between degrees, minutes, seconds, suffix (`str`). `s_D_M_S` - Optional keyword arguments `s_D=str`, `s_M=str` `s_S=str` and `s_DMS=True` to override any or cancel all DMS symbols, defaults S_DEG, S_MIN respectively S_SEC. Returns: Degrees in the specified form (`str`). See Also: Functions pygeodesy.toDMS and pygeodesy.latDMS.

### lrstrip (txt, lrpairs=`{``'``(``'``:` `'``)``'``,` `'``<``'``:` `'``>``'``,` `'``[``'``:` `'``]``'``,` `'``{``'``:` `'``}``'``}`) |
Left- and right-strip parentheses, brackets, etc. from a string. Arguments: `txt` - String to be stripped (`str`). `lrpairs` - Parentheses, etc. to remove (`dict` of one or several `(Left, Right)` pairs). Returns: Stripped `txt` (`str`).

### luneOf (lon1, lon2, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds) |
Generate an ellipsoidal or spherical lune-shaped path or polygon. Arguments: `lon1` - Left longitude (`degrees90`). `lon2` - Right longitude (`degrees90`). `closed` - Optionally, close the path (`bool`). `LatLon` - Class to use (LatLon_). `LatLon_kwds` - Optional, additional `LatLon` keyword arguments. Returns: A tuple of 4 or 5 `LatLon` instances outlining the lune shape. See Also: Latitude-longitude quadrangle.

### m2NM (meter) |
Convert meter to nautical miles (NM). Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `NM` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2SM (meter) |
Convert meter to statute miles (SM). Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `SM` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2chain (meter) |
Convert meter to UK chains. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `chains` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2degrees (distance, radius=6371008.771415, lat=0) |
Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. Arguments: `distance` - Distance (`meter`, same units as `radius`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, an Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Angle (`degrees`) or `INF` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `distance`, `radius` or `lat`. See Also: Function m2radians and degrees2m.

### m2fathom (meter) |
Convert meter to Imperial fathoms. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `fathoms` (`float`). Raises: `ValueError` - Invalid `meter`. See Also: Function m2toise, Fathom and Klafter.

### m2ft (meter, usurvey=False, pied=False, fuss=False) |
Convert meter to International, US Survey, French or or German feet (`ft`). Arguments: `meter` - Value in meter (`scalar`). `usurvey` - If `True`, convert to US Survey foot else ... `pied` - If `True`, convert to French pied-du-Roi else ... `fuss` - If `True`, convert to German Fuss, otherwise to International foot. Returns: Value in `feet` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2furlong (meter) |
Convert meter to furlongs. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `furlongs` (`float`). Raises: `ValueError` - Invalid `meter`.

### m2km (meter) |
Convert meter to kilo meter (Km). Arguments: `meter` - Value in meter (`scalar`). Returns: Value in Km (`float`). Raises: `ValueError` - Invalid `meter`.

### m2radians (distance, radius=6371008.771415, lat=0) |
Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. Arguments: `distance` - Distance (`meter`, same units as `radius`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, an Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Angle (`radians`) or `INF` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `distance`, `radius` or `lat`. See Also: Function m2degrees and radians2m.

### m2toise (meter) |
Convert meter to French toises. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `toises` (`float`). Raises: `ValueError` - Invalid `meter`. See Also: Function m2fathom.

### m2yard (meter) |
Convert meter to UK yards. Arguments: `meter` - Value in meter (`scalar`). Returns: Value in `yards` (`float`). Raises: `ValueError` - Invalid `meter`.

### machine() |
Return standard `platform.machine`, but distinguishing Intel native from Intel emulation on Apple Silicon (on macOS only). Returns: Machine `'arm64'` for Apple Silicon native, `'x86_64'` for Intel native, `"arm64_x86_64"` for Intel emulation, etc. (`str` with `comma`s replaced by `underscore`s).

### map1 (fun1, *xs) |
Call a single-argument function to each `xs` and return a `tuple` of results. Arguments: `fun1` - 1-Arg function (`callable`). `xs` - Arguments (`any positional`). Returns: Function results (`tuple`).

### map2 (fun, *xs) |
Like Python's `map` but returning a `tuple` of results. Unlike Python 2's built-in `map`, Python 3+ `map` returns a `map` object, an iterator-like object which generates the results only once. Converting the `map` object to a tuple maintains the Python 2 behavior. Arguments: `fun` - Function (`callable`). `xs` - Arguments (`all positional`). Returns: Function results (`tuple`).

### meeus2 (point1, point2, point3, circum=False, useZ=True) |
Return the radius and Meeus' Type of the smallest circle through or containing three (2- or 3-D) points. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `circum` - If `True` return the `circumradius` and `circumcenter` always, overriding Meeus' Type II case (`bool`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: Meeus2Tuple`(radius, Type)`, with `Type` the `circumcenter` iff `circum=True`. Raises: `IntersectionError` - Near-coincident or -colinear points, iff `circum=True`. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Functions pygeodesy.circum3 and pygeodesy.circum4_ and Meeus, J. Astronomical Algorithms, 2nd Ed. 1998, page 127ff, circumradius and circumcircle.

### modulename (clas, prefixed=None) |
Return the class name optionally prefixed with the module name. Arguments: `clas` - The class (any `class`). `prefixed` - Include the module name (`bool`), see function `classnaming`. Returns: The `class`'s `[module.]class` name (`str`).

### n2e2 (n) |
Return `e2`, the 1st eccentricity squared for a given 3rd flattening. Arguments: `n` - The 3rd flattening (-1 <= `scalar` < 1). Returns: The signed, (1st) eccentricity squared (`float` or NINF), 4 * n / (1 + n)**2. Note: The result is positive for oblate, negative for prolate or `0` for near-spherical ellipsoids. See Also: Flattening.

### n2f (n) |
Return `f`, the flattening for a given 3rd flattening. Arguments: `n` - The 3rd flattening (-1 <= `scalar` < 1). Returns: The flattening (`scalar` or NINF), 2 * n / (1 + n). See Also: Eccentricity conversions and Flattening.

### n2f_ (n) |
Return `f_`, the inverse flattening for a given 3rd flattening. Arguments: `n` - The 3rd flattening (-1 <= `scalar` < 1). Returns: The inverse flattening (`scalar` or `0`), 1 / f. See Also: n2f and f2f_.

### n_xyz2latlon (x, y, z, **name) |
Convert `n-vector` components to lat- and longitude in `degrees`. Arguments: `x` - X component (`scalar`). `y` - Y component (`scalar`). `z` - Z component (`scalar`). `name` - Optional `name=NN` (`str`). Returns: A LatLon2Tuple`(lat, lon)`. See Also: Function n_xyz2philam.

### n_xyz2philam (x, y, z, **name) |
Convert `n-vector` components to lat- and longitude in `radians`. Arguments: `x` - X component (`scalar`). `y` - Y component (`scalar`). `z` - Z component (`scalar`). `name` - Optional `name=NN` (`str`). Returns: A PhiLam2Tuple`(phi, lam)`. See Also: Function n_xyz2latlon.

### nameof (inst) |
Get the name of an instance. Arguments: `inst` - The object (any `type`). Returns: The instance' name (`str`) or `""`.

### nearestOn (point, point1, point2, within=True, useZ=True, Vector=None, **Vector_kwds) |
Locate the point between two points closest to a reference (2- or 3-D). Arguments: `point` - Reference point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point1` - Start point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `point2` - End point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `within` - If `True` return the closest point between both given points, otherwise the closest point on the extended line through both points (`bool`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). `Vector` - Class to return closest point (`Cartesian`, Vector3d or `Vector3Tuple`) or `None`. `Vector_kwds` - Optional, additional `Vector` keyword arguments, ignored if `Vector is None`. Returns: Closest point, either `point1` or `point2` or an instance of the `point`'s (sub-)class or `Vector` if not `None`. Raises: `TypeError` - Invalid `point`, `point1` or `point2`. See Also: 3-D Point-Line Distance, `Cartesian` and `LatLon` methods `nearestOn`, method sphericalTrigonometry.LatLon.nearestOn3 and function sphericalTrigonometry.nearestOn3.

### nearestOn5 (point, points, closed=False, wrap=False, adjust=True, limit=9, **LatLon_and_kwds) |
Locate the point on a path or polygon closest to a reference point. The closest point on each polygon edge is either the nearest of that edge's end points or a point in between. Arguments: `point` - The reference point (`LatLon`). `points` - The path or polygon points (`LatLon`[]). `closed` - Optionally, close the path or polygon (`bool`). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). `adjust` - See function pygeodesy.equirectangular4 (`bool`). `limit` - See function pygeodesy.equirectangular4 (`degrees`), default `9 degrees` is about `1,000 Kmeter` (for mean spherical earth radius R_KM). `LatLon_and_kwds` - Optional, `LatLon=None` class to use for the closest point and additional `LatLon` keyword arguments, ignored if `LatLon is None` or not given. Returns: A NearestOn3Tuple`(closest, distance, angle)` with the {closest} point (`LatLon`) or if `LatLon is None`, a NearestOn5Tuple`(lat, lon, distance, angle, height)`. The `distance` is the pygeodesy.equirectangular distance between the `closest` and reference `point` in `degrees`. The `angle` from the `point` to the `closest` is in compass `degrees`, like function pygeodesy.compassAngle. Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. Note: Distances are approximated by function pygeodesy.equirectangular4. For more accuracy use one of the `LatLon.nearestOn6` methods. See Also: Function pygeodesy.degrees2m.

### nearestOn6 (point, points, closed=False, useZ=True, **Vector_and_kwds) |
Locate the point on a path or polygon closest to a reference point. The closest point on each polygon edge is either the nearest of that edge's end points or a point in between. Arguments: `point` - Reference point (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `points` - The path or polygon points (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`[]). `closed` - Optionally, close the path or polygon (`bool`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). `Vector_and_kwds` - Optional class `Vector=None` to return the closest point and optional, additional `Vector` keyword arguments, otherwise `point`'s (sub-)class. Returns: A NearestOn6Tuple`(closest, distance, fi, j, start, end)` with the `closest`, the `start` and the `end` point each an instance of the `Vector` keyword argument of if {Vector=None} or not specified, an instance of the reference `point`'s (sub-)class. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Non-cartesian `point` and `points`. Note: Distances measured with method Vector3d.equirectangular. For geodetic distances use function nearestOn5 or one of the `LatLon.nearestOn6` methods.

### neg (x, neg0=None) |
Negate `x` and optionally, negate `0.0` and `-0.0`. Arguments: `neg0` - Defines the return value for zero `x`: if `None` return `0.0`, if `True` return `NEG0 if x=0.0` and `0.0 if x=NEG0` or if `False` return `x` as-is (`bool` or `None`). Returns: `-x if x else 0.0, NEG0 or x`.

### neg_ (*xs) |
Negate all `xs` with neg. Returns: A `map(neg, xs)`.

### norm2 (x, y) |
Normalize a 2-dimensional vector. Arguments: `x` - X component (`scalar`). `y` - Y component (`scalar`). Returns: 2-Tuple `(x, y)`, normalized. Raises: `ValueError` - Invalid `x` or `y` or zero norm.

### normDMS (strDMS, norm=None, **s_D_M_S) |
Normalize all degrees, minutes and seconds (DMS) symbols in a string to the default symbols S_DEG, S_MIN, S_SEC. Arguments: `strDMS` - Original DMS string (`str`). `norm` - Optional replacement symbol (`str`) or `None` for the default DMS symbols). Use `norm=""` to remove all DMS symbols. `s_D_M_S` - Optional, alternate DMS symbols `s_D=str`, `s_M=str`, `s_S=str` and/or `s_R=str` for radians, each to be replaced by `norm`. Returns: Normalized DMS (`str`).

### norm_ (*xs) |
Normalize all n-dimensional vector components. Arguments: `xs` - Components (`scalar`s), all positional. Returns: Yield each component, normalized. Raises: `ValueError` - Invalid or insufficent `xs` or zero norm.

### normal (lat, lon, **name) |
Normalize a lat- and longitude pair in `degrees`. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `name` - Optional, overriding `name="normal"` (`str`). Returns: LatLon2Tuple`(lat, lon)` with `abs(lat) <= 90` and `abs(lon) <= 180`. See Also: Functions normal_ and isnormal.

### normal_ (phi, lam, **name) |
Normalize a lat- and longitude pair in `radians`. Arguments: `phi` - Latitude (`radians`). `lam` - Longitude (`radians`). `name` - Optional, overriding `name="normal_"` (`str`). Returns: PhiLam2Tuple`(phi, lam)` with `abs(phi) <= PI/2` and `abs(lam) <= PI`. See Also: Functions normal and isnormal_.

### notImplemented (inst, *args, **kwds) |
Raise a `NotImplementedError` for a missing instance method or property or for a missing caller feature. Arguments: `inst` - Caller instance (`any`) or `None` for function. `args` - Method or property positional arguments (any `type`s). `kwds` - Method or property keyword arguments (any `type`s), except `callername=NN`, `underOK=False` and `up=2`.

### notOverloaded (inst, *args, **kwds) |
Raise an `AssertionError` for a method or property not overloaded. Arguments: `inst` - Instance (`any`). `args` - Method or property positional arguments (any `type`s). `kwds` - Method or property keyword arguments (any `type`s), except `callername=NN`, `underOK=False` and `up=2`.

### opposing (bearing1, bearing2, margin=90.0) |
Compare the direction of two bearings given in `degrees`. Arguments: `bearing1` - First bearing (compass `degrees`). `bearing2` - Second bearing (compass `degrees`). `margin` - Optional, interior angle bracket (`degrees`). Returns: `True` if both bearings point in opposite, `False` if in similar or `None` if in perpendicular directions. See Also: Function opposing_.

### opposing_ (radians1, radians2, margin=1.5707963267948966) |
Compare the direction of two bearings given in `radians`. Arguments: `radians1` - First bearing (`radians`). `radians2` - Second bearing (`radians`). `margin` - Optional, interior angle bracket (`radians`). Returns: `True` if both bearings point in opposite, `False` if in similar or `None` if in perpendicular directions. See Also: Function opposing.

### pairs (items, prec=6, fmt='F', ints=False, sep='=') |
Convert items to name=value strings, with `float`s handled like fstr. Arguments: `items` - Name-value pairs (`dict` or 2-{tuple}s of any `type`s). `prec` - The `float` precision, number of decimal digits (0..9). Trailing zero decimals are stripped if `prec` is positive, but kept for negative `prec` values. `fmt` - Optional `float` format (`letter`). `ints` - Optionally, remove the decimal dot for `int` values (`bool`). `sep` - Separator joining names and values (`str`). Returns: A `tuple(sep.join(t) for t in items))` of `str`s.

### parse3d (str3d, sep=',', Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds) |
Parse an `"x, y, z"` string. Arguments: `str3d` - X, y and z values (`str`). `sep` - Optional separator (`str`). `Vector` - Optional class (Vector3d). `Vector_kwds` - Optional `Vector` keyword arguments, ignored if `Vector is None`. Returns: A `Vector` instance or if `Vector is None`, a named Vector3Tuple`(x, y, z)`. Raises: `VectorError` - Invalid `str3d`.

### parse3llh (strllh, height=0, sep=',', clipLat=90, clipLon=180, wrap=False, **s_D_M_S) |
Parse a string `"lat, lon [, h]"` representing lat-, longitude in `degrees` and optional height in `meter`. The lat- and longitude value must be separated by a separator character. If height is present it must follow, separated by another separator. The lat- and longitude values may be swapped, provided at least one ends with the proper compass point. Arguments: `strllh` - Latitude, longitude[, height] (`str`, ...). `height` - Optional, default height (`meter`) or `None`. `sep` - Optional separator between `"lat lon [h] suffix"` (`str`). `clipLat` - Limit latitude to range `-/+clipLat` (`degrees`). `clipLon` - Limit longitude to range `-/+clipLon` (`degrees`). `wrap` - If `True`, wrap or normalize the lat- and longitude, overriding `clipLat` and `clipLon` (`bool`). `s_D_M_S` - Optional, alternate symbol for degrees `s_D=str`, minutes `s_M=str` and/or seconds `s_S=str`. Returns: A LatLon3Tuple`(lat, lon, height)` in `degrees`, `degrees` and `float`. Raises: `RangeError` - Lat- or longitude value of `strllh` outside the valid `-/+clipLat` or `-/+clipLon` range and rangerrors is `True`. `ValueError` - Invalid `strllh` or `height`. Note: See the Notes at function parseDMS. See Also: Functions pygeodesy.parseDDDMMSS, pygeodesy.parseDMS, pygeodesy.parseDMS2 and pygeodesy.toDMS.

### parseDDDMMSS (strDDDMMSS, suffix=`'``NSEW``'`, sep='', clip=0, sexagecimal=False) |
Parse a lat- or longitude represention forms as [D]DDMMSS in degrees. Arguments: `strDDDMMSS` - Degrees in any of several forms (`str`) and types (`float`, `int`, other). `suffix` - Optional, valid compass points (`str`, `tuple`). `sep` - Optional separator between "[D]DD", "MM", "SS", `suffix` (S_SEP). `clip` - Optionally, limit value to range `-/+clip` (`degrees`). `sexagecimal` - If `True`, convert `"D.MMSS"` or `float(D.MMSS)` to `base-60` "MM" and "SS" digits. See `form`s F_D60, F_D60_ and F_D60__. Returns: Degrees (`float`). Raises: `ParseError` - Invalid `strDDDMMSS` or `clip` or the form of `strDDDMMSS` is incompatible with the suffixed or `suffix` compass point. `RangeError` - Value of `strDDDMMSS` outside the valid `-/+clip` range and rangerrors is `True`. Notes: Type `str` values "[D]DD", "[D]DDMM", "[D]DDMMSS" and "[D]DD.MMSS" for `strDDDMMSS` are parsed properly only if either unsigned and suffixed with a valid, compatible, `cardinal` compassPoint or signed or unsigned, unsuffixed and with keyword argument `suffix`="NS", `suffix`="EW" or a compatible compassPoint. Unlike function parseDMS, type `float`, `int` and other non-`str` `strDDDMMSS` values are interpreted as `form` [D]DDMMSS or [D]DD.MMSS. For example, `int(1230)` is returned as 12.5 and not 1230.0 degrees. However, `int(345)` is considered `form` "DDD" 345 and not "DDMM" 0345, unless `suffix` specifies the compass point. Also, `float(15.0523)` is returned as 15.0523 decimal degrees and not 15°5′23″ sexagecimal. To consider the latter, use `float(15.0523)` or `"15.0523"` and specify the keyword argument `sexagecimal=True`. See Also: Functions pygeodesy.parseDMS, pygeodesy.parseDMS2 and pygeodesy.parse3llh.

### parseDMS (strDMS, suffix=`'``NSEW``'`, sep='', clip=0, **s_D_M_S) |
Parse a lat- or longitude representation in `degrees`. This is very flexible on formats, allowing signed decimal degrees, degrees and minutes or degrees minutes and seconds optionally suffixed by a cardinal compass point. A variety of symbols, separators and suffixes are accepted, for example "3°37′09″W". Minutes and seconds may be omitted. Arguments: `strDMS` - Degrees in any of several forms (`str`) and types (`float`, `int`, other). `suffix` - Optional, valid compass points (`str`, `tuple`). `sep` - Optional separator between deg°, min′, sec″, `suffix` (`''`). `clip` - Optionally, limit value to range `-/+clip` (`degrees`). `s_D_M_S` - Optional, alternate symbol for degrees `s_D=str`, minutes `s_M=str` and/or seconds `s_S=str`. Returns: Degrees (`float`). Raises: `ParseError` - Invalid `strDMS` or `clip`. `RangeError` - Value of `strDMS` outside the valid `-/+clip` range and rangerrors is `True`. Note: Unlike function parseDDDMMSS, type `float`, `int` and other non-`str` `strDMS` values are considered decimal (and not sexagecimal) degrees. For example, `int(1230)` is returned as 1230.0 and not as 12.5 degrees and `float(345)` as 345.0 and not as 3.75 degrees! See Also: Functions pygeodesy.parseDDDMMSS, pygeodesy.parseDMS2, pygeodesy.parse3llh and pygeodesy.toDMS.

### parseDMS2 (strLat, strLon, sep='', clipLat=90, clipLon=180, wrap=False, **s_D_M_S) |
Parse a lat- and a longitude representions `"lat, lon"` in `degrees`. Arguments: `strLat` - Latitude in any of several forms (`str` or `degrees`). `strLon` - Longitude in any of several forms (`str` or `degrees`). `sep` - Optional separator between deg°, min′, sec″, suffix (`''`). `clipLat` - Limit latitude to range `-/+clipLat` (`degrees`). `clipLon` - Limit longitude to range `-/+clipLon` (`degrees`). `wrap` - If `True`, wrap or normalize the lat- and longitude, overriding `clipLat` and `clipLon` (`bool`). `s_D_M_S` - Optional, alternate symbol for degrees `s_D=str`, minutes `s_M=str` and/or seconds `s_S=str`. Returns: A LatLon2Tuple`(lat, lon)` in `degrees`. Raises: `ParseError` - Invalid `strLat` or `strLon`. `RangeError` - Value of `strLat` or `strLon` outside the valid `-/+clipLat` or `-/+clipLon` range and rangerrors is `True`. Note: See the Notes at function parseDMS. See Also: Functions pygeodesy.parseDDDMMSS, pygeodesy.parseDMS, pygeodesy.parse3llh and pygeodesy.toDMS.

### parseETM5 (strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, **name) |
Parse a string representing a UTM coordinate, consisting of `"zone[band] hemisphere easting northing"`. Arguments: `strUTM` - A UTM coordinate (`str`). `datum` - Optional datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `Etm` - Optional class to return the UTM coordinate (Etm) or `None`. `falsed` - Both easting and northing are `falsed` (`bool`). `name` - Optional `Etm` `name=NN` (`str`). Returns: The UTM coordinate (`Etm`) or if `Etm is None`, a UtmUps5Tuple`(zone, hemipole, easting, northing, band)` with `hemipole` is the hemisphere `'N'|'S'`. Raises: `ETMError` - Invalid `strUTM`. `TypeError` - Invalid or near-spherical `datum`.

### parseMGRS (strMGRS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, **name) |
Parse a string representing a MGRS grid reference, consisting of `"[zone]Band, EN, easting, northing"`. Arguments: `strMGRS` - MGRS grid reference (`str`). `datum` - Optional datum to use (Datum). `Mgrs` - Optional class to return the MGRS grid reference (Mgrs) or `None`. `name` - Optional `Mgrs` `name=NN` (`str`). Returns: The MGRS grid reference as `Mgrs` or if `Mgrs is None` as an Mgrs4Tuple`(zone, EN, easting, northing)`. Raises: `MGRSError` - Invalid `strMGRS`.

### parseOSGR (strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, **name_Osgr_kwds) |
Parse a string representing an OS Grid Reference, consisting of `"[GD] easting northing"`. Accepts standard OS Grid References like "SU 387 148", with or without whitespace separators, from 2- up to 22-digit references, or all-numeric, comma-separated references in meters, for example "438700,114800". Arguments: `strOSGR` - An OSGR coordinate (`str`). `Osgr` - Optional class to return the OSGR coordinate (Osgr) or `None`. `name_Osgr_kwds` - Optional `name=NN` (`str`) and optional, additional `Osgr` keyword arguments, ignored if `Osgr is None`. Returns: An (`Osgr`) instance or if `Osgr is None`, an EasNor2Tuple`(easting, northing)`. Raises: `OSGRError` - Invalid `strOSGR`.

### parseRad (strRad, suffix=`'``NSEW``'`, clip=0) |
Parse a string representing angle in `radians`. Arguments: `strRad` - Degrees in any of several forms (`str` or `radians`). `suffix` - Optional, valid compass points (`str`, `tuple`). `clip` - Optionally, limit value to range `-/+clip` (`radians`). Returns: Radians (`float`). Raises: `ParseError` - Invalid `strRad` or `clip`. `RangeError` - Value of `strRad` outside the valid `-/+clip` range and rangerrors is `True`.

### parseUPS5 (strUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Ups=<class 'pygeodesy.ups.Ups'>, falsed=True, **name) |
Parse a string representing a UPS coordinate, consisting of `"[zone][band] pole easting northing"` where `zone` is pseudo zone `"00"|"0"|""` and `band` is `'A'|'B'|'Y'|'Z'|''`. Arguments: `strUPS` - A UPS coordinate (`str`). `datum` - Optional datum to use (Datum). `Ups` - Optional class to return the UPS coordinate (Ups) or `None`. `falsed` - If `True`, both `easting` and `northing` are falsed (`bool`). `name` - Optional `Ups` `name=NN` (`str`). Returns: The UPS coordinate (`Ups`) or if `Ups is None`, a UtmUps5Tuple`(zone, hemipole, easting, northing, band)`. The `hemipole` is the `'N'|'S'` pole, the UPS projection top/center. Raises: `UPSError` - Invalid `strUPS`.

### parseUTM5 (strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, **name) |
Parse a string representing a UTM coordinate, consisting of `"zone[band] hemisphere easting northing"`. Arguments: `strUTM` - A UTM coordinate (`str`). `datum` - Optional datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `Utm` - Optional class to return the UTM coordinate (Utm) or `None`. `falsed` - Use `falsed=False` if both easting and northing are not falsed (`bool`). `name` - Optional `name=NN` (`str`). Returns: The UTM coordinate (`Utm`) or if `Utm is None`, a UtmUps5Tuple`(zone, hemipole, easting, northing, band)`. The `hemipole` is the `'N'|'S'` hemisphere. Raises: `UTMError` - Invalid `strUTM`. `TypeError` - Invalid `datum`.

### parseUTMUPS5 (strUTMUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, **name) |
Parse a string representing a UTM or UPS coordinate, consisting of `"zone[band] hemisphere/pole easting northing"`. Arguments: `strUTMUPS` - A UTM or UPS coordinate (`str`). `datum` - Optional datum to use (Datum). `Utm` - Optional class to return the UTM coordinate (Utm) or `None`. `Ups` - Optional class to return the UPS coordinate (Ups) or `None`. `name` - Optional `Utm` or `Ups` `name=NN` (`str`). Returns: The UTM or UPS instance (`Utm` or `Ups`) or a UtmUps5Tuple`(zone, hemipole, easting, northing, band)` if `Utm` respectively `Ups` or both are `None`. The `hemipole` is `'N'|'S'`, the UTM hemisphere or UPS pole, the UPS projection top/center. Raises: `UTMUPSError` - Invalid `strUTMUPS`. See Also: Functions pygeodesy.parseUTM5 and pygeodesy.parseUPS5.

### parseWM (strWM, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, **name) |
Parse a string `"e n [r]"` representing a WM coordinate, consisting of easting, northing and an optional radius. Arguments: `strWM` - A WM coordinate (`str`). `radius` - Optional earth radius (`meter`), needed in case `strWM` doesn't include `r`. `Wm` - Optional class to return the WM coordinate (Wm) or `None`. `name` - Optional `name=NN` (`str`). Returns: The WM coordinate (`Wm`) or if `Wm is None`, an EasNorRadius3Tuple`(easting, northing, radius)`. Raises: `WebMercatorError` - Invalid `strWM`.

### perimeterOf (points, closed=False, adjust=True, radius=6371008.771415, wrap=True) |
Approximate the perimeter of a path, polygon. or composite. Arguments: `points` - The path or polygon points or clips (`LatLon`[], BooleanFHP or BooleanGH). `closed` - Optionally, close the path or polygon (`bool`). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `radius` - Mean earth radius (`meter`). `wrap` - If `True`, wrap or normalize and unroll the `points` (`bool`). Returns: Approximate perimeter (`meter`, same units as `radius`). Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - Invalid `radius` or `closed=False` with `points` a composite. Note: This perimeter is based on the pygeodesy.equirectangular4 distance approximation and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. See Also: Functions sphericalTrigonometry.perimeterOf and ellipsoidalKarney.perimeterOf.

### philam2n_xyz (phi, lam, **name) |
Convert lat-, longitude to `n-vector` (normal to the earth's surface) X, Y and Z components. Arguments: `phi` - Latitude (`radians`). `lam` - Longitude (`radians`). `name` - Optional name (`str`). Returns: A Vector3Tuple`(x, y, z)`. See Also: Function latlon2n_xyz. Note: These are `n-vector` x, y and z components, NOT geocentric ECEF x, y and z coordinates!

### pierlot (point1, point2, point3, alpha12, alpha23, useZ=False, eps=2.220446049250313e-16, **Clas_and_kwds) |
3-Point resection using Pierlot's method `ToTal` with approximate limits for the (pseudo-)singularities. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `alpha12` - Angle subtended from `point1` to `point2` or `alpha2 - alpha1` (`degrees`). `alpha23` - Angle subtended from `point2` to `point3` or `alpha3 - alpha2`(`degrees`). `useZ` - If `True`, interpolate the survey point's Z component, otherwise use `z=INT0` (`bool`). `eps` - Tolerance for `cot` (pseudo-)singularities (`float`). `Clas_and_kwds` - Optional class `Clas=point1.classof` to return the survey point with optionally other `Clas` keyword arguments to instantiate the survey point. Returns: The survey (or robot) point, an instance of `Clas` or `point1`'s (sub-)class. Raises: `ResectionError` - Near-coincident, -colinear or -concyclic points or invalid `alpha12` or `alpha23` or non-positive `eps`. `TypeError` - Invalid `point1`, `point2` or `point3`. Note: Typically, `point1`, `point2` and `point3` are ordered by angle, modulo 360, counter-clockwise. See Also: Pierlot's C function triangulationPierlot, V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation Algorithm for Mobile Robot Positioning", Vincent Pierlot, Marc Van Droogenbroeck, "18 Triangulation Algorithms for 2D Positioning (also known as the Resection Problem)" and functions pierlotx, cassini, collins5 and tienstra7.

### pierlotx (point1, point2, point3, alpha1, alpha2, alpha3, useZ=False, **Clas_and_kwds) |
3-Point resection using Pierlot's method `ToTal` with exact limits for the (pseudo-)singularities. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `alpha1` - Angle at `point1` (`degrees`, counter-clockwise). `alpha2` - Angle at `point2` (`degrees`, counter-clockwise). `alpha3` - Angle at `point3` (`degrees`, counter-clockwise). `useZ` - If `True`, interpolate the survey point's Z component, otherwise use `z=INT0` (`bool`). `Clas_and_kwds` - Optional class `Clas=point1.classof` to return the survey point with optionally other `Clas` keyword arguments to instantiate the survey point. Returns: The survey (or robot) point, an instance of `Clas` or `point1`'s (sub-)class. Raises: `ResectionError` - Near-coincident, -colinear or -concyclic points or invalid `alpha1`, `alpha2` or `alpha3`. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Pierlot's C function triangulationPierlot2 and function pierlot, cassini, collins5 and tienstra7.

### points2 (points, closed=True, base=None, Error=<class 'pygeodesy.errors.PointsError'>) |
Check a path or polygon represented by points. Arguments: `points` - The path or polygon points (`LatLon`[]) `closed` - Optionally, consider the polygon closed, ignoring any duplicate or closing final `points` (`bool`). `base` - Optionally, check all `points` against this base class, if `None` don't check. `Error` - Exception to raise (`ValueError`). Returns: A Points2Tuple`(number, points)` with the number of points and the points `list` or `tuple`. Raises: `PointsError` - Insufficient number of `points`. `TypeError` - Some `points` are not `base` compatible or composite `points`.

### precision (form, prec=None) |
Set the default precison for a given F_ form. Arguments: `form` - F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F_D60, F__E, F__F, F__G or F_RAD (`str`). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. Returns: Previous precision for the `form` (`int`). Raises: `ValueError` - Invalid `form` or `prec` or `prec` outside range `-9..+9`.

### print_ (*args, **nl_nt_prec_prefix__end_file_flush_sep__kwds) |
Python 3+ `print`-like formatting and printing. Arguments: `args` - Values to be converted to `str` and joined by `sep`, all positional. See Also: Function printf for further details.

### printf (fmt, *args, **nl_nt_prec_prefix__end_file_flush_sep__kwds) |
`Printf-style` and Python 3+ `print`-like formatting and printing. Arguments: `fmt` - Printf-style format specification (`str`). `args` - Arguments to be formatted (any `type`, all positional). `nl_nt_prec_prefix__end_file_flush_sep__kwds` - Optional keyword arguments `nl=0` for the number of leading blank lines (`int`), `nt=0` the number of trailing blank lines (`int`), `prefix=NN` to be inserted before the formatted text (`str`) and Python 3+ `print` keyword arguments `end`, `sep`, `file` and `flush`. Any remaining `kwds` are `printf-style` name-value pairs to be formatted, iff no `args` are present using `prec=6` for the number of decimal digits (`int`). Returns: Number of bytes written.

### property_doc_ (doc) |
Decorator for a standard `property` with basic documentation. Arguments: `doc` - The property documentation (`str`). Example: >>>class Clas(object): >>> >>> @property_doc_("documentation text.") >>> def name(self): >>> ... >>> >>> @name.setter >>> def name(self, value): >>> ...

### quadOf (latS, lonW, latN, lonE, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds) |
Generate a quadrilateral path or polygon from two points. Arguments: `latS` - Souther-nmost latitude (`degrees90`). `lonW` - Western-most longitude (`degrees180`). `latN` - Norther-nmost latitude (`degrees90`). `lonE` - Eastern-most longitude (`degrees180`). `closed` - Optionally, close the path (`bool`). `LatLon` - Class to use (LatLon_). `LatLon_kwds` - Optional, additional `LatLon` keyword arguments. Returns: Return a tuple of 4 or 5 `LatLon` instances outlining the quadrilateral. See Also: Function boundsOf.

### radians2m (rad, radius=6371008.771415, lat=0) |
Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. Arguments: `rad` - The angle (`radians`). `radius` - Mean earth radius, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Distance (`meter`, same units as `radius` or equatorial and polar radii) or `0.0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `rad`, `radius` or `lat`. See Also: Function degrees2m and m2radians.

### radiansPI (deg) |
Convert and wrap degrees to radians [-PI..+PI]. Arguments: `deg` - Angle (`degrees`). Returns: Radians, wrapped (`radiansPI`)

### radiansPI2 (deg) |
Convert and wrap degrees to radians [0..+2PI). Arguments: `deg` - Angle (`degrees`). Returns: Radians, wrapped (`radiansPI2`)

### radiansPI_2 (deg) |
Convert and wrap degrees to radians [-3PI/2..+PI/2]. Arguments: `deg` - Angle (`degrees`). Returns: Radians, wrapped (`radiansPI_2`)

### radical2 (distance, radius1, radius2, **name) |
Compute the radical ratio and radical line of two intersecting circles. The radical line is perpendicular to the axis thru the centers of the circles at `(0, 0)` and `(distance, 0)`. Arguments: `distance` - Distance between the circle centers (`scalar`). `radius1` - Radius of the first circle (`scalar`). `radius2` - Radius of the second circle (`scalar`). `name` - Optional `name=NN` (`str`). Returns: A Radical2Tuple`(ratio, xline)` where `0.0 <= ratio <= 1.0` and `xline` is along the `distance`. Raises: `IntersectionError` - The `distance` exceeds the sum of `radius1` and `radius2`. `UnitError` - Invalid `distance`, `radius1` or `radius2`. See Also: Circle-Circle Intersection.

### radii11 (point1, point2, point3, useZ=True) |
Return the radii of the `In-`, Soddy and `Tangent` circles of a (2- or 3-D) triangle. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: Radii11Tuple`(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)`. Raises: `TriangleError` - Near-coincident or -colinear points. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Circumradius, Incircle, Soddy Circles and Tangent Circles.

### randomrangenerator (seed) |
Return a `seed`ed random range function generator. Arguments: `seed` - Initial, internal Random state (`hashable` or `None`). Returns: A function to generate random ranges. Note: Random with `seed is None` seeds from the current time or from a platform-specific randomness source, if available. Example:
    >>> rrange = randomrangenerator('R')
    >>> for r in rrange(n):
    >>>    ...  # r is random in 0..n-1

### rangerrors (raiser=None) |
Get/set the throwing of RangeErrors. Arguments: `raiser` - Choose `True` to raise or `False` to ignore RangeError exceptions. Use `None` to leave the setting unchanged. Returns: Previous setting (`bool`).

### reprs (objs, prec=6, fmt='F', ints=False) |
Convert objects to `repr` strings, with `float`s handled like fstr. Arguments: `objs` - List, sequence, tuple, etc. (any `type`s). `prec` - The `float` precision, number of decimal digits (0..9). Trailing zero decimals are stripped if `prec` is positive, but kept for negative `prec` values. `fmt` - Optional `float` format (`letter`). `ints` - Optionally, remove the decimal dot for `int` values (`bool`). Returns: A `tuple(map(fstr|repr, objs))` of `str`s.

### rtp2xyz (r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds) |
Convert spherical, polar `(r, theta, phi)` to cartesian `(x, y, z)` coordinates. Arguments: `theta` - Inclination `theta` (`degrees` with respect to the positive z-axis), required if `r_rtp` is `scalar`, ignored otherwise. `phi` - Azimuthal angle `phi` (`degrees`), like `theta`. See Also: Function rtp2xyz_ for further details.

### rtp2xyz_ (r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds) |
Convert spherical, polar `(r, theta, phi)` to cartesian `(x, y, z)` coordinates. Arguments: `r_rtp` - Radial distance (`scalar`, conventially `meter`) or a previous RadiusThetaPhi3Tuple instance. `theta` - Inclination `theta` (`radians` with respect to the positive z-axis), required if `r_rtp` is `scalar`, ignored otherwise. `phi` - Azimuthal angle `phi` (`radians`), like `theta`. `name_Cartesian_and_kwds` - Optional `name=NN` (`str`), a `Cartesian=None` class to return the coordinates and optional, additional `Cartesian` keyword arguments. Returns: A `Cartesian(x, y, z)` instance or if no `Cartesian` keyword argument is given a Vector3Tuple`(x, y, z)`, with `x`, `y` and `z` in the same units as radius `r`, `meter` conventionally. Raises: `TypeError` - Invalid `r_rtp`, `theta`, `phi` or `name_Cartesian_and_kwds` item. See Also: Physics convention (ISO 80000-2:2019), class RadiusThetaPhi3Tuple and functions rtp2xyz and xyz2rtp.

### signBit (x) |
Return `signbit(x)`, like C++. Returns: `True` if `x < 0` or `NEG0` (`bool`).

### signOf (x) |
Return sign of `x` as `int`. Returns: -1, 0 or +1 (`int`).

### simplify1 (points, distance=0.001, radius=6371008.771415, indices=False, **options) |
Basic simplification of a path of `LatLon` points. Eliminates any points closer together than the given distance tolerance. Arguments: `points` - Path points (`LatLon`[]). `distance` - Tolerance (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `indices` - If `True` return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function pygeodesy.equirectangular4. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `ValueError` - Tolerance `distance` or `radius` too small.

### simplifyRDP (points, distance=0.001, radius=6371008.771415, shortest=False, indices=False, **options) |
Ramer-Douglas-Peucker (RDP) simplification of a path of `LatLon` points. Eliminates any points too close together or closer to an edge than the given distance tolerance. This `RDP` method exhaustively searches for the point with the largest distance, resulting in worst-case complexity O(n**2) where n is the number of points. Arguments: `points` - Path points (`LatLon`[]). `distance` - Tolerance (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `shortest` - If `True` use the shortest otherwise the perpendicular distance (`bool`). `indices` - If `True` return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function pygeodesy.equirectangular4. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `ValueError` - Tolerance `distance` or `radius` too small.

### simplifyRDPm (points, distance=0.001, radius=6371008.771415, shortest=False, indices=False, **options) |
Modified Ramer-Douglas-Peucker (RDPm) simplification of a path of `LatLon` points. Eliminates any points too close together or closer to an edge than the given distance tolerance. This `RDPm` method stops at the first point farther than the given distance tolerance, significantly reducing the run time (but producing results different from the original `RDP` method). Arguments: `points` - Path points (`LatLon`[]). `distance` - Tolerance (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `shortest` - If `True` use the shortest otherwise the perpendicular distance (`bool`). `indices` - If `True` return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function pygeodesy.equirectangular4. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `ValueError` - Tolerance `distance` or `radius` too small.

### simplifyRW (points, pipe=0.001, radius=6371008.771415, shortest=False, indices=False, **options) |
Reumann-Witkam (RW) simplification of a path of `LatLon` points. Eliminates any points too close together or within the given pipe tolerance along an edge. Arguments: `points` - Path points (`LatLon`[]). `pipe` - Pipe radius, half-width (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `shortest` - If `True` use the shortest otherwise the perpendicular distance (`bool`). `indices` - If `True` return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function pygeodesy.equirectangular4. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `ValueError` - Tolerance `pipe` or `radius` too small.

### simplifyVW (points, area=0.001, radius=6371008.771415, attr=None, indices=False, **options) |
Visvalingam-Whyatt (VW) simplification of a path of `LatLon` points. Eliminates any points too close together or with a triangular area not exceeding the given area tolerance squared. This `VW` method exhaustively searches for the single point with the smallest triangular area, resulting in worst-case complexity O(n**2) where n is the number of points. Arguments: `points` - Path points (`LatLon`[]). `area` - Tolerance (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `attr` - Optional, points attribute to save the area value (`str`). `indices` - If `True` return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function pygeodesy.equirectangular4. Returns: Simplified points (`LatLon`[]). Raises: `AttributeError` - If an `attr` is specified for Numpy2 `points`. `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `ValueError` - Tolerance `area` or `radius` too small.

### simplifyVWm (points, area=0.001, radius=6371008.771415, attr=None, indices=False, **options) |
Modified Visvalingam-Whyatt (VWm) simplification of a path of `LatLon` points. Eliminates any points too close together or with a triangular area not exceeding the given area tolerance squared. This `VWm` method removes all points with a triangular area below the tolerance in each iteration, significantly reducing the run time (but producing results different from the original `VW` method). Arguments: `points` - Path points (`LatLon`[]). `area` - Tolerance (`meter`, same units as `radius`). `radius` - Mean earth radius (`meter`). `attr` - Optional, points attribute to save the area value (`str`). `indices` - If `True` return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function pygeodesy.equirectangular4. Returns: Simplified points (`LatLon`[]). Raises: `AttributeError` - If an `attr` is specified for Numpy2 `points`. `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function pygeodesy.equirectangular4. `ValueError` - Tolerance `area` or `radius` too small.

### sincos2 (rad) |
Return the `sine` and `cosine` of an angle in `radians`. Arguments: `rad` - Angle (`radians`). Returns: 2-Tuple (`sin(rad)`, `cos(rad)`). See Also: GeographicLib function sincosd and C++ sincosd.

### sincos2_ (*rads) |
Return the `sine` and `cosine` of angle(s) in `radians`. Arguments: `rads` - One or more angles (`radians`). Returns: Yield the `sin(rad)` and `cos(rad)` for each angle. See Also: function sincos2.

### sincos2d (deg, **adeg) |
Return the `sine` and `cosine` of an angle in `degrees`. Arguments: `deg` - Angle (`degrees`). `adeg` - Optional correction (`degrees`). Returns: 2-Tuple (`sin(deg_)`, `cos(deg_)`, `deg_ = deg + adeg`). See Also: GeographicLib function sincosd and C++ sincosd.

### sincos2d_ (*degs) |
Return the `sine` and `cosine` of angle(s) in `degrees`. Arguments: `degs` - One or more angles (`degrees`). Returns: Yield the `sin(deg)` and `cos(deg)` for each angle. See Also: Function sincos2d.

### sincostan3 (rad) |
Return the `sine`, `cosine` and `tangent` of an angle in `radians`. Arguments: `rad` - Angle (`radians`). Returns: 3-Tuple (`sin(rad)`, `cos(rad)`, `tan(rad)`). See Also: Function sincos2.

### snellius3 (a, b, degC, alpha, beta) |
Snellius' surveying using Snellius Pothenot. Arguments: `a` - Length of the triangle side between corners `B` and `C` and opposite of triangle corner `A` (`scalar`, non-negative `meter`, conventionally). `b` - Length of the triangle side between corners `C` and `A` and opposite of triangle corner `B` (`scalar`, non-negative `meter`, conventionally). `degC` - Angle at triangle corner `C`, opposite triangle side `c` (non-negative `degrees`). `alpha` - Angle subtended by triangle side `b` (non-negative `degrees`). `beta` - Angle subtended by triangle side `a` (non-negative `degrees`). Returns: Survey3Tuple`(PA, PB, PC)` with distance from survey point `P` to each of the triangle corners `A`, `B` and `C`, same units as triangle sides `a`, `b` and `c`. Raises: `TriangleError` - Invalid `a`, `b` or `degC` or negative `alpha` or `beta`. See Also: Function wildberger3.

### soddy4 (point1, point2, point3, eps=8.881784197001252e-16, useZ=True) |
Return the radius and center of the `inner` Soddy circle of a (2- or 3-D) triangle. Arguments: `point1` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point2` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `point3` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `eps` - Tolerance for function pygeodesy.trilaterate3d2 if `useZ is True` otherwise pygeodesy.trilaterate2d2. `useZ` - If `True`, use the Z components, otherwise force `z=INT0` (`bool`). Returns: Soddy4Tuple`(radius, center, deltas, outer)`. The `center`, an instance of `point1`'s (sub-)class, is co-planar with the three given points. The `outer` Soddy radius may be `INF`. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10 and `useZ is True`. `IntersectionError` - Near-coincident or -colinear points or a trilateration or `numpy` issue. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Functions radii11 and circum3 and Soddy Circles.

### splice (iterable, n=2, **fill) |
Split an iterable into `n` slices. Arguments: `iterable` - Items to be spliced (`list`, `tuple`, ...). `n` - Number of slices to generate (`int`). `fill` - Optional fill value for missing items. Returns: A generator for each of `n` slices, iterable[i::n] for i=0..n. Raises: `TypeError` - Invalid `n`. Note: Each generated slice is a `tuple` or a `list`, the latter only if the `iterable` is a `list`. Example:
    >>> from pygeodesy import splice
    >>> a, b = splice(range(10))
    >>> a, b
    ((0, 2, 4, 6, 8), (1, 3, 5, 7, 9))
    >>> a, b, c = splice(range(10), n=3)
    >>> a, b, c
    ((0, 3, 6, 9), (1, 4, 7), (2, 5, 8))
    >>> a, b, c = splice(range(10), n=3, fill=-1)
    >>> a, b, c
    ((0, 3, 6, 9), (1, 4, 7, -1), (2, 5, 8, -1))
    >>> tuple(splice(list(range(9)), n=5))
    ([0, 5], [1, 6], [2, 7], [3, 8], [4])
    >>> splice(range(9), n=1)
    <generator object splice at 0x0...>

### sqrt0 (x, Error=None) |
Return the square root `sqrt(x)` iff `x >` EPS02, preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). `Error` - Error to raise for negative `x`. Returns: Square root (`float` or Fsum) or `0.0`. Raises: `TypeeError` - Invalid `x`. Note: Any `x <` EPS02 including `x < 0` returns `0.0`.

### sqrt3 (x) |
Return the square root, cubed sqrt(x)**3 or sqrt(x**3), preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). Returns: Square root cubed (`float` or Fsum). Raises: `TypeeError` - Invalid `x`. `ValueError` - Negative `x`. See Also: Functions cbrt and cbrt2.

### sqrt_a (h, b) |
Compute `a` side of a right-angled triangle from `sqrt(h**2 - b**2)`. Arguments: `h` - Hypotenuse or outer annulus radius (`scalar`). `b` - Triangle side or inner annulus radius (`scalar`). Returns: `copysign(a, h)` or `unsigned 0.0` (`float`). Raises: `TypeError` - Non-scalar `h` or `b`. `ValueError` - If `abs(h) < abs(b)`. See Also: Inner tangent chord d of an annulus and function annulus_area.

### strs (objs, prec=6, fmt='F', ints=False) |
Convert objects to `str` strings, with `float`s handled like fstr. Arguments: `objs` - List, sequence, tuple, etc. (any `type`s). `prec` - The `float` precision, number of decimal digits (0..9). Trailing zero decimals are stripped if `prec` is positive, but kept for negative `prec` values. `fmt` - Optional `float` format (`letter`). `ints` - Optionally, remove the decimal dot for `int` values (`bool`). Returns: A `tuple(map(fstr|str, objs))` of `str`s.

### tanPI_2_2 (rad) |
Compute the tangent of half angle, 90 degrees rotated. Arguments: `rad` - Angle (`radians`). Returns: tan((rad + PI/2) / 2) (`float`).

### tan_2 (rad, **semi) |
Compute the tangent of half angle. Arguments: `rad` - Angle (`radians`). `semi` - Angle or edge name and index for semi-circular error. Returns: tan(rad / 2) (`float`). Raises: `ValueError` - If `rad` is semi-circular and `semi` is given.

### tand (deg, **error_kwds) |
Return the `tangent` of an angle in `degrees`. Arguments: `deg` - Angle (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: `tan(deg)`. Raises: `ValueError` - If pygeodesy.isnear0`(cos(deg)`.

### tand_ (*degs, **error_kwds) |
Return the `tangent` of angle(s) in `degrees`. Arguments: `degs` - One or more angles (`degrees`). `error_kwds` - Error to raise (`ValueError`). Returns: Yield the `tan(deg)` for each angle. Raises: `ValueError` - See pygeodesy.tand.

### thomas (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, wrap=False) |
Compute the distance between two (ellipsoidal) points using Thomas' formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `datum` - Datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as the `datum`'s ellipsoid axes). Raises: `TypeError` - Invalid `datum`. See Also: Functions thomas_, cosineAndoyerLambert, cosineForsytheAndoyerLambert, cosineLaw, equirectangular, euclidean, flatLocal/hubeny, flatPolar, haversine, vincentys and method Ellipsoid.distance2.

### thomas_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`) |
Compute the angular distance between two (ellipsoidal) points using Thomas' formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). `datum` - Datum or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). Returns: Angular distance (`radians`). Raises: `TypeError` - Invalid `datum`. See Also: Functions thomas, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_ and vincentys_ and Geodesy-PHP.

### tienstra7 (pointA, pointB, pointC, alpha, beta=None, gamma=None, useZ=False, **Clas_and_kwds) |
3-Point resection using Tienstra's formula. Arguments: `pointA` - First point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `pointB` - Second point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `pointC` - Third point (`Cartesian`, Vector3d, `Vector3Tuple`, `Vector4Tuple` or `Vector2Tuple` if `useZ=False`). `alpha` - Angle subtended by triangle side `a` from `pointB` to `pointC` (`degrees`, non-negative). `beta` - Angle subtended by triangle side `b` from `pointA` to `pointC` (`degrees`, non-negative) or `None` if `gamma is not None`. `gamma` - Angle subtended by triangle side `c` from `pointA` to `pointB` (`degrees`, non-negative) or `None` if `beta is not None`. `useZ` - If `True`, use and interpolate the Z component, otherwise force `z=INT0` (`bool`). `Clas_and_kwds` - Optional class `Clas=pointA.classof` to return the survey point with optionally other `Clas` keyword arguments to instantiate the survey point. Returns: Tienstra7Tuple`(pointP, A, B, C, a, b, c)` with survey `pointP`, an instance of `Clas` or `pointA`'s (sub-)class, with triangle angles `A` at `pointA`, `B` at `pointB` and `C` at `pointC` in `degrees` and with triangle sides `a`, `b` and `c` in `meter`, conventionally. Raises: `ResectionError` - Near-coincident, -colinear or -concyclic points or sum of `alpha`, `beta` and `gamma` not `360` or negative `alpha`, `beta` or `gamma`. `TypeError` - Invalid `pointA`, `pointB` or `pointC`. Note: Points `pointA`, `pointB` and `pointC` are ordered clockwise. See Also: 3-Point Resection Solver, V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation...", 18 Triangulation Algorithms... and functions cassini, collins5, pierlot and pierlotx.

### toCss (latlon, cs0=None, height=None, Css=<class 'pygeodesy.css.Css'>, **name) |
Convert an (ellipsoidal) geodetic point to a Cassini-Soldner location. Arguments: `latlon` - Ellipsoidal point (`LatLon` or LatLon4Tuple). `cs0` - Optional, the Cassini-Soldner projection to use (CassiniSoldner). `height` - Optional height for the point, overriding the default height (`meter`). `Css` - Optional class to return the location (Css) or `None`. `name` - Optional `Css` `name=NN` (`str`). Returns: The Cassini-Soldner location (`Css`) or if `Css is None`, an EasNor3Tuple`(easting, northing, height)`. Raises: `CSSError` - Ellipsoidal mismatch of `latlon` and `cs0`. `ImportError` - Package geographiclib not installed or not found. `TypeError` - If `latlon` is not ellipsoidal.

### toDMS (deg, form=`'``dms``'`, prec=2, sep='', ddd=2, neg='-', pos='+', **s_D_M_S) |
Convert signed `degrees` to string, without suffix. Arguments: `deg` - Degrees to be formatted (`scalar degrees`). `form` - Format specifier for `deg` (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F_D60, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F_D60_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F_D60__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Number of decimal digits (0..9 or `None` for default). Trailing zero decimals are stripped for `prec` values of 1 and above, but kept for negative `prec`. `sep` - Separator between degrees, minutes, seconds, suffix (`str`). `ddd` - Number of digits for `deg`° (2 or 3). `neg` - Prefix for negative `deg` (`'-'`). `pos` - Prefix for positive `deg` and signed `form` (`'+'`). `s_D_M_S` - Optional keyword arguments `s_D=str`, `s_M=str` `s_S=str` and `s_DMS=True` to override any or cancel all DMS symbols, defaults S_DEG, S_MIN respectively S_SEC. See Notes below. Returns: Degrees in the specified form (`str`). Notes: The degrees, minutes and seconds (DMS) symbol can be overridden in this and other `*DMS` functions by using optional keyword argments `s_D="d"`, `s_M="'"` respectively `s_S='"'`. Using keyword argument `s_DMS`=None cancels all `DMS` symbols to `S_NUL=NN`. Sexagecimal format `F_D60` supports overridable pseudo-DMS symbols positioned at `"[D]DD<s_D>MM<s_M>SS<s_S>"` with defaults `s_D="."`, `s_M=sep` and `s_S=`pygeodesy.NN. Formats `F__E`, `F__F` and `F__G` can be extended with a `D`-only symbol if defined with keyword argument `s_D=str`. Likewise for `F_RAD` formats with keyword argument `s_R=str`. See Also: Function pygeodesy.degDMS

### toEtm8 (latlon, lon=None, datum=None, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, strict=True, zone=None, **name_cmoff) |
Convert a geodetic lat-/longitude to an ETM coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` instance. `lon` - Optional longitude (`degrees`), required if `latlon` is `degrees`, ignored otherwise. `datum` - Optional datum for the ETM coordinate, overriding `latlon`'s datum (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `Etm` - Optional class to return the ETM coordinate (Etm) or `None`. `falsed` - False both easting and northing (`bool`). `strict` - Restrict `lat` to UTM ranges (`bool`). `zone` - Optional UTM zone to enforce (`int` or `str`). `name_cmoff` - Optional `Etm` `name=NN` (`str`) and DEPRECATED keyword argument `cmoff=True` to offset the longitude from the zone's central meridian (`bool`), use `falsed` instead. Returns: The ETM coordinate as `Etm` or if `Etm is None` or not `falsed`, a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, gamma, scale)`. The `hemipole` is the `'N'|'S'` hemisphere. Raises: `ETMError` - No convergence transforming to ETM easting and northing. `ETMError` - Invalid `zone` or near-spherical or incompatible `datum` or `ellipsoid`. `RangeError` - If `lat` outside the valid UTM bands or if `lat` or `lon` outside the valid range and rangerrors is `True`. `TypeError` - Invalid or near-spherical `datum` or `latlon` not ellipsoidal. `ValueError` - The `lon` value is missing or `latlon` is invalid.

### toLcc (latlon, conic=Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0`...`, height=None, Lcc=<class 'pygeodesy.lcc.Lcc'>, **name_Lcc_kwds) |
Convert an (ellipsoidal) geodetic point to a Lambert location. Arguments: `latlon` - Ellipsoidal point (`LatLon`). `conic` - Optional Lambert projection to use (Conic). `height` - Optional height for the point, overriding the default height (`meter`). `Lcc` - Class to return the Lambert location (Lcc). `name_Lcc_kwds` - Optional `name=NN` (`str`) and optional, additional `Lcc` keyword arguments, ignored if `Lcc` is None. Returns: The Lambert location (Lcc) or if `Lcc is None`, an EasNor3Tuple`(easting, northing, height)`. Raises: `TypeError` - If `latlon` is not ellipsoidal.

### toMgrs (utmups, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, **name_Mgrs_kwds) |
Convert a UTM or UPS coordinate to an MGRS grid reference. Arguments: `utmups` - A UTM or UPS coordinate (Utm, Etm or Ups). `Mgrs` - Optional class to return the MGRS grid reference (Mgrs) or `None`. `name_Mgrs_kwds` - Optional `name=NN` (`str`) and optional, additional `Mgrs` keyword arguments, ignored if `Mgrs is None`. Returns: The MGRS grid reference as `Mgrs` or if `Mgrs is None` as an Mgrs6Tuple`(zone, EN, easting, northing, band, datum)`. Raises: `MGRSError` - Invalid `utmups`. `TypeError` - If `utmups` is not Utm, Etm nor Ups.

### toOsgr (latlon, lon=None, kTM=False, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Osgr=<class 'pygeodesy.osgr.Osgr'>, **prec_name_Osgr_kwds) |
Convert a lat-/longitude point to an OSGR coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Optional longitude in degrees (scalar or `None`). `kTM` - If `True` use Karney's Krüger method from module ktm, otherwise use the Ordnance Survey formulation (`bool`). `datum` - Optional datum to convert `lat, lon` from (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `Osgr` - Optional class to return the OSGR coordinate (Osgr) or `None`. `prec_name_Osgr_kwds` - Optional `name=NN` (`str`), optional truncate precision `prec=ndigits` and additional `Osgr` keyword arguments, ignored if `Osgr is None`. Returns: An (`Osgr`) instance or if `Osgr is None` an EasNor2Tuple`(easting, northing)`. Raises: `OSGRError` - Invalid `latlon` or `lon`. `TypeError` - Non-ellipsoidal `latlon` or invalid `datum`, `Osgr`, `Osgr_kwds` or conversion to `Datums.OSGB36` failed. Note: If isint`(prec)` both easting and northing are truncated to the given number of digits.

### toUps8 (latlon, lon=None, datum=None, Ups=<class 'pygeodesy.ups.Ups'>, pole='', falsed=True, strict=True, **name) |
Convert a lat-/longitude point to a UPS coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Optional longitude (`degrees`) or `None` if `latlon` is a `LatLon`. `datum` - Optional datum for this UPS coordinate, overriding `latlon`'s datum (`Datum`, Ellipsoid, Ellipsoid2 or a_f2Tuple). `Ups` - Optional class to return the UPS coordinate (Ups) or `None`. `pole` - Optional top/center of (stereographic) projection (`str`, `'N[orth]'` or `'S[outh]'`). `falsed` - If `True`, false both easting and northing (`bool`). `strict` - Restrict `lat` to UPS ranges (`bool`). `name` - Optional `Ups` `name=NN` (`str`). Returns: The UPS coordinate (`Ups`) or if `Ups is None`, a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, gamma, scale)` where `hemipole` is the `'N'|'S'` pole, the UPS projection top/center. Raises: `RangeError` - If `strict` and `lat` outside the valid UPS bands or if `lat` or `lon` outside the valid range and rangerrors is `True`. `TypeError` - If `latlon` is not ellipsoidal or if `datum` is invalid. `ValueError` - If `lon` value is missing or if `latlon` is invalid. See Also: Karney's C++ class UPS.

### toUtm8 (latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, strict=True, zone=None, **name_cmoff) |
Convert a lat-/longitude point to a UTM coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Longitude (`degrees`), required if `latlon` is `degrees`, ignored otherwise. `datum` - Optional datum for this UTM coordinate, overriding `latlon`'s datum (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `Utm` - Optional class to return the UTM coordinate (Utm) or `None`. `falsed` - If `True`, false both easting and northing (`bool`). `strict` - If `True`, restrict `lat` to UTM ranges (`bool`). `zone` - Optional UTM zone to enforce (`int` or `str`). `name_cmoff` - Optional `name=NN` (`str`) and DEPRECATED keyword argument `cmoff=True` to offset the longitude from the zone's central meridian (`bool`), use `falsed` instead. Returns: The UTM coordinate (`Utm`) or if `Utm is None` or `falsed is False`, a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, gamma, scale)` where `hemipole` is the `'N'|'S'` hemisphere. Raises: `RangeError` - If `lat` outside the valid UTM bands or if `lat` or `lon` outside the valid range and rangerrors is `True`. `TypeError` - Invalid `datum` or `latlon` not ellipsoidal. `UTMError` - Invalid `zone`. `ValueError` - If `lon` is missing or `latlon` is invalid. Note: Implements Karney’s method, using 8-th order Krüger series, giving results accurate to 5 nm (or better) for distances up to 3,900 Km from the central meridian.

### toUtmUps8 (latlon, lon=None, datum=None, falsed=True, Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, pole='', **name_cmoff) |
Convert a lat-/longitude point to a UTM or UPS coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Longitude (`degrees`), required if `latlon` is `degrees`, ignored otherwise. `datum` - Optional datum to use this UTM coordinate, overriding the `latlon`'s datum (`Datum`). `falsed` - If `True`, false both easting and northing (`bool`). `Utm` - Optional class to return the UTM coordinate (Utm) or `None`. `Ups` - Optional class to return the UPS coordinate (Ups) or `None`. `pole` - Optional top/center of UPS (stereographic) projection (`str`, `'N[orth]'` or `'S[outh]'`). `name_cmoff` - Optional `name=NN` (`str`) and DEPRECATED keyword argument `cmoff=True` to offset the longitude from the zone's central meridian (`bool`), use `falsed` instead and for UTM only. Returns: The UTM or UPS coordinate (`Utm` respectively `Ups`) or a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, gamma, scale)` if `Utm` respectively `Ups is None` or if `falsed is False`. Raises: `RangeError` - If `lat` outside the valid UTM or UPS bands or if `lat` or `lon` outside the valid range and rangerrors is `True`. `TypeError` - If `latlon` is not ellipsoidal or `lon` is missing or `datum` is invalid. `UTMUPSError` - UTM or UPS validation failed. `ValueError` - Invalid `lat` or `lon`. See Also: Functions pygeodesy.toUtm8 and pygeodesy.toUps8.

### toWm (latlon, lon=None, earth=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, **name_Wm_kwds_radius) |
Convert a lat-/longitude point to a WM coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal or spherical) geodetic `LatLon` point. `lon` - Optional longitude (`degrees` or `None`). `earth` - Earth radius (`meter`), datum or ellipsoid (Datum, a_f2Tuple, Ellipsoid or Ellipsoid2), overridden by `latlon`'s datum if present. `Wm` - Optional class to return the WM coordinate (Wm) or `None`. `name_Wm_kwds_radius` - Optional `name=NN` (`str`), optional, additional `Wm` keyword arguments, ignored if `Wm is None` and DEPRECATED keyword argument `radius=earth`, use `earth`. Returns: The WM coordinate (`Wm`) or if `Wm is None`, an EasNorRadius3Tuple`(easting, northing, radius)`. Raises: `ValueError` - If `earth` is invalid, if `lon` value is missing, if `latlon` is not scalar, or if `latlon` is beyond the valid WM range and rangerrrors is `True`.

### toise2m (toises) |
Convert French toises to meter. Arguments: `toises` - Value in toises (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `toises`. See Also: Function fathom2m.

### trfTransform0 (reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False) |
Get a Helmert transform to convert one `reframe` observed at `epoch` to an other `reframe2` at observed at `epoch2 or epoch`. Returns: A TransformXform instance, a `0-tuple` for unity, identity or `None` if no conversion exists. See Also: Function trfTransforms for futher details.

### trfTransforms (reframe, reframe2, epoch=None, epoch2=None, indirect=True, inverse=True, exhaust=False) |
Yield all Helmert transform to convert one `reframe` observed at `epoch` to an other `reframe2` at observed at `epoch2 or epoch`. Arguments: `reframe` - The frame to convert from (RefFrame or `str`). `reframe2` - The frame to convert to (RefFrame or `str`). `epoch` - Epoch to observe from (Epoch, `scalar` or `str`), otherwise `reframe`'s `epoch`. `epoch2` - Optional epoch to observe to (Epoch, `scalar` or `str`), otherwise `epoch`. `indirect` - If `True`, include transforms via one intermediate reframe, otherwise only direct `reframe` to `reframe2` transforms (`bool`). `inverse` - If `True`, include inverse, otherwise only forward transforms (`bool`). `exhaust` - If `True`, exhaustively generate all transforms, forward and inverse and via any number of intermediate reframes (`bool`). Returns: A TransformXform instance for each available conversion, without duplicates. Raises: `TRFError` - Invalid `reframe`, `reframe2`, `epoch` or `epoch2`. `TypeError` - Invalid `reframe` or `reframe2`.

### trfXform (reframe1, reframe2, epoch=None, xform=None, rates=None, raiser=True) |
Define a new Terrestrial Reference Frame (TRF) converter or get an existing one. Arguments: `reframe1` - Source frame (RefFrame or `str`), converting from. `reframe2` - Destination frame (RefFrame or `str`), converting to. `epoch` - Epoch, a fractional year (Epoch, `scalar` or `str`) or `None` for `reframe2`'s epoch. `xform` - Transform parameters (TRFXform7Tuple). `rates` - Rate parameters (TRFXform7Tuple), as `xform`, but in `units-per-year`. `raiser` - If `False`, do not raise an error if the converter exists, replace it (`bool`). Returns: The new TRF converter (TRFXform) or if no `epoch`, `xform` and `rates` are given, return the existing one (TRFXform) or `None` if not available. Raises: `TRFError` - Invalid `reframe1`, `reframe2`, `epoch`, `xform` or `rates` or the TRF converter already exists.

### triAngle (a, b, c) |
Compute one angle of a triangle. Arguments: `a` - Adjacent triangle side length (`scalar`, non-negative `meter`, conventionally). `b` - Adjacent triangle side length (`scalar`, non-negative `meter`, conventionally). `c` - Opposite triangle side length (`scalar`, non-negative `meter`, conventionally). Returns: Angle in `radians` at triangle corner `C`, opposite triangle side `c`. Raises: `TriangleError` - Invalid or negative `a`, `b` or `c`. See Also: Functions triAngle5 and triSide.

### triAngle5 (a, b, c) |
Compute the angles of a triangle. Arguments: `a` - Length of the triangle side opposite of triangle corner `A` (`scalar`, non-negative `meter`, conventionally). `b` - Length of the triangle side opposite of triangle corner `B` (`scalar`, non-negative `meter`, conventionally). `c` - Length of the triangle side opposite of triangle corner `C` (`scalar`, non-negative `meter`, conventionally). Returns: TriAngle5Tuple`(radA, radB, radC, rIn, area)` with angles `radA`, `radB` and `radC` at triangle corners `A`, `B` and `C`, all in `radians`, the `InCircle` radius `rIn` aka `inradius`, same units as triangle sides `a`, `b` and `c` and the triangle `area` in those same units squared. Raises: `TriangleError` - Invalid or negative `a`, `b` or `c`. See Also: Functions triAngle and triArea.

### triArea (a, b, c) |
Compute the area of a triangle using Heron's `stable` formula. Arguments: `a` - Length of the triangle side opposite of triangle corner `A` (`scalar`, non-negative `meter`, conventionally). `b` - Length of the triangle side opposite of triangle corner `B` (`scalar`, non-negative `meter`, conventionally). `c` - Length of the triangle side opposite of triangle corner `C` (`scalar`, non-negative `meter`, conventionally). Returns: The triangle area (`float`, conventionally `meter` or same units as `a`, `b` and `c` squared). Raises: `TriangleError` - Invalid or negative `a`, `b` or `c`.

### triSide (a, b, radC) |
Compute one side of a triangle. Arguments: `a` - Adjacent triangle side length (`scalar`, non-negative `meter`, conventionally). `b` - Adjacent triangle side length (`scalar`, non-negative `meter`, conventionally). `radC` - Angle included by sides `a` and `b`, opposite triangle side `c` (`radians`). Returns: Length of triangle side `c`, opposite triangle corner `C` and angle `radC`, same units as `a` and `b`. Raises: `TriangleError` - Invalid `a`, `b` or `radC`. See Also: Functions sqrt_a, triAngle, triSide2 and triSide4.

### triSide2 (b, c, radB) |
Compute a side and its opposite angle of a triangle. Arguments: `b` - Adjacent triangle side length (`scalar`, non-negative `meter`, conventionally). `c` - Adjacent triangle side length (`scalar`, non-negative `meter`, conventionally). `radB` - Angle included by sides `a` and `c`, opposite triangle side `b` (`radians`). Returns: TriSide2Tuple`(a, radA)` with triangle angle `radA` in `radians` and length of the opposite triangle side `a`, same units as `b` and `c`. Raises: `TriangleError` - Invalid `b` or `c` or either `b` or `radB` near zero. See Also: Functions sqrt_a, triSide and triSide4.

### triSide4 (radA, radB, c) |
Compute two sides and the height of a triangle. Arguments: `radA` - Angle at triangle corner `A`, opposite triangle side `a` (non-negative `radians`). `radB` - Angle at triangle corner `B`, opposite triangle side `b` (non-negative `radians`). `c` - Length of triangle side between triangle corners `A` and `B`, (`scalar`, non-negative `meter`, conventionally). Returns: TriSide4Tuple`(a, b, radC, d)` with triangle sides `a` and `b` and triangle height `d` perpendicular to triangle side `c`, all in the same units as `c` and interior angle `radC` in `radians` at triangle corner `C`, opposite triangle side `c`. Raises: `TriangleError` - Invalid or negative `radA`, `radB` or `c`. See Also: Triangulation, Surveying and functions sqrt_a, triSide and triSide2.

### trilaterate2d2 (x1, y1, radius1, x2, y2, radius2, x3, y3, radius3, eps=None, **Vector_and_kwds) |
Trilaterate three circles, each given as a (2-D) center and a radius. Arguments: `x1` - Center `x` coordinate of the 1st circle (`scalar`). `y1` - Center `y` coordinate of the 1st circle (`scalar`). `radius1` - Radius of the 1st circle (`scalar`). `x2` - Center `x` coordinate of the 2nd circle (`scalar`). `y2` - Center `y` coordinate of the 2nd circle (`scalar`). `radius2` - Radius of the 2nd circle (`scalar`). `x3` - Center `x` coordinate of the 3rd circle (`scalar`). `y3` - Center `y` coordinate of the 3rd circle (`scalar`). `radius3` - Radius of the 3rd circle (`scalar`). `eps` - Tolerance to check the trilaterated point delta on all 3 circles (`scalar`) or `None` for no checking. `Vector_and_kwds` - Optional class `Vector=None` to return the trilateration and optional, additional `Vector` keyword arguments, otherwise (Vector3d). Returns: Trilaterated point as `Vector(x, y, **Vector_kwds)` or Vector2Tuple`(x, y)` if `Vector is None`.. Raises: `IntersectionError` - No intersection, near-concentric or -colinear centers, trilateration failed some other way or the trilaterated point is off one circle by more than `eps`. `UnitError` - Invalid `radius1`, `radius2` or `radius3`. See Also: Issue #49, Find X location using 3 known (X,Y) location using trilateration and function pygeodesy.trilaterate3d2.

### trilaterate3d2 (center1, radius1, center2, radius2, center3, radius3, eps=2.220446049250313e-16, **Vector_and_kwds) |
Trilaterate three spheres, each given as a (3-D) center and a radius. Arguments: `center1` - Center of the 1st sphere (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius1` - Radius of the 1st sphere (same `units` as `x`, `y` and `z`). `center2` - Center of the 2nd sphere (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius2` - Radius of this sphere (same `units` as `x`, `y` and `z`). `center3` - Center of the 3rd sphere (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `radius3` - Radius of the 3rd sphere (same `units` as `x`, `y` and `z`). `eps` - Pertubation tolerance (`scalar`), same units as `x`, `y` and `z` or `None` for no pertubations. `Vector_and_kwds` - Optional class `Vector=None` to return the trilateration and optional, additional `Vector` keyword arguments, otherwise `center1`'s (sub-)class. Returns: 2-Tuple with two trilaterated points, each a `Vector` instance. Both points are the same instance if all three spheres abut/intersect in a single point. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10. `IntersectionError` - Near-concentric, -colinear, too distant or non-intersecting spheres. `NumPyError` - Some `numpy` issue. `TypeError` - Invalid `center1`, `center2` or `center3`. `UnitError` - Invalid `radius1`, `radius2` or `radius3`. See Also: Norrdine, A. An Algebraic Solution to the Multilateration Problem, the implementation and function pygeodesy.trilaterate2d2.

### truncate (x, ndigits=None) |
Truncate to the given number of digits. Arguments: `x` - Value to truncate (`scalar`). `ndigits` - Number of digits (`int`), aka precision. Returns: Truncated `x` (`float`). See Also: Python function `round`.

### tyr3d (tilt=0, yaw=0, roll=0, Vector=<class 'pygeodesy.vector3d.Vector3d'>, **name_Vector_kwds) |
Convert an attitude pose into a (3-D) direction vector. Arguments: `tilt` - Pitch, elevation from horizontal (`degrees`), negative down (clockwise rotation along and around the x-axis). `yaw` - Bearing, heading (compass `degrees360`), clockwise from North (counter-clockwise rotation along and around the z-axis). `roll` - Roll, bank (`degrees`), positive to the right and down (clockwise rotation along and around the y-axis). `Vector` - Class to return the direction vector (`Cartesian`, Vector3d or `Vector3Tuple`) or `None`. `name_Vector_kwds` - Optional `name=NN` (`str`) and optional, additional `Vector` keyword arguments, ignored if `Vector is None`. Returns: A named `Vector` instance or if `Vector is None`, a named Vector3Tuple`(x, y, z)`. Raises: `AttitudeError` - Invalid `tilt`, `yaw` or `roll`. `TypeError` - Invalid `Vector` or `name_Vector_kwds`. See Also: Yaw, pitch, and roll rotations and function pygeodesy.hartzell argument `los`, Line-Of-Sight.

### unroll180 (lon1, lon2, wrap=True) |
Unroll longitudinal delta and wrap longitude in degrees. Arguments: `lon1` - Start longitude (`degrees`). `lon2` - End longitude (`degrees`). `wrap` - If `True`, wrap and unroll to the (-180..+180] range (`bool`). Returns: 2-Tuple `(lon2-lon1, lon2)` unrolled (`degrees`, `degrees`). See Also: Capability `LONG_UNROLL` in GeographicLib.

### unrollPI (rad1, rad2, wrap=True) |
Unroll longitudinal delta and wrap longitude in radians. Arguments: `rad1` - Start longitude (`radians`). `rad2` - End longitude (`radians`). `wrap` - If `True`, wrap and unroll to the (-PI..+PI] range (`bool`). Returns: 2-Tuple `(rad2-rad1, rad2)` unrolled (`radians`, `radians`). See Also: Capability `LONG_UNROLL` in GeographicLib.

### unsigned0 (x) |
Unsign if `0.0`. Returns: `x` if `x` else `0.0`.

### unstr (where, *args, **kwds) |
Return the string representation of an invokation. Arguments: `where` - Class, function, method (`type`) or name (`str`). `args` - Optional positional arguments. `kwds` - Optional keyword arguments, except `_fmt=Fmt.g` and `_ELLIPSIS=False`. Returns: Representation (`str`).

### upsZoneBand5 (lat, lon, strict=True, **name) |
Return the UTM/UPS zone number, polar Band letter, pole and clipped lat- and longitude for a given location. Arguments: `lat` - Latitude in degrees (`scalar` or `str`). `lon` - Longitude in degrees (`scalar` or `str`). `strict` - Restrict `lat` to UPS ranges (`bool`). `name` - Optional `Ups` `name=NN` (`str`). Returns: A UtmUpsLatLon5Tuple`(zone, band, hemipole, lat, lon)` where `hemipole` is the `'N'|'S'` pole, the UPS projection top/center and `lon` [-180..180). Raises: `RangeError` - If `strict` is True and `lat` within the UTM but not the UPS range or if `lat` or `lon` outside the valid range and rangerrors is `True`. `ValueError` - Invalid `lat` or `lon`. Note: The `lon` is set to `0` if `lat` is `-90` or `90`, see env variable `PYGEODESY_UPS_POLES` in module ups.

### utmZoneBand5 (lat, lon, cmoff=False, **name) |
Return the UTM zone number, Band letter, hemisphere and (clipped) lat- and longitude for a given location. Arguments: `lat` - Latitude in degrees (`scalar` or `str`). `lon` - Longitude in degrees (`scalar` or `str`). `cmoff` - If `True`, offset longitude from the zone's central meridian (`bool`). `name` - Optional `name=NN` (`str`). Returns: A UtmUpsLatLon5Tuple`(zone, band, hemipole, lat, lon)` where `hemipole` is the `'N'|'S'` UTM hemisphere. Raises: `RangeError` - If `lat` outside the valid UTM bands or if `lat` or `lon` outside the valid range and rangerrors is `True`. `ValueError` - Invalid `lat` or `lon`.

### utmupsValidate (coord, falsed=False, MGRS=False, Error=<class 'pygeodesy.utmups.UTMUPSError'>) |
Check a UTM or UPS coordinate. Arguments: `coord` - The UTM or UPS coordinate (Utm, Etm, Ups or `5+Tuple`). `falsed` - If `True`, easting and northing are falsed in the `coord 5+Tuple` (`bool`), ignored otherwise. `MGRS` - Increase easting and northing ranges (`bool`). `Error` - Optional error to raise, overriding the default (UTMUPSError). Returns: `None` if validation passed. Raises: `Error` - Validation failed. See Also: Function utmupsValidateOK.

### utmupsValidateOK (coord, falsed=False, ok=True) |
Check a UTM or UPS coordinate. Arguments: `coord` - The UTM or UPS coordinate (Utm, Ups or `5+Tuple`). `falsed` - If `True`, easting and northing are falsed in the `coord 5+Tuple` (`bool`), ignored otherwise. `ok` - Result to return if validation passed (`ok`). Returns: `ok` if validation passed, otherwise the UTMUPSError. See Also: Function utmupsValidate.

### utmupsZoneBand5 (lat, lon, cmoff=False, **name) |
Return the UTM/UPS zone number, Band letter, hemisphere/pole and clipped lat- and longitude for a given location. Arguments: `lat` - Latitude in degrees (`scalar` or `str`). `lon` - Longitude in degrees (`scalar` or `str`). `cmoff` - If `True`, offset longitude from the zone's central meridian, for UTM only (`bool`). `name` - Optional `name=NN` (`str`). Returns: A UtmUpsLatLon5Tuple`(zone, band, hemipole, lat, lon)` where `hemipole` is `'N'|'S'`, the UTM hemisphere or UPS pole, projection top/center. Raises: `RangeError` - If `lat` outside the valid UTM or UPS bands or if `lat` or `lon` outside the valid range and rangerrors is `True`. `ValueError` - Invalid `lat` or `lon`. See Also: Functions pygeodesy.utmZoneBand5 and pygeodesy.upsZoneBand5.

### vincentys (lat1, lon1, lat2, lon2, radius=6371008.771415, wrap=False) |
Compute the distance between two (spherical) points using Vincenty's spherical formula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Mean earth radius (`meter`), datum (Datum) or ellipsoid (Ellipsoid, Ellipsoid2 or a_f2Tuple) to use. `wrap` - If `True`, wrap or normalize and unroll `lat2` and `lon2` (`bool`). Returns: Distance (`meter`, same units as `radius`). Raises: `UnitError` - Invalid `radius`. See Also: Functions vincentys_, cosineAndoyerLambert, cosineForsytheAndoyerLambert,cosineLaw, equirectangular, euclidean, flatLocal/hubeny, flatPolar, haversine and thomas and methods Ellipsoid.distance2, `LatLon.distanceTo*` and `LatLon.equirectangularTo`. Note: See note at function vincentys_.

### vincentys_ (phi2, phi1, lam21) |
Compute the angular distance between two (spherical) points using Vincenty's spherical formula. Arguments: `phi2` - End latitude (`radians`). `phi1` - Start latitude (`radians`). `lam21` - Longitudinal delta, end-start (`radians`). Returns: Angular distance (`radians`). See Also: Functions vincentys, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_ and thomas_. Note: Functions vincentys_, haversine_ and cosineLaw_ produce equivalent results, but vincentys_ is suitable for antipodal points and slightly more expensive (3 cos, 3 sin, 1 hypot, 1 atan2, 6 mul, 2 add) than haversine_ (2 cos, 2 sin, 2 sqrt, 1 atan2, 5 mul, 1 add) and cosineLaw_ (3 cos, 3 sin, 1 acos, 3 mul, 1 add).

### wildberger3 (a, b, c, alpha, beta, R3=<built-in function min>) |
Snellius' surveying using Rational Trigonometry. Arguments: `a` - Length of the triangle side between corners `B` and `C` and opposite of triangle corner `A` (`scalar`, non-negative `meter`, conventionally). `b` - Length of the triangle side between corners `C` and `A` and opposite of triangle corner `B` (`scalar`, non-negative `meter`, conventionally). `c` - Length of the triangle side between corners `A` and `B` and opposite of triangle corner `C` (`scalar`, non-negative `meter`, conventionally). `alpha` - Angle subtended by triangle side `b` (`degrees`, non-negative). `beta` - Angle subtended by triangle side `a` (`degrees`, non-negative). `R3` - Callable to determine `R3` from `(R3 - C)**2 = D`, typically standard Python function `min` or `max`, invoked with 2 arguments. Returns: Survey3Tuple`(PA, PB, PC)` with distance from survey point `P` to each of the triangle corners `A`, `B` and `C`, same units as `a`, `b` and `c`. Raises: `TriangleError` - Invalid `a`, `b` or `c` or negative `alpha` or `beta` or `R3` not `callable`. See Also: Wildberger, Norman J., Devine Proportions, page 252 and function snellius3.

### wrap180 (deg) |
Wrap degrees to [-180..+180]. Arguments: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees180`).

### wrap360 (deg) |
Wrap degrees to [0..+360). Arguments: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees360`).

### wrap90 (deg) |
Wrap degrees to [-90..+90]. Arguments: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees90`).

### wrapPI (rad) |
Wrap radians to [-PI..+PI]. Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI`).

### wrapPI2 (rad) |
Wrap radians to [0..+2PI). Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI2`).

### wrapPI_2 (rad) |
Wrap radians to [-PI/2..+PI/2]. Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI_2`).

### wrap_normal (*normal) |
Define the operation for the keyword argument `wrap=True`, across pygeodesy: wrap, normalize or no-op. For backward compatibility, the default is wrap. Arguments: `normal` - If `True`, normalize lat- and longitude using normal or normal_, if `False`, wrap the lat- and longitude individually by wrap90 or wrapPI_2 respectively wrap180, wrapPI or if `None`, leave lat- and longitude unchanged. Do not supply any value to get the current setting. Returns: The previous wrap_normal setting (`bool` or `None`).

### xyz2rtp (x_xyz, y=0, z=0, **name) |
Convert cartesian `(x, y, z)` to spherical, polar `(r, theta, phi)` coordinates. Returns: RadiusThetaPhi3Tuple`(r, theta, phi)` with `theta` and `phi`, both in Degrees. See Also: Function xyz2rtp_ for further details.

### xyz2rtp_ (x_xyz, y=0, z=0, **name) |
Convert cartesian `(x, y, z)` to spherical, polar `(r, theta, phi)` coordinates. Arguments: `x_xyz` - X component (`scalar`) or a cartesian (`Cartesian`, Ecef9Tuple, `Nvector`, Vector3d, Vector3Tuple, Vector4Tuple or a `tuple` or `list` of 3+ `scalar` items) if no `y_z` specified. `y` - Y component (`scalar`), required if `x_xyz` is `scalar`, ignored otherwise. `z` - Z component (`scalar`), like `y`. `name` - Optional `name=NN` (`str`). Returns: RadiusThetaPhi3Tuple`(r, theta, phi)` with radial distance `r` (`meter`, same units as `x`, `y` and `z`), inclination `theta` (with respect to the positive z-axis) and azimuthal angle `phi`, both in Radians. See Also: Physics convention (ISO 80000-2:2019), class RadiusThetaPhi3Tuple and function xyz2rtp.

### yard2m (yards) |
Convert UK yards to meter. Arguments: `yards` - Value in yards (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `yards`.

### zcrt (x) |
Return the 6-th, zenzi-cubic root, x**(1 / 6), preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). Returns: Zenzi-cubic root (`float` or Fsum). Raises: `TypeeError` - Invalid `x`. `ValueError` - Negative `x`. See Also: Functions bqrt and zqrt.

### zqrt (x) |
Return the 8-th, zenzi-quartic or squared-quartic root, x**(1 / 8), preserving `type(x)`. Arguments: `x` - Value (`scalar` or an Fsum or Fsum2Tuple). Returns: Zenzi-quartic root (`float` or Fsum). Raises: `TypeeError` - Invalid `x`. `ValueError` - Negative `x`. See Also: Functions bqrt and zcrt.

Variables Details

  ### pygeodesy_abspath Fully qualified `pygeodesy` directory name (`str`). Value:
      '..../PyGeodesy/p
      ygeodesy'

  ### Conics Registered, predefined conics (`enum-like`). Value:
      Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=4
      5, E0=0, N0=0, k0=1, SP=2, datum=Datum(name='WGS84', ellipsoid=Ellipso
      ids.WGS84, transform=Transforms.WGS84))

  ### Datums Registered, predefined datums (`enum-like`). Value:
      Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipsoids.Airy1830, tra
      nsform=Transforms.OSGB36),
      Datums.GRS80: Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transfor
      m=Transforms.WGS84),
      Datums.WGS84: Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transfor
      m=Transforms.WGS84),
      Datums.Sphere: Datum(name='Sphere', ellipsoid=Ellipsoids.Sphere, trans
      form=Transforms.WGS84)

  ### Ellipsoids Registered, predefined ellipsoids (`enum-like`). Value:
      Ellipsoids.Sphere: Ellipsoid(name='Sphere', a=6371008.771415, f=0, f_=
      0, b=6371008.771415),
      Ellipsoids.GRS80: Ellipsoid(name='GRS80', a=6378137, f=0.00335281, f_=
      298.2572221, b=6356752.31414035),
      Ellipsoids.WGS84: Ellipsoid(name='WGS84', a=6378137, f=0.00335281, f_=
      298.25722356, b=6356752.31424518),
      Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a=6377563.396, f=0.003
      34085, f_=299.3249646, b=6356256.90923729)

  ### RefFrames Registered, predefined reference frames (`enum-like`). Value:
      RefFrames.ETRF89: RefFrame(name='ETRF89', epoch=1989, datum=Datums.GRS
      80),
      RefFrames.NAD83cors96: RefFrame(name='NAD83cors96', epoch=1997, datum=
      Datums.GRS80),
      RefFrames.GDA2020: RefFrame(name='GDA2020', epoch=2020, datum=Datums.G
      RS80),
      RefFrames.ETRF92: RefFrame(name='ETRF92', epoch=1992, datum=Datums.GRS
      80),
      ...

  ### Transforms Registered, predefined transforms (`enum-like`). Value:
      Transforms.OSGB36: Transform(name='OSGB36', tx=-446.45, ty=125.16, tz=
      -542.06, s1=1.0, rx=-7.2819e-07, ry=-1.1975e-06, rz=-4.0826e-06, s=20.
      489, sx=-0.1502, sy=-0.247, sz=-0.8421),
      Transforms.WGS84: Transform(name='WGS84', tx=0.0, ty=0.0, tz=0.0, s1=1
      .0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0),
      Transforms.Identity: Transform(name='Identity', tx=0.0, ty=0.0, tz=0.0
      , s1=1.0, rx=0.0, ry=0.0, rz=0.0, s=0.0, sx=0.0, sy=0.0, sz=0.0)