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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 and approximate methods for geodetic (lat-/longitude) and geocentric (ECEF cartesian) coordinates.

Transcoded from JavaScript originals by Chris Veness (C) 2005-2019 and from several C++ classes by Charles F.F. Karney (C) 2008-2021 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, initial and final bearing, intermediate and nearest points, circle intersections, path intersections, trilateration (by intersection, by overlap and on 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), UPS (Universal Polar Stereographic), UTM (Exact and Universal Transverse Mercator) and Web Mercator (Pseudo-Mercator) coordinates, MGRS (NATO Military Grid Reference System) 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 a path or polygon of `LatLon` points using the Cohen-Sutherland, the Liang-Barsky and the 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 interpolate the `height` of `LatLon` points and `Geoid` models or compute various Fréchet or Hausdorff distances.

# Installation

To install PyGeodesy, type `pip install PyGeodesy` or `easy_install PyGeodesy` in a terminal or command window.

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] setup.py test` or 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 the `HeightIDW...` ones. Functions circum3, jekel4_ and trilaterate3d2`/-5` and the corresponding `Cartesian`, `LatLon`, `Nvector` and Vector3d methods require numpy.

Modules ellipsoidalGeodSolve and geodsolve and azimuthal classes EquidistantGeodSolve and GnomonicGeodSolve depend on Karney's C++ utility GeodSolve to be executable.

# 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 have been run with Python 3.9.6 (with geographiclib 1.52), Python 3.8.10 (withgeographiclib 1.52, GeodSolve 1.51, numpy 1.19.2 and scipy 1.5.2) and macOS' Python 2.7.16 (with GeodSolve 1.51 and numpy 1.16.6), all on macOS 11.5.1 (10.16) Big Sur and in 64-bit (and Intel) only. The tests are run with and without `lazy import` for Python 3 and with command line option `-W always` and environment variable `PYGEODESY_WARNINGS=on` for all Python versions. The results of only those tests are included in the distribution files.

Test coverage has been measured with coverage 4.5.4 using Python 3.9.6 (with geographiclib 1.52), Python 3.8.10 (with geographiclib 1.52, numpy 1.19.2 and scipy 1.5.2) and macOS' Python 2.7.16 (with numpy 1.16.6). The complete coverage report in HTML and a PDF summary are included in the distribution files.

The tests also ran with Python 3.8.0, 3.7.1, 3.6.7, 2.7.15 and PyPy 7.1.1 (Python 3.6.1 and 2.7.13) (and geographiclib 1.52) on Ubuntu 16.04 and with Python 3.9.1 (and geographiclib 1.52) on Debian 9, all in 64-bit only and with Python 3.8.0, 3.7.5 and 2.7.17 (all with geographiclib 1.52) on Windows Server 2012R2 in both 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 3.9.0-5, 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 11.0-5 Big Sur, 10.15.3, 10.15.5-7 Catalina, macOS 10.14 Mojave, macOS 10.13.6 High Sierra, macOS 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 and/or iPhone10, 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 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 3.9.6, both in 64-bit on macOS 11.5.1 (10.16) Big Sur (Intel).

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

Some function and method names differ from the JavaScript version. In such cases documentation tag JS name: shows the original JavaScript name.

# Env vars

The following environment variables are observed by `PyGeodesy`:

- `PYGEODESY_EXCEPTION_CHAINING` - see module pygeodesy.errors.
- `PYGEODESY_GEODSOLVE` - see module pygeodesy.geodsolve.
- `PYGEODESY_LAZY_IMPORT` - see module pygeodesy.lazily and variable isLazy.
- `PYGEODESY_BOOL_STD_REPR` - see method pygeodesy.Bool`.__repr__`.
- `PYGEODESY_FLOAT_STD_REPR` - see method pygeodesy.Float`.__repr__`.
- `PYGEODESY_INT_STD_REPR` - see method pygeodesy.Int`.__repr__`.
- `PYGEODESY_METER_STD_REPR` - see method pygeodesy.Meter`.__repr__`.
- `PYGEODESY_STR_STD_REPR` - see method pygeodesy.Str`.__repr__`.

plus during development:

- `PYGEODESY_FOR_DOCS` - for extended documentation by `epydoc`.
- `PYGEODESY_WARNINGS` - see module pygeodesy.props and function DeprecationWarnings.
- `PYTHONDEVMODE` - see modules pygeodesy.errors and pygeodesy.props.

# License

**) Copyright (C) 2016-2021 -- 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: 21.08.08

Submodules
pygeodesy.__main__: Print pygeodesy version, etc. pygeodesy.albers: Albers Equal-Area projections. pygeodesy.azimuthal: Equidistant, Equal-Area, and other Azimuthal projections. pygeodesy.basics: Some, basic definitions and functions. pygeodesy.cartesianBase: (INTERNAL) Base classes for elliposiodal, spherical and N-/vectorial `Cartesian`s. pygeodesy.clipy: Clip a path or polygon. pygeodesy.css: Cassini-Soldner (CSS) projection. pygeodesy.datums: Datums and transformations thereof. pygeodesy.deprecated: DEPRECATED classes, functions, methods, etc. pygeodesy.deprecated.bases: DEPRECATED, use module latlonBase instead. pygeodesy.deprecated.datum: DEPRECATED, use module datums or ellipsoids instead. pygeodesy.deprecated.nvector: DEPRECATED, use module nvectorBase instead. pygeodesy.dms: Parsers and formatters of degrees, minutes and seconds. pygeodesy.ecef: Geocentric Earth-Centered, Earth-Fixed (ECEF) coordinates. pygeodesy.elevations: Web-services-based elevations and geoid heights. pygeodesy.ellipsoidalBase: (INTERNAL) Ellipsoidal geodesy base classes `CartesianEllipsoidalBase` and `LatLonEllipsoidalBase`. pygeodesy.ellipsoidalBaseDI: (INTERNAL) 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 and exception chaining. pygeodesy.etm: Karney's Exact Transverse Mercator (ETM) projection. pygeodesy.fmath: Precision floating point functions, classes and utilities. pygeodesy.formy: Formulary of basic geodesy functions and approximations. pygeodesy.frechet: Fréchet distances. pygeodesy.gars: Global Area Reference System (GARS) en-/decoding. pygeodesy.geodesicx: A 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 Python version of Karney's C++ class GeodesicExact. pygeodesy.geodesicx.gxarea: Slightly enhanced versions of Karney's Python classes PolygonArea and `Accumulator`. pygeodesy.geodesicx.gxbases: Base geodesicx classes, functions and constants. pygeodesy.geodesicx.gxline: A 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 interpolations. pygeodesy.hausdorff: Hausdorff distances. pygeodesy.heights: Height interpolation methods. pygeodesy.interns: Single-instance `float`s and `str`ings, `intern`'ed across modules. pygeodesy.iters: Iterators with options. pygeodesy.karney: Karney's geographiclib `geodesic`, wrapped. pygeodesy.latlonBase: (INTERNAL) Base class LatLonBase for elliposiodal, spherical and N-vectorial `LatLon`s. 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) Base classes for elliposiodal and spherical `Nvector`s. pygeodesy.osgr: Ordinance Survey Grid References (OSGR) references. pygeodesy.points: Utilities for point lists, tuples, etc. pygeodesy.props: Im-/mutable, caching or memoizing properties and deprecation decorators. pygeodesy.simplify: Simplify or linearize a path. pygeodesy.sphericalBase: (INTERNAL) Spherical geodesy bases. 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.units: Various `Float`, `Int` and `Str`ing units. 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) ETM, Epsg, Mgrs, UTM and UPS bases. pygeodesy.vector3d: Extended 3-D vector class Vector3d and functions. pygeodesy.vector3dBase: Veness' 3-D vector base class `Vector3dBase`. pygeodesy.webmercator: Web Mercator (WM) projection. pygeodesy.wgrs: World Geographic Reference System (WGRS) en-/decoding.

Classes
| LazyImportError Raised if `lazy import` is not supported, disabled or failed some other way.
| Ned3Tuple 3-Tuple `(north, east, down)`.
| VincentyError Error raised from 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.
| 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.
| 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.
| Bool Named `bool`, a sub-class of `int` like Python's `bool`.
| 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.
| 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.
| ClipCS3Tuple 3-Tuple `(start, end, index)`.
| 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.
| 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` (`int`) of the original path edge start and end points and fractional indices `fi` and `fj` (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`).
| 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, paths 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`.
| ETMError Exact Transverse Mercator (ETM) parse, projection or other Etm issue.
| 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`.
| EasNorExact4Tuple 4-Tuple `(easting, northing, convergence, scale)` in `meter`, `meter`, `degrees` and `scalar`.
| 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.
| EcefCartesian DEPRECATED, use class LocalCartesian.
| EcefError An ECEF or `Ecef*` related issue.
| EcefFarrell21 Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates based on Jay A. Farrell's Table 2.1, page 29.
| EcefFarrell22 Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates based on Jay A. Farrell's Table 2.2, page 30.
| EcefKarney Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates transcoded from Karney's C++ Geocentric methods.
| EcefMatrix A rotation matrix.
| EcefSudano Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates based on John J. Sudano's paper.
| EcefVeness Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates transcoded from Chris Veness' JavaScript classes LatLonEllipsoidal, Cartesian.
| EcefYou Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates using Rey-Jer You's transformation.
| 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 integral, function, 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 A Python version of Karney's TransverseMercatorExact C++ class, a numerically exact transverse mercator projection, here referred to as `TMExact`.
| FIx A named Fractional Index, an `int` or `float` index into a `list` or `tuple` of `points`, typically.
| Fdot Precision dot product.
| Feet Named `float` representing a distance or length in `feet`.
| Fhorner Precision polynomial evaluation using the Horner form.
| 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 a local projection of a `Frustum`, each an Xyz4Tuple.
| Fpolynomial Precision polynomial evaluation.
| 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 cosineAndoyerLambert_.
| FrechetCosineForsytheAndoyerLambert Compute the `Frechet` distance based on the angular distance in `radians` from function cosineForsytheAndoyerLambert_.
| FrechetCosineLaw Compute the `Frechet` distance based on the angular distance in `radians` from function cosineLaw_.
| FrechetDegrees Frechet base class for distances in `degrees` from `LatLon` points in `degrees`.
| FrechetDistanceTo Compute the `Frechet` distance based on the distance from the points' `LatLon.distanceTo` method, conventionally in `meter`.
| FrechetEquirectangular Compute the `Frechet` distance based on the `equirectangular` distance in `radians squared` like function equirectangular_.
| FrechetError Fréchet issue.
| FrechetEuclidean Compute the `Frechet` distance based on the `Euclidean` distance in `radians` from function 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 flatLocal_/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 haversine_.
| FrechetHubeny Compute the `Frechet` distance based on the angular distance in `radians squared` like function flatLocal_/hubeny_.
| FrechetKarney Compute the `Frechet` distance based on the angular distance in `degrees` from Karney's geographiclib Geodesic Inverse method.
| FrechetRadians Frechet base class for distances in `radians` or `radians squared` from `LatLon` points converted from `degrees` to `radians`.
| FrechetThomas Compute the `Frechet` distance based on the angular distance in `radians` from function thomas_.
| FrechetVincentys Compute the `Frechet` distance based on the angular distance in `radians` from function vincentys_.
| Frustum A rectangular pyramid, typically representing a camera's field of view (fov) and the intersection with (or projection to) a local tangent plane.
| Fsum Precision summation similar to standard Python function `math.fsum`.
| GDict Basic `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`, distance `s12` and reduced length `m12` in `meter`, area `S12` in `meter` squared and geodesic scales `M12` and `M21` `scalar`, see GeodSolve.
| 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 geodesicx's methods for lack of convergence or other issues.
| GeodesicExact A pure Python version of Karney's C++ class GeodesicExact, modeled after Karney's Python class Geodesic.
| GeodesicLineExact A pure Python version of Karney's C++ class GeodesicLineExact, modeled after Karney's Python class 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 cosineAndoyerLambert_.
| HausdorffCosineForsytheAndoyerLambert Compute the `Hausdorff` distance based on the angular distance in `radians` from function cosineForsytheAndoyerLambert_.
| HausdorffCosineLaw Compute the `Hausdorff` distance based on the angular distance in `radians` from function 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 equirectangular_.
| HausdorffError Hausdorff issue.
| HausdorffEuclidean Compute the `Hausdorff` distance based on the `Euclidean` distance in `radians` from function 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 flatLocal_/hubeny_.
| HausdorffFlatPolar Compute the `Hausdorff` distance based on the angular distance in `radians` from function flatPolar_.
| HausdorffHaversine Compute the `Hausdorff` distance based on the angular distance in `radians` from function haversine_.
| HausdorffHubeny Compute the `Hausdorff` distance based on the angular distance in `radians squared` like function flatLocal_/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 thomas_.
| HausdorffVincentys Compute the `Hausdorff` distance based on the angular distance in `radians` from function 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.
| HeightIDW DEPRECATED, use class HeightIDWeuclidean.
| HeightIDW2 DEPRECATED, use class HeightIDWequirectangular.
| HeightIDW3 DEPRECATED, use class HeightIDWhaversine.
| HeightIDWcosineAndoyerLambert Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function cosineAndoyerLambert_.
| HeightIDWcosineForsytheAndoyerLambert Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function cosineForsytheAndoyerLambert_.
| HeightIDWcosineLaw Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function 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 equirectangular_.
| HeightIDWeuclidean Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function euclidean_.
| HeightIDWflatLocal Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians squared` like function flatLocal_/hubeny_.
| HeightIDWflatPolar Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function flatPolar_.
| HeightIDWhaversine Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function haversine_.
| HeightIDWhubeny Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians squared` like function flatLocal_/hubeny_.
| HeightIDWkarney Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `degrees` from Karney's geographiclib Geodesic Inverse method.
| HeightIDWthomas Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function thomas_.
| HeightIDWvincentys Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in `radians` from function vincentys_.
| HeightLSQBiSpline Height interpolator using `SciPy` LSQSphereBivariateSpline.
| HeightLinear Height interpolator based on `SciPy` interp2d `kind='linear'`.
| HeightSmoothBiSpline Height interpolator using `SciPy` SmoothSphereBivariateSpline.
| Int Named `int`.
| Int_ Named `int` with optional limits `low` and `high`.
| 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 stat and end point of the first line.
| IntersectionError Error raised for path or circle intersection issues.
| 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 sines and cosines of initial and final (forward) azimuths.
| Jekel4Tuple 4-Tuple `(radius, center, rank, residuals)` with `radius` and `center` of a sphere fitted through given points and the `rank` and `residuals` -if any- from numpy.linalg.lstsq.
| LCCError Lambert Conformal Conic `LCC` or other Lcc issue.
| Lam Named `float` representing a longitude in `radians`.
| Lam_ Named `float` representing a longitude in `radians` converted from `degrees`.
| LambertEqualArea Lambert-equal-area projection for the sphere** (aka Lambert zenithal equal-area projection, see Snyder, pp 185-187 and MathWorld-Wolfram.
| 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, convergence, scale)` in `degrees90`, `degrees180`, Datum, `degrees` and `float`.
| LatLonExact4Tuple 4-Tuple `(lat, lon, convergence, scale)` in `degrees180`, `degrees180`, `degrees` and `scalar`.
| 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 for Numpy2LatLon and Tuple2LatLon.
| Lat_ Named `float` representing a latitude in `degrees` within limits `low` and `high`.
| Lcc Lambert conformal conic East-/Northing location.
| LenError Error raised for mis-matching `len` values.
| LimitError Error raised for lat- or longitudinal deltas exceeding the `limit` in functions equirectangular and equirectangular_ and `nearestOn*` and `simplify*` functions or methods.
| 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`.
| Ltp A local tangent plan LTP, a sub-class of `LocalCartesian` with configurable ECEF converter and without optional rotation matrix.
| 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, digraph, easting, northing)`, `zone` and `digraph` as `str`, `easting` and `northing` in `meter`.
| Mgrs6Tuple 6-Tuple `(zone, digraph, easting, northing, band, datum)`, `zone`, `digraph` and `band` as `str`, `easting` and `northing` in `meter` and `datum` a Datum.
| 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`.
| NearestOn5Tuple 5-Tuple `(lat, lon, distance, angle, height)` all in `degrees`, except `height`.
| 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` errors.
| Number_ Named `int` representing a non-negative number.
| Numpy2LatLon Wrapper for `NumPy` arrays as "on-the-fly" `LatLon` points.
| OSGRError Ordinance Survey Grid References (OSGR) parse or other Osgr issue.
| Orthographic Orthographic projection for the sphere**, see Snyder, pp 148-153 and MathWorld-Wolfram.
| Osgr Ordinance Survey Grid References (OSGR) coordinate.
| 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.
| Phi_ 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`
| Radius Named `float` representing a radius, conventionally in `meter`.
| 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` or `limit` range in function clipDegrees, clipRadians, parse3llh, parseDMS, parseDMS2 or parseRad.
| RefFrame Terrestrial Reference Frame (TRF) parameters.
| RefFrameError DEPRECATED, use class TRFError.
| 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` errors.
| SciPyWarning Error thrown for `SciPy` warnings.
| Shape2Tuple 2-Tuple `(nrows, ncols)`, the number of rows and columns, both `int`.
| Stereographic Stereographic projection for the sphere**, see Snyder, pp 157-160 and MathWorld-Wolfram.
| Str Named `str`.
| TRFError Terrestrial Reference Frame (TRF), Epoch, RefFrame or RefFrame conversion issue.
| Transform Helmert transformation.
| Transform7Tuple 7-Tuple `(tx, ty, tz, s, sx, sy, sz)` Helmert transformation with translations `tx`, `ty` and `tz` in `millimeter`, scale `s` in `ppb` and rotations `sx`, `sy` and `sz` in `milliarcseconds`.
| 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` and the `area` of a spherical triangle in square `meter`.
| Triangle8Tuple 8-Tuple `(A, a, B, b, C, c, D, E)` with interior angles `A`, `B` and `C`, spherical sides `a`, `b` and `c`, spherical deficit `D` and spherical excess `E` of a spherical triangle, all in `radians`.
| 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.
| 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.
| UtmUps4Tuple OBSOLETE, expect a UtmUps5Tuple from method `Mgrs.toUtm(utm=None)`.
| 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 the (polar) UPS band `'A'|'B'|'Y'|'Z'`.
| UtmUps8Tuple 8-Tuple `(zone, hemipole, easting, northing, band, datum, convergence, 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 the (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.
| Vector2Tuple 2-Tuple `(x, y)` of (geocentric) components, both in `meter` or `units`.
| Vector3Tuple 3-Tuple `(x, y, z)` of (geocentric) components, all in `meter` or `units`.
| Vector3d Extended 3-D vector.
| Vector4Tuple 4-Tuple `(x, y, z, h)` of (geocentric) components, all in `meter` or `units`.
| VectorError Vector3d, `Cartesian*` or `*Nvector` issues.
| WebMercatorError Web Mercator (WM) parser or Wm issue.
| Wm Web Mercator (WM) coordinate.
| Xyz4Tuple 4-Tuple `(x, y, z, ltp)`, all in `meter` except `ltp`.
| XyzLocal Local `(x, y, z)` in a local tangent plane (LTP) and base class for local Enu, Ned and Aer.
| 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

Functions
DeprecationWarnings() Get the `DeprecationWarning`s reported or raised. |
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=`'``_``'`) DEPRECATED, use function anstr. |
anstr(name, OKd=`'``._-``'`, sub=`'``_``'`) Make a valid name of alphanumeric and OKd characters. |
antipode(lat, lon) Return the antipode, the point diametrically opposite to a given point in `degrees`. |
antipode_(phi, lam) Return the antipode, the point diametrically opposite to a given point in `radians`. |
areaOf(points, adjust=True, radius=6371008.77141, wrap=True) Approximate the area of a polygon. |
areaof(points, adjust=True, radius=6371008.77141, wrap=True) DEPRECATED, use function areaOf. |
asin1(x) Return `math.asin(max(-1, min(1, x)))`. |
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 `azi2`). |
atand(y_x) Return `atan(y_x)` angle in `degrees`. |
attrs(inst, *names, **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, **options) Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. |
bearingDMS(bearing, form=`'``d``'`, prec=None, sep='') Convert bearing to a string. |
bearing_(phi1, lam1, phi2, lam2, final=False, wrap=False) Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. |
bounds(points, wrap=True, LatLon=None) DEPRECATED, use function boundsOf. |
boundsOf(points, wrap=True, LatLon=None) Determine the lower-left SW and upper-right NE corners of a path or polygon. |
callername(up=1, dflt='', source=False) Get the name of the calling callable. |
cbrt(x) Compute the cubic root x**(1/3). |
cbrt2(x) Compute the cubic root squared x**(2/3). |
centroidOf(points, wrap=True, LatLon=None) Determine the centroid of a polygon. |
chain2m(chains) Convert UK chains to meter. |
circle4(earth, lat) Get the equatorial or a parallel circle of latitude. |
circum3(point1, point2, point3, circum=True, eps=8.881784197e-16, useZ=True) Return the radius and center of the smallest circle through or containing three (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. |
clipCS3(points, lowerleft, upperright, closed=False, inull=False) DEPRECATED, use function clipCS4. |
clipCS4(points, lowerleft, upperright, closed=False, inull=False) Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm. |
clipDMS(deg, limit) DEPRECATED, use function clipDegrees. |
clipDegrees(deg, limit) Clip a lat- or longitude to the given range. |
clipLB6(points, lowerleft, upperright, 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. |
clipStr(bstr, limit=50, white='') DEPRECATED, use function clips. |
clips(bstr, limit=50, white='') Clip a string to the given length limit. |
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='') Convert bearing to a string suffixed with compass point. |
compassPoint(bearing, prec=3) Convert bearing 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 fromula. |
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 fromula. |
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=6371008.77141, 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. |
crosserrors(raiser=None) Report or ignore vectorial cross product errors. |
date2epoch(year, month, day) Return the reference frame `epoch` for a calendar day. |
decodeEPSG2(arg) DEPRECATED, use function epsg.decode2. |
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 gradians or gons). |
degrees2m(deg, radius=6371008.77141, 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 [-270..+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. |
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) DEPRECATED, use function enstr2. |
encodeEPSG(zone, hemipole='', band='') DEPRECATED, use function epsg.encode. |
enstr2(easting, northing, prec, *extras) Return 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=6371008.77141, **options) Compute the distance between two points using the Equirectangular Approximation / Projection. |
equirectangular3(lat1, lon1, lat2, lon2, **options) DEPRECATED, use function `equirectangular_`. |
equirectangular_(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=6371008.77141, 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(error=None) Get the previous exception's or exception chaining setting. |
excessAbc(A, b, c) Compute the spherical excess `E` of a (spherical) triangle from two sides and the included angle. |
excessGirard(A, B, C) Compute the spherical excess `E` of a (spherical) triangle using Girard's formula. |
excessKarney(lat1, lon1, lat2, lon2, radius=6371008.77141, 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 Theorem. |
excessQuad(lat1, lon1, lat2, lon2, radius=6371008.77141, 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. |
fStr(floats, prec=6, fmt='f', ints=False, sep=', ') DEPRECATED, use function fstr. |
fStrzs(floatstr) DEPRECATED, use function fstrzs. |
f_2f(f_) Return `f`, the flattening for a given inverse flattening. |
facos1(x) Fast approximation of acos1`(x)`. |
false2f(value, name=`'``value``'`, false=True, Error=<type 'exceptions.ValueError'>) DEPRECATED, use function falsed2f. |
falsed2f(falsed=True, Error=<type 'exceptions.ValueError'>, **name_value) DEPRECATED, use class Easting or Northing. |
fasin1(x) Fast approximation of 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 UK fathom to meter. |
favg(v1, v2, f=0.5) Return the average of two values. |
fdot(a, *b) Return the precision dot product sum(a[i] * b[i] for i=0..len(a)). |
fdot3(a, b, c, start=0) Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)). |
fhorner(x, *cs) Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) using the Horner form. |
fidw(xs, ds, beta=2) Interpolate using using Inverse Distance Weighting (IDW). |
flatLocal(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, 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`...`) Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula. |
flatPolar(lat1, lon1, lat2, lon2, radius=6371008.77141, 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. |
fmean(xs) Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs). |
fmean_(*xs) Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs). |
fpolynomial(x, *cs) Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)). |
fpowers(x, n, alts=0) Return a series of powers [x**i for i=1..n]. |
fprod(iterable, start=1.0) Iterable product, like `math.prod` or `numpy.prod`. |
fractional(points, fi, LatLon=None, **LatLon_kwds) Return the point at a given fractional index. |
frange(start, number, step=1) Generate a range of `float`s. |
frechet_(points1, points2, distance=None, units='') Compute the discrete Fréchet distance between two paths given as sets 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. |
fstr(floats, prec=6, fmt='F', ints=False, sep=', ', strepr=None) 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(iterable) Return an accurate floating point sum of values in the iterable. |
fsum2(x, y) Precision summation of 2 positional arguments. |
fsum_(*xs) Precision summation of all positional arguments. |
ft2m(feet, usurvey=False) Convert International or US Survey feet to meter. |
furlong2m(furlongs) Convert a UK 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 gradians or gons). |
grades2degrees(gon) Convert grades (aka gradians or gons) to `degrees`. |
grades2radians(gon) Convert grades (aka gradians or gons) to `radians`. |
grades400(rad) Convert radians to grades (aka gradians or gons) and wrap [0..+400). |
halfs2(str2) Split a string in 2 halfs. |
hartzell(pov, los=None, earth=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, LatLon=None, **LatLon_kwds) Compute the intersection of a Line-Of-Sight from a Point-Of-View in space with the surface of the earth. |
hausdorff_(model, target, both=False, early=True, seed=None, units='', distance=None, point=<function _point at 0x7fa244e1ea50>) 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=6371008.77141, 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=6371008.77141) Determine the height above the (spherical) earth' surface after traveling along a straight line at a given tilt. |
horizon(height, radius=6371008.77141, 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`...`, 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`...`) 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 `sum(x**2 for x in xs)`. |
hypot3(x, y, z) DEPRECATED, use function hypot_. |
hypot_(*xs) Compute the norm sqrt(sum(x**2 for x in xs)). |
inStr(inst, *args, **kwds) DEPRECATED, use function instr. |
instr(inst, *args, **kwds) Return the string representation of an instantiation. |
intersection3d3(start1, end1, start2, end2, eps=2.22044604925e-16, useZ=True, Vector=None, **Vector_kwds) Compute the intersection point of two lines, each defined by or through a start and end point (3-D). |
intersections2(center1, radius1, center2, radius2, sphere=True, Vector=None, **Vector_kwds) Compute the intersection of two spheres or circles, each defined by a (3-D) center point and a radius. |
isNumpy2(obj) Check for an `Numpy2LatLon` points wrapper. |
isPoints2(obj) Check for an `LatLon2psxy` points wrapper. |
isTuple2(obj) Check for an `Tuple2LatLon` points wrapper. |
isantipode(lat1, lon1, lat2, lon2, eps=2.22044604925e-16) Check whether two points are antipodal, on diametrically opposite sides of the earth. |
isantipode_(phi1, lam1, phi2, lam2, eps=2.22044604925e-16) Check whether two points are antipodal, on diametrically opposite sides of the earth. |
isbool(obj) Check whether an object is `bool`ean. |
isclass(obj) Return `True` if `obj` is a `class`. |
isclockwise(points, adjust=False, wrap=True) Determine the direction of a path or polygon. |
iscolinearWith(point, point1, point2, eps=2.22044604925e-16) Check whether a point is colinear with two other (3-D) points. |
isconvex(points, adjust=False, wrap=True) Determine whether a polygon is convex. |
isconvex_(points, adjust=False, wrap=True) Determine whether a polygon is convex and clockwise. |
isenclosedBy(point, points, wrap=False) Determine whether a point is enclosed by a polygon. |
isenclosedby(point, points, wrap=False) DEPRECATED, use function isenclosedBy. |
isfinite(obj) Check for `Inf` and `NaN` values. |
isidentifier(obj) Return `True` if `obj` is a valid Python identifier. |
bool |
isinf(x) Check if float x is infinite (positive or negative). |
isint(obj, both=False) Check for `int` type or an integer `float` value. |
iskeyword(x, y) y in x. |
bool |
isnan(x) Check if float x is not a number (NaN). |
isnear0(x) Is `x` near zero? |
isneg0(x) Check for NEG0, negative `0.0`. |
isnon0(x) Is `x` non-zero? |
isodd(x) Is `x` odd? |
ispolar(points, wrap=False) Check whether a polygon encloses a pole. |
isscalar(obj) Check for scalar types. |
issequence(obj, *excluded) Check for sequence types. |
isstr(obj) Check for string types. |
issubclassof(Sub, *Supers) Check whether a class is a sub-class of some class(es). |
iterNumpy2(obj) Iterate over Numpy2 wrappers or other sequences exceeding the threshold. |
iterNumpy2over(n=None) Get or set the iterNumpy2 threshold. |
jekel4_(*points, **Vector_Vector_kwds) Best-fit a sphere through two or more (3-D) points. |
joined(*words, **sep) DEPRECATED, use `NN(...)`, `NN.join_` or `sep.join`. |
joined_(*words, **sep) DEPRECATED, use `_SPACE_(...)`, `_SPACE_.join_` or `sep.join`, sep=" ". |
latDMS(deg, form=`'``dms``'`, prec=2, sep='') 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, form=`'``dms``'`, prec=None, sep=None) 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=2, sep='') Convert longitude to a string, optionally suffixed with E or W. |
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). |
m2degrees(distance, radius=6371008.77141, lat=0) Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. |
m2ft(meter, usurvey=False) Convert meter to International or US Survey feet (`ft`). |
m2km(meter) Convert meter to kilo meter (km). |
m2radians(distance, radius=6371008.77141, lat=0) Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. |
m2yard(meter) Convert meter to UK yards. |
map1(fun1, *xs) Apply each argument to a single-argument function and return a `tuple` of results. |
map2(func, *xs) Apply arguments to a function and return a `tuple` of results. |
meeus2(point1, point2, point3, circum=False, useZ=True) Return the radius and Meeus' Type of the smallest circle containing or through three (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. |
nearestOn3(point, points, closed=False, wrap=False, **options) DEPRECATED, use function nearestOn5. |
nearestOn4(point, points, closed=False, wrap=False, **options) DEPRECATED, use function nearestOn5. |
nearestOn5(point, points, closed=False, wrap=False, LatLon=None, **options) Locate the point on a path or polygon closest to an other point. |
neg(x) Negate `x` unless `zero` or `NEG0`. |
neg_(*xs) Negate all of `xs` with neg. |
norm2(x, y) Normalize a 2-dimensional vector. |
normDMS(strDMS, norm='') Normalize all degree ˚, minute ' and second " symbols in a string to the default symbols %s, %s and %s. |
norm_(*xs) Normalize all n-dimensional vector components. |
notImplemented(inst, *args, **kwds) Raise a `NotImplementedError` for a missing method or property. |
notOverloaded(inst, *args, **kwds) Raise an `AssertionError` for a method or property not overloaded. |
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) Parse a string `"lat lon [h]"` representing lat-, longitude in `degrees` and optional height in `meter`. |
parseDDDMMSS(strDDDMMSS, suffix=`'``NSEW``'`, sep='', clip=0) Parse a lat- or longitude represention form [D]DDMMSS in degrees. |
parseDMS(strDMS, suffix=`'``NSEW``'`, sep='', clip=0) Parse a lat- or longitude representation `"lat, lon"` in `degrees`. |
parseDMS2(strLat, strLon, sep='', clipLat=90, clipLon=180) Parse a lat- and a longitude representions 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 `"zoneBand, grid, easting, northing"`. |
parseOSGR(strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, name='') Parse a string representing an OSGR grid reference, consisting of `"[grid] 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'|''`. |
parseUTM(strUTM, datum=_UTM, Utm=_UTM, name='') DEPRECATED, use function parseUTM5. |
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=6371008.77141, wrap=True) Approximate the perimeter of a path or polygon. |
perimeterof(points, closed=False, adjust=True, radius=6371008.77141, wrap=True) DEPRECATED, use function perimeterOf. |
philam2n_xyz(phi, lam, name='') Convert lat-, longitude to `n-vector` (normal to the earth's surface) X, Y and Z components. |
points2(points, closed=True, base=None, Error=<class 'pygeodesy.errors.PointsError'>) Check a path or polygon represented by points. |
polygon(points, closed=True, base=None) DEPRECATED, use function points2. |
precision(form, prec=None) Set the default precison for a given F_ form. |
print_(*args, **nl_nt_prefix_end_file_flush_sep) Python 3-style `print` function. |
printf(fmt, *args, **nl_nt_prefix_end_file_flush_sep) C-style `printf` function. |
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=6371008.77141, 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) Compute the radical ratio and radical line of two intersecting circles. |
randomrangenerator(seed) Return a `seed`ed random range function generator. |
rangerrors(raiser=None) Get/set the throwing of RangeErrors. |
reprs(objs, prec=6, fmt='F', ints=False) Convert objects to `repr` strings, with `float`s handled like fstr. |
scalar(value, low=2.22044604925e-16, high=1.0, name=`'``scalar``'`, Error=<type 'exceptions.ValueError'>) DEPRECATED, use class Number_ or Scalar_. |
signOf(x) Return sign of `x` as `int`. |
simplify1(points, distance=0.001, radius=6371008.77141, indices=False, **options) Basic simplification of a path of `LatLon` points. |
simplify2(points, pipe, radius=6371008.77141, shortest=False, indices=False, **options) DEPRECATED, use function simplifyRW. |
simplifyRDP(points, distance=0.001, radius=6371008.77141, shortest=False, indices=False, **options) Ramer-Douglas-Peucker (RDP) simplification of a path of `LatLon` points. |
simplifyRDPm(points, distance=0.001, radius=6371008.77141, shortest=False, indices=False, **options) Modified Ramer-Douglas-Peucker (RDPm) simplification of a path of `LatLon` points. |
simplifyRW(points, pipe=0.001, radius=6371008.77141, shortest=False, indices=False, **options) Reumann-Witkam (RW) simplification of a path of `LatLon` points. |
simplifyVW(points, area=0.001, radius=6371008.77141, attr=None, indices=False, **options) Visvalingam-Whyatt (VW) simplification of a path of `LatLon` points. |
simplifyVWm(points, area=0.001, radius=6371008.77141, attr=None, indices=False, **options) Modified Visvalingam-Whyatt (VWm) simplification of a path of `LatLon` points. |
sincos2(*rad) Return the `sine` and `cosine` of angle(s). |
sincos2d(*deg) Return the `sine` and `cosine` of angle(s) in `degrees`. |
splice(iterable, n=2, **fill) Split an iterable into `n` slices. |
sqrt0(x) Compute the square root iff `x > EPS0**2`. |
sqrt3(x) Compute the square root, cubed sqrt(x)**3 or sqrt(x**3). |
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. |
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. |
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='') Convert signed `degrees` to string, without suffix. |
toEtm8(latlon, lon=None, datum=None, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, name='', zone=None, **cmoff) Convert a lat-/longitude point 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(utm, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name='', **Mgrs_kwds) Convert a UTM coordinate to an MGRS grid reference. |
toOsgr(latlon, lon=None, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Osgr=<class 'pygeodesy.osgr.Osgr'>, 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. |
toUtm(latlon, lon=None, datum=None, Utm=_UTM, cmoff=True, name='') DEPRECATED, use function toUtm8. |
toUtm8(latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, name='', zone=None, **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, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name='', **Wm_kwds) Convert a lat-/longitude point to a WM coordinate. |
trfXform(reframe1, reframe2, epoch=None, xform=None, rates=None) Define a new Terrestrial Reference Frame (TRF) conversion. |
trilaterate2d2(x1, y1, radius1, x2, y2, radius2, x3, y3, radius3, eps=None, Vector=None, **Vector_kwds) Trilaterate three circles, each given as a (2-D) center and a radius. |
trilaterate3d2(center1, radius1, center2, radius2, center3, radius3, eps=2.22044604925e-16, Vector=None, **Vector_kwds) Trilaterate three spheres, each given as a (3-D) center and a radius. |
ub2str(ub) Convert `unicode` or `bytes` to `str`. |
unStr(name, *args, **kwds) DEPRECATED, use function unstr. |
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. |
unsign0(x) Return unsigned `0.0`. |
unstr(named, *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. |
utmZoneBand2(lat, lon) DEPRECATED, use function utmZoneBand5. |
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=6371008.77141, 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. |
wrap180(deg) Wrap degrees to [-180..+180]. |
wrap360(deg) Wrap degrees to [0..+360). |
wrap90(deg) Wrap degrees to [-270..+90]. |
wrapPI(rad) Wrap radians to [-PI..+PI]. |
wrapPI2(rad) Wrap radians to [0..+2PI). |
wrapPI_2(rad) Wrap radians to [-3PI/2..+PI/2]. |
yard2m(yards) Convert UK yards to meter. |

Variables
| pygeodesy_abspath = ``'``..../PyGe``...`` Fully qualified `pygeodesy` directory name (`str`).
| version = ``'``21.8.8``'`` Normalized `PyGeodesy` version (`str`).
| Caps = `Caps()`
| Conics = `Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97`...`` Registered conics (`enum-like`).
| DIG = `15` System's float decimal digits = 15 (`int`).
| Datums = `Datums.OSGB36: Datum(name='OSGB36', ellipsoid=Ellipso`...`` Registered datums (`enum-like`).
| EPS = `2.22044604925e-16` System's epsilon ≈ 2.220446049e-16 (`float`).
| EPS0 = `4.93038065763e-32` EPS**2 ≈ 4.9e-32 for near-zero comparison
| EPS02 = `2.43086534291e-63` EPS**4 ≈ 2.4e-63 for near-zero squared comparison
| EPS1 = `1.0` 1 - EPS ≈ 0.9999999999999998 (`float`).
| EPS1_2 = `1.0` 1 - EPS_2 ≈ 0.9999999999999999 (`float`).
| EPS2 = `4.4408920985e-16` EPS * 2 ≈ 4.440892098501e-16 (`float`).
| EPS4 = `8.881784197e-16` EPS * 4 ≈ 8.881784197001e-16 (`float`).
| EPS_2 = `1.11022302463e-16` EPS / 2 ≈ 1.110223024625e-16 (`float`).
| Ellipsoids = `Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a`...`` Registered ellipsoids (`enum-like`).
| F_D = ``'``d``'`` Format degrees as unsigned "deg°" plus suffix `N, S, W` or `E` (`str`).
| F_DEG = ``'``deg``'`` Format degrees as unsigned "[D]DD" plus suffix without symbol (`str`).
| F_DEG_ = ``'``-deg``'`` Format degrees as signed "-/[D]DD" without suffix and symbol (`str`).
| F_DEG__ = ``'``+deg``'`` Format degrees as signed "-/+[D]DD" without suffix and symbol (`str`).
| F_DM = ``'``dm``'`` Format degrees as unsigned "deg°min′" plus suffix (`str`).
| F_DMS = ``'``dms``'`` Format degrees as unsigned "deg°min′sec″" plus suffix (`str`).
| F_DMS_ = ``'``-dms``'`` Format degrees as signed "-/deg°min′sec″" without suffix (`str`).
| F_DMS__ = ``'``+dms``'`` Format degrees as signed "-/+deg°min′sec″" without suffix (`str`).
| F_DM_ = ``'``-dm``'`` Format degrees as signed "-/deg°min′" without suffix (`str`).
| F_DM__ = ``'``+dm``'`` Format degrees as signed "-/+deg°min′" without suffix (`str`).
| F_D_ = ``'``-d``'`` Format degrees as signed "-/deg°" without suffix (`str`).
| F_D__ = ``'``+d``'`` Format degrees as signed "-/+deg°" without suffix (`str`).
| F_MIN = ``'``min``'`` Format degrees as unsigned "[D]DDMM" plus suffix without symbols (`str`).
| F_MIN_ = ``'``-min``'`` Format degrees as signed "-/[D]DDMM" without suffix and symbols (`str`).
| F_MIN__ = ``'``+min``'`` Format degrees as signed "-/+[D]DDMM" without suffix and symbols (`str`).
| F_RAD = ``'``rad``'`` Convert degrees to radians and format as unsigned "RR" plus suffix (`str`).
| F_RAD_ = ``'``-rad``'`` Convert degrees to radians and format as signed "-/RR" without suffix (`str`).
| F_RAD__ = ``'``+rad``'`` Convert degrees to radians and format as signed "-/+RR" without suffix (`str`).
| F_SEC = ``'``sec``'`` Format degrees as unsigned "[D]DDMMSS" plus suffix without symbols (`str`).
| F_SEC_ = ``'``-sec``'`` Format degrees as signed "-/[D]DDMMSS" without suffix and symbols (`str`).
| F_SEC__ = ``'``+sec``'`` Format degrees as signed "-/+[D]DDMMSS" without suffix and symbols (`str`).
| F__E = ``'``e``'`` Format degrees as unsigned "%E" plus suffix without symbol (`str`).
| F__E_ = ``'``-e``'`` Format degrees as signed "-%E" without suffix and symbol (`str`).
| F__E__ = ``'``+e``'`` Format degrees as signed "-/+%E" without suffix and symbol (`str`).
| F__F = ``'``f``'`` Format degrees as unsigned "%F" plus suffix without symbol (`str`).
| F__F_ = ``'``-f``'`` Format degrees as signed "-%F" without suffix and symbol (`str`).
| F__F__ = ``'``+f``'`` Format degrees as signed "-/+%F" without suffix and symbol (`str`).
| F__G = ``'``g``'`` Format degrees as unsigned "%G" plus suffix without symbol (`str`).
| F__G_ = ``'``-g``'`` Format degrees as signed "-%G" without suffix and symbol (`str`).
| F__G__ = ``'``+g``'`` Format degrees as signed "-/+%G" without suffix and symbol (`str`).
| INF = `inf` Infinity (`float`), see function isinf, isfinite.
| MANTIS = `53` DEPRECATED, use `MANT_DIG`.
| MANT_DIG = `53` System's float mantissa bits = 53 (`int`).
| MAX = `1.79769313486e+308` System's float max ≈ 1.798e+308 (`float`).
| MIN = `2.22507385851e-308` System's float min ≈ 2.225e-308 (`float`).
| NAN = `nan` Not-A-Number (`float`), see function isnan.
| NEG0 = `-0.0` Negative 0.0 (`float`), see function isneg0.
| NN = `''` Empty (`str`), Nomen Nescio.
| OK = ``'``OK``'``
| PI = `3.14159265359` Constant math.pi (`float`).
| PI2 = `6.28318530718` Two PI, PI * 2, aka Tau (`float`).
| PI3 = `9.42477796077` Three PI, PI * 3 (`float`).
| PI3_2 = `4.71238898038` One and a half PI, PI * 3 / 2 (`float`).
| PI4 = `12.5663706144` Four PI, PI * 4 (`float`).
| PI_2 = `1.57079632679` Half PI, PI / 2 (`float`).
| PI_4 = `0.785398163397` 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 = `6371.008771415` 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 = `3440.06953446921` Mean (spherical) earth radius (`NM`, nautical miles).
| R_SM = `3958.753395372691` Mean (spherical) earth radius (`SM`, statute miles).
| R_VM = `6366707.0194937` Aviation/Navigation earth radius (`meter`).
| RefFrames = `` Registered reference frames (`enum-like`).
| S_DEG = ``'``°``'`` Degrees symbol "°" (`str`).
| S_MIN = ``'``\xe2\x80\xb2``'`` Minutes symbol "′" (`str`).
| S_RAD = `''` Radians symbol "" (`str`).
| S_SEC = ``'``″``'`` Seconds symbol "″" (`str`).
| S_SEP = `''` Separator between deg°, min′ and sec″ "" (`str`).
| Transforms = `Transforms.OSGB36: Transform(name='OSGB36', tx=-4`...`` Registered transforms (`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

### DeprecationWarnings() |
Get the `DeprecationWarning`s reported or raised. Returns: The number of `DeprecationWarning`s (`int`) or `None` if not enabled. Note: To get `DeprecationWarning`s if any, run `python` with environment variable `PYGEODESY_WARNINGS` set to a non-empty string AND use `python` command line option `-X dev`, `-W always`, or `-W error`, etc.

### 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 (longitudinal) zone with/-out Band letter for UTM or for UPS zone `"00"` or `0` (`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) Band letter `'C'|'D'..'W'|'X'` or UPS (polar) Band letter `'A'|'B'|'Y'|'Z'` (`str`). `datum` - Optional, the coordinate's datum (Datum). `falsed` - Both `easting` and `northing` are falsed (`bool`). `name` - Optional name (`str`). Returns: New UTM or UPS instance (Utm or Ups). Raises: `TypeError` - Invalid B({`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 (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 (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 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 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 (`float` 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 2nd flattening (`float` 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 (`float` 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 3rd flattening (`float` 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=`'``_``'`) |
DEPRECATED, use function anstr. Decorators: `@deprecated_function`

### 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) |
Return the antipode, the point diametrically opposite to a given point in `degrees`. Arguments: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). Returns: A LatLon2Tuple`(lat, lon)`. See Also: Geosphere.

### antipode_ (phi, lam) |
Return the antipode, the point diametrically opposite to a given point in `radians`. Arguments: `phi` - Latitude (`radians`). `lam` - Longitude (`radians`). Returns: A PhiLam2Tuple`(phi, lam)`. See Also: Geosphere.

### areaOf (points, adjust=True, radius=6371008.77141, wrap=True) |
Approximate the area of a polygon. Arguments: `points` - The polygon points (`LatLon`[]). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `radius` - Mean earth radius (`meter`) or `None`. `wrap` - Wrap lat-, wrap and unroll longitudes (`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 and ellipsoidalKarney.areaOf.

### areaof (points, adjust=True, radius=6371008.77141, wrap=True) |
DEPRECATED, use function areaOf. Decorators: `@deprecated_function`

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

### atan2d (y, x, reverse=False) |
Return `atan2(y, x)` in degrees [-180..+180], optionally reversed (by 180 degrees for `azi2`). See Also: Karney's C++ function Math.atan2d.

### atand (y_x) |
Return `atan(y_x)` angle in `degrees`. See Also: Function atan2d.

### attrs (inst, *names, **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 (`str`s). `pairs_kwds` - Keyword argument for function pairs, except `Nones=True` to in- or exclude missing or 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, **options) |
Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `options` - Optional keyword arguments for function bearing_. Returns: Initial or final bearing (compass `degrees360`) or zero if start and end point coincide.

### bearingDMS (bearing, form=`'``d``'`, prec=None, sep='') |
Convert bearing to a string. Arguments: `bearing` - Bearing from North (compass `degrees360`). `form` - Optional `bearing` format (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Optional 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` - Optional separator (`str`). Returns: Compass degrees per the specified `form` (`str`). JS name: toBrng.

### bearing_ (phi1, lam1, phi2, lam2, final=False, wrap=False) |
Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. Arguments: `phi1` - Start latitude (`radians`). `lam1` - Start longitude (`radians`). `phi2` - End latitude (`radians`). `lam2` - End longitude (`radians`). `final` - Return final bearing if `True`, initial otherwise (`bool`). `wrap` - Wrap and unrollPI longitudes (`bool`). Returns: Initial or final bearing (compass `radiansPI2`) or zero if start and end point coincide.

### bounds (points, wrap=True, LatLon=None) |
DEPRECATED, use function boundsOf. Returns: 2-Tuple `(latlonSW, latlonNE)` as `LatLon` or 4-Tuple `(latS, lonW, latN, lonE)` if `LatLon` is `None`. Decorators: `@deprecated_function`

### boundsOf (points, wrap=True, LatLon=None) |
Determine the lower-left SW and upper-right NE corners of a path or polygon. Arguments: `points` - The path or polygon points (`LatLon`[]). `wrap` - Wrap lat- and longitudes (`bool`). `LatLon` - Optional class to return the `bounds` corners (`LatLon`) or `None`. Returns: A Bounds2Tuple`(latlonSW, latlonNE)` as `LatLon`s 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. Example:
    >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
    >>> boundsOf(b)  # False
    >>> 45.0, 1.0, 46.0, 2.0

### callername (up=1, dflt='', source=False) |
Get the name of the calling callable. Arguments: `up` - Number of call stack frames up (`int`). `dflt` - Default return value (`any`). `source` - Include source file name and line number (`bool`). Returns: Name of the non-internal callable (`str`) or `dflt` if none found.

### cbrt (x) |
Compute the cubic root x**(1/3). Arguments: `x` - Value (`scalar`). Returns: Cubic root (`float`). See Also: Functions cbrt2 and sqrt3.

### cbrt2 (x) |
Compute the cubic root squared x**(2/3). Arguments: `x` - Value (`scalar`). Returns: Cubic root squared (`float`). See Also: Functions cbrt and sqrt3.

### centroidOf (points, wrap=True, LatLon=None) |
Determine the centroid of a polygon. Arguments: `points` - The polygon points (`LatLon`[]). `wrap` - Wrap lat-, wrap and unroll longitudes (`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`.

### 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 set to `True`. `TypeError` - Invalid `earth`. `ValueError` - `earth` or `lat`.

### circum3 (point1, point2, point3, circum=True, eps=8.881784197e-16, useZ=True) |
Return the radius and center of the smallest circle through or containing three (3-D) points. Arguments: `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 trilaterate3d2 if `useZ=True` else trilaterate2d2. `useZ` - If `True`, use the Z components, otherwise use `z=0` (`bool`). Returns: A Circum3Tuple`(radius, center, deltas)`. The `center`, an instance of `point1`'s (sub-)class, is coplanar with the three given points. Raises: `ImportError` - Package `numpy` not found, not installed or older than version 1.10 and `useZ=True`. `IntersectionError` - Near-concentric, coincident or colinear points or a trilateration or `numpy` issue. `TypeError` - Invalid `point2` or `point3`. See Also: Jean Meeus, "Astronomical Algorithms", 2nd Ed. 1998, page 127ff, circumradius, circumcircle, function meeus2 and methods `circum3` and `meeus2`.

### 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`).

### clipCS3 (points, lowerleft, upperright, closed=False, inull=False) |
DEPRECATED, use function clipCS4. Returns: Yield a ClipCS3Tuple`(start, end, index)` for each edge of the clipped path. Decorators: `@deprecated_function`

### clipCS4 (points, lowerleft, upperright, 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`). `upperright` - 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 `upperright` corners specify an invalid clip box. `PointsError` - Insufficient number of `points`.

### clipDMS (deg, limit) |
DEPRECATED, use function clipDegrees. Decorators: `@deprecated_function`

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

### clipLB6 (points, lowerleft, upperright, 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`). `upperright` - 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 `upperright` 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..+limit` range (`radians`). Returns: Clipped value (`radians`). Raises: `RangeError` - If `abs(rad)` beyond `limit` and rangerrors set to `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`.

### clipStr (bstr, limit=50, white='') |
DEPRECATED, use function clips. Decorators: `@deprecated_function`

### clips (bstr, limit=50, white='') |
Clip a string to the given length limit. Arguments: `bstr` - String (`bytes` or `str`). `limit` - Length limit (`int`). `white` - Optionally, replace all whitespace (`str`). Returns: The clipped or unclipped `bstr`.

### 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 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` - Wrap and unroll180 longitudes (`bool`). Returns: Compass angle from North (`degrees360`). Note: Courtesy Martin Schultz. See Also: Local, flat earth approximation.

### compassDMS (bearing, form=`'``d``'`, prec=None, sep='') |
Convert bearing to a string suffixed with compass point. Arguments: `bearing` - Bearing from North (compass `degrees360`). `form` - Optional `bearing` format (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Optional 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` - Optional separator (`str`). Returns: Compass degrees and point in the specified form (`str`).

### compassPoint (bearing, prec=3) |
Convert bearing to a compass point. Arguments: `bearing` - Bearing from North (compass `degrees360`). `prec` - Optional precision (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 `prec`. See Also: Dms.compassPoint and Compass rose. Example:
    >>> p = compassPoint(24, 1)  # 'N'
    >>> p = compassPoint(24, 2)  # 'NE'
    >>> p = compassPoint(24, 3)  # 'NNE'
    >>> p = compassPoint(24)     # 'NNE'
    >>> p = compassPoint(11, 4)  # 'NbE'
    >>> p = compassPoint(30, 4)  # 'NEbN'
    >>> p = compassPoint(11.249)  # 'N'
    >>> p = compassPoint(11.25)   # 'NNE'
    >>> p = compassPoint(-11.25)  # 'N'
    >>> p = compassPoint(348.749) # 'NNW'

### copysign0 (x, y) |
Like `math.copysign(x, y)` except `zero`, unsigned. Returns: `math.copysign(x, y)` if `x` else `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 fromula. Arguments: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `datum` - Datum or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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 fromula. 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 cosineAndoyerLambert, cosineForsytheAndoyerLambert_, cosineLaw_, equirectangular_, 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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). Returns: Angular distance (`radians`). Raises: `TypeError` - Invalid `datum`. See Also: Functions cosineForsytheAndoyerLambert, cosineAndoyerLambert_, cosineLaw_, equirectangular_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_ and Geodesy-PHP.

### cosineLaw (lat1, lon1, lat2, lon2, radius=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_, equirectangular_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_. Note: See note at function vincentys_.

### 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 reference frame `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.

### decodeEPSG2 (arg) |
DEPRECATED, use function epsg.decode2. Returns: 2-Tuple `(zone, hemipole)` Decorators: `@deprecated_function`

### 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`). `prec` - Optional 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` - Symbol for degrees (`str`). `s_M` - Symbol for minutes (`str`) or `""`. `s_S` - Symbol for seconds (`str`) or `""`. `neg` - Optional sign for negative (`'-'`). `pos` - Optional sign for positive (`''`). Returns: Either degrees, minutes or seconds (`str`).

### 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 gradians or gons). Arguments: `deg` - Angle (`degrees`). Returns: Angle (`grades`).

### degrees2m (deg, radius=6371008.77141, 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 ellipsoidal and polar radii) or `0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors set to `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 [-270..+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.

### 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-, Type-, URL-` or `ValueError` as a string (`str`). See Also: USGS National Map, the FAQ, geoid.py, module geoids, classes GeoidG2012B, GeoidKarney and GeoidPGM.

### enStr2 (easting, northing, prec, *extras) |
DEPRECATED, use function enstr2. Decorators: `@deprecated_function`

### encodeEPSG (zone, hemipole='', band='') |
DEPRECATED, use function epsg.encode. Returns: `EPSG` code (`int`). Decorators: `@deprecated_function`

### enstr2 (easting, northing, prec, *extras) |
Return easting, northing string representations. Arguments: `easting` - Easting from false easting (`meter`). `northing` - Northing from from false northing (`meter`). `prec` - Precision in number of digits (`int`, [1..5]). `extras` - Optional leading items (`str`s). Returns: `extras` + 2-Tuple `(eastingStr, northingStr)`. Raises: `ValueError` - Invalid `prec`.

### 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 for the projection (`str`). Returns: An EquidistantExact, EquidistantGeodSolve, EquidistantKarney or Equidistant instance. Raises: `AzimuthalError` - Invalid `lat0`, `lon0` or (spherical) `datum`. `TypeError` - Invalid `datum`.

### equirectangular (lat1, lon1, lat2, lon2, radius=6371008.77141, **options) |
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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `options` - Optional keyword arguments for function equirectangular_. Returns: Distance (`meter`, same units as `radius` or the ellipsoid or datum axes). Raises: `TypeError` - Invalid `radius`. See Also: Function equirectangular_ for more details, the available `options`, errors, restrictions and other, approximate or accurate distance functions.

### equirectangular3 (lat1, lon1, lat2, lon2, **options) |
DEPRECATED, use function `equirectangular_`. Returns: 3-Tuple `(distance2, delta_lat, delta_lon)`. Decorators: `@deprecated_function`

### equirectangular_ (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 the 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` - Wrap and unroll180 longitudes (`bool`). Returns: A Distance4Tuple`(distance2, delta_lat, delta_lon, unroll_lon2)`. Raises: `LimitError` - If the lat- and/or longitudinal delta exceeds the `-limit..+limit` range and limiterrors set to `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`). `y` - Y component (`scalar`). Returns: Appoximate norm (`float`). See Also: Function euclid_.

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

### euclidean (lat1, lon1, lat2, lon2, radius=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `adjust` - Adjust the longitudinal delta by the cosine of the mean latitude (`bool`). `wrap` - Wrap and unroll180 longitudes (`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_, equirectangular_, flatLocal_/hubeny_, flatPolar_, haversine_, thomas_ and vincentys_.

### exception_chaining (error=None) |
Get the previous exception's or exception chaining setting. Arguments: `error` - An error instance (`Exception`) or `None`. Returns: If `error is None`, return `True` if exception chaining is enabled for PyGeodesy errors, `False` if turned off and `None` if not available. If `error` is not `None`, return the previous, chained error or `None` otherwise. Note: Set `env` variable `PYGEODESY_EXCEPTION_CHAINING` to any non-empty value prior to `import pygeodesy` to enable exception chaining for `pygeodesy` errors.

### excessAbc (A, b, c) |
Compute the spherical excess `E` of a (spherical) triangle from two sides and the included 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: Function excessGirard, excessLHuilier, 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, Spherical trigonometry.

### excessKarney (lat1, lon1, lat2, lon2, radius=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple) or `None`. `wrap` - Wrap and unroll180 longitudes (`bool`). Returns: Surface area, signed (square `meter`, or units of `radius` squared) or spherical excess (`radians`) if `radius` is `None` or `0`. Raises: `TypeError` - Invalid `radius`. `UnitError` - Invalid `lat2` or `lat1`. `ValueError` - Semi-circular longitudinal delta. See Also: Function 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, Area of a spherical polygon.

### excessLHuilier (a, b, c) |
Compute the spherical excess `E` of a (spherical) triangle using L'Huilier'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 excessGirard, Spherical trigonometry.

### excessQuad (lat1, lon1, lat2, lon2, radius=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple) or `None`. `wrap` - Wrap and unroll180 longitudes (`bool`). Returns: Surface area, signed (square `meter`, or units of `radius` squared) or spherical excess (`radians`) if `radius` is `None` or `0`. 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, Spherical trigonometry.

### f2e2 (f) |
Return `e2`, the 1st eccentricity squared for a given flattening. Arguments: `f` - Flattening (`scalar` < 1, negative for prolate). Returns: The (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 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 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 2nd flattening (`float` 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 (`float` 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 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.

### fStr (floats, prec=6, fmt='f', ints=False, sep=', ') |
DEPRECATED, use function fstr. Decorators: `@deprecated_function`

### fStrzs (floatstr) |
DEPRECATED, use function fstrzs. Decorators: `@deprecated_function`

### f_2f (f_) |
Return `f`, the flattening for a given inverse flattening. Arguments: `f_` - Inverse flattening (`scalar` >>> 1). Returns: The flattening (`float` 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 acos1`(x)`. See Also: ShaderFastLibs.h.

### false2f (value, name=`'``value``'`, false=True, Error=<type 'exceptions.ValueError'>) |
DEPRECATED, use function falsed2f. Decorators: `@deprecated_function`

### falsed2f (falsed=True, Error=<type 'exceptions.ValueError'>, **name_value) |
DEPRECATED, use class Easting or Northing. Convert a falsed east-/northing to non-negative `float`. Arguments: `falsed` - Value includes false origin (`bool`). `Error` - Optional, overriding error (`Exception`). `name_value` - One `name=value` pair. Returns: The value (`float`). Decorators: `@deprecated_function` Raises: `Error` - Invalid or negative `name=value`.

### fasin1 (x) |
Fast approximation of 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 UK fathom to meter. Arguments: `fathoms` - Value in fathoms (`scalar`). Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `fathoms`.

### favg (v1, v2, f=0.5) |
Return the average of two values. Arguments: `v1` - One value (`scalar`). `v2` - Other value (`scalar`). `f` - Optional fraction (`float`). Returns: v1 + f * (v2 - v1) (`float`).

### fdot (a, *b) |
Return the precision dot product sum(a[i] * b[i] for i=0..len(a)). Arguments: `a` - List, sequence, tuple, etc. (`scalar`s). `b` - All positional arguments (`scalar`s). Returns: Dot product (`float`). Raises: `LenError` - Unequal `len(a)` and `len(b)`. See Also: Class Fdot.

### fdot3 (a, b, c, start=0) |
Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)). Arguments: `a` - List, sequence, tuple, etc. (`scalar`[]). `b` - List, sequence, tuple, etc. (`scalar`[]). `c` - List, sequence, tuple, etc. (`scalar`[]). `start` - Optional bias (`scalar`). Returns: Dot product (`float`). Raises: `LenError` - Unequal `len(a)`, `len(b)` and/or `len(c)`. `OverflowError` - Partial `2sum` overflow.

### fhorner (x, *cs) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) using the Horner form. Arguments: `x` - Polynomial argument (`scalar`). `cs` - Polynomial coeffients (`scalar`[]). Returns: Horner value (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar `x`. `ValueError` - No `cs` coefficients or `x` is not finite. See Also: Function fpolynomial and class Fhorner.

### fidw (xs, ds, beta=2) |
Interpolate using using Inverse Distance Weighting (IDW). Arguments: `xs` - Known values (`scalar`[]). `ds` - Non-negative distances (`scalar`[]). `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)`. `ValueError` - Invalid `beta`, negative `ds` value, 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`...`, 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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_/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`...`) |
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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). 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/hubeny, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatPolar_, equirectangular_, euclidean_, haversine_, thomas_ and vincentys_ and local, flat earth approximation.

### flatPolar (lat1, lon1, lat2, lon2, radius=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_, equirectangular_, euclidean_, flatLocal_/hubeny_, haversine_, thomas_ and vincentys_.

### fmean (xs) |
Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs). Arguments: `xs` - Values (`scalar`s). Returns: Mean value (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `ValueError` - No `xs` values.

### fmean_ (*xs) |
Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs). Arguments: `xs` - Values (`scalar`s). Returns: Mean value (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `ValueError` - No `xs` values.

### fpolynomial (x, *cs) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)). Arguments: `x` - Polynomial argument (`scalar`). `cs` - Polynomial coeffients (`scalar`[]). Returns: Polynomial value (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar `x`. `ValueError` - No `cs` coefficients or `x` is not finite. See Also: Function fhorner and class Fpolynomial.

### fpowers (x, n, alts=0) |
Return a series of powers [x**i for i=1..n]. Arguments: `x` - Value (`scalar`). `n` - Highest exponent (`int`). `alts` - Only alternating powers, starting with this exponent (`int`). Returns: Powers of `x` (`float`s or `int`s). Raises: `TypeError` - Non-scalar `x` or `n` not `int`. `ValueError` - Non-finite `x` or non-positive `n`.

### fprod (iterable, start=1.0) |
Iterable product, like `math.prod` or `numpy.prod`. Arguments: `iterable` - Terms to be multiplied (`scalar`[]). `start` - Initial term, also the value returned for an empty iterable (`scalar`). Returns: The product (`float`). See Also: NumPy.prod.

### fractional (points, fi, LatLon=None, **LatLon_kwds) |
Return the point at a given fractional index. Arguments: `points` - The points (`LatLon`[], Numpy2LatLon[], Tuple2LatLon[] or `other`[]). `fi` - The fractional index (FIx, `float` or `int`). `LatLon` - Optional class to return the intermediate, fractional point (`LatLon`) or `None`. `LatLon_kwds` - Optional `LatLon` keyword arguments, ignored of `LatLon is None`. Returns: A `LatLon` or if `LatLon` is `None`, a LatLon2Tuple`(lat, lon)` for `points[fi]` if fractional index `fi` is `int`, otherwise the intermediate point between `points[int(fi)]` and `points[int(fi) + 1]` for `float` fractional index `fi`. Raises: `IndexError` - Fractional index `fi` invalid or `points` not subscriptable or not closed. See Also: Class FIx and method FIx.fractional.

### 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_ (points1, points2, distance=None, units='') |
Compute the discrete Fréchet distance between two paths given as sets of points. Arguments: `points1` - First set of points (`LatLon`[], Numpy2LatLon[], Tuple2LatLon[] or `other`[]). `points2` - Second set of points (`LatLon`[], Numpy2LatLon[], Tuple2LatLon[] or `other`[]). `distance` - Callable returning the distance between a `points1` and a `points2` 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 `points1` respectively `points2`. Raises: `FrechetError` - Insufficient number of `points1` or `points2`. `RecursionError` - Recursion depth exceeded, see sys.getrecursionlimit(). `TypeError` - If `distance` is not a callable. Note: Function frechet_ does not support fractional indices for intermediate `points1` and `points2`.

### 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

### fstr (floats, prec=6, fmt='F', ints=False, sep=', ', strepr=None) |
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 (`str`). `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. 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 (iterable) |
Return an accurate floating point sum of values in the iterable. Assumes IEEE-754 floating point arithmetic.

### fsum2 (x, y) |
Precision summation of 2 positional arguments. Arguments: `x` - Value to be added (`scalar`[]). `x` - Value to be added (`scalar`[]). Returns: Accurate fsum (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar `xs` value. `ValueError` - Invalid or non-finite `xs` value.

### fsum_ (*xs) |
Precision summation of all positional arguments. Arguments: `xs` - Values to be added (`scalar`[]). Returns: Accurate fsum (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar `xs` value. `ValueError` - Invalid or non-finite `xs` value.

### ft2m (feet, usurvey=False) |
Convert International or US Survey feet to meter. Arguments: `feet` - Value in feet (`scalar`). `usurvey` - Convert US Survey feet (`bool`), International feet otherwise. Returns: Value in `meter` (`float`). Raises: `ValueError` - Invalid `feet`.

### furlong2m (furlongs) |
Convert a UK 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-, Type-, URL-` or `ValueError` 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 an GnomonicGeodSolve instance. `name` - Optional name for the projection (`str`). Returns: A GnomonicExact, GnomonicGeodSolve, GnomonicKarney or Gnomonic instance. Raises: `AzimuthalError` - Invalid `lat0`, `lon0` or (spherical) `datum`. `TypeError` - Invalid `datum`.

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

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

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

### grades400 (rad) |
Convert radians to grades (aka gradians or gons) 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=None, earth=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, LatLon=None, **LatLon_kwds) |
Compute the intersection of a Line-Of-Sight from a Point-Of-View in space with the surface of the earth. Arguments: `pov` - Point-Of-View outside the earth (`Cartesian`, Ecef9Tuple or Vector3d). `los` - Line-Of-Sight, direction to earth (Vector3d) or `None` to point to the earth' center. `earth` - The earth model (Datum, Ellipsoid, Ellipsoid2, a_f2Tuple or `scalar` radius in `meter`. `LatLon` - Class to convert insection point (`LatLon`, LatLon_). `LatLon_kwds` - Optional, additional `LatLon` keyword arguments, ignored if `LatLon is None`. Returns: The earth intersection (Vector3d, `Cartesian type` of `pov` or `LatLon`). Raises: `IntersectionError` - Null `pov` or `los` vector, `pov` is inside the earth or `los` points outside the earth or points in an opposite direction. `TypeError` - Invalid `pov`, `los` or `earth`. See Also: Stephen Hartzell.

### hausdorff_ (model, target, both=False, early=True, seed=None, units='', distance=None, point=<function _point at 0x7fa244e1ea50>) |
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=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_, equirectangular_, euclidean_, flatLocal_/hubeny_, flatPolar_, thomas_ and vincentys_. Note: See note at function vincentys_.

### heightOf (angle, distance, radius=6371008.77141) |
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).

### horizon (height, radius=6371008.77141, 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 (`str`). `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`...`, 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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_/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`...`) |
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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). 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/hubeny, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatPolar_, equirectangular_, euclidean_, haversine_, thomas_ and vincentys_ and local, flat earth approximation.

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

### hypot2 (x, y) |
Compute the squared norm x**2 + y**2. Arguments: `x` - Argument (`scalar`). `y` - Argument (`scalar`). Returns: `x**2 + y**2` (`float`).

### hypot2_ (*xs) |
Compute the squared norm `sum(x**2 for x in xs)`. Arguments: `xs` - X arguments, positional (`scalar`[]). Returns: Squared norm (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `ValueError` - Invalid or no `xs` value. See Also: Function hypot_.

### hypot3 (x, y, z) |
DEPRECATED, use function hypot_. Decorators: `@deprecated_function`

### hypot_ (*xs) |
Compute the norm sqrt(sum(x**2 for x in xs)). Arguments: `xs` - X arguments, positional (`scalar`[]). Returns: Norm (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `ValueError` - Invalid or no `xs` value. See Also: Similar to Python 3.8+ n-dimension math.hypot, but handling of exceptions, `nan` and `infinite` values is different. 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) |
DEPRECATED, use function instr. Decorators: `@deprecated_function`

### 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`).

### intersection3d3 (start1, end1, start2, end2, eps=2.22044604925e-16, useZ=True, Vector=None, **Vector_kwds) |
Compute the intersection point of two lines, each defined by or through a start and end point (3-D). 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`). `start2` - Start point of the second line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `end2` - End point of the second line (`Cartesian`, Vector3d, `Vector3Tuple` or `Vector4Tuple`). `eps` - Tolerance for skew line distance and length (`EPS`). `useZ` - If `True`, use the Z components, otherwise use `z=0` (`bool`). `Vector` - Class to return intersections (`Cartesian`, Vector3d or `Vector3Tuple`) or `None` for Vector3d. `Vector_kwds` - Optional, additional `Vector` keyword arguments, ignored if `Vector is None`. Returns: An Intersection3Tuple`(point, outside1, outside2)` with `point` an instance of `Vector` or `start1`'s (sub-)class. Raises: `IntersectionError` - Invalid, skew, non-coplanar or otherwise non-intersecting lines. See Also: Line-line intersection and line-line distance, skew lines and point-line distance.

### intersections2 (center1, radius1, center2, radius2, sphere=True, Vector=None, **Vector_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` - Class to return intersections (`Cartesian`, Vector3d or `Vector3Tuple`) or `None` for an instance of `center1`'s (sub-)class. `Vector_kwds` - Optional, additional `Vector` keyword arguments, ignored if `Vector is None`. Returns: If `sphere` is `True`, a 2-tuple of the `center` and `radius` of the intersection of the spheres. The `radius` is `0.0` for abutting spheres (and the `center` is aka 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 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.

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

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

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

### isantipode (lat1, lon1, lat2, lon2, eps=2.22044604925e-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: Geosphere.

### isantipode_ (phi1, lam1, phi2, lam2, eps=2.22044604925e-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: Geosphere.

### isbool (obj) |
Check whether an object is `bool`ean. Arguments: `obj` - The object (any `type`). Returns: `True` if `obj` is `bool`ean, `False` otherwise.

### isclass (obj) |
Return `True` if `obj` is a `class`. See Also: Python's `inspect.isclass`.

### 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` - Wrap lat-, wrap and unroll longitudes (`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. Example:
    >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
    >>> isclockwise(f)  # False
    >>> isclockwise(reversed(f))  # True

### iscolinearWith (point, point1, point2, eps=2.22044604925e-16) |
Check whether a point is colinear with two other (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`. Returns: `True` if `point` is colinear `point1` and `point2`, `False` otherwise. Raises: `TypeError` - Invalid `point`, `point1` or `point2`. See Also: Function nearestOn.

### isconvex (points, adjust=False, wrap=True) |
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` - Wrap lat-, wrap and unroll longitudes (`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`. Example:
    >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
    >>> isconvex(t)  # True
    >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
    >>> isconvex(f)  # False

### isconvex_ (points, adjust=False, wrap=True) |
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` - Wrap lat-, wrap and unroll longitudes (`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`. Example:
    >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
    >>> isconvex_(t)  # +1
    >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
    >>> isconvex_(f)  # 0

### isenclosedBy (point, points, wrap=False) |
Determine whether a point is enclosed by a polygon. Arguments: `point` - The point (`LatLon` or 2-tuple `(lat, lon)`). `points` - The polygon points (`LatLon`[]). `wrap` - Wrap lat-, wrap and unroll longitudes (`bool`). Returns: `True` if `point` is inside the polygon, `False` otherwise. Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - Invalid `point`, lat- or longitude. See Also: sphericalNvector.LatLon.isenclosedBy, sphericalTrigonometry.LatLon.isenclosedBy and MultiDop GeogContainPt (Shapiro et al. 2009, JTECH and Potvin et al. 2012, JTECH).

### isenclosedby (point, points, wrap=False) |
DEPRECATED, use function isenclosedBy. Decorators: `@deprecated_function`

### isfinite (obj) |
Check for `Inf` and `NaN` values. Arguments: `obj` - Value (`scalar`). Returns: `False` if `obj` is `INF` or `NAN`, `True` otherwise. Raises: `TypeError` - Non-scalar `obj`.

### isint (obj, both=False) |
Check for `int` type or an integer `float` value. Arguments: `obj` - The object (any `type`). `both` - Optionally, check `float` type and value (`bool`). Returns: `True` if `obj` is `int` or an integer `float`, `False` otherwise. Note: `isint(True)` or `isint(False)` returns `False` (and no longer `True`).

### isnear0 (x) |
Is `x` near zero? Arguments: `x` - Value (`scalar`). Returns: `True` if `abs(x) < EPS0`, `False` otherwise. See Also: Function isnon0.

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

### isnon0 (x) |
Is `x` non-zero? Arguments: `x` - Value (`scalar`). Returns: `True` if `abs(x) > EPS0`, `False` otherwise. See Also: Function isnear0.

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

### ispolar (points, wrap=False) |
Check whether a polygon encloses a pole. Arguments: `points` - The polygon points (`LatLon`[]). `wrap` - Wrap and unroll longitudes (`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) |
Check for scalar types. Arguments: `obj` - The object (any `type`). Returns: `True` if `obj` is `scalar`, `False` otherwise.

### issequence (obj, *excluded) |
Check for sequence types. Arguments: `obj` - The object (any `type`). `excluded` - Optional exclusions (`type`). Returns: `True` if `obj` is a sequence, `False` otherwise. Note: Excluding `tuple` implies excluding `namedtuple`.

### isstr (obj) |
Check for string types. Arguments: `obj` - The object (any `type`). Returns: `True` if `obj` is `str`, `False` otherwise.

### issubclassof (Sub, *Supers) |
Check whether a class is a sub-class of some class(es). Arguments: `Sub` - The sub-class (`class`). `Supers` - One or more C(super) classes (`class`). Returns: `True` if `Sub` is a sub-class of any `Supers`, `False` otherwise (`bool`).

### 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`.

### jekel4_ (*points, **Vector_Vector_kwds) |
Best-fit a sphere through two or more (3-D) points. Arguments: `points` - The points (each a `Cartesian`, Vector3d, `Vector3Tuple`, or `Vector4Tuple`). `Vector_Vector_kwds` - Optional class `Vector=None` to return the center and additional `Vector` keyword arguments. Returns: Jekel4Tuple`(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. `TypeError` - One of the `points` is invalid. `ValueError` - Too few `points`. See Also: Charles F. Jekel, "Least Squares Sphere Fit", Sep 13, 2015 and Appendix A, numpy.linalg.lstsq, Eberly 6 and function `circum3`.

### joined (*words, **sep) |
DEPRECATED, use `NN(...)`, `NN.join_` or `sep.join`. Decorators: `@deprecated_function`

### joined_ (*words, **sep) |
DEPRECATED, use `_SPACE_(...)`, `_SPACE_.join_` or `sep.join`, sep=" ". Decorators: `@deprecated_function`

### latDMS (deg, form=`'``dms``'`, prec=2, sep='') |
Convert latitude to a string, optionally suffixed with N or S. Arguments: `deg` - Latitude to be formatted (`degrees`). `form` - Optional `deg` format (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G, F_D_, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_ F_SEC_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Optional 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` - Optional separator (`str`). Returns: Degrees in the specified form (`str`). JS name: toLat.

### 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 (`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, form=`'``dms``'`, prec=None, sep=None) |
Convert one or more `LatLon` instances to strings. Arguments: `lls` - Single or a list, sequence, tuple, etc. (`LatLon`s). `form` - Optional `deg` format (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Optional 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 joining `lls` (`str` or `None`). Returns: A `str` or `tuple` of `sep` is `None` or `NN`.

### 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=2, sep='') |
Convert longitude to a string, optionally suffixed with E or W. Arguments: `deg` - Longitude to be formatted (`degrees`). `form` - Optional `deg` format (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Optional 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` - Optional separator (`str`). Returns: Degrees in the specified form (`str`). JS name: toLon.

### 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`.

### m2degrees (distance, radius=6371008.77141, 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 set to `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `distance`, `radius` or `lat`. See Also: Function m2radians and degrees2m.

### m2ft (meter, usurvey=False) |
Convert meter to International or US Survey feet (`ft`). Arguments: `meter` - Value in meter (`scalar`). `usurvey` - Convert to US Survey feet (`bool`), International feet otherwise. Returns: Value in `feet` (`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=6371008.77141, 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 set to `True`. `TypeError` - Invalid `radius`. `ValueError` - Invalid `distance`, `radius` or `lat`. See Also: Function m2degrees and radians2m.

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

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

### map2 (func, *xs) |
Apply arguments to a function and return 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 Python 2 behavior. Arguments: `func` - Function to apply (`callable`). `xs` - Arguments to apply (`list, tuple, ...`). Returns: Function results (`tuple`).

### meeus2 (point1, point2, point3, circum=False, useZ=True) |
Return the radius and Meeus' Type of the smallest circle containing or through three (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 non-zero `circumradius` always, ignoring the Meeus' Type I case (`bool`). `useZ` - If `True`, use the Z components, otherwise use `z=0` (`bool`). Returns: Meeus2Tuple`(radius, Type)`. Raises: `IntersectionError` - Coincident or linear points, iff `circum=True`. `TypeError` - Invalid `point1`, `point2` or `point3`. See Also: Jean Meeus, "Astronomical Algorithms", 2nd Ed. 1998, page 127ff, circumradius, circumcircle, function circum3 and methods `circum3` and `meeus2`.

### 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 (1st) eccentricity squared (`float` or -INF), 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 (`float` or -INF), 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 (`float` 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 (`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 (`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 `""`.

### nearestOn3 (point, points, closed=False, wrap=False, **options) |
DEPRECATED, use function nearestOn5. Returns: 3-Tuple `(lat, lon, distance)` Decorators: `@deprecated_function`

### nearestOn4 (point, points, closed=False, wrap=False, **options) |
DEPRECATED, use function nearestOn5. Returns: 4-Tuple `(lat, lon, distance, angle)` Decorators: `@deprecated_function`

### nearestOn5 (point, points, closed=False, wrap=False, LatLon=None, **options) |
Locate the point on a path or polygon closest to an other point. If the given point is within the extent of a polygon edge, the closest point is on that edge, otherwise the closest point is the nearest of that edge's end points. Distances are approximated by function equirectangular_, subject to the supplied `options`. Arguments: `point` - The other, reference point (`LatLon`). `points` - The path or polygon points (`LatLon`[]). `closed` - Optionally, close the path or polygon (`bool`). `wrap` - Wrap and unroll180 longitudes and longitudinal delta (`bool`) in function equirectangular_. `LatLon` - Optional class to return the closest point (`LatLon`) or `None`. `options` - Other keyword arguments for function equirectangular_. 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 equirectangular_ distance between the `closest` and reference `point` in `degrees`. The `angle` from the reference `point` to the `closest` is in compass `degrees360`, like function compassAngle. Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function equirectangular_. `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. See Also: Function degrees2m to convert `degrees` to `meter`.

### neg (x) |
Negate `x` unless `zero` or `NEG0`. Returns: `-x` if `x` else `0.0`.

### neg_ (*xs) |
Negate all of `xs` with neg. Returns: A `tuple(neg(x) for x in 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='') |
Normalize all degree ˚, minute ' and second " symbols in a string to the default symbols %s, %s and %s. Arguments: `strDMS` - DMS (`str`). `norm` - Optional replacement symbol, default symbol otherwise (`str`). Returns: Normalized DMS (`str`).

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

### notImplemented (inst, *args, **kwds) |
Raise a `NotImplementedError` for a missing method or property. Arguments: `inst` - Instance (`any`). `args` - Method or property positional arguments (any `type`s). `kwds` - Method or property keyword arguments (any `type`s).

### 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).

### 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 (`str`). `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 zip(names, reprs(values,...)))` 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: New `Vector` or if `Vector` is `None`, a named Vector3Tuple`(x, y, z)`. Raises: `VectorError` - Invalid `str3d`.

### parse3llh (strllh, height=0, sep=',', clipLat=90, clipLon=180) |
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 (`str`). `clipLat` - Keep latitude in `-clipLat..+clipLat` (`degrees`). `clipLon` - Keep longitude in `-clipLon..+clipLon` range (`degrees`). Returns: A LatLon3Tuple`(lat, lon, height)` in `degrees`, `degrees` and `float`. Raises: `RangeError` - Lat- or longitude value of `strllh` outside valid range and rangerrors set to `True`. `ValueError` - Invalid `strllh` or `height`. Note: See the Notes at function parseDMS. See Also: Functions parseDDDMMSS, parseDMS and parseDMS2. Example:
    >>> parse3llh('000°00′05.31″W, 51° 28′ 40.12″ N')
    (51.4778°N, 000.0015°W, 0)

### parseDDDMMSS (strDDDMMSS, suffix=`'``NSEW``'`, sep='', clip=0) |
Parse a lat- or longitude represention form [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" and "SS" (''). `clip` - Optionally, limit value to -clip..+clip (`degrees`). Returns: Degrees (`float`). Raises: `ParseError` - Invalid `strDDDMMSS` or `clip` or the `strDDDMMSS` form is incompatible with the suffixed or `suffix` compass point. `RangeError` - Value of `strDDDMMSS` outside the valid range and rangerrors set to `True`. Notes: Type `str` values "[D]DD", "[D]DDMM" and "[D]DDMMSS" for `strDDDMMSS` are parsed properly only if either unsigned and suffixed with a valid, compatible, `cardinal` compassPoint or if unsigned or signed, unsuffixed and with keyword argument `suffix` set to 'NS', 'EW' or a compatible compassPoint. Unlike function parseDMS, type `float`, `int` and other non-`str` `strDDDMMSS` values are interpreted form [D]DDMMSS. 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 compass point 'NS'. See Also: Functions parseDMS, parseDMS2 and parse3llh.

### parseDMS (strDMS, suffix=`'``NSEW``'`, sep='', clip=0) |
Parse a lat- or longitude representation `"lat, lon"` 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′ and sec″ ("''"). `clip` - Optionally, limit value to -clip..+clip (`degrees`). Returns: Degrees (`float`). Raises: `ParseError` - Invalid `strDMS` or `clip`. `RangeError` - Value of `strDMS` outside the valid range and rangerrors set to `True`. Note: Inlike function parseDDDMMSS, type `float`, `int` and other non-`str` `strDMS` values are considered as decimal 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 parseDDDMMSS, parseDMS2 and parse3llh.

### parseDMS2 (strLat, strLon, sep='', clipLat=90, clipLon=180) |
Parse a lat- and a longitude representions 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′ and sec″ (''). `clipLat` - Keep latitude in `-clipLat..+clipLat` range (`degrees`). `clipLon` - Keep longitude in `-clipLon..+clipLon` range (`degrees`). Returns: A LatLon2Tuple`(lat, lon)` in `degrees`. Raises: `ParseError` - Invalid `strLat` or `strLon`. `RangeError` - Value of `strLat` or `strLon` outside the valid range and rangerrors set to `True`. Note: See the Notes at function parseDMS. See Also: Functions parseDDDMMSS, parseDMS and parse3llh.

### 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 (`str`). Returns: The UTM coordinate (`Etm`) or if `Etm` is `None`, a UtmUps5Tuple`(zone, hemipole, easting, northing, band)`. The `hemipole` is the hemisphere `'N'|'S'`. Raises: `ETMError` - Invalid `strUTM`. `TypeError` - Invalid `datum`. Example:
    >>> u = parseETM5('31 N 448251 5411932')
    >>> u.toRepr()  # [Z:31, H:N, E:448251, N:5411932]
    >>> u = parseETM5('31 N 448251.8 5411932.7')
    >>> u.toStr()  # 31 N 448252 5411933

### 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 `"zoneBand, grid, 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 (`str`). Returns: The MGRS grid reference as `Mgrs` or if `Mgrs is None` as an Mgrs4Tuple`(zone, digraph, easting, northing)`. Raises: `MGRSError` - Invalid `strMGRS`. Example:
    >>> m = parseMGRS('31U DQ 48251 11932')
    >>> str(m)  # 31U DQ 48251 11932
    >>> m = parseMGRS('31UDQ4825111932')
    >>> repr(m)  # [Z:31U, G:DQ, E:48251, N:11932]
    >>> m = mgrs.parseMGRS('42SXD0970538646')
    >>> str(m)  # 42S XD 09705 38646
    >>> m = mgrs.parseMGRS('42SXD9738')  # Km
    >>> str(m)  # 42S XD 97000 38000

### parseOSGR (strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, name='') |
Parse a string representing an OSGR grid reference, consisting of `"[grid] easting northing"`. Accepts standard OS Grid References like 'SU 387 148', with or without whitespace separators, from 2- up to 10-digit references (1 m × 1 m square), 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` - Optional `Osgr` name (`str`). Returns: The OSGR coordinate (`Osgr`) or an EasNor2Tuple`(easting, northing)` if `Osgr` is `None`. Raises: `OSGRError` - Invalid `strOSGR`. Example:
    >>> g = parseOSGR('TG 51409 13177')
    >>> str(g)  # TG 51409 13177
    >>> g = parseOSGR('TG5140913177')
    >>> str(g)  # TG 51409 13177
    >>> g = parseOSGR('TG51409 13177')
    >>> str(g)  # TG 51409 13177
    >>> g = parseOSGR('651409,313177')
    >>> str(g)  # TG 51409 13177
    >>> g.toStr(prec=0)  # 651409,313177

### 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 -clip..+clip (`radians`). Returns: Radians (`float`). Raises: `ParseError` - Invalid `strRad` or `clip`. `RangeError` - Value of `strRad` outside the valid range and rangerrors set to `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` - Both `easting` and `northing` are falsed (`bool`). `name` - Optional `Ups` name (`str`). Returns: The UPS coordinate (`Ups`) or a UtmUps5Tuple`(zone, hemipole, easting, northing, band)` if `Ups` is `None`. The `hemipole` is the `'N'|'S'` pole, the UPS projection top/center. Raises: `UPSError` - Invalid `strUPS`.

### parseUTM (strUTM, datum=_UTM, Utm=_UTM, name='') |
DEPRECATED, use function parseUTM5. Returns: The UTM coordinate (Utm) or 4-tuple `(zone, hemisphere, easting, northing)` if `Utm` is `None`. Decorators: `@deprecated_function`

### 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` - Both easting and northing are falsed (`bool`). `name` - Optional `Utm` name (`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`. Example:
    >>> u = parseUTM5('31 N 448251 5411932')
    >>> u.toRepr()  # [Z:31, H:N, E:448251, N:5411932]
    >>> u = parseUTM5('31 N 448251.8 5411932.7')
    >>> u.toStr()  # 31 N 448252 5411933

### 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 instance name (`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 parseUTM5 and 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`). `Wm` - Optional class to return the WM coordinate (Wm) or `None`. `name` - Optional name (`str`). Returns: The WM coordinate (`Wm`) or an EasNorRadius3Tuple`(easting, northing, radius)` if `Wm` is `None`. Raises: `WebMercatorError` - Invalid `strWM`. Example:
    >>> u = parseWM('448251 5411932')
    >>> u.toRepr()  # [E:448251, N:5411932]

### perimeterOf (points, closed=False, adjust=True, radius=6371008.77141, wrap=True) |
Approximate the perimeter of a path or polygon. Arguments: `points` - The path or polygon points (`LatLon`[]). `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` - Wrap lat-, wrap and unroll longitudes (`bool`). Returns: Approximate perimeter (`meter`, same units as `radius`). Raises: `PointsError` - Insufficient number of `points` `TypeError` - Some `points` are not `LatLon`. `ValueError` - Invalid `radius`. Note: This perimeter is based on the equirectangular_ distance approximation and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. See Also: sphericalTrigonometry.perimeterOf and ellipsoidalKarney.perimeterOf.

### perimeterof (points, closed=False, adjust=True, radius=6371008.77141, wrap=True) |
DEPRECATED, use function perimeterOf. Decorators: `@deprecated_function`

### 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!

### 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.

### polygon (points, closed=True, base=None) |
DEPRECATED, use function points2. Decorators: `@deprecated_function`

### 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__E, F__F, F__G or F_RAD (`str`). `prec` - Optional 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 (`int`). Raises: `ValueError` - Invalid `form` or `prec` or `prec` outside valid range.

### print_ (*args, **nl_nt_prefix_end_file_flush_sep) |
Python 3-style `print` function. Arguments: `args` - Values to be converted to `str` and concatenated (`any` types). `nl=0` - Number of leading blank lines (`int`). `nt=0` - Number of additional , trailing blank lines (`int`). `prefix=NN` - To be inserted before the formatted text (`str`). Note: Python 3+ keyword arguments `end`, `file` and `flush` are silently ignored.

### printf (fmt, *args, **nl_nt_prefix_end_file_flush_sep) |
C-style `printf` function. Arguments: `fmt` - C-style formating text (`str`). `args` - Values to be formatted (`any` types). `nl=0` - Number of leading blank lines (`int`). `nt=0` - Number of additional , trailing blank lines (`int`). `prefix=NN` - To be inserted before the formatted text (`str`). Note: Python 3+ keyword arguments `end`, `file`, `flush` and `sep` are silently ignored.

### property_doc_ (doc) |
Decorator for a standard `property` with basic documentation. Arguments: `doc` - The property documentation (`str`). Example:
    >>> @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` - Southernmost latitude (`degrees90`). `lonW` - Westernmost longitude (`degrees180`). `latN` - Northernmost latitude (`degrees90`). `lonE` - Easternmost 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=6371008.77141, 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 ellipsoidal and polar radii) or `0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors set to `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) |
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`). 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.

### 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 (`str`). `ints` - Optionally, remove the decimal dot for `int` values (`bool`). Returns: A `tuple(map(fstr|repr, objs))` of `str`s.

### scalar (value, low=2.22044604925e-16, high=1.0, name=`'``scalar``'`, Error=<type 'exceptions.ValueError'>) |
DEPRECATED, use class Number_ or Scalar_. Returns: New value (`float` or `int` for `int` `low`). Decorators: `@deprecated_function` Raises: `Error` - Invalid `value`.

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

### simplify1 (points, distance=0.001, radius=6371008.77141, 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` - Optionally return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function equirectangular_. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function equirectangular_. `ValueError` - Tolerance `distance` or `radius` too small.

### simplify2 (points, pipe, radius=6371008.77141, shortest=False, indices=False, **options) |
DEPRECATED, use function simplifyRW. Decorators: `@deprecated_function`

### simplifyRDP (points, distance=0.001, radius=6371008.77141, 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` - Optional, shortest or perpendicular distance (`bool`). `indices` - Optionally return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function equirectangular_. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function equirectangular_. `ValueError` - Tolerance `distance` or `radius` too small.

### simplifyRDPm (points, distance=0.001, radius=6371008.77141, 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` - Optional, shortest or perpendicular distance (`bool`). `indices` - Optionally return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function equirectangular_. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function equirectangular_. `ValueError` - Tolerance `distance` or `radius` too small.

### simplifyRW (points, pipe=0.001, radius=6371008.77141, 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` - Optional, shortest or perpendicular distance (`bool`). `indices` - Optionally return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function equirectangular_. Returns: Simplified points (`LatLon`[]). Raises: `LimitError` - Lat- and/or longitudinal delta exceeds the `limit`, see function equirectangular_. `ValueError` - Tolerance `pipe` or `radius` too small.

### simplifyVW (points, area=0.001, radius=6371008.77141, 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` - Optionally return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function equirectangular_. 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 equirectangular_. `ValueError` - Tolerance `area` or `radius` too small.

### simplifyVWm (points, area=0.001, radius=6371008.77141, 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` - Optionally return the simplified point indices instead of the simplified points (`bool`). `options` - Optional keyword arguments passed thru to function equirectangular_. 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 equirectangular_. `ValueError` - Tolerance `area` or `radius` too small.

### sincos2 (*rad) |
Return the `sine` and `cosine` of angle(s). Arguments: `rad` - One or more angles (`radians`). Returns: The `sin(rad)` and `cos(rad)` for each angle. See Also: GeographicLib function sincosd and C++ sincosd.

### sincos2d (*deg) |
Return the `sine` and `cosine` of angle(s) in `degrees`. Arguments: `deg` - One or more angles (`degrees`). Returns: The `sin(deg)` and `cos(deg)` for each angle. See Also: GeographicLib function sincosd and C++ sincosd.

### 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) |
Compute the square root iff `x > EPS0**2`. Arguments: `x` - Value (`scalar`). Returns: Square root (`float`) or `0.0`.

### sqrt3 (x) |
Compute the square root, cubed sqrt(x)**3 or sqrt(x**3). Arguments: `x` - Value (`scalar`). Returns: Cubed square root (`float`). Raises: `ValueError` - Negative `x`. See Also: Functions cbrt and cbrt2.

### 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 (`str`). `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.

### 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 or ellipsoid to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_, equirectangular_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_ and vincentys_ and Geodesy-PHP.

### 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 (`str`). Returns: The Cassini-Soldner location (`Css`) or an EasNor3Tuple`(easting, northing, height)` if `Css` is `None`. 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='') |
Convert signed `degrees` to string, without suffix. Arguments: `deg` - Degrees to be formatted (`degrees`). `form` - Optional `deg` format (`str` or F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G, F_RAD, F_D_, F_DM_, F_DMS_, F_DEG_, F_MIN_, F_SEC_, F__E_, F__F_, F__G_, F_RAD_, F_D__, F_DM__, F_DMS__, F_DEG__, F_MIN__, F_SEC__, F__E__, F__F__, F__G__ or F_RAD__). `prec` - Optional 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` - Optional separator (`str`). `ddd` - Optional number of digits for deg° (2 or 3). `neg` - Optional sign for negative degrees ('-'). `pos` - Optional sign for positive degrees (''). Returns: Degrees in the specified form (`str`).

### toEtm8 (latlon, lon=None, datum=None, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, name='', zone=None, **cmoff) |
Convert a lat-/longitude point to an ETM coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Optional longitude (`degrees`) or `None`. `datum` - Optional datum for this 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`). `name` - Optional `Utm` name (`str`). `zone` - Optional UTM zone to enforce (`int` or `str`). `cmoff` - DEPRECATED, use `falsed`. Offset longitude from the zone's central meridian (`bool`). Returns: The ETM coordinate (`Etm`) or a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, convergence, scale)` if `Etm` is `None` or not `falsed`. The `hemipole` is the `'N'|'S'` hemisphere. Raises: `EllipticError` - No convergence. `ETMError` - Invalid `zone`. `RangeError` - If `lat` outside the valid UTM bands or if `lat` or `lon` outside the valid range and rangerrors set to `True`. `TypeError` - Invalid `datum` or `latlon` not ellipsoidal. `ValueError` - If `lon` value is missing or if `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` - Optional class to return the Lambert location (Lcc). `name` - Optional `Lcc` name (`str`). `Lcc_kwds` - Optional, additional `Lcc` keyword arguments, ignored if `Lcc` is `None`. Returns: The Lambert location (Lcc) or an EasNor3Tuple`(easting, northing, height)` if `Lcc is None`. Raises: `TypeError` - If `latlon` is not ellipsoidal.

### toMgrs (utm, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name='', **Mgrs_kwds) |
Convert a UTM coordinate to an MGRS grid reference. Arguments: `utm` - A UTM coordinate (Utm or Etm). `Mgrs` - Optional class to return the MGRS grid reference (Mgrs) or `None`. `name` - Optional `Mgrs` name (`str`). `Mgrs_kwds` - 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, digraph, easting, northing, band, datum)`. Raises: `TypeError` - If `utm` is not Utm nor Etm. `MGRSError` - Invalid `utm`. Example:
    >>> u = Utm(31, 'N', 448251, 5411932)
    >>> m = u.toMgrs()  # 31U DQ 48251 11932

### toOsgr (latlon, lon=None, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Osgr=<class 'pygeodesy.osgr.Osgr'>, 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`). `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`. `name` - Optional `Osgr` name (`str`). `Osgr_kwds` - Optional, additional `Osgr` keyword arguments, ignored if `Osgr is None`. Returns: The OSGR coordinate (`Osgr`) or an EasNor2Tuple`(easting, northing)` if `Osgr` is `None`. Raises: `OSGRError` - Invalid `latlon` or `lon`. `TypeError` - Non-ellipsoidal `latlon` or invalid `datum` or conversion failed. Example:
    >>> p = LatLon(52.65798, 1.71605)
    >>> r = toOsgr(p)  # TG 51409 13177
    >>> # for conversion of (historical) OSGB36 lat-/longitude:
    >>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36)

### 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` - False both easting and northing (`bool`). `strict` - Restrict `lat` to UPS ranges (`bool`). `name` - Optional `Ups` name (`str`). Returns: The UPS coordinate (`Ups`) or a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, convergence, scale)` if `Ups` is `None`. The `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 set to `True`. `TypeError` - If `latlon` is not ellipsoidal or `datum` invalid. `ValueError` - If `lon` value is missing or if `latlon` is invalid. See Also: Karney's C++ class UPS.

### toUtm (latlon, lon=None, datum=None, Utm=_UTM, cmoff=True, name='') |
DEPRECATED, use function toUtm8. Returns: The UTM coordinate (`Utm`) or a 6-tuple `(zone, easting, northing, band, convergence, scale)` if `Utm` is `None` or `cmoff` is `False`. Decorators: `@deprecated_function`

### toUtm8 (latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, name='', zone=None, **cmoff) |
Convert a lat-/longitude point to a UTM coordinate. Arguments: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Optional longitude (`degrees`) or `None`. `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` - False both easting and northing (`bool`). `name` - Optional `Utm` name (`str`). `zone` - Optional UTM zone to enforce (`int` or `str`). `cmoff` - DEPRECATED, use `falsed`. Offset longitude from the zone's central meridian (`bool`). Returns: The UTM coordinate (`Utm`) or if `Utm` is `None` or not `falsed`, a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, convergence, scale)`. The `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 set to `True`. `TypeError` - Invalid `datum` or `latlon` not ellipsoidal. `UTMError` - Invalid `zone`. `ValueError` - If `lon` value is missing or if `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 3900 km from the central meridian. Example:
    >>> p = LatLon(48.8582, 2.2945)  # 31 N 448251.8 5411932.7
    >>> u = toUtm(p)  # 31 N 448252 5411933
    >>> p = LatLon(13.4125, 103.8667) # 48 N 377302.4 1483034.8
    >>> u = toUtm(p)  # 48 N 377302 1483035

### 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` - Optional longitude (`degrees`) or `None`. `datum` - Optional datum to use this UTM coordinate, overriding `latlon`'s datum (`Datum`). `falsed` - 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` - Optional name (`str`). `cmoff` - DEPRECATED, use `falsed`. Offset longitude from zone's central meridian, for UTM only (`bool`). Returns: The UTM or UPS coordinate (`Utm` respectively `Ups`) or a UtmUps8Tuple`(zone, hemipole, easting, northing, band, datum, convergence, scale)` if `Utm` respectively `Ups` is `None` or `cmoff` is `False`. Raises: `RangeError` - If `lat` outside the valid UTM or UPS bands or if `lat` or `lon` outside the valid range and rangerrors set to `True`. `TypeError` - If `latlon` is not ellipsoidal or `lon` value is missing of `datum` is invalid. `UTMUPSError` - UTM or UPS validation failed. `ValueError` - Invalid `lat` or `lon`. See Also: Functions toUtm8 and toUps8.

### toWm (latlon, lon=None, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name='', **Wm_kwds) |
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`). `radius` - Optional earth radius (`meter`). `Wm` - Optional class to return the WM coordinate (Wm) or `None`. `name` - Optional name (`str`). `Wm_kwds` - Optional, additional `Wm` keyword arguments, ignored if `Wm is None`. Returns: The WM coordinate (`Wm`) or an EasNorRadius3Tuple`(easting, northing, radius)` if `Wm` is `None`. Raises: `ValueError` - If `lon` value is missing, if `latlon` is not scalar, if `latlon` is beyond the valid WM range and rangerrors is set to `True` or if `radius` is invalid. Example:
    >>> p = LatLon(48.8582, 2.2945)  # 448251.8 5411932.7
    >>> w = toWm(p)  # 448252 5411933
    >>> p = LatLon(13.4125, 103.8667)  # 377302.4 1483034.8
    >>> w = toWm(p)  # 377302 1483035

### trfXform (reframe1, reframe2, epoch=None, xform=None, rates=None) |
Define a new Terrestrial Reference Frame (TRF) conversion. Arguments: `reframe1` - Source reframe (RefFrame), converting from. `reframe2` - Destination reframe (RefFrame), converting to. `epoch` - Epoch, a fractional calendar year (`scalar` or `str`) or `None` for `reframe2.epoch`. `xform` - Helmert transform (`Tranform7Tuple`). `rates` - Helmert transform (`Tranform7Tuple`). Raises: `TRFError` - Invalid `epoch` or TRF conversion already exists.

### trilaterate2d2 (x1, y1, radius1, x2, y2, radius2, x3, y3, radius3, eps=None, Vector=None, **Vector_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` - Check the trilaterated point delta on all 3 circles (`scalar`) or `None`. `Vector` - Class to return the trilateration (Vector3d) or `None`. `Vector_kwds` - Optional, additional `Vector` keyword arguments, ignored if `Vector is None`. Returns: Trilaterated point as `Vector(x, y, **Vector_kwds)` or Vector2Tuple`(x, y)` if `Vector is None`.. Raises: `IntersectionError` - No intersection, colinear or near-concentric 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 trilaterate3d2.

### trilaterate3d2 (center1, radius1, center2, radius2, center3, radius3, eps=2.22044604925e-16, Vector=None, **Vector_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` - Tolerance (`scalar`), same units as `x`, `y`, and `z`. `Vector` - Class to return intersections (`Cartesian`, Vector3d or `Vector3Tuple`) or `None` for `center1`'s (sub-)class. `Vector_kwds` - Optional, additional `Vector` keyword arguments, ignored if `Vector is None`. 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 and implementation and trilaterate2d2.

### unStr (name, *args, **kwds) |
DEPRECATED, use function unstr. Decorators: `@deprecated_function`

### unroll180 (lon1, lon2, wrap=True) |
Unroll longitudinal delta and wrap longitude in degrees. Arguments: `lon1` - Start longitude (`degrees`). `lon2` - End longitude (`degrees`). `wrap` - 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` - 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.

### unsign0 (x) |
Return unsigned `0.0`. Returns: `x` if `x` else `0.0`.

### unstr (named, *args, **kwds) |
Return the string representation of an invokation. Arguments: `named` - Function, method or class name (`str`). `args` - Optional positional arguments. `kwds` - Optional keyword arguments. 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 name (`str`). Returns: A UtmUpsLatLon5Tuple`(zone, band, hemipole, lat, lon)` where `hemipole` is the `'N'|'S'` pole, the UPS projection top/center. Raises: `RangeError` - If `strict` and `lat` in the UTM and not the UPS range or if `lat` or `lon` outside the valid range and rangerrors set to `True`. `ValueError` - Invalid `lat` or `lon`.

### utmZoneBand2 (lat, lon) |
DEPRECATED, use function utmZoneBand5. Returns: 2-Tuple `(zone, band)`. Decorators: `@deprecated_function`

### 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` - Offset longitude from the zone's central meridian (`bool`). `name` - Optional name (`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 set to `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, Ups or `5+Tuple`). `falsed` - `5+Tuple` easting and northing are falsed (`bool`). `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` - `5+Tuple` easting and northing are falsed (`bool`). `ok` - Result to return if validation passed (`ok`). Returns: `ok` if validation passed, the UTMUPSError otherwise. 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` - Offset longitude from the zone's central meridian, for UTM only (`bool`). `name` - Optional name (`str`). Returns: A UtmUpsLatLon5Tuple`(zone, band, hemipole, lat, lon)` where `hemipole` is `'N'|'S'`, the UTM hemisphere or UPS pole, the UPS 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 set to `True`. `ValueError` - Invalid `lat` or `lon`. See Also: Functions utmZoneBand5 and upsZoneBand5.

### vincentys (lat1, lon1, lat2, lon2, radius=6371008.77141, 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, ellipsoid or datum (`meter`, Ellipsoid, Ellipsoid2, Datum or a_f2Tuple). `wrap` - Wrap and unroll180 longitudes (`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_, equirectangular_, 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).

### 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 [-270..+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 [-3PI/2..+PI/2]. Arguments: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI_2`).

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

Variables Details

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

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

  ### Ellipsoids Registered ellipsoids (`enum-like`). Value:
      Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a=6377563.396, b=63562
      56.90923729, f_=299.3249646, f=0.00334085, f2=0.00335205, n=0.00167322
      , e=0.08167337, e2=0.00667054, e22=0.00671533, e32=0.00334643, A=63669
      14.60892522, L=10001126.0807165, R1=6370461.23374576, R2=6370459.65470
      808, R3=6370453.30994572, Rbiaxial=6366919.065224, Rtriaxial=6372243.4
      5317691),
      Ellipsoids.Sphere: Ellipsoid(name='Sphere', a=6371008.771415, b=637100
      8.771415, f_=0, f=0, f2=0, n=0, e=0, e2=0, e22=0, e32=0, A=6371008.771
      ...

  ### Transforms Registered transforms (`enum-like`). Value:
      Transforms.OSGB36: Transform(name='OSGB36', tx=-446.448, ty=125.157, t
      z=-542.06, rx=-0, ry=-0, rz=-0, s=20.4894, s1=1.00002, sx=-0.1502, sy=
      -0.247, sz=-0.8421),
      Transforms.WGS84: Transform(name='WGS84', tx=0, ty=0, tz=0, rx=0, ry=0
      , rz=0, s=0, s1=1, sx=0, sy=0, sz=0)