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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 and approximate methods for geodetic (lat-/longitude) and geocentric cartesian (x/y/z) coordinates.

Transcribed from JavaScript originals by Chris Veness (C) 2005-2016 and a C++ class by Charles Karney (C) 2008-2017 and published under the same MIT License**.

There are three modules for ellipsoidal earth models, ellipsoidalKarney, -Vincenty and -Nvector and two for spherical ones, sphericalTrigonometry and -Nvector. Each module provides a LatLon class with methods and functions to compute distance, initial and final bearing, intermediate and nearest points, area, perimeter, conversions and unrolling, among other things. For more information and further details see the documentation, the descriptions of Latitude/Longitude, Vincenty and Vector-based geodesy, the original JavaScript source or docs and the Python GeographicLib.

Also included are modules for conversions to and from UTM (Universal Transverse Mercator) and Web Mercator (Pseudo-Mercator) coordinates, MGRS (NATO Military Grid Reference System) and OSGR (British Ordinance Survery Grid Reference) grid references and a module for encoding and decoding Geohashes.

Other modules provide Lambert conformal conic projections and positions (from John P. Snyder, "Map Projections -- A Working Manual", 1987, pp 107-109), functions to clip a path or polygon of `LatLon` points using the Cohen–Sutherland 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 Reumann-Witkam the algorithms and modified versions of the former and classes to interpolate the height of `LatLon` points and several `Geoid` models.

# Testing

All Python source code has been statically checked with PyChecker, PyFlakes, PyCodeStyle (formerly Pep8) and McCabe using Python 2.7.16 and with Flake8 using Python 3.7.3, both in 64-bit on macOS 10.13.6 High Sierra.

The tests have been run with Python 2.7.16 and 3.7.3 (both with geographiclib 1.49, numpy 1.16.1 and scipy 1.2.1) and with PyPy 6.0.0 (Python 2.7.13 and 3.5.3) on macOS 10.13.6 High Sierra. The results of those tests are included in the distribution files.

The tests also run with Python 2.6.9, 2.7.14, 3.5.6 and 3.6.3 (and geographiclib 1.49) on Ubuntu 14.04 and with Python 3.7.3 (and geographiclib 1.49) on Debian 9 all in 64-bit only and with Python 2.7.15, 3.6.8 and 3.7.2 (all with geographiclib 1.49) on Windows Server 2012R2 in both 32- and 64-bit.

On Python 3.7+, the tests run with and without `lazy import`.

Previously, the tests were run with Python 2.6.9 (and numpy 1.6.2), 2.7.10 (and numpy 1.8.0rc1), 2.7.13, 2.7.14, 2.7.15 (and numpy 1.13.1, 1.14.0 or 1.15.2), 3.5.3, 3.6.2, 3.6.3, 3.6.4, 3.6.5, 3.7.0, 3.7.2 and Intel-Python 3.5.3 (and numpy 1.11.3) on MacOS X 10.10 Yosemite, MacOS X 10.11 El Capitan, macOS 10.12 Sierra, macOS 10.13.5 High Sierra and macOS 10.14 Mojave, with Pythonista 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 on iPad4, with Pythonista 3.2 on iOS 11.4.1 and 12.0 on iPad4, iPhone7 and/or iPhone10, all in 64-bit only and with 32-bit Python 2.6.6 on Windows XP SP3 and with 32-bit Python 2.7.14 on Windows 10 Pro.

# Documentation

In addition to the PyGeodesy package, the 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`).

# 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 setup.py install`. To run all PyGeodesy tests, type `python setup.py test` before installation.

Installation of GeographicLib, NumPy and SciPy is optional. However, the former is required for module `ellipsoidalKarney` classes `LatLon` and `Cartesian` and functions `areaOf` and `perimeterOf`. The latter are needed for the `Geoid...` and `Height...` interpolators, except GeoidKarney, HeightIDW, HeightIDW2 and HeightIDW3.

# Notes

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

__

**) Copyright (C) 2016-2019 -- mrJean1 at Gmail dot com

`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: 19.04.08

Submodules
pygeodesy.bases: (INTERNAL) Common base classes. pygeodesy.clipy: Functions to clip a path or polygon of `LatLon` points. pygeodesy.datum: Classes Datum, Ellipsoid and Transform and registries thereof. pygeodesy.dms: Functions to parse and format bearing, compass, lat- and longitudes in various forms of degrees, minutes and seconds. pygeodesy.elevations: Functions to obtain elevations and geoid heights thru web services, for (lat, lon) locations, currently limited to the Conterminous US (CONUS), see also module geoids and classes GeoidG2012B, GeoidKarney and GeoidPGM and USGS10mElev.py. pygeodesy.ellipsoidalBase: (INTERNAL) Ellipsoidal base classes. pygeodesy.ellipsoidalKarney: Ellipsoidal geodetic (lat-/longitude) and cartesian (x/y/z) classes LatLon and Cartesian and functions areaOf and perimeterOf based on the Python implementation of Charles F. F. Karney's GeographicLib. pygeodesy.ellipsoidalNvector: N-vector-based ellipsoidal geodetic (lat-/longitude) and cartesion (x/y/z) classes LatLon, Ned, Nvector and Cartesian and functions meanOf and toNed. pygeodesy.ellipsoidalVincenty: Vincenty's ellipsoidal geodetic (lat-/longitude) and cartesian (x/y/z) classes LatLon, Cartesian and VincentyError and functions areaOf and perimeterOf. pygeodesy.fmath: Precision floating point functions, utilities and constants. pygeodesy.formy: Formulary of basic geodesy functions and approximations. pygeodesy.geohash: Class Geohash and several functions to encode, decode and inspect geohashes. pygeodesy.geoids: Classes GeoidG2012B, GeoidKarney and GeoidPGM to interpolate the height of various geoids at `LatLon` locations or separate lat-/longitudes using different interpolation methods. pygeodesy.heights: Classes to interpolate the height of `LatLon` locations or separate lat-/longitudes. pygeodesy.lazily: Lazily import `pygeodesy` modules and attributes. pygeodesy.lcc: Lambert conformal conic projection for 1- or 2-Standard Parallels class Conic, Conics registry and position class Lcc. pygeodesy.mgrs: Military Grid Reference System (MGRS/NATO) class Mgrs and functions parseMGRS and toMgrs. pygeodesy.nvector: N-vector base class Nvector and function sumOf. pygeodesy.osgr: Ordinance Survey Grid References (OSGR) class Osgr and functions parseOSGR and toOsgr. pygeodesy.points: Functions to handle collections and sequences of `LatLon` points specified as 2-d NumPy, `arrays` or tuples as `LatLon` or as `pseudo-x/-y` pairs. pygeodesy.simplify: Seven functions to simplify or linearize a path of `LatLon` points. pygeodesy.sphericalBase: (INTERNAL) Spherical base classes. pygeodesy.sphericalNvector: N-vector-based spherical geodetic (lat-/longitude) classes LatLon and Nvector and functions areaOf, intersection, meanOf, nearestOn2, triangulate and trilaterate. pygeodesy.sphericalTrigonometry: Trigonometric spherical geodetic (lat-/longitude) class LatLon and functions areaOf, intersection, isPoleEnclosedBy, meanOf, nearestOn2 and perimeterOf. pygeodesy.utily: Geometric and other utility functions and constants. pygeodesy.utm: Universal Transverse Mercator (UTM) class Utm and functions parseUTM and toUtm. pygeodesy.vector3d: Generic 3-D vector base class Vector3d and function sumOf. pygeodesy.webmercator: Web Mercator (WM) class Wm and functions parseWM and toWm.

Classes
| LazyImportError Lazy import is not supported, disabled or failed some other way.
| CrossError Error raised for zero or near-zero vectorial cross products, occurring for coincident or colinear points, paths or bearings.
| Geohash Geohash class, sub-class of str.
| VincentyError Error raised from Vincenty's direct and inverse methods for coincident points or lack of convergence.
| Conic Lambert conformal conic projection (1- or 2-SP).
| Datum Ellipsoid and transform parameters for an earth model.
| Ellipsoid Ellipsoid with semi-major, semi-minor axis, inverse flattening and several other pre-computed, frequently used values.
| Fdot Precision dot product.
| Fhorner Precision polynomial evaluation using the Horner form.
| Fpolynomial Precision polynomial evaluation.
| Fsum Precision summation similar to standard Python function `math.fsum`.
| GeoidError Geoid interpolator or interpolation error.
| 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.
| GeoidKarney Geoid height interpolator for Charles Karney's GeographicLib Earth Gravitational Model (EGM) geoid egm*.pgm datasets using bilinear or cubic interpolation and caching in pure Python transcribed from Karney's C++ class Geoid.
| GeoidPGM Geoid height interpolator for Charles Karney's GeographicLib Earth Gravitational Model (EGM) geoid egm*.pgm datasets but based on `SciPy` RectBivariateSpline or interp2d interpolation.
| HeightCubic Height interpolator based on `SciPy` interp2d `kind='cubic'`.
| HeightError Height interpolator or interpolation error.
| HeightIDW Height interpolator using Inverse Distance Weighting (IDW) and the angular `Euclidean` distance from function euclidean_.
| HeightIDW2 Height interpolator using Inverse Distance Weighting (IDW) and the `equirectangular` distance (in radians squared) like function equirectangular_.
| HeightIDW3 Height interpolator using Inverse Distance Weighting (IDW) and the angular `Haversine` distance from function haversine_.
| HeightLSQBiSpline Height interpolator using `SciPy` LSQSphereBivariateSpline.
| HeightLinear Height interpolator based on `SciPy` interp2d `kind='linear]`.
| HeightSmoothBiSpline Height interpolator using `SciPy` SmoothSphereBivariateSpline.
| LatLon2psxy Wrapper for `LatLon` points as "on-the-fly" pseudo-xy coordinates.
| LatLonHeightBase (INTERNAL) Base class for `LatLon` points on spherical or ellipsiodal earth models.
| LatLon_ Low-overhead `LatLon` class for Numpy2LatLon and Tuple2LatLon.
| Lcc Lambert conformal conic East-/Northing location.
| LimitError Error raised for lat- or longitudinal deltas exceeding the limit in functions equirectangular and equirectangular_.
| Mgrs Military Grid Reference System (MGRS/NATO) references, with method to convert to UTM coordinates.
| Numpy2LatLon Wrapper for `NumPy` arrays as "on-the-fly" `LatLon` points.
| Osgr Ordinance Survey Grid References (OSGR) coordinate.
| PGMError Error parsing or cropping an `egm*.pgm` geoid dataset.
| RangeError Error raised for lat- or longitude values outside the clip, clipLat, clipLon or limit range in function clipDMS, parse3llh, parseDMS or parseDMS2.
| SciPyError Error raised for `SciPy` errors.
| SciPyWarning Exception thrown for `SciPy` warnings.
| Transform Helmert transformation.
| Tuple2LatLon Wrapper for tuple sequences as "on-the-fly" `LatLon` points.
| UTMError UTM parse or other error.
| Utm Universal Transverse Mercator (UTM) coordinate.
| Wm Web Mercator (WM) coordinate.
| _Based (INTERNAL) Base class with name.
| _Enum (INTERNAL) Enum-like `dict` sub-class.
| _GeoidBase (INTERNAL) Base class for `Geoid...`s.
| _Named (INTERNAL) Base class for named objects.
| _Registered (INTERNAL) Base class for registered instances.
| _VectorBased (INTERNAL) Base class for Vector3d.

Functions
crosserrors(raiser=None) Get/set raising of vectorial cross product errors. |
areaof(*args, **kwds) DEPRECATED, use function `areaOf`. |
bounds(*args, **kwds) DEPRECATED, use function `boundsOf`. |
isenclosedby(*args, **kwds) DEPRECATED, use function `isenclosedBy`. |
perimeterof(*args, **kwds) DEPRECATED, use function `perimeterOf`. |
acos1(x) Return math.acos(max(-1, min(1, x))). |
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. |
areaOf(points, adjust=True, radius=6371008.77141, wrap=True) Approximate the area of a polygon. |
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_(a1, b1, a2, b2, final=False, wrap=False) Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. |
boundsOf(points, wrap=True, LatLon=None) Determine the lower-left SW and upper-right NE corners of a path or polygon. |
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. |
classname(inst, prefixed=None) Return an instance' module and class name. |
classnaming(prefixed=None) Set the default class naming for `[module.]class` names. |
clipCS3(points, lowerleft, upperright, closed=False, inull=False) Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm. |
clipDMS(deg, limit) Clip a lat- or longitude to the given range. |
clipSH(points, corners, inull=False, closed=False) Clip a polygon against a clip region or box using the Sutherland_Hodgman algorithm. |
clipSH3(points, corners, inull=False, closed=False) Clip a polygon against a clip region or box using the Sutherland_Hodgman algorithm. |
clipStr(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. |
degrees(x) Convert angle x from radians to degrees. |
degrees180(rad) Convert radians to degrees and wrap (-180..+180]. |
degrees2m(deg, radius=6371008.77141, lat=0) Convert angle to distance along equator or at other latitude. |
degrees360(rad) Convert radians to degrees and wrap (0..+360]. |
degrees90(rad) Convert radians to degrees and wrap (-270..+90]. |
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) Return easting, northing string representations. |
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. |
euclidean(lat1, lon1, lat2, lon2, radius=6371008.77141, adjust=True, wrap=False) Approximate the `Euclidian` distance between two (spherical) points. |
euclidean_(a2, a1, b21, adjust=True) Approximate the angular `Euclidean` distance between two (spherical) points. |
fStr(floats, prec=6, sep=`'``,` `'`, fmt=`'``%.*f``'`, ints=False) Convert floats to string, optionally with trailing zero decimals stripped. |
fStrzs(fstr) Strip trailing zero decimals from a float string. |
false2f(value, name=`'``value``'`, false=True) Convert a false east-/northing to non-negative float. |
favg(v1, v2, f=0.5) Return the weighted 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. |
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 `numpy.prod`. |
frange(start, number, step=1) Generate a range of `float`s. |
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. |
fsum(iterable) Return an accurate floating point sum of values in the iterable. |
fsum_(*xs) Precision summation of the positional argument vulues. |
ft2m(feet) Convert International feet to meter (m). |
geoidHeight2(lat, lon, model=0, timeout=2.0) Get the `NAVD88` geoid height at an `NAD83` location. |
halfs2(str2) Split a string in 2 halfs. |
haversine(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False) Compute the distance between two (spherical) points using the Haversine formula. |
haversine_(a2, a1, b21) 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 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. |
hypot(x, y) Return the Euclidean distance, sqrt(x*x + y*y). |
hypot1(x) Compute the norm sqrt(1 + x**2). |
hypot3(x, y, z) Compute the norm sqrt(x**2 + y**2 + z**2). |
inStr(inst, *args, **kwds) Return the string representation of an instance. |
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. |
isclockwise(points, adjust=False, wrap=True) Determine the direction of a path or polygon. |
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. |
isfinite(obj) Check for `Inf` and `NaN` values. |
isint(obj, both=False) Check for integer type or integer value. |
ispolar(points, wrap=False) Check whether a polygon encloses a pole. |
isscalar(obj) Check for scalar types. |
issequence(obj, *excluded) Check for sequence types. |
iterNumpy2(obj) Iterate over Numpy2 wrappers or other sequences exceeding the threshold. |
iterNumpy2over(n=None) Get or set the iterNumpy2 threshold. |
latDMS(deg, form=`'``dms``'`, prec=2, sep=`'````'`) Convert latitude to a string suffixed with N or S. |
len2(seq) Make built-in function `len` work for generators, iterators, etc. |
limiterrors(raiser=None) Get/set the raising of limit errors. |
lonDMS(deg, form=`'``dms``'`, prec=2, sep=`'````'`) Convert longitude to a string suffixed with E or W. |
m2NM(meter) Convert meter to nautical miles (NM). |
m2SM(meter) Convert meter to statute miles (SM). |
m2degrees(meter, radius=6371008.77141) Convert distance to angle along equator. |
m2ft(meter) Convert meter to International feet (ft). |
m2km(meter) Convert meter to kilo meter (km). |
map1(func, *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. |
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, **options) Locate the point on a path or polygon closest to an other point. |
normDMS(strDMS, norm=`'````'`) Normalize all degree ˚, minute ' and second " symbols in a string to the default symbols °, ′ and ″. |
parse3llh(strll, height=0, sep=`'``,``'`, clipLat=90, clipLon=180) Parse a string representing lat-, longitude and height point. |
parseDMS(strDMS, suffix=`'``NSEW``'`, sep=`'````'`, clip=0) Parse a string representing deg°min′sec″ to degrees. |
parseDMS2(strLat, strLon, sep=`'````'`, clipLat=90, clipLon=180) Parse lat- and longitude representions. |
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 and northing. |
parseOSGR(strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, name=`'````'`) Parse an OSGR coordinate string to an Osgr instance. |
parseUTM(strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Utm=<class 'pygeodesy.utm.Utm'>, name=`'````'`) Parse a string representing a UTM coordinate, consisting of zone, hemisphere, easting and northing. |
parseWM(strWM, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name=`'````'`) Parse a string 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. |
points2(points, closed=True, base=None) Check a 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. |
property_RO(method) Decorator for `Read_Only` property. |
radians(x) Convert angle x from degrees to radians. |
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]. |
rangerrors(raiser=None) Gert/set raising of range errors. |
scalar(value, low=2.22044604925e-16, high=1.0, name=`'``scalar``'`) Validate a scalar. |
simplify1(points, distance, 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, radius=6371008.77141, shortest=False, indices=False, **options) Ramer-Douglas-Peucker (RDP) simplification of a path of `LatLon` points. |
simplifyRDPm(points, distance, radius=6371008.77141, shortest=False, indices=False, **options) Modified Ramer-Douglas-Peucker (RDPm) simplification of a path of `LatLon` points. |
simplifyRW(points, pipe, radius=6371008.77141, shortest=False, indices=False, **options) Reumann-Witkam (RW) simplification of a path of `LatLon` points. |
simplifyVW(points, area, radius=6371008.77141, attr=None, indices=False, **options) Visvalingam-Whyatt (VW) simplification of a path of `LatLon` points. |
simplifyVWm(points, area, 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 an angle. |
splice(iterable, n=2, fill=object()) Split an iterable into `n` slices. |
sqrt3(x) Compute the square root cubed sqrt(x)**3 or sqrt(x**3). |
tanPI_2_2(rad) Compute the tangent of half angle, 90 degrees rotated. |
tan_2(rad) Compute the tangent of half angle. |
toDMS(deg, form=`'``dms``'`, prec=2, sep=`'````'`, ddd=2, neg=`'``-``'`, pos=`'````'`) Convert signed degrees to string, without suffix. |
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=`'````'`) Convert an (ellipsoidal) geodetic point to a Lambert location. |
toMgrs(utm, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name=`'````'`) 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=`'````'`) Convert a lat-/longitude point to an OSGR coordinate. |
toUtm(latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, name=`'````'`, cmoff=True) Convert a lat-/longitude point to a UTM coordinate. |
toWm(latlon, lon=None, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name=`'````'`) Convert a lat-/longitude point to a WM coordinate. |
unStr(name, *args, **kwds) Return the string representation of an invokation. |
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. |
utmZoneBand2(lat, lon) Return the UTM zone number and UTM Band letter for a location. |
vincentys(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False) Compute the distance between two (spherical) points using Vincenty's spherical formula. |
vincentys_(a2, a1, b21) 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]. |

Variables
| pygeodesy_abspath = ``'``..../PyGe``...`` Fully qualified `pygeodesy` directory name (`str`).
| version = ``'``19.4.8``'`` Normalized `PyGeodesy` version (`str`).
| Conics = `Conics.Be08Lb: Conic(name='Be08Lb', lat0=50.797815, l`...`` Registered conics (`enum-like`).
| Datums = `Datums.BD72: Datum(name='BD72', ellipsoid=Ellipsoids.`...`` Registered datums (`enum-like`).
| EPS = `2.22044604925e-16` System's epsilon (`float`)
| EPS1 = `1.0` 1 - EPS (`float`), about 0.9999999999999998
| Ellipsoids = `Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a`...`` Registered ellipsoids (`enum-like`).
| F_D = ``'``d``'`` Format degrees as deg° (`str`).
| F_DEG = ``'``deg``'`` Format degrees as [D]DD without symbol (`str`).
| F_DM = ``'``dm``'`` Format degrees as deg°min′ (`str`).
| F_DMS = ``'``dms``'`` Format degrees as deg°min′sec″ (`str`).
| F_MIN = ``'``min``'`` Format degrees as [D]DDMM without symbols (`str`).
| F_RAD = ``'``rad``'`` Convert degrees to radians and format as RR (`str`).
| F_SEC = ``'``sec``'`` Format degrees as [D]DDMMSS without symbols (`str`).
| PI = `3.14159265359` Constant math.pi (`float`)
| PI2 = `6.28318530718` Two PI, math.pi * 2 (`float`)
| PI_2 = `1.57079632679` Half PI, math.pi / 2 (`float`)
| PI_4 = `0.785398163397`
| R_FM = `6371000.0` Former FAI Sphere earth radius (`meter`).
| R_KM = `6371.00877142` Mean, spherical earth radius (`km`, kilometer).
| R_M = `6371008.77141` Mean, spherical earth radius (`meter`).
| R_MA = `6378137.0` Equatorial earth radius (`meter`) WGS84, EPSG:3785.
| R_MB = `6356752.0` Polar earth radius (`meter`) WGS84, EPSG:3785.
| R_NM = `3440.06953447` Mean, spherical earth radius (`NM`, nautical miles).
| R_SM = `3958.75339537` Mean, spherical earth radius (`SM`, statute miles).
| R_VM = `6366707.01949` Aviation/Navigation earth radius (`meter`).
| S_DEG = ``'``\xc2\xb0``'`` Degrees symbol "°" (`str`).
| S_MIN = ``'``\xe2\x80\xb2``'`` Minutes symbol "′" (`str`).
| S_RAD = ``'````'`` Radians symbol "" (`str`).
| S_SEC = ``'``\xe2\x80\xb3``'`` Seconds symbol "″" (`str`).
| S_SEP = ``'````'`` Separator between deg°, min′ and sec″ "" (`str`).
| Transforms = `Transforms.BD72: Transform(name='BD72', tx=106.86`...`` Registered transforms (`enum-like`).
| isLazy = `None` hash(x)

Function Details

### crosserrors(raiser=None) |
Get/set raising of vectorial cross product errors. Parameters: `raiser` - Use `True` to raise or `False` to ignore CrossError exceptions. Use `None` to leave the setting unchanged. Returns: Previous setting (`bool`).

### anStr(name, OKd=`'``._-``'`, sub=`'``_``'`) |
Make a valid name of alphanumeric and OKd characters. Parameters: `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 and intermediate whitespace characters are coalesced and substituted.

### antipode(lat, lon) |
Return the antipode, the point diametrically opposite to a given point. Parameters: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). Returns: 2-Tuple (lat, lon) of the antipodal point (`degrees`, `degrees180`). See Also: Geosphere.

### areaOf(points, adjust=True, radius=6371008.77141, wrap=True) |
Approximate the area of a polygon. Parameters: `points` - The polygon points (`LatLon`[]). `adjust` - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (`bool`). `radius` - Optional, mean earth radius (`meter`). `wrap` - Wrap lat-, wrap and unroll longitudes (`bool`). Returns: Approximate area (`meter`, same units as radius, squared). Raises: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. Note: This is an area approximation with limited accuracy, ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. See Also: sphericalNvector.areaOf, sphericalTrigonometry.areaOf and ellipsoidalKarney.areaOf.

### bearing(lat1, lon1, lat2, lon2, **options) |
Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. Parameters: `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. Parameters: `bearing` - Bearing from North (compass `degrees360`). `form` - Optional format, F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC or F_RAD for deg°, deg°min′, deg°min′sec″, [D]DD, [D]DDMM, [D]DDMMSS or radians (`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 values. `sep` - Optional separator (`str`). Returns: Compass degrees per the specified form (`str`). JS name: toBrng.

### bearing_(a1, b1, a2, b2, final=False, wrap=False) |
Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point. Parameters: `a1` - Start latitude (`radians`). `b1` - Start longitude (`radians`). `a2` - End latitude (`radians`). `b2` - 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.

### boundsOf(points, wrap=True, LatLon=None) |
Determine the lower-left SW and upper-right NE corners of a path or polygon. Parameters: `points` - The path or polygon points (`LatLon`[]). `wrap` - Wrap lat- and longitudes (`bool`). `LatLon` - Optional (sub-)class to use to return bounds (`LatLon`) or `None`. Returns: 2-Tuple (loLatLon, hiLatLon) of LatLon for the lower-left respectively upper-right corner or 4-tuple (loLat, loLon, hiLat, hiLon) of bounds (`degrees`) if LatLon is `None`. Raises: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. 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

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

### cbrt2(x) |
Compute the cubic root squared x**(2/3). Parameters: `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. Parameters: `points` - The polygon points (`LatLon`[]). `wrap` - Wrap lat-, wrap and unroll longitudes (`bool`). `LatLon` - Optional (sub-)class for the centroid (`LatLon`) or `None`. Returns: Centroid location (LatLon) or as 2-tuple (lat, lon) in `degrees` if LatLon is `None`. Raises: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points or points enclose a pole or zero area. See Also: Centroid and Calculating The Area And Centroid Of A Polygon.

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

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

### clipCS3(points, lowerleft, upperright, closed=False, inull=False) |
Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm. Parameters: `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, include null edges if inside (`bool`). Returns: Yield a 3-tuple (start, end, index) 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 and the index `int` of the edge in the original path. Raises: `ValueError` - The lowerleft corner is not below and/or not to the left of the upperright corner.

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

### clipSH(points, corners, inull=False, closed=False) |
Clip a polygon against a clip region or box using the Sutherland_Hodgman algorithm. Parameters: `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. `inull` - Optionally, include null edges (`bool`). `closed` - Close the clipped points (`bool`). Returns: Yield the clipped points (`LatLon`[]). Raises: `ValueError` - Insufficient number of points or the corners specify a polar, zero-area, non-convex or otherwise invalid clip region.

### clipSH3(points, corners, inull=False, closed=False) |
Clip a polygon against a clip region or box using the Sutherland_Hodgman algorithm. Parameters: `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. `inull` - Optionally, include null edges (`bool`). `closed` - Close the clipped points (`bool`). Returns: Yield a 3-tuple (start, end, original) for each edge of the clipped polygon. The start and end points `LatLon` of the portion of the edge inside or on the clip region. The original `bool` indicates whether the edge is part of the original polygon or part of the clip region. Raises: `ValueError` - Insufficient number of points or the corners specify a polar, zero-area, non-convex or otherwise invalid clip region.

### clipStr(bstr, limit=50, white=`'````'`) |
Clip a string to the given length limit. Parameters: `bstr` - String (`bytes` or `str`). `limit` - Length limit (`int`). `white` - Whitespace replacement (`str`). Returns: Clipped `bytes` or `str`.

### 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, non-near-polar vectors up to a few hundred Km or Miles. Use function bearing for longer vectors. Parameters: `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. Parameters: `bearing` - Bearing from North (compass `degrees360`). `form` - Optional format, F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC or F_RAD for deg°, deg°min′, deg°min′sec″, [D]DD, [D]DDMM, [D]DDMMSS or radians (`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 values. `sep` - Optional separator (`str`). Returns: Compass degrees and point in the specified form (`str`).

### compassPoint(bearing, prec=3) |
Convert bearing to a compass point. Parameters: `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'

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

### degrees2m(deg, radius=6371008.77141, lat=0) |
Convert angle to distance along equator or at other latitude. Parameters: `deg` - Angle (`degrees`). `radius` - Mean earth radius (`meter`). `lat` - Latitude adjusting the distance (`degrees90`). Returns: Distance (`meter`, same units as radius). Raises: `RangeError` - Latitude lat outside valid range and rangerrrors set to `True`.

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

### degrees90(rad) |
Convert radians to degrees and wrap (-270..+90]. Parameters: `rad` - Angle (`radians`). Returns: Angle in degrees, wrapped (`degrees90`).

### egmGeoidHeights(GeoidHeights_dat) |
Generate geoid egm*.pgm height tests from GeoidHeights.dat Test data for Geoids. Parameters: `GeoidHeights_dat` - The un-gz-ed `GeoidHeights.dat` file (`str` or `file` handle). Returns: For each test, yield a 5-Tuple `(lat, lon, egm84, egm96, egm2008)` with the expected heights for 3 different EGM grids in `-90.0 <= lat <= 90.0` and `-180.0 <= lat <= 180.0` degrees. Raises: `GeoidError` - Invalid GeoidHeights_dat. Note: Function egmGeoidHeights is used to test 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. Parameters: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `timeout` - Optional, query timeout (seconds). Returns: 2-Tuple (`elevation, data_source`) in (`meter, str`) or (`None, error`). 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) |
Return easting, northing string representations. Parameters: `easting` - Easting from false easting (`meter`). `northing` - Northing from from false northing (`meter`). `prec` - Precision in number of digits (`int`). `extras` - Optional leading items (strings). Returns: extras + 2-Tuple (eastingStr, northingStr). Raises: `ValueError` - Invalid prec.

### equirectangular(lat1, lon1, lat2, lon2, radius=6371008.77141, **options) |
Compute the distance between two points using the Equirectangular Approximation / Projection. Parameters: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Optional, mean earth radius (`meter`). `options` - Optional keyword arguments for function equirectangular_. Returns: Distance (`meter`, same units as 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).

### 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. Parameters: `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: 4-Tuple (distance2, delta_lat, delta_lon, unroll_lon2) with the distance in `degrees squared`, the latitudinal delta lat2-lat1, the wrapped, unrolled, and adjusted longitudinal delta lon2-lon1 and the unrollment for lon2. Use Function degrees2m to convert `degrees squared` to distance in `meter` as degrees2m(sqrt(distance2), ...) or degrees2m(hypot(delta_lat, delta_lon), ...). 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, euclidean, haversine and vincentys and methods Ellipsoid.distance2, `LatLon` distanceTo* and equirectangularTo.

### euclidean(lat1, lon1, lat2, lon2, radius=6371008.77141, adjust=True, wrap=False) |
Approximate the `Euclidian` distance between two (spherical) points. Parameters: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Optional, mean earth radius (`meter`). `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). See Also: Distance between two (spherical) points, functions equirectangular, haversine and vincentys and methods Ellipsoid.distance2, `LatLon` distanceTo* and equirectangularTo.

### euclidean_(a2, a1, b21, adjust=True) |
Approximate the angular `Euclidean` distance between two (spherical) points. Parameters: `a2` - End latitude (`radians`). `a1` - Start latitude (`radians`). `b21` - 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 euclidean, equirectangular_, haversine_ and vincentys_.

### fStr(floats, prec=6, sep=`'``,` `'`, fmt=`'``%.*f``'`, ints=False) |
Convert floats to string, optionally with trailing zero decimals stripped. Parameters: `floats` - List, sequence, tuple, etc. (`scalar`s). `prec` - Optional precision, number of decimal digits (0..9). Trailing zero decimals are stripped for prec values of 1 and above, but kept for negative prec values. `sep` - Optional, separator to join (string). `fmt` - Optional, float format (string). `ints` - Optionally, remove decimal dot (`bool`). Returns: The floats as 'f, f, ... f' (string).

### fStrzs(fstr) |
Strip trailing zero decimals from a float string. Parameters: `fstr` - Float (string). Returns: Float (string).

### false2f(value, name=`'``value``'`, false=True) |
Convert a false east-/northing to non-negative float. Parameters: `value` - Value to convert (`scalar`). `name` - Optional name of the value (`str`). `false` - Optionally, value includes false origin (`bool`). Returns: The value (`float`). Raises: `ValueError` - Invalid or negative value.

### favg(v1, v2, f=0.5) |
Return the weighted average of two values. Parameters: `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)). Parameters: `a` - List, sequence, tuple, etc. (`scalar`s). `b` - All positional arguments (`scalar`s). Returns: Dot product (`float`). Raises: `ValueError` - 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)). Parameters: `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: `ValueError` - Unequal `len`(a), `len`(b) and/or `len`(c).

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

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

### fpolynomial(x, *cs) |
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)). Parameters: `x` - Polynomial argument (`scalar`). `cs` - Polynomial coeffients (`scalar`[]). Returns: Polynomial value (`float`). Raises: `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]. Parameters: `x` - Value (`scalar`). `n` - Highest exponent (`int`). `alts` - Only alternating powers, starting with this exponent (`int`). Returns: Powers of x (`float`[]). Raises: `TypeError` - Non-scalar x or n not `int`. `ValueError` - Non-positive n or x is not finite.

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

### frange(start, number, step=1) |
Generate a range of `float`s. Parameters: `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.

### 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

### fsum(iterable) |
Return an accurate floating point sum of values in the iterable. Assumes IEEE-754 floating point arithmetic.

### fsum_(*xs) |
Precision summation of the positional argument vulues. Parameters: `xs` - Values to be added (`scalar`[]). Returns: Accurate fsum (`float`). Raises: `OverflowError` - Partial `2sum` overflow. `TypeError` - Non-scalar arg value. `ValueError` - Invalid or infinite arg value.

### ft2m(feet) |
Convert International feet to meter (m). Parameters: `feet` - Value in feet (`scalar`). Returns: Value in m (`float`).

### geoidHeight2(lat, lon, model=0, timeout=2.0) |
Get the `NAVD88` geoid height at an `NAD83` location. Parameters: `lat` - Latitude (`degrees`). `lon` - Longitude (`degrees`). `model` - Optional, geoid model ID (`int`). `timeout` - Optional, query timeout (seconds). Returns: 2-Tuple (`height, model_name`) in (`meter, str`) or `(None, error`). 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 Survery, Geoid, USGS10mElev.py, module geoids, classes GeoidG2012B, GeoidKarney and GeoidPGM.

### halfs2(str2) |
Split a string in 2 halfs. Parameters: `str2` - String to split (`str`). Returns: 2-Tuple (1st, 2nd) half (`str`). Raises: `ValueError` - Zero or odd `len`(str2).

### haversine(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False) |
Compute the distance between two (spherical) points using the Haversine formula. Parameters: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Optional, mean earth radius (`meter`). `wrap` - Wrap and unroll180 longitudes (`bool`). Returns: Distance (`meter`, same units as radius). See Also: Distance between two (spherical) points, functions equirectangular, euclidean and vincentys and methods Ellipsoid.distance2, `LatLon` distanceTo* and equirectangularTo.

### haversine_(a2, a1, b21) |
Compute the angular distance between two (spherical) points using the Haversine formula. Parameters: `a2` - End latitude (`radians`). `a1` - Start latitude (`radians`). `b21` - Longitudinal delta, end-start (`radians`). Returns: Angular distance (`radians`). See Also: Functions haversine, equirectangular_, euclidean_ and vincentys_.

### heightOf(angle, distance, radius=6371008.77141) |
Determine the height above the (spherical) earth after traveling along a straight line at a given tilt. Parameters: `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. Parameters: `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.

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

### hypot3(x, y, z) |
Compute the norm sqrt(x**2 + y**2 + z**2). Parameters: `x` - X argument (`scalar`). `y` - Y argument (`scalar`). `z` - Z argument (`scalar`). Returns: Norm (`float`).

### inStr(inst, *args, **kwds) |
Return the string representation of an instance. Parameters: `inst` - The instance (any type). `args` - Optional positional arguments. `kwds` - Optional keyword arguments. Returns: The inst's representation (`str`).

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

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

### isTuple2(obj) |
Check for an Tuple2LatLon points wrapper. Parameters: `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. Parameters: `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.

### isclockwise(points, adjust=False, wrap=True) |
Determine the direction of a path or polygon. Parameters: `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: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points or 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

### isconvex(points, adjust=False, wrap=True) |
Determine whether a polygon is convex. Parameters: `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. `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. 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. Parameters: `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. `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. 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. Parameters: `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: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points or invalid point. See Also: sphericalNvector.LatLon.isEnclosedBy, sphericalTrigonometry.LatLon.isEnclosedBy and MultiDop GeogContainPt (Shapiro et al. 2009, JTECH and Potvin et al. 2012, JTECH).

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

### isint(obj, both=False) |
Check for integer type or integer value. Parameters: `obj` - The object (any `type`). `both` - Optionally, check both type and value (`bool`). Returns: `True` if obj is `int`, `False` otherwise.

### ispolar(points, wrap=False) |
Check whether a polygon encloses a pole. Parameters: `points` - The polygon points (`LatLon`[]). `wrap` - Wrap and unroll longitudes (`bool`). Returns: `True` if a pole is enclosed by the polygon, `False` otherwise. Raises: `ValueError` - 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. Parameters: `obj` - The object (any `type`). Returns: `True` if obj is `scalar`, `False` otherwise.

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

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

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

### latDMS(deg, form=`'``dms``'`, prec=2, sep=`'````'`) |
Convert latitude to a string suffixed with N or S. Parameters: `deg` - Latitude to be formatted (`degrees`). `form` - Optional format, F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC or F_RAD for deg°, deg°min′, deg°min′sec″, DD, DDMM, DDMMSS or radians (`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 values. `sep` - Optional separator (`str`). Returns: Degrees in the specified form (`str`). JS name: toLat.

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

### limiterrors(raiser=None) |
Get/set the raising of limit errors. Parameters: `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 suffixed with E or W. Parameters: `deg` - Longitude to be formatted (`degrees`). `form` - Optional format, F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC or F_RAD for deg°, deg°min′, deg°min′sec″, DDD, DDDMM, DDDMMSS or radians (`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 values. `sep` - Optional separator (`str`). Returns: Degrees in the specified form (`str`). JS name: toLon.

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

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

### m2degrees(meter, radius=6371008.77141) |
Convert distance to angle along equator. Parameters: `meter` - Distance (`meter`, same units as radius). `radius` - Mean earth radius (`meter`). Returns: Angle (`degrees`). Raises: `ValueError` - Invalid radius.

### m2ft(meter) |
Convert meter to International feet (ft). Parameters: `meter` - Value in meter (`scalar`). Returns: Value in ft (`float`).

### m2km(meter) |
Convert meter to kilo meter (km). Parameters: `meter` - Value in meter (`scalar`). Returns: Value in km (`float`).

### map1(func, *xs) |
Apply each argument to a single-argument function and return a tuple of results. Parameters: `func` - 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. Parameters: `func` - Function to apply (`callable`). `xs` - Arguments to apply (`list, tuple, ...`). Returns: Function results (`tuple`).

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

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

### nearestOn5(point, points, closed=False, wrap=False, **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. Parameters: `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_. `options` - Other keyword arguments for function equirectangular_. Returns: 5-Tuple (lat, lon, distance, angle, height) all in `degrees` except height. The distance is the equirectangular_ distance between the closest and the reference point in `degrees`. The angle from the reference point to the closest point is in compass `degrees360`, like function compassAngle. The height is the (interpolated) height at the closest point in `meter` or zero. Raises: `LimitError` - Lat- and/or longitudinal delta exceeds limit, see function equirectangular_. `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. See Also: Use function degrees2m to convert `degrees` to `meter`.

### normDMS(strDMS, norm=`'````'`) |
Normalize all degree ˚, minute ' and second " symbols in a string to the default symbols °, ′ and ″. Parameters: `strDMS` - DMS (`str`). `norm` - Optional replacement symbol, default symbol otherwise (`str`). Returns: Normalized DMS (`str`).

### parse3llh(strll, height=0, sep=`'``,``'`, clipLat=90, clipLon=180) |
Parse a string representing lat-, longitude and height point. 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. Parameters: `strll` - Latitude, longitude[, height] (`str`, ...). `height` - Optional, default height (`meter`). `sep` - Optional separator (`str`). `clipLat` - Keep latitude in -clipLat..+clipLat (`degrees`). `clipLon` - Keep longitude in -clipLon..+clipLon range (`degrees`). Returns: 3-Tuple (lat, lon, height) as (`degrees90`, `degrees180`, `float`). Raises: `RangeError` - Lat- or longitude value of strll outside valid range and rangerrrors set to `True`. `ValueError` - Invalid strll. See Also: Functions parseDMS and parseDMS2 for more details on the forms and symbols accepted. Example:
    >>> parse3llh('000°00′05.31″W, 51° 28′ 40.12″ N')
    (51.4778°N, 000.0015°W, 0)

### parseDMS(strDMS, suffix=`'``NSEW``'`, sep=`'````'`, clip=0) |
Parse a string representing deg°min′sec″ to degrees. This is very flexible on formats, allowing signed decimal degrees, degrees and minutes or degrees minutes and seconds optionally suffixed by compass direction NSEW. A variety of symbols, separators and suffixes are accepted, for example 3° 37′ 09″W. Minutes and seconds may be omitted. Parameters: `strDMS` - Degrees in any of several forms (`str` or `degrees`). `suffix` - Optional, valid compass directions (NSEW). `sep` - Optional separator between deg°, min′ and sec″ (''). `clip` - Optionally, limit value to -clip..+clip (`degrees`). Returns: Degrees (`float`). Raises: `RangeError` - Value of strDMS outside the valid range and rangerrrors set to `True`. `ValueError` - Invalid strDMS. See Also: Function parse3llh to parse a string with lat-, longitude and height values.

### parseDMS2(strLat, strLon, sep=`'````'`, clipLat=90, clipLon=180) |
Parse lat- and longitude representions. Parameters: `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: 2-Tuple (lat, lon) in (`degrees`, `degrees`). Raises: `RangeError` - Value of strLat or strLon outside the valid range and rangerrrors set to `True`. `ValueError` - Invalid strLat or strLon. See Also: Function parse3llh to parse a string with lat-, longitude and height values and function parseDMS to parse individual lat- or longitudes.

### 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 and northing. Parameters: `strMGRS` - MGRS grid reference (`str`). `datum` - Optional datum to use (Datum). `Mgrs` - Optional (sub-)class to use for the MGRS grid reference (Mgrs) or `None`. `name` - Optional Mgrs name (`str`). Returns: The MGRS grid reference (Mgrs) or 4-tuple (zone, ENdigraph, easting, northing) if Mgrs is `None`. Raises: `ValueError` - 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]

### parseOSGR(strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, name=`'````'`) |
Parse an OSGR coordinate string to an Osgr instance. 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 fully numeric, comma-separated references in metres, for example '438700,114800'. Parameters: `strOSGR` - An OSGR coordinate (`str`). `Osgr` - Optional (sub-)class to use for the OSGR coordinate (Osgr) or `None`. `name` - Optional Osgr name (`str`). Returns: The OSGR coordinate (Osgr) or the 2-tuple (easting, northing) if Osgr is `None`. Raises: `ValueError` - 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

### parseUTM(strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran`...`, Utm=<class 'pygeodesy.utm.Utm'>, name=`'````'`) |
Parse a string representing a UTM coordinate, consisting of zone, hemisphere, easting and northing. Parameters: `strUTM` - A UTM coordinate (`str`). `datum` - Optional datum to use (Datum). `Utm` - Optional (sub-)class to use for the UTM coordinate (Utm) or `None`. `name` - Optional Utm name (`str`). Returns: The UTM coordinate (Utm) or 4-tuple (zone, hemisphere, easting, northing) if Utm is `None`. Raises: `UTMError` - Invalid strUTM. Example:
    >>> u = parseUTM('31 N 448251 5411932')
    >>> u.toStr2()  # [Z:31, H:N, E:448251, N:5411932]
    >>> u = parseUTM('31 N 448251.8 5411932.7')
    >>> u.toStr()  # 31 N 448252 5411933

### parseWM(strWM, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name=`'````'`) |
Parse a string representing a WM coordinate, consisting of easting, northing and an optional radius. Parameters: `strWM` - A WM coordinate (`str`). `radius` - Optional earth radius (`meter`). `Wm` - Optional (sub-)class to use (Wm) or `None`. `name` - Optional name (`str`). Returns: The WM coordinate (Wm) or 3-tuple (easting, northing, radius) if Wm is `None`. Raises: `ValueError` - Invalid strWM. Example:
    >>> u = parseWM('448251 5411932')
    >>> u.toStr2()  # [E:448251, N:5411932]

### perimeterOf(points, closed=False, adjust=True, radius=6371008.77141, wrap=True) |
Approximate the perimeter of a path or polygon. Parameters: `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` - Optional, mean earth radius (`meter`). `wrap` - Wrap lat-, wrap and unroll longitudes (`bool`). Returns: Approximate perimeter (`meter`, same units as radius). Raises: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points. 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.

### points2(points, closed=True, base=None) |
Check a polygon represented by points. Parameters: `points` - The polygon points (`LatLon`[]) `closed` - Optionally, consider the polygon closed, ignoring any duplicate or closing final points (`bool`). `base` - Optionally, check the points against this base class `None`. Returns: 2-Tuple (n, points) with the number (`int`) of points and the points `list` or `tuple`. Raises: `TypeError` - Some points are not `LatLon`. `ValueError` - Insufficient number of points.

### precision(form, prec=None) |
Set the default precison for a given F_ form. Parameters: `form` - F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC 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 values. Returns: Previous precision (`int`). Raises: `ValueError` - Invalid form or prec or beyond valid range.

### property_RO(method) |
Decorator for `Read_Only` property. Parameters: `method` - The callable to be decorated as `property.getter`. Note: Like standard Python `property` without a `property.setter` with a more descriptive error message when set.

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

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

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

### rangerrors(raiser=None) |
Gert/set raising of range errors. Parameters: `raiser` - Choose `True` to raise or `False` to ignore RangeError exceptions. Use `None` to leave the setting unchanged. Returns: Previous setting (`bool`). Note: Out-of-range lat- and longitude values are always clipped to the nearest range limit.

### scalar(value, low=2.22044604925e-16, high=1.0, name=`'``scalar``'`) |
Validate a scalar. Parameters: `value` - The value (`scalar`). `low` - Optional lower bound (`scalar`). `high` - Optional upper bound (`scalar`). `name` - Optional name of value (`str`). Returns: New value (`type` of low). Raises: `TypeError` - Non-scalar value. `ValueError` - Out-of-bounds value.

### simplify1(points, distance, radius=6371008.77141, indices=False, **options) |
Basic simplification of a path of `LatLon` points. Eliminates any points closer together than the given distance tolerance. Parameters: `points` - Path points (`LatLon`[]). `distance` - Tolerance (`meter`, same units as radius). `radius` - Optional, 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 limit, see function equirectangular_. `ValueError` - Tolerance distance or radius too small.

### simplifyRDP(points, distance, 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. Parameters: `points` - Path points (`LatLon`[]). `distance` - Tolerance (`meter`, same units as radius). `radius` - Optional, 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 limit, see function equirectangular_. `ValueError` - Tolerance distance or radius too small.

### simplifyRDPm(points, distance, 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 RDP 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). Parameters: `points` - Path points (`LatLon`[]). `distance` - Tolerance (`meter`, same units as radius). `radius` - Optional, 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 limit, see function equirectangular_. `ValueError` - Tolerance distance or radius too small.

### simplifyRW(points, pipe, 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. Parameters: `points` - Path points (`LatLon`[]). `pipe` - Half pipe width (`meter`, same units as radius). `radius` - Optional, 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 limit, see function equirectangular_. `ValueError` - Tolerance pipe or radius too small.

### simplifyVW(points, area, 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. Parameters: `points` - Path points (`LatLon`[]). `area` - Tolerance (`meter`, same units as radius). `radius` - Optional, mean earth radius (`meter`). `attr` - Optional, points attribute save 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 attr is specified for Numpy2 points. `LimitError` - Lat- and/or longitudinal delta exceeds limit, see function equirectangular_. `ValueError` - Tolerance area or radius too small.

### simplifyVWm(points, area, 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 VW method removes all points with a triangular area below the tolerance each iteration, significantly reducing the run time (but producing results different from the original VW method). Parameters: `points` - Path points (`LatLon`[]). `area` - Tolerance (`meter`, same units as radius). `radius` - Optional, mean earth radius (`meter`). `attr` - Optional 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 attr is specified for Numpy2 points. `LimitError` - Lat- and/or longitudinal delta exceeds limit, see function equirectangular_. `ValueError` - Tolerance area or radius too small.

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

### splice(iterable, n=2, fill=object()) |
Split an iterable into `n` slices. Parameters: `iterable` - Items to be spliced (`list`, `tuple`, ...). `n` - Number of slices to generate (`int`). `fill` - Fill value for missing items. Returns: Generator of n slices iterable[i::n] for i=0..n. Raises: `ValueError` - Non-`int` or non-positive 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))
    >>> list(splice(range(12), n=5))
    [(0, 5, 10), (1, 6, 11), (2, 7), (3, 8), (4, 9)]
    >>> splice(range(9), n=1)
    <generator object splice at 0x0...>

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

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

### tan_2(rad) |
Compute the tangent of half angle. Parameters: `rad` - Angle (`radians`). Returns: tan(rad / 2) (`float`).

### toDMS(deg, form=`'``dms``'`, prec=2, sep=`'````'`, ddd=2, neg=`'``-``'`, pos=`'````'`) |
Convert signed degrees to string, without suffix. Parameters: `deg` - Degrees to be formatted (`degrees`). `form` - Optional format, F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC or F_RAD for deg°, deg°min′, deg°min′sec″, [D]DD, [D]DDMM, [D]DDMMSS or radians (`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 values. `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`).

### 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=`'````'`) |
Convert an (ellipsoidal) geodetic point to a Lambert location. Parameters: `latlon` - Ellipsoidal point (`LatLon`). `conic` - Optional Lambert projection to use (Conic). `height` - Optional height for the point, overriding the default height (`meter`). `Lcc` - Optional (sub-)class to use for the Lambert location (Lcc). `name` - Optional Lcc name (`str`). Returns: The Lambert location (Lcc) or 3-tuple (easting, northing, height) if Lcc is `None`. Raises: `TypeError` - If latlon is not ellipsoidal.

### toMgrs(utm, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name=`'````'`) |
Convert a UTM coordinate to an MGRS grid reference. Parameters: `utm` - A UTM coordinate (Utm). `Mgrs` - Optional (sub-)class to use for the MGRS grid reference (Mgrs). `name` - Optional Mgrs name (`str`). Returns: The MGRS grid reference (Mgrs). Raises: `TypeError` - If utm is not Utm. `ValueError` - 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=`'````'`) |
Convert a lat-/longitude point to an OSGR coordinate. Parameters: `latlon` - Latitude (`degrees`) or an (ellipsoidal) geodetic `LatLon` point. `lon` - Optional longitude in degrees (scalar or `None`). `datum` - Optional datum to convert (`Datum`). `Osgr` - Optional (sub-)class to use for the OSGR coordinate (Osgr) or `None`. `name` - Optional Osgr name (`str`). Returns: The OSGR coordinate (Osgr) or 2-tuple (easting, northing) if Osgr is `None`. Raises: `TypeError` - Non-ellipsoidal latlon or datum conversion failed. `ValueError` - Invalid latlon or lon. 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)

### toUtm(latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, name=`'````'`, cmoff=True) |
Convert a lat-/longitude point to a UTM coordinate. Parameters: `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`). `Utm` - Optional (sub-)class to use for the UTM coordinate (Utm) or `None`. `name` - Optional Utm name (`str`). `cmoff` - Offset longitude from zone's central meridian, apply false easting and false northing (`bool`). Returns: The UTM coordinate (Utm) or a 6-tuple (zone, easting, northing, band, convergence, scale) if Utm is `None` or cmoff is `False`. Raises: `TypeError` - If latlon is not ellipsoidal. `RangeError` - If lat is outside the valid UTM bands or if lat or lon outside the valid range and rangerrrors set to `True`. `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

### toWm(latlon, lon=None, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name=`'````'`) |
Convert a lat-/longitude point to a WM coordinate. Parameters: `latlon` - Latitude (`degrees`) or an (ellipsoidal or spherical) geodetic `LatLon` point. `lon` - Optional longitude (`degrees` or `None`). `radius` - Optional earth radius (`meter`). `Wm` - Optional (sub-)class for the WM coordinate (Wm) or `None`. `name` - Optional name (`str`). Returns: The WM coordinate (Wm) or 3-tuple (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

### unStr(name, *args, **kwds) |
Return the string representation of an invokation. Parameters: `name` - Function, method or class name (`str`). `args` - Optional positional arguments. `kwds` - Optional keyword arguments. Returns: Representation (`str`).

### unroll180(lon1, lon2, wrap=True) |
Unroll longitudinal delta and wrap longitude in degrees. Parameters: `lon1` - Start longitude (`degrees`). `lon2` - End longitude (`degrees`). `wrap` - Wrap and unroll to the (-180..+180] range (`bool`). Returns: 2-Tuple (delta 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. Parameters: `rad1` - Start longitude (`radians`). `rad2` - End longitude (`radians`). `wrap` - Wrap and unroll to the (-PI..+PI] range (`bool`). Returns: 2-Tuple (delta rad2-rad1, rad2) unrolled (`radians`, `radians`). See Also: Capability LONG_UNROLL in GeographicLib.

### utmZoneBand2(lat, lon) |
Return the UTM zone number and UTM Band letter for a location. Parameters: `lat` - Latitude (`degrees`) or string. `lon` - Longitude (`degrees`) or string. Returns: 2-Tuple (zone, Band) as (int, string). Raises: `RangeError` - If lat is outside the valid UTM bands or if lat or lon outside the valid range and rangerrrors set to `True`. `ValueError` - Invalid lat or lon.

### vincentys(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False) |
Compute the distance between two (spherical) points using Vincenty's spherical formula. Parameters: `lat1` - Start latitude (`degrees`). `lon1` - Start longitude (`degrees`). `lat2` - End latitude (`degrees`). `lon2` - End longitude (`degrees`). `radius` - Optional, mean earth radius (`meter`). `wrap` - Wrap and unroll180 longitudes (`bool`). Returns: Distance (`meter`, same units as radius). See Also: Functions equirectangular, euclidean and haversine and methods Ellipsoid.distance2, `LatLon` distanceTo* and equirectangularTo. Note: See note under vincentys_.

### vincentys_(a2, a1, b21) |
Compute the angular distance between two (spherical) points using Vincenty's spherical formula. Parameters: `a2` - End latitude (`radians`). `a1` - Start latitude (`radians`). `b21` - Longitudinal delta, end-start (`radians`). Returns: Angular distance (`radians`). See Also: Functions vincentys, equirectangular_, euclidean_ and haversine_. Note: Functions vincentys_ and haversine_ produce equivalent results, but vincentys_ is suitable for antipodal points and slightly more expensive than haversine_ (3 cos, 3 sin, 1 hypot, 1 atan2, 7 mul, 2 add versus 2 cos, 2 sin, 2 sqrt, 1 atan2, 5 mul, 1 add).

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

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

### wrap90(deg) |
Wrap degrees to (-270..+90]. Parameters: `deg` - Angle (`degrees`). Returns: Degrees, wrapped (`degrees90`).

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

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

### wrapPI_2(rad) |
Wrap radians to (-3PI/2..+PI/2]. Parameters: `rad` - Angle (`radians`). Returns: Radians, wrapped (`radiansPI_2`).

Variables Details

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

  ### Conics Registered conics (`enum-like`). Value:
      Conics.Be08Lb: Conic(name='Be08Lb', lat0=50.797815, lon0=4.35921583, p
      ar1=49.833333, par2=51.166667, E0=649328, N0=665262, k0=1, SP=2, datum
      =(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84
      ),
      Conics.Be72Lb: Conic(name='Be72Lb', lat0=90, lon0=4.3674867, par1=49.8
      333339, par2=51.1666672, E0=150000.013, N0=5400088.438, k0=1, SP=2, da
      tum=(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NA
      D83),
      ...

  ### Datums Registered datums (`enum-like`). Value:
      Datums.BD72: Datum(name='BD72', ellipsoid=Ellipsoids.Intl1924, transfo
      rm=Transforms.BD72),
      Datums.DHDN: Datum(name='DHDN', ellipsoid=Ellipsoids.Bessel1841, trans
      form=Transforms.DHDN),
      Datums.ED50: Datum(name='ED50', ellipsoid=Ellipsoids.Intl1924, transfo
      rm=Transforms.ED50),
      Datums.GRS80: Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transfor
      m=Transforms.WGS84),
      ...

  ### Ellipsoids Registered ellipsoids (`enum-like`). Value:
      Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a=6377563.396, b=63562
      56.909, f_=299.3249646, f=0.003340851, e=0.081673374, e2=0.00667054, e
      22=0.006715335, n=0.00167322, R1=6370461.233666666, R2=6370459.6545894
      42, R3=6370453.309866445, Rr=6366914.608805893, Rs=6366901.239881964),
      Ellipsoids.AiryModified: Ellipsoid(name='AiryModified', a=6377340.189,
       b=6356034.448, f_=299.3249646, f=0.003340851, e=0.081673374, e2=0.006
      67054, e22=0.006715335, n=0.00167322, R1=6370238.275333334, R2=6370236
      .696361165, R3=6370230.351810658, Rr=6366691.774649803, Rs=6366678.406
      ...

  ### Transforms Registered transforms (`enum-like`). Value:
      Transforms.BD72: Transform(name='BD72', tx=106.86863, ty=-52.29778, tz
      =103.72389, rx=-0, ry=-0, rz=-0.00001, s=1.2727, s1=1, sx=-0.33657, sy
      =-0.45696, sz=-1.84218),
      Transforms.Bessel1841: Transform(name='Bessel1841', tx=-582, ty=-105,
      tz=-414, rx=-0.00001, ry=-0, rz=0.00001, s=-8.3, s1=0.99999, sx=-1.04,
       sy=-0.35, sz=3.08),
      Transforms.Clarke1866: Transform(name='Clarke1866', tx=8, ty=-160, tz=
      -176, rx=0, ry=0, rz=0, s=0, s1=1, sx=0, sy=0, sz=0),
      ...