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

Transcribed from JavaScript originals by Chris Veness (C) 2005-2019 and several C++ classes by Charles F.F. Karney (C) 2008-2020 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 geodetic LatLon and a geocentric Cartesian class with methods and functions to compute distance, area, perimeter, initial and final bearing, intermediate and nearest points, intersections of circles, path intersections, trilateration (by intersection, overlap and 3d), conversions and unrolling, among other things. For more information and further details see the documentation, the descriptions of Latitude/Longitude, Vincenty and Vector-based geodesy, the original JavaScript source or docs and the Python geographiclib.

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

Other modules provide Albers Equal-Area projections, azimuthal projections and Lambert conformal conic projections and positions (from John P. Snyder, "Map Projections -- A Working Manual", 1987), 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 tLon points (or a NumPy array), including implementations of the Ramer-Douglas-Peucker the Visvalingam-Whyatt and the Reumann-Witkam algorithms and modified versions of the former. Other classes interpolate the height of LatLon points and several Geoid models or compute various Fréchet or Hausdorff distances.

Installation

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

Alternatively, download PyGeodesy-yy.m.d.zip from PyPI or GitHub, unzip the downloaded file, cd to directory Pygeodesy-yy.m.d and type python setup.py install. To run all PyGeodesy tests, type python setup.py test before or after installation.

Installation of geographiclib, numpy and scipy is optional. However, the former is required to use classes EquidistantKarney, GnomonicKarney, CassiniSoldner and Css and function toCss, for module ellipsoidalKarney classes LatLon and Cartesian and functions areaOf, intersections2 and perimeterOf and for the HeightIDWkarney interpolator. Both the latter are needed for the Geoid... and Height... interpolator classes, except the GeoidKarney and all HeightIDW... classes.

Documentation

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

Tests

The tests have been run with Python 3.9.0 (with geographiclib 1.50 only), Python 3.8.6 (with geographiclib 1.50, numpy 1.19.2 and scipy 1.5.2) and macOS' Python 2.7.16 (and only numpy 1.16.6), all on macOS 10.15.7 Catalina and all in 64-bit only. The tests run with and without lazy import for Python 3. The results of those tests are included in the distribution files.

Test coverage has been measured with coverage 4.5.4 using Python 3.9.0 (with geographiclib 1.50 only), Python 3.8.6 (with geographiclib 1.50, numpy 1.19.2 and scipy 1.5.2) and macOS' Python 2.7.16 (and only numpy 1.16.6). The full coverage report in HTML and a PDF summary are included in the distribution files.

The tests also ran with Python 2.7.14, 3.6.3, 3.7.1, 3.8.0 and PyPy 7.1.1 (Python 2.7.13 and 3.6.1) (and geographiclib 1.49 or 1.50) on Ubuntu 14.04 and with Python 3.7.3 (and geographiclib 1.49 or 1.50) on Debian 9 all in 64-bit only and with Python 2.7.15, 3.6.8, 3.7.2, and 3.8.0 (all with geographiclib 1.49 or 1.50) on Windows Server 2012R2 in both 32- and 64-bit.

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

Previously, the tests were run with Python 2.6.9 (and numpy 1.6.2), 2.7.10 (and numpy 1.8.0rc1), 2.7.13 thru 2.7.17 (with numpy 1.13.1, 1.14.0, 1.15.2, 1.16.2 or 1.19.0 and scipy 1.5.0), 3.5.3, 3.6.2 thru 3.6.5, 3.7.0, 3.7.2 thru 3.7.6, 3.8 thru 3.8.5, PyPy 6.0.0 (Python 2.7.13 and 3.5.3), PyPy 7.3.0 (Python 2.7.13 and 3.6.9) 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 10.13.6 High Sierra, macOS 10.14 Mojave and/or macOS 10.15.3, 10.15.5 and 10.15.6 Catalina, with Pythonista 3.1 on iOS 10.3.3, 11.0.3, 11.1.2 and 11.3 on iPad4, with Pythonista 3.2 (with geographiclib 1.49 or 1.50 and numpy 1.8.0) on iOS 11.4.1, 12.0, 12.2 and 12.3 on iPad4, iPhone6 and/or iPhone10, all in 64-bit only and with 32-bit Python 2.6.6 on Windows XP SP3 and with 32-bit Python 2.7.14 on Windows 10 Pro.

Notes

All Python source code has been statically checked with PyChecker, PyFlakes, PyCodeStyle (formerly Pep8) and McCabe using Python 2.7.18 and with Flake8 using Python 3.9.0, both in 64-bit on macOS 10.15.6 Catalina.

Classes with a name ending in -Karney and several more are transcribed from Karney's C++ classes or require Karney's geographiclib package to be installed. A complete list is in module karney.

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

License

**) Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.


Version: 20.10.14

Submodules

Classes
  LazyImportError
Raised if lazy import is not supported, disabled or failed some other way.
  VincentyError
Error raised from Vincenty's direct and inverse methods for coincident points or lack of convergence.
  Epsg
EPSG class, a named int.
  EPSGError
EPSG encode, decode or other Epsg issue.
  Garef
Garef class, a named str.
  GARSError
Global Area Reference System (GARS) encode, decode or other Garef issue.
  Geohash
Geohash class, a named str.
  GeohashError
Geohash encode, decode or other Geohash issue.
  Georef
Georef class, a named str.
  WGRSError
World Geographic Reference System (WGRS) encode, decode or other Georef issue.
  AlbersEqualArea
An Albers equal-area (authalic) projection with a single standard parallel.
  AlbersEqualArea2
An Albers equal-area (authalic) projection with two standard parallels.
  AlbersEqualArea4
An Albers equal-area (authalic) projection specified by the sin and cos of both standard parallels.
  AlbersEqualAreaCylindrical
An AlbersEqualArea projection at lat=0 and k0=1 degenerating to the cylindrical-equal-area projection.
  AlbersEqualAreaNorth
An azimuthal AlbersEqualArea projection at lat=90 and k0=1 degenerating to the azimuthal LambertEqualArea projection.
  AlbersEqualAreaSouth
An azimuthal AlbersEqualArea projection at lat=-90 and k0=1 degenerating to the azimuthal LambertEqualArea projection.
  AlbersError
An AlbersEqualArea, AlbersEqualArea2, AlbersEqualArea4, AlbersEqualAreaCylindrical, AlbersEqualAreaNorth, AlbersEqualAreaSouth or Albers7Tuple issue.
  AzimuthalError
An azimuthal Equidistant, EquidistantKarney, Gnomonic, LambertEqualArea, Orthographic, Stereographic or {Azimuthal7Tuple} issue.
  Band
Named str representing a UTM/UPS band letter, unchecked.
  Bearing
Named float representing a bearing in compass degrees from (true) North.
  Bearing_
Named float representing a bearing in radians from compass degrees from (true) North.
  Bool
Named bool, a sub-class of int like Python's bool.
  CSSError
Cassini-Soldner (CSS) conversion or other Css issue.
  CassiniSoldner
Cassini-Soldner projection, a Python version of Karney's C++ class CassiniSoldner.
  ClipError
Clip box or clip region issue.
  Conic
Lambert conformal conic projection (1- or 2-SP).
  CrossError
Error raised for zero or near-zero vectorial cross products, occurring for coincident or colinear points, paths or bearings.
  Css
Cassini-Soldner East-/Northing location.
  Datum
Ellipsoid and transform parameters for an earth model.
  Degrees
Named float representing a coordinate in degrees, optionally clipped.
  Degrees2
Named float representing a distance in degrees squared.
  Degrees_
Named Degrees representing a coordinate in degrees with optional limits low and high.
  Distance
Named float representing a distance, conventionally in meter.
  Distance_
Named float with optional low and high limits representing a distance, conventionally in meter.
  ETMError
Exact Transverse Mercator (ETM) parse, projection or other Etm issue.
  Easting
Named float representing an easting, conventionally in meter.
  EcefCartesian
Conversion between geodetic (lat, lon, height) and local cartesian (x, y, z) coordinates with a local cartesian origin at (lat0, lon0, height0), transcribed from Karney's C++ class LocalCartesian.
  EcefError
An ECEF or Ecef* related issue.
  EcefKarney
Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates based on Karney's Geocentric methods.
  EcefMatrix
A rotation matrix.
  EcefSudano
Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates based on John J. Sudano's paper.
  EcefVeness
Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates transcribed from Chris Veness' JavaScript classes LatLonEllipsoidal, Cartesian.
  EcefYou
Conversion between geodetic and geocentric, aka Earth-Centered, Earth-Fixed (ECEF) coordinates using Rey-Jer You's transformations.
  Ellipsoid
Ellipsoid with equatorial and polar radius, flattening, inverse flattening and other, often used, cached attributes, supporting spherical and oblate and prolate ellipsoidal models.
  Ellipsoid2
Like Ellipsoid, but specified by equatorial radius and flattening.
  Elliptic
Elliptic integrals and functions.
  EllipticError
Elliptic integral, function, convergence or other Elliptic issue.
  Epoch
Named epoch with optional low and high limits representing a fractional calendar year.
  Equidistant
Azimuthal equidistant projection for the sphere**, see Snyder, pp 195-197 and MathWorld-Wolfram.
  EquidistantKarney
Azimuthal equidistant projection, a Python version of Karney's C++ class AzimuthalEquidistant, requiring package geographiclib to be installed.
  Etm
Exact Transverse Mercator (ETM) coordinate, a sub-class of Utm, a Universal Transverse Mercator (UTM) coordinate using the ExactTransverseMercator projection for highest accuracy.
  ExactTransverseMercator
A Python version of Karney's TransverseMercatorExact C++ class, a numerically exact transverse mercator projection, here referred to as TMExact.
  Fdot
Precision dot product.
  Feet
Named float representing a distance or length in feet.
  Fhorner
Precision polynomial evaluation using the Horner form.
  Float
Named float.
  Float_
Named float with optional low and high limit.
  Fpolynomial
Precision polynomial evaluation.
  Frechet
Frechet base class, requires method Frechet.distance to be overloaded.
  FrechetCosineAndoyerLambert
Compute the Frechet distance based on the angular distance in radians from function cosineAndoyerLambert_.
  FrechetCosineForsytheAndoyerLambert
Compute the Frechet distance based on the angular distance in radians from function cosineForsytheAndoyerLambert_.
  FrechetCosineLaw
Compute the Frechet distance based on the angular distance in radians from function cosineLaw_.
  FrechetDegrees
Frechet base class for distances in degrees from LatLon points in degrees.
  FrechetDistanceTo
Compute the Frechet distance based on the distance from the points' LatLon.distanceTo method, conventionally in meter.
  FrechetEquirectangular
Compute the Frechet distance based on the equirectangular distance in radians squared like function equirectangular_.
  FrechetError
Fréchet issue.
  FrechetEuclidean
Compute the Frechet distance based on the Euclidean distance in radians from function euclidean_.
  FrechetFlatLocal
Compute the Frechet distance based on the angular distance in radians squared like function flatLocal_/hubeny_.
  FrechetFlatPolar
Compute the Frechet distance based on the angular distance in radians from function flatPolar_.
  FrechetHaversine
Compute the Frechet distance based on the angular distance in radians from function haversine_.
  FrechetHubeny
Compute the Frechet distance based on the angular distance in radians squared like function flatLocal_/hubeny_.
  FrechetKarney
Compute the Frechet distance based on the angular distance in degrees from Karney's geographiclib Geodesic Inverse method.
  FrechetRadians
Frechet base class for distances in radians or radians squared from LatLon points converted from degrees to radians.
  FrechetThomas
Compute the Frechet distance based on the angular distance in radians from function thomas_.
  FrechetVincentys
Compute the Frechet distance based on the angular distance in radians from function vincentys_.
  Fsum
Precision summation similar to standard Python function math.fsum.
  GeoidError
Geoid interpolator Geoid... or interpolation issue.
  GeoidG2012B
Geoid height interpolator for GEOID12B Model grids CONUS, Alaska, Hawaii, Guam and Northern Mariana Islands, Puerto Rico and U.S. Virgin Islands and American Samoa based on SciPy RectBivariateSpline or interp2d interpolation.
  GeoidKarney
Geoid height interpolator for Karney's GeographicLib Earth Gravitational Model (EGM) geoid egm*.pgm datasets using bilinear or cubic interpolation and caching in pure Python transcribed from Karney's C++ class Geoid.
  GeoidPGM
Geoid height interpolator for Karney's GeographicLib Earth Gravitational Model (EGM) geoid egm*.pgm datasets but based on SciPy RectBivariateSpline or interp2d interpolation.
  Gnomonic
Azimuthal gnomonic projection for the sphere**, see Snyder, pp 164-168 and MathWorld-Wolfram.
  GnomonicKarney
Azimuthal gnomonic projection, a Python version of Karney's C++ class Gnomonic, requiring package geographiclib to be installed.
  Hausdorff
Hausdorff base class, requires method Hausdorff.distance to be overloaded.
  HausdorffCosineAndoyerLambert
Compute the Hausdorff distance based on the angular distance in radians from function cosineAndoyerLambert_.
  HausdorffCosineForsytheAndoyerLambert
Compute the Hausdorff distance based on the angular distance in radians from function cosineForsytheAndoyerLambert_.
  HausdorffCosineLaw
Compute the Hausdorff distance based on the angular distance in radians from function cosineLaw_.
  HausdorffDegrees
Hausdorff base class for distances from LatLon points in degrees.
  HausdorffDistanceTo
Compute the Hausdorff distance based on the distance from the points' LatLon.distanceTo method, conventionally in meter.
  HausdorffEquirectangular
Compute the Hausdorff distance based on the equirectangular distance in radians squared like function equirectangular_.
  HausdorffError
Hausdorff issue.
  HausdorffEuclidean
Compute the Hausdorff distance based on the Euclidean distance in radians from function euclidean_.
  HausdorffFlatLocal
Compute the Hausdorff distance based on the angular distance in radians squared like function flatLocal_/hubeny_.
  HausdorffFlatPolar
Compute the Hausdorff distance based on the angular distance in radians from function flatPolar_.
  HausdorffHaversine
Compute the Hausdorff distance based on the angular distance in radians from function haversine_.
  HausdorffHubeny
Compute the Hausdorff distance based on the angular distance in radians squared like function flatLocal_/hubeny_.
  HausdorffKarney
Compute the Hausdorff distance based on the angular distance in degrees from Karney's geographiclib Geodesic Inverse method.
  HausdorffRadians
Hausdorff base class for distances from LatLon points converted from degrees to radians.
  HausdorffThomas
Compute the Hausdorff distance based on the angular distance in radians from function thomas_.
  HausdorffVincentys
Compute the Hausdorff distance based on the angular distance in radians from function vincentys_.
  Height
Named float representing a height, conventionally in meter.
  HeightCubic
Height interpolator based on SciPy interp2d kind='cubic'.
  HeightError
Height interpolator Height... or interpolation issue.
  HeightIDW
DEPRECATED, use class HeightIDWeuclidean.
  HeightIDW2
DEPRECATED, use class HeightIDWequirectangular.
  HeightIDW3
DEPRECATED, use class HeightIDWhaversine.
  HeightIDWcosineAndoyerLambert
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function cosineAndoyerLambert_.
  HeightIDWcosineForsytheAndoyerLambert
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function cosineForsytheAndoyerLambert_.
  HeightIDWcosineLaw
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function cosineLaw_.
  HeightIDWdistanceTo
Height interpolator using Inverse Distance Weighting (IDW) and the distance from the points' LatLon.distanceTo method, conventionally in meter.
  HeightIDWequirectangular
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians squared like function equirectangular_.
  HeightIDWeuclidean
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function euclidean_.
  HeightIDWflatLocal
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians squared like function flatLocal_/hubeny_.
  HeightIDWflatPolar
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function flatPolar_.
  HeightIDWhaversine
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function haversine_.
  HeightIDWhubeny
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians squared like function flatLocal_/hubeny_.
  HeightIDWkarney
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in degrees from Karney's geographiclib Geodesic Inverse method.
  HeightIDWthomas
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function thomas_.
  HeightIDWvincentys
Height interpolator using Inverse Distance Weighting (IDW) and the angular distance in radians from function vincentys_.
  HeightLSQBiSpline
Height interpolator using SciPy LSQSphereBivariateSpline.
  HeightLinear
Height interpolator based on SciPy interp2d kind='linear'.
  HeightSmoothBiSpline
Height interpolator using SciPy SmoothSphereBivariateSpline.
  Int
Named int.
  Int_
Named int with optional limits low and high.
  IntersectionError
Error raised for path or circle intersection issues.
  LCCError
Lambert Conformal Conic LCC or other Lcc issue.
  Lam
Named float representing a longitude in radians.
  Lam_
Named float representing a longitude in radians converted from degrees.
  LambertEqualArea
Lambert-equal-area projection for the sphere**, see Snyder, pp 185-187 and MathWorld-Wolfram.
  Lat
Named float representing a latitude in degrees.
  LatLon2psxy
Wrapper for LatLon points as "on-the-fly" pseudo-xy coordinates.
  LatLon_
Low-overhead LatLon class for Numpy2LatLon and Tuple2LatLon.
  Lat_
Named float representing a latitude in degrees within limits low and high.
  Lcc
Lambert conformal conic East-/Northing location.
  LenError
Error raised for mis-matching len values.
  LimitError
Error raised for lat- or longitudinal deltas exceeding the limit in functions equirectangular and equirectangular_ and nearestOn* and simplify* functions or methods.
  Lon
Named float representing a longitude in degrees.
  Lon_
Named float representing a longitude in degrees within limits low and high.
  MGRSError
Military Grid Reference System (MGRS) parse or other Mgrs issue.
  Meter
Named float representing a distance or length in meter.
  Mgrs
Military Grid Reference System (MGRS/NATO) references, with method to convert to UTM coordinates.
  Northing
Named float representing a northing, conventionally in meter.
  Number_
Named int representing a non-negative number.
  Numpy2LatLon
Wrapper for NumPy arrays as "on-the-fly" LatLon points.
  OSGRError
Ordinance Survey Grid References (OSGR) parse or other Osgr issue.
  Orthographic
Orthographic projection for the sphere**, see Snyder, pp 148-153 and MathWorld-Wolfram.
  Osgr
Ordinance Survey Grid References (OSGR) coordinate.
  PGMError
Issue parsing or cropping an egm*.pgm geoid dataset.
  ParseError
Error parsing degrees, radians or several other formats.
  Phi
Named float representing a latitude in radians.
  Phi_
Named float representing a latitude in radians converted from degrees.
  PointsError
Error for an insufficient number of points.
  Precision_
Named int with optional low and high limits representing a precision.
  Radians
Named float representing a coordinate in radians, optionally clipped.
  Radians2
Named float representing a distance in radians squared.
  Radius
Named float representing a radius, conventionally in meter.
  Radius_
Named float with optional low and high limits representing a radius, conventionally in meter.
  RangeError
Error raised for lat- or longitude values outside the clip, clipLat, clipLon or limit range in function clipDegrees, clipRadians, parse3llh, parseDMS, parseDMS2 or parseRad.
  RefFrame
Terrestrial Reference Frame (TRF) parameters.
  RefFrameError
DEPRECATED, use class TRFError.
  Scalar
Named float representing a factor, fraction, scale, etc.
  Scalar_
Named float with optional low and high limits representing a factor, fraction, scale, etc.
  SciPyError
Error raised for SciPy errors.
  SciPyWarning
Error thrown for SciPy warnings.
  Stereographic
Stereographic projection for the sphere**, see Snyder, pp 157-160 and MathWorld-Wolfram.
  Str
Named str.
  TRFError
Terrestrial Reference Frame (TRF), Epoch, RefFrame or RefFrame conversion issue.
  Transform
Helmert transformation.
  Tuple2LatLon
Wrapper for tuple sequences as "on-the-fly" LatLon points.
  UPSError
Universal Polar Stereographic (UPS) parse or other Ups issue.
  UTMError
Universal Transverse Mercator (UTM parse or other Utm issue.
  UTMUPSError
Universal Transverse Mercator/Universal Polar Stereographic (UTM/UPS) parse, validate or other issue.
  UnitError
Default exception for units issues.
  Ups
Universal Polar Stereographic (UPS) coordinate.
  Utm
Universal Transverse Mercator (UTM) coordinate.
  Vector3d
Generic 3-D vector manipulation.
  VectorError
Vector3d or *Nvector issue.
  WebMercatorError
Web Mercator (WM) parser or Wm issue.
  Wm
Web Mercator (WM) coordinate.
  Zone
Named int representing a UTM/UPS zone number.
  a_f2Tuple
2-Tuple (a, f) specifying an ellipsoid by equatorial radius a (meter) and scalar flattening f.
  property_RO
Functions
 
UtmUps(zone, hemipole, easting, northing, band='', datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., falsed=True, name='')
Class-like function to create a UTM/UPS coordinate.
 
a_b2e(a, b)
Return e, the eccentricity for a given equatorial and polar radius.
 
a_b2e2(a, b)
Return e2, the eccentricity squared for a given equatorial and polar radius.
 
a_b2e22(a, b)
Return e22, the 2nd eccentricity squared for a given equatorial and polar radius.
 
a_b2e32(a, b)
Return e32, the 3rd eccentricity squared for a given equatorial and polar radius.
 
a_b2f(a, b)
Return f, the flattening for a given equatorial and polar radius.
 
a_b2f2(a, b)
Return f2, the 2nd flattening for a given equatorial and polar radius.
 
a_b2f_(a, b)
Return f_, the inverse flattening for a given equatorial and polar radius.
 
a_b2n(a, b)
Return n, the 3rd flattening for a given equatorial and polar radius.
 
a_f2b(a, f)
Return b, the polar radius for a given equatorial radius and flattening.
 
a_f_2b(a, f_)
Return b, the polar radius for a given equatorial radius and inverse flattening.
 
acos1(x)
Return math.acos(max(-1, min(1, x))).
 
anStr(name, OKd='._-', sub='_')
DEPRECATED, use function anstr.
 
anstr(name, OKd='._-', sub='_')
Make a valid name of alphanumeric and OKd characters.
 
antipode(lat, lon)
Return the antipode, the point diametrically opposite to a given point in degrees.
 
antipode_(phi, lam)
Return the antipode, the point diametrically opposite to a given point in radians.
 
areaOf(points, adjust=True, radius=6371008.77141, wrap=True)
Approximate the area of a polygon.
 
areaof(points, adjust=True, radius=_R_M, wrap=True)
DEPRECATED, use function areaOf.
 
asin1(x)
Return math.asin(max(-1, min(1, x))).
 
atan2b(y, x)
Compute atan2(y, x) as degrees [0..+360].
 
atan2d(y, x)
Compute atan2(y, x) as degrees [-180..+180].
 
attrs(inst, *names, **kwds)
Get instance attributes as name=value strings, with floats handled like fstr.
 
b_f2a(b, f)
Return a, the equatorial radius for a given polar radius and flattening.
 
b_f_2a(b, f_)
Return a, the equatorial radius for a given polar radius and inverse flattening.
 
bearing(lat1, lon1, lat2, lon2, **options)
Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point.
 
bearingDMS(bearing, form='d', prec=None, sep='')
Convert bearing to a string.
 
bearing_(phi1, lam1, phi2, lam2, final=False, wrap=False)
Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point.
 
bounds(points, wrap=True, LatLon=None)
DEPRECATED, use function boundsOf.
 
boundsOf(points, wrap=True, LatLon=None)
Determine the lower-left SW and upper-right NE corners of a path or polygon.
 
callername(up=1, dflt='', source=False)
Get the name of the calling callable.
 
cbrt(x)
Compute the cubic root x**(1/3).
 
cbrt2(x)
Compute the cubic root squared x**(2/3).
 
centroidOf(points, wrap=True, LatLon=None)
Determine the centroid of a polygon.
 
classname(inst, prefixed=None)
Return the instance' class name optionally prefixed with the module name.
 
classnaming(prefixed=None)
Get/set the default class naming for [module.]class names.
 
clipCS3(points, lowerleft, upperright, closed=False, inull=False)
Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm.
 
clipDMS(deg, limit)
DEPRECATED, use function clipDegrees.
 
clipDegrees(deg, limit)
Clip a lat- or longitude to the given range.
 
clipRadians(rad, limit)
Clip a lat- or longitude to the given range.
 
clipSH(points, corners, closed=False, inull=False)
Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm.
 
clipSH3(points, corners, closed=False, inull=False)
Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm.
 
clipStr(bstr, limit=50, white='')
DEPRECATED, use function clips.
 
clips(bstr, limit=50, white='')
Clip a string to the given length limit.
 
compassAngle(lat1, lon1, lat2, lon2, adjust=True, wrap=False)
Return the angle from North for the direction vector (lon2 - lon1, lat2 - lat1) between two points.
 
compassDMS(bearing, form='d', prec=None, sep='')
Convert bearing to a string suffixed with compass point.
 
compassPoint(bearing, prec=3)
Convert bearing to a compass point.
 
cosineAndoyerLambert(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)
Compute the distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines fromula.
 
cosineAndoyerLambert_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)
Compute the angular distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines fromula.
 
cosineForsytheAndoyerLambert(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)
Compute the distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula.
 
cosineForsytheAndoyerLambert_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)
Compute the angular distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula.
 
cosineLaw(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)
Compute the distance between two points using the spherical Law of Cosines formula.
 
cosineLaw_(phi2, phi1, lam21)
Compute the angular distance between two points using the spherical Law of Cosines formula.
 
crosserrors(raiser=None)
Report or ignore vectorial cross product errors.
 
date2epoch(year, month, day)
Return the reference frame epoch for a calendar day.
 
decodeEPSG2(arg)
DEPRECATED, use function epsg.decode2.
 
degDMS(deg, prec=6, s_D='°', s_M='\xe2\x80\xb2', s_S='', neg='-', pos='')
Convert degrees to a string in degrees, minutes or seconds.
 
degrees(x)
Convert angle x from radians to degrees.
 
degrees180(rad)
Convert radians to degrees and wrap [-180..+180].
 
degrees2m(deg, radius=6371008.77141, lat=0)
Convert angle to distance along the equator or along a parallel at an 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)
DEPRECATED, use function enstr2.
 
encodeEPSG(zone, hemipole='', band='')
DEPRECATED, use function epsg.encode.
 
enstr2(easting, northing, prec, *extras)
Return easting, northing string representations.
 
epoch2date(epoch)
Return the date for a reference frame epoch.
 
equidistant(lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., name='')
If Karney's geographiclib package is installed, return an EquidistantKarney otherwise an Equidistant instance.
 
equirectangular(lat1, lon1, lat2, lon2, radius=6371008.77141, **options)
Compute the distance between two points using the Equirectangular Approximation / Projection.
 
equirectangular3(lat1, lon1, lat2, lon2, **options)
DEPRECATED, use function equirectangular_.
 
equirectangular_(lat1, lon1, lat2, lon2, adjust=True, limit=45, wrap=False)
Compute the distance between two points using the Equirectangular Approximation / Projection.
 
euclid(x, y)
Appoximate the norm sqrt(x**2 + y**2) by max(abs(x), abs(y)) + min(abs(x), abs(y)) * 0.4142....
 
euclid_(*xs)
Appoximate the norm sqrt(sum(x**2 for x in xs)) by cascaded euclid.
 
euclidean(lat1, lon1, lat2, lon2, radius=6371008.77141, adjust=True, wrap=False)
Approximate the Euclidean distance between two (spherical) points.
 
euclidean_(phi2, phi1, lam21, adjust=True)
Approximate the angular Euclidean distance between two (spherical) points.
 
exception_chaining(error=None)
Get the previous exception's or exception chaining setting.
 
f2e2(f)
Return e2, the eccentricity squared for a given flattening.
 
f2e22(f)
Return e22, the 2nd eccentricity squared for a given flattening.
 
f2e32(f)
Return e32, the 3rd eccentricity squared for a given flattening.
 
f2f2(f)
Return f2, the 2nd flattening for a given flattening.
 
f2f_(f)
Return f_, the inverse flattening for a given flattening.
 
f2n(f)
Return n, the 3rd flattening for a given flattening.
 
fStr(floats, prec=6, fmt='%.*f', ints=False, sep=', ')
DEPRECATED, use function fstr.
 
fStrzs(floatstr)
DEPRECATED, use function fstrzs.
 
f_2f(f_)
Return f, the flattening for a given inverse flattening.
 
false2f(value, name='value', false=True, Error=<type 'exceptions.ValueError'>)
DEPRECATED, use function falsed2f.
 
falsed2f(falsed=True, Error=<type 'exceptions.ValueError'>, **name_value)
DEPRECATED, use class Easting or Northing.
 
favg(v1, v2, f=0.5)
Return the average of two values.
 
fdot(a, *b)
Return the precision dot product sum(a[i] * b[i] for i=0..len(a)).
 
fdot3(a, b, c, start=0)
Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)).
 
fhorner(x, *cs)
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) using the Horner form.
 
fidw(xs, ds, beta=2)
Interpolate using using Inverse Distance Weighting (IDW).
 
flatLocal(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)
Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.
 
flatLocal_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)
Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.
 
flatPolar(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)
Compute the distance between two (spherical) points using the polar coordinate flat-Earth formula.
 
flatPolar_(phi2, phi1, lam21)
Compute the angular distance between two (spherical) points using the polar coordinate flat-Earth formula.
 
fmean(xs)
Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs).
 
fpolynomial(x, *cs)
Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)).
 
fpowers(x, n, alts=0)
Return a series of powers [x**i for i=1..n].
 
fprod(iterable, start=1.0)
Iterable product, like math.prod or numpy.prod.
 
fractional(points, fi, LatLon=None, **LatLon_kwds)
Return the point at a given fractional index.
 
frange(start, number, step=1)
Generate a range of floats.
 
frechet_(points1, points2, distance=None, units='')
Compute the discrete Fréchet distance between two paths given as sets of points.
value
freduce(function, sequence, initial=...)
Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value.
 
fstr(floats, prec=6, fmt='F', ints=False, sep=', ', strepr=None)
Convert one or more floats to string, optionally stripped of trailing zero decimals.
 
fstrzs(efstr, ap1z=False)
Strip trailing zero decimals from a float string.
 
fsum(iterable)
Return an accurate floating point sum of values in the iterable.
 
fsum_(*xs)
Precision summation of the positional argument vulues.
 
ft2m(feet, usurvey=False)
Convert International or US Survey feet to meter.
 
geoidHeight2(lat, lon, model=0, timeout=2.0)
Get the NAVD88 geoid height at an NAD83 location.
 
gnomonic(lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., name='')
If Karney's geographiclib package is installed, return an GnomonicKarney otherwise an Gnomonic instance.
 
halfs2(str2)
Split a string in 2 halfs.
 
hausdorff_(model, target, both=False, early=True, seed=None, units='', distance=None, point=<function _point at 0x7f8035e44e50>)
Compute the directed or symmetric Hausdorff distance between 2 sets of points with or without early breaking and random sampling.
 
haversine(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)
Compute the distance between two (spherical) points using the Haversine formula.
 
haversine_(phi2, phi1, lam21)
Compute the angular distance between two (spherical) points using the Haversine formula.
 
heightOf(angle, distance, radius=6371008.77141)
Determine the height above the (spherical) earth after traveling along a straight line at a given tilt.
 
horizon(height, radius=6371008.77141, refraction=False)
Determine the distance to the horizon from a given altitude above the (spherical) earth.
 
hstr(height, prec=2, fmt='%+.*f', ints=False, m='')
Return a string for the height value.
 
hubeny(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)
Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.
 
hubeny_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)
Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.
 
hypot(x, y)
Return the Euclidean distance, sqrt(x*x + y*y).
 
hypot1(x)
Compute the norm sqrt(1 + x**2).
 
hypot2(x, y)
Compute the squared norm x**2 + y**2.
 
hypot2_(*xs)
Compute the squared norm sum(x**2 for x in xs).
 
hypot3(x, y, z)
DEPRECATED, use function hypot_.
 
hypot_(*xs)
Compute the norm sqrt(sum(x**2 for x in xs)).
 
inStr(inst, *args, **kwds)
DEPRECATED, use function instr.
 
instr(inst, *args, **kwds)
Return the string representation of an instantiation.
 
intersections2(center1, radius1, center2, radius2, sphere=True, Vector=None, **Vector_kwds)
Compute the intersection of two spheres or circles, each defined by a center point and a radius.
 
isNumpy2(obj)
Check for an Numpy2LatLon points wrapper.
 
isPoints2(obj)
Check for an LatLon2psxy points wrapper.
 
isTuple2(obj)
Check for an Tuple2LatLon points wrapper.
 
isantipode(lat1, lon1, lat2, lon2, eps=2.22044604925e-16)
Check whether two points are antipodal, on diametrically opposite sides of the earth.
 
isantipode_(phi1, lam1, phi2, lam2, eps=2.22044604925e-16)
Check whether two points are antipodal, on diametrically opposite sides of the earth.
 
isclass(obj)
Return True if obj is a class.
 
isclockwise(points, adjust=False, wrap=True)
Determine the direction of a path or polygon.
 
iscolinearWith(point, point1, point2, eps=2.22044604925e-16)
Check whether a point is colinear with two other points.
 
isconvex(points, adjust=False, wrap=True)
Determine whether a polygon is convex.
 
isconvex_(points, adjust=False, wrap=True)
Determine whether a polygon is convex and clockwise.
 
isenclosedBy(point, points, wrap=False)
Determine whether a point is enclosed by a polygon.
 
isenclosedby(point, points, wrap=False)
DEPRECATED, use function isenclosedBy.
 
isfinite(obj)
Check for Inf and NaN values.
 
isidentifier(obj)
Return True if obj is a valid Python identifier.
bool
isinf(x)
Check if float x is infinite (positive or negative).
 
isint(obj, both=False)
Check for int type or an integer float value.
 
iskeyword(x, y)
y in x.
bool
isnan(x)
Check if float x is not a number (NaN).
 
isneg0(obj)
Check for NEG0, negative 0.0.
 
ispolar(points, wrap=False)
Check whether a polygon encloses a pole.
 
isscalar(obj)
Check for scalar types.
 
issequence(obj, *excluded)
Check for sequence types.
 
isstr(obj)
Check for string types.
 
issubclassof(Sub, Super)
Check whether a class is a sub-class of a super class.
 
iterNumpy2(obj)
Iterate over Numpy2 wrappers or other sequences exceeding the threshold.
 
iterNumpy2over(n=None)
Get or set the iterNumpy2 threshold.
 
joined(*words, **sep)
Joined words by separator sep=NN.
 
joined_(*words, **sep)
Joined words by separator sep=" ".
 
latDMS(deg, form='dms', prec=2, sep='')
Convert latitude to a string, optionally suffixed with N or S.
 
latlon2n_xyz(lat, lon)
Convert lat-, longitude to n-vector (normal to the earth's surface) X, Y and Z components.
 
latlonDMS(lls, form='dms', prec=None, sep=None)
Convert one or more LatLon instances to strings.
 
len2(items)
Make built-in function len work for generators, iterators, etc.
 
limiterrors(raiser=None)
Get/set the throwing of LimitErrors.
 
lonDMS(deg, form='dms', prec=2, sep='')
Convert longitude to a string, optionally suffixed with E or W.
 
luneOf(lon1, lon2, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds)
Generate an ellipsoidal or spherical lune-shaped path or polygon.
 
m2NM(meter)
Convert meter to nautical miles (NM).
 
m2SM(meter)
Convert meter to statute miles (SM).
 
m2degrees(meter, radius=6371008.77141, lat=0)
Convert distance to angle along equator or along a parallel at an other latitude.
 
m2ft(meter, usurvey=False)
Convert meter to International or US Survey 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.
 
modulename(clas, prefixed=None)
Return the class name optionally prefixed with the module name.
 
n2e2(n)
Return e2, the eccentricity squared for a given 3rd flattening.
 
n2f(n)
Return f, the flattening for a given 3rd flattening.
 
n_xyz2latlon(x, y, z)
Convert n-vector components to lat- and longitude in degrees.
 
n_xyz2philam(x, y, z)
Convert n-vector components to lat- and longitude in radians.
 
nameof(inst)
Get the name of an instance.
 
nearestOn3(point, points, closed=False, wrap=False, **options)
DEPRECATED, use function nearestOn5.
 
nearestOn4(point, points, closed=False, wrap=False, **options)
DEPRECATED, use function nearestOn5.
 
nearestOn5(point, points, closed=False, wrap=False, LatLon=None, **options)
Locate the point on a path or polygon closest to an other point.
 
normDMS(strDMS, norm='')
Normalize all degree ˚, minute ' and second " symbols in a string to the default symbols %s, %s and %s.
 
notImplemented(inst, name, *args, **kwds)
Raise a NotImplementedError for a missing method or property.
 
notOverloaded(inst, name, *args, **kwds)
Raise an AssertionError for a method or property not overloaded.
 
pairs(items, prec=6, fmt='F', ints=False, sep='=')
Convert items to name=value strings, with floats handled like fstr.
 
parse3d(str3d, sep=',', name='', Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds)
Parse an "x, y, z" string.
 
parse3llh(strllh, height=0, sep=',', clipLat=90, clipLon=180)
Parse a string "lat lon [h]" representing lat-, longitude in degrees and optional height in meter.
 
parseDDDMMSS(strDDDMMSS, suffix='NSEW', sep='', clip=0)
Parse a lat- or longitude represention form [D]DDMMSS in degrees.
 
parseDMS(strDMS, suffix='NSEW', sep='', clip=0)
Parse a lat- or longitude representation "lat, lon" in degrees.
 
parseDMS2(strLat, strLon, sep='', clipLat=90, clipLon=180)
Parse a lat- and a longitude representions in degrees.
 
parseETM5(strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, name='')
Parse a string representing a UTM coordinate, consisting of "zone[band] hemisphere easting northing".
 
parseMGRS(strMGRS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name='')
Parse a string representing a MGRS grid reference, consisting of "zoneBand, grid, easting, northing".
 
parseOSGR(strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, name='')
Parse a string representing an OSGR grid reference, consisting of "[grid] easting northing".
 
parseRad(strRad, suffix='NSEW', clip=0)
Parse a string representing angle in radians.
 
parseUPS5(strUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Ups=<class 'pygeodesy.ups.Ups'>, falsed=True, name='')
Parse a string representing a UPS coordinate, consisting of "[zone][band] pole easting northing" where zone is pseudo zone "00"|"0"|"" and band is 'A'|'B'|'Y'|'Z'|''.
 
parseUTM(strUTM, datum=_R_M, Utm=_R_M, name='')
DEPRECATED, use function parseUTM5.
 
parseUTM5(strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, name='')
Parse a string representing a UTM coordinate, consisting of "zone[band] hemisphere easting northing".
 
parseUTMUPS5(strUTMUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, name='')
Parse a string representing a UTM or UPS coordinate, consisting of "zone[band] hemisphere/pole easting northing".
 
parseWM(strWM, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name='')
Parse a string "e n [r]" representing a WM coordinate, consisting of easting, northing and an optional radius.
 
perimeterOf(points, closed=False, adjust=True, radius=6371008.77141, wrap=True)
Approximate the perimeter of a path or polygon.
 
perimeterof(points, closed=False, adjust=True, radius=_R_M, wrap=True)
DEPRECATED, use function perimeterOf.
 
philam2n_xyz(phi, lam)
Convert lat-, longitude to n-vector (normal to the earth's surface) X, Y and Z components.
 
points2(points, closed=True, base=None, Error=<class 'pygeodesy.errors.PointsError'>)
Check a path or polygon represented by points.
 
polygon(points, closed=True, base=None)
DEPRECATED, use function points2.
 
precision(form, prec=None)
Set the default precison for a given F_ form.
 
property_doc_(doc)
Decorator for a property with documentation.
 
quadOf(lat1, lon1, lat2, lon2, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds)
Generate a quadrilateral path or polygon from two points.
 
radians(x)
Convert angle x from degrees to radians.
 
radiansPI(deg)
Convert and wrap degrees to radians [-PI..+PI].
 
radiansPI2(deg)
Convert and wrap degrees to radians [0..+2PI).
 
radiansPI_2(deg)
Convert and wrap degrees to radians [-3PI/2..+PI/2].
 
radical2(distance, radius1, radius2)
Compute the radical ratio and radical line of two intersecting circles.
 
randomrangenerator(seed)
Return a seeded random range function generator.
 
rangerrors(raiser=None)
Get/set the throwing of RangeErrors.
 
reprs(objs, prec=6, fmt='F', ints=False)
Convert objects to repr strings, with floats handled like fstr.
 
scalar(value, low=2.22044604925e-16, high=1.0, name='scalar', Error=<type 'exceptions.ValueError'>)
DEPRECATED, use class Number_ or Scalar_.
 
simplify1(points, distance, radius=6371008.77141, indices=False, **options)
Basic simplification of a path of LatLon points.
 
simplify2(points, pipe, radius=_R_M, 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 angle(s) in degrees.
 
splice(iterable, n=2, **fill)
Split an iterable into n slices.
 
sqrt3(x)
Compute the square root, cubed sqrt(x)**3 or sqrt(x**3).
 
strs(objs, prec=6, fmt='F', ints=False)
Convert objects to str strings, with floats handled like fstr.
 
tanPI_2_2(rad)
Compute the tangent of half angle, 90 degrees rotated.
 
tan_2(rad)
Compute the tangent of half angle.
 
thomas(lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)
Compute the distance between two (ellipsoidal) points using Thomas' formula.
 
thomas_(phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)
Compute the angular distance between two (ellipsoidal) points using Thomas' formula.
 
toCss(latlon, cs0=None, height=None, Css=<class 'pygeodesy.css.Css'>, name='')
Convert an (ellipsoidal) geodetic point to a Cassini-Soldner location.
 
toDMS(deg, form='dms', prec=2, sep='', ddd=2, neg='-', pos='')
Convert signed degrees to string, without suffix.
 
toEtm8(latlon, lon=None, datum=None, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, name='', zone=None, **cmoff)
Convert a lat-/longitude point to an ETM coordinate.
 
toLcc(latlon, conic=Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0..., height=None, Lcc=<class 'pygeodesy.lcc.Lcc'>, name='', **Lcc_kwds)
Convert an (ellipsoidal) geodetic point to a Lambert location.
 
toMgrs(utm, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name='', **Mgrs_kwds)
Convert a UTM coordinate to an MGRS grid reference.
 
toOsgr(latlon, lon=None, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Osgr=<class 'pygeodesy.osgr.Osgr'>, name='', **Osgr_kwds)
Convert a lat-/longitude point to an OSGR coordinate.
 
toUps8(latlon, lon=None, datum=None, Ups=<class 'pygeodesy.ups.Ups'>, pole='', falsed=True, strict=True, name='')
Convert a lat-/longitude point to a UPS coordinate.
 
toUtm(latlon, lon=None, datum=None, Utm=_R_M, cmoff=True, name='')
DEPRECATED, use function toUtm8.
 
toUtm8(latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, name='', zone=None, **cmoff)
Convert a lat-/longitude point to a UTM coordinate.
 
toUtmUps8(latlon, lon=None, datum=None, falsed=True, Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, pole='', name='', **cmoff)
Convert a lat-/longitude point to a UTM or UPS coordinate.
 
toWm(latlon, lon=None, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name='', **Wm_kwds)
Convert a lat-/longitude point to a WM coordinate.
 
trilaterate3d2(center1, radius1, center2, radius2, center3, radius3, eps=2.22044604925e-16, Vector=None, **Vector_kwds)
Trilaterate three spheres, each given as a (3d) center point and radius.
 
ub2str(ub)
Convert unicode or bytes to str.
 
unStr(name, *args, **kwds)
DEPRECATED, use function unstr.
 
unroll180(lon1, lon2, wrap=True)
Unroll longitudinal delta and wrap longitude in degrees.
 
unrollPI(rad1, rad2, wrap=True)
Unroll longitudinal delta and wrap longitude in radians.
 
unstr(name, *args, **kwds)
Return the string representation of an invokation.
 
upsZoneBand5(lat, lon, strict=True)
Return the UTM/UPS zone number, (polar) Band letter, pole and clipped lat- and longitude for a given location.
 
utmZoneBand2(lat, lon)
DEPRECATED, use function utmZoneBand5.
 
utmZoneBand5(lat, lon, cmoff=False)
Return the UTM zone number, Band letter, hemisphere and (clipped) lat- and longitude for a given location.
 
utmupsValidate(coord, falsed=False, MGRS=False, Error=<class 'pygeodesy.utmups.UTMUPSError'>)
Check a UTM or UPS coordinate.
 
utmupsValidateOK(coord, falsed=False, ok=True)
Check a UTM or UPS coordinate.
 
utmupsZoneBand5(lat, lon, cmoff=False)
Return the UTM/UPS zone number, Band letter, hemisphere/pole and clipped lat- and longitude for a given location.
 
vincentys(lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)
Compute the distance between two (spherical) points using Vincenty's spherical formula.
 
vincentys_(phi2, phi1, lam21)
Compute the angular distance between two (spherical) points using Vincenty's spherical formula.
 
wrap180(deg)
Wrap degrees to [-180..+180].
 
wrap360(deg)
Wrap degrees to [0..+360).
 
wrap90(deg)
Wrap degrees to [-270..+90].
 
wrapPI(rad)
Wrap radians to [-PI..+PI].
 
wrapPI2(rad)
Wrap radians to [0..+2PI).
 
wrapPI_2(rad)
Wrap radians to [-3PI/2..+PI/2].
Variables
  pygeodesy_abspath = '..../PyGe...
Fully qualified pygeodesy directory name (str).
  version = '20.10.14'
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 ≈ 2.2202e-16 (float).
  EPS1 = 1.0
1 - EPS ≈ 0.9999999999999998 (float).
  EPS1_2 = 1.0
1 - EPS_2 ≈ 0.9999999999999999 (float).
  EPS2
EPS * 2 ≈ 4.4409e-16 (float).
  EPS_2 = 1.11022302463e-16
EPS / 2 ≈ 1.1102e-16 (float).
  Ellipsoids = Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a...
Registered ellipsoids (enum-like).
  F_D = 'd'
Format degrees as unsigned "deg°" plus suffix (str).
  F_DEG = 'deg'
Format degrees as unsigned "[D]DD" plus suffix without symbol (str).
  F_DEG_ = '-deg'
Format degrees as signed "-/[D]DD" without suffix and symbol (str).
  F_DEG__ = '+deg'
Format degrees as signed "-/+[D]DD" without suffix and symbol (str).
  F_DM = 'dm'
Format degrees as unsigned "deg°min′" plus suffix (str).
  F_DMS = 'dms'
Format degrees as unsigned "deg°min′sec″" plus suffix (str).
  F_DMS_ = '-dms'
Format degrees as signed "-/deg°min′sec″" without suffix (str).
  F_DMS__ = '+dms'
Format degrees as signed "-/+deg°min′sec″" without suffix (str).
  F_DM_ = '-dm'
Format degrees as signed "-/deg°min′" without suffix (str).
  F_DM__ = '+dm'
Format degrees as signed "-/+deg°min′" without suffix (str).
  F_D_ = '-d'
Format degrees as signed "-/deg°" without suffix (str).
  F_D__ = '+d'
Format degrees as signed "-/+deg°" without suffix (str).
  F_MIN = 'min'
Format degrees as unsigned "[D]DDMM" plus suffix without symbols (str).
  F_MIN_ = '-min'
Format degrees as signed "-/[D]DDMM" without suffix and symbols (str).
  F_MIN__ = '+min'
Format degrees as signed "-/+[D]DDMM" without suffix and symbols (str).
  F_RAD = 'rad'
Convert degrees to radians and format as unsigned "RR" plus suffix (str).
  F_RAD_ = '-rad'
Convert degrees to radians and format as signed "-/RR" without suffix (str).
  F_RAD__ = '+rad'
Convert degrees to radians and format as signed "-/+RR" without suffix (str).
  F_SEC = 'sec'
Format degrees as unsigned "[D]DDMMSS" plus suffix without symbols (str).
  F_SEC_ = '-sec'
Format degrees as signed "-/[D]DDMMSS" without suffix and symbols (str).
  F_SEC__ = '+sec'
Format degrees as signed "-/+[D]DDMMSS" without suffix and symbols (str).
  F__E = 'e'
Format degrees as unsigned "%E" plus suffix without symbol (str).
  F__E_ = '-e'
Format degrees as signed "-%E" without suffix and symbol (str).
  F__E__ = '+e'
Format degrees as signed "-/+%E" without suffix and symbol (str).
  F__F = 'f'
Format degrees as unsigned "%F" plus suffix without symbol (str).
  F__F_ = '-f'
Format degrees as signed "-%F" without suffix and symbol (str).
  F__F__ = '+f'
Format degrees as signed "-/+%F" without suffix and symbol (str).
  F__G = 'g'
Format degrees as unsigned "%G" plus suffix without symbol (str).
  F__G_ = '-g'
Format degrees as signed "-%G" without suffix and symbol (str).
  F__G__ = '+g'
Format degrees as signed "-/+%G" without suffix and symbol (str).
  INF = inf
Infinity (float), see function isinf, isfinite.
  MANTIS = 53
System's mantissa bits = 53 (int).
  MAX = 1.79769313486e+308
System's float max ≈ 1.798e+308 (float).
  MIN = 2.22507385851e-308
System's float min ≈ 2.225e-308 (float).
  NAN = nan
Not-A-Number (float), see function isnan.
  NEG0 = -0.0
Negative 0.0 (float), see function isneg0.
  NN = ''
Empty (str), Nomen Nescio.
  OK = 'OK'
  PI = 3.14159265359
Constant math.pi (float).
  PI2 = 6.28318530718
Two PI, PI * 2, aka Tau (float).
  PI4 = 12.5663706144
Four PI, PI * 4 (float).
  PI_2 = 1.57079632679
Half PI, PI / 2 (float).
  PI_4 = 0.785398163397
Quarter PI, PI / 4 (float).
  R_FM = 6371000.0
Former FAI-Sphere earth radius (meter).
  R_KM = 6371.008771415
Mean (spherical) earth radius (km, kilometer).
  R_M = 6371008.77141
Mean (spherical) earth radius (meter).
  R_MA = 6378137.0
Equatorial (major) earth radius (meter), WGS84, EPSG:3785.
  R_MB = 6356752.0
Polar (minor) earth radius (meter), WGS84, EPSG:3785.
  R_NM = 3440.06953446921
Mean (spherical) earth radius (NM, nautical miles).
  R_SM = 3958.753395372691
Mean (spherical) earth radius (SM, statute miles).
  R_VM = 6366707.0194937
Aviation/Navigation earth radius (meter).
  RefFrames = RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoc...
Registered reference frames (enum-like).
  S_DEG = '°'
Degrees symbol "°" (str).
  S_MIN = '\xe2\x80\xb2'
Minutes symbol "′" (str).
  S_RAD = ''
Radians symbol "" (str).
  S_SEC = ''
Seconds symbol "″" (str).
  S_SEP = ''
Separator between deg°, min′ and sec″ "" (str).
  Transforms = Transforms.BD72: Transform(name='BD72', tx=106.86...
Registered transforms (enum-like).
  isLazy = None
hash(x)
Function Details

UtmUps (zone, hemipole, easting, northing, band='', datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., falsed=True, name='')

 

Class-like function to create a UTM/UPS coordinate.

Arguments:
  • zone - The UTM (longitudinal) zone with/-out Band letter for UTM or for UPS zone "00" or 0 (str or int).
  • hemipole - UTM hemisphere or UPS top/center of projection (str, 'N[orth]' or 'S[outh]').
  • easting - Easting, see falsed (meter).
  • northing - Northing, see falsed (meter).
  • band - Optional, UTM (latitudinal) Band letter 'C'|'D'..'W'|'X' or UPS (polar) Band letter 'A'|'B'|'Y'|'Z' (str).
  • datum - Optional, the coordinate's datum (Datum).
  • falsed - Both easting and northing are falsed (bool).
  • name - Optional name (str).
Returns:
New UTM or UPS instance (Utm or Ups).
Raises:
  • TypeError - Invalid B({datum}.
  • UTMUPSError - UTM or UPS validation failed.

See Also: Classes Utm and Ups and Karney's UTMUPS.

a_b2e (a, b)

 

Return e, the eccentricity for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The eccentricity (float or 0), sqrt(1 - (b / a)**2).

Note: The result is 0 for prolate and near-spherical ellipsoids.

a_b2e2 (a, b)

 

Return e2, the eccentricity squared for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The eccentricity squared (float or 0), 1 - (b / a)**2.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_b2e22 (a, b)

 

Return e22, the 2nd eccentricity squared for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The 2nd eccentricity squared (float or 0), (a / b)**2 - 1.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_b2e32 (a, b)

 

Return e32, the 3rd eccentricity squared for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The 3rd eccentricity squared (float or 0), (a**2 - b**2) / (a**2 + b**2).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_b2f (a, b)

 

Return f, the flattening for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The flattening (float or 0), (a - b) / a.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_b2f2 (a, b)

 

Return f2, the 2nd flattening for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The 2nd flattening (float or 0), (a - b) / b.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_b2f_ (a, b)

 

Return f_, the inverse flattening for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The inverse flattening (float or 0), a / (a - b).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_b2n (a, b)

 

Return n, the 3rd flattening for a given equatorial and polar radius.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • b - Polar (minor) radius (scalar > 0).
Returns:
The 3rd flattening (float or 0), (a - b) / (a + b).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

a_f2b (a, f)

 

Return b, the polar radius for a given equatorial radius and flattening.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • f - Flattening (scalar < 1).
Returns:
The polar (minor) radius (float), a * (1 - f).

a_f_2b (a, f_)

 

Return b, the polar radius for a given equatorial radius and inverse flattening.

Arguments:
  • a - Equatorial (major) radius (scalar > 0).
  • f_ - Inverse flattening (scalar >>> 1).
Returns:
The polar (minor) radius (float), a * (f_ - 1) / f_.

anstr (name, OKd='._-', sub='_')

 

Make a valid name of alphanumeric and OKd characters.

Arguments:
  • name - The original name (str).
  • OKd - Other acceptable characters (str).
  • sub - Substitute for invalid charactes (str).
Returns:
The modified name (str).

Note: Leading and trailing whitespace characters are removed and intermediate whitespace characters are coalesced and substituted.

antipode (lat, lon)

 

Return the antipode, the point diametrically opposite to a given point in degrees.

Arguments:
  • lat - Latitude (degrees).
  • lon - Longitude (degrees).
Returns:
A LatLon2Tuple(lat, lon).

See Also: Geosphere.

antipode_ (phi, lam)

 

Return the antipode, the point diametrically opposite to a given point in radians.

Arguments:
  • phi - Latitude (radians).
  • lam - Longitude (radians).
Returns:
A PhiLam2Tuple(phi, lam).

See Also: Geosphere.

areaOf (points, adjust=True, radius=6371008.77141, wrap=True)

 

Approximate the area of a polygon.

Arguments:
  • points - The polygon points (LatLon[]).
  • adjust - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (bool).
  • radius - Mean earth radius (meter).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
Returns:
Approximate area (meter, same units as radius, squared).
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.
  • ValueError - Invalid radius.

Note: This area approximation has limited accuracy and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes.

See Also: sphericalNvector.areaOf, sphericalTrigonometry.areaOf and ellipsoidalKarney.areaOf.

atan2b (y, x)

 

Compute atan2(y, x) as degrees [0..+360].

See Also: Function atan2d.

atan2d (y, x)

 

Compute atan2(y, x) as degrees [-180..+180].

See Also: Karney's C++ function Math.atan2d.

attrs (inst, *names, **kwds)

 

Get instance attributes as name=value strings, with floats handled like fstr.

Arguments:
  • inst - The instance (any type).
  • names - The attribute names (strs).
  • kwds - Keyword argument for function pairs, except Nones=True to in-/exclude missing or attributes with a None value.
Returns:
A tuple(sep.join(t) for t in zip(names, reprs(values, ...))) of strs.

b_f2a (b, f)

 

Return a, the equatorial radius for a given polar radius and flattening.

Arguments:
  • b - Polar (minor) radius (scalar > 0).
  • f - Flattening (scalar < 1).
Returns:
The equatorial (major) radius (float), b / (1 - f).

b_f_2a (b, f_)

 

Return a, the equatorial radius for a given polar radius and inverse flattening.

Arguments:
  • b - Polar (minor) radius (scalar > 0).
  • f_ - Inverse flattening (scalar >>> 1).
Returns:
The equatorial (major) radius (float), b * f_ / (f_ - 1).

bearing (lat1, lon1, lat2, lon2, **options)

 

Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • options - Optional keyword arguments for function bearing_.
Returns:
Initial or final bearing (compass degrees360) or zero if start and end point coincide.

bearingDMS (bearing, form='d', prec=None, sep='')

 

Convert bearing to a string.

Arguments:
Returns:
Compass degrees per the specified form (str).

JS name: toBrng.

bearing_ (phi1, lam1, phi2, lam2, final=False, wrap=False)

 

Compute the initial or final bearing (forward or reverse azimuth) between a (spherical) start and end point.

Arguments:
  • phi1 - Start latitude (radians).
  • lam1 - Start longitude (radians).
  • phi2 - End latitude (radians).
  • lam2 - End longitude (radians).
  • final - Return final bearing if True, initial otherwise (bool).
  • wrap - Wrap and unrollPI longitudes (bool).
Returns:
Initial or final bearing (compass radiansPI2) or zero if start and end point coincide.

bounds (points, wrap=True, LatLon=None)

 

DEPRECATED, use function boundsOf.

Returns:
2-Tuple (latlonSW, latlonNE) as LatLon or 4-Tuple (latS, lonW, latN, lonE) if LatLon is None.

boundsOf (points, wrap=True, LatLon=None)

 

Determine the lower-left SW and upper-right NE corners of a path or polygon.

Arguments:
  • points - The path or polygon points (LatLon[]).
  • wrap - Wrap lat- and longitudes (bool).
  • LatLon - Optional class to return the bounds corners (LatLon) or None.
Returns:
A Bounds2Tuple(latlonSW, latlonNE) as LatLons if LatLon is None a Bounds4Tuple(latS, lonW, latN, lonE).
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.

Example:

>>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
>>> boundsOf(b)  # False
>>> 45.0, 1.0, 46.0, 2.0

callername (up=1, dflt='', source=False)

 

Get the name of the calling callable.

Arguments:
  • up - Number of call stack frames up (int).
  • dflt - Default return value (any).
  • source - Include source file name and line number (bool).
Returns:
Name of the non-internal callable (str) or dflt if none found.

cbrt (x)

 

Compute the cubic root x**(1/3).

Arguments:
  • x - Value (scalar).
Returns:
Cubic root (float).

See Also: Functions cbrt2 and sqrt3.

cbrt2 (x)

 

Compute the cubic root squared x**(2/3).

Arguments:
  • x - Value (scalar).
Returns:
Cubic root squared (float).

See Also: Functions cbrt and sqrt3.

centroidOf (points, wrap=True, LatLon=None)

 

Determine the centroid of a polygon.

Arguments:
  • points - The polygon points (LatLon[]).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
  • LatLon - Optional class to return the centroid (LatLon) or None.
Returns:
Centroid location (LatLon) or a LatLon2Tuple(lat, lon) if LatLon is None.
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.
  • ValueError - The points enclose a pole or near-zero area.

See Also: Centroid and Paul Bourke's Calculating The Area And Centroid Of A Polygon, 1988.

classname (inst, prefixed=None)

 

Return the instance' class name optionally prefixed with the module name.

Arguments:
  • inst - The object (any type).
  • prefixed - Include the module name (bool), see function classnaming.
Returns:
The inst's [module.]class name (str).

classnaming (prefixed=None)

 

Get/set the default class naming for [module.]class names.

Arguments:
  • prefixed - Include the module name (bool).
Returns:
Previous class naming setting (bool).

clipCS3 (points, lowerleft, upperright, closed=False, inull=False)

 

Clip a path against a rectangular clip box using the Cohen-Sutherland algorithm.

Arguments:
  • points - The points (LatLon[]).
  • lowerleft - Bottom-left corner of the clip box (LatLon).
  • upperright - Top-right corner of the clip box (LatLon).
  • closed - Optionally, close the path (bool).
  • inull - Optionally, retain null edges if inside (bool).
Returns:
Yield a ClipCS3Tuple(start, end, index) for each edge of the clipped path.
Raises:
  • ClipError - The lowerleft and upperright corners specify an invalid clip box.
  • PointsError - Insufficient number of points.

clipDegrees (deg, limit)

 

Clip a lat- or longitude to the given range.

Arguments:
  • deg - Unclipped lat- or longitude (degrees).
  • limit - Valid -limit..+limit range (degrees).
Returns:
Clipped value (degrees).
Raises:

clipRadians (rad, limit)

 

Clip a lat- or longitude to the given range.

Arguments:
  • rad - Unclipped lat- or longitude (radians).
  • limit - Valid -limit..+limit range (radians).
Returns:
Clipped value (radians).
Raises:

clipSH (points, corners, closed=False, inull=False)

 

Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm.

Arguments:
  • points - The polygon points (LatLon[]).
  • corners - Three or more points defining a convex clip region (LatLon[]) or two points to specify a rectangular clip box.
  • closed - Close the clipped points (bool).
  • inull - Optionally, include null edges (bool).
Returns:
Yield the clipped points (LatLon[]).
Raises:
  • ClipError - The corners specify a polar, zero-area, non-convex or otherwise invalid clip box or region.
  • PointsError - Insufficient number of points.

clipSH3 (points, corners, closed=False, inull=False)

 

Clip a polygon against a clip region or box using the Sutherland-Hodgman algorithm.

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

clips (bstr, limit=50, white='')

 

Clip a string to the given length limit.

Arguments:
  • bstr - String (bytes or str).
  • limit - Length limit (int).
  • white - Optionally, replace all whitespace (str).
Returns:
The clipped or unclipped bstr.

compassAngle (lat1, lon1, lat2, lon2, adjust=True, wrap=False)

 

Return the angle from North for the direction vector (lon2 - lon1, lat2 - lat1) between two points.

Suitable only for short, non-near-polar vectors up to a few hundred Km or Miles. Use function bearing for longer vectors.

Arguments:
  • lat1 - From latitude (degrees).
  • lon1 - From longitude (degrees).
  • lat2 - To latitude (degrees).
  • lon2 - To longitude (degrees).
  • adjust - Adjust the longitudinal delta by the cosine of the mean latitude (bool).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Compass angle from North (degrees360).

Note: Courtesy Martin Schultz.

See Also: Local, flat earth approximation.

compassDMS (bearing, form='d', prec=None, sep='')

 

Convert bearing to a string suffixed with compass point.

Arguments:
Returns:
Compass degrees and point in the specified form (str).

compassPoint (bearing, prec=3)

 

Convert bearing to a compass point.

Arguments:
  • bearing - Bearing from North (compass degrees360).
  • prec - Optional precision (1 for cardinal or basic winds, 2 for intercardinal or ordinal or principal winds, 3 for secondary-intercardinal or half-winds or 4 for quarter-winds).
Returns:
Compass point (1-, 2-, 3- or 4-letter str).
Raises:
  • ValueError - Invalid prec.

See Also: Dms.compassPoint and Compass rose.

Example:

>>> p = compassPoint(24, 1)  # 'N'
>>> p = compassPoint(24, 2)  # 'NE'
>>> p = compassPoint(24, 3)  # 'NNE'
>>> p = compassPoint(24)     # 'NNE'
>>> p = compassPoint(11, 4)  # 'NbE'
>>> p = compassPoint(30, 4)  # 'NEbN'
>>> p = compassPoint(11.249)  # 'N'
>>> p = compassPoint(11.25)   # 'NNE'
>>> p = compassPoint(-11.25)  # 'N'
>>> p = compassPoint(348.749) # 'NNW'

cosineAndoyerLambert (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)

 

Compute the distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines fromula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as the datum's ellipsoid axes).
Raises:
  • TypeError - Invalid datum.

cosineAndoyerLambert_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)

 

Compute the angular distance between two (ellipsoidal) points using the Andoyer-Lambert correction of the Law of Cosines fromula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
Returns:
Angular distance (radians).
Raises:
  • TypeError - Invalid datum.

cosineForsytheAndoyerLambert (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)

 

Compute the distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as the datum's ellipsoid axes).
Raises:
  • TypeError - Invalid datum.

cosineForsytheAndoyerLambert_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)

 

Compute the angular distance between two (ellipsoidal) points using the Forsythe-Andoyer-Lambert correction of the Law of Cosines formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
Returns:
Angular distance (radians).
Raises:
  • TypeError - Invalid datum.

cosineLaw (lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)

 

Compute the distance between two points using the spherical Law of Cosines formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • radius - Mean earth radius (meter).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as radius).
Raises:
  • TypeError - Invalid radius.

cosineLaw_ (phi2, phi1, lam21)

 

Compute the angular distance between two points using the spherical Law of Cosines formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
Returns:
Angular distance (radians).

crosserrors (raiser=None)

 

Report or ignore vectorial cross product errors.

Arguments:
  • raiser - Use True to throw or False to ignore CrossError exceptions. Use None to leave the setting unchanged.
Returns:
Previous setting (bool).

See Also: Property Vector3d.crosserrors.

date2epoch (year, month, day)

 

Return the reference frame epoch for a calendar day.

Arguments:
  • year - Year of the date (scalar).
  • month - Month in the year (scalar, 1..12).
  • day - Day in the month (scalar, 1..31).
Returns:
Epoch, the fractional year (float).
Raises:
  • TRFError - Invalid year, month or day.

Note: Any year is considered a leap year, i.e. having 29 days in February.

decodeEPSG2 (arg)

 

DEPRECATED, use function epsg.decode2.

Returns:
2-Tuple (zone, hemipole)

degDMS (deg, prec=6, s_D='°', s_M='\xe2\x80\xb2', s_S='', neg='-', pos='')

 

Convert degrees to a string in degrees, minutes or seconds.

Arguments:
  • deg - Value in degrees (scalar).
  • prec - Optional number of decimal digits (0..9 or None for default). Trailing zero decimals are stripped for prec values of 1 and above, but kept for negative prec.
  • s_D - Symbol for degrees (str).
  • s_M - Symbol for minutes (str) or "".
  • s_S - Symbol for seconds (str) or "".
  • neg - Optional sign for negative ('-').
  • pos - Optional sign for positive ('').
Returns:
Either degrees, minutes or seconds (str).

degrees180 (rad)

 

Convert radians to degrees and wrap [-180..+180].

Arguments:
  • rad - Angle (radians).
Returns:
Angle in degrees, wrapped (degrees180).

degrees2m (deg, radius=6371008.77141, lat=0)

 

Convert angle to distance along the equator or along a parallel at an other latitude.

Arguments:
  • deg - Angle (degrees).
  • radius - Mean earth radius (meter).
  • lat - Parallel latitude (degrees90, str).
Returns:
Distance (meter, same units as radius).
Raises:
  • RangeError - Latitude lat outside valid range and rangerrors set to True.
  • ValueError - Invalid deg, radius or lat.

See Also: Function m2degrees.

degrees360 (rad)

 

Convert radians to degrees and wrap [0..+360).

Arguments:
  • rad - Angle (radians).
Returns:
Angle in degrees, wrapped (degrees360).

degrees90 (rad)

 

Convert radians to degrees and wrap [-270..+90].

Arguments:
  • 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.

Arguments:
  • GeoidHeights_dat - The un-gz-ed GeoidHeights.dat file (str or file handle).
Returns:
For each test, yield a GeoidHeight5Tuple(lat, lon, egm84, egm96, egm2008).
Raises:

Note: Function egmGeoidHeights is used to test the geoids GeoidKarney and GeoidPGM, see PyGeodesy module test/testGeoids.py.

elevation2 (lat, lon, timeout=2.0)

 

Get the geoid elevation at an NAD83 to NAVD88 location.

Arguments:
  • lat - Latitude (degrees).
  • lon - Longitude (degrees).
  • timeout - Optional, query timeout (seconds).
Returns:
An Elevation2Tuple(elevation, data_source) or (None, "error") in case of errors.
Raises:
  • ValueError - Invalid timeout.

Note: The returned elevation is None if lat or lon is invalid or outside the Conterminous US (CONUS), if conversion failed or if the query timed out. The error is the HTTP-, IO-, SSL-, Type-, URL- or ValueError as a string (str).

See Also: USGS National Map, the FAQ, geoid.py, module geoids, classes GeoidG2012B, GeoidKarney and GeoidPGM.

encodeEPSG (zone, hemipole='', band='')

 

DEPRECATED, use function epsg.encode.

Returns:
EPSG code (int).

enstr2 (easting, northing, prec, *extras)

 

Return easting, northing string representations.

Arguments:
  • easting - Easting from false easting (meter).
  • northing - Northing from from false northing (meter).
  • prec - Precision in number of digits (int, [1..5]).
  • extras - Optional leading items (strs).
Returns:
extras + 2-Tuple (eastingStr, northingStr).
Raises:
  • ValueError - Invalid prec.

epoch2date (epoch)

 

Return the date for a reference frame epoch.

Arguments:
  • epoch - Fractional year (scalar).
Returns:
3-Tuple (year, month, day).
Raises:

Note: Any year is considered a leap year, i.e. having 29 days in February.

equidistant (lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., name='')

 

If Karney's geographiclib package is installed, return an EquidistantKarney otherwise an Equidistant instance.

Arguments:
  • lat0 - Latitude of center point (degrees90).
  • lon0 - Longitude of center point (degrees180).
  • datum - Optional datum or ellipsoid (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple) or scalar earth radius (meter).
  • name - Optional name for the projection (str).
Returns:
An EquidistantKarney or Equidistant instance.
Raises:
  • AzimuthalError - Invalid lat0, lon0 or sperical datum.
  • TypeError - Invalid datum.

equirectangular (lat1, lon1, lat2, lon2, radius=6371008.77141, **options)

 

Compute the distance between two points using the Equirectangular Approximation / Projection.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • radius - Mean earth radius (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.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • adjust - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (bool).
  • limit - Optional limit for lat- and longitudinal deltas (degrees) or None or 0 for unlimited.
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
A Distance4Tuple(distance2, delta_lat, delta_lon, unroll_lon2).
Raises:
  • LimitError - If the lat- and/or longitudinal delta exceeds the -limit..+limit range and limiterrors set to True.

euclid (x, y)

 

Appoximate the norm sqrt(x**2 + y**2) by max(abs(x), abs(y)) + min(abs(x), abs(y)) * 0.4142....

Arguments:
  • x - X component (scalar).
  • y - Y component (scalar).
Returns:
Appoximate norm (float).

See Also: Function euclid_.

euclid_ (*xs)

 

Appoximate the norm sqrt(sum(x**2 for x in xs)) by cascaded euclid.

Arguments:
  • xs - X arguments, positional (scalar[]).
Returns:
Appoximate norm (float).

See Also: Function euclid.

euclidean (lat1, lon1, lat2, lon2, radius=6371008.77141, adjust=True, wrap=False)

 

Approximate the Euclidean distance between two (spherical) points.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • radius - Mean earth radius (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).
Raises:
  • TypeError - Invalid radius.

euclidean_ (phi2, phi1, lam21, adjust=True)

 

Approximate the angular Euclidean distance between two (spherical) points.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
  • adjust - Adjust the longitudinal delta by the cosine of the mean latitude (bool).
Returns:
Angular distance (radians).

exception_chaining (error=None)

 

Get the previous exception's or exception chaining setting.

Arguments:
  • error - An error instance (Exception) or None.
Returns:
If error=None, return True if exception chaining is enabled for PyGeodesy errors, False if turned off and None if not available. If error is not None, return the previous, chained error or None otherwise.

Note: Set env variable PYGEODESY_EXCEPTION_CHAINING to any non-empty value prior to import pygeodesy to enable exception chaining for pygeodesy errors.

f2e2 (f)

 

Return e2, the eccentricity squared for a given flattening.

Arguments:
  • f - Flattening (scalar < 1).
Returns:
The (1st) eccentricity squared (float < 1), f * (2 - f).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

See Also: Eccentricity conversions and Flattening.

f2e22 (f)

 

Return e22, the 2nd eccentricity squared for a given flattening.

Arguments:
  • f - Flattening (scalar < 1).
Returns:
The 2nd eccentricity squared (float > -1 or INF), f * (2 - f) / (1 - f)**2.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

See Also: Eccentricity conversions.

f2e32 (f)

 

Return e32, the 3rd eccentricity squared for a given flattening.

Arguments:
  • f - Flattening (scalar < 1).
Returns:
The 3rd eccentricity squared (float), f * (2 - f) / (1 + (1 - f)**2).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

See Also: Eccentricity conversions.

f2f2 (f)

 

Return f2, the 2nd flattening for a given flattening.

Arguments:
  • f - Flattening (scalar < 1).
Returns:
The 2nd flattening (float or INF), f / (1 - f).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

See Also: Eccentricity conversions and Flattening.

f2f_ (f)

 

Return f_, the inverse flattening for a given flattening.

Arguments:
  • f - Flattening (scalar < 1).
Returns:
The inverse flattening (float or 0), 1 / f.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

f2n (f)

 

Return n, the 3rd flattening for a given flattening.

Arguments:
  • f - Flattening (scalar < 1).
Returns:
The 3rd flattening (-1 < float < 1), f / (2 - f).

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

See Also: Eccentricity conversions and Flattening.

f_2f (f_)

 

Return f, the flattening for a given inverse flattening.

Arguments:
  • f_ - Inverse flattening (scalar >>> 1).
Returns:
The flattening (float or 0), 1 / f_.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

falsed2f (falsed=True, Error=<type 'exceptions.ValueError'>, **name_value)

 

DEPRECATED, use class Easting or Northing.

Convert a falsed east-/northing to non-negative float.

Arguments:
  • falsed - Value includes false origin (bool).
  • Error - Optional, overriding error (Exception).
  • name_value - One name=value pair.
Returns:
The value (float).
Raises:
  • Error - Invalid or negative name=value.

favg (v1, v2, f=0.5)

 

Return the average of two values.

Arguments:
  • v1 - One value (scalar).
  • v2 - Other value (scalar).
  • f - Optional fraction (float).
Returns:
v1 + f * (v2 - v1) (float).

fdot (a, *b)

 

Return the precision dot product sum(a[i] * b[i] for i=0..len(a)).

Arguments:
  • a - List, sequence, tuple, etc. (scalars).
  • b - All positional arguments (scalars).
Returns:
Dot product (float).
Raises:

See Also: Class Fdot.

fdot3 (a, b, c, start=0)

 

Return the precision dot product start + sum(a[i] * b[i] * c[i] for i=0..len(a)).

Arguments:
  • a - List, sequence, tuple, etc. (scalar[]).
  • b - List, sequence, tuple, etc. (scalar[]).
  • c - List, sequence, tuple, etc. (scalar[]).
  • start - Optional bias (scalar).
Returns:
Dot product (float).
Raises:
  • LenError - Unequal len(a), len(b) and/or len(c).
  • OverflowError - Partial 2sum overflow.

fhorner (x, *cs)

 

Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)) using the Horner form.

Arguments:
  • x - Polynomial argument (scalar).
  • cs - Polynomial coeffients (scalar[]).
Returns:
Horner value (float).
Raises:
  • OverflowError - Partial 2sum overflow.
  • TypeError - Non-scalar x.
  • ValueError - No cs coefficients or x is not finite.

See Also: Function fpolynomial and class Fhorner.

fidw (xs, ds, beta=2)

 

Interpolate using using Inverse Distance Weighting (IDW).

Arguments:
  • xs - Known values (scalar[]).
  • ds - Non-negative distances (scalar[]).
  • beta - Inverse distance power (int, 0, 1, 2, or 3).
Returns:
Interpolated value x (float).
Raises:
  • LenError - Unequal or zero len(ds) and len(xs).
  • ValueError - Invalid beta, negative ds value, weighted ds below EPS.

Note: Using beta=0 returns the mean of xs.

flatLocal (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)

 

Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as the datum's ellipsoid axes).
Raises:
  • TypeError - Invalid datum.

Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude.

See Also: Functions flatLocal_/hubeny_, cosineLaw, flatPolar, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, haversine, thomas, vincentys, method Ellipsoid.distance2 and local, flat earth approximation.

flatLocal_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)

 

Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
Returns:
Angular distance (radians).
Raises:
  • TypeError - Invalid datum.

Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude.

See Also: Functions flatLocal/hubeny, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatPolar_, equirectangular_, euclidean_, haversine_, thomas_ and vincentys_ and local, flat earth approximation.

flatPolar (lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)

 

Compute the distance between two (spherical) points using the polar coordinate flat-Earth formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • radius - Mean earth radius (meter).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as radius).
Raises:
  • TypeError - Invalid radius.

flatPolar_ (phi2, phi1, lam21)

 

Compute the angular distance between two (spherical) points using the polar coordinate flat-Earth formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
Returns:
Angular distance (radians).

fmean (xs)

 

Compute the accurate mean sum(xs[i] for i=0..len(xs)) / len(xs).

Arguments:
  • xs - Values (scalars).
Returns:
Mean value (float).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ValueError - No xs values.

fpolynomial (x, *cs)

 

Evaluate the polynomial sum(cs[i] * x**i for i=0..len(cs)).

Arguments:
  • x - Polynomial argument (scalar).
  • cs - Polynomial coeffients (scalar[]).
Returns:
Polynomial value (float).
Raises:
  • OverflowError - Partial 2sum overflow.
  • TypeError - Non-scalar x.
  • ValueError - No cs coefficients or x is not finite.

See Also: Function fhorner and class Fpolynomial.

fpowers (x, n, alts=0)

 

Return a series of powers [x**i for i=1..n].

Arguments:
  • x - Value (scalar).
  • n - Highest exponent (int).
  • alts - Only alternating powers, starting with this exponent (int).
Returns:
Powers of x (float[]).
Raises:
  • TypeError - Non-scalar x or n not int.
  • ValueError - Non-finite x or non-positive n.

fprod (iterable, start=1.0)

 

Iterable product, like math.prod or numpy.prod.

Arguments:
  • iterable - Terms to be multiplied (scalar[]).
  • start - Initial term, also the value returned for an empty iterable (scalar).
Returns:
The product (float).

See Also: NumPy.prod.

fractional (points, fi, LatLon=None, **LatLon_kwds)

 

Return the point at a given fractional index.

Arguments:
  • points - The points (LatLon[], Numpy2LatLon[], Tuple2LatLon[] or other[]).
  • fi - The fractional index (float or int).
  • LatLon - Optional class to return the intermediate, fractional point (LatLon) or None.
  • LatLon_kwds - Optional LatLon keyword arguments, ignored of LatLon=None.
Returns:
A LatLon or if LatLon is None, a LatLon2Tuple(lat, lon) for points[fi] if fractional index fi is int, otherwise the intermediate point between points[int(fi)] and points[int(fi) + 1] for float fractional index fi.
Raises:
  • IndexError - Fractional index fi invalid or points not subscriptable.

frange (start, number, step=1)

 

Generate a range of floats.

Arguments:
  • start - First value (float).
  • number - The number of floats to generate (int).
  • step - Increment value (float).
Returns:
A generator (floats).

See Also: NumPy.prod.

frechet_ (points1, points2, distance=None, units='')

 

Compute the discrete Fréchet distance between two paths given as sets of points.

Arguments:
  • points1 - First set of points (LatLon[], Numpy2LatLon[], Tuple2LatLon[] or other[]).
  • points2 - Second set of points (LatLon[], Numpy2LatLon[], Tuple2LatLon[] or other[]).
  • distance - Callable returning the distance between a points1 and a points2 point (signature (point1, point2)).
  • units - Optional, the distance units (Unit or str).
Returns:
A Frechet6Tuple(fd, fi1, fi2, r, n, units) where fi1 and fi2 are type int indices into points1 respectively points2.
Raises:

Note: Function frechet_ does not support fractional indices for intermediate points1 and points2.

freduce (function, sequence, initial=...)

 

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

Returns: value

fstr (floats, prec=6, fmt='F', ints=False, sep=', ', strepr=None)

 

Convert one or more floats to string, optionally stripped of trailing zero decimals.

Arguments:
  • floats - Single or a list, sequence, tuple, etc. (scalars).
  • prec - The float precision, number of decimal digits (0..9). Trailing zero decimals are stripped if prec is positive, but kept for negative prec values.
  • fmt - Optional, float format (str).
  • ints - Optionally, remove the decimal dot for int values (bool).
  • sep - Separator joining the floats (str).
  • strepr - Optional callable to format non-floats (typically repr, str) or None to raise a TypeError.
Returns:
The sep.join(strs(floats, ...) joined (str) or single strs((floats,), ...) (str) if floats is scalar.

fstrzs (efstr, ap1z=False)

 

Strip trailing zero decimals from a float string.

Arguments:
  • efstr - Float with or without exponent (str).
  • ap1z - Append the decimal point and one zero decimal if the efstr is all digits (bool).
Returns:
Float (str).

fsum (iterable)

 

Return an accurate floating point sum of values in the iterable. Assumes IEEE-754 floating point arithmetic.

fsum_ (*xs)

 

Precision summation of the positional argument vulues.

Arguments:
  • xs - Values to be added (scalar[]).
Returns:
Accurate fsum (float).
Raises:
  • OverflowError - Partial 2sum overflow.
  • TypeError - Non-scalar xs value.
  • ValueError - Invalid or non-finite xs value.

ft2m (feet, usurvey=False)

 

Convert International or US Survey feet to meter.

Arguments:
  • feet - Value in feet (scalar).
  • usurvery - Convert US Survey feet (bool), International feet otherwise.
Returns:
Value in meter (float).
Raises:
  • ValueError - Invalid feet.

geoidHeight2 (lat, lon, model=0, timeout=2.0)

 

Get the NAVD88 geoid height at an NAD83 location.

Arguments:
  • lat - Latitude (degrees).
  • lon - Longitude (degrees).
  • model - Optional, geoid model ID (int).
  • timeout - Optional, query timeout (seconds).
Returns:
An GeoidHeight2Tuple(height, model_name) or (None, "error") in case of errors.
Raises:
  • ValueError - Invalid timeout.

Note: The returned height is None if lat or lon is invalid or outside the Conterminous US (CONUS), if the model was invalid, if conversion failed or if the query timed out. The error is the HTTP-, IO-, SSL-, Type-, URL- or ValueError as a string (str).

See Also: NOAA National Geodetic Survey, Geoid, USGS10mElev.py, module geoids, classes GeoidG2012B, GeoidKarney and GeoidPGM.

gnomonic (lat0, lon0, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., name='')

 

If Karney's geographiclib package is installed, return an GnomonicKarney otherwise an Gnomonic instance.

Arguments:
  • lat0 - Latitude of center point (degrees90).
  • lon0 - Longitude of center point (degrees180).
  • datum - Optional datum or ellipsoid (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple) or scalar earth radius (meter).
  • name - Optional name for the projection (str).
Returns:
An GnomonicKarney or Gnomonic instance.
Raises:
  • AzimuthalError - Invalid lat0, lon0 or sperical datum.
  • TypeError - Invalid datum.

halfs2 (str2)

 

Split a string in 2 halfs.

Arguments:
  • str2 - String to split (str).
Returns:
2-Tuple (_1st, _2nd) half (str).
Raises:
  • ValueError - Zero or odd len(str2).

hausdorff_ (model, target, both=False, early=True, seed=None, units='', distance=None, point=<function _point at 0x7f8035e44e50>)

 

Compute the directed or symmetric Hausdorff distance between 2 sets of points with or without early breaking and random sampling.

Arguments:
  • model - First set of points (LatLon[], Numpy2LatLon[], Tuple2LatLon[] or other[]).
  • target - Second set of points (LatLon[], Numpy2LatLon[], Tuple2LatLon[] or other[]).
  • both - Return the directed (forward only) or the symmetric (combined forward and reverse) Hausdorff distance (bool).
  • early - Enable or disable early breaking (bool).
  • seed - Random sampling seed (any) or None, 0 or False for no random sampling.
  • units - Optional, the distance units (Unit or str).
  • distance - Callable returning the distance between a model and target point (signature (point1, point2)).
  • point - Callable returning the model or target point suitable for distance (signature (point)).
Returns:
A Hausdorff6Tuple(hd, i, j, mn, md, units).
Raises:
  • HausdorffError - Insufficient number of model or target points.
  • TypeError - If distance or point is not callable.

haversine (lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)

 

Compute the distance between two (spherical) points using the Haversine formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • radius - Mean earth radius (meter).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as radius).
Raises:
  • TypeError - Invalid radius.

See Also: Distance between two (spherical) points, functions cosineLaw, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, flatLocal/hubeny, flatPolar, thomas and vincentys and methods Ellipsoid.distance2, LatLon.distanceTo* and LatLon.equirectangularTo.

Note: See note at function vincentys_.

haversine_ (phi2, phi1, lam21)

 

Compute the angular distance between two (spherical) points using the Haversine formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
Returns:
Angular distance (radians).

heightOf (angle, distance, radius=6371008.77141)

 

Determine the height above the (spherical) earth after traveling along a straight line at a given tilt.

Arguments:
  • angle - Tilt angle above horizontal (degrees).
  • distance - Distance along the line (meter or same units as radius).
  • radius - Optional mean earth radius (meter).
Returns:
Height (meter, same units as distance and radius).
Raises:
  • ValueError - Invalid angle, distance or radius.

horizon (height, radius=6371008.77141, refraction=False)

 

Determine the distance to the horizon from a given altitude above the (spherical) earth.

Arguments:
  • height - Altitude (meter or same units as radius).
  • radius - Optional mean earth radius (meter).
  • refraction - Consider atmospheric refraction (bool).
Returns:
Distance (meter, same units as height and radius).
Raises:
  • ValueError - Invalid height or radius.

See Also: Distance to horizon.

hstr (height, prec=2, fmt='%+.*f', ints=False, m='')

 

Return a string for the height value.

Arguments:
  • height - Height value (float).
  • prec - The float precision, number of decimal digits (0..9). Trailing zero decimals are stripped if prec is positive, but kept for negative prec values.
  • fmt - Optional, float format (str).
  • ints - Optionally, remove the decimal dot for int values (bool).
  • m - Optional unit of the height (str).

hubeny (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)

 

Compute the distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as the datum's ellipsoid axes).
Raises:
  • TypeError - Invalid datum.

Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude.

See Also: Functions flatLocal_/hubeny_, cosineLaw, flatPolar, cosineAndoyerLambert, cosineForsytheAndoyerLambert, equirectangular, euclidean, haversine, thomas, vincentys, method Ellipsoid.distance2 and local, flat earth approximation.

hubeny_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)

 

Compute the angular distance between two (ellipsoidal) points using the ellipsoidal Earth to plane projection aka Hubeny formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
Returns:
Angular distance (radians).
Raises:
  • TypeError - Invalid datum.

Note: The meridional and prime_vertical radii of curvature are taken and scaled at the mean of both latitude.

See Also: Functions flatLocal/hubeny, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, flatPolar_, equirectangular_, euclidean_, haversine_, thomas_ and vincentys_ and local, flat earth approximation.

hypot1 (x)

 

Compute the norm sqrt(1 + x**2).

Arguments:
  • x - Argument (scalar).
Returns:
Norm (float).

hypot2 (x, y)

 

Compute the squared norm x**2 + y**2.

Arguments:
  • x - Argument (scalar).
  • y - Argument (scalar).
Returns:
x**2 + y**2 (float).

hypot2_ (*xs)

 

Compute the squared norm sum(x**2 for x in xs).

Arguments:
  • xs - X arguments, positional (scalar[]).
Returns:
Squared norm (float).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ValueError - Invalid or no xs value.

See Also: Function hypot_.

hypot_ (*xs)

 

Compute the norm sqrt(sum(x**2 for x in xs)).

Arguments:
  • xs - X arguments, positional (scalar[]).
Returns:
Norm (float).
Raises:
  • OverflowError - Partial 2sum overflow.
  • ValueError - Invalid or no xs value.

See Also: Similar to Python 3.8+ math.hypot, but handling of exceptions, nan and infinite values is different.

Note: The Python 3.8+ math.dist Euclidian distance between 2 n-dimensional points p1 and p2 can be computed as hypot_(*((c1 - c2) for c1, c2 in zip(p1, p2))), provided p1 and p2 have the same, non-zero length n.

instr (inst, *args, **kwds)

 

Return the string representation of an instantiation.

Arguments:
  • inst - The instance (any type).
  • args - Optional positional arguments.
  • kwds - Optional keyword arguments.
Returns:
Representation (str).

intersections2 (center1, radius1, center2, radius2, sphere=True, Vector=None, **Vector_kwds)

 

Compute the intersection of two spheres or circles, each defined by a center point and a radius.

Arguments:
  • center1 - Center of the first sphere or circle (Vector3d, Vector3Tuple or Vector4Tuple).
  • radius1 - Radius of the first sphere or circle (same units as the center1 coordinates).
  • center2 - Center of the second sphere or circle (Vector3d, Vector3Tuple or Vector4Tuple).
  • radius2 - Radius of the second sphere or circle (same units as the center1 and center2 coordinates).
  • sphere - If True compute the center and radius of the intersection of two spheres. If False, ignore the z-component and compute the intersection of two circles (bool).
  • Vector - Class to return intersections (Vector3d or Vector3Tuple) or None for Vector3d.
  • Vector_kwds - Optional, additional Vector keyword arguments, ignored if Vector=None.
Returns:
If sphere is True, a 2-Tuple of the center and radius of the intersection of the spheres. The radius is 0.0 for abutting spheres.

If sphere is False, a 2-tuple of the intersection points of two circles. For abutting circles, both points are the same Vector instance.

Raises:

See Also: Sphere-Sphere and circle-circle intersections.

isNumpy2 (obj)

 

Check for an Numpy2LatLon points wrapper.

Arguments:
  • obj - The object (any type).
Returns:
True if obj is an Numpy2LatLon instance, False otherwise.

isPoints2 (obj)

 

Check for an LatLon2psxy points wrapper.

Arguments:
  • obj - The object (any type).
Returns:
True if obj is an LatLon2psxy instance, False otherwise.

isTuple2 (obj)

 

Check for an Tuple2LatLon points wrapper.

Arguments:
  • obj - The object (any).
Returns:
True if obj is an Tuple2LatLon instance, False otherwise.

isantipode (lat1, lon1, lat2, lon2, eps=2.22044604925e-16)

 

Check whether two points are antipodal, on diametrically opposite sides of the earth.

Arguments:
  • lat1 - Latitude of one point (degrees).
  • lon1 - Longitude of one point (degrees).
  • lat2 - Latitude of the other point (degrees).
  • lon2 - Longitude of the other point (degrees).
  • eps - Tolerance for near-equality (degrees).
Returns:
True if points are antipodal within the eps tolerance, False otherwise.

See Also: Geosphere.

isantipode_ (phi1, lam1, phi2, lam2, eps=2.22044604925e-16)

 

Check whether two points are antipodal, on diametrically opposite sides of the earth.

Arguments:
  • phi1 - Latitude of one point (radians).
  • lam1 - Longitude of one point (radians).
  • phi2 - Latitude of the other point (radians).
  • lam2 - Longitude of the other point (radians).
  • eps - Tolerance for near-equality (radians).
Returns:
True if points are antipodal within the eps tolerance, False otherwise.

See Also: Geosphere.

isclass (obj)

 

Return True if obj is a class.

See Also: Python's inspect.isclass.

isclockwise (points, adjust=False, wrap=True)

 

Determine the direction of a path or polygon.

Arguments:
  • points - The path or polygon points (LatLon[]).
  • adjust - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (bool).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
Returns:
True if points are clockwise, False otherwise.
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.
  • ValueError - The points enclose a pole or zero area.

Example:

>>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1)
>>> isclockwise(f)  # False
>>> isclockwise(reversed(f))  # True

iscolinearWith (point, point1, point2, eps=2.22044604925e-16)

 

Check whether a point is colinear with two other points.

Arguments:
  • point - The point (Vector3d, Vector3Tuple or Vector4Tuple).
  • point1 - Another point (Vector3d, Vector3Tuple or Vector4Tuple).
  • point2 - Another point (Vector3d, Vector3Tuple or Vector4Tuple).
  • eps - Tolerance (scalar), same units as x, y and z.
Returns:
True if colinear, False otherwise.
Raises:
  • TypeError - Invalid point, point1 or point2.

See Also: Function nearestOn.

isconvex (points, adjust=False, wrap=True)

 

Determine whether a polygon is convex.

Arguments:
  • points - The polygon points (LatLon[]).
  • adjust - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (bool).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
Returns:
True if points are convex, False otherwise.
Raises:
  • CrossError - Some points are colinear.
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.

Example:

>>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
>>> isconvex(t)  # True
>>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
>>> isconvex(f)  # False

isconvex_ (points, adjust=False, wrap=True)

 

Determine whether a polygon is convex and clockwise.

Arguments:
  • points - The polygon points (LatLon[]).
  • adjust - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (bool).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
Returns:
+1 if points are convex clockwise, -1 for convex counter-clockwise points, 0 otherwise.
Raises:
  • CrossError - Some points are colinear.
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.

Example:

>>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
>>> isconvex_(t)  # +1
>>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
>>> isconvex_(f)  # 0

isenclosedBy (point, points, wrap=False)

 

Determine whether a point is enclosed by a polygon.

Arguments:
  • point - The point (LatLon or 2-tuple (lat, lon)).
  • points - The polygon points (LatLon[]).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
Returns:
True if point is inside the polygon, False otherwise.
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.
  • ValueError - Invalid point, lat- or longitude.

isfinite (obj)

 

Check for Inf and NaN values.

Arguments:
  • obj - Value (scalar).
Returns:
False if obj is INF or NAN, True otherwise.
Raises:
  • TypeError - Non-scalar obj.

isint (obj, both=False)

 

Check for int type or an integer float value.

Arguments:
  • obj - The object (any type).
  • both - Optionally, check float type and value (bool).
Returns:
True if obj is int or an integer float, False otherwise.

isneg0 (obj)

 

Check for NEG0, negative 0.0.

Arguments:
  • obj - Value (scalar).
Returns:
True if obj is NEG0 or -0.0, False otherwise.

ispolar (points, wrap=False)

 

Check whether a polygon encloses a pole.

Arguments:
  • points - The polygon points (LatLon[]).
  • wrap - Wrap and unroll longitudes (bool).
Returns:
True if the polygon encloses a pole, False otherwise.
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon or don't have bearingTo2, initialBearingTo and finalBearingTo methods.

isscalar (obj)

 

Check for scalar types.

Arguments:
  • obj - The object (any type).
Returns:
True if obj is scalar, False otherwise.

issequence (obj, *excluded)

 

Check for sequence types.

Arguments:
  • obj - The object (any type).
  • excluded - Optional exclusions (type).
Returns:
True if obj is a sequence, False otherwise.

Note: Excluding tuple implies excluding namedtuple.

isstr (obj)

 

Check for string types.

Arguments:
  • obj - The object (any type).
Returns:
True if obj is str, False otherwise.

issubclassof (Sub, Super)

 

Check whether a class is a sub-class of a super class.

Arguments:
  • Sub - The sub-class (class).
  • Super - The super class (class).
Returns:
True if Sub is a sub-class of Super, False otherwise (bool).

iterNumpy2 (obj)

 

Iterate over Numpy2 wrappers or other sequences exceeding the threshold.

Arguments:
  • obj - Points array, list, sequence, set, etc. (any).
Returns:
True do, False don't iterate.

iterNumpy2over (n=None)

 

Get or set the iterNumpy2 threshold.

Arguments:
  • n - Optional, new threshold (int).
Returns:
Previous threshold (int).
Raises:
  • ValueError - Invalid n.

joined (*words, **sep)

 

Joined words by separator sep=NN.

Arguments:
  • words - One, two or more words (strs).
  • sep - Separator C({str}), default NN.
Returns:
Joined words C({str}).

joined_ (*words, **sep)

 

Joined words by separator sep=" ".

Arguments:
  • words - One, two or more words (strs).
  • sep - Separator C({str}), default " ".
Returns:
Joined words C({str}).

latDMS (deg, form='dms', prec=2, sep='')

 

Convert latitude to a string, optionally suffixed with N or S.

Arguments:
Returns:
Degrees in the specified form (str).

JS name: toLat.

latlon2n_xyz (lat, lon)

 

Convert lat-, longitude to n-vector (normal to the earth's surface) X, Y and Z components.

Arguments:
  • lat - Latitude (degrees).
  • lon - Longitude (degrees).
Returns:
A Vector3Tuple(x, y, z).

See Also: Function philam2n_xyz.

Note: These are n-vector x, y and z components, NOT geocentric ECEF x, y and z coordinates!

latlonDMS (lls, form='dms', prec=None, sep=None)

 

Convert one or more LatLon instances to strings.

Arguments:
Returns:
A str or tuple of sep is None or NN.

len2 (items)

 

Make built-in function len work for generators, iterators, etc. since those can only be started exactly once.

Arguments:
  • items - Generator, iterator, list, range, tuple, etc.
Returns:
2-Tuple (n, items) of the number of items (int) and the items (list or tuple).

limiterrors (raiser=None)

 

Get/set the throwing of LimitErrors.

Arguments:
  • raiser - Choose True to raise or False to ignore LimitError exceptions. Use None to leave the setting unchanged.
Returns:
Previous setting (bool).

lonDMS (deg, form='dms', prec=2, sep='')

 

Convert longitude to a string, optionally suffixed with E or W.

Arguments:
Returns:
Degrees in the specified form (str).

JS name: toLon.

luneOf (lon1, lon2, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds)

 

Generate an ellipsoidal or spherical lune-shaped path or polygon.

Arguments:
  • lon1 - Left longitude (degrees90).
  • lon2 - Right longitude (degrees90).
  • closed - Optionally, close the path (bool).
  • LatLon - Class to use (LatLon_).
  • LatLon_kwds - Optional, additional LatLon keyword arguments.
Returns:
Yield 4 or 5 LatLon instances outlining the lune shape.

m2NM (meter)

 

Convert meter to nautical miles (NM).

Arguments:
  • meter - Value in meter (scalar).
Returns:
Value in NM (float).
Raises:
  • ValueError - Invalid meter.

m2SM (meter)

 

Convert meter to statute miles (SM).

Arguments:
  • meter - Value in meter (scalar).
Returns:
Value in SM (float).
Raises:
  • ValueError - Invalid meter.

m2degrees (meter, radius=6371008.77141, lat=0)

 

Convert distance to angle along equator or along a parallel at an other latitude.

Arguments:
  • meter - Distance (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • lat - Parallel latitude (degrees90, str).
Returns:
Angle (degrees).
Raises:
  • RangeError - Latitude lat outside valid range and rangerrors set to True.
  • ValueError - Invalid meter, radius or lat.

See Also: Function degrees2m.

m2ft (meter, usurvey=False)

 

Convert meter to International or US Survey feet (ft).

Arguments:
  • meter - Value in meter (scalar).
  • usurvery - Convert to US Survey feet (bool), International feet otherwise.
Returns:
Value in feet (float).
Raises:
  • ValueError - Invalid meter.

m2km (meter)

 

Convert meter to kilo meter (km).

Arguments:
  • meter - Value in meter (scalar).
Returns:
Value in km (float).
Raises:
  • ValueError - Invalid meter.

map1 (func, *xs)

 

Apply each argument to a single-argument function and return a tuple of results.

Arguments:
  • 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.

Arguments:
  • func - Function to apply (callable).
  • xs - Arguments to apply (list, tuple, ...).
Returns:
Function results (tuple).

modulename (clas, prefixed=None)

 

Return the class name optionally prefixed with the module name.

Arguments:
  • clas - The class (any class).
  • prefixed - Include the module name (bool), see function classnaming.
Returns:
The class's [module.]class name (str).

n2e2 (n)

 

Return e2, the eccentricity squared for a given 3rd flattening.

Arguments:
  • n - The 3rd flattening (-1 < scalar < 1).
Returns:
The (1st) eccentricity squared (float or -INF), 4 * n / (1 + n)**2.

Note: The result is negative for prolate or 0 for near-spherical ellipsoids.

See Also: Flattening.

n2f (n)

 

Return f, the flattening for a given 3rd flattening.

Arguments:
  • n - The 3rd flattening (-1 <= scalar <= 1).
Returns:
The flattening (float or -INF), 2 * n / (1 + n).

n_xyz2latlon (x, y, z)

 

Convert n-vector components to lat- and longitude in degrees.

Arguments:
  • x - X component (scalar).
  • y - Y component (scalar).
  • z - Z component (scalar).
Returns:
A LatLon2Tuple(lat, lon).

See Also: Function n_xyz2philam.

n_xyz2philam (x, y, z)

 

Convert n-vector components to lat- and longitude in radians.

Arguments:
  • x - X component (scalar).
  • y - Y component (scalar).
  • z - Z component (scalar).
Returns:
A PhiLam2Tuple(phi, lam).

See Also: Function n_xyz2latlon.

nameof (inst)

 

Get the name of an instance.

Arguments:
  • inst - The object (any type).
Returns:
The instance' name (str) or "".

nearestOn3 (point, points, closed=False, wrap=False, **options)

 

DEPRECATED, use function nearestOn5.

Returns:
3-Tuple (lat, lon, distance)

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, LatLon=None, **options)

 

Locate the point on a path or polygon closest to an other point.

If the given point is within the extent of a polygon edge, the closest point is on that edge, otherwise the closest point is the nearest of that edge's end points.

Distances are approximated by function equirectangular_, subject to the supplied options.

Arguments:
  • point - The other, reference point (LatLon).
  • points - The path or polygon points (LatLon[]).
  • closed - Optionally, close the path or polygon (bool).
  • wrap - Wrap and unroll180 longitudes and longitudinal delta (bool) in function equirectangular_.
  • LatLon - Optional class to return the closest point (LatLon) or None.
  • options - Other keyword arguments for function equirectangular_.
Returns:
A NearestOn3Tuple(closest, distance, angle) with the {closest} point (LatLon) or if LatLon is None a NearestOn5Tuple(lat, lon, distance, angle, height). The distance is the equirectangular_ distance between the closest and reference point in degrees. The angle from the reference point to the closest is in compass degrees360, like function compassAngle.
Raises:

See Also: Function degrees2m to convert degrees to meter.

normDMS (strDMS, norm='')

 

Normalize all degree ˚, minute ' and second " symbols in a string to the default symbols %s, %s and %s.

Arguments:
  • strDMS - DMS (str).
  • norm - Optional replacement symbol, default symbol otherwise (str).
Returns:
Normalized DMS (str).

notImplemented (inst, name, *args, **kwds)

 

Raise a NotImplementedError for a missing method or property.

Arguments:
  • inst - Instance (any).
  • name - Method, property or name (str or callable).
  • args - Method or property positional arguments (any types).
  • kwds - Method or property keyword arguments (any types).

notOverloaded (inst, name, *args, **kwds)

 

Raise an AssertionError for a method or property not overloaded.

Arguments:
  • inst - Instance (any).
  • name - Method, property or name (str or callable).
  • args - Method or property positional arguments (any types).
  • kwds - Method or property keyword arguments (any types).

pairs (items, prec=6, fmt='F', ints=False, sep='=')

 

Convert items to name=value strings, with floats handled like fstr.

Arguments:
  • items - Name-value pairs (dict or 2-{tuple}s of any types).
  • prec - The float precision, number of decimal digits (0..9). Trailing zero decimals are stripped if prec is positive, but kept for negative prec values.
  • fmt - Optional, float format (str).
  • ints - Optionally, remove the decimal dot fir int values (bool).
  • sep - Separator joining names and values (str).
Returns:
A tuple(sep.join(t) for t in zip(names, reprs(values,...))) of strs.

parse3d (str3d, sep=',', name='', Vector=<class 'pygeodesy.vector3d.Vector3d'>, **Vector_kwds)

 

Parse an "x, y, z" string.

Arguments:
  • str3d - X, y and z values (str).
  • sep - Optional separator (str).
  • name - Optional instance name (str).
  • Vector - Optional class (Vector3d).
  • Vector_kwds - Optional Vector keyword arguments, ignored if Vector=None.
Returns:
New Vector or if Vector is None, a Vector3Tuple(x, y, z).
Raises:

parse3llh (strllh, height=0, sep=',', clipLat=90, clipLon=180)

 

Parse a string "lat lon [h]" representing lat-, longitude in degrees and optional height in meter.

The lat- and longitude value must be separated by a separator character. If height is present it must follow, separated by another separator.

The lat- and longitude values may be swapped, provided at least one ends with the proper compass point.

Arguments:
  • strllh - Latitude, longitude[, height] (str, ...).
  • height - Optional, default height (meter) or None.
  • sep - Optional separator (str).
  • clipLat - Keep latitude in -clipLat..+clipLat (degrees).
  • clipLon - Keep longitude in -clipLon..+clipLon range (degrees).
Returns:
A LatLon3Tuple(lat, lon, height) in degrees, degrees and float.
Raises:
  • RangeError - Lat- or longitude value of strllh outside valid range and rangerrors set to True.
  • ValueError - Invalid strllh or height.

Note: See the Notes at function parseDMS.

See Also: Functions parseDDDMMSS, parseDMS and parseDMS2.

Example:

>>> parse3llh('000°00′05.31″W, 51° 28′ 40.12″ N')
(51.4778°N, 000.0015°W, 0)

parseDDDMMSS (strDDDMMSS, suffix='NSEW', sep='', clip=0)

 

Parse a lat- or longitude represention form [D]DDMMSS in degrees.

Arguments:
  • strDDDMMSS - Degrees in any of several forms (str) and types (float, int, other).
  • suffix - Optional, valid compass points (str, tuple).
  • sep - Optional separator between "[D]DD", "MM" and "SS" ('').
  • clip - Optionally, limit value to -clip..+clip (degrees).
Returns:
Degrees (float).
Raises:
  • ParseError - Invalid strDDDMMSS or clip or the strDDDMMSS form is incompatible with the suffixed or suffix compass point.
  • RangeError - Value of strDDDMMSS outside the valid range and rangerrors set to True.
Notes:
  • Type str values "[D]DD", "[D]DDMM" and "[D]DDMMSS" for strDDDMMSS are parsed properly only if either unsigned and suffixed with a valid, compatible, cardinal compassPoint or if unsigned or signed, unsuffixed and with keyword argument suffix set to 'NS', 'EW' or a compatible compassPoint.
  • Unlike function parseDMS, type float, int and other non-str strDDDMMSS values are interpreted form [D]DDMMSS. For example, int(1230) is returned as 12.5 and not 1230.0 degrees. However, int(345) is considered form "DDD" 345 and not "DDMM" 0345, unless suffix specifies compass point 'NS'.

See Also: Functions parseDMS, parseDMS2 and parse3llh.

parseDMS (strDMS, suffix='NSEW', sep='', clip=0)

 

Parse a lat- or longitude representation "lat, lon" in degrees.

This is very flexible on formats, allowing signed decimal degrees, degrees and minutes or degrees minutes and seconds optionally suffixed by a cardinal compass point.

A variety of symbols, separators and suffixes are accepted, for example "3°37′09″W". Minutes and seconds may be omitted.

Arguments:
  • strDMS - Degrees in any of several forms (str) and types (float, int, other).
  • suffix - Optional, valid compass points (str, tuple).
  • sep - Optional separator between deg°, min′ and sec″ ("''").
  • clip - Optionally, limit value to -clip..+clip (degrees).
Returns:
Degrees (float).
Raises:

Note: Inlike function parseDDDMMSS, type float, int and other non-str strDMS values are considered as decimal degrees. For example, int(1230) is returned as 1230.0 and not as 12.5 degrees and float(345) as 345.0 and not as 3.75 degrees!

See Also: Functions parseDDDMMSS, parseDMS2 and parse3llh.

parseDMS2 (strLat, strLon, sep='', clipLat=90, clipLon=180)

 

Parse a lat- and a longitude representions in degrees.

Arguments:
  • strLat - Latitude in any of several forms (str or degrees).
  • strLon - Longitude in any of several forms (str or degrees).
  • sep - Optional separator between deg°, min′ and sec″ ('').
  • clipLat - Keep latitude in -clipLat..+clipLat range (degrees).
  • clipLon - Keep longitude in -clipLon..+clipLon range (degrees).
Returns:
A LatLon2Tuple(lat, lon) in degrees.
Raises:

Note: See the Notes at function parseDMS.

See Also: Functions parseDDDMMSS, parseDMS and parse3llh.

parseETM5 (strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, name='')

 

Parse a string representing a UTM coordinate, consisting of "zone[band] hemisphere easting northing".

Arguments:
  • strUTM - A UTM coordinate (str).
  • datum - Optional datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • Etm - Optional class to return the UTM coordinate (Etm) or None.
  • falsed - Both easting and northing are falsed (bool).
  • name - Optional Etm name (str).
Returns:
The UTM coordinate (Etm) or if Etm is None, a UtmUps5Tuple(zone, hemipole, easting, northing, band). The hemipole is the hemisphere 'N'|'S'.
Raises:
  • ETMError - Invalid strUTM.
  • TypeError - Invalid datum.

Example:

>>> u = parseETM5('31 N 448251 5411932')
>>> u.toStr2()  # [Z:31, H:N, E:448251, N:5411932]
>>> u = parseETM5('31 N 448251.8 5411932.7')
>>> u.toStr()  # 31 N 448252 5411933

parseMGRS (strMGRS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name='')

 

Parse a string representing a MGRS grid reference, consisting of "zoneBand, grid, easting, northing".

Arguments:
  • strMGRS - MGRS grid reference (str).
  • datum - Optional datum to use (Datum).
  • Mgrs - Optional class to return the MGRS grid reference (Mgrs) or None.
  • name - Optional Mgrs name (str).
Returns:
The MGRS grid reference (Mgrs) or an Mgrs4Tuple(zone, digraph, easting, northing) if Mgrs is None.
Raises:

Example:

>>> m = parseMGRS('31U DQ 48251 11932')
>>> str(m)  # 31U DQ 48251 11932
>>> m = parseMGRS('31UDQ4825111932')
>>> repr(m)  # [Z:31U, G:DQ, E:48251, N:11932]
>>> m = mgrs.parseMGRS('42SXD0970538646')
>>> str(m)  # 42S XD 09705 38646
>>> m = mgrs.parseMGRS('42SXD9738')  # Km
>>> str(m)  # 42S XD 97000 38000

parseOSGR (strOSGR, Osgr=<class 'pygeodesy.osgr.Osgr'>, name='')

 

Parse a string representing an OSGR grid reference, consisting of "[grid] easting northing".

Accepts standard OS Grid References like 'SU 387 148', with or without whitespace separators, from 2- up to 10-digit references (1 m × 1 m square), or fully numeric, comma-separated references in meters, for example '438700,114800'.

Arguments:
  • strOSGR - An OSGR coordinate (str).
  • Osgr - Optional class to return the OSGR coordinate (Osgr) or None.
  • name - Optional Osgr name (str).
Returns:
The OSGR coordinate (Osgr) or an EasNor2Tuple(easting, northing) if Osgr is None.
Raises:

Example:

>>> g = parseOSGR('TG 51409 13177')
>>> str(g)  # TG 51409 13177
>>> g = parseOSGR('TG5140913177')
>>> str(g)  # TG 51409 13177
>>> g = parseOSGR('TG51409 13177')
>>> str(g)  # TG 51409 13177
>>> g = parseOSGR('651409,313177')
>>> str(g)  # TG 51409 13177
>>> g.toStr(prec=0)  # 651409,313177

parseRad (strRad, suffix='NSEW', clip=0)

 

Parse a string representing angle in radians.

Arguments:
  • strRad - Degrees in any of several forms (str or radians).
  • suffix - Optional, valid compass points (str, tuple).
  • clip - Optionally, limit value to -clip..+clip (radians).
Returns:
Radians (float).
Raises:

parseUPS5 (strUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Ups=<class 'pygeodesy.ups.Ups'>, falsed=True, name='')

 

Parse a string representing a UPS coordinate, consisting of "[zone][band] pole easting northing" where zone is pseudo zone "00"|"0"|"" and band is 'A'|'B'|'Y'|'Z'|''.

Arguments:
  • strUPS - A UPS coordinate (str).
  • datum - Optional datum to use (Datum).
  • Ups - Optional class to return the UPS coordinate (Ups) or None.
  • falsed - Both easting and northing are falsed (bool).
  • name - Optional Ups name (str).
Returns:
The UPS coordinate (Ups) or a UtmUps5Tuple(zone, hemipole, easting, northing, band) if Ups is None. The hemipole is the 'N'|'S' pole, the UPS projection top/center.
Raises:

parseUTM (strUTM, datum=_R_M, Utm=_R_M, name='')

 

DEPRECATED, use function parseUTM5.

Returns:
The UTM coordinate (Utm) or 4-tuple (zone, hemisphere, easting, northing) if Utm is None.

parseUTM5 (strUTM, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, name='')

 

Parse a string representing a UTM coordinate, consisting of "zone[band] hemisphere easting northing".

Arguments:
  • strUTM - A UTM coordinate (str).
  • datum - Optional datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • Utm - Optional class to return the UTM coordinate (Utm) or None.
  • falsed - Both easting and northing are falsed (bool).
  • name - Optional Utm name (str).
Returns:
The UTM coordinate (Utm) or if Utm is None, a UtmUps5Tuple(zone, hemipole, easting, northing, band). The hemipole is the 'N'|'S' hemisphere.
Raises:
  • UTMError - Invalid strUTM.
  • TypeError - Invalid datum.

Example:

>>> u = parseUTM5('31 N 448251 5411932')
>>> u.toStr2()  # [Z:31, H:N, E:448251, N:5411932]
>>> u = parseUTM5('31 N 448251.8 5411932.7')
>>> u.toStr()  # 31 N 448252 5411933

parseUTMUPS5 (strUTMUPS, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, name='')

 

Parse a string representing a UTM or UPS coordinate, consisting of "zone[band] hemisphere/pole easting northing".

Arguments:
  • strUTMUPS - A UTM or UPS coordinate (str).
  • datum - Optional datum to use (Datum).
  • Utm - Optional class to return the UTM coordinate (Utm) or None.
  • Ups - Optional class to return the UPS coordinate (Ups) or None.
  • name - Optional instance name (str).
Returns:
The UTM or UPS instance (Utm or Ups) or a UtmUps5Tuple(zone, hemipole, easting, northing, band) if Utm respectively Ups or both are None. The hemipole is 'N'|'S', the UTM hemisphere or UPS pole, the UPS projection top/center.
Raises:

See Also: Functions parseUTM5 and parseUPS5.

parseWM (strWM, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name='')

 

Parse a string "e n [r]" representing a WM coordinate, consisting of easting, northing and an optional radius.

Arguments:
  • strWM - A WM coordinate (str).
  • radius - Optional earth radius (meter).
  • Wm - Optional class to return the WM coordinate (Wm) or None.
  • name - Optional name (str).
Returns:
The WM coordinate (Wm) or an EasNorRadius3Tuple(easting, northing, radius) if Wm is None.
Raises:

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.

Arguments:
  • points - The path or polygon points (LatLon[]).
  • closed - Optionally, close the path or polygon (bool).
  • adjust - Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (bool).
  • radius - Mean earth radius (meter).
  • wrap - Wrap lat-, wrap and unroll longitudes (bool).
Returns:
Approximate perimeter (meter, same units as radius).
Raises:
  • PointsError - Insufficient number of points
  • TypeError - Some points are not LatLon.
  • ValueError - Invalid radius.

Note: This perimeter is based on the equirectangular_ distance approximation and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes.

See Also: sphericalTrigonometry.perimeterOf and ellipsoidalKarney.perimeterOf.

philam2n_xyz (phi, lam)

 

Convert lat-, longitude to n-vector (normal to the earth's surface) X, Y and Z components.

Arguments:
  • phi - Latitude (radians).
  • lam - Longitude (radians).
Returns:
A Vector3Tuple(x, y, z).

See Also: Function latlon2n_xyz.

Note: These are n-vector x, y and z components, NOT geocentric ECEF x, y and z coordinates!

points2 (points, closed=True, base=None, Error=<class 'pygeodesy.errors.PointsError'>)

 

Check a path or polygon represented by points.

Arguments:
  • points - The path or polygon points (LatLon[])
  • closed - Optionally, consider the polygon closed, ignoring any duplicate or closing final points (bool).
  • base - Optionally, check all points against this base class, if None don't check.
  • Error - Exception to raise (ValueError).
Returns:
A Points2Tuple(number, points) with the number of points and the points list or tuple.
Raises:
  • PointsError - Insufficient number of points.
  • TypeError - Some points are not base compatible.

precision (form, prec=None)

 

Set the default precison for a given F_ form.

Arguments:
  • form - F_D, F_DM, F_DMS, F_DEG, F_MIN, F_SEC, F__E, F__F, F__G or F_RAD (str).
  • prec - Optional number of decimal digits (0..9 or None for default). Trailing zero decimals are stripped for prec values of 1 and above, but kept for negative prec.
Returns:
Previous precision (int).
Raises:
  • ValueError - Invalid form or prec or prec outside valid range.

property_doc_ (doc)

 

Decorator for a property with documentation.

Arguments:
  • doc - The property documentation (str).

Example:

>>> @property_doc_("documentation text.")
>>> def name(self):
>>>     ...
>>>
>>> @name.setter
>>> def name(self, value):
>>>     ...

quadOf (lat1, lon1, lat2, lon2, closed=False, LatLon=<class 'pygeodesy.points.LatLon_'>, **LatLon_kwds)

 

Generate a quadrilateral path or polygon from two points.

Arguments:
  • lat1 - Lower latitude (degrees90).
  • lon1 - Left longitude (degrees180).
  • lat2 - Upper latitude (degrees90).
  • lon2 - Right longitude (degrees180).
  • closed - Optionally, close the path (bool).
  • LatLon - Class to use (LatLon_).
  • LatLon_kwds - Optional, additional LatLon keyword arguments.
Returns:
Yield 4 or 5 LatLon instances outlining the quadrilateral.

radiansPI (deg)

 

Convert and wrap degrees to radians [-PI..+PI].

Arguments:
  • deg - Angle (degrees).
Returns:
Radians, wrapped (radiansPI)

radiansPI2 (deg)

 

Convert and wrap degrees to radians [0..+2PI).

Arguments:
  • deg - Angle (degrees).
Returns:
Radians, wrapped (radiansPI2)

radiansPI_2 (deg)

 

Convert and wrap degrees to radians [-3PI/2..+PI/2].

Arguments:
  • deg - Angle (degrees).
Returns:
Radians, wrapped (radiansPI_2)

radical2 (distance, radius1, radius2)

 

Compute the radical ratio and radical line of two intersecting circles.

The radical line is perpendicular to the axis thru the centers of the circles at (0, 0) and (distance, 0).

Arguments:
  • distance - Distance between the circle centers (scalar).
  • radius1 - Radius of the first circle (scalar).
  • radius2 - Radius of the second circle (scalar).
Returns:
A Radical2Tuple(ratio, xline) where 0.0 <= ratio <= 1.0 and xline is along the distance.
Raises:

randomrangenerator (seed)

 

Return a seeded random range function generator.

Arguments:
  • seed - Initial, internal Random state (hashable or None).
Returns:
A function to generate random ranges.

Note: Random seed=None seeds from the current time or from a platform-specific randomness source, if available.

Example:

>>> rrange = randomrangenerator('R')
>>> for r in rrange(n):
>>>    ...  # r is random in 0..n-1

rangerrors (raiser=None)

 

Get/set the throwing of RangeErrors.

Arguments:
  • raiser - Choose True to raise or False to ignore RangeError exceptions. Use None to leave the setting unchanged.
Returns:
Previous setting (bool).

reprs (objs, prec=6, fmt='F', ints=False)

 

Convert objects to repr strings, with floats handled like fstr.

Arguments:
  • objs - List, sequence, tuple, etc. (any types).
  • prec - The float precision, number of decimal digits (0..9). Trailing zero decimals are stripped if prec is positive, but kept for negative prec values.
  • fmt - Optional, float format (str).
  • ints - Optionally, remove the decimal dot fir int values (bool).
Returns:
A tuple(map(fstr|repr, objs)) of strs.

scalar (value, low=2.22044604925e-16, high=1.0, name='scalar', Error=<type 'exceptions.ValueError'>)

 

DEPRECATED, use class Number_ or Scalar_.

Arguments:
  • value - The value (scalar).
  • low - Optional lower bound (scalar).
  • high - Optional upper bound (scalar).
  • name - Optional name of value (str).
  • Error - Exception to raise (ValueError).
Returns:
New value (float or int for int low).
Raises:
  • Error - Invalid 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.

Arguments:
  • points - Path points (LatLon[]).
  • distance - Tolerance (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • indices - Optionally return the simplified point indices instead of the simplified points (bool).
  • options - Optional keyword arguments passed thru to function equirectangular_.
Returns:
Simplified points (LatLon[]).
Raises:
  • LimitError - Lat- and/or longitudinal delta exceeds the limit, see function equirectangular_.
  • ValueError - Tolerance distance or radius too small.

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.

Arguments:
  • points - Path points (LatLon[]).
  • distance - Tolerance (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • shortest - Optional, shortest or perpendicular distance (bool).
  • indices - Optionally return the simplified point indices instead of the simplified points (bool).
  • options - Optional keyword arguments passed thru to function equirectangular_.
Returns:
Simplified points (LatLon[]).
Raises:
  • LimitError - Lat- and/or longitudinal delta exceeds the limit, see function equirectangular_.
  • ValueError - Tolerance distance or radius too small.

simplifyRDPm (points, distance, radius=6371008.77141, shortest=False, indices=False, **options)

 

Modified Ramer-Douglas-Peucker (RDPm) simplification of a path of LatLon points.

Eliminates any points too close together or closer to an edge than the given distance tolerance.

This RDPm method stops at the first point farther than the given distance tolerance, significantly reducing the run time (but producing results different from the original RDP method).

Arguments:
  • points - Path points (LatLon[]).
  • distance - Tolerance (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • shortest - Optional, shortest or perpendicular distance (bool).
  • indices - Optionally return the simplified point indices instead of the simplified points (bool).
  • options - Optional keyword arguments passed thru to function equirectangular_.
Returns:
Simplified points (LatLon[]).
Raises:
  • LimitError - Lat- and/or longitudinal delta exceeds the limit, see function equirectangular_.
  • ValueError - Tolerance distance or radius too small.

simplifyRW (points, pipe, radius=6371008.77141, shortest=False, indices=False, **options)

 

Reumann-Witkam (RW) simplification of a path of LatLon points.

Eliminates any points too close together or within the given pipe tolerance along an edge.

Arguments:
  • points - Path points (LatLon[]).
  • pipe - Half pipe width (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • shortest - Optional, shortest or perpendicular distance (bool).
  • indices - Optionally return the simplified point indices instead of the simplified points (bool).
  • options - Optional keyword arguments passed thru to function equirectangular_.
Returns:
Simplified points (LatLon[]).
Raises:
  • LimitError - Lat- and/or longitudinal delta exceeds the limit, see function equirectangular_.
  • ValueError - Tolerance pipe or radius too small.

simplifyVW (points, area, radius=6371008.77141, attr=None, indices=False, **options)

 

Visvalingam-Whyatt (VW) simplification of a path of LatLon points.

Eliminates any points too close together or with a triangular area not exceeding the given area tolerance (squared).

This VW method exhaustively searches for the single point with the smallest triangular area, resulting in worst-case complexity O(n**2) where n is the number of points.

Arguments:
  • points - Path points (LatLon[]).
  • area - Tolerance (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • attr - Optional, points attribute 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 an attr is specified for Numpy2 points.
  • LimitError - Lat- and/or longitudinal delta exceeds the limit, see function equirectangular_.
  • ValueError - Tolerance area or radius too small.

simplifyVWm (points, area, radius=6371008.77141, attr=None, indices=False, **options)

 

Modified Visvalingam-Whyatt (VWm) simplification of a path of LatLon points.

Eliminates any points too close together or with a triangular area not exceeding the given area tolerance (squared).

This VWm method removes all points with a triangular area below the tolerance in each iteration, significantly reducing the run time (but producing results different from the original VW method).

Arguments:
  • points - Path points (LatLon[]).
  • area - Tolerance (meter, same units as radius).
  • radius - Mean earth radius (meter).
  • attr - Optional attribute to save the area value (str).
  • indices - Optionally return the simplified point indices instead of the simplified points (bool).
  • options - Optional keyword arguments passed thru to function equirectangular_.
Returns:
Simplified points (LatLon[]).
Raises:
  • AttributeError - If an attr is specified for Numpy2 points.
  • LimitError - Lat- and/or longitudinal delta exceeds the limit, see function equirectangular_.
  • ValueError - Tolerance area or radius too small.

sincos2 (*rad)

 

Return the sine and cosine of angle(s).

Arguments:
  • rad - One or more angles (radians).
Returns:
The sin(rad) and cos(rad) for each angle.

See Also: GeographicLib function sincosd and C++ sincosd.

sincos2d (*deg)

 

Return the sine and cosine of angle(s) in degrees.

Arguments:
  • deg - One or more angles (degrees).
Returns:
The sin(deg) and cos(deg) for each angle.

See Also: GeographicLib function sincosd and C++ sincosd.

splice (iterable, n=2, **fill)

 

Split an iterable into n slices.

Arguments:
  • iterable - Items to be spliced (list, tuple, ...).
  • n - Number of slices to generate (int).
  • fill - Optional fill value for missing items.
Returns:
A generator for each of n slices, iterable[i::n] for i=0..n.
Raises:
  • ValueError - Invalid n.

Note: Each generated slice is a tuple or a list, the latter only if the iterable is a list.

Example:

>>> from pygeodesy import splice
>>> a, b = splice(range(10))
>>> a, b
((0, 2, 4, 6, 8), (1, 3, 5, 7, 9))
>>> a, b, c = splice(range(10), n=3)
>>> a, b, c
((0, 3, 6, 9), (1, 4, 7), (2, 5, 8))
>>> a, b, c = splice(range(10), n=3, fill=-1)
>>> a, b, c
((0, 3, 6, 9), (1, 4, 7, -1), (2, 5, 8, -1))
>>> tuple(splice(list(range(9)), n=5))
([0, 5], [1, 6], [2, 7], [3, 8], [4])
>>> splice(range(9), n=1)
<generator object splice at 0x0...>

sqrt3 (x)

 

Compute the square root, cubed sqrt(x)**3 or sqrt(x**3).

Arguments:
  • x - Value (scalar).
Returns:
Cubed square root (float).
Raises:
  • ValueError - Negative x.

See Also: Functions cbrt and cbrt2.

strs (objs, prec=6, fmt='F', ints=False)

 

Convert objects to str strings, with floats handled like fstr.

Arguments:
  • objs - List, sequence, tuple, etc. (any types).
  • prec - The float precision, number of decimal digits (0..9). Trailing zero decimals are stripped if prec is positive, but kept for negative prec values.
  • fmt - Optional, float format (str).
  • ints - Optionally, remove the decimal dot fir int values (bool).
Returns:
A tuple(map(fstr|str, objs)) of strs.

tanPI_2_2 (rad)

 

Compute the tangent of half angle, 90 degrees rotated.

Arguments:
  • rad - Angle (radians).
Returns:
tan((rad + PI/2) / 2) (float).

tan_2 (rad)

 

Compute the tangent of half angle.

Arguments:
  • rad - Angle (radians).
Returns:
tan(rad / 2) (float).

thomas (lat1, lon1, lat2, lon2, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., wrap=False)

 

Compute the distance between two (ellipsoidal) points using Thomas' formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as the datum's ellipsoid axes).
Raises:
  • TypeError - Invalid datum.

thomas_ (phi2, phi1, lam21, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...)

 

Compute the angular distance between two (ellipsoidal) points using Thomas' formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
  • datum - Ellipsoidal datum to use (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
Returns:
Angular distance (radians).
Raises:
  • TypeError - Invalid datum.

toCss (latlon, cs0=None, height=None, Css=<class 'pygeodesy.css.Css'>, name='')

 

Convert an (ellipsoidal) geodetic point to a Cassini-Soldner location.

Arguments:
  • latlon - Ellipsoidal point (LatLon or LatLon4Tuple).
  • cs0 - Optional, the Cassini-Soldner projection to use (CassiniSoldner).
  • height - Optional height for the point, overriding the default height (meter).
  • Css - Optional class to return the location (Css) or None.
  • name - Optional Css name (str).
Returns:
The Cassini-Soldner location (Css) or an EasNor3Tuple(easting, northing, height) if Css is None.
Raises:
  • CSSError - Ellipsoidal mismatch of latlon and cs0.
  • ImportError - Package geographiclib missing.
  • TypeError - If latlon is not ellipsoidal.

toDMS (deg, form='dms', prec=2, sep='', ddd=2, neg='-', pos='')

 

Convert signed degrees to string, without suffix.

Arguments:
Returns:
Degrees in the specified form (str).

toEtm8 (latlon, lon=None, datum=None, Etm=<class 'pygeodesy.etm.Etm'>, falsed=True, name='', zone=None, **cmoff)

 

Convert a lat-/longitude point to an ETM coordinate.

Arguments:
  • latlon - Latitude (degrees) or an (ellipsoidal) geodetic LatLon point.
  • lon - Optional longitude (degrees) or None.
  • datum - Optional datum for this ETM coordinate, overriding latlon's datum (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • Etm - Optional class to return the ETM coordinate (Etm) or None.
  • falsed - False both easting and northing (bool).
  • name - Optional Utm name (str).
  • zone - Optional UTM zone to enforce (int or str).
  • cmoff - DEPRECATED, use falsed. Offset longitude from the zone's central meridian (bool).
Returns:
The ETM coordinate (Etm) or a UtmUps8Tuple(zone, hemipole, easting, northing, band, datum, convergence, scale) if Etm is None or not falsed. The hemipole is the 'N'|'S' hemisphere.
Raises:
  • EllipticError - No convergence.
  • ETMError - Invalid zone.
  • RangeError - If lat outside the valid UTM bands or if lat or lon outside the valid range and rangerrors set to True.
  • TypeError - Invalid datum or latlon not ellipsoidal.
  • ValueError - If lon value is missing or if latlon is invalid.

toLcc (latlon, conic=Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0..., height=None, Lcc=<class 'pygeodesy.lcc.Lcc'>, name='', **Lcc_kwds)

 

Convert an (ellipsoidal) geodetic point to a Lambert location.

Arguments:
  • latlon - Ellipsoidal point (LatLon).
  • conic - Optional Lambert projection to use (Conic).
  • height - Optional height for the point, overriding the default height (meter).
  • Lcc - Optional class to return the Lambert location (Lcc).
  • name - Optional Lcc name (str).
  • Lcc_kwds - Optional, additional Lcc keyword arguments, ignored if Lcc=None.
Returns:
The Lambert location (Lcc) or an EasNor3Tuple(easting, northing, height) if Lcc is None.
Raises:
  • TypeError - If latlon is not ellipsoidal.

toMgrs (utm, Mgrs=<class 'pygeodesy.mgrs.Mgrs'>, name='', **Mgrs_kwds)

 

Convert a UTM coordinate to an MGRS grid reference.

Arguments:
  • utm - A UTM coordinate (Utm or Etm).
  • Mgrs - Optional class to return the MGRS grid reference (Mgrs) or None.
  • name - Optional Mgrs name (str).
  • Mgrs_kwds - Optional, additional Mgrs keyword arguments, ignored if Mgrs=None.
Returns:
The MGRS grid reference (Mgrs) or an Mgrs6Tuple(zone, digraph, easting, northing, band, datum) if Mgrs is None.
Raises:

Example:

>>> u = Utm(31, 'N', 448251, 5411932)
>>> m = u.toMgrs()  # 31U DQ 48251 11932

toOsgr (latlon, lon=None, datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran..., Osgr=<class 'pygeodesy.osgr.Osgr'>, name='', **Osgr_kwds)

 

Convert a lat-/longitude point to an OSGR coordinate.

Arguments:
  • latlon - Latitude (degrees) or an (ellipsoidal) geodetic LatLon point.
  • lon - Optional longitude in degrees (scalar or None).
  • datum - Optional datum to convert lat, lon from (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • Osgr - Optional class to return the OSGR coordinate (Osgr) or None.
  • name - Optional Osgr name (str).
  • Osgr_kwds - Optional, additional Osgr keyword arguments, ignored if Osgr=None.
Returns:
The OSGR coordinate (Osgr) or an EasNor2Tuple(easting, northing) if Osgr is None.
Raises:
  • OSGRError - Invalid latlon or lon.
  • TypeError - Non-ellipsoidal latlon or invalid datum or conversion failed.

Example:

>>> p = LatLon(52.65798, 1.71605)
>>> r = toOsgr(p)  # TG 51409 13177
>>> # for conversion of (historical) OSGB36 lat-/longitude:
>>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36)

toUps8 (latlon, lon=None, datum=None, Ups=<class 'pygeodesy.ups.Ups'>, pole='', falsed=True, strict=True, name='')

 

Convert a lat-/longitude point to a UPS coordinate.

Arguments:
  • latlon - Latitude (degrees) or an (ellipsoidal) geodetic LatLon point.
  • lon - Optional longitude (degrees) or None if latlon is a LatLon.
  • datum - Optional datum for this UPS coordinate, overriding latlon's datum (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • Ups - Optional class to return the UPS coordinate (Ups) or None.
  • pole - Optional top/center of (stereographic) projection (str, 'N[orth]' or 'S[outh]').
  • falsed - False both easting and northing (bool).
  • strict - Restrict lat to UPS ranges (bool).
  • name - Optional Ups name (str).
Returns:
The UPS coordinate (Ups) or a UtmUps8Tuple(zone, hemipole, easting, northing, band, datum, convergence, scale) if Ups is None. The hemipole is the 'N'|'S' pole, the UPS projection top/center.
Raises:
  • RangeError - If strict and lat outside the valid UPS bands or if lat or lon outside the valid range and rangerrors set to True.
  • TypeError - If latlon is not ellipsoidal or datum invalid.
  • ValueError - If lon value is missing or if latlon is invalid.

See Also: Karney's C++ class UPS.

toUtm (latlon, lon=None, datum=None, Utm=_R_M, cmoff=True, name='')

 

DEPRECATED, use function toUtm8.

Returns:
The UTM coordinate (Utm) or a 6-tuple (zone, easting, northing, band, convergence, scale) if Utm is None or cmoff is False.

toUtm8 (latlon, lon=None, datum=None, Utm=<class 'pygeodesy.utm.Utm'>, falsed=True, name='', zone=None, **cmoff)

 

Convert a lat-/longitude point to a UTM coordinate.

Arguments:
  • latlon - Latitude (degrees) or an (ellipsoidal) geodetic LatLon point.
  • lon - Optional longitude (degrees) or None.
  • datum - Optional datum for this UTM coordinate, overriding latlon's datum (Datum, Ellipsoid, Ellipsoid2 or a_f2Tuple).
  • Utm - Optional class to return the UTM coordinate (Utm) or None.
  • falsed - False both easting and northing (bool).
  • name - Optional Utm name (str).
  • zone - Optional UTM zone to enforce (int or str).
  • cmoff - DEPRECATED, use falsed. Offset longitude from the zone's central meridian (bool).
Returns:
The UTM coordinate (Utm) or if Utm is None or not falsed, a UtmUps8Tuple(zone, hemipole, easting, northing, band, datum, convergence, scale). The hemipole is the 'N'|'S' hemisphere.
Raises:
  • RangeError - If lat outside the valid UTM bands or if lat or lon outside the valid range and rangerrors set to True.
  • TypeError - Invalid datum or latlon not ellipsoidal.
  • UTMError - Invalid zone.
  • ValueError - If lon value is missing or if latlon is invalid.

Note: Implements Karney’s method, using 8-th order Krüger series, giving results accurate to 5 nm (or better) for distances up to 3900 km from the central meridian.

Example:

>>> p = LatLon(48.8582, 2.2945)  # 31 N 448251.8 5411932.7
>>> u = toUtm(p)  # 31 N 448252 5411933
>>> p = LatLon(13.4125, 103.8667) # 48 N 377302.4 1483034.8
>>> u = toUtm(p)  # 48 N 377302 1483035

toUtmUps8 (latlon, lon=None, datum=None, falsed=True, Utm=<class 'pygeodesy.utm.Utm'>, Ups=<class 'pygeodesy.ups.Ups'>, pole='', name='', **cmoff)

 

Convert a lat-/longitude point to a UTM or UPS coordinate.

Arguments:
  • latlon - Latitude (degrees) or an (ellipsoidal) geodetic LatLon point.
  • lon - Optional longitude (degrees) or None.
  • datum - Optional datum to use this UTM coordinate, overriding latlon's datum (Datum).
  • falsed - False both easting and northing (bool).
  • Utm - Optional class to return the UTM coordinate (Utm) or None.
  • Ups - Optional class to return the UPS coordinate (Ups) or None.
  • pole - Optional top/center of UPS (stereographic) projection (str, 'N[orth]' or 'S[outh]').
  • name - Optional name (str).
  • cmoff - DEPRECATED, use falsed. Offset longitude from zone's central meridian, for UTM only (bool).
Returns:
The UTM or UPS coordinate (Utm respectively Ups) or a UtmUps8Tuple(zone, hemipole, easting, northing, band, datum, convergence, scale) if Utm respectively Ups is None or cmoff is False.
Raises:
  • RangeError - If lat outside the valid UTM or UPS bands or if lat or lon outside the valid range and rangerrors set to True.
  • TypeError - If latlon is not ellipsoidal or lon value is missing of datum is invalid.
  • UTMUPSError - UTM or UPS validation failed.
  • ValueError - Invalid lat or lon.

See Also: Functions toUtm8 and toUps8.

toWm (latlon, lon=None, radius=6378137.0, Wm=<class 'pygeodesy.webmercator.Wm'>, name='', **Wm_kwds)

 

Convert a lat-/longitude point to a WM coordinate.

Arguments:
  • latlon - Latitude (degrees) or an (ellipsoidal or spherical) geodetic LatLon point.
  • lon - Optional longitude (degrees or None).
  • radius - Optional earth radius (meter).
  • Wm - Optional class to return the WM coordinate (Wm) or None.
  • name - Optional name (str).
  • Wm_kwds - Optional, additional Wm keyword arguments, ignored if Wm=None.
Returns:
The WM coordinate (Wm) or an EasNorRadius3Tuple(easting, northing, radius) if Wm is None.
Raises:
  • ValueError - If lon value is missing, if latlon is not scalar, if latlon is beyond the valid WM range and rangerrors is set to True or if radius is invalid.

Example:

>>> p = LatLon(48.8582, 2.2945)  # 448251.8 5411932.7
>>> w = toWm(p)  # 448252 5411933
>>> p = LatLon(13.4125, 103.8667)  # 377302.4 1483034.8
>>> w = toWm(p)  # 377302 1483035

trilaterate3d2 (center1, radius1, center2, radius2, center3, radius3, eps=2.22044604925e-16, Vector=None, **Vector_kwds)

 

Trilaterate three spheres, each given as a (3d) center point and radius.

Arguments:
  • center1 - Center of the 1st sphere (Vector3d, Vector3Tuple or Vector4Tuple).
  • radius1 - Radius of the 1st sphere (same units as x, y and z).
  • center2 - Center of the 2nd sphere (Vector3d, Vector3Tuple or Vector4Tuple).
  • radius2 - Radius of this sphere (same units as x, y and z).
  • center3 - Center of the 3rd sphere (Vector3d, Vector3Tuple or Vector4Tuple).
  • radius3 - Radius of the 3rd sphere (same units as x, y and z).
  • eps - Tolerance (scalar), same units as x, y, and z.
  • Vector - Class to return intersections (Vector3d or Vector3Tuple) or None for Vector3d.
  • Vector_kwds - Optional, additional Vector keyword arguments, ignored if Vector=None.
Returns:
2-Tuple with two trilaterated points, each a Vector instance. Both points are the same instance if all three spheres abut/intersect in a single point.
Raises:
  • ImportError - Package numpy not found, not installed or older than version 1.15.
  • IntersectionError - No intersection, colinear or concentric centers or trilateration failed some other way.
  • TypeError - Invalid center1, center2 or center3.
  • UnitError - Invalid radius1, radius2 or radius3.

Note: Package numpy is required, version 1.15 or later.

See Also: Norrdine, A. An Algebraic Solution to the Multilateration Problem and implementation.

unroll180 (lon1, lon2, wrap=True)

 

Unroll longitudinal delta and wrap longitude in degrees.

Arguments:
  • lon1 - Start longitude (degrees).
  • lon2 - End longitude (degrees).
  • wrap - Wrap and unroll to the (-180..+180] range (bool).
Returns:
2-Tuple (lon2-lon1, lon2) unrolled (degrees, degrees).

See Also: Capability LONG_UNROLL in GeographicLib.

unrollPI (rad1, rad2, wrap=True)

 

Unroll longitudinal delta and wrap longitude in radians.

Arguments:
  • rad1 - Start longitude (radians).
  • rad2 - End longitude (radians).
  • wrap - Wrap and unroll to the (-PI..+PI] range (bool).
Returns:
2-Tuple (rad2 - rad1, rad2) unrolled (radians, radians).

See Also: Capability LONG_UNROLL in GeographicLib.

unstr (name, *args, **kwds)

 

Return the string representation of an invokation.

Arguments:
  • name - Function, method or class name (str).
  • args - Optional positional arguments.
  • kwds - Optional keyword arguments.
Returns:
Representation (str).

upsZoneBand5 (lat, lon, strict=True)

 

Return the UTM/UPS zone number, (polar) Band letter, pole and clipped lat- and longitude for a given location.

Arguments:
  • lat - Latitude in degrees (scalar or str).
  • lon - Longitude in degrees (scalar or str).
  • strict - Restrict lat to UPS ranges (bool).
Returns:
A UtmUpsLatLon5Tuple(zone, band, hemipole, lat, lon) where hemipole is the 'N'|'S' pole, the UPS projection top/center.
Raises:
  • RangeError - If strict and lat in the UTM and not the UPS range or if lat or lon outside the valid range and rangerrors set to True.
  • ValueError - Invalid lat or lon.

utmZoneBand2 (lat, lon)

 

DEPRECATED, use function utmZoneBand5.

Returns:
2-Tuple (zone, band).

utmZoneBand5 (lat, lon, cmoff=False)

 

Return the UTM zone number, Band letter, hemisphere and (clipped) lat- and longitude for a given location.

Arguments:
  • lat - Latitude in degrees (scalar or str).
  • lon - Longitude in degrees (scalar or str).
  • cmoff - Offset longitude from the zone's central meridian (bool).
Returns:
A UtmUpsLatLon5Tuple(zone, band, hemipole, lat, lon) where hemipole is the 'N'|'S' UTM hemisphere.
Raises:
  • RangeError - If lat outside the valid UTM bands or if lat or lon outside the valid range and rangerrors set to True.
  • ValueError - Invalid lat or lon.

utmupsValidate (coord, falsed=False, MGRS=False, Error=<class 'pygeodesy.utmups.UTMUPSError'>)

 

Check a UTM or UPS coordinate.

Arguments:
  • coord - The UTM or UPS coordinate (Utm, Ups or 5+Tuple).
  • falsed - 5+Tuple easting and northing are falsed (bool).
  • MGRS - Increase easting and northing ranges (bool).
  • Error - Optional error to raise, overriding the default (UTMUPSError).
Returns:
None if validation passed.
Raises:
  • Error - Validation failed.

See Also: Function utmupsValidateOK.

utmupsValidateOK (coord, falsed=False, ok=True)

 

Check a UTM or UPS coordinate.

Arguments:
  • coord - The UTM or UPS coordinate (Utm, Ups or 5+Tuple).
  • falsed - 5+Tuple easting and northing are falsed (bool).
  • ok - Result to return if validation passed (ok).
Returns:
ok if validation passed, the UTMUPSError otherwise.

See Also: Function utmupsValidate.

utmupsZoneBand5 (lat, lon, cmoff=False)

 

Return the UTM/UPS zone number, Band letter, hemisphere/pole and clipped lat- and longitude for a given location.

Arguments:
  • lat - Latitude in degrees (scalar or str).
  • lon - Longitude in degrees (scalar or str).
  • cmoff - Offset longitude from the zone's central meridian, for UTM only (bool).
Returns:
A UtmUpsLatLon5Tuple(zone, band, hemipole, lat, lon) where hemipole is 'N'|'S', the UTM hemisphere or UPS pole, the UPS projection top/center.
Raises:
  • RangeError - If lat outside the valid UTM or UPS bands or if lat or lon outside the valid range and rangerrors set to True.
  • ValueError - Invalid lat or lon.

See Also: Functions utmZoneBand5 and upsZoneBand5.

vincentys (lat1, lon1, lat2, lon2, radius=6371008.77141, wrap=False)

 

Compute the distance between two (spherical) points using Vincenty's spherical formula.

Arguments:
  • lat1 - Start latitude (degrees).
  • lon1 - Start longitude (degrees).
  • lat2 - End latitude (degrees).
  • lon2 - End longitude (degrees).
  • radius - Mean earth radius (meter).
  • wrap - Wrap and unroll180 longitudes (bool).
Returns:
Distance (meter, same units as radius).
Raises:
  • TypeError - Invalid radius.

See Also: Functions vincentys_, cosineAndoyerLambert, cosineForsytheAndoyerLambert,cosineLaw, equirectangular, euclidean, flatLocal/hubeny, flatPolar, haversine and thomas and methods Ellipsoid.distance2, LatLon.distanceTo* and LatLon.equirectangularTo.

Note: See note at function vincentys_.

vincentys_ (phi2, phi1, lam21)

 

Compute the angular distance between two (spherical) points using Vincenty's spherical formula.

Arguments:
  • phi2 - End latitude (radians).
  • phi1 - Start latitude (radians).
  • lam21 - Longitudinal delta, end-start (radians).
Returns:
Angular distance (radians).

See Also: Functions vincentys, cosineAndoyerLambert_, cosineForsytheAndoyerLambert_, cosineLaw_, equirectangular_, euclidean_, flatLocal_/hubeny_, flatPolar_, haversine_ and thomas_.

Note: Functions vincentys_, haversine_ and cosineLaw_ produce equivalent results, but vincentys_ is suitable for antipodal points and slightly more expensive (3 cos, 3 sin, 1 hypot, 1 atan2, 6 mul, 2 add) than haversine_ (2 cos, 2 sin, 2 sqrt, 1 atan2, 5 mul, 1 add) and cosineLaw_ (3 cos, 3 sin, 1 acos, 3 mul, 1 add).

wrap180 (deg)

 

Wrap degrees to [-180..+180].

Arguments:
  • deg - Angle (degrees).
Returns:
Degrees, wrapped (degrees180).

wrap360 (deg)

 

Wrap degrees to [0..+360).

Arguments:
  • deg - Angle (degrees).
Returns:
Degrees, wrapped (degrees360).

wrap90 (deg)

 

Wrap degrees to [-270..+90].

Arguments:
  • deg - Angle (degrees).
Returns:
Degrees, wrapped (degrees90).

wrapPI (rad)

 

Wrap radians to [-PI..+PI].

Arguments:
  • rad - Angle (radians).
Returns:
Radians, wrapped (radiansPI).

wrapPI2 (rad)

 

Wrap radians to [0..+2PI).

Arguments:
  • rad - Angle (radians).
Returns:
Radians, wrapped (radiansPI2).

wrapPI_2 (rad)

 

Wrap radians to [-3PI/2..+PI/2].

Arguments:
  • rad - Angle (radians).
Returns:
Radians, wrapped (radiansPI_2).

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\
=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=Datum(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transfor\
ms.NAD83),
...

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.GDA2020: Datum(name='GDA2020', ellipsoid=Ellipsoids.GRS80, tran\
sform=Transforms.WGS84),
...

Ellipsoids

Registered ellipsoids (enum-like).
Value:
Ellipsoids.Airy1830: Ellipsoid(name='Airy1830', a=6377563.396, b=63562\
56.90923729, f_=299.3249646, f=0.00334085, f2=0.00335205, n=0.00167322\
, e=0.08167337, e2=0.00667054, e22=0.00671533, e32=0.00334643, L=10001\
126.0807165, R1=6370461.23374576, R2=6370459.65470808, R3=6370453.3099\
4572),
Ellipsoids.AiryModified: Ellipsoid(name='AiryModified', a=6377340.189,\
 b=6356034.44793853, f_=299.3249646, f=0.00334085, f2=0.00335205, n=0.\
00167322, e=0.08167337, e2=0.00667054, e22=0.00671533, e32=0.00334643,\
...

RefFrames

Registered reference frames (enum-like).
Value:
RefFrames.ETRF2000: RefFrame(name='ETRF2000', epoch=2005, ellipsoid=El\
lipsoid(name='GRS80'),
RefFrames.GDA94: RefFrame(name='GDA94', epoch=1994, ellipsoid=Ellipsoi\
d(name='GRS80'),
RefFrames.ITRF2000: RefFrame(name='ITRF2000', epoch=1997, ellipsoid=El\
lipsoid(name='GRS80'),
RefFrames.ITRF2005: RefFrame(name='ITRF2005', epoch=2000, ellipsoid=El\
lipsoid(name='GRS80'),
...

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),
...