Package pygeodesy :: Module ellipsoids :: Class Ellipsoid |
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# Class Ellipsoid

      object --+
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    named._Named --+
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    named._NamedBase --+
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    named._NamedEnumItem --+
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                          Ellipsoid

Known Subclasses:
  - Ellipsoid2

Ellipsoid with equatorial and polar radii, flattening, inverse flattening and other, often used, cached attributes, supporting oblate and prolate ellipsoidal and spherical earth models.

Instance Methods
__init__(self, a, b=None, f_=None, f=None, **name) New Ellipsoid from the equatorial radius and either the polar radius or inverse flattening or flattening. |
__eq__(self, other) Compare this and an other ellipsoid. |
__hash__(self) hash(x) |
auxAuthalic(self, lat, inverse=False) Compute the authalic auxiliary latitude or the inverse thereof. |
auxConformal(self, lat, inverse=False) Compute the conformal auxiliary latitude or the inverse thereof. |
auxGeocentric(self, lat, inverse=False) Compute the geocentric auxiliary latitude or the inverse thereof. |
auxIsometric(self, lat, inverse=False) Compute the isometric auxiliary latitude or the inverse thereof. |
auxParametric(self, lat, inverse=False) Compute the parametric auxiliary latitude or the inverse thereof. |
auxReduced(self, lat, inverse=False) Compute the parametric auxiliary latitude or the inverse thereof. |
auxRectifying(self, lat, inverse=False) Compute the rectifying auxiliary latitude or the inverse thereof. |
circle4(self, lat) Get the equatorial or a parallel circle of latitude. |
degrees2m(self, deg, lat=0) Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude. |
distance2(self, lat0, lon0, lat1, lon1) Approximate the distance and (initial) bearing between two points based on the local, flat earth approximation aka Hubeny formula. |
ecef(self, Ecef=None) Return ECEF converter. |
e2s(self, s) Compute norm sqrt(1 - e2 * s**2). |
e2s2(self, s) Compute 1 - e2 * s**2. |
es_atanh(self, x) Compute es * atanh(es * x) or -es * atan(es * x) for oblate respectively prolate ellipsoids where es is the signed (1st) eccentricity. |
es_tauf(self, taup) Compute Karney's equations (19), (20) and (21). |
es_taupf(self, tau) Compute Karney's equations (7), (8) and (9). |
geodesic_(self, exact=True) Get the an exact `Geodesic...` instance for this ellipsoid. |
hartzell4(self, pov, los=None) Compute the intersection of this ellipsoid's surface and a Line-Of-Sight from a Point-Of-View in space. |
height4(self, xyz, normal=True) Compute the projection on and the height of a cartesian above or below this ellipsoid's surface. |
Llat(self, lat) Return the meridional length, the distance along a meridian between the equator and a (geodetic) latitude, see `L`. |
Lmeridian(self, lat) Return the meridional length, the distance along a meridian between the equator and a (geodetic) latitude, see `L`. |
m2degrees(self, distance, lat=0) Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude. |
m2radians(self, distance, lat=0) Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude. |
radians2m(self, rad, lat=0) Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude. |
Rgeocentric(self, lat) Compute the geocentric earth radius of (geodetic) latitude. |
rhumb_(self, exact=True) Get the an exact `Rhumb...` instance for this ellipsoid. |
Rlat(self, lat) Approximate the earth radius of (geodetic) latitude. |
roc1_(self, sa, ca=None) Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, unscaled. |
roc2(self, lat, scaled=False) Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude. |
roc2_(self, phi, scaled=False) Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude. |
rocBearing(self, lat, bearing) Compute the directional radius of curvature of (geodetic) latitude and compass direction. |
rocGauss(self, lat) Compute the Gaussian radius of curvature of (geodetic) latitude. |
rocMean(self, lat) Compute the mean radius of curvature of (geodetic) latitude. |
rocMeridional(self, lat) Compute the meridional radius of curvature of (geodetic) latitude. |
rocPrimeVertical(self, lat) Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature. |
rocTransverse(self, lat) Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature. |
toEllipsoid2(self, **name) Get a copy of this ellipsoid as an Ellipsoid2. |
toStr(self, prec=8, terse=4, **sep_name) Return this ellipsoid as a text string. |
toTriaxial(self, **name) Convert this ellipsoid to a Triaxial_. |
Inherited from `named._NamedEnumItem`: `unregister` Inherited from `named._NamedBase`: `__repr__`, `__str__`, `others`, `toRepr` Inherited from `named._Named`: `__imatmul__`, `__matmul__`, `__rmatmul__`, `attrs`, `classof`, `copy`, `dup`, `methodname`, `rename`, `renamed`, `toStr2` Inherited from `object`: `__delattr__`, `__format__`, `__getattribute__`, `__new__`, `__reduce__`, `__reduce_ex__`, `__setattr__`, `__sizeof__`, `__subclasshook__`

Properties
| a
| a2
| a2_
| a_b
| a2_b
| a2_b2
| a_f
| A
| AlphaKs
| area
| areax
| b
| b_a
| b2
| b2_a
| b2_a2
| BetaKs
| c
| c2
| c2x
| e
| e12
| e2
| e2abs
| e21
| e22
| e22abs
| e32
| e32abs
| e4
| eccentricity
| eccentricity1st2
| eccentricity2nd2
| eccentricity3rd2
| equatoradius
| es
| es_c
| f
| f_
| f1
| f2
| geodesic
| geodesicw
| geodesicx
| geodsolve Get this ellipsoid's GeodesicSolve, the wrapper around utility GeodSolve, provided the path to the `GeodSolve` executable is specified with env variable `PYGEODESY_GEODSOLVE` or re-/set with this property..
| isEllipsoidal
| isOblate
| isProlate
| isSpherical
| KsOrder Class `property` with a `.name` attribute.
| L
| majoradius
| minoradius
| n
| flattening
| flattening1st
| flattening2nd
| flattening3rd
| polaradius
| quarteradius
| R1
| Rmean
| R2
| Rauthalic
| R2x
| Rauthalicx
| R3
| Rvolumetric
| Rbiaxial
| Requatorial
| Rgeometric
| rhumbaux
| rhumbekx
| rhumbsolve Get this ellipsoid's RhumbSolve, the wrapper around utility RhumbSolve, provided the path to the `RhumbSolve` executable is specified with env variable `PYGEODESY_RHUMBSOLVE` or re-/set with this property.
| rhumbx
| Rpolar
| rocEquatorial2
| rocPolar
| Rquadratic
| Rr
| Rrectifying
| Rs
| Rtriaxial
| volume
Inherited from `named._NamedEnumItem`: `name` Inherited from `named._Named`: `classname`, `classnaming`, `iteration`, `named`, `named2`, `named3`, `named4`, `sizeof` Inherited from `object`: `__class__`

Method Details

### __init__ (self, a, b=None, f_=None, f=None, **name) (Constructor) |
New Ellipsoid from the equatorial radius and either the polar radius or inverse flattening or flattening. Arguments: `a` - Equatorial radius, semi-axis (`meter`). `b` - Optional polar radius, semi-axis (`meter`). `f_` - Inverse flattening: a / (a - b) (`float` >>> 1.0). `f` - Flattening: (a - b) / a (`scalar`, near zero for spherical). `name` - Optional, unique `name=NN` (`str`). Raises: `NameError` - Ellipsoid with the same `name` already exists. `ValueError` - Invalid `a`, `b`, `f_` or `f` or `f_` and `f` are incompatible. Overrides: object.__init__ Note: abs(f_) > 1 / EPS or abs(1 / f_) < EPS is forced to 1 / f_ = 0, spherical.

### __eq__ (self, other) (Equality operator) |
Compare this and an other ellipsoid. Arguments: `other` - The other ellipsoid (Ellipsoid or Ellipsoid2). Returns: `True` if equal, `False` otherwise.

### __hash__ (self) (Hashing function) |
hash(x) Overrides: object.__hash__ (inherited documentation)

### auxAuthalic (self, lat, inverse=False) |
Compute the authalic auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or authalic) latitude (`degrees90`). `inverse` - If `True`, `lat` is the authalic and return the geodetic latitude (`bool`). Returns: The authalic (or geodetic) latitude in `degrees90`. See Also: Inverse-/AuthalicLatitude, Authalic latitude, and Snyder, p 16.

### auxConformal (self, lat, inverse=False) |
Compute the conformal auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or conformal) latitude (`degrees90`). `inverse` - If `True`, `lat` is the conformal and return the geodetic latitude (`bool`). Returns: The conformal (or geodetic) latitude in `degrees90`. See Also: Inverse-/ConformalLatitude, Conformal latitude, and Snyder, pp 15-16.

### auxGeocentric (self, lat, inverse=False) |
Compute the geocentric auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or geocentric) latitude (`degrees90`). `inverse` - If `True`, `lat` is the geocentric and return the geocentric latitude (`bool`). Returns: The geocentric (or geodetic) latitude in `degrees90`. See Also: Inverse-/GeocentricLatitude, Geocentric latitude, and Snyder, pp 17-18.

### auxIsometric (self, lat, inverse=False) |
Compute the isometric auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or isometric) latitude (`degrees`). `inverse` - If `True`, `lat` is the isometric and return the geodetic latitude (`bool`). Returns: The isometric (or geodetic) latitude in `degrees`. Note: The isometric latitude for geodetic `+/-90` is far outside the `[-90..+90]` range but the inverse thereof is the original geodetic latitude. See Also: Inverse-/IsometricLatitude, Isometric latitude, and Snyder, pp 15-16.

### auxParametric (self, lat, inverse=False) |
Compute the parametric auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or parametric) latitude (`degrees90`). `inverse` - If `True`, `lat` is the parametric and return the geodetic latitude (`bool`). Returns: The parametric (or geodetic) latitude in `degrees90`. See Also: Inverse-/ParametricLatitude, Parametric latitude, and Snyder, p 18.

### auxReduced (self, lat, inverse=False) |
Compute the parametric auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or parametric) latitude (`degrees90`). `inverse` - If `True`, `lat` is the parametric and return the geodetic latitude (`bool`). Returns: The parametric (or geodetic) latitude in `degrees90`. See Also: Inverse-/ParametricLatitude, Parametric latitude, and Snyder, p 18.

### auxRectifying (self, lat, inverse=False) |
Compute the rectifying auxiliary latitude or the inverse thereof. Arguments: `lat` - The geodetic (or rectifying) latitude (`degrees90`). `inverse` - If `True`, `lat` is the rectifying and return the geodetic latitude (`bool`). Returns: The rectifying (or geodetic) latitude in `degrees90`. See Also: Inverse-/RectifyingLatitude, Rectifying latitude, and Snyder, pp 16-17.

### circle4 (self, lat) |
Get the equatorial or a parallel circle of latitude. Arguments: `lat` - Geodetic latitude (`degrees90`, `str`). Returns: A Circle4Tuple`(radius, height, lat, beta)` instance. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `lat`. `ValueError` - Invalid `lat`. See Also: Definition of p and z under Parametric (or reduced) latitude, Karney's C++ CircleRadius and CircleHeight and method `Rlat`.

### degrees2m (self, deg, lat=0) |
Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude. Arguments: `deg` - The angle (`degrees`). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Distance (`meter`, same units as the equatorial and polar radii) or `0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `ValueError` - Invalid `deg` or `lat`.

### distance2 (self, lat0, lon0, lat1, lon1) |
Approximate the distance and (initial) bearing between two points based on the local, flat earth approximation aka Hubeny formula. Suitable only for distances of several hundred Km or Miles and only between points not near-polar. Arguments: `lat0` - From latitude (`degrees`). `lon0` - From longitude (`degrees`). `lat1` - To latitude (`degrees`). `lon1` - To longitude (`degrees`). Returns: A Distance2Tuple`(distance, initial)` with `distance` in same units as this ellipsoid's axes. Note: The meridional and prime_vertical radii of curvature are taken and scaled at the initial latitude, see `roc2`. See Also: Function pygeodesy.flatLocal/pygeodesy.hubeny.

### ecef (self, Ecef=None) |
Return ECEF converter. Arguments: `Ecef` - ECEF class to use, default EcefKarney. Returns: An ECEF converter for this `ellipsoid`. Raises: `TypeError` - Invalid `Ecef`. See Also: Module pygeodesy.ecef.

### e2s (self, s) |
Compute norm sqrt(1 - e2 * s**2). Arguments: `s` - Sine value (`scalar`). Returns: Norm (`float`). Raises: `ValueError` - Invalid `s`.

### e2s2 (self, s) |
Compute 1 - e2 * s**2. Arguments: `s` - Sine value (`scalar`). Returns: Result (`float`). Raises: `ValueError` - Invalid `s`.

### es_atanh (self, x) |
Compute es * atanh(es * x) or -es * atan(es * x) for oblate respectively prolate ellipsoids where es is the signed (1st) eccentricity. Raises: `ValueError` - Invalid `x`. See Also: Function Math::eatanhe.

### es_tauf (self, taup) |
Compute Karney's equations (19), (20) and (21). See Also: Karney's C++ method Math::tauf and and Veness' JavaScript method toLatLon.

### es_taupf (self, tau) |
Compute Karney's equations (7), (8) and (9). See Also: Karney's C++ method Math::taupf.

### geodesic_ (self, exact=True) |
Get the an exact `Geodesic...` instance for this ellipsoid. Arguments: `exact` - If `bool` return GeodesicExact`(exact=exact, ...)`, otherwise a Geodesic, GeodesicExact or GeodesicSolve instance for this ellipsoid. Returns: The `exact` geodesic (`Geodesic...`). Raises: `TypeError` - Invalid `exact`. `ValueError` - Incompatible `exact` ellipsoid.

### hartzell4 (self, pov, los=None) |
Compute the intersection of this ellipsoid's surface and a Line-Of-Sight from a Point-Of-View in space. Arguments: `pov` - Point-Of-View outside this ellipsoid (`Cartesian`, Ecef9Tuple or Vector3d). `los` - Line-Of-Sight, direction to this ellipsoid (Vector3d) or `None` to point to this ellipsoid's center. Returns: Vector4Tuple`(x, y, z, h)` with the cartesian coordinates `x`, `y` and `z` of the projection on or the intersection with this ellipsoid and the distance `h` from `pov` to `(x, y, z)` along `los`, all in `meter`, conventionally. Raises: `IntersectionError` - Null `pov` or `los` vector, or `pov` is inside this ellipsoid or `los` points outside this ellipsoid or points in an opposite direction. `TypeError` - Invalid `pov` or `los`. See Also: Satellite Line-of-Sight Intersection with Earth and methods Ellipsoid.height4 and Triaxial.hartzell4.

### height4 (self, xyz, normal=True) |
Compute the projection on and the height of a cartesian above or below this ellipsoid's surface. Arguments: `xyz` - The cartesian (`Cartesian`, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple). `normal` - If `True`, the projection is perpendicular to (the nearest point on) this ellipsoid's surface, otherwise the `radial` line to this ellipsoid's center (`bool`). Returns: Vector4Tuple`(x, y, z, h)` with the cartesian coordinates `x`, `y` and `z` of the projection on and the height `h` above or below this ellipsoid's surface, all in `meter`, conventionally. Raises: `ValueError` - Null `xyz`. `TypeError` - Non-cartesian `xyz`. See Also: Distance to and intersection with an ellipse and methods Ellipsoid.hartzell4 and Triaxial.height4.

### Llat (self, lat) |
Return the meridional length, the distance along a meridian between the equator and a (geodetic) latitude, see `L`. Arguments: `lat` - Geodetic latitude (`degrees90`). Returns: The meridional length at `lat`, negative on southern hemisphere (`meter`).

### Lmeridian (self, lat) |
Return the meridional length, the distance along a meridian between the equator and a (geodetic) latitude, see `L`. Arguments: `lat` - Geodetic latitude (`degrees90`). Returns: The meridional length at `lat`, negative on southern hemisphere (`meter`).

### m2degrees (self, distance, lat=0) |
Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude. Arguments: `distance` - Distance (`meter`). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Angle (`degrees`) or `INF` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `ValueError` - Invalid `distance` or `lat`.

### m2radians (self, distance, lat=0) |
Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude. Arguments: `distance` - Distance (`meter`). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Angle (`radians`) or `INF` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `ValueError` - Invalid `distance` or `lat`.

### radians2m (self, rad, lat=0) |
Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude. Arguments: `rad` - The angle (`radians`). `lat` - Parallel latitude (`degrees90`, `str`). Returns: Distance (`meter`, same units as the equatorial and polar radii) or `0` for near-polar `lat`. Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `ValueError` - Invalid `rad` or `lat`.

### Rgeocentric (self, lat) |
Compute the geocentric earth radius of (geodetic) latitude. Arguments: `lat` - Latitude (`degrees90`). Returns: Geocentric earth radius (`meter`). Raises: `ValueError` - Invalid `lat`. See Also: Geocentric Radius

### rhumb_ (self, exact=True) |
Get the an exact `Rhumb...` instance for this ellipsoid. Arguments: `exact` - If `bool` or `None` return Rhumb`(exact=exact, ...)`, otherwise a Rhumb, RhumbAux or RhumbSolve instance for this ellipsoid. Returns: The `exact` rhumb (`Rhumb...`). Raises: `TypeError` - Invalid `exact`. `ValueError` - Incompatible `exact` ellipsoid.

### Rlat (self, lat) |
Approximate the earth radius of (geodetic) latitude. Arguments: `lat` - Latitude (`degrees90`). Returns: Approximate earth radius (`meter`). Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `TypeError` - Invalid `lat`. `ValueError` - Invalid `lat`. Note: `Rlat(90)` equals `Rpolar`. See Also: Method `circle4`.

### roc1_ (self, sa, ca=None) |
Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, unscaled. Arguments: `sa` - Sine of the latitude (`float`, [-1.0..+1.0]). `ca` - Optional cosine of the latitude (`float`, [-1.0..+1.0]) to use an alternate formula. Returns: The prime-vertical radius of curvature (`float`). Note: The delta between both formulae with `Ellipsoids.WGS84` is less than 2 nanometer over the entire latitude range. See Also: Method roc2_ and class EcefYou.

### roc2 (self, lat, scaled=False) |
Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude. Arguments: `lat` - Latitude (`degrees90`). `scaled` - Scale prime_vertical by `cos(radians(lat))` (`bool`). Returns: An Curvature2Tuple`(meridional, prime_vertical)` with the radii of curvature. Raises: `ValueError` - Invalid `lat`. See Also: Methods roc2_ and roc1_, Local, flat earth approximation and meridional and prime vertical Radii of Curvature.

### roc2_ (self, phi, scaled=False) |
Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude. Arguments: `phi` - Latitude (`radians`). `scaled` - Scale prime_vertical by `cos(phi)` (`bool`). Returns: An Curvature2Tuple`(meridional, prime_vertical)` with the radii of curvature. Raises: `ValueError` - Invalid `phi`. See Also: Methods roc2 and roc1_, property rocEquatorial2, Local, flat earth approximation and the meridional and prime vertical Radii of Curvature.

### rocBearing (self, lat, bearing) |
Compute the directional radius of curvature of (geodetic) latitude and compass direction. Arguments: `lat` - Latitude (`degrees90`). `bearing` - Direction (compass `degrees360`). Returns: Directional radius of curvature (`meter`). Raises: `RangeError` - Latitude `lat` outside valid range and rangerrors is `True`. `ValueError` - Invalid `lat` or `bearing`. See Also: Radii of Curvature

### rocGauss (self, lat) |
Compute the Gaussian radius of curvature of (geodetic) latitude. Arguments: `lat` - Latitude (`degrees90`). Returns: Gaussian radius of curvature (`meter`). Raises: `ValueError` - Invalid `lat`. See Also: Non-directional Radii of Curvature

### rocMean (self, lat) |
Compute the mean radius of curvature of (geodetic) latitude. Arguments: `lat` - Latitude (`degrees90`). Returns: Mean radius of curvature (`meter`). Raises: `ValueError` - Invalid `lat`. See Also: Non-directional Radii of Curvature

### rocMeridional (self, lat) |
Compute the meridional radius of curvature of (geodetic) latitude. Arguments: `lat` - Latitude (`degrees90`). Returns: Meridional radius of curvature (`meter`). Raises: `ValueError` - Invalid `lat`. See Also: Methods roc2 and roc2_, Local, flat earth approximation and Radii of Curvature.

### rocPrimeVertical (self, lat) |
Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature. Arguments: `lat` - Latitude (`degrees90`). Returns: Prime-vertical radius of curvature (`meter`). Raises: `ValueError` - Invalid `lat`. See Also: Methods roc2, roc2_ and roc1_, Local, flat earth approximation and Radii of Curvature.

### rocTransverse (self, lat) |
Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature. Arguments: `lat` - Latitude (`degrees90`). Returns: Prime-vertical radius of curvature (`meter`). Raises: `ValueError` - Invalid `lat`. See Also: Methods roc2, roc2_ and roc1_, Local, flat earth approximation and Radii of Curvature.

### toEllipsoid2 (self, **name) |
Get a copy of this ellipsoid as an Ellipsoid2. Arguments: `name` - Optional, unique `name=NN` (`str`). See Also: Property `a_f`.

### toStr (self, prec=8, terse=4, **sep_name) |
Return this ellipsoid as a text string. Arguments: `prec` - Number of decimal digits, unstripped (`int`). `terse` - Limit the number of items (`int`, 0...18), use `terse=0` or `=None` for all. `sep_name` - Optional `name=NN` (`str`) or `None` to exclude this ellipsoid's name and separator `sep=", "` to join the items (`str`). Returns: This `Ellipsoid`'s attributes (`str`). Overrides: named._Named.toStr

### toTriaxial (self, **name) |
Convert this ellipsoid to a Triaxial_. Arguments: `name` - Optional `name=NN` (`str`). Returns: A Triaxial_ or Triaxial with the `X` axis pointing east and `Z` pointing north. See Also: Method Triaxial_.toEllipsoid.

Property Details

### a Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a2_ Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a_b Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a2_b Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a2_b2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### a_f Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### A Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### AlphaKs Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### area Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### areax Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### b Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### b_a Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### b2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### b2_a Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### b2_a2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### BetaKs Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### c Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### c2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### c2x Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e12 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e2abs Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e21 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e22 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e22abs Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e32 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e32abs Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### e4 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### eccentricity Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### eccentricity1st2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### eccentricity2nd2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### eccentricity3rd2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### equatoradius Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### es Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### es_c Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### f Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### f_ Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### f1 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### f2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### geodesic Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### geodesicw Get method: geodesicw(self) - Get this ellipsoid's wrapped geodesicw.Geodesic, provided Karney's geographiclib package is installed. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### geodesicx Get method: geodesicx(self) - Get this ellipsoid's exact GeodesicExact. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### geodsolve Get this ellipsoid's GeodesicSolve, the wrapper around utility GeodSolve, provided the path to the `GeodSolve` executable is specified with env variable `PYGEODESY_GEODSOLVE` or re-/set with this property.. Get method: geodsolve(self) - Get this ellipsoid's GeodesicSolve, the wrapper around utility GeodSolve, provided the path to the `GeodSolve` executable is specified with env variable `PYGEODESY_GEODSOLVE` or re-/set with this property.. Set method: geodsolve(self, path) - Re-/set the (fully qualified) path to the GeodSolve executable, overriding env variable `PYGEODESY_GEODSOLVE` (`str`).

### isEllipsoidal Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### isOblate Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### isProlate Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### isSpherical Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### KsOrder Class `property` with a `.name` attribute. Get method: KsOrder(self) - Get the Krüger series' order (`int` 4, 6 or 8). Set method: KsOrder(self, order) - Set the Krüger series' order (`int` 4, 6 or 8).

### L Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### majoradius Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### minoradius Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### n Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### flattening Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### flattening1st Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### flattening2nd Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### flattening3rd Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### polaradius Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### quarteradius Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### R1 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rmean Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### R2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rauthalic Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### R2x Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rauthalicx Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### R3 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rvolumetric Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rbiaxial Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Requatorial Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rgeometric Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### rhumbaux Get method: rhumbaux(self) - Get this ellipsoid's Auxiliary `rhumb.RhumbAux`. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### rhumbekx Get method: rhumbekx(self) - Get this ellipsoid's Elliptic, Krüger `rhumb.Rhumb`. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### rhumbsolve Get this ellipsoid's RhumbSolve, the wrapper around utility RhumbSolve, provided the path to the `RhumbSolve` executable is specified with env variable `PYGEODESY_RHUMBSOLVE` or re-/set with this property. Get method: rhumbsolve(self) - Get this ellipsoid's RhumbSolve, the wrapper around utility RhumbSolve, provided the path to the `RhumbSolve` executable is specified with env variable `PYGEODESY_RHUMBSOLVE` or re-/set with this property. Set method: rhumbsolve(self, path) - Re-/set the (fully qualified) path to the RhumbSolve executable, overriding env variable `PYGEODESY_RHUMBSOLVE` (`str`).

### rhumbx Get method: rhumbx(self) - DEPRECATED on 2023.11.28, use property `rhumbekx`. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rpolar Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### rocEquatorial2 Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### rocPolar Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rquadratic Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rr Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rrectifying Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rs Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### Rtriaxial Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.

### volume Get method: _fget(inst) - Get and cache/memoize the `property` value. Set method: _fset_error(inst, val) - Throws an `AttributeError`, always. Delete Method: _fdel(inst) - Zap the cached/memoized `property` value.