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

Ellipsoid with equatorial (major) and minor radius, (inverse) flattening and other pre-computed, frequently used attributes, supporting both oblate and prolate ellipsoids and spheres.

Instance Methods
 
__init__(self, a, b=None, f_=None, name='')
New Ellipsoid.
 
__eq__(self, other)
Compare this and an other ellipsoid.
 
auxAuthalic(self, lat, inverse=False)
Compute the authalic auxiliary latitude or inverse thereof.
 
auxConformal(self, lat, inverse=False)
Compute the conformal auxiliary latitude or inverse thereof.
 
auxGeocentric(self, lat, inverse=False)
Compute the geocentric auxiliary latitude or inverse thereof.
 
auxIsometric(self, lat, inverse=False)
Compute the isometric auxiliary latitude or inverse thereof.
 
auxParametric(self, lat, inverse=False)
Compute the parametric auxiliary latitude or inverse thereof.
 
auxReduced(self, lat, inverse=False)
Compute the parametric auxiliary latitude or inverse thereof.
 
auxRectifying(self, lat, inverse=False)
Compute the rectifying auxiliary latitude or inverse thereof.
 
degrees2m(self, deg, lat=0)
Convert an angle to distance along the equator or along a parallel at the given 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) 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).
 
_hubeny2_(self, phi2, phi1, lam21)
(INTERNAL) like function flatLocal_/hubeny_ but returning the angular distance in radians squared.
 
Llat(self, lat)
Return the meridional length, the distance along a meridian between the equator and the given latitude (Meter).
 
Lmeridian(self, lat)
Return the meridional length, the distance along a meridian between the equator and the given latitude (Meter).
 
m2degrees(self, meter, lat=0)
Convert distance to angle along equator or along a parallel at an other latitude.
 
Rgeocentric(self, lat)
Compute the geocentric earth radius at the given latitude.
 
Rlat(self, lat)
Approximate the earth radius at the given latitude.
 
roc2(self, lat, scaled=False)
Compute the meridional and prime-vertical, normal radii of curvature at the given latitude.
 
roc2_(self, phi, scaled=False)
Compute the meridional and prime-vertical, normal radii of curvature at the given latitude.
 
rocBearing(self, lat, bearing)
Compute the directional radius of curvature at a given latitude and compass direction.
 
rocGauss(self, lat)
Compute the Gaussian radius of curvature at the given latitude.
 
rocMean(self, lat)
Compute the mean radius of curvature at the given latitude.
 
rocMeridional(self, lat)
Compute the meridional radius of curvature at the given latitude.
 
rocPrimeVertical(self, lat)
Compute the prime-vertical, normal radius of curvature at the given latitude, aka the transverse radius of curvature.
 
rocTransverse(self, lat)
Compute the prime-vertical, normal radius of curvature at the given latitude, aka the transverse radius of curvature.
 
toStr(self, prec=8)
Return this ellipsoid as a text string.

Inherited from named._NamedEnumItem: __ne__, unregister

Inherited from named._NamedBase: __repr__, __str__, others, toRepr

Inherited from named._Named: _dot_, attrs, classof, copy, toStr2

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Class Variables
  _f_ = 0
Inverse flattening: a / (a - b) = 1 / f
  _a2_ = None
(1 / a**2) # for .ellipsiodalNvector.Cartesian.toNvector
Properties
  a
Get the equatorial (major) radius, semi-axis (meter).
  majoradius
Get the equatorial (major) radius, semi-axis (meter).
  equatoradius
Get the equatorial (major) radius, semi-axis (meter).
  a_b
Get ratio a / b (float).
  a2
Get the equatorial (major) radius squared (float), a**2.
  a2_
Get the inverse of the equatorial (major) radius squared (float), 1 / a**2.
  a2_b
Get the polar meridional radius of curvature (meter), a**2 / b, see rocPolar.
  area
Get the ellipsoid's surface area (meter**2), 4 * PI * R2**2 or 4 * PI * a**2.
  A
Get the UTM meridional radius (meter).
  AlphaKs
Get the Krüger Alpha series coefficients (KsOrder-tuple).
  b
Get the polar (minor) radius, semi-axis (meter).
  polaradius
Get the polar (minor) radius, semi-axis (meter).
  minoradius
Get the polar (minor) radius, semi-axis (meter).
  b_a
Get ratio b / a (float), 1 - f.
  b2
Get the polar (minor) radius squared (float), b**2.
  b2_a
Get the equatorial meridional radius of curvature (meter), b**2 / a.
  b2_a2
Get ratio (b / a) squared (float), (1 - f)**2.
  BetaKs
Get the Krüger Beta series coefficients (KsOrder-tuple).
  c
Get the authalic earth radius (meter), see R2.
  e
Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)).
  eccentricity
Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)).
  e2
Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.
  eccentricity2
Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.
  e22
Get the 2nd eccentricity squared (float), e2 / (1 - e2) == (a / b)**2 - 1.
  eccentricity2nd2
Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.
  e32
Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2).
  eccentricity3rd2
Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2).
  e12
Get 1 - e**2 = (1 - f)**2 (float).
  e4
Get the (1st) eccentricity to 4th power (float), e**4 == e2**2.
  es
Get the (1st) eccentricity signed (float).
  es_c
Get (1 - f) * exp(es_atanh(1)) (float), b_a * exp(es_atanh(1)).
  f
Get the flattening (float), (a - b) / a.
  flattening
Get the flattening (float), (a - b) / a.
  f_
Get the Inverse flattening (float), 1 / f == a / (a - b).
  f2
Get the 2nd flattening (float), (a - b) / b == f / (1 - f).
  flattening2nd
Get the 2nd flattening (float), (a - b) / b == f / (1 - f).
  geodesic
Get this ellipsoid's wrapped Karney Geodesic, provided the geographiclib package is installed.
  isEllipsoidal
Is this model ellipsoidal (bool)?
  isOblate
Is this ellipsoid oblate (bool)? Prolate or spherical otherwise.
  isProlate
Is this ellipsoid prolate (bool)? Oblate or spherical otherwise.
  isSpherical
Is this model spherical (bool)?
  KsOrder
Property to get and set the Krüger series' order (int).
  L
Get the quarter meridian L (aka polar distance) the distance along a meridian between the equatorand a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.
  quarteradius
Get the quarter meridian L (aka polar distance) the distance along a meridian between the equatorand a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.
  Mabcd
Get the OSGR meridional coefficients (4-Tuple), Airy130 only.
  n
Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b).
  flattening3rd
Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b).
  R1
Get the mean earth radius per IUGG (meter), (2 * a + b) / 3.
  Rmean
Get the mean earth radius per IUGG (meter), (2 * a + b) / 3.
  R2
Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atanh(e) / e) / 2).
  Rauthalic
Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atanh(e) / e) / 2).
  R3
Get the volumetric earth radius (meter), (a * a * b)**(1/3).
  Rvolumetric
Get the volumetric earth radius (meter), (a * a * b)**(1/3).
  Rr
Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
  Rrectifying
Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
  Rs
Get the biaxial, mean earth radius (meter), sqrt(a * b).
  Rbiaxial
Get the biaxial, mean earth radius (meter), sqrt(a * b).
  rocPolar
Get the polar radius of curvature (meter), see .a2_b.
  volume
Get the ellipsoid's volume (meter**3), 4 / 3 * PI * a**2 * b.

Inherited from named._NamedEnumItem: name

Inherited from named._Named: classname, classnaming, named, named2

Inherited from object: __class__

Method Details

__init__ (self, a, b=None, f_=None, name='')
(Constructor)

 

New Ellipsoid.

Arguments:
  • a - Equatorial (major) radius, semi-axis (meter).
  • b - Optional polar (minor) radius, semi-axis (meter).
  • f_ - Inverse flattening: a / (a - b) (float >>> 1.0).
  • name - Optional, unique name (str).
Raises:
  • NameError - Ellipsoid with that name already exists.
  • ValueError - Invalid a, b or f_.
Overrides: object.__init__

__eq__ (self, other)
(Equality operator)

 

Compare this and an other ellipsoid.

Arguments:
Returns:
True if equal, False otherwise.

auxAuthalic (self, lat, inverse=False)

 

Compute the authalic auxiliary latitude or 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.

auxConformal (self, lat, inverse=False)

 

Compute the conformal auxiliary latitude or 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.

auxGeocentric (self, lat, inverse=False)

 

Compute the geocentric auxiliary latitude or 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.

auxIsometric (self, lat, inverse=False)

 

Compute the isometric auxiliary latitude or 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 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.

auxReduced (self, lat, inverse=False)

 

Compute the parametric auxiliary latitude or 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.

auxRectifying (self, lat, inverse=False)

 

Compute the rectifying auxiliary latitude or 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.

degrees2m (self, deg, lat=0)

 

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

Arguments:
  • deg - Angle (degrees).
  • lat - Parallel latitude (degrees90, str).
Returns:
Angle (degrees).
Raises:
  • RangeError - Latitude lat outside valid range and rangerrors set to 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 Also: Function flatLocal/hubeny.

ecef (self, Ecef=None)

 

Return ECEF converter.

Arguments:
Returns:
An ECEF converter for this ellipsoid (EcefKarney, EcefVeness or EcefYou).
Raises:
  • TypeError - Invalid Ecef.

e2s (self, s)

 

Compute norm sqrt(1 - e2 * s**2).

Arguments:
  • s - S value (scalar).
Returns:
Norm (float).
Raises:
  • ValueError - Invalid s.

e2s2 (self, s)

 

Compute 1 - e2 * s**2.

Arguments:
  • s - S value (scalar).
Returns:
Result (float).
Raises:
  • ValueError - Invalid s.

es_atanh (self, x)

 

Compute es * atanh(es * x) 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: Math::tauf.

es_taupf (self, tau)

 

Compute Karney's equations (7), (8) and (9).

See Also: Math::taupf.

Llat (self, lat)

 

Return the meridional length, the distance along a meridian between the equator and the given latitude (Meter).

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 the given latitude (Meter).

Arguments:
  • lat - Geodetic latitude (degrees90).
Returns:
The meridional length at lat, negative on southern hemisphere (meter).

m2degrees (self, meter, lat=0)

 

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

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

Rgeocentric (self, lat)

 

Compute the geocentric earth radius at the given latitude.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Geocentric earth radius (meter).
Raises:
  • ValueError - Invalid lat.

See Also: Geocentric Radius

Rlat (self, lat)

 

Approximate the earth radius at the given latitude.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Approximate earth radius (meter).
Raises:
  • ValueError - Invalid lat.

roc2 (self, lat, scaled=False)

 

Compute the meridional and prime-vertical, normal radii of curvature at the given 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: Method .roc2_, Local, flat earth approximation and Radii of Curvature.

roc2_ (self, phi, scaled=False)

 

Compute the meridional and prime-vertical, normal radii of curvature at the given 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: Method .roc2, Local, flat earth approximation and meridional and prime vertical Radii of Curvature.

rocBearing (self, lat, bearing)

 

Compute the directional radius of curvature at a given 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 set to True.
  • ValueError - Invalid lat or bearing.

See Also: Radii of Curvature

rocGauss (self, lat)

 

Compute the Gaussian radius of curvature at the given latitude.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Gaussian radius of curvature (meter).
Raises:
  • ValueError - Invalid lat.

See Also: Radii of Curvature

rocMean (self, lat)

 

Compute the mean radius of curvature at the given latitude.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Mean radius of curvature (meter).
Raises:
  • ValueError - Invalid lat.

See Also: Radii of Curvature

rocMeridional (self, lat)

 

Compute the meridional radius of curvature at the given latitude.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Meridional radius of curvature (meter).
Raises:
  • ValueError - Invalid lat.

rocPrimeVertical (self, lat)

 

Compute the prime-vertical, normal radius of curvature at the given latitude, aka the transverse radius of curvature.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Prime-vertical radius of curvature (meter).
Raises:
  • ValueError - Invalid lat.

rocTransverse (self, lat)

 

Compute the prime-vertical, normal radius of curvature at the given latitude, aka the transverse radius of curvature.

Arguments:
  • lat - Latitude (degrees90).
Returns:
Prime-vertical radius of curvature (meter).
Raises:
  • ValueError - Invalid lat.

toStr (self, prec=8)

 

Return this ellipsoid as a text string.

Arguments:
  • prec - Optional number of decimals, unstripped (int).
Returns:
Ellipsoid attributes (str).
Raises:
Overrides: named._Named.toStr

Property Details

a

Get the equatorial (major) radius, semi-axis (meter).

Get method:
a(self) - Get the equatorial (major) radius, semi-axis (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

majoradius

Get the equatorial (major) radius, semi-axis (meter).

Get method:
a(self) - Get the equatorial (major) radius, semi-axis (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

equatoradius

Get the equatorial (major) radius, semi-axis (meter).

Get method:
a(self) - Get the equatorial (major) radius, semi-axis (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

a_b

Get ratio a / b (float).

Get method:
a_b(self) - Get ratio a / b (float).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

a2

Get the equatorial (major) radius squared (float), a**2.

Get method:
a2(self) - Get the equatorial (major) radius squared (float), a**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

a2_

Get the inverse of the equatorial (major) radius squared (float), 1 / a**2.

Get method:
a2_(self) - Get the inverse of the equatorial (major) radius squared (float), 1 / a**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

a2_b

Get the polar meridional radius of curvature (meter), a**2 / b, see rocPolar.

Get method:
a2_b(self) - Get the polar meridional radius of curvature (meter), a**2 / b, see rocPolar.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Radii of Curvature and Moritz, H. (1980), Geodetic Reference System 1980.

Note: Symbol c is used by IUGG and IERS for the polar radius of curvature.

area

Get the ellipsoid's surface area (meter**2), 4 * PI * R2**2 or 4 * PI * a**2.

Get method:
area(self) - Get the ellipsoid's surface area (meter**2), 4 * PI * R2**2 or 4 * PI * a**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

A

Get the UTM meridional radius (meter).

Get method:
A(self) - Get the UTM meridional radius (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

AlphaKs

Get the Krüger Alpha series coefficients (KsOrder-tuple).

Get method:
AlphaKs(self) - Get the Krüger Alpha series coefficients (KsOrder-tuple).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

b

Get the polar (minor) radius, semi-axis (meter).

Get method:
b(self) - Get the polar (minor) radius, semi-axis (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

polaradius

Get the polar (minor) radius, semi-axis (meter).

Get method:
b(self) - Get the polar (minor) radius, semi-axis (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

minoradius

Get the polar (minor) radius, semi-axis (meter).

Get method:
b(self) - Get the polar (minor) radius, semi-axis (meter).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

b_a

Get ratio b / a (float), 1 - f.

Get method:
b_a(self) - Get ratio b / a (float), 1 - f.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

b2

Get the polar (minor) radius squared (float), b**2.

Get method:
b2(self) - Get the polar (minor) radius squared (float), b**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

b2_a

Get the equatorial meridional radius of curvature (meter), b**2 / a.

Get method:
b2_a(self) - Get the equatorial meridional radius of curvature (meter), b**2 / a.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Radii of Curvature.

b2_a2

Get ratio (b / a) squared (float), (1 - f)**2.

Get method:
b2_a2(self) - Get ratio (b / a) squared (float), (1 - f)**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

BetaKs

Get the Krüger Beta series coefficients (KsOrder-tuple).

Get method:
BetaKs(self) - Get the Krüger Beta series coefficients (KsOrder-tuple).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

c

Get the authalic earth radius (meter), see R2.

Get method:
c(self) - Get the authalic earth radius (meter), see R2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.
Notes:

e

Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)).

Get method:
e(self) - Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity

Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)).

Get method:
e(self) - Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e2

Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.

Get method:
e2(self) - Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity2

Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.

Get method:
e2(self) - Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e22

Get the 2nd eccentricity squared (float), e2 / (1 - e2) == (a / b)**2 - 1.

Get method:
e22(self) - Get the 2nd eccentricity squared (float), e2 / (1 - e2) == (a / b)**2 - 1.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity2nd2

Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.

Get method:
e2(self) - Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e32

Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2).

Get method:
e32(self) - Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity3rd2

Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2).

Get method:
e32(self) - Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e12

Get 1 - e**2 = (1 - f)**2 (float).

Get method:
e12(self) - Get 1 - e**2 = (1 - f)**2 (float).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e4

Get the (1st) eccentricity to 4th power (float), e**4 == e2**2.

Get method:
e4(self) - Get the (1st) eccentricity to 4th power (float), e**4 == e2**2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

es

Get the (1st) eccentricity signed (float).

Get method:
es(self) - Get the (1st) eccentricity signed (float).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

es_c

Get (1 - f) * exp(es_atanh(1)) (float), b_a * exp(es_atanh(1)).

Get method:
es_c(self) - Get (1 - f) * exp(es_atanh(1)) (float), b_a * exp(es_atanh(1)).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

f

Get the flattening (float), (a - b) / a.

Get method:
f(self) - Get the flattening (float), (a - b) / a.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

flattening

Get the flattening (float), (a - b) / a.

Get method:
f(self) - Get the flattening (float), (a - b) / a.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

f_

Get the Inverse flattening (float), 1 / f == a / (a - b).

Get method:
f_(self) - Get the Inverse flattening (float), 1 / f == a / (a - b).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

f2

Get the 2nd flattening (float), (a - b) / b == f / (1 - f).

Get method:
f2(self) - Get the 2nd flattening (float), (a - b) / b == f / (1 - f).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

flattening2nd

Get the 2nd flattening (float), (a - b) / b == f / (1 - f).

Get method:
f2(self) - Get the 2nd flattening (float), (a - b) / b == f / (1 - f).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

geodesic

Get this ellipsoid's wrapped Karney Geodesic, provided the geographiclib package is installed.

Get method:
geodesic(self) - Get this ellipsoid's wrapped Karney Geodesic, provided the geographiclib package is installed.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

isEllipsoidal

Is this model ellipsoidal (bool)?

Get method:
isEllipsoidal(self) - Is this model ellipsoidal (bool)?
Set method:
immutable(inst, value) - Throws an AttributeError, always.

isOblate

Is this ellipsoid oblate (bool)? Prolate or spherical otherwise.

Get method:
isOblate(self) - Is this ellipsoid oblate (bool)? Prolate or spherical otherwise.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

isProlate

Is this ellipsoid prolate (bool)? Oblate or spherical otherwise.

Get method:
isProlate(self) - Is this ellipsoid prolate (bool)? Oblate or spherical otherwise.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

isSpherical

Is this model spherical (bool)?

Get method:
isSpherical(self) - Is this model spherical (bool)?
Set method:
immutable(inst, value) - Throws an AttributeError, always.

KsOrder

Property to get and set the Krüger series' order (int).

Get method:
KsOrder(self) - Get the Krüger series order (int 4, 6 or 8).
Set method:
KsOrder(self, order) - Set the Krüger series' order.

L

Get the quarter meridian L (aka polar distance) the distance along a meridian between the equatorand a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.

Get method:
L(self) - Get the quarter meridian L (aka polar distance) the distance along a meridian between the equatorand a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

quarteradius

Get the quarter meridian L (aka polar distance) the distance along a meridian between the equatorand a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.

Get method:
L(self) - Get the quarter meridian L (aka polar distance) the distance along a meridian between the equatorand a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

Mabcd

Get the OSGR meridional coefficients (4-Tuple), Airy130 only.

Get method:
Mabcd(self) - Get the OSGR meridional coefficients (4-Tuple), Airy130 only.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

n

Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b).

Get method:
n(self) - Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

flattening3rd

Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b).

Get method:
n(self) - Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

R1

Get the mean earth radius per IUGG (meter), (2 * a + b) / 3.

Get method:
R1(self) - Get the mean earth radius per IUGG (meter), (2 * a + b) / 3.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius and method .Rs.

Rmean

Get the mean earth radius per IUGG (meter), (2 * a + b) / 3.

Get method:
R1(self) - Get the mean earth radius per IUGG (meter), (2 * a + b) / 3.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius and method .Rs.

R2

Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atanh(e) / e) / 2).

Get method:
R2(self) - Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atanh(e) / e) / 2).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius, .area and c.

Rauthalic

Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atanh(e) / e) / 2).

Get method:
R2(self) - Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atanh(e) / e) / 2).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius, .area and c.

R3

Get the volumetric earth radius (meter), (a * a * b)**(1/3).

Get method:
R3(self) - Get the volumetric earth radius (meter), (a * a * b)**(1/3).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius.

Rvolumetric

Get the volumetric earth radius (meter), (a * a * b)**(1/3).

Get method:
R3(self) - Get the volumetric earth radius (meter), (a * a * b)**(1/3).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius.

Rr

Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).

Get method:
Rr(self) - Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius.

Rrectifying

Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).

Get method:
Rr(self) - Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Earth radius.

Rs

Get the biaxial, mean earth radius (meter), sqrt(a * b).

Get method:
Rs(self) - Get the biaxial, mean earth radius (meter), sqrt(a * b).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Method .R1.

Rbiaxial

Get the biaxial, mean earth radius (meter), sqrt(a * b).

Get method:
Rs(self) - Get the biaxial, mean earth radius (meter), sqrt(a * b).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Method .R1.

rocPolar

Get the polar radius of curvature (meter), see .a2_b.

Get method:
rocPolar(self) - Get the polar radius of curvature (meter), see .a2_b.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

volume

Get the ellipsoid's volume (meter**3), 4 / 3 * PI * a**2 * b.

Get method:
volume(self) - Get the ellipsoid's volume (meter**3), 4 / 3 * PI * a**2 * b.
Set method:
immutable(inst, value) - Throws an AttributeError, always.