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:

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

Instance Methods
 
__init__(self, a, b=None, f_=None, name='')
New Ellipsoid from equatorial and polar radius or equatorial radius and inverse flattening.
 
__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 the 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
hash(x)
  _a2_ = None
hash(x)
Properties
  a
Get the equatorial (major) radius, semi-axis (meter).
  equatoradius
Get the equatorial (major) radius, semi-axis (meter).
  a2
Get the equatorial (major) radius squared (float), a**2.
  a2_
Get the inverse of the equatorial (major) radius squared (float), 1 / a**2.
  a_b
Get ratio a / b (float).
  a2_b
Get the polar meridional radius of curvature (meter), a**2 / b, see rocPolar.
  a_f
Get equatorial radius and flattening (a_f2Tuple).
  A
Get the UTM meridional radius (meter).
  area
Get the ellipsoid's surface area (meter**2), 4 * PI * R2**2 or 4 * PI * a**2.
  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).
  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, see rocMeridional(0).
  b2_a2
Get ratio (b / a)**2 (float), (1 - f)**2, see e12.
  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)), see a_b2e.
  eccentricity
Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)), see a_b2e.
  e2
Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
  eccentricity2
Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
  e22
Get the 2nd eccentricity squared (float), e2 / (1 - e2) == (a / b)**2 - 1, see a_b2e22.
  eccentricity2nd2
Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
  e32
Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see a_b2e32.
  eccentricity3rd2
Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see a_b2e32.
  e12
Get 1 - e**2 (float), (1 - f)**2, b**2 / a**2, see b2_a2.
  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, 0 for spherical.
  flattening
Get the flattening (float), (a - b) / a, 0 for spherical.
  f_
Get the inverse flattening (float), 1 / f == a / (a - b), 0 for spherical, see a_b2f_.
  f2
Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.
  flattening2nd
Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.
  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 equator and a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.
  quarteradius
DEPRECATED, use L.
  Mabcd
Get the OSGR meridional coefficients (4-Tuple), Airy130 only.
  majoradius
DEPRECATED, use a or Requatorial.
  minoradius
DEPRECATED, use b or Rpolar.
  n
Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.
  flattening3rd
Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.
  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).
  Rbiaxial
Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).
  Requatorial
Get the equatorial (major) radius, semi-axis (meter).
  Rgeometric
Get the geometric mean earth radius (meter), sqrt(a * b).
  Rs
DEPRECATED, use Rgeometric.
  Rpolar
Get the polar (minor) radius, semi-axis (meter).
  Rquadratic
Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).
  Rrectifying
Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
  Rr
DEPRECATED, use Rrectifying.
  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, named3, named4

Inherited from object: __class__

Method Details

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

 

New Ellipsoid from equatorial and polar radius or equatorial radius and inverse flattening.

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__

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:
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 the 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 roc2.

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.

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.

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.

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.

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_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.

a_f

Get equatorial radius and flattening (a_f2Tuple).

Get method:
a_f(self) - Get equatorial radius and flattening (a_f2Tuple).
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.

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.

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.

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, see rocMeridional(0).

Get method:
b2_a(self) - Get the equatorial meridional radius of curvature (meter), b**2 / a, see rocMeridional(0).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

See Also: Radii of Curvature.

b2_a2

Get ratio (b / a)**2 (float), (1 - f)**2, see e12.

Get method:
b2_a2(self) - Get ratio (b / a)**2 (float), (1 - f)**2, see e12.
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)), see a_b2e.

Get method:
e(self) - Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)), see a_b2e.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity

Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)), see a_b2e.

Get method:
e(self) - Get the (1st) eccentricity (float), sqrt(1 - (b / a)**2)), see a_b2e.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e2

Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.

Get method:
e2(self) - Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity2

Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.

Get method:
e2(self) - Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e22

Get the 2nd eccentricity squared (float), e2 / (1 - e2) == (a / b)**2 - 1, see a_b2e22.

Get method:
e22(self) - Get the 2nd eccentricity squared (float), e2 / (1 - e2) == (a / b)**2 - 1, see a_b2e22.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

eccentricity2nd2

Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.

Get method:
e2(self) - Get the (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
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), see a_b2e32.

Get method:
e32(self) - Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see a_b2e32.
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), see a_b2e32.

Get method:
e32(self) - Get the 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see a_b2e32.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

e12

Get 1 - e**2 (float), (1 - f)**2, b**2 / a**2, see b2_a2.

Get method:
e12(self) - Get 1 - e**2 (float), (1 - f)**2, b**2 / a**2, see b2_a2.
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, 0 for spherical.

Get method:
f(self) - Get the flattening (float), (a - b) / a, 0 for spherical.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

flattening

Get the flattening (float), (a - b) / a, 0 for spherical.

Get method:
f(self) - Get the flattening (float), (a - b) / a, 0 for spherical.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

f_

Get the inverse flattening (float), 1 / f == a / (a - b), 0 for spherical, see a_b2f_.

Get method:
f_(self) - Get the inverse flattening (float), 1 / f == a / (a - b), 0 for spherical, see a_b2f_.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

f2

Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.

Get method:
f2(self) - Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

flattening2nd

Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.

Get method:
f2(self) - Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.
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 equator and 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 equator and a pole (meter), b * Elliptic(-e2 / (1 - e2)).E or a * PI / 2.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

quarteradius

DEPRECATED, use L.

Get method:
L(self) - Get the quarter meridian L (aka polar distance) the distance along a meridian between the equator and 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.

majoradius

DEPRECATED, use a or Requatorial.

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

minoradius

DEPRECATED, use b or Rpolar.

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

n

Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.

Get method:
n(self) - Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.
Set method:
immutable(inst, value) - Throws an AttributeError, always.

flattening3rd

Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.

Get method:
n(self) - Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.
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 Rgeometric.

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 Rgeometric.

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.

Rbiaxial

Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).

Get method:
Rbiaxial(self) - Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

Requatorial

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.

Rgeometric

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

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

See Also: Method R1.

Rs

DEPRECATED, use Rgeometric.

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

See Also: Method R1.

Rpolar

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.

Rquadratic

Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).

Get method:
Rbiaxial(self) - Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).
Set method:
immutable(inst, value) - Throws an AttributeError, always.

Rrectifying

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

Get method:
Rrectifying(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.

Rr

DEPRECATED, use Rrectifying.

Get method:
Rrectifying(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.

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.