Package pygeodesy :: Module ellipsoids :: Class Ellipsoid
[frames] | no frames]

Class Ellipsoid

  object --+            
           |            
named._Named --+        
               |        
named._NamedBase --+    
                   |    
named._NamedEnumItem --+
                       |
                      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.
 
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) 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 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.
 
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.
 
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, rename, toStr2

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

Class Variables
  _f_ = 0
hash(x)
Properties
  a
Get the equatorial radius, semi-axis (meter).
  equatoradius
Get the equatorial radius, semi-axis (meter).
  a2
Get the equatorial radius squared (float), a**2.
  a2_
Get the inverse of the equatorial radius squared (float), 1 / a**2.
  a_b
Get the ratio equatorial over polar radius (float), a / b == 1 / (1 - f).
  a2_b
Get the polar meridional radius of curvature (meter), a**2 / b.
  a2_b2
Get the ratio equatorial over polar radius squared (float), (a / b)**2 == 1 / (1 - e**2) == 1 / (1 - e2) == 1 / e12.
  a_f
Get the equatorial radius and flattening (a_f2Tuple).
  A
Get the UTM meridional (or rectifying) radius (meter).
  AlphaKs
Get the Krüger Alpha series coefficients (KsOrder-tuple).
  area
Get the ellipsoid's surface area (meter**2), 4 * PI * R2**2.
  b
Get the polar radius, semi-axis (meter).
  polaradius
Get the polar radius, semi-axis (meter).
  b_a
Get the ratio polar over equatorial radius (float), b / a == 1 - f.
  b2
Get the polar radius squared (float), b**2.
  b2_a
Get the equatorial meridional radius of curvature (meter), b**2 / a, see rocMeridional(0).
  b2_a2
Get the ratio polar over equatorial radius squared (float), (b / a)**2 == (1 - f)**2 == 1 - e**2 == e12.
  BetaKs
Get the Krüger Beta series coefficients (KsOrder-tuple).
  c
DEPRECATED, use property R2 or Rauthalic.
  c2
Get the authalic earth radius squared (meter**2), see area, 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.
  e2abs
Get abs value of the (1st) eccentricity squared (float).
  e12
Get 1 less (1st) eccentricity squared (float), 1 - e**2 == (1 - f)**2 == b**2 / a**2, see b2_a2.
  e22
Get the 2nd eccentricity squared (float), e2 / (1 - e2) == e2 / (1 - f)**2 == (a / b)**2 - 1, see a_b2e22.
  eccentricity2nd2
Get the 2nd eccentricity squared (float), e2 / (1 - e2) == e2 / (1 - f)**2 == (a / b)**2 - 1, see a_b2e22.
  e22abs
Get abs value of the (2nd) eccentricity squared (float).
  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.
  e32abs
Get abs value of the (3rd) eccentricity squared (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, 0 for spherical, negative for prolate.
  flattening
Get the flattening (float), (a - b) / a, 0 for spherical, negative for prolate.
  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), see AlphaKs, BetaKs.
  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.
  Mabcd
Get the OSGR meridional coefficients (4-Tuple), Airy130 only.
  majoradius
DEPRECATED, use property a or Requatorial.
  minoradius
DEPRECATED, use property 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.
  quarteradius
DEPRECATED, use property L or Llat.
  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 * atan[h](e) / e) / 2).
  Rauthalic
Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atan[h](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 radius, semi-axis (meter).
  Rgeometric
Get the geometric mean earth radius (meter), sqrt(a * b).
  Rpolar
Get the polar radius, semi-axis (meter).
  Rquadratic
Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).
  Rr
DEPRECATED, use property Rrectifying.
  Rrectifying
Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
  Rs
DEPRECATED, use property Rgeometric.
  rocPolar
Get the polar meridional radius of curvature (meter), a**2 / b.
  volume
Get the ellipsoid's volume (meter**3), 4 / 3 * PI * R3**3.

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 radius, semi-axis (meter).
  • b - Optional, polar 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.

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 set to True.
  • TypeError - Invalid lat.
  • ValueError - Invalid lat.

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 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 - Sine 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 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 set to 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 set to 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 set to 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

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 set to True.
  • TypeError - Invalid lat.
  • ValueError - Invalid lat.

Note: Rlat(90) equals Rpolar.

See Also: Method Rparallel.

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_ and 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_ and 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 set to 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: 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: 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.

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.

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.

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 radius, semi-axis (meter).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

equatoradius

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

a2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

a2_

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

a_b

Get the ratio equatorial over polar radius (float), a / b == 1 / (1 - f).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

a2_b

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

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.

a2_b2

Get the ratio equatorial over polar radius squared (float), (a / b)**2 == 1 / (1 - e**2) == 1 / (1 - e2) == 1 / e12.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

a_f

Get the equatorial radius and flattening (a_f2Tuple).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

A

Get the UTM meridional (or rectifying) radius (meter).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

AlphaKs

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

area

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: c2 and R2.

b

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

polaradius

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

b_a

Get the ratio polar over equatorial radius (float), b / a == 1 - f.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

b2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

b2_a

Get the equatorial meridional radius of curvature (meter), b**2 / a, see rocMeridional(0).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Radii of Curvature.

b2_a2

Get the ratio polar over equatorial radius squared (float), (b / a)**2 == (1 - f)**2 == 1 - e**2 == e12.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

BetaKs

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

c

DEPRECATED, use property R2 or Rauthalic.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

c2

Get the authalic earth radius squared (meter**2), see area, R2.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

eccentricity

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

eccentricity2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e2abs

Get abs value of the (1st) eccentricity squared (float).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e12

Get 1 less (1st) eccentricity squared (float), 1 - e**2 == (1 - f)**2 == b**2 / a**2, see b2_a2.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e22

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

eccentricity2nd2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e22abs

Get abs value of the (2nd) eccentricity squared (float).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e32

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

eccentricity3rd2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e32abs

Get abs value of the (3rd) eccentricity squared (float).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

e4

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

es

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

es_c

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

f

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

flattening

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

f_

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

f2

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

flattening2nd

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

geodesic

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

isEllipsoidal

Is this model ellipsoidal (bool)?

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

isOblate

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

isProlate

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

isSpherical

Is this model spherical (bool)?

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

KsOrder

Property to get and set the Krüger series' order (int), see AlphaKs, BetaKs.

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

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:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

Mabcd

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

majoradius

DEPRECATED, use property a or Requatorial.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

minoradius

DEPRECATED, use property b or Rpolar.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

n

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

flattening3rd

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

quarteradius

DEPRECATED, use property L or Llat.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

R1

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius and method Rgeometric.

Rmean

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius and method Rgeometric.

R2

Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atan[h](e) / e) / 2).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius, area and c2.

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

Rauthalic

Get the authalic earth radius (meter), sqrt((a**2 + b**2 * atan[h](e) / e) / 2).

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius, area and c2.

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

R3

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius and volume.

Rvolumetric

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius and volume.

Rbiaxial

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

Requatorial

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

Rgeometric

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: R1.

Rpolar

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

Rquadratic

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

Rr

DEPRECATED, use property Rrectifying.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

Rrectifying

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: Earth radius.

Rs

DEPRECATED, use property Rgeometric.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

rocPolar

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

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

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.

volume

Get the ellipsoid's volume (meter**3), 4 / 3 * PI * R3**3.

Get method:
_fget(inst)
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst)

See Also: R3.