Package pygeodesy :: Module datum :: 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 major and minor radius, semi-axis, (inverse) flattening and other pre-computed, frequently used attributes.

Instance Methods
 
__init__(self, a, b, f_, name='')
New Ellipsoid.
 
__eq__(self, other)
Compare this and an other ellipsoid.
 
distance2(self, lat0, lon0, lat1, lon1)
Approximate the distance and (initial) bearing between two points based on the radii of curvature at the initial point.
 
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).
 
_flatRad2_(self, phi2, phi1, lam21)
(INTERNAL) like function flatLocal_ but returning the angular distance in radians squared.
 
m2degrees(self, meter)
Convert distance to angle along equator.
 
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 the 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.
 
toStr(self, prec=9)
Return this ellipsoid as a text string.

Inherited from named._NamedEnumItem: __ne__, unregister

Inherited from named._NamedBase: __repr__, __str__, others, toStr2

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

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
  a2
  a2_
  a_b
  a2_b
  area
  A
  AlphaKs
  b
  b2
  b2_a
  BetaKs
  c
  e
  e12
  e2
  e22
  e4
  es
  es_c
  f
  f_
  f2
  geodesic
  isEllipsoidal
  isSpherical
  KsOrder
Property to get and set the Krüger series' order (int).
  Mabcd
  n
  R1
  R2
  R3
  Rr
  Rs
  volume

Inherited from named._NamedEnumItem: name

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

Inherited from object: __class__

Method Details

__init__ (self, a, b, f_, name='')
(Constructor)

 

New Ellipsoid.

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

__eq__ (self, other)
(Equality operator)

 

Compare this and an other ellipsoid.

Arguments:
Returns:
True if equal, False otherwise.

distance2 (self, lat0, lon0, lat1, lon1)

 

Approximate the distance and (initial) bearing between two points based on the radii of curvature at the initial point.

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.

See Also: Function flatLocal, local, flat earth approximation and meridional and prime vertical Radii of Curvature.

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.

See Also: Function Math::eatanhe.

es_tauf (self, taup)

 

Compute Karney's equations (19), (20) and (21).

See Also: Function Math::tauf.

es_taupf (self, tau)

 

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

See Also: Function Math::taupf.

m2degrees (self, meter)

 

Convert distance to angle along equator.

Arguments:
  • meter - Distance (meter).
Returns:
Angle (degrees).

Rgeocentric (self, lat)

 

Compute the geocentric earth radius at the given latitude.

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

See Also: Geocentric Radius

Rlat (self, lat)

 

Approximate the earth radius at the given latitude.

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

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(phi) (bool).
Returns:
An Curvature2Tuple(meridional, prime_vertical) with the radii of curvature.

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.

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 the given latitude and compass direction.

Arguments:
  • lat - Latitude (degrees90).
  • bearing - Direction (compass degrees360).
Returns:
Directional radius of curvature (meter).

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).

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).

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).

rocPrimeVertical (self, lat)

 

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

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

toStr (self, prec=9)

 

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

a2

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

a2_

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

a_b

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

a2_b

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

area

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

A

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

AlphaKs

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

b

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

b2

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

b2_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.

BetaKs

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

c

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

e

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

e12

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

e2

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 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.

e4

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

es_c

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

f

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

f_

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

geodesic

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

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

isSpherical

Get method:
isSpherical(self) - Check whether this model is 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.

Mabcd

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

n

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

R2

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.

R3

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

Rr

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.

Rs

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

volume

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.