pygeodesy :: ellipsoids :: Ellipsoid :: Class Ellipsoid

Class Ellipsoid

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named._Named --+        
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named._NamedBase --+    
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                      Ellipsoid

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

Instance Methods

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.

Rgeocentric(self, lat)
Compute the geocentric earth radius of (geodetic) latitude.

Rlat(self, lat)
Average the earth radius between equatoradius at 0 and polaradius at +/-90 degrees latitude.

__eq__(self, other)
Compare this and an other ellipsoid.

__hash__(self)
hash(x)

__init__(self, a, b=None, f_=None, f=None, **name)
New Ellipsoid from the equatorial radius and either the polar radius or inverse flattening or flattening.

auxAuthalic(self, lat, inverse=False)
Compute the authalic auxiliary latitude (Xi) or the inverse thereof.

auxConformal(self, lat, inverse=False)
Compute the conformal auxiliary latitude (Chi) or the inverse thereof.

auxGeocentric(self, lat, inverse=False, height=0.0)
Compute the geocentric auxiliary latitude (Theta) or the inverse thereof.

auxIsometric(self, lat, inverse=False)
Compute the isometric auxiliary latitude (Psi) or the inverse thereof.

auxParametric(self, lat, inverse=False)
Compute the parametric auxiliary latitude (Beta) or the inverse thereof.

auxRectifying(self, lat, inverse=False)
Compute the rectifying auxiliary latitude (Mu) or the inverse thereof.

auxReduced(self, lat, inverse=False)
Compute the parametric auxiliary latitude (Beta) or the inverse thereof.

circle4(self, lat)
Get the equatorial or a parallel circle of latitude.

degrees2m(self, deg, lat=0)
Convert an arc in degrees to a 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.

e2s(self, s)
Compute norm sqrt(1 - e2 * s**2).

e2s2(self, s)
Compute 1 - e2 * s**2.

ecef(self, Ecef=None)
Return ECEF converter.

es_atanh(self, x)
Compute es * atanh(es * x) or -es * atan(es * x) for oblate respectively prolate ellipsoids where es is the signed (1st) eccentricity.

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

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

geodesic_(self, exact=True)
Get the an exact Geodesic... instance for this ellipsoid.

hartzell4(self, pov, los=None)
Compute the intersection of this ellipsoid's surface and a Line-Of-Sight from a Point-Of-View in space.

height4(self, xyz, normal=True)
Compute the projection on and the height of a cartesian above or below this ellipsoid's surface.

m2degrees(self, distance, lat=0)
Convert a distance to an arc in degrees 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.

rhumb_(self, exact=True)
Get the an exact Rhumb... instance for this ellipsoid.

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.

rocAzimuth(self, lat, azimuth)
Compute the directional radius of curvature of (geodetic) latitude and azimuth compass direction.

rocBearing(self, lat, bearing)
Compute the directional radius of curvature of (geodetic) latitude and bearing 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.

toEllipse(self, **name)
Get this ellipsoid's meridional ellipse Ellipse.

toEllipsoid2(self, **name)
Get a copy of this ellipsoid as an Ellipsoid2.

toStr(self, prec=8, terse=4, **sep_name)
Return this ellipsoid as a text string.

toTriaxial(self, **name)
Convert this ellipsoid to a Triaxial_.

Inherited from named._NamedEnumItem: unregister

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

Inherited from named._Named: __format__, __imatmul__, __matmul__, __rmatmul__, attrs, classof, copy, dup, methodname, rename, renamed, toStr2

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

Properties
	A Get the UTM meridional (or rectifying) radius (`meter`).
	AlphaKs Get the Krüger Alpha series coefficients (`KsOrder-tuple`).
	BetaKs Get the Krüger Beta series coefficients (`KsOrder-tuple`).
	KsOrder Class `property` with a `.name` attribute.
	L Get the quarter meridian `L`, aka the `polar distance` along a meridian between the equator and a pole (`meter`), b Elliptic(-e2 / (1 - e2)).cE* or b PI / 2*.
	R1 Get the mean earth radius per IUGG (`meter`), (2 a + b) / 3 == a * (1 - f / 3)*.
	R2 Get the authalic earth radius (`meter`), sqrt(c2).
	R2x Get the authalic earth radius (`meter`), sqrt(c2x).
	R3 Get the volumetric earth radius (`meter`), (a a * b)*(1/3).
	Rauthalic Get the authalic earth radius (`meter`), sqrt(c2).
	Rauthalicx Get the authalic earth radius (`meter`), sqrt(c2x).
	Rbiaxial Get the biaxial, quadratic mean earth radius (`meter`), sqrt((a2 + b2) / 2).
	Requatorial Get the equatorial radius, semi-axis (`meter`).
	Rgeometric Get the geometric mean earth radius (`meter`), sqrt(a b)*.
	Rmean Get the mean earth radius per IUGG (`meter`), (2 a + b) / 3 == a * (1 - f / 3)*.
	Rpolar Get the polar radius, semi-axis (`meter`).
	Rquadratic DEPRECATED, use property `Rbiaxial` or `Rtriaxial`.
	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`.
	Rtriaxial Get the triaxial, quadratic mean earth radius (`meter`), sqrt((3 a2 + b2) / 4)*.
	Rvolumetric Get the volumetric earth radius (`meter`), (a a * b)*(1/3).
	a Get the equatorial radius, semi-axis (`meter`).
	a2 Get the equatorial radius squared (`meter` squared), a2.
	a2_ Get the inverse of the equatorial radius squared (`meter` squared), 1 / a2.
	a2_b Get the polar meridional (or polar) radius of curvature (`meter`), a2 / b.
	a2_b2 Get the ratio equatorial over polar radius squared (`float`), (a / b)2 == 1 / (1 - e2) == 1 / (1 - e2) == 1 / e21.
	a_b Get the ratio equatorial over polar radius (`float`), a / b == 1 / (1 - f).
	a_f Get the equatorial radius and flattening (`a_f2Tuple`), see method `toEllipsoid2`.
	a_f2 Get the equatorial radius and flattening (`a_f2Tuple`), see method `toEllipsoid2`.
	area Get the ellipsoid's surface area (`meter` squared), 4 PI * c2*.
	areax Get the ellipsoid's surface area (`meter` squared), 4 PI * c2x, more accurate for very oblate* ellipsoids.
	b Get the polar radius, semi-axis (`meter`).
	b2 Get the polar radius squared (`float`), b2.
	b2_a Get the equatorial meridional radius of curvature (`meter`), b2 / a, see `rocMeridional(0)`.
	b2_a2 Get the ratio polar over equatorial radius squared (`float`), (b / a)2 == (1 - f)2 == 1 - e2 == `e21`.
	b_a Get the ratio polar over equatorial radius (`float`), b / a == f1 == 1 - f.
	c DEPRECATED, use property `R2` or `Rauthalic`.
	c2 Get the authalic earth radius squared (`meter` squared).
	c2x Get the authalic earth radius squared (`meter` squared), more accurate for very oblate ellipsoids.
	e Get the unsigned, (1st) eccentricity (`float`), sqrt(1 - (b / a)2)), see `a_b2e`.
	e12 DEPRECATED, use property `e21`.
	e2 Get the signed, (1st) eccentricity squared (`float`), f (2 - f) == 1 - (b / a)*2, see `a_b2e2`.
	e21 Get 1 less 1st eccentricity squared (`float`), 1 - e2 == 1 - e2 == (1 - f)2 == b2 / a2, see `b2_a2`.
	e22 Get the signed, 2nd eccentricity squared (`float`), e2 / (1 - e2) == e2 / (1 - f)2 == (a / b)2 - 1, see `a_b2e22`.
	e22abs Get the unsigned, 2nd eccentricity squared (`float`).
	e2abs Get the unsigned, (1st) eccentricity squared (`float`).
	e32 Get the signed, 3rd eccentricity squared (`float`), e2 / (2 - e2) == (a2 - b2) / (a2 + b2), see `a_b2e32`.
	e32abs Get the unsigned, 3rd eccentricity squared (`float`).
	e4 Get the unsignd, (1st) eccentricity to 4th power (`float`), e4 == e22.
	eccentricity Get the unsigned, (1st) eccentricity (`float`), sqrt(1 - (b / a)2)), see `a_b2e`.
	eccentricity1st2 Get the signed, (1st) eccentricity squared (`float`), f (2 - f) == 1 - (b / a)*2, see `a_b2e2`.
	eccentricity2nd2 Get the signed, 2nd eccentricity squared (`float`), e2 / (1 - e2) == e2 / (1 - f)2 == (a / b)2 - 1, see `a_b2e22`.
	eccentricity3rd2 Get the signed, 3rd eccentricity squared (`float`), e2 / (2 - e2) == (a2 - b2) / (a2 + b2), see `a_b2e32`.
	equatoradius Get the equatorial radius, semi-axis (`meter`).
	equatorimeter Get the ellipsoid's equatorial perimeter (`meter`).
	es Get the signed (1st) eccentricity (`float`).
	es_c Get (1 - f) exp(es_atanh(1))* (`float`), b_a exp(es_atanh(1))*.
	f Get the flattening (`scalar`), (a - b) / a, `0` for spherical, negative for prolate.
	f1 Get the 1 - flattening (`float`), f1 == 1 - f == b / a.
	f2 Get the 2nd flattening (`float`), (a - b) / b == f / (1 - f), `0` for spherical, see `a_b2f2`.
	f_ Get the inverse flattening (`scalar`), 1 / f == a / (a - b), `0` for spherical, see `a_b2f_`.
	flattening Get the flattening (`scalar`), (a - b) / a, `0` for spherical, negative for prolate.
	flattening1st Get the flattening (`scalar`), (a - b) / a, `0` for spherical, negative for prolate.
	flattening2nd Get the 2nd flattening (`float`), (a - b) / b == f / (1 - f), `0` for spherical, see `a_b2f2`.
	flattening3rd Get the 3rd flattening (`float`), f / (2 - f) == (a - b) / (a + b), see `a_b2n`.
	geodesic DEPRECATED, use property `geodesicw`.
	geodesicw Get this ellipsoid's wrapped geodesicw.Geodesic, provided Karney's geographiclib package is installed.
	geodesicx Get this ellipsoid's exact `GeodesicExact`.
	geodsolve Get this ellipsoid's `GeodesicSolve`, the wrapper around utility GeodSolve, provided the path to the `GeodSolve` executable is specified with env variable `PYGEODESY_GEODSOLVE` or re-/set with this property..
	isEllipsoidal 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 ellipsoid spherical (`bool`)?
	majoradius DEPRECATED, use property `a` or `Requatorial`.
	minoradius DEPRECATED, use property `b`, `polaradius` or `Rpolar`.
	n Get the 3rd flattening (`float`), f / (2 - f) == (a - b) / (a + b), see `a_b2n`.
	polaradius Get the polar radius, semi-axis (`meter`).
	polarimeter Get the ellipsoid's polar, meridional perimeter (`meter`).
	quarteradius DEPRECATED, use property `L` or method `Llat`.
	rhumbaux Get this ellipsoid's Auxiliary `rhumb.RhumbAux`.
	rhumbekx Get this ellipsoid's Elliptic, Krüger `rhumb.Rhumb`.
	rhumbsolve Get this ellipsoid's `RhumbSolve`, the wrapper around utility RhumbSolve, provided the path to the `RhumbSolve` executable is specified with env variable `PYGEODESY_RHUMBSOLVE` or re-/set with this property.
	rhumbx DEPRECATED on 2023.11.28, use property `rhumbekx`.
	rocEquatorial2 Get the meridional and prime-vertical, normal radii of curvature at the equator as `Curvature2Tuple(meridional, prime_vertical)`.
	rocPolar Get the polar meridional (or polar) radius of curvature (`meter`), a2 / 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`, `iteration`, `named`, `named2`, `named3`, `named4`, `sizeof`, `typename` Inherited from `object`: `__class__`

Method Details

Llat(self, lat)

Return the meridional length, the distance along a meridian between the equator and a (geodetic) latitude, see L.

Parameters:

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.

Parameters:

lat - Geodetic latitude (degrees90).

Returns:

The meridional length at lat, negative on southern hemisphere (meter).

Rgeocentric(self, lat)

Compute the geocentric earth radius of (geodetic) latitude.

Parameters:

lat - Latitude (degrees90).

Returns:

Geocentric earth radius (meter).

Raises:

ValueError - Invalid lat.

See Also: Geocentric Radius

Rlat(self, lat)

Average the earth radius between equatoradius at 0 and polaradius at +/-90 degrees latitude.

Parameters:

lat - Latitude (degrees90, str or Ang).

Returns:

Averaged earth radius (meter).

Raises:

RangeError - Latitude lat outside valid range, only if rangerrors is True.
TypeError - Invalid lat.
ValueError - Invalid lat.

eq(self, other)
(Equality operator)

Compare this and an other ellipsoid.

Parameters:

other - The other ellipsoid (Ellipsoid or Ellipsoid2).

Returns:

True if equal, False otherwise.

hash(self)
(Hashing function)

hash(x)

Overrides: object.__hash__: (inherited documentation)

init(self, a, b=None, f_=None, f=None, **name)
(Constructor)

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

Parameters:

a - Equatorial radius, semi-axis (meter).
b - Optional polar radius, semi-axis (meter).
f_ - Inverse flattening: a / (a - b) (float >>> 1.0).
f - Flattening: (a - b) / a (scalar, near zero for spherical).
name - Optional, unique name=NN (str).

Raises:

NameError - Ellipsoid with the same name already exists.
ValueError - Invalid a, b, f_ or f or f_ and f are incompatible.

Overrides: object.__init__

Note: abs(f_) > 1 / EPS or abs(1 / f_) < EPS is forced to 1 / f_ = 0, spherical.

auxAuthalic(self, lat, inverse=False)

Compute the authalic auxiliary latitude (Xi) or the inverse thereof.

Parameters:

lat - The geodetic (or authalic) latitude (degrees90).
inverse - If True, lat is the authalic and return the geodetic latitude (bool).

Returns:

The authalic (or geodetic) latitude in degrees90.

See Also: Inverse-/AuthalicLatitude, Authalic latitude, and Snyder, p 16.

auxConformal(self, lat, inverse=False)

Compute the conformal auxiliary latitude (Chi) or the inverse thereof.

Parameters:

lat - The geodetic (or conformal) latitude (degrees90).
inverse - If True, lat is the conformal and return the geodetic latitude (bool).

Returns:

The conformal (or geodetic) latitude in degrees90.

See Also: Inverse-/ConformalLatitude, Conformal latitude, and Snyder, pp 15-16.

auxGeocentric(self, lat, inverse=False, height=0.0)

Compute the geocentric auxiliary latitude (Theta) or the inverse thereof.

Parameters:

lat - The geodetic (or geocentric) latitude (degrees90).
inverse - If True, lat is the geocentric and return the geocentric latitude (bool).
height - Optional, ellipsoidal height (meter).

Returns:

The geocentric (or geodetic) latitude in degrees90.

See Also: Inverse-/GeocentricLatitude, Geocentric latitude, and Snyder, pp 17-18.

auxIsometric(self, lat, inverse=False)

Compute the isometric auxiliary latitude (Psi) or the inverse thereof.

Parameters:

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 (Beta) or the inverse thereof.

Parameters:

lat - The geodetic (or parametric) latitude (degrees90).
inverse - If True, lat is the parametric and return the geodetic latitude (bool).

Returns:

The parametric (or geodetic) latitude in degrees90.

See Also: Inverse-/ParametricLatitude, Parametric latitude, and Snyder, p 18.

auxRectifying(self, lat, inverse=False)

Compute the rectifying auxiliary latitude (Mu) or the inverse thereof.

Parameters:

lat - The geodetic (or rectifying) latitude (degrees90).
inverse - If True, lat is the rectifying and return the geodetic latitude (bool).

Returns:

The rectifying (or geodetic) latitude in degrees90.

See Also: Inverse-/RectifyingLatitude, Rectifying latitude, and Snyder, pp 16-17.

auxReduced(self, lat, inverse=False)

Compute the parametric auxiliary latitude (Beta) or the inverse thereof.

Parameters:

lat - The geodetic (or parametric) latitude (degrees90).
inverse - If True, lat is the parametric and return the geodetic latitude (bool).

Returns:

The parametric (or geodetic) latitude in degrees90.

See Also: Inverse-/ParametricLatitude, Parametric latitude, and Snyder, p 18.

circle4(self, lat)

Get the equatorial or a parallel circle of latitude.

Parameters:

lat - Geodetic latitude (degrees90 or str).

Returns:

A Circle4Tuple

(radius, height, 
          lat, beta)

Raises:

RangeError - Latitude lat outside valid range, only if rangerrors is True.
TypeError - Invalid lat.
ValueError - Invalid lat.

See Also: Definition of p and z under Parametric (or reduced) latitude, Karney's C++ CircleRadius and CircleHeight and method Triaxial.ellipse5.

degrees2m(self, deg, lat=0)

Convert an arc in degrees to a distance along the equator or along a parallel of (geodetic) latitude.

Parameters:

deg - The angle (degrees).
lat - Parallel latitude (degrees90, str).

Returns:

Distance (meter, same units as the equatorial and polar radii) or 0 for near-polar lat.

Raises:

RangeError - Latitude lat outside valid range and rangerrors is True.
ValueError - Invalid deg or lat.

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

Approximate the distance and (initial) bearing between two points based on the local, flat earth approximation aka Hubeny formula.

Suitable only for distances of several hundred Km or Miles and only between points not near-polar.

Parameters:

lat0 - From latitude (degrees).
lon0 - From longitude (degrees).
lat1 - To latitude (degrees).
lon1 - To longitude (degrees).

Returns:

A Distance2Tuple

(distance, 
          initial)

with distance in same units as this ellipsoid's axes.

Note: The meridional and prime_vertical radii of curvature are taken and scaled at the initial latitude, see roc2.

See Also: Function pygeodesy.flatLocal/pygeodesy.hubeny.

e2s(self, s)

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

Parameters:

s - Sine value (scalar).

Returns:

Norm (float).

Raises:

ValueError - Invalid s.

e2s2(self, s)

Compute 1 - e2 * s**2.

Parameters:

s - Sine value (scalar).

Returns:

Result (float).

Raises:

ValueError - Invalid s.

ecef(self, Ecef=None)

Return ECEF converter.

Parameters:

Ecef - ECEF class to use, default EcefKarney.

Returns:

An ECEF converter for this ellipsoid.

Raises:

TypeError - Invalid Ecef.

See Also: Module pygeodesy.ecef.

es_atanh(self, x)

Compute es * atanh(es * x) or -es * atan(es * x) for oblate respectively prolate ellipsoids where es is the signed (1st) eccentricity.

Raises:

ValueError - Invalid x.

See Also: Function Math::eatanhe.

es_tauf(self, taup)

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

See Also: Karney's C++ method Math::tauf and and Veness' JavaScript method toLatLon.

es_taupf(self, tau)

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

See Also: Karney's C++ method Math::taupf.

geodesic_(self, exact=True)

Get the an exact Geodesic... instance for this ellipsoid.

Parameters:

exact - If bool return GeodesicExact(exact=exact, ...), otherwise a Geodesic, GeodesicExact or GeodesicSolve instance for this ellipsoid.

Returns:

The exact geodesic (Geodesic...).

Raises:

TypeError - Invalid exact.
ValueError - Incompatible exact ellipsoid.

hartzell4(self, pov, los=None)

Compute the intersection of this ellipsoid's surface and a Line-Of-Sight from a Point-Of-View in space.

Parameters:

pov - Point-Of-View outside this ellipsoid (Cartesian, Ecef9Tuple or Vector3d).
los - Line-Of-Sight, direction to this ellipsoid (Los, Vector3d) or True for the normal, perpendicular, plumb to the surface of this ellipsoid or False or None to point to its center.

Returns:

Vector4Tuple(x, y, z, h) with the cartesian coordinates x, y and z of the projection on or the intersection with this ellipsoid and the distance h from pov to (x, y, z) along los, all in meter, conventionally.

Raises:

IntersectionError - Null pov or los vector, or pov is inside this ellipsoid or los points outside this ellipsoid or in opposite direction.
TypeError - Invalid pov or los.

See Also: Satellite Line-of-Sight Intersection with Earth and methods Ellipsoid.height4 and Triaxial.hartzell4.

height4(self, xyz, normal=True)

Compute the projection on and the height of a cartesian above or below this ellipsoid's surface.

Parameters:

xyz - The cartesian (Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
normal - If True, the projection is perpendicular to (the nearest point on) this ellipsoid's surface, otherwise the radial line to this ellipsoid's center (bool).

Returns:

Vector4Tuple(x, y, z, h) with the cartesian coordinates x, y and z of the projection on and the height h above or below this ellipsoid's surface, all in meter, conventionally.

Raises:

ValueError - Null xyz.
TypeError - Non-cartesian xyz.

See Also: Distance to and intersection with an ellipse and methods Ellipsoid.hartzell4 and Triaxial.height4.

m2degrees(self, distance, lat=0)

Convert a distance to an arc in degrees along the equator or along a parallel of (geodetic) latitude.

Parameters:

distance - Distance (meter).
lat - Parallel latitude (degrees90, str).

Returns:

Angle (degrees) or 0 for near-polar lat.

Raises:

RangeError - Latitude lat outside valid range and rangerrors is True.
ValueError - Invalid distance or lat.

m2radians(self, distance, lat=0)

Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude.

Parameters:

distance - Distance (meter).
lat - Parallel latitude (degrees90, str).

Returns:

Angle (radians) or INF for near-polar lat.

Raises:

RangeError - Latitude lat outside valid range and rangerrors is True.
ValueError - Invalid distance or lat.

radians2m(self, rad, lat=0)

Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude.

Parameters:

rad - The angle (radians).
lat - Parallel latitude (degrees90, str).

Returns:

Distance (meter, same units as the equatorial and polar radii) or 0 for near-polar lat.

Raises:

RangeError - Latitude lat outside valid range and rangerrors is True.
ValueError - Invalid rad or lat.

rhumb_(self, exact=True)

Get the an exact Rhumb... instance for this ellipsoid.

Parameters:

exact - If bool or None return Rhumb(exact=exact, ...), otherwise a Rhumb, RhumbAux or RhumbSolve instance for this ellipsoid.

Returns:

The exact rhumb (Rhumb...).

Raises:

TypeError - Invalid exact.
ValueError - Incompatible exact ellipsoid.

roc1_(self, sa, ca=None)

Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, unscaled.

Parameters:

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.

Parameters:

lat - Latitude (degrees90).
scaled - Scale prime_vertical by cos(radians(lat)) (bool).

Returns:

An Curvature2Tuple

(meridional, 
          prime_vertical)

with the radii of curvature.

Raises:

ValueError - Invalid lat.

See Also: Methods roc2_ and roc1_, Local, flat earth approximation and meridional and prime vertical Radii of Curvature.

roc2_(self, phi, scaled=False)

Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude.

Parameters:

phi - Latitude (radians).
scaled - Scale prime_vertical by cos(phi) (bool).

Returns:

An Curvature2Tuple

(meridional, 
          prime_vertical)

with the radii of curvature.

Raises:

ValueError - Invalid phi.

See Also: Methods roc2 and roc1_, property rocEquatorial2, Local, flat earth approximation and the meridional and prime vertical Radii of Curvature.

rocAzimuth(self, lat, azimuth)

Compute the directional radius of curvature of (geodetic) latitude and azimuth compass direction.

See Also: Method rocBearing for details, using azimuth for bearing.

rocBearing(self, lat, bearing)

Compute the directional radius of curvature of (geodetic) latitude and bearing compass direction.

Parameters:

lat - Latitude (degrees90).
bearing - Direction (compass degrees360).

Returns:

Directional radius of curvature (meter).

Raises:

RangeError - Latitude lat outside valid range and rangerrors is True.
ValueError - Invalid lat or bearing.

See Also: Radii of Curvature

rocGauss(self, lat)

Compute the Gaussian radius of curvature of (geodetic) latitude.

Parameters:

lat - Latitude (degrees90).

Returns:

Gaussian radius of curvature (meter).

Raises:

ValueError - Invalid lat.

See Also: Non-directional Radii of Curvature

rocMean(self, lat)

Compute the mean radius of curvature of (geodetic) latitude.

Parameters:

lat - Latitude (degrees90).

Returns:

Mean radius of curvature (meter).

Raises:

ValueError - Invalid lat.

See Also: Non-directional Radii of Curvature

rocMeridional(self, lat)

Compute the meridional radius of curvature of (geodetic) latitude.

Parameters:

lat - Latitude (degrees90).

Returns:

Meridional radius of curvature (meter).

Raises:

ValueError - Invalid lat.

See Also: Methods roc2 and roc2_, Local, flat earth approximation and Radii of Curvature.

rocPrimeVertical(self, lat)

Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature.

Parameters:

lat - Latitude (degrees90).

Returns:

Prime-vertical radius of curvature (meter).

Raises:

ValueError - Invalid lat.

See Also: Methods roc2, roc2_ and roc1_, Local, flat earth approximation and Radii of Curvature.

rocTransverse(self, lat)

Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature.

Parameters:

lat - Latitude (degrees90).

Returns:

Prime-vertical radius of curvature (meter).

Raises:

ValueError - Invalid lat.

See Also: Methods roc2, roc2_ and roc1_, Local, flat earth approximation and Radii of Curvature.

toEllipse(self, **name)

Get this ellipsoid's meridional ellipse Ellipse.

Parameters:

name - Optional, unique name=NN (str).

toEllipsoid2(self, **name)

Get a copy of this ellipsoid as an Ellipsoid2.

Parameters:

name - Optional, unique name=NN (str).

See Also: Property a_f.

toStr(self, prec=8, terse=4, **sep_name)

Return this ellipsoid as a text string.

Parameters:

prec - Number of decimal digits, unstripped (int).
terse - Limit the number of items (int, 0...18), use terse=0 or =None for all.
sep_name - Optional name=NN (str) or None to exclude this ellipsoid's name and separator sep=", " to join the items (str).

Returns:

This Ellipsoid's attributes (str).

Overrides: named._Named.toStr

toTriaxial(self, **name)

Convert this ellipsoid to a Triaxial_.

Parameters:

name - Optional name=NN (str).

Returns:

A Triaxial_ or Triaxial with the X axis pointing east and Z pointing north.

See Also: Method Triaxial_.toEllipsoid.

Property Details

A

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

Get Method:: unreachable.A(self) - Get the UTM meridional (or rectifying) radius (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Note: A * PI / 2 ≈= L, the quarter meridian.

See Also: Meridian arc unit Q, the mean, meridional length per radian.

AlphaKs

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

Get Method:: unreachable.AlphaKs(self) - Get the Krüger Alpha series coefficients (KsOrder-tuple).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

BetaKs

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

Get Method:: unreachable.BetaKs(self) - Get the Krüger Beta series coefficients (KsOrder-tuple).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

KsOrder

Class property with a .name attribute.

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

L

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

Get Method:: unreachable.L(self) - Get the quarter meridian L, aka the polar distance along a meridian between the equator and a pole (meter), b * Elliptic(-e2 / (1 - e2)).cE or b * PI / 2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

R1

Get the mean earth radius per IUGG (meter), (2 * a + b) / 3 == a * (1 - f / 3).

Get Method:: unreachable.R1(self) - Get the mean earth radius per IUGG (meter), (2 * a + b) / 3 == a * (1 - f / 3).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Earth radius and method Rgeometric.

R2

Get the authalic earth radius (meter), sqrt(c2).

Get Method:: unreachable.R2(self) - Get the authalic earth radius (meter), sqrt(c2).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: R2x, c2, area and Earth radius.

R2x

Get the authalic earth radius (meter), sqrt(c2x).

Get Method:: unreachable.R2x(self) - Get the authalic earth radius (meter), sqrt(c2x).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: R2, c2x and areax.

R3

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

Get Method:: unreachable.R3(self) - Get the volumetric earth radius (meter), (a * a * b)**(1/3).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Earth radius and volume.

Rauthalic

Get the authalic earth radius (meter), sqrt(c2).

Get Method:: unreachable.R2(self) - Get the authalic earth radius (meter), sqrt(c2).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: R2x, c2, area and Earth radius.

Rauthalicx

Get the authalic earth radius (meter), sqrt(c2x).

Get Method:: unreachable.R2x(self) - Get the authalic earth radius (meter), sqrt(c2x).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: R2, c2x and areax.

Rbiaxial

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

Get Method:: unreachable.Rbiaxial(self) - Get the biaxial, quadratic mean earth radius (meter), sqrt((a**2 + b**2) / 2).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Rtriaxial

Requatorial

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

Get Method:: unreachable.a(self) - Get the equatorial radius, semi-axis (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Rgeometric

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

Get Method:: unreachable.Rgeometric(self) - Get the geometric mean earth radius (meter), sqrt(a * b).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: R1.

Rmean

Get the mean earth radius per IUGG (meter), (2 * a + b) / 3 == a * (1 - f / 3).

Get Method:: unreachable.R1(self) - Get the mean earth radius per IUGG (meter), (2 * a + b) / 3 == a * (1 - f / 3).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Earth radius and method Rgeometric.

Rpolar

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

Get Method:: unreachable.b(self) - Get the polar radius, semi-axis (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Rquadratic

DEPRECATED, use property Rbiaxial or Rtriaxial.

Get Method:: unreachable.Rquadratic(self) - DEPRECATED, use property Rbiaxial or Rtriaxial.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Rr

DEPRECATED, use property Rrectifying.

Get Method:: unreachable.Rr(self) - DEPRECATED, use property Rrectifying.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Rrectifying

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

Get Method:: unreachable.Rrectifying(self) - Get the rectifying earth radius (meter), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Earth radius.

Rs

DEPRECATED, use property Rgeometric.

Get Method:: unreachable.Rs(self) - DEPRECATED, use property Rgeometric.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Rtriaxial

Get the triaxial, quadratic mean earth radius (meter), sqrt((3 * a**2 + b**2) / 4).

Get Method:: unreachable.Rtriaxial(self) - Get the triaxial, quadratic mean earth radius (meter), sqrt((3 * a**2 + b**2) / 4).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Rbiaxial

Rvolumetric

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

Get Method:: unreachable.R3(self) - Get the volumetric earth radius (meter), (a * a * b)**(1/3).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Earth radius and volume.

a

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

Get Method:: unreachable.a(self) - Get the equatorial radius, semi-axis (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

a2

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

Get Method:: unreachable.a2(self) - Get the equatorial radius squared (meter squared), a**2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

a2_

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

Get Method:: unreachable.a2_(self) - Get the inverse of the equatorial radius squared (meter squared), 1 / a**2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

a2_b

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

Get Method:: unreachable.a2_b(self) - Get the polar meridional (or polar) radius of curvature (meter), a**2 / b.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Note: Symbol c is used by IUGG and IERS for the polar radius of curvature, see c2 and R2 or Rauthalic.

a2_b2

Get the ratio equatorial over polar radius squared (float), (a / b)**2 == 1 / (1 - e**2) == 1 / (1 - e2) == 1 / e21.

Get Method:: unreachable.a2_b2(self) - Get the ratio equatorial over polar radius squared (float), (a / b)**2 == 1 / (1 - e**2) == 1 / (1 - e2) == 1 / e21.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

a_b

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

Get Method:: unreachable.a_b(self) - Get the ratio equatorial over polar radius (float), a / b == 1 / (1 - f).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

a_f

Get the equatorial radius and flattening (a_f2Tuple), see method toEllipsoid2.

Get Method:: unreachable.a_f(self) - Get the equatorial radius and flattening (a_f2Tuple), see method toEllipsoid2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

a_f2

Get the equatorial radius and flattening (a_f2Tuple), see method toEllipsoid2.

Get Method:: unreachable.a_f(self) - Get the equatorial radius and flattening (a_f2Tuple), see method toEllipsoid2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

area

Get the ellipsoid's surface area (meter squared), 4 * PI * c2.

Get Method:: unreachable.area(self) - Get the ellipsoid's surface area (meter squared), 4 * PI * c2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Properties areax, c2 and R2 and functions ellipsoidalExact.areaOf and ellipsoidalKarney.areaOf.

areax

Get the ellipsoid's surface area (meter squared), 4 * PI * c2x, more accurate for very oblate ellipsoids.

Get Method:: unreachable.areax(self) - Get the ellipsoid's surface area (meter squared), 4 * PI * c2x, more accurate for very oblate ellipsoids.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Properties area, c2x and R2x, class GeodesicExact and functions ellipsoidalExact.areaOf and ellipsoidalKarney.areaOf.

b

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

Get Method:: unreachable.b(self) - Get the polar radius, semi-axis (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

b2

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

Get Method:: unreachable.b2(self) - Get the polar radius squared (float), b**2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

b2_a

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

Get Method:: unreachable.b2_a(self) - Get the equatorial meridional radius of curvature (meter), b**2 / a, see rocMeridional(0).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

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 == e21.

Get Method:: unreachable.b2_a2(self) - Get the ratio polar over equatorial radius squared (float), (b / a)**2 == (1 - f)**2 == 1 - e**2 == e21.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

b_a

Get the ratio polar over equatorial radius (float), b / a == f1 == 1 - f.

Get Method:: unreachable.b_a(self) - Get the ratio polar over equatorial radius (float), b / a == f1 == 1 - f.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Property f1.

c

DEPRECATED, use property R2 or Rauthalic.

Get Method:: unreachable.c(self) - DEPRECATED, use property R2 or Rauthalic.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

c2

Get the authalic earth radius squared (meter squared).

Get Method:: unreachable.c2(self) - Get the authalic earth radius squared (meter squared).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Properties c2x, area, R2, Rauthalic, Karney's equation (60) and C++ Ellipsoid.Area, Authalic radius, Surface area and surface area.

c2x

Get the authalic earth radius squared (meter squared), more accurate for very oblate ellipsoids.

Get Method:: unreachable.c2x(self) - Get the authalic earth radius squared (meter squared), more accurate for very oblate ellipsoids.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Properties c2, areax, R2x, Rauthalicx, class GeodesicExact and Karney's comments at C++ attribute GeodesicExact._c2.

e

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

Get Method:: unreachable.e(self) - Get the unsigned, (1st) eccentricity (float), sqrt(1 - (b / a)**2)), see a_b2e.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Property es.

e12

DEPRECATED, use property e21.

Get Method:: unreachable.e12(self) - DEPRECATED, use property e21.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e2

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

Get Method:: unreachable.e2(self) - Get the signed, (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e21

Get 1 less 1st eccentricity squared (float), 1 - e**2 == 1 - e2 == (1 - f)**2 == b**2 / a**2, see b2_a2.

Get Method:: unreachable.e21(self) - Get 1 less 1st eccentricity squared (float), 1 - e**2 == 1 - e2 == (1 - f)**2 == b**2 / a**2, see b2_a2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e22

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

Get Method:: unreachable.e22(self) - Get the signed, 2nd eccentricity squared (float), e2 / (1 - e2) == e2 / (1 - f)**2 == (a / b)**2 - 1, see a_b2e22.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e22abs

Get the unsigned, 2nd eccentricity squared (float).

Get Method:: unreachable.e22abs(self) - Get the unsigned, 2nd eccentricity squared (float).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e2abs

Get the unsigned, (1st) eccentricity squared (float).

Get Method:: unreachable.e2abs(self) - Get the unsigned, (1st) eccentricity squared (float).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e32

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

Get Method:: unreachable.e32(self) - Get the signed, 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see a_b2e32.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e32abs

Get the unsigned, 3rd eccentricity squared (float).

Get Method:: unreachable.e32abs(self) - Get the unsigned, 3rd eccentricity squared (float).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

e4

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

Get Method:: unreachable.e4(self) - Get the unsignd, (1st) eccentricity to 4th power (float), e**4 == e2**2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

eccentricity

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

Get Method:: unreachable.e(self) - Get the unsigned, (1st) eccentricity (float), sqrt(1 - (b / a)**2)), see a_b2e.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Property es.

eccentricity1st2

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

Get Method:: unreachable.e2(self) - Get the signed, (1st) eccentricity squared (float), f * (2 - f) == 1 - (b / a)**2, see a_b2e2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

eccentricity2nd2

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

Get Method:: unreachable.e22(self) - Get the signed, 2nd eccentricity squared (float), e2 / (1 - e2) == e2 / (1 - f)**2 == (a / b)**2 - 1, see a_b2e22.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

eccentricity3rd2

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

Get Method:: unreachable.e32(self) - Get the signed, 3rd eccentricity squared (float), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see a_b2e32.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

equatoradius

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

Get Method:: unreachable.a(self) - Get the equatorial radius, semi-axis (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

equatorimeter

Get the ellipsoid's equatorial perimeter (meter).

Get Method:: unreachable.equatorimeter(self) - Get the ellipsoid's equatorial perimeter (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

es

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

Get Method:: unreachable.es(self) - Get the signed (1st) eccentricity (float).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Property e.

es_c

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

Get Method:: unreachable.es_c(self) - Get (1 - f) * exp(es_atanh(1)) (float), b_a * exp(es_atanh(1)).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

f

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

Get Method:: unreachable.f(self) - Get the flattening (scalar), (a - b) / a, 0 for spherical, negative for prolate.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

f1

Get the 1 - flattening (float), f1 == 1 - f == b / a.

Get Method:: unreachable.f1(self) - Get the 1 - flattening (float), f1 == 1 - f == b / a.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Property b_a.

f2

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

Get Method:: unreachable.f2(self) - Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

f_

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

Get Method:: unreachable.f_(self) - Get the inverse flattening (scalar), 1 / f == a / (a - b), 0 for spherical, see a_b2f_.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

flattening

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

Get Method:: unreachable.f(self) - Get the flattening (scalar), (a - b) / a, 0 for spherical, negative for prolate.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

flattening1st

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

Get Method:: unreachable.f(self) - Get the flattening (scalar), (a - b) / a, 0 for spherical, negative for prolate.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

flattening2nd

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

Get Method:: unreachable.f2(self) - Get the 2nd flattening (float), (a - b) / b == f / (1 - f), 0 for spherical, see a_b2f2.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

flattening3rd

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

Get Method:: unreachable.n(self) - Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

geodesic

DEPRECATED, use property geodesicw.

Get Method:: unreachable.geodesic(self) - DEPRECATED, use property geodesicw.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

geodesicw

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

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

geodesicx

Get this ellipsoid's exact GeodesicExact.

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

geodsolve

Get this ellipsoid's GeodesicSolve, the wrapper around utility GeodSolve, provided the path to the GeodSolve executable is specified with env variable PYGEODESY_GEODSOLVE or re-/set with this property..

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

isEllipsoidal

Is this model ellipsoidal (bool)?

Get Method:: unreachable.isEllipsoidal(self) - Is this model ellipsoidal (bool)?
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

isOblate

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

Get Method:: unreachable.isOblate(self) - Is this ellipsoid oblate (bool)? Prolate or spherical otherwise.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

isProlate

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

Get Method:: unreachable.isProlate(self) - Is this ellipsoid prolate (bool)? Oblate or spherical otherwise.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

isSpherical

Is this ellipsoid spherical (bool)?

Get Method:: unreachable.isSpherical(self) - Is this ellipsoid spherical (bool)?
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

majoradius

DEPRECATED, use property a or Requatorial.

Get Method:: unreachable.majoradius(self) - DEPRECATED, use property a or Requatorial.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

minoradius

DEPRECATED, use property b, polaradius or Rpolar.

Get Method:: unreachable.minoradius(self) - DEPRECATED, use property b, polaradius or Rpolar.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

n

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

Get Method:: unreachable.n(self) - Get the 3rd flattening (float), f / (2 - f) == (a - b) / (a + b), see a_b2n.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

polaradius

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

Get Method:: unreachable.b(self) - Get the polar radius, semi-axis (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

polarimeter

Get the ellipsoid's polar, meridional perimeter (meter).

Get Method:: unreachable.polarimeter(self) - Get the ellipsoid's polar, meridional perimeter (meter).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

quarteradius

DEPRECATED, use property L or method Llat.

Get Method:: unreachable.quarteradius(self) - DEPRECATED, use property L or method Llat.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

rhumbaux

Get this ellipsoid's Auxiliary rhumb.RhumbAux.

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

rhumbekx

Get this ellipsoid's Elliptic, Krüger rhumb.Rhumb.

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

rhumbsolve

Get this ellipsoid's RhumbSolve, the wrapper around utility RhumbSolve, provided the path to the RhumbSolve executable is specified with env variable PYGEODESY_RHUMBSOLVE or re-/set with this property.

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

rhumbx

DEPRECATED on 2023.11.28, use property rhumbekx.

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

rocEquatorial2

Get the meridional and prime-vertical, normal radii of curvature at the equator as Curvature2Tuple(meridional, prime_vertical).

Get Method:: unreachable.rocEquatorial2(self) - Get the meridional and prime-vertical, normal radii of curvature at the equator as Curvature2Tuple(meridional, prime_vertical).
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: Methods rocMeridional and rocPrimeVertical, properties b2_a, a2_b, rocPolar and polar and equatorial Radii of Curvature.

rocPolar

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

Get Method:: unreachable.a2_b(self) - Get the polar meridional (or polar) radius of curvature (meter), a**2 / b.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

Note: Symbol c is used by IUGG and IERS for the polar radius of curvature, see c2 and R2 or Rauthalic.

volume

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

Get Method:: unreachable.volume(self) - Get the ellipsoid's volume (meter**3), 4 / 3 * PI * R3**3.
Set Method:: unreachable._fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: unreachable._fdel(inst) - Zap the cached/memoized property value.

See Also: R3.

Class Ellipsoid

Llat(self, lat)

Lmeridian(self, lat)

Rgeocentric(self, lat)

Rlat(self, lat)

__eq__(self, other) (Equality operator)

__hash__(self) (Hashing function)

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

auxAuthalic(self, lat, inverse=False)

auxConformal(self, lat, inverse=False)

auxGeocentric(self, lat, inverse=False, height=0.0)

auxIsometric(self, lat, inverse=False)

auxParametric(self, lat, inverse=False)

auxRectifying(self, lat, inverse=False)

auxReduced(self, lat, inverse=False)

circle4(self, lat)

degrees2m(self, deg, lat=0)

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

e2s(self, s)

e2s2(self, s)

ecef(self, Ecef=None)

es_atanh(self, x)

es_tauf(self, taup)

es_taupf(self, tau)

geodesic_(self, exact=True)

hartzell4(self, pov, los=None)

height4(self, xyz, normal=True)

m2degrees(self, distance, lat=0)

m2radians(self, distance, lat=0)

radians2m(self, rad, lat=0)

rhumb_(self, exact=True)

roc1_(self, sa, ca=None)

roc2(self, lat, scaled=False)

roc2_(self, phi, scaled=False)

rocAzimuth(self, lat, azimuth)

rocBearing(self, lat, bearing)

rocGauss(self, lat)

rocMean(self, lat)

rocMeridional(self, lat)

rocPrimeVertical(self, lat)

rocTransverse(self, lat)

toEllipse(self, **name)

toEllipsoid2(self, **name)

toStr(self, prec=8, terse=4, **sep_name)

toTriaxial(self, **name)

A

AlphaKs

BetaKs

KsOrder

L

R1

R2

R2x

R3

Rauthalic

Rauthalicx

Rbiaxial

Requatorial

Rgeometric

Rmean

Rpolar

Rquadratic

Rr

Rrectifying

Rs

Rtriaxial

Rvolumetric

a

a2

a2_

a2_b

a2_b2

a_b

a_f

a_f2

area

areax

b

b2

b2_a

eq(self, other)
(Equality operator)

hash(self)
(Hashing function)

init(self, a, b=None, f_=None, f=None, **name)
(Constructor)