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object --+ | named._Named --+ | named._NamedBase --+ | named._NamedEnumItem --+ | 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.
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Inherited from Inherited from Inherited from Inherited from |
Class Variables | |
_f_ = 0 hash(x) |
Properties | |
a Get the equatorial radius, semi-axis ( meter ).
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equatoradius Get the equatorial radius, semi-axis ( meter ).
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a2 Get the equatorial radius squared ( meter**2 ), a**2.
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a2_ Get the inverse of the equatorial radius squared ( meter**2 ), 1 / a**2.
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a_b Get the ratio equatorial over polar radius ( float ), a / b == 1
/ (1 - f).
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a2_b Get the polar meridional radius of curvature ( meter ), a**2 / b.
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a2_b2 Get the ratio equatorial over polar radius squared ( float ), (a / b)**2
== 1 / (1 - e**2) == 1 / (1 -
e2) == 1 / e12.
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a_f Get the equatorial radius and flattening (a_f2Tuple). |
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A Get the UTM meridional (or rectifying) radius ( meter ).
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AlphaKs Get the Krüger Alpha series coefficients ( KsOrder -tuple ).
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area Get the ellipsoid's surface area ( meter**2 ), 4 * PI * c2.
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areax Get the ellipsoid's surface area ( meter**2 ), 4 * PI * c2x, more accurate for very oblate
ellipsoids.
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b Get the polar radius, semi-axis ( meter ).
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polaradius Get the polar radius, semi-axis ( meter ).
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b_a Get the ratio polar over equatorial radius ( float ), b / a == 1
- f.
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b2 Get the polar radius squared ( float ), b**2.
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b2_a Get the equatorial meridional radius of curvature ( meter ), b**2 / a, see
rocMeridional (0) .
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b2_a2 Get the ratio polar over equatorial radius squared ( float ), (b / a)**2
== (1 - f)**2 == 1 - e**2 ==
e12 .
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BetaKs Get the Krüger Beta series coefficients ( KsOrder -tuple ).
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c DEPRECATED, use property R2 or Rauthalic .
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c2 Get the authalic earth radius squared ( meter**2 ).
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c2x Get the authalic earth radius squared ( meter**2 ), more accurate for very oblate
ellipsoids.
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e Get the (1st) eccentricity ( float ), sqrt(1 - (b / a)**2)), see a_b2e .
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eccentricity Get the (1st) eccentricity ( float ), sqrt(1 - (b / a)**2)), see a_b2e .
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e2 Get the (1st) eccentricity squared ( float ), f * (2 - f) == 1 - (b / a)**2, see
a_b2e2 .
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eccentricity2 Get the (1st) eccentricity squared ( float ), f * (2 - f) == 1 - (b / a)**2, see
a_b2e2 .
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e2abs Get abs value of the (1st) eccentricity squared
(float ).
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e12 Get 1 less (1st) eccentricity squared ( float ), 1 - e**2 == (1 - f)**2 == b**2 /
a**2, see b2_a2 .
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e22 Get the 2nd eccentricity squared ( float ), e2 / (1 - e2) == e2 / (1 - f)**2 == (a / b)**2 - 1,
see a_b2e22 .
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eccentricity2nd2 Get the 2nd eccentricity squared ( float ), e2 / (1 - e2) == e2 / (1 - f)**2 == (a / b)**2 - 1,
see a_b2e22 .
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e22abs Get abs value of the (2nd) eccentricity squared
(float ).
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e32 Get the 3rd eccentricity squared ( float ), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see
a_b2e32 .
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eccentricity3rd2 Get the 3rd eccentricity squared ( float ), e2 / (2 - e2) == (a**2 - b**2) / (a**2 + b**2), see
a_b2e32 .
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e32abs Get abs value of the (3rd) eccentricity squared
(float ).
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e4 Get the (1st) eccentricity to 4th power ( float ),
e**4 == e2**2.
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es Get the (1st) eccentricity signed ( float ).
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es_c Get (1 - f) * exp(es_atanh(1)) ( float ), b_a * exp(es_atanh(1)).
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f Get the flattening ( float ), (a -
b) / a, 0 for spherical, negative for prolate.
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flattening Get the flattening ( float ), (a -
b) / a, 0 for spherical, negative for prolate.
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f_ Get the inverse flattening ( float ), 1 / f == a / (a - b),
0 for spherical, see a_b2f_ .
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f2 Get the 2nd flattening ( float ), (a - b) / b == f / (1 - f), 0 for
spherical, see a_b2f2 .
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flattening2nd Get the 2nd flattening ( float ), (a - b) / b == f / (1 - f), 0 for
spherical, see a_b2f2 .
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geodesic Get this ellipsoid's wrapped Karney Geodesic, provided the geographiclib package is installed. |
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geodesicx Get this ellipsoid's GeodesicExact. |
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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 .
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isEllipsoidal Is this model ellipsoidal ( bool )?
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isOblate Is this ellipsoid oblate ( bool )? Prolate
or spherical otherwise.
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isProlate Is this ellipsoid prolate ( bool )? Oblate
or spherical otherwise.
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isSpherical Is this model spherical ( bool )?
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KsOrder Property to get and set the Krüger series' order ( int ), see properties AlphaKs ,
BetaKs .
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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.
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Mabcd Get the OSGR meridional coefficients ( 4-Tuple ),
Airy130 only.
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majoradius DEPRECATED, use property a or Requatorial .
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minoradius DEPRECATED, use property b or Rpolar .
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n Get the 3rd flattening ( float ), f
/ (2 - f) == (a - b) / (a + b), see a_b2n .
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flattening3rd Get the 3rd flattening ( float ), f
/ (2 - f) == (a - b) / (a + b), see a_b2n .
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quarteradius DEPRECATED, use property L or method Llat .
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R1 Get the mean earth radius per IUGG ( meter ), (2 * a + b) / 3.
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Rmean Get the mean earth radius per IUGG ( meter ), (2 * a + b) / 3.
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R2 Get the authalic earth radius ( meter ), sqrt(c2).
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Rauthalic Get the authalic earth radius ( meter ), sqrt(c2).
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R2x Get the authalic earth radius ( meter ), sqrt(c2x).
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Rauthalicx Get the authalic earth radius ( meter ), sqrt(c2x).
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R3 Get the volumetric earth radius ( meter ), (a * a * b)**(1/3).
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Rvolumetric Get the volumetric earth radius ( meter ), (a * a * b)**(1/3).
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Rbiaxial Get the biaxial, quadratic mean earth radius ( meter ), sqrt((a**2 + b**2) / 2).
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Requatorial Get the equatorial radius, semi-axis ( meter ).
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Rgeometric Get the geometric mean earth radius ( meter ), sqrt(a * b).
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Rpolar Get the polar radius, semi-axis ( meter ).
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Rquadratic DEPRECATED, use property Rbiaxial or
Rtriaxial .
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Rr DEPRECATED, use property Rrectifying .
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Rrectifying Get the rectifying earth radius ( meter ), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
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rocPolar Get the polar meridional radius of curvature ( meter ), a**2 / b.
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Rs DEPRECATED, use property Rgeometric .
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Rtriaxial Get the triaxial, quadratic mean earth radius ( meter ), sqrt((3 * a**2 + b**2) /
4).
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volume Get the ellipsoid's volume ( meter**3 ), 4 / 3 * PI * R3**3.
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Inherited from Inherited from Inherited from |
Method Details |
New Ellipsoid from equatorial and polar radius or equatorial radius and inverse flattening.
Note: abs(f_) > 1 / EPS or abs(1 / f_) < EPS is forced to 1 / f_ = 0, spherical. |
Compare this and an other ellipsoid.
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Compute the authalic auxiliary latitude or inverse thereof.
See Also: Inverse-/AuthalicLatitude, Authalic latitude, and Snyder, p 16. |
Compute the conformal auxiliary latitude or inverse thereof.
See Also: Inverse-/ConformalLatitude, Conformal latitude, and Snyder, pp 15-16. |
Compute the geocentric auxiliary latitude or inverse thereof.
See Also: Inverse-/GeocentricLatitude, Geocentric latitude, and Snyder<, pp 17-18. |
Compute the isometric auxiliary latitude or inverse thereof.
Note:
The isometric latitude for geodetic See Also: Inverse-/IsometricLatitude, Isometric latitude, and Snyder, pp 15-16. |
Compute the parametric auxiliary latitude or inverse thereof.
See Also: Inverse-/ParametricLatitude, Parametric latitude, and Snyder, p 18. |
Compute the parametric auxiliary latitude or inverse thereof.
See Also: Inverse-/ParametricLatitude, Parametric latitude, and Snyder, p 18. |
Compute the rectifying auxiliary latitude or inverse thereof.
See Also: Inverse-/RectifyingLatitude, Rectifying latitude, and Snyder, pp 16-17. |
Get the equatorial or a parallel circle of latitude.
See Also: Definition of p and z under Parametric (or reduced) latitude and Karney's C++ CircleRadius and CircleHeight. |
Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude.
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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.
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Return ECEF converter.
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Compute norm sqrt(1 - e2 * s**2).
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Compute 1 - e2 * s**2.
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Compute es * atanh(es * x) where es is the signed (1st) eccentricity.
See Also: Function Math::eatanhe. |
Compute Karney's equations (19), (20) and (21). See Also: Math::tauf. |
Compute Karney's equations (7), (8) and (9). See Also: Math::taupf. |
Return the meridional length, the distance along a meridian
between the equator and a (geodetic) latitude, see
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Return the meridional length, the distance along a meridian
between the equator and a (geodetic) latitude, see
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Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude.
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Convert a distance to an angle along the equator or along a parallel of (geodetic) latitude.
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Convert an angle to the distance along the equator or along a parallel of (geodetic) latitude.
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Compute the geocentric earth radius of (geodetic) latitude.
See Also: Geocentric Radius |
Approximate the earth radius of (geodetic) latitude.
Note:
See Also:
Method |
Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, unscaled.
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Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude.
See Also: Methods roc2_ and roc1_ and Local, flat earth approximation and meridional and prime vertical Radii of Curvature. |
Compute the meridional and prime-vertical, normal radii of curvature of (geodetic) latitude.
See Also: Methods roc2 and roc1_ and Local, flat earth approximation and the meridional and prime vertical Radii of Curvature. |
Compute the directional radius of curvature of (geodetic) latitude and compass direction.
See Also: Radii of Curvature |
Compute the Gaussian radius of curvature of (geodetic) latitude.
See Also: Radii of Curvature |
Compute the mean radius of curvature of (geodetic) latitude.
See Also: Radii of Curvature |
Compute the meridional radius of curvature of (geodetic) latitude.
See Also: Methods roc2 and roc2_ and Local, flat earth approximation and Radii of Curvature. |
Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature.
See Also: Methods roc2, roc2_ and roc1_ and Local, flat earth approximation and Radii of Curvature. |
Compute the prime-vertical, normal radius of curvature of (geodetic) latitude, aka the transverse radius of curvature.
See Also: Methods roc2, roc2_ and roc1_ and Local, flat earth approximation and Radii of Curvature. |
Return this ellipsoid as a text string.
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Property Details |
aGet the equatorial radius, semi-axis (
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equatoradiusGet the equatorial radius, semi-axis (
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a2Get the equatorial radius squared
(
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a2_Get the inverse of the equatorial radius squared
(
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a_bGet the ratio equatorial over polar radius
(
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a2_bGet the polar meridional radius of curvature
(
See Also: Radii of Curvature and Moritz, H. (1980), Geodetic Reference System 1980. Note:
Symbol |
a2_b2Get the ratio equatorial over polar radius
squared (
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a_fGet the equatorial radius and flattening (a_f2Tuple).
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AGet the UTM meridional (or rectifying) radius
(
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AlphaKsGet the Krüger Alpha series coefficients
(
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areaGet the ellipsoid's surface area (
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areaxGet the ellipsoid's surface area (
See Also: area, c2x, R2x and GeodesicExact. |
bGet the polar radius, semi-axis (
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polaradiusGet the polar radius, semi-axis (
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b_aGet the ratio polar over equatorial radius
(
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b2Get the polar radius squared (
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b2_aGet the equatorial meridional radius of curvature
(
See Also: Radii of Curvature. |
b2_a2Get the ratio polar over equatorial radius
squared (
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BetaKsGet the Krüger Beta series coefficients
(
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cDEPRECATED, use property
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c2Get the authalic earth radius squared
(
See Also: c2x, area, R2, Rauthalic, Karney's equation 60 and C++ Ellipsoid.Area(), Authalic radius, Surface area and surface area. |
c2xGet the authalic earth radius squared
(
See Also: c2, areax, R2x, Rauthalicx, GeodesicExact and Karney's comments at C++ attribute GeodesicExact._c2. |
eGet the (1st) eccentricity (
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eccentricityGet the (1st) eccentricity (
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e2Get the (1st) eccentricity squared (
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eccentricity2Get the (1st) eccentricity squared (
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e2absGet
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e12Get 1 less (1st) eccentricity squared (
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e22Get the 2nd eccentricity squared (
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eccentricity2nd2Get the 2nd eccentricity squared (
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e22absGet
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e32Get the 3rd eccentricity squared (
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eccentricity3rd2Get the 3rd eccentricity squared (
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e32absGet
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e4Get the (1st) eccentricity to 4th power (
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esGet the (1st) eccentricity signed (
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es_cGet (1 - f) * exp(es_atanh(1))
(
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fGet the flattening (
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flatteningGet the flattening (
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f_Get the inverse flattening (
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f2Get the 2nd flattening (
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flattening2ndGet the 2nd flattening (
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geodesicGet this ellipsoid's wrapped Karney Geodesic, provided the geographiclib package is installed.
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geodesicxGet this ellipsoid's GeodesicExact.
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geodsolveGet this ellipsoid's GeodesicSolve, the wrapper around utility GeodSolve, provided the path to the
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isEllipsoidalIs this model ellipsoidal (
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isOblateIs this ellipsoid oblate (
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isProlateIs this ellipsoid prolate (
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isSphericalIs this model spherical (
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KsOrderProperty to get and set the Krüger series' order
(
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LGet the quarter meridian
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MabcdGet the OSGR meridional coefficients (
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majoradiusDEPRECATED, use property
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minoradiusDEPRECATED, use property
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nGet the 3rd flattening (
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flattening3rdGet the 3rd flattening (
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quarteradiusDEPRECATED, use property
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R1Get the mean earth radius per IUGG (
See Also:
Earth radius and method |
RmeanGet the mean earth radius per IUGG (
See Also:
Earth radius and method |
R2Get the authalic earth radius (
See Also:
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RauthalicGet the authalic earth radius (
See Also:
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R2xGet the authalic earth radius (
See Also:
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RauthalicxGet the authalic earth radius (
See Also:
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R3Get the volumetric earth radius (
See Also:
Earth radius and |
RvolumetricGet the volumetric earth radius (
See Also:
Earth radius and |
RbiaxialGet the biaxial, quadratic mean earth radius
(
See Also:
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RequatorialGet the equatorial radius, semi-axis (
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RgeometricGet the geometric mean earth radius (
See Also:
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RpolarGet the polar radius, semi-axis (
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RquadraticDEPRECATED, use property
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RrDEPRECATED, use property
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RrectifyingGet the rectifying earth radius (
See Also: Earth radius. |
rocPolarGet the polar meridional radius of curvature
(
See Also: Radii of Curvature and Moritz, H. (1980), Geodetic Reference System 1980. Note:
Symbol |
RsDEPRECATED, use property
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RtriaxialGet the triaxial, quadratic mean earth radius
(
See Also:
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volumeGet the ellipsoid's volume (
See Also:
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