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object --+ | named._Named --+ | named._NamedBase --+ | named._NamedEnumItem --+ | Ellipsoid
Ellipsoid with equatorial and polar radius, flattening, inverse flattening and other, often used, cached attributes, supporting spherical and oblate and prolate ellipsoidal models.
Instance Methods | |||
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Inherited from Inherited from Inherited from Inherited from |
Class Variables | |
_f_ = 0 hash(x) |
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_a2_ = None hash(x) |
Properties | |
a Get the equatorial (major) radius, semi-axis ( meter ).
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equatoradius Get the equatorial (major) radius, semi-axis ( meter ).
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a2 Get the equatorial (major) radius squared ( float ), a**2.
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a2_ Get the inverse of the equatorial (major) radius squared ( float ), 1 / a**2.
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a_b Get ratio a / b ( float ).
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a2_b Get the polar meridional radius of curvature ( meter ), a**2 / b, see
rocPolar .
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a_f Get equatorial radius and flattening (a_f2Tuple). |
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A Get the UTM meridional radius ( meter ).
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area Get the ellipsoid's surface area ( meter**2 ), 4 * PI * R2**2 or 4 * PI * a**2.
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AlphaKs Get the Krüger Alpha series coefficients ( KsOrder -tuple).
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b Get the polar (minor) radius, semi-axis ( meter ).
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polaradius Get the polar (minor) radius, semi-axis ( meter ).
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b_a Get ratio b / a ( float ), 1 - f.
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b2 Get the polar (minor) 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 ratio (b / a)**2 ( float ), (1 - f)**2, see e12 .
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BetaKs Get the Krüger Beta series coefficients ( KsOrder -tuple).
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c Get the authalic earth radius ( meter ), see
R2 .
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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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e22 Get the 2nd eccentricity squared ( float ), e2 / (1 - e2) == (a / b)**2 - 1, see
a_b2e22 .
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eccentricity2nd2 Get the (1st) eccentricity squared ( float ), f * (2 - f) == 1 - (b / a)**2, see
a_b2e2 .
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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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e12 Get 1 - e**2 ( float ), (1 - f)**2, b**2 / a**2, see
b2_a2 .
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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.
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flattening Get the flattening ( float ), (a -
b) / a, 0 for spherical.
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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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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 ).
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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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quarteradius DEPRECATED, use L .
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Mabcd Get the OSGR meridional coefficients ( 4-Tuple ),
Airy130 only.
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majoradius DEPRECATED, use a or Requatorial .
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minoradius DEPRECATED, use 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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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((a**2 + b**2 * atanh(e) / e) / 2).
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Rauthalic Get the authalic earth radius ( meter ), sqrt((a**2 + b**2 * atanh(e) / e) / 2).
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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 (major) radius, semi-axis ( meter ).
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Rgeometric Get the geometric mean earth radius ( meter ), sqrt(a * b).
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Rs DEPRECATED, use Rgeometric .
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Rpolar Get the polar (minor) radius, semi-axis ( meter ).
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Rquadratic Get the biaxial, quadratic mean earth radius ( meter ), sqrt((a**2 + b**2) / 2).
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Rrectifying Get the rectifying earth radius ( meter ), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
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Rr DEPRECATED, use Rrectifying .
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rocPolar Get the polar radius of curvature ( meter ), see
a2_b .
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volume Get the ellipsoid's volume ( meter**3 ), 4 / 3 * PI * a**2 * b.
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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. |
Convert an angle to the distance along the equator or along a parallel at the given 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 the given latitude (
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Return the meridional length, the distance along a meridian
between the equator and the given latitude (
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Convert distance to angle along equator or along a parallel at an other latitude.
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Compute the geocentric earth radius at the given latitude.
See Also: Geocentric Radius |
Approximate the earth radius at the given latitude.
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Compute the meridional and prime-vertical, normal radii of curvature at the given latitude.
See Also:
Method |
Compute the meridional and prime-vertical, normal radii of curvature at the given latitude.
See Also:
Method |
Compute the directional radius of curvature at a given latitude and compass direction.
See Also: Radii of Curvature |
Compute the Gaussian radius of curvature at the given latitude.
See Also: Radii of Curvature |
Compute the mean radius of curvature at the given latitude.
See Also: Radii of Curvature |
Compute the meridional radius of curvature at the given latitude.
See Also: Local, flat earth approximation and Radii of Curvature. |
Compute the prime-vertical, normal radius of curvature at the given latitude, aka the transverse radius of curvature.
See Also: Local, flat earth approximation and Radii of Curvature. |
Compute the prime-vertical, normal radius of curvature at the given latitude, aka the transverse radius of curvature.
See Also: Local, flat earth approximation and Radii of Curvature. |
Return this ellipsoid as a text string.
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Property Details |
aGet the equatorial (major) radius, semi-axis
(
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equatoradiusGet the equatorial (major) radius, semi-axis
(
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a2Get the equatorial (major) radius squared
(
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a2_Get the inverse of the equatorial (major) radius squared
(
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a_bGet ratio a / b (
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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 |
a_fGet equatorial radius and flattening (a_f2Tuple).
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AGet the UTM meridional radius (
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areaGet the ellipsoid's surface area (
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AlphaKsGet the Krüger Alpha series coefficients
(
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bGet the polar (minor) radius, semi-axis
(
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polaradiusGet the polar (minor) radius, semi-axis
(
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b_aGet ratio b / a (
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b2Get the polar (minor) radius squared
(
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b2_aGet the equatorial meridional radius of curvature
(
See Also: Radii of Curvature. |
b2_a2Get ratio (b / a)**2 (
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BetaKsGet the Krüger Beta series coefficients
(
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cGet the authalic earth radius (
Notes:
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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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e22Get the 2nd eccentricity squared (
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eccentricity2nd2Get the (1st) eccentricity squared (
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e32Get the 3rd eccentricity squared (
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eccentricity3rd2Get the 3rd eccentricity squared (
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e12Get 1 - e**2 (
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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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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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quarteradiusDEPRECATED, use
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MabcdGet the OSGR meridional coefficients (
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majoradiusDEPRECATED, use
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minoradiusDEPRECATED, use
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nGet the 3rd flattening (
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flattening3rdGet the 3rd flattening (
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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:
Earth radius, |
RauthalicGet the authalic earth radius (
See Also:
Earth radius, |
R3Get the volumetric earth radius (
See Also: Earth radius. |
RvolumetricGet the volumetric earth radius (
See Also: Earth radius. |
RbiaxialGet the biaxial, quadratic mean earth radius
(
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RequatorialGet the equatorial (major) radius, semi-axis
(
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RgeometricGet the geometric mean earth radius (
See Also:
Method |
RsDEPRECATED, use
See Also:
Method |
RpolarGet the polar (minor) radius, semi-axis
(
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RquadraticGet the biaxial, quadratic mean earth radius
(
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RrectifyingGet the rectifying earth radius (
See Also: Earth radius. |
RrDEPRECATED, use
See Also: Earth radius. |
rocPolarGet the polar radius of curvature (
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volumeGet the ellipsoid's volume (
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