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object --+ | named._Named --+ | named._NamedBase --+ | named._NamedEnumItem --+ | Ellipsoid
Ellipsoid with major and minor radius, semi-axis, (inverse) flattening and other pre-computed, frequently used attributes.
Instance Methods | |||
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Inherited from Inherited from Inherited from Inherited from |
Class Variables | |
_f_ = 0 Inverse flattening: a / (a - b) = 1 / f |
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_a2_ = None (1 / a**2) # for ellipsiodalNvector.Cartesian.toNvector |
Properties | |
a Get the major (equatorial) radius, semi-axis ( meter ).
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a_b Get ratio a / b ( float ).
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a2 Get the major radius squared ( float ), a**2.
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a2_ Get the inverse of the major radius squared ( float ), 1 / a**2.
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a2_b Get the polar meridional radius of curvature ( meter ), a**2 / b, see rocPolar .
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area Get the ellipsoid's surface area ( meter**2 ), 4 * PI * R2**2.
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A Get the UTM meridional radius ( meter ).
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AlphaKs Get the Krüger Alpha series coefficients ( KsOrder -tuple).
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b Get the minor (polar) radius, semi-axis ( meter ).
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b_a Get ratio b / a ( float ), 1 - f.
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b2 Get the minor radius squared ( float ), b**2.
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b2_a Get the equatorial meridional radius of curvature ( meter ), b**2 / a.
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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)).
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e12 Get 1 - e**2 ( float ).
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e2 Get the (1st) Eccentricity squared ( float ), f * (2 - f) == 1 - (b / a)**2.
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e22 Get the 2nd Eccentricity squared ( float ), e2 / (1 - e2) == (a / b)**2 - 1.
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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.
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f_ Get the Inverse flattening ( float ), 1 /
f or a / (a - b).
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f2 Get the 2nd Flattening ( float ), (a - b)
/ b.
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geodesic Get this ellipsoid's wrapped Karney Geodesic, provided the GeographicLib package is installed. |
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isEllipsoidal Check whether this model is ellipsoidal ( bool ).
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isSpherical Check whether this model is spherical ( bool ).
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KsOrder Property to get and set the Krüger series' order ( int ).
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Mabcd Get the OSGR meridional coefficients ( 4-Tuple ),
Airy130 only.
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n Get the 3rd Flattening ( float ), f / (2 -
f) == (a - b) / (a + b).
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R1 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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R3 Get the volumetric earth radius ( meter ), (a * a * b)**(1/3).
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Rr Get the rectifying earth radius ( meter ), ((a**(3/2) + b**(3/2)) / 2)**(2/3).
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Rs Get another mean earth radius ( meter ), sqrt(a * b).
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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.
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Compare this and an other ellipsoid.
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Convert angle to distance along the equator or along a parallel at an other latitude.
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Approximate the distance and (initial) bearing between two points based on the radii of curvature at the initial point. Suitable only for distances of several hundred Km or Miles and only between points not near-polar.
See Also: Function flatLocal, local, flat earth approximation and meridional and prime vertical Radii of Curvature. |
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: Function Math::tauf. |
Compute Karney's equations (7), (8) and (9). See Also: Function Math::taupf. |
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 the 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.
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 major (equatorial) radius, semi-axis (
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a_bGet ratio a / b (
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a2Get the major radius squared (
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a2_Get the inverse of the major radius squared
(
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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 |
areaGet the ellipsoid's surface area (
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AGet the UTM meridional radius (
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AlphaKsGet the Krüger Alpha series coefficients
(
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bGet the minor (polar) radius, semi-axis (
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b_aGet ratio b / a (
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b2Get the minor radius squared (
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b2_aGet the equatorial meridional radius of curvature
(
See Also: Radii of Curvature. |
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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e12Get 1 - e**2 (
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e2Get the (1st) Eccentricity squared (
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e22Get the 2nd Eccentricity squared (
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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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f_Get the Inverse flattening (
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f2Get the 2nd Flattening (
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geodesicGet this ellipsoid's wrapped Karney Geodesic, provided the GeographicLib package is installed.
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isEllipsoidalCheck whether this model is ellipsoidal (
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isSphericalCheck whether this model is spherical (
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KsOrderProperty to get and set the Krüger series' order
(
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MabcdGet the OSGR meridional coefficients (
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nGet the 3rd Flattening (
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R1Get the mean earth radius per IUGG (
See Also: Earth radius. |
R2Get the authalic earth radius (
See Also: Earth radius and c. |
R3Get the volumetric earth radius (
See Also: Earth radius. |
RrGet the rectifying earth radius (
See Also: Earth radius. |
RsGet another mean earth radius (
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rocPolarGet the polar radius of curvature (
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volumeGet the ellipsoid's volume (
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