Package pygeodesy :: Package triaxials :: Module triaxial3 :: Class Triaxial3

Class Triaxial3

      object --+                        
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    named._Named --+                    
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    named._NamedBase --+                
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    named._NamedEnumItem --+            
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bases._UnOrderedTriaxialBase --+        
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      bases._OrderedTriaxialBase --+    
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                bases._Triaxial3Base --+
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                                      Triaxial3

Known Subclasses:

Triaxial3B

Ordered triaxial ellipsoid convering between cartesian and lat-/longitudes using using class Ang.

See Also: Triaxial for details.

Instance Methods

forwardBetOmg(self, bet, omg, height=0, **unit_name)
Convert an ellipsoidal lat- and longitude to a cartesian on this triaxial's surface.

forwardBetaOmega(self, bet, omg, height=0, **unit_name)
Convert an ellipsoidal lat- and longitude to a cartesian on this triaxial's surface.

forwardBetaOmega_(self, sbeta, cbeta, somega, comega, **name)
DEPRECATED on 2025.11.15, like Triaxial.forwardBetaOmega_.

forwardBetOmgAlp2(self, bet, omg, alp, height=0, **unit_name)
Convert an ellipsoidal lat-, longitude and heading to a cartesian and a direction on this triaxial's surface.

forwardCartesian(self, x_ct, y=None, z=None, normal=True, **eps_llk_name)
Project any cartesian onto this triaxial's surface.

forwardLatLon(self, lat, lon, height=0, llk='ELLIPSOIDAL', **unit_name)
Convert any lat-/longitude kind to a cartesian on this triaxial's surface.

forwardPhiLam(self, phi, lam, height=0, llk='GEODETIC', **unit_name)
Convert any lat-/longitude kind to a cartesian on this triaxial's surface.

forwardPhiLamZet2(self, phi, lam, zet, height=0, llk='GEODETIC', **unit_name)
Convert a lat-, longitude and heading to a cartesian and a direction on this trixial's surface.

normed2(self, x_ct, y=None, z=None, dir3d=None, **llk_name)
Scale a cartesian and direction to this triaxial's surface.

reverseBetOmg(self, x_ct, y=None, z=None, **llk_name)
Convert a cartesian on this triaxial's surface to an ellipsoidal lat-/longitude.

reverseBetaOmega(self, x_ct, y=None, z=None, **llk_name)
Convert a cartesian on this triaxial's surface to an ellipsoidal lat-/longitude.

reverseBetOmgAlp(self, x_ct, y=None, z=None, dir3d=None, **llk_name)
Convert a cartesian and direction on this triaxial's surface to an ellipsoidal lat-, longitude and heading.

reverseCartesian(self, x_ct, y=None, z=None, height=0, normal=True, **llk_name)
"Unproject" a cartesian off this triaxial's surface.

reverseLatLon(self, x_ct, y=None, z=None, **llk_name)
Convert a cartesian on this triaxial's surface to a lat-/longitude.

reversePhiLam(self, x_ct, y=None, z=None, **llk_name)
Convert a cartesian on this triaxial's surface to lat-/longitude.

reversePhiLamZet(self, x_ct, y=None, z=None, dir3d=None, **llk_name)
Convert a cartesian and direction to lat-, longitude and azimuth.

random2(self, llk='ELLIPSOIDAL', both=False, _rand=<built-in method random of Random object at 0x7fdc52894e20>)
Return a random cartesian with/out direction on this triaxial's surface.

toOther(self, lat, lon, llk1='GEODETIC', llk2='GEODETIC', **unit_name)
Convert one lat-/longitude kind to an other.

toTriaxial5(self, x_ct, y=None, z=None, **triaxial_h_llk_name)
Find the closest cartesian on this or on another triaxial's surface.

Inherited from bases._OrderedTriaxialBase: __init__

Inherited from bases._UnOrderedTriaxialBase: __str__, area_p, hartzell4, height4, normal3d, normal4, sideOf, toBiaxial, toEllipsoid, toStr

Inherited from named._NamedEnumItem: unregister

Inherited from named._NamedBase: __repr__, others, toRepr

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

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

Properties

Inherited from bases._Triaxial3Base: Lon0, e2, isBiaxial, isOblate, isProlate, k2, kp2

Inherited from bases._OrderedTriaxialBase: area

Inherited from bases._UnOrderedTriaxialBase: a, a2, b, b2, c, c2, e2ab, e2ac, e2bc, isOrdered, isSpherical, unOrdered, volume

Inherited from named._NamedEnumItem: name

Inherited from named._Named: classname, classnaming, iteration, named, named2, named3, named4, sizeof, typename

Inherited from object: __class__

Method Details

forwardBetOmg (self, bet, omg, height=0, **unit_name)

Convert an ellipsoidal lat- and longitude to a cartesian on this triaxial's surface.

Arguments:

bet - Ellipsoidal latitude (Ang or unit).
omg - Ellipsoidal longitude (Ang or unit).
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
unit_name - Optional name=NN (str) and scalar unit=Radians (or Degrees).

Returns:

A Cartesian5Tuple(x, y, z, h, llk) with h=height and kind llk=LLK.ELLIPSOIDAL.

See Also: Method Triaxial3.reverseBetOmg.

forwardBetaOmega (self, bet, omg, height=0, **unit_name)

Convert an ellipsoidal lat- and longitude to a cartesian on this triaxial's surface.

Arguments:

bet - Ellipsoidal latitude (Ang or unit).
omg - Ellipsoidal longitude (Ang or unit).
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
unit_name - Optional name=NN (str) and scalar unit=Radians (or Degrees).

Returns:

A Cartesian5Tuple(x, y, z, h, llk) with h=height and kind llk=LLK.ELLIPSOIDAL.

See Also: Method Triaxial3.reverseBetOmg.

forwardBetOmgAlp2 (self, bet, omg, alp, height=0, **unit_name)

Convert an ellipsoidal lat-, longitude and heading to a cartesian and a direction on this triaxial's surface.

Arguments:

bet - Ellipsoidal latitude (Ang or unit).
omg - Ellipsoidal longitude (Ang or unit).
alp - Azimuth of the heading (Ang, unit or None).
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
unit_name - Optional name=NN (str), scalar unit=Radians (or Degrees).

Returns:

2-Tuple (cartesian, direction) with cartesian a Cartesian5Tuple(x, y, z, h, llk) with h=height, kind llk=LLK.ELLIPSOIDAL and direction a Vector3d tangent to this triaxial's surface or None.

See Also: Method Triaxial3.reverseBetOmgAlp.

forwardCartesian (self, x_ct, y=None, z=None, normal=True, **eps_llk_name)

Project any cartesian onto this triaxial's surface.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
normal - If True, the projection is perpendicular to the surface, otherwise radial to the center of this triaxial (bool).
eps_llk_name - Root finder tolerance eps=EPS, kind llk=None overriding x_ct.llk and optional name="height4" (str).

Returns:

A Cartesian5Tuple(x, y, z, h, llk).

See Also: Method Triaxial3.reverseCartesian to reverse the projection and function height4 for more details.

forwardLatLon (self, lat, lon, height=0, llk='ELLIPSOIDAL', **unit_name)

Convert any lat-/longitude kind to a cartesian on this triaxial's surface.

Arguments:

lat - Latitude (Ang or unit).
lon - Longitude (Ang or unit).
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
llk - The kind (an LLK).
unit_name - Optional name=NN (str) and scalar unit=Degrees (or Radians).

Returns:

A Cartesian5Tuple(x, y, z, h, llk) with height h=height and kind llk=llk.

See Also: Method Triaxial3.reverseLatLon.

forwardPhiLam (self, phi, lam, height=0, llk='GEODETIC', **unit_name)

Convert any lat-/longitude kind to a cartesian on this triaxial's surface.

Arguments:

phi - Latitude (Ang or unit).
lam - Longitude (Ang or unit).
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
llk - The kind (an LLK).
unit_name - Optional name=NN (str) and scalar unit=Radians (or Degrees).

Returns:

A Cartesian5Tuple(x, y, z, h, llk) with height h=0 and kind llk=llk.

Note: Longitude lam -= Lon0 if llk is LLK.GEODETIC_LON0.

See Also: Method Triaxial3.reverseLatLon.

forwardPhiLamZet2 (self, phi, lam, zet, height=0, llk='GEODETIC', **unit_name)

Convert a lat-, longitude and heading to a cartesian and a direction on this trixial's surface.

Arguments:

phi - Latitude (Ang or unit).
lam - Longitude (Ang or unit).
zet - Azimuth of the heading (Ang, unit or None).
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
llk - The kind (an LLK).
unit_name - Optional name=NN (str) and scalar unit=Radians (or Degrees).

Returns:

2-Tuple (cartesian, direction) with the cartesian a Cartesian5Tuple(x, y, z, h, llk) with height h=0, kind llk=llk and direction, a Vector3d on and tangent to this triaxial's surface.

Note: Longitude lam -= Lon0 if llk is LLK.GEODETIC_LON0.

See Also: Method Triaxial3.reversePhiLamZet.

normed2 (self, x_ct, y=None, z=None, dir3d=None, **llk_name)

Scale a cartesian and direction to this triaxial's surface.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
dir3d - The direction (Vector3d or None).
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

2-Tuple (cartesian, direction) with the cartesian a Cartesian5Tuple(x, y, z, h, llk) and direction, a Vector3d tangent to this triaxial's surface or None iff dir3d is None.

reverseBetOmg (self, x_ct, y=None, z=None, **llk_name)

Convert a cartesian on this triaxial's surface to an ellipsoidal lat-/longitude.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

A BetOmgAlp5Tuple

(bet, omg, alp, h, 
          llk)

with alp=None and llk=LLK.ELLIPSOIDAL.

reverseBetaOmega (self, x_ct, y=None, z=None, **llk_name)

Convert a cartesian on this triaxial's surface to an ellipsoidal lat-/longitude.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

A BetOmgAlp5Tuple

(bet, omg, alp, h, 
          llk)

with alp=None and llk=LLK.ELLIPSOIDAL.

reverseBetOmgAlp (self, x_ct, y=None, z=None, dir3d=None, **llk_name)

Convert a cartesian and direction on this triaxial's surface to an ellipsoidal lat-, longitude and heading.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_ct is scalar, ignored otherwise.
z - Z component (scalar), like y.
dir3d - The direction (Vector3d or None).
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

A BetOmgAlp5Tuple

(bet, omg, alp, h, 
          llk)

with alp=None if

dir3d is 
          None

and llk=LLK.ELLIPSOIDAL.

reverseCartesian (self, x_ct, y=None, z=None, height=0, normal=True, **llk_name)

"Unproject" a cartesian off this triaxial's surface.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
height - Height above or below this triaxial's surface (meter, same units as this triaxial's semi-axes).
normal - If True, height is perpendicular to the surface, otherwise radial to the center of this triaxial (bool).
llk_name - Optional name=NN (str) and kind llk overriding x_ct.llk.

Returns:

Cartesian5Tuple(x, y, z, h, llk).

Raises:

TrialError - Cartesian x_ct or (x, y, z) not on this triaxial's surface.

See Also: Methods Triaxial3.forwardCartesian.

reverseLatLon (self, x_ct, y=None, z=None, **llk_name)

Convert a cartesian on this triaxial's surface to a lat-/longitude.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

A BetOmgAlp5Tuple

(bet, omg, alp, h, 
          llk)

with alp=None or a PhiLamZet5Tuple

(phi, lam, zet, h, 
          llk)

with zet=None.

Note: Longitude lam += Lon0 if llk is LLK.GEODETIC_LON0.

reversePhiLam (self, x_ct, y=None, z=None, **llk_name)

Convert a cartesian on this triaxial's surface to lat-/longitude.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

A PhiLamZet5Tuple

(phi, lam, zet, h, 
          llk)

with zet=None.

Note: Longitude lam += Lon0 if llk is LLK.GEODETIC_LON0.

reversePhiLamZet (self, x_ct, y=None, z=None, dir3d=None, **llk_name)

Convert a cartesian and direction to lat-, longitude and azimuth.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
dir3d - Optional direction (Vector3d or None).
llk_name - Optional name=NN (str) and kind llk=None overriding x_ct.llk.

Returns:

A PhiLamZet5Tuple

(phi, lam, zet, h, 
          llk)

with zet=None if

dir3d is 
          None

Note: Longitude lam += Lon0 if llk is LLK.GEODETIC_LON0.

random2 (self, llk='ELLIPSOIDAL', both=False, _rand=<built-in method random of Random object at 0x7fdc52894e20>)

Return a random cartesian with/out direction on this triaxial's surface.

Arguments:

llk - The kind (an LLK).
both - If True, generate a random direction (bool).

Returns:

2-Tuple (cartesian, direction) with the cartesian a Cartesian5Tuple(x, y, z, h, llk) and direction, a Vector3d tangent to this triaxial's surface or None iff both is False.

toOther (self, lat, lon, llk1='GEODETIC', llk2='GEODETIC', **unit_name)

Convert one lat-/longitude kind to an other.

Arguments:

lat - Latitude (Ang or unit).
lon - Longitude (Ang or unit).
llk1 - The given kind (an LLK).
llk2 - The result kind (an LLK).
name - Optional name=NN (str).

Returns:

A BetOmgAlp5Tuple

(bet, omg, alp, h, 
          llk)

with alp=None or a PhiLamZet5Tuple

(phi, lam, zet, h, 
          llk)

with zet=None.

See Also: Methods Triaxial3.forwardLatLon and -reverseLatLon.

toTriaxial5 (self, x_ct, y=None, z=None, **triaxial_h_llk_name)

Find the closest cartesian on this or on another triaxial's surface.

Arguments:

x_ct - X component (scalar) or a cartesian (Cartesian5Tuple or any Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
triaxial_llk_name - Optional triaxial=self (Triaxial3), name=NN (str), height h and kind llk overriding x_ct.h respectively x_ct.llk.

Returns:

Cartesian5Tuple(x, y, z, h, llk)

Raises:

TriaxialError - If triaxial is not a Triaxial3.

See Also: Functions hartzell4 and height4 and methods.