Package pygeodesy :: Module triaxials :: Class Triaxial_

Class Triaxial_

  object --+            
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named._Named --+        
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named._NamedBase --+    
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named._NamedEnumItem --+
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                      Triaxial_

Known Subclasses:

Triaxial

Unordered triaxial ellipsoid and base class.

Triaxial ellipsoids with right-handed semi-axes a, b and c, oriented such that the large principal ellipse ab is the equator Z=0, beta=0, while the small principal ellipse ac is the prime meridian, plane Y=0, omega=0.

The four umbilic points, abs(omega) = abs(beta) = PI/2, lie on the middle principal ellipse bc in plane X=0, omega=PI/2.

Note: Geodetic lat- and longitudes are in degrees, geodetic phi and lambda are in radians, but ellipsoidal lat- and longitude beta and omega are in Radians by default (or in Degrees if converted).

Instance Methods

__init__(self, a_triaxial, b=None, c=None, **name)
New unordered Triaxial_.

__str__(self)
Default str(self).

area_p(self, p=1.6075)
Approximate the surface area (meter squared).

hartzell4(self, pov, los=False, **name)
Compute the intersection of this triaxial's surface with a Line-Of-Sight from a Point-Of-View in space.

height4(self, x_xyz, y=None, z=None, normal=True, eps=2.220446049250313e-16, **name)
Compute the projection on and the height above or below this triaxial's surface.

normal3d(self, x_xyz, y=None, z=None, length=1.0)
Get a 3-D vector on and perpendicular to this triaxial's surface.

normal4(self, x_xyz, y=None, z=None, height=0, normal=True)
Compute a cartesian above or below this triaxial's surface.

sideOf(self, x_xyz, y=None, z=None, eps=8.881784197001252e-16)
Is a cartesian on, above or below the surface of this triaxial?

toEllipsoid(self, **name)
Convert this triaxial to a biaxial Ellipsoid, provided 2 axes match.

toBiaxial(self, **name)
Convert this triaxial to a biaxial Ellipsoid, provided 2 axes match.

toStr(self, prec=9, **name)
Return this Triaxial as a string.

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
	a Get the `largest, x` semi-axis (`meter`, conventionally).
	a2 Get `a**2`.
	area Get the surface area (`meter` squared).
	b Get the `middle, y` semi-axis (`meter`, same units as `a`).
	b2 Get `b**2`.
	c Get the `smallest, z` semi-axis (`meter`, same units as `a`).
	c2 Get `c**2`.
	e2ab Get the `ab` ellipse' (1st) eccentricity squared (`scalar`), 1 - (b/a)2.
	e2ac Get the `ac` ellipse' (1st) eccentricity squared (`scalar`), 1 - (c/a)2.
	e2bc Get the `bc` ellipse' (1st) eccentricity squared (`scalar`), 1 - (c/b)2.
	isOrdered Is this triaxial ordered and not spherical (`bool`)?
	isSpherical Is this triaxial spherical (`Radius` or INT0)?
	unOrdered Is this triaxial un-ordered and not spherical (`bool`)?
	volume Get the volume (`meter*3`), 4 / 3 * PI * a * b * c*.
Inherited from `named._NamedEnumItem`: `name` Inherited from `named._Named`: `classname`, `classnaming`, `iteration`, `named`, `named2`, `named3`, `named4`, `sizeof`, `typename` Inherited from `object`: `__class__`

Method Details

init (self, a_triaxial, b=None, c=None, **name)
(Constructor)

New unordered Triaxial_.

Arguments:

a_triaxial - Large, X semi-axis (scalar, conventionally in meter) or an other Triaxial or Triaxial_ instance.
b - Middle, Y semi-axis (meter, same units as a), required if a_triaxial is scalar, ignored otherwise.
c - Small, Z semi-axis (meter, like b).
name - Optional name=NN (str).

Raises:

TriaxialError - Invalid semi-axis or -axes.

Overrides: object.__init__

str (self)
(Informal representation operator)

Default str(self).

Overrides: object.__str__: (inherited documentation)

area_p (self, p=1.6075)

Approximate the surface area (meter squared).

Arguments:

p - Exponent (scalar > 0), 1.6 for near-spherical or 1.5849625007 for "near-flat" triaxials.

See Also: Surface area.

hartzell4 (self, pov, los=False, **name)

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

See Also: Function hartzell4 for further details.

height4 (self, x_xyz, y=None, z=None, normal=True, eps=2.220446049250313e-16, **name)

Compute the projection on and the height above or below this triaxial's surface.

Arguments:

x_xyz - X component (scalar) or a cartesian (Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz if scalar, ignored otherwise.
z - Z component (scalar), like y.
normal - If True, the projection is the perpendicular, plumb to the triaxial's surface, otherwise the radial line to the center of this triaxial (bool).
eps - Tolerance for root finding and validation (scalar), use a negative value to skip validation.
name - Optional name="height4" (str).

Returns:

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

Raises:

TriaxialError - Non-cartesian xyz, invalid eps, no convergence in root finding or validation failed.

See Also: Methods Triaxial.normal3d and Ellipsoid.height4, Eberly's Distance from a Point to ... and Bektas' Shortest Distance from a Point to Triaxial Ellipsoid.

normal3d (self, x_xyz, y=None, z=None, length=1.0)

Get a 3-D vector on and perpendicular to this triaxial's surface.

Arguments:

x_xyz - X component (scalar) or a cartesian (Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz if scalar, ignored otherwise.
z - Z component (scalar), like y.
length - Optional, signed length in out-/inward direction (scalar).

Returns:

A Vector3d(x_, y_, z_) normalized to length, pointing out- or inward for postive respectively negative length.

Raises:

TriaxialError - Zero length cartesian or vector.

Note: Cartesian (x, y, z) must be on this triaxial's surface, use method Triaxial.sideOf to validate.

See Also: Methods Triaxial.height4 and Triaxial.sideOf.

normal4 (self, x_xyz, y=None, z=None, height=0, normal=True)

Compute a cartesian above or below this triaxial's surface.

Arguments:

x_xyz - X component (scalar) or a cartesian (Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz if scalar, ignored otherwise.
z - Z component (scalar), like y.
height - The signed height (scalar, same units as the triaxial axes).
normal - If True, the height is perpendicular, plumb to the triaxial's surface, otherwise radially to the center of this triaxial (bool).
name - Optional name="normal4" (str).

Returns:

Vector4Tuple(x, y, z, h) with the cartesian coordinates x, y and z and h the signed, normal distance to the triaxial's surface in meter, conventionally. Positive h indicates, the cartesian is outside the triaxial, negative h means inside.

Raises:

TriaxialError - Zero length cartesian or vector.

Note: Cartesian (x, y, z) must be on this triaxial's surface, use method Triaxial.sideOf to validate.

See Also: Methods Triaxial.normal3d and Triaxial.height4.

sideOf (self, x_xyz, y=None, z=None, eps=8.881784197001252e-16)

Is a cartesian on, above or below the surface of this triaxial?

Arguments:

x_xyz - X component (scalar) or a cartesian (Cartesian, Ecef9Tuple, Vector3d, Vector3Tuple or Vector4Tuple).
y - Y component (scalar), required if x_xyz is scalar, ignored otherwise.
z - Z component (scalar), like y.
eps - On-surface tolerance (scalar, distance squared).

Returns:

INT0 if (x, y, z) is near this triaxial's surface within tolerance eps, otherwise the signed, radial distance squared (float), negative for in- or positive for outside this triaxial.

See Also: Methods Triaxial.height4 and Triaxial.normal3d.

toEllipsoid (self, **name)

Convert this triaxial to a biaxial Ellipsoid, provided 2 axes match.

Arguments:

name - Optional name=NN (str).

Returns:

An Ellipsoid with north along this Z axis if a == b, this Y axis if

a 
          == c

or this X axis if b == c.

Raises:

TriaxialError - This a != b, b != c and c != a.

See Also: Method Ellipsoid.toTriaxial.

toBiaxial (self, **name)

Convert this triaxial to a biaxial Ellipsoid, provided 2 axes match.

Arguments:

name - Optional name=NN (str).

Returns:

An Ellipsoid with north along this Z axis if a == b, this Y axis if

a 
          == c

or this X axis if b == c.

Raises:

TriaxialError - This a != b, b != c and c != a.

See Also: Method Ellipsoid.toTriaxial.

toStr (self, prec=9, **name)

Return this Triaxial as a string.

Arguments:

prec - Precision, number of decimal digits (0..9).
name - Optional name (str), to override or None to exclude this triaxial's name.

Returns:

This Triaxial's attributes (str).

Overrides: named._Named.toStr

Property Details

a

Get the largest, x semi-axis (meter, conventionally).

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

a2

Get a**2.

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

area

Get the surface area (meter squared).

Get method:: area(self) - Get the surface area (meter squared).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

b

Get the middle, y semi-axis (meter, same units as a).

Get method:: b(self) - Get the middle, y semi-axis (meter, same units as a).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

b2

Get b**2.

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

c

Get the smallest, z semi-axis (meter, same units as a).

Get method:: c(self) - Get the smallest, z semi-axis (meter, same units as a).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

c2

Get c**2.

Get method:: c2(self) - Get c**2.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

e2ab

Get the ab ellipse' (1st) eccentricity squared (scalar), 1 - (b/a)**2.

Get method:: e2ab(self) - Get the ab ellipse' (1st) eccentricity squared (scalar), 1 - (b/a)**2.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

e2ac

Get the ac ellipse' (1st) eccentricity squared (scalar), 1 - (c/a)**2.

Get method:: e2ac(self) - Get the ac ellipse' (1st) eccentricity squared (scalar), 1 - (c/a)**2.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

e2bc

Get the bc ellipse' (1st) eccentricity squared (scalar), 1 - (c/b)**2.

Get method:: e2bc(self) - Get the bc ellipse' (1st) eccentricity squared (scalar), 1 - (c/b)**2.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isOrdered

Is this triaxial ordered and not spherical (bool)?

Get method:: isOrdered(self) - Is this triaxial ordered and not spherical (bool)?
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isSpherical

Is this triaxial spherical (Radius or INT0)?

Get method:: isSpherical(self) - Is this triaxial spherical (Radius or INT0)?
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

unOrdered

Is this triaxial un-ordered and not spherical (bool)?

Get method:: unOrdered(self) - Is this triaxial un-ordered and not spherical (bool)?
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

volume

Get the volume (meter**3), 4 / 3 * PI * a * b * c.

Get method:: volume(self) - Get the volume (meter**3), 4 / 3 * PI * a * b * c.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

Class Triaxial_

__init__ (self, a_triaxial, b=None, c=None, **name) (Constructor)

__str__ (self) (Informal representation operator)

area_p (self, p=1.6075)

hartzell4 (self, pov, los=False, **name)

height4 (self, x_xyz, y=None, z=None, normal=True, eps=2.220446049250313e-16, **name)

normal3d (self, x_xyz, y=None, z=None, length=1.0)

normal4 (self, x_xyz, y=None, z=None, height=0, normal=True)

sideOf (self, x_xyz, y=None, z=None, eps=8.881784197001252e-16)

toEllipsoid (self, **name)

toBiaxial (self, **name)

toStr (self, prec=9, **name)

a

a2

area

b

b2

c

c2

e2ab

e2ac

e2bc

isOrdered

isSpherical

unOrdered

volume

init (self, a_triaxial, b=None, c=None, **name)
(Constructor)

str (self)
(Informal representation operator)