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PyGeometry
Package geometry :: Package manifolds :: Module special_euclidean_group :: Class SE_group
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Class SE_group

source code

This is the Special Euclidean group SE(n) describing roto-translations of Euclidean space. Implemented only for n=2,3.

Note that you have to supply a coefficient *alpha* that weights rotation and translation when defining distances.

Nested Classes [hide private]

Inherited from group.Group: __metaclass__

Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism

Instance Methods [hide private]
 
__init__(self, N)
:param N: :type N: ``int,(2|3)``		 source code
 
__repr__(self)
repr(x)		 source code
 
algebra_from_group(self, a)
Converts an element of the group to the algebra.		 source code
 
belongs(self, x)
:param x: :type x: ``array[NxN]``		 source code
 
friendly(self, x)
Returns a friendly description string for a point on the manifold.		 source code
 
group_from_algebra(self, g)
Converts an element of the algebra to the group.		 source code
 
interesting_points(self)
Returns a list of "interesting points" on this manifold that should be used for testing various properties.		 source code
 
sample_uniform(self) source code

Inherited from matrix_lie_group.MatrixLieGroup: belongs_algebra, distance, expmap, get_algebra, inverse, logmap, multiply, project_ts, tangent_bundle, unity, velocity_from_points

Inherited from group.Group: identity

Inherited from differentiable_manifold.DifferentiableManifold: assert_close, belongs_ts, can_convert_to, can_represent, convert_to, embed_in, embeddable_in, from_yaml, geodesic, get_dimension, project_from, project_to, relations_descriptions, to_yaml

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

Static Methods [hide private]

Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables [hide private]
  __abstractmethods__ = frozenset([])
  _abc_cache = <_weakrefset.WeakSet object at 0x24af0d0>

Inherited from group.Group (private): _abc_negative_cache, _abc_negative_cache_version, _abc_registry

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, N)
(Constructor)

source code 

:param N: :type N: ``int,(2|3)``

Overrides: object.__init__

__repr__(self)
(Representation operator)

source code 

repr(x)

Overrides: object.__repr__
(inherited documentation)

algebra_from_group(self, a)

source code  

           Converts an element of the group to the algebra. 
           Uses generic matrix logarithm plus projection.
       


:param g: 
:type g:  ``belongs``

:rtype:  ``belongs_algebra``
Overrides: matrix_lie_group.MatrixLieGroup.algebra_from_group
(inherited documentation)

belongs(self, x)

source code 

:param x: :type x: ``array[NxN]``

Overrides: differentiable_manifold.DifferentiableManifold.belongs

friendly(self, x)

source code  

           Returns a friendly description string for a point on the manifold. 
       


:param a: 
:type a:  ``belongs``
Overrides: differentiable_manifold.DifferentiableManifold.friendly
(inherited documentation)

group_from_algebra(self, g)

source code  

           Converts an element of the algebra to the group. 
       
           Uses generic matrix exponential.
       


:param a: 
:type a:  ``belongs_algebra``

:rtype:  ``belongs``
Overrides: matrix_lie_group.MatrixLieGroup.group_from_algebra
(inherited documentation)

interesting_points(self)

source code  

           Returns a list of "interesting points" on this manifold that
           should be used for testing various properties. 
       


:rtype:  ``list(belongs)``
Overrides: differentiable_manifold.DifferentiableManifold.interesting_points
(inherited documentation)

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