symforce.geo.pose2 module¶
- class Pose2(R=None, t=None)[source]¶
Bases:
LieGroup
Group of two-dimensional rigid body transformations - R2 x SO(2).
The storage space is a complex (real, imag) for rotation followed by a position (x, y).
The tangent space is one angle for rotation followed by two elements for translation in the non-rotated frame.
For Lie group enthusiasts: This class is on the PRODUCT manifold. On this class, the group operations (e.g. compose and between) operate as you’d expect for a Pose or SE(2), but the manifold operations (e.g. retract and local_coordinates) operate on the product manifold SO(2) x R2. This means that:
retract(a, vec) != compose(a, from_tangent(vec))
local_coordinates(a, b) != to_tangent(between(a, b))
There is no hat operator, because from_tangent/to_tangent is not the matrix exp/log
If you need a type that has these properties in symbolic expressions, you should use Pose2_SE2. There is no runtime equivalent of Pose2_SE2, see the docstring on that class for more information.
- rotation()[source]¶
Accessor for the rotation component
Does not make a copy. Also accessible as self.R
- Return type:
- position()[source]¶
Accessor for the position component
Does not make a copy. Also accessible as self.t
- Return type:
- to_storage()[source]¶
Flat list representation of the underlying storage, length of STORAGE_DIM. This is used purely for plumbing, it is NOT like a tangent space.
- Return type:
List
[float
]
- classmethod from_storage(vec)[source]¶
Construct from a flat list representation. Opposite of .to_storage().
- Parameters:
vec (
Sequence
[float
]) –- Return type:
- classmethod from_tangent(v, epsilon=0.0)[source]¶
Mapping from the tangent space vector about identity into a group element.
- Parameters:
v (
Sequence
[float
]) –epsilon (
float
) –
- Return type:
- to_tangent(epsilon=0.0)[source]¶
Mapping from this element to the tangent space vector about identity.
- Parameters:
epsilon (
float
) –- Return type:
List
[float
]
- storage_D_tangent()[source]¶
Note: generated from symforce/notebooks/storage_D_tangent.ipynb
- Return type:
- tangent_D_storage()[source]¶
Note: generated from symforce/notebooks/tangent_D_storage.ipynb
- Return type:
- retract(vec, epsilon=0.0)[source]¶
Apply a tangent space perturbation vec to self. Often used in optimization to update nonlinear values from an update step in the tangent space.
Implementation is simply compose(self, from_tangent(vec)). Conceptually represents “self + vec” if self is a vector.
- local_coordinates(b, epsilon=0.0)[source]¶
Computes a tangent space perturbation around self to produce b. Often used in optimization to minimize the distance between two group elements.
Implementation is simply to_tangent(between(self, b)). Tangent space perturbation that conceptually represents “b - self” if self is a vector.
- Parameters:
self (Pose2T) –
b (Pose2T) –
epsilon (T.Scalar) –
- Return type:
T.List[T.Scalar]