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# pypose.Act¶

class pypose.Act(X, p)[source]

Apply the batched transform to points in Euclidean or homogeneous coordinates.

$y_i = X_i * p_i,$

where $$X$$ is the batched transform and $$p_i \in \mathbb{R^{*\times3}}$$ or $$p_i \in \mathbb{R^{*\times4}}$$ denotes the points to be transformed.

Parameters
• X (LieTensor) – the input LieTensor (Lie Group).

• p (Tensor) – the points to be transformed.

Returns

the transformed points in Euclidean or homogeneous coordinates.

Return type

Tensor

Examples

• $$\mathrm{Act}$$: (SO3, Tensor) $$\mapsto$$ Tensor

>>> p = torch.randn(3)     # batch size 1, Euclidean coordinates
>>> X = pp.identity_SO3(2) # batch size 2
>>> X.Act(p)               # equivalent to: pp.Act(X, p)
tensor([[ 1.7576,  1.1503, -0.9920],
[ 1.7576,  1.1503, -0.9920]])

• $$\mathrm{Act}$$: (SE3, Tensor) $$\mapsto$$ Tensor

>>> p = torch.tensor([[0, 0, 0, 1.], [0, 0, 0, 1.]]) # batch size 2, homogeneous coordinates
>>> X = pp.randn_SE3()                               # batch size 1
>>> X.Act(p)                                         # apply same transform
tensor([[-0.5676, -0.0452, -0.0929,  1.0000],
[-0.5676, -0.0452, -0.0929,  1.0000]])

• $$\mathrm{Act}$$: (Sim3, Tensor) $$\mapsto$$ Tensor

>>> p = torch.tensor([[0, 0, 0, 1.], [0, 0, 0, 1.]])  # batch size 2
>>> X = pp.randn_Sim3(2)                              # batch size 2
>>> X.Act(p)                                          # apply transform respectively.
tensor([[ 0.1551,  2.2930,  0.4531,  1.0000],
[-0.6140, -1.1263,  2.7607,  1.0000]])

• $$\mathrm{Act}$$: (RxSO3, Tensor) $$\mapsto$$ Tensor

>>> p = torch.tensor([[0, 0, 0.], [0, 0, 0.]])  # batch size 2, Euclidean coordinates
>>> X = pp.randn_RxSO3(2)                       # batch size 2
>>> X.Act(p)                                    # apply transform respectively.
tensor([[0., 0., 0.],
[0., 0., 0.]])


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