pypose.Act

class pypose.Act(X, p)

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.]])