pypose.sim3

pypose.sim3 = functools.partial(<class 'pypose.lietensor.lietensor.LieTensor'>, ltype=<pypose.lietensor.lietensor.sim3Type object>)

Alias of sim3 type LieTensor.

Parameters:

data (Tensor, or list, or ‘int…’) –

A Tensor object, or constructing a Tensor object from list, which defines tensor data (see below), or from ‘int…’, which defines tensor shape.

The shape of Tensor object must be (*, 7), where * is empty, one, or more batched dimensions (the lshape of this LieTensor), otherwise error will be raised.

Internally, sim3 LieTensors are stored by concatenating the log translation vector with the corresponding rxso3:

\[\mathrm{data}[*, :] = [\tau_x, \tau_y, \tau_z, \delta_x, \delta_y, \delta_z, \log s], \]

where \(\begin{pmatrix} \tau_x & \tau_y & \tau_z \end{pmatrix}^T = \mathbf{W}^{-1} \begin{pmatrix} t_x & t_y & t_z \end{pmatrix}^T\) is the product between the inverse of the \(\mathbf{W}\)-matrix and the translation vector, and \(\begin{pmatrix} \delta_x & \delta_y & \delta_z & \log s \end{pmatrix}^T\) represents the rotation and scaling, as in pypose.rxso3. More details about \(\mathbf{W}\)-matrix go to pypose.Log() with Sim3_type input.

Examples

>>> pp.Sim3(torch.randn(2, 7))
sim3Type LieTensor:
sim3Type LieTensor:
tensor([[ 0.1477, -1.3500, -2.1571,  0.8893, -0.7821, -0.9889, -0.7887],
        [ 0.2251,  0.3512,  0.0485,  0.0163, -1.7090, -0.0417, -0.3842]])
>>> pp.sim3([0, 0, 0, 0, 0, 0, 1])
sim3Type LieTensor:
tensor([0., 0., 0., 0., 0., 0., 1.])

If data is tensor-like, the last dimension should correspond to the 7 elements of the above embedding.

Note

It is not advised to construct sim3 Tensors by specifying storage sizes with ‘int…’, which does not initialize data.

Consider using pypose.randn_sim3 or pypose.identity_sim3 instead.

See pypose.Exp, pypose.Inv for implementations of relevant operations.