pypose.so3

pypose.so3 = functools.partial(<class 'pypose.lietensor.lietensor.LieTensor'>, ltype=<pypose.lietensor.lietensor.so3Type object>)

Alias of so3 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 (*, 3), where * is empty, one, or more batched dimensions (the lshape of this LieTensor), otherwise error will be raised.

Internally, so3 LieTensors are stored in the axis-angle format:

\[\mathrm{data}[*, :] = [\delta_x, \delta_y, \delta_z], \]

with \(\delta = \begin{pmatrix} \delta_x & \delta_y & \delta_z \end{pmatrix}\top\) being the axis of rotation and \(\theta = \|{\delta}\|\) being the angle.

Examples

>>> pp.so3(torch.randn(2, 3))
so3Type LieTensor:
tensor([[ 0.1571,  0.2203, -0.2457],
        [-0.3311,  0.5412, -0.7028]])
>>> pp.so3([0, 0, 1])
so3Type LieTensor:
tensor([0., 0., 1.])

If data is tensor-like, the last dimension should correspond to the 3 elements of the above embedding.

Note

It is not advised to construct so3 Tensors by specifying storage sizes with ‘int…’, which does not initialize data.

Consider using pypose.randn_so3 or pypose.identity_so3 instead.

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