fastdev.xform.warp_rotation
===========================

.. py:module:: fastdev.xform.warp_rotation




Module Contents
---------------

.. py:function:: axis_angle_to_matrix(axis: jaxtyping.Float[torch.Tensor, ... 3], angle: jaxtyping.Float[torch.Tensor, ...]) -> jaxtyping.Float[torch.Tensor, ... 3 3]

   Converts axis angles to rotation matrices using Rodrigues formula.

   :param axis: axis, the shape could be [..., 3].
   :type axis: torch.Tensor
   :param angle: angle, the shape could be [...].
   :type angle: torch.Tensor

   :returns: Rotation matrices [..., 3, 3].
   :rtype: torch.Tensor

   .. rubric:: Example

   >>> axis = torch.tensor([1.0, 0.0, 0.0])
   >>> angle = torch.tensor(0.5)
   >>> axis_angle_to_matrix(axis, angle)
   tensor([[ 1.0000,  0.0000,  0.0000],
           [ 0.0000,  0.8776, -0.4794],
           [ 0.0000,  0.4794,  0.8776]])


.. py:function:: euler_angles_to_matrix(euler_angles: jaxtyping.Float[torch.Tensor, ... 3], axes: _AXES = 'sxyz') -> jaxtyping.Float[torch.Tensor, ... 3 3]

   Converts Euler angles to rotation matrices.

   :param euler_angles: Tensor of Euler angles with shape [..., 3].
   :type euler_angles: torch.Tensor
   :param axes: Axis specification string, one of 24 possible sequences (e.g., "sxyz"). If only 3 characters are provided, "s" will be prefixed.
   :type axes: str

   :returns: Rotation matrices with shape [..., 3, 3].
   :rtype: torch.Tensor

   .. rubric:: Example

   >>> euler_angles = torch.tensor([1.0, 0.5, 2.0])
   >>> euler_angles_to_matrix(euler_angles, axes="sxyz")
   tensor([[-0.3652, -0.6592,  0.6574],
           [ 0.7980,  0.1420,  0.5857],
           [-0.4794,  0.7385,  0.4742]])
   >>> euler_angles_to_matrix(euler_angles, axes="rxyz")
   tensor([[-0.3652, -0.7980,  0.4794],
           [ 0.3234, -0.5917, -0.7385],
           [ 0.8729, -0.1146,  0.4742]])


.. py:function:: matrix_to_quaternion(rot_mat: jaxtyping.Float[torch.Tensor, ... 3 3], scalar_first: bool = True, canonical: bool = True) -> jaxtyping.Float[torch.Tensor, ... 4]

   Converts rotation matrices to quaternions.

   :param rot_mat: Rotation matrices with shape [..., 3, 3].
   :type rot_mat: torch.Tensor

   :returns: Quaternions with shape [..., 4].
   :rtype: torch.Tensor

   .. rubric:: Example

   >>> rot_mat = torch.tensor([[-0.2533, -0.6075,  0.7529],
   ...                         [ 0.8445, -0.5185, -0.1343],
   ...                         [ 0.4720,  0.6017,  0.6443]])
   >>> matrix_to_quaternion(rot_mat)
   tensor([0.4671, 0.3940, 0.1503, 0.7772])

   .. note::
       The gradient of this function differs from the pytorch3d implementation, but it
       should be okay for most use cases. Ref_

   .. _Ref: https://github.com/facebookresearch/pytorch3d/issues/503#issuecomment-755493515


.. py:function:: matrix_to_quaternion_numpy(rot_mat: jaxtyping.Float[numpy.ndarray, ... 3 3], scalar_first: bool = True, canonical: bool = True) -> jaxtyping.Float[numpy.ndarray, ... 4]

   Converts rotation matrices to quaternions.

   :param rot_mat: Rotation matrices with shape [..., 3, 3].
   :type rot_mat: np.ndarray

   :returns: Quaternions with shape [..., 4].
   :rtype: np.ndarray

   .. rubric:: Example

   >>> rot_mat = np.array([[ 0.45930517, -0.11985919, -0.88015485],
   ...                     [-0.4041326 ,  0.85417026, -0.32721555],
   ...                     [ 0.7910219 ,  0.50599104,  0.3438858 ]])
   >>> matrix_to_quaternion_numpy(rot_mat)
   array([ 0.8150708 ,  0.25556272, -0.5125865 , -0.08719288], dtype=float32)