fastdev.xform.warp_rotation

Module Contents

fastdev.xform.warp_rotation.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.

Parameters:

• axis (torch.Tensor) – axis, the shape could be […, 3].

• angle (torch.Tensor) – angle, the shape could be […].

Returns:

Rotation matrices […, 3, 3].

Return type:

torch.Tensor

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]])

fastdev.xform.warp_rotation.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.

Parameters:

• euler_angles (torch.Tensor) – Tensor of Euler angles with shape […, 3].

• axes (str) – Axis specification string, one of 24 possible sequences (e.g., “sxyz”). If only 3 characters are provided, “s” will be prefixed.

Returns:

Rotation matrices with shape […, 3, 3].

Return type:

torch.Tensor

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]])

fastdev.xform.warp_rotation.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.

Parameters:

• rot_mat (torch.Tensor) – Rotation matrices with shape […, 3, 3].

• scalar_first (bool)

• canonical (bool)

Returns:

Quaternions with shape […, 4].

Return type:

torch.Tensor

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

fastdev.xform.warp_rotation.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.

Parameters:

• rot_mat (np.ndarray) – Rotation matrices with shape […, 3, 3].

• scalar_first (bool)

• canonical (bool)

Returns:

Quaternions with shape […, 4].

Return type:

np.ndarray

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)