rofunc.utils.datalab.poselib.poselib.core.rotation3d

1.  Module Contents

1.1.  Functions

quat_mul	quaternion multiplication
quat_pos	make all the real part of the quaternion positive
quat_abs	quaternion norm (unit quaternion represents a 3D rotation, which has norm of 1)
quat_unit	normalized quaternion with norm of 1
quat_conjugate	quaternion with its imaginary part negated
quat_real	real component of the quaternion
quat_imaginary	imaginary components of the quaternion
quat_norm_check	verify that a quaternion has norm 1
quat_normalize	Construct 3D rotation from quaternion (the quaternion needs not to be normalized).
quat_from_xyz	Construct 3D rotation from the imaginary component
quat_identity	Construct 3D identity rotation given shape
quat_from_angle_axis	Create a 3D rotation from angle and axis of rotation. The rotation is counter-clockwise along the axis.
quat_from_rotation_matrix	Construct a 3D rotation from a valid 3x3 rotation matrices. Reference can be found here: http://www.cg.info.hiroshima-cu.ac.jp/~miyazaki/knowledge/teche52.html
quat_mul_norm	Combine two set of 3D rotations together using *** operator. The shape needs to be broadcastable
quat_rotate	Rotate a 3D vector with the 3D rotation
quat_inverse	The inverse of the rotation
quat_identity_like	Construct identity 3D rotation with the same shape
quat_angle_axis	The (angle, axis) representation of the rotation. The axis is normalized to unit length. The angle is guaranteed to be between [0, pi].
quat_yaw_rotation	Yaw rotation (rotation along z-axis)
transform_from_rotation_translation	Construct a transform from a quaternion and 3D translation. Only one of them can be None.
transform_identity	Identity transformation with given shape
transform_rotation	Get rotation from transform
transform_translation	Get translation from transform
transform_inverse	Inverse transformation
transform_identity_like	identity transformation with the same shape
transform_mul	Combine two transformation together
transform_apply	Transform a 3D vector
rot_matrix_det	Return the determinant of the 3x3 matrix. The shape of the tensor will be as same as the shape of the matrix
rot_matrix_integrity_check	Verify that a rotation matrix has a determinant of one and is orthogonal
rot_matrix_from_quaternion	Construct rotation matrix from quaternion
euclidean_to_rotation_matrix	Get the rotation matrix on the top-left corner of a Euclidean transformation matrix
euclidean_integrity_check
euclidean_translation	Get the translation vector located at the last column of the matrix
euclidean_inverse	Compute the matrix that represents the inverse rotation
euclidean_to_transform	Construct a transform from a Euclidean transformation matrix

1.2.  API

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_mul(a, b)

quaternion multiplication

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_pos(x)

make all the real part of the quaternion positive

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_abs(x)

quaternion norm (unit quaternion represents a 3D rotation, which has norm of 1)

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_unit(x)

normalized quaternion with norm of 1

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_conjugate(x)

quaternion with its imaginary part negated

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_real(x)

real component of the quaternion

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_imaginary(x)

imaginary components of the quaternion

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_norm_check(x)

verify that a quaternion has norm 1

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_normalize(q)

Construct 3D rotation from quaternion (the quaternion needs not to be normalized).

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_from_xyz(xyz)

Construct 3D rotation from the imaginary component

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_identity(shape: List[int])

Construct 3D identity rotation given shape

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_from_angle_axis(angle, axis, degree: bool = False)

Create a 3D rotation from angle and axis of rotation. The rotation is counter-clockwise along the axis.

The rotation can be interpreted as a_R_b where frame “b” is the new frame that gets rotated counter-clockwise along the axis from frame “a”

Parameters:

• angle (Tensor) – angle of rotation

• axis (Tensor) – axis of rotation

• degree (bool, optional, default=False) – put True here if the angle is given by degree

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_from_rotation_matrix(m)

Construct a 3D rotation from a valid 3x3 rotation matrices. Reference can be found here: http://www.cg.info.hiroshima-cu.ac.jp/~miyazaki/knowledge/teche52.html

Parameters:

m (Tensor) – 3x3 orthogonal rotation matrices.

Return type:

Tensor

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_mul_norm(x, y)

Combine two set of 3D rotations together using *** operator. The shape needs to be broadcastable

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_rotate(rot, vec)

Rotate a 3D vector with the 3D rotation

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_inverse(x)

The inverse of the rotation

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_identity_like(x)

Construct identity 3D rotation with the same shape

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_angle_axis(x)

The (angle, axis) representation of the rotation. The axis is normalized to unit length. The angle is guaranteed to be between [0, pi].

rofunc.utils.datalab.poselib.poselib.core.rotation3d.quat_yaw_rotation(x, z_up: bool = True)

Yaw rotation (rotation along z-axis)

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_from_rotation_translation(r: Optional[torch.Tensor] = None, t: Optional[torch.Tensor] = None)

Construct a transform from a quaternion and 3D translation. Only one of them can be None.

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_identity(shape: List[int])

Identity transformation with given shape

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_rotation(x)

Get rotation from transform

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_translation(x)

Get translation from transform

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_inverse(x)

Inverse transformation

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_identity_like(x)

identity transformation with the same shape

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_mul(x, y)

Combine two transformation together

rofunc.utils.datalab.poselib.poselib.core.rotation3d.transform_apply(rot, vec)

Transform a 3D vector

rofunc.utils.datalab.poselib.poselib.core.rotation3d.rot_matrix_det(x)

Return the determinant of the 3x3 matrix. The shape of the tensor will be as same as the shape of the matrix

rofunc.utils.datalab.poselib.poselib.core.rotation3d.rot_matrix_integrity_check(x)

Verify that a rotation matrix has a determinant of one and is orthogonal

rofunc.utils.datalab.poselib.poselib.core.rotation3d.rot_matrix_from_quaternion(q)

Construct rotation matrix from quaternion

rofunc.utils.datalab.poselib.poselib.core.rotation3d.euclidean_to_rotation_matrix(x)

Get the rotation matrix on the top-left corner of a Euclidean transformation matrix

rofunc.utils.datalab.poselib.poselib.core.rotation3d.euclidean_integrity_check(x)

rofunc.utils.datalab.poselib.poselib.core.rotation3d.euclidean_translation(x)

Get the translation vector located at the last column of the matrix

rofunc.utils.datalab.poselib.poselib.core.rotation3d.euclidean_inverse(x)

Compute the matrix that represents the inverse rotation

rofunc.utils.datalab.poselib.poselib.core.rotation3d.euclidean_to_transform(transformation_matrix)

Construct a transform from a Euclidean transformation matrix