API Documentation

This is the detailed documentation of all public classes and functions. You can also search for specific modules, classes, or functions in the Index.

pytransform3d.rotations

Rotations in three dimensions - SO(3).

See SO(3): 3D Rotations for more information.

Rotation Matrix

check_matrix(R[, tolerance, strict_check])	Input validation of a rotation matrix.
matrix_requires_renormalization(R[, tolerance])	Check if a rotation matrix needs renormalization.
norm_matrix(R)	Orthonormalize rotation matrix.
plot_basis([ax, R, p, s, ax_s, strict_check])	Plot basis of a rotation matrix.
assert_rotation_matrix(R, *args, **kwargs)	Raise an assertion if a matrix is not a rotation matrix.
passive_matrix_from_angle(basis, angle)	Compute passive rotation matrix from rotation about basis vector.
active_matrix_from_angle(basis, angle)	Compute active rotation matrix from rotation about basis vector.
matrix_from_two_vectors(a, b)	Compute rotation matrix from two vectors.
matrix_from_euler(e, i, j, k, extrinsic)	General method to compute active rotation matrix from any Euler angles.
matrix_from_axis_angle(a)	Compute rotation matrix from axis-angle.
matrix_from_compact_axis_angle(a)	Compute rotation matrix from compact axis-angle.
matrix_from_quaternion(q)	Compute rotation matrix from quaternion.
matrix_from_rotor(rotor)	Compute rotation matrix from rotor.

Euler Angles

euler_near_gimbal_lock(e, i, j, k[, tolerance])	Check if Euler angles are close to gimbal lock.
norm_euler(e, i, j, k)	Normalize Euler angle range.
assert_euler_equal(e1, e2, i, j, k, *args, ...)	Raise an assertion if two Euler angles are not approximately equal.
euler_from_quaternion(q, i, j, k, extrinsic)	General method to extract any Euler angles from quaternions.
euler_from_matrix(R, i, j, k, extrinsic[, ...])	General method to extract any Euler angles from active rotation matrix.

Axis-Angle

check_axis_angle(a)	Input validation of axis-angle representation.
check_compact_axis_angle(a)	Input validation of compact axis-angle representation.
compact_axis_angle_near_pi(a[, tolerance])	Check if angle of compact axis-angle representation is near pi.
norm_axis_angle(a)	Normalize axis-angle representation.
norm_compact_axis_angle(a)	Normalize compact axis-angle representation.
random_axis_angle([rng])	Generate random axis-angle.
random_compact_axis_angle([rng])	Generate random compact axis-angle.
plot_axis_angle([ax, a, p, s, ax_s])	Plot rotation axis and angle.
assert_axis_angle_equal(a1, a2, *args, **kwargs)	Raise an assertion if two axis-angle are not approximately equal.
assert_compact_axis_angle_equal(a1, a2, ...)	Raise an assertion if two axis-angle are not approximately equal.
axis_angle_slerp(start, end, t)	Spherical linear interpolation.
axis_angle_from_two_directions(a, b)	Compute axis-angle representation from two direction vectors.
axis_angle_from_matrix(R[, strict_check, check])	Compute axis-angle from rotation matrix.
axis_angle_from_quaternion(q)	Compute axis-angle from quaternion.
axis_angle_from_compact_axis_angle(a)	Compute axis-angle from compact axis-angle representation.
axis_angle_from_mrp(mrp)	Compute axis-angle representation from modified Rodrigues parameters.
compact_axis_angle(a)	Compute 3-dimensional axis-angle from a 4-dimensional one.
compact_axis_angle_from_matrix(R[, check])	Compute compact axis-angle from rotation matrix.
compact_axis_angle_from_quaternion(q)	Compute compact axis-angle from quaternion (logarithmic map).

Logarithm of Rotation

check_rot_log(V[, tolerance, strict_check])	Input validation of a skew-symmetric matrix.
check_skew_symmetric_matrix(V[, tolerance, ...])	Input validation of a skew-symmetric matrix.
rot_log_from_compact_axis_angle(v)	Generate the cross-product matrix of a vector.
cross_product_matrix(v)	Generate the cross-product matrix of a vector.

Quaternion

check_quaternion(q[, unit])	Input validation of quaternion representation.
check_quaternions(Q[, unit])	Input validation of quaternion representation.
quaternion_requires_renormalization(q[, ...])	Check if a unit quaternion requires renormalization.
quaternion_double(q)	Create another quaternion that represents the same orientation.
pick_closest_quaternion(quaternion, ...)	Resolve quaternion ambiguity and pick the closest one to the target.
random_quaternion([rng])	Generate random quaternion.
assert_quaternion_equal(q1, q2, *args, **kwargs)	Raise an assertion if two quaternions are not approximately equal.
concatenate_quaternions(q1, q2)	Concatenate two quaternions.
q_prod_vector(q, v)	Apply rotation represented by a quaternion to a vector.
q_conj(q)	Conjugate of quaternion.
quaternion_slerp(start, end, t[, shortest_path])	Spherical linear interpolation.
quaternion_dist(q1, q2)	Compute distance between two quaternions.
quaternion_diff(q1, q2)	Compute the rotation in angle-axis format that rotates q2 into q1.
quaternion_gradient(Q[, dt])	Time-derivatives of a sequence of quaternions.
quaternion_integrate(Qd[, q0, dt])	Integrate angular velocities to quaternions.
quaternion_from_angle(basis, angle)	Compute quaternion from rotation about basis vector.
quaternion_from_euler(e, i, j, k, extrinsic)	General conversion to quaternion from any Euler angles.
quaternion_from_matrix(R[, strict_check])	Compute quaternion from rotation matrix.
quaternion_from_axis_angle(a)	Compute quaternion from axis-angle.
quaternion_from_compact_axis_angle(a)	Compute quaternion from compact axis-angle (exponential map).
quaternion_from_mrp(mrp)	Compute quaternion from modified Rodrigues parameters.
quaternion_xyzw_from_wxyz(q_wxyz)	Converts from w, x, y, z to x, y, z, w convention.
quaternion_wxyz_from_xyzw(q_xyzw)	Converts from x, y, z, w to w, x, y, z convention.

Rotor

check_rotor(rotor)	Input validation of rotor.
plot_bivector([ax, a, b, ax_s])	Plot bivector from wedge product of two vectors a and b.
wedge(a, b)	Outer product of two vectors (also exterior or wedge product).
plane_normal_from_bivector(B)	Convert bivector to normal vector of a plane.
geometric_product(a, b)	Geometric product of two vectors.
concatenate_rotors(rotor1, rotor2)	Concatenate rotors.
rotor_reverse(rotor)	Invert rotor.
rotor_apply(rotor, v)	Apply rotor to vector.
rotor_slerp(start, end, t[, shortest_path])	Spherical linear interpolation.
rotor_from_two_directions(v_from, v_to)	Construct the rotor that rotates one vector to another.
rotor_from_plane_angle(B, angle)	Compute rotor from plane bivector and angle.

Modified Rodrigues Parameters

check_mrp(mrp)	Input validation of modified Rodrigues parameters.
mrp_near_singularity(mrp[, tolerance])	Check if modified Rodrigues parameters are close to singularity.
norm_mrp(mrp)	Normalize angle of modified Rodrigues parameters to range [-pi, pi].
assert_mrp_equal(mrp1, mrp2, *args, **kwargs)	Raise an assertion if two MRPs are not approximately equal.
mrp_double(mrp)	Other modified Rodrigues parameters representing the same orientation.
concatenate_mrp(mrp1, mrp2)	Concatenate two rotations defined by modified Rodrigues parameters.
mrp_prod_vector(mrp, v)	Apply rotation represented by MRPs to a vector.
mrp_from_axis_angle(a)	Compute modified Rodrigues parameters from axis-angle representation.
mrp_from_quaternion(q)	Compute modified Rodrigues parameters from quaternion.

Jacobians

left_jacobian_SO3(omega)	Left Jacobian of SO(3) at theta (angle of rotation).
left_jacobian_SO3_series(omega, n_terms)	Left Jacobian of SO(3) at theta from Taylor series.
left_jacobian_SO3_inv(omega)	Inverse left Jacobian of SO(3) at theta (angle of rotation).
left_jacobian_SO3_inv_series(omega, n_terms)	Inverse left Jacobian of SO(3) at theta from Taylor series.

Utility Functions

norm_angle(a)	Normalize angle to (-pi, pi].
norm_vector(v)	Normalize vector.
perpendicular_to_vectors(a, b)	Compute perpendicular vector to two other vectors.
angle_between_vectors(a, b[, fast])	Compute angle between two vectors.
vector_projection(a, b)	Orthogonal projection of vector a on vector b.
plane_basis_from_normal(plane_normal)	Compute two basis vectors of a plane from the plane's normal vector.
random_vector([rng, n])	Generate an nd vector with normally distributed components.

Deprecated Functions

quaternion_from_extrinsic_euler_xyz(e)	Compute quaternion from extrinsic xyz Euler angles.
active_matrix_from_intrinsic_euler_xzx(e)	Compute active rotation matrix from intrinsic xzx Euler angles.
active_matrix_from_extrinsic_euler_xzx(e)	Compute active rotation matrix from extrinsic xzx Euler angles.
active_matrix_from_intrinsic_euler_xyx(e)	Compute active rotation matrix from intrinsic xyx Euler angles.
active_matrix_from_extrinsic_euler_xyx(e)	Compute active rotation matrix from extrinsic xyx Euler angles.
active_matrix_from_intrinsic_euler_yxy(e)	Compute active rotation matrix from intrinsic yxy Euler angles.
active_matrix_from_extrinsic_euler_yxy(e)	Compute active rotation matrix from extrinsic yxy Euler angles.
active_matrix_from_intrinsic_euler_yzy(e)	Compute active rotation matrix from intrinsic yzy Euler angles.
active_matrix_from_extrinsic_euler_yzy(e)	Compute active rotation matrix from extrinsic yzy Euler angles.
active_matrix_from_intrinsic_euler_zyz(e)	Compute active rotation matrix from intrinsic zyz Euler angles.
active_matrix_from_extrinsic_euler_zyz(e)	Compute active rotation matrix from extrinsic zyz Euler angles.
active_matrix_from_intrinsic_euler_zxz(e)	Compute active rotation matrix from intrinsic zxz Euler angles.
active_matrix_from_extrinsic_euler_zxz(e)	Compute active rotation matrix from extrinsic zxz Euler angles.
active_matrix_from_intrinsic_euler_xzy(e)	Compute active rotation matrix from intrinsic xzy Cardan angles.
active_matrix_from_extrinsic_euler_xzy(e)	Compute active rotation matrix from extrinsic xzy Cardan angles.
active_matrix_from_intrinsic_euler_xyz(e)	Compute active rotation matrix from intrinsic xyz Cardan angles.
active_matrix_from_extrinsic_euler_xyz(e)	Compute active rotation matrix from extrinsic xyz Cardan angles.
active_matrix_from_intrinsic_euler_yxz(e)	Compute active rotation matrix from intrinsic yxz Cardan angles.
active_matrix_from_extrinsic_euler_yxz(e)	Compute active rotation matrix from extrinsic yxz Cardan angles.
active_matrix_from_intrinsic_euler_yzx(e)	Compute active rotation matrix from intrinsic yzx Cardan angles.
active_matrix_from_extrinsic_euler_yzx(e)	Compute active rotation matrix from extrinsic yzx Cardan angles.
active_matrix_from_intrinsic_euler_zyx(e)	Compute active rotation matrix from intrinsic zyx Cardan angles.
active_matrix_from_extrinsic_euler_zyx(e)	Compute active rotation matrix from extrinsic zyx Cardan angles.
active_matrix_from_intrinsic_euler_zxy(e)	Compute active rotation matrix from intrinsic zxy Cardan angles.
active_matrix_from_extrinsic_euler_zxy(e)	Compute active rotation matrix from extrinsic zxy Cardan angles.
active_matrix_from_extrinsic_roll_pitch_yaw(rpy)	Compute active rotation matrix from extrinsic roll, pitch, and yaw.
intrinsic_euler_xzx_from_active_matrix(R[, ...])	Compute intrinsic xzx Euler angles from active rotation matrix.
extrinsic_euler_xzx_from_active_matrix(R[, ...])	Compute extrinsic xzx Euler angles from active rotation matrix.
intrinsic_euler_xyx_from_active_matrix(R[, ...])	Compute intrinsic xyx Euler angles from active rotation matrix.
extrinsic_euler_xyx_from_active_matrix(R[, ...])	Compute extrinsic xyx Euler angles from active rotation matrix.
intrinsic_euler_yxy_from_active_matrix(R[, ...])	Compute intrinsic yxy Euler angles from active rotation matrix.
extrinsic_euler_yxy_from_active_matrix(R[, ...])	Compute extrinsic yxy Euler angles from active rotation matrix.
intrinsic_euler_yzy_from_active_matrix(R[, ...])	Compute intrinsic yzy Euler angles from active rotation matrix.
extrinsic_euler_yzy_from_active_matrix(R[, ...])	Compute extrinsic yzy Euler angles from active rotation matrix.
intrinsic_euler_zyz_from_active_matrix(R[, ...])	Compute intrinsic zyz Euler angles from active rotation matrix.
extrinsic_euler_zyz_from_active_matrix(R[, ...])	Compute extrinsic zyz Euler angles from active rotation matrix.
intrinsic_euler_zxz_from_active_matrix(R[, ...])	Compute intrinsic zxz Euler angles from active rotation matrix.
extrinsic_euler_zxz_from_active_matrix(R[, ...])	Compute extrinsic zxz Euler angles from active rotation matrix.
intrinsic_euler_xzy_from_active_matrix(R[, ...])	Compute intrinsic xzy Cardan angles from active rotation matrix.
extrinsic_euler_xzy_from_active_matrix(R[, ...])	Compute extrinsic xzy Cardan angles from active rotation matrix.
intrinsic_euler_xyz_from_active_matrix(R[, ...])	Compute intrinsic xyz Cardan angles from active rotation matrix.
extrinsic_euler_xyz_from_active_matrix(R[, ...])	Compute extrinsic xyz Cardan angles from active rotation matrix.
intrinsic_euler_yxz_from_active_matrix(R[, ...])	Compute intrinsic yxz Cardan angles from active rotation matrix.
extrinsic_euler_yxz_from_active_matrix(R[, ...])	Compute extrinsic yxz Cardan angles from active rotation matrix.
intrinsic_euler_yzx_from_active_matrix(R[, ...])	Compute intrinsic yzx Cardan angles from active rotation matrix.
extrinsic_euler_yzx_from_active_matrix(R[, ...])	Compute extrinsic yzx Cardan angles from active rotation matrix.
intrinsic_euler_zyx_from_active_matrix(R[, ...])	Compute intrinsic zyx Cardan angles from active rotation matrix.
extrinsic_euler_zyx_from_active_matrix(R[, ...])	Compute extrinsic zyx Cardan angles from active rotation matrix.
intrinsic_euler_zxy_from_active_matrix(R[, ...])	Compute intrinsic zxy Cardan angles from active rotation matrix.
extrinsic_euler_zxy_from_active_matrix(R[, ...])	Compute extrinsic zxy Cardan angles from active rotation matrix.

pytransform3d.transformations

Transformations in three dimensions - SE(3).

See SE(3): 3D Transformations for more information.

Transformation Matrix

check_transform(A2B[, strict_check])	Input validation of transform.
transform_requires_renormalization(A2B[, ...])	Check if transformation matrix requires renormalization.
random_transform([rng, mean, cov])	Generate random transform.
concat(A2B, B2C[, strict_check, check])	Concatenate transformations.
invert_transform(A2B[, strict_check, check])	Invert transform.
transform(A2B, PA[, strict_check])	Transform point or list of points or directions.
vector_to_point(v)	Convert 3D vector to position.
vectors_to_points(V)	Convert 3D vectors to positions.
vector_to_direction(v)	Convert 3D vector to direction.
vectors_to_directions(V)	Convert 3D vectors to directions.
adjoint_from_transform(A2B[, strict_check, ...])	Compute adjoint representation of a transformation matrix.
plot_transform([ax, A2B, s, ax_s, name, ...])	Plot transform.
assert_transform(A2B, *args, **kwargs)	Raise an assertion if the transform is not a homogeneous matrix.
transform_from(R, p[, strict_check])	Make transformation from rotation matrix and translation.
translate_transform(A2B, p[, strict_check, ...])	Sets the translation of a transform.
rotate_transform(A2B, R[, strict_check, check])	Sets the rotation of a transform.
transform_from_pq(pq)	Compute transformation matrix from position and quaternion.
transform_from_exponential_coordinates(Stheta)	Compute transformation matrix from exponential coordinates.
transform_from_transform_log(transform_log)	Compute transformation from matrix logarithm of transformation.
transform_from_dual_quaternion(dq)	Compute transformation matrix from dual quaternion.

Position and Quaternion

check_pq(pq)	Input validation for position and orientation quaternion.
pq_slerp(start, end, t)	Spherical linear interpolation of position and quaternion.
pq_from_transform(A2B[, strict_check])	Compute position and quaternion from transformation matrix.
pq_from_dual_quaternion(dq)	Compute position and quaternion from dual quaternion.

Screw Parameters

check_screw_parameters(q, s_axis, h)	Input validation of screw parameters.
plot_screw([ax, q, s_axis, h, theta, A2B, ...])	Plot transformation about and along screw axis.
assert_screw_parameters_equal(q1, s_axis1, ...)	Raise an assertion if two sets of screw parameters are not similar.
screw_parameters_from_screw_axis(screw_axis)	Compute screw parameters from screw axis.
screw_parameters_from_dual_quaternion(dq)	Compute screw parameters from dual quaternion.

Screw Axis

check_screw_axis(screw_axis)	Input validation of screw axis.
random_screw_axis([rng])	Generate random screw axis.
screw_axis_from_screw_parameters(q, s_axis, h)	Compute screw axis representation from screw parameters.
screw_axis_from_exponential_coordinates(Stheta)	Compute screw axis and theta from exponential coordinates.
screw_axis_from_screw_matrix(screw_matrix)	Compute screw axis from screw matrix.

Exponential Coordinates

check_exponential_coordinates(Stheta)	Input validation for exponential coordinates of transformation.
norm_exponential_coordinates(Stheta)	Normalize exponential coordinates of transformation.
random_exponential_coordinates([rng, cov])	Generate random exponential coordinates.
assert_exponential_coordinates_equal(...)	Raise an assertion if exp.
exponential_coordinates_from_transform(A2B)	Compute exponential coordinates from transformation matrix.
exponential_coordinates_from_screw_axis(...)	Compute exponential coordinates from screw axis and theta.
exponential_coordinates_from_transform_log(...)	Compute exponential coordinates from logarithm of transformation.

Screw Matrix

check_screw_matrix(screw_matrix[, ...])	Input validation for screw matrix.
screw_matrix_from_screw_axis(screw_axis)	Compute screw matrix from screw axis.
screw_matrix_from_transform_log(transform_log)	Compute screw matrix from logarithm of transformation.

Logarithm of Transformation

check_transform_log(transform_log[, ...])	Input validation for logarithm of transformation.
transform_log_from_exponential_coordinates(Stheta)	Compute matrix logarithm of transformation from exponential coordinates.
transform_log_from_screw_matrix(...)	Compute matrix logarithm of transformation from screw matrix and theta.
transform_log_from_transform(A2B[, strict_check])	Compute matrix logarithm of transformation from transformation.

Dual Quaternion

check_dual_quaternion(dq[, unit])	Input validation of dual quaternion representation.
dual_quaternion_requires_renormalization(dq)	Check if dual quaternion requires renormalization.
assert_unit_dual_quaternion(dq, *args, **kwargs)	Raise an assertion if the dual quaternion does not have unit norm.
assert_unit_dual_quaternion_equal(dq1, dq2, ...)	Raise an assertion if unit dual quaternions are not approximately equal.
dual_quaternion_double(dq)	Create another dual quaternion that represents the same transformation.
dq_conj(dq)	Conjugate of dual quaternion.
dq_q_conj(dq)	Quaternion conjugate of dual quaternion.
concatenate_dual_quaternions(dq1, dq2)	Concatenate dual quaternions.
dq_prod_vector(dq, v)	Apply transform represented by a dual quaternion to a vector.
dual_quaternion_power(dq, t)	Compute power of unit dual quaternion with respect to scalar.
dual_quaternion_sclerp(start, end, t)	Screw linear interpolation (ScLERP) for dual quaternions.
dual_quaternion_from_transform(A2B)	Compute dual quaternion from transformation matrix.
dual_quaternion_from_pq(pq)	Compute dual quaternion from position and quaternion.
dual_quaternion_from_screw_parameters(q, ...)	Compute dual quaternion from screw parameters.

Jacobians

left_jacobian_SE3(Stheta)	Left Jacobian of SE(3).
left_jacobian_SE3_series(Stheta, n_terms)	Left Jacobian of SE(3) at theta from Taylor series.
left_jacobian_SE3_inv(Stheta)	Left inverse Jacobian of SE(3).
left_jacobian_SE3_inv_series(Stheta, n_terms)	Left inverse Jacobian of SE(3) at theta from Taylor series.

Deprecated Functions

scale_transform(A2B[, s_xr, s_yr, s_zr, ...])

Scale a transform from A to reference frame B.

pytransform3d.batch_rotations

Batch operations on rotations in three dimensions - SO(3).

Conversions from this module operate on batches of orientations or rotations and can be orders of magnitude faster than a loop of individual conversions.

All functions operate on nd arrays, where the last dimension (vectors) or the last two dimensions (matrices) contain individual rotations.

Rotation Matrices

active_matrices_from_angles(basis, angles[, out])	Compute active rotation matrices from rotation about basis vectors.
active_matrices_from_intrinsic_euler_angles(...)	Compute active rotation matrices from intrinsic Euler angles.
active_matrices_from_extrinsic_euler_angles(...)	Compute active rotation matrices from extrinsic Euler angles.
matrices_from_compact_axis_angles([A, axes, ...])	Compute rotation matrices from compact axis-angle representations.
matrices_from_quaternions(Q[, ...])	Compute rotation matrices from quaternions.

Axis-Angle Representation

norm_axis_angles(a)	Normalize axis-angle representation.
axis_angles_from_matrices(Rs[, traces, out])	Compute compact axis-angle representations from rotation matrices.
axis_angles_from_quaternions(qs)	Compute axis-angle from quaternion.
cross_product_matrices(V)	Generate the cross-product matrices of vectors.

Quaternions

batch_concatenate_quaternions(Q1, Q2[, out])	Concatenate two batches of quaternions.
batch_q_conj(Q)	Conjugate of quaternions.
quaternion_slerp_batch(start, end, t[, ...])	Spherical linear interpolation for a batch of steps.
smooth_quaternion_trajectory(Q[, ...])	Smooth quaternion trajectory.
quaternions_from_matrices(Rs[, out])	Compute quaternions from rotation matrices.
batch_quaternion_wxyz_from_xyzw(Q_xyzw[, out])	Converts from x, y, z, w to w, x, y, z convention.
batch_quaternion_xyzw_from_wxyz(Q_wxyz[, out])	Converts from w, x, y, z to x, y, z, w convention.

Utility Functions

norm_vectors(V[, out])	Normalize vectors.
angles_between_vectors(A, B)	Compute angle between two vectors.

pytransform3d.trajectories

Trajectories in three dimensions - SE(3).

Conversions from this module operate on batches of poses or transformations and can be 400 to 1000 times faster than a loop of individual conversions.

Transformation Matrices

invert_transforms(A2Bs)	Invert transforms.
concat_one_to_many(A2B, B2Cs)	Concatenate transformation A2B with multiple transformations B2C.
concat_many_to_one(A2Bs, B2C)	Concatenate multiple transformations A2B with transformation B2C.
concat_many_to_many(A2B, B2C)	Concatenate multiple transformations A2B with transformation B2C.
concat_dynamic(A2B, B2C)	Concatenate multiple transformations A2B,B2C with different shapes.
transforms_from_pqs(P[, normalize_quaternions])	Get sequence of homogeneous matrices from positions and quaternions.
transforms_from_exponential_coordinates(Sthetas)	Compute transformations from exponential coordinates.
transforms_from_dual_quaternions(dqs)	Get transformations from dual quaternions.

Positions and Quaternions

plot_trajectory([ax, P, ...])	Plot pose trajectory.
pqs_from_transforms(A2Bs)	Get sequence of positions and quaternions from homogeneous matrices.
pqs_from_dual_quaternions(dqs)	Get positions and quaternions from dual quaternions.

Screw Parameters

screw_parameters_from_dual_quaternions(dqs)

Compute screw parameters from dual quaternions.

Exponential Coordinates

mirror_screw_axis_direction(Sthetas)	Switch to the other representation of the same transformation.
exponential_coordinates_from_transforms(A2Bs)	Compute exponential coordinates from transformations.

Dual Quaternions

batch_dq_conj(dqs)	Conjugate of dual quaternions.
batch_dq_q_conj(dqs)	Quaternion conjugate of dual quaternions.
batch_concatenate_dual_quaternions(dqs1, dqs2)	Concatenate dual quaternions.
batch_dq_prod_vector(dqs, V)	Apply transforms represented by a dual quaternions to vectors.
dual_quaternions_from_pqs(pqs)	Get dual quaternions from positions and quaternions.
dual_quaternions_power(dqs, ts)	Compute power of unit dual quaternions with respect to scalar.
dual_quaternions_sclerp(starts, ends, ts)	Screw linear interpolation (ScLERP) for array of dual quaternions.
dual_quaternions_from_screw_parameters(qs, ...)	Compute dual quaternions from arrays of screw parameters.

pytransform3d.uncertainty

Operations related to uncertain transformations.

See Uncertainty in Transformations for more information.

estimate_gaussian_transform_from_samples(samples)	Estimate Gaussian distribution over transformations from samples.
invert_uncertain_transform(mean, cov)	Invert uncertain transform.
concat_globally_uncertain_transforms(...)	Concatenate two independent globally uncertain transformations.
concat_locally_uncertain_transforms(...)	Concatenate two independent locally uncertain transformations.
pose_fusion(means, covs)	Fuse Gaussian distributions of multiple poses.
to_ellipsoid(mean, cov)	Compute error ellipsoid.
to_projected_ellipsoid(mean, cov[, factor, ...])	Compute projected error ellipsoid.
plot_projected_ellipsoid(ax, mean, cov[, ...])	Plots projected equiprobable ellipsoid in 3D.

pytransform3d.coordinates

Conversions between coordinate systems to represent positions.

cartesian_from_cylindrical(p)	Convert cylindrical coordinates to Cartesian coordinates.
cartesian_from_spherical(p)	Convert spherical coordinates to Cartesian coordinates.
cylindrical_from_cartesian(p)	Convert Cartesian coordinates to cylindrical coordinates.
cylindrical_from_spherical(p)	Convert spherical coordinates to cylindrical coordinates.
spherical_from_cartesian(p)	Convert Cartesian coordinates to spherical coordinates.
spherical_from_cylindrical(p)	Convert cylindrical coordinates to spherical coordinates.

pytransform3d.transform_manager

Manage complex chains of transformations.

See Organizing Transformations in a Graph for more information.

TransformGraphBase([strict_check, check])	Base class for all graphs of rigid transformations.
TransformManager([strict_check, check])	Manage transformations between frames.
TemporalTransformManager([strict_check, check])	Manage time-varying transformations.
TimeVaryingTransform()	Time-varying rigid transformation.
StaticTransform(A2B)	Transformation, which does not change over time.
NumpyTimeseriesTransform(time, pqs[, ...])	Transformation sequence, represented in a numpy array.

pytransform3d.editor

Modify transformations visually.

TransformEditor(transform_manager, base_frame)

GUI to edit transformations.

pytransform3d.urdf

Load transformations from URDF files.

See Organizing Transformations in a Graph for more information.

UrdfTransformManager([strict_check, check])	Transformation manager that can load URDF files.
Link()	Link from URDF file.
Joint()	Joint from URDF file.
Geometry(frame, mesh_path, package_dir, color)	Geometrical object.
Box(frame, mesh_path, package_dir, color)	Geometrical object: box.
Sphere(frame, mesh_path, package_dir, color)	Geometrical object: sphere.
Cylinder(frame, mesh_path, package_dir, color)	Geometrical object: cylinder.
Mesh(frame, mesh_path, package_dir, color)	Geometrical object: mesh.

parse_urdf(urdf_xml[, mesh_path, ...])	Parse information from URDF file.
initialize_urdf_transform_manager(tm, ...)	Initializes transform manager from previously parsed URDF data.

pytransform3d.camera

Transformations related to cameras.

See Camera for more information.

make_world_grid([n_lines, ...])	Generate grid in world coordinate frame.
make_world_line(p1, p2, n_points)	Generate line in world coordinate frame.
cam2sensor(P_cam, focal_length[, kappa])	Project points from 3D camera coordinate system to sensor plane.
sensor2img(P_sensor, sensor_size, image_size)	Project points from 2D sensor plane to image coordinate system.
world2image(P_world, cam2world, sensor_size, ...)	Project points from 3D world coordinate system to 2D image.
plot_camera([ax, M, cam2world, ...])	Plot camera in world coordinates.

pytransform3d.plot_utils

Utilities for plotting.

make_3d_axis(ax_s[, pos, unit, n_ticks])	Generate new 3D axis.
remove_frame(ax[, left, bottom, right, top])	Remove axis and scale bbox.
plot_vector([ax, start, direction, s, ...])	Plot Vector.
plot_length_variable([ax, start, end, name, ...])	Plot length with text at its center.
plot_box([ax, size, A2B, ax_s, wireframe, ...])	Plot box.
plot_sphere([ax, radius, p, ax_s, ...])	Plot sphere.
plot_spheres([ax, radius, p, ax_s, ...])	Plot multiple spheres.
plot_cylinder([ax, length, radius, ...])	Plot cylinder.
plot_mesh([ax, filename, A2B, s, ax_s, ...])	Plot mesh.
plot_ellipsoid([ax, radii, A2B, ax_s, ...])	Plot ellipsoid.
plot_capsule([ax, A2B, height, radius, ...])	Plot capsule.
plot_cone([ax, height, radius, A2B, ax_s, ...])	Plot cone.

Arrow3D(xs, ys, zs, *args, **kwargs)	A Matplotlib patch that represents an arrow in 3D.
Frame(A2B[, label, s])	A Matplotlib artist that displays a frame represented by its basis.
LabeledFrame(A2B[, label, s])	Displays a frame represented by its basis with axis labels.
Trajectory(H[, show_direction, n_frames, s])	A Matplotlib artist that displays a trajectory.
Camera(M, cam2world[, ...])	A Matplotlib artist that displays a camera.

pytransform3d.visualizer

Optional 3D renderer based on Open3D’s visualizer.

figure([window_name, width, height, ...])

Create a new figure.

Figure([window_name, width, height, ...])	The top level container for all the plot elements.
Artist()	Abstract base class for objects that can be rendered.
Line3D(P[, c])	A line.
PointCollection3D(P[, s, c])	Collection of points.
Vector3D([start, direction, c])	A vector.
Frame(A2B[, label, s])	Coordinate frame.
Trajectory(H[, n_frames, s, c])	Trajectory of poses.
Sphere([radius, A2B, resolution, c])	Sphere.
Box([size, A2B, c])	Box.
Cylinder([length, radius, A2B, resolution, ...])	Cylinder.
Mesh(filename[, A2B, s, c, convex_hull])	Mesh.
Ellipsoid(radii[, A2B, resolution, c])	Ellipsoid.
Capsule([height, radius, A2B, resolution, c])	Capsule.
Cone([height, radius, A2B, resolution, c])	Cone.
Plane([normal, d, point_in_plane, s, c])	Plane.
Graph(tm, frame[, show_frames, ...])	Graph of connected frames.
Camera(M[, cam2world, ...])	Camera.