Class inertialsim::geometry::RigidTransformBase¶

template <typename Derived>

ClassList > inertialsim > geometry > RigidTransformBase

CRTP base for 3-dimensional rigid body transform types. More...

#include <rigid_transform_base.h>

Inherits the following classes: inertialsim::geometry::MatrixLieGroup

Public Types¶

Type	Name
typedef MatrixLieGroup< Derived, 4, 6 >	Base

Public Types inherited from inertialsim::geometry::MatrixLieGroup¶

See inertialsim::geometry::MatrixLieGroup

Type	Name
typedef Eigen::Matrix< Scalar, AlgebraDimension, Eigen::Dynamic >	AlgebraArray Matrix of algebra elements (rows = axes, cols = samples).
typedef Eigen::Matrix< Scalar, AlgebraDimension, 1 >	AlgebraElement Algebra element type (vector).
typedef std::vector< GroupElement >	GroupArray Array of group elements.
typedef Eigen::Matrix< Scalar, GroupDimension, GroupDimension >	GroupElement Group element type (square matrix).
typedef Eigen::Matrix< Scalar, AlgebraDimension, AlgebraDimension >	JacobianMatrix Jacobian matrix (algebra to algebra).
typedef std::vector< JacobianMatrix >	JacobianMatrixArray Array of Jacobian matrices.

Public Functions¶

Type	Name
TransformMatrixArray	AsHomogeneousMatrix () const Return homogeneous transform matrices.
const Rotation &	AsRotation () const Return rotation component.
std::pair< Rotation, Translation >	AsRotationTranslation () const Return rotation and translation components.
const Translation &	AsTranslation () const Return translation component.
std::tuple< Vector3D, Vector3D >	Error (const RigidTransformBase< OtherDerived > & reference) const Calculate error compared to a reference transform.
int	num_transforms () const Number of transforms stored.

Public Functions inherited from inertialsim::geometry::MatrixLieGroup¶

See inertialsim::geometry::MatrixLieGroup

Type	Name
Vector3D	Apply (const Vector3D & vectors) const Apply the group action to an array of vectors.
Derived	Interpolate (const Timestamps & interp_time, Interpolator method=Interpolator::LINEAR) const Interpolate at given times.
Derived	Inverse () const Invert an instance.
Derived	Slice (int start, int end) const Get a slice of elements.
AlgebraArray	TimeDerivative (int order=1, int accuracy=4, const std::string & side="right") const Compute time derivative using finite differences.
int	num_elements () const Number of elements stored in the instance.
Derived	operator* (const Derived & rhs) const Composition operator on the matrix group. Supports broadcasting: if either lhs or rhs has size 1, it will be broadcast against all elements of the other operand. Derived classes may implement more efficient methods.
Derived	operator[] (int index) const Get a single element by index.
const std::optional< Timestamps > &	time () const Time array (or nullopt if not set).
virtual	~MatrixLieGroup () = default

Public Static Functions¶

Type	Name
Derived	FromHomogeneousMatrix (const TransformMatrixArray & matrices, const std::optional< Timestamps > & time=std::nullopt, bool orthonormalize=false) Construct a RigidTransform from homogeneous transform matrices.
Derived	FromRotationTranslation (const Rotation & rotation, const Translation & translation, const std::optional< Timestamps > & time=std::nullopt) Construct a RigidTransform from rotation and translation.
Derived	FromRotationTranslation (const RotationMatrixArray & matrix, const Vector3D & xyz, const std::optional< Timestamps > & time=std::nullopt, bool orthonormalize=false) Construct from rotation matrices and translation vectors.

Public Static Functions inherited from inertialsim::geometry::MatrixLieGroup¶

See inertialsim::geometry::MatrixLieGroup

Type	Name
Derived	Compose (const std::vector< Derived > & instances) Compose a sequence of instances (first to last).
Derived	FromIdentity (int num_elements=1) Create identity elements.
Derived	FromRandom (int num_elements=1, std::optional< Eigen::numext::uint64_t > seed=std::nullopt) Create random elements.

Protected Functions¶

Type	Name
Vector3D	ApplyImpl (const Vector3D & vectors) const Apply transform to vectors.
AlgebraArray	AsAlgebraImpl () const Return as algebra elements (for CRTP interface).
GroupArray	AsGroupImpl () const Return as group elements (for CRTP interface).
Derived	InverseImpl () const Return the inverse transform.
	RigidTransformBase () Default constructor.
	RigidTransformBase (const Rotation & rotation, const Translation & translation, const std::optional< Timestamps > & time=std::nullopt) Construct from rotation and translation.
int	num_elements_impl () const Number of transforms stored.

Protected Functions inherited from inertialsim::geometry::MatrixLieGroup¶

See inertialsim::geometry::MatrixLieGroup

Type	Name
AlgebraArray	AsAlgebra () const Get the algebra elements.
GroupArray	AsGroup () const Get the group elements.
Derived	CubicHermiteInterpolate (const Timestamps & time) const Cubic Hermite spline interpolation.
Derived	LinearInterpolate (const Timestamps & time) const Linear interpolation implementation.
	MatrixLieGroup (const std::optional< Timestamps > & time=std::nullopt) Constructor.
Derived &	derived () CRTP helper to access derived class.
const Derived &	derived () const
int	num_times () const

Protected Static Functions¶

Type	Name
GroupElement	ExpImpl (const AlgebraElement & vector) Exponential map: se(3) to SE(3).
Derived	FromAlgebraImpl (const AlgebraArray & algebra, const std::optional< Timestamps > & time) Construct from algebra elements (for CRTP interface).
Derived	FromGroupImpl (const GroupArray & elements, const std::optional< Timestamps > & time) Construct from group elements (for CRTP interface).
Derived	FromIdentityImpl (int num_elements) Construct identity transforms.
Derived	FromRandomImpl (int num_transforms, std::optional< uint64_t > seed=std::nullopt) Construct uniformly distributed random transforms.
Eigen::Matrix3d	JacobianAuxiliary (const Eigen::Vector3d & rv, const Eigen::Vector3d & t) Auxiliary matrix Q for SE(3) Jacobians.
JacobianMatrixArray	JacobianImpl (const AlgebraArray & algebra, const std::string & side="left", bool inverse=false) Left or Right Jacobian of SE(3).
AlgebraElement	LogImpl (const GroupElement & element) Logarithm map: SE(3) to se(3).

Protected Static Functions inherited from inertialsim::geometry::MatrixLieGroup¶

See inertialsim::geometry::MatrixLieGroup

Type	Name
GroupElement	Exp (const AlgebraElement & vector) Exponential map from algebra to group.
Derived	FromAlgebra (const AlgebraArray & elements, const std::optional< Timestamps > & time) Create instance from algebra elements.
Derived	FromGroup (const GroupArray & elements, const std::optional< Timestamps > & time) Create instance from group elements.
JacobianMatrixArray	Jacobian (const AlgebraArray & algebra, const std::string & side="left", bool inverse=false) Calculate the Jacobian given algebra elements.
AlgebraElement	Log (const GroupElement & element) Logarithm map from group to algebra.

Detailed Description¶

Template parameters:

Derived The derived class (RigidTransform, Pose, or CoordinateTransform).

Public Types Documentation¶

typedef Base¶

using inertialsim::geometry::RigidTransformBase< Derived >::Base =  MatrixLieGroup<Derived, 4, 6>;

Public Functions Documentation¶

function AsHomogeneousMatrix¶

Return homogeneous transform matrices.

inline TransformMatrixArray inertialsim::geometry::RigidTransformBase::AsHomogeneousMatrix () const

Returns:

Vector of 4x4 matrices.

function AsRotation¶

Return rotation component.

inline const Rotation & inertialsim::geometry::RigidTransformBase::AsRotation () const

Returns:

Rotation instance.

function AsRotationTranslation¶

Return rotation and translation components.

inline std::pair< Rotation , Translation > inertialsim::geometry::RigidTransformBase::AsRotationTranslation () const

Returns:

Tuple of Rotation and Translation.

function AsTranslation¶

Return translation component.

inline const Translation & inertialsim::geometry::RigidTransformBase::AsTranslation () const

Returns:

Translation instance.

function Error¶

Calculate error compared to a reference transform.

template<typename OtherDerived>
inline std::tuple< Vector3D, Vector3D > inertialsim::geometry::RigidTransformBase::Error (
    const RigidTransformBase < OtherDerived > & reference
) const

Parameters:

reference Reference transform.

Returns:

Tuple of rotation error and translation error.

function num_transforms¶

Number of transforms stored.

inline int inertialsim::geometry::RigidTransformBase::num_transforms () const

Public Static Functions Documentation¶

function FromHomogeneousMatrix¶

Construct a RigidTransform from homogeneous transform matrices.

static inline Derived inertialsim::geometry::RigidTransformBase::FromHomogeneousMatrix (
    const TransformMatrixArray & matrices,
    const std::optional< Timestamps > & time=std::nullopt,
    bool orthonormalize=false
)

The input matrices must have 4x4 block structure [[R, t], [0, 1]] where R is a valid rotation matrix and t is a translation vector.

See Rotation::FromMatrix() for additional details regarding the rotation matrix block.

Parameters:

matrices Vector of 4x4 homogeneous transform matrices.
time Optional time array of unique, strictly increasing times corresponding to each matrix input.
orthonormalize If true, enforce orthonormality of the rotation component of the input.

Returns:

Derived instance.

function FromRotationTranslation [½]¶

Construct a RigidTransform from rotation and translation.

static inline Derived inertialsim::geometry::RigidTransformBase::FromRotationTranslation (
    const Rotation & rotation,
    const Translation & translation,
    const std::optional< Timestamps > & time=std::nullopt
)

The inputs must be compatible (dimension, time, etc.) or a ValueError is raised.

Parameters:

rotation Rotation instance.
translation Translation instance.
time Optional time array (ignored if rotation has time).

Returns:

Derived instance.

function FromRotationTranslation [2/2]¶

Construct from rotation matrices and translation vectors.

static inline Derived inertialsim::geometry::RigidTransformBase::FromRotationTranslation (
    const RotationMatrixArray & matrix,
    const Vector3D & xyz,
    const std::optional< Timestamps > & time=std::nullopt,
    bool orthonormalize=false
)

Parameters:

rotation_matrices Vector of 3x3 rotation matrices.
translation_xyz Translation coordinates (3xN).
time Optional time array.
orthonormalize If true, enforce orthonormality.

Returns:

Derived instance.

Protected Functions Documentation¶

function ApplyImpl¶

Apply transform to vectors.

inline Vector3D inertialsim::geometry::RigidTransformBase::ApplyImpl (
    const Vector3D & vectors
) const

Parameters:

vectors Vectors to transform (3xN matrix).

Returns:

Transformed vectors.

function AsAlgebraImpl¶

Return as algebra elements (for CRTP interface).

inline AlgebraArray inertialsim::geometry::RigidTransformBase::AsAlgebraImpl () const

Returns:

Matrix of algebra elements (6 x N).

function AsGroupImpl¶

Return as group elements (for CRTP interface).

inline GroupArray inertialsim::geometry::RigidTransformBase::AsGroupImpl () const

Returns:

Vector of 4x4 matrices.

function InverseImpl¶

Return the inverse transform.

inline Derived inertialsim::geometry::RigidTransformBase::InverseImpl () const

Returns:

Derived with inverted transformation.

function RigidTransformBase [½]¶

Default constructor.

inline inertialsim::geometry::RigidTransformBase::RigidTransformBase ()

function RigidTransformBase [2/2]¶

Construct from rotation and translation.

inline inertialsim::geometry::RigidTransformBase::RigidTransformBase (
    const Rotation & rotation,
    const Translation & translation,
    const std::optional< Timestamps > & time=std::nullopt
)

Parameters:

rotation Rotation component.
translation Translation component.
time Optional time array.

function num_elements_impl¶

Number of transforms stored.

inline int inertialsim::geometry::RigidTransformBase::num_elements_impl () const

Protected Static Functions Documentation¶

function ExpImpl¶

Exponential map: se(3) to SE(3).

static inline GroupElement inertialsim::geometry::RigidTransformBase::ExpImpl (
    const AlgebraElement & vector
)

Parameters:

vector 6D algebra element [rotation_vector, translation].

Returns:

4x4 homogeneous transform matrix.

function FromAlgebraImpl¶

Construct from algebra elements (for CRTP interface).

static inline Derived inertialsim::geometry::RigidTransformBase::FromAlgebraImpl (
    const AlgebraArray & algebra,
    const std::optional< Timestamps > & time
)

Parameters:

algebra Algebra elements (N x 6 matrix).
time Optional time array.

Returns:

Derived instance.

function FromGroupImpl¶

Construct from group elements (for CRTP interface).

static inline Derived inertialsim::geometry::RigidTransformBase::FromGroupImpl (
    const GroupArray & elements,
    const std::optional< Timestamps > & time
)

Parameters:

elements Array of 4x4 homogeneous transform matrices.
time Optional time array.

Returns:

Derived instance.

function FromIdentityImpl¶

Construct identity transforms.

static inline Derived inertialsim::geometry::RigidTransformBase::FromIdentityImpl (
    int num_elements
)

Parameters:

num_elements Number of identity transforms.

Returns:

Derived instance.

function FromRandomImpl¶

Construct uniformly distributed random transforms.

static inline Derived inertialsim::geometry::RigidTransformBase::FromRandomImpl (
    int num_transforms,
    std::optional< uint64_t > seed=std::nullopt
)

Rotation components are uniformly distributed on the unit sphere (SO(3)). Translation components are uniformly distributed between 0 and 1.

Parameters:

num_transforms Number of random transforms to create.
seed Optional random seed for reproducibility.

Returns:

Derived instance with random transforms.

function JacobianAuxiliary¶

Auxiliary matrix Q for SE(3) Jacobians.

static inline Eigen::Matrix3d inertialsim::geometry::RigidTransformBase::JacobianAuxiliary (
    const Eigen::Vector3d & rv,
    const Eigen::Vector3d & t
)

Parameters:

rv Rotation vector.
t Translation vector.

Returns:

3x3 auxiliary matrix.

function JacobianImpl¶

Left or Right Jacobian of SE(3).

static inline JacobianMatrixArray inertialsim::geometry::RigidTransformBase::JacobianImpl (
    const AlgebraArray & algebra,
    const std::string & side="left",
    bool inverse=false
)

Parameters:

algebra Algebra elements (N x 6 matrix).
side "left" (default) or "right".
inverse If true, return inverse Jacobian.

Returns:

Vector of 6x6 Jacobian matrices.

function LogImpl¶

Logarithm map: SE(3) to se(3).

static inline AlgebraElement inertialsim::geometry::RigidTransformBase::LogImpl (
    const GroupElement & element
)

Parameters:

element 4x4 homogeneous transform matrix.

Returns:

6D algebra element [rotation_vector, translation].

The documentation for this class was generated from the following file cpp/include/inertialsim/geometry/rigid_transform_base.h