Class inertialsim::geometry::RigidTransformBase

template <typename Derived>

ClassList > inertialsim > geometry > RigidTransformBase

Base class 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 Array of algebra elements.
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 Compose elements of the group.
Derived	operator[] (int index) const Get a single element by index.
const std::optional< Timestamps > &	time () const Time array corresponding to each element.
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
	RigidTransformBase () Default constructor.
	RigidTransformBase (const Rotation & rotation, const Translation & translation, const std::optional< Timestamps > & time=std::nullopt) Construct from rotation and translation.

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.
	MatrixLieGroup (const std::optional< Timestamps > & time=std::nullopt) Constructor.
int	num_times () const

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 of the exponential map.
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>;

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Public Functions Documentation

function AsHomogeneousMatrix

Return homogeneous transform matrices.

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

Returns:

Vector of 4x4 matrices.

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function AsRotation

Return rotation component.

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

Returns:

Rotation instance.

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function AsRotationTranslation

Return rotation and translation components.

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

Returns:

Pair containing:

• Rotation component
• Translation component

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function AsTranslation

Return translation component.

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

Returns:

Translation instance.

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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 containing:

• Rotation error
• Translation error

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function num_transforms

Number of transforms stored.

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

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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.

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function FromRotationTranslation [1/2]

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.

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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.

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Protected Functions Documentation

function RigidTransformBase [1/2]

Default constructor.

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

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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.

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