Class inertialsim::geometry::CoordinateTransform¶

ClassList > inertialsim > geometry > CoordinateTransform

3-dimensional coordinate frame transforms (passive convention). More...

#include <coordinate_transform.h>

Inherits the following classes: inertialsim::geometry::RigidTransformBase

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

See inertialsim::geometry::RigidTransformBase

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.
	CoordinateTransform () Default constructor.
	CoordinateTransform (const Rotation & rotation, const Translation & translation, const std::optional< Timestamps > & time=std::nullopt) Construct from base Rotation andTranslation .
	CoordinateTransform (const CoordinateRotation & rotation, const CoordinateTranslation & translation, const std::optional< Timestamps > & time=std::nullopt) Construct from rotation and translation.

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

See inertialsim::geometry::RigidTransformBase

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
CoordinateTransform	FromHomogeneousMatrix (const TransformMatrixArray & matrices, const std::optional< Timestamps > & time=std::nullopt, bool orthonormalize=false) Construct from homogeneous transform matrices.

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

See inertialsim::geometry::RigidTransformBase

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 inherited from inertialsim::geometry::RigidTransformBase¶

See inertialsim::geometry::RigidTransformBase

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¶

CoordinateTransform uses the passive convention where transforms act to convert the description of physical vectors between different coordinate systems. The passive convention is commonly used in inertial navigation and aerospace applications.

Transform conventions

There are a large variety of rotation and transform conventions and they are a common source of errors. Because many of these conventions cannot be automatically validated, users must be aware of them and manage interfaces with other software accordingly. InertialSim conventions are documented in each method.

Active vs passive transform convention

Transforms stored in this class represent a passive transformation. In the passive convention, transforms act to convert the description of physical vectors between different coordinate systems. This contrasts with the active convention used by the RigidTransform class, where transforms act to rotate and translate an object relative to a fixed coordinate system. In general, the two should not be mixed.

Some references use the terminology alibi (active) and alias (passive). Reference [02], Reference [05], and Reference [11] discuss active vs. passive transforms in greater detail.

See also: CoordinateRotation for rotation-only coordinate transforms.

Public Functions Documentation¶

function AsHomogeneousMatrix¶

Return homogeneous transform matrices.

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

Returns matrices with block structure [[C, -C*t], [0, 1]].

Returns:

Homogeneous transform matrices.

function CoordinateTransform [1/3]¶

Default constructor.

inline inertialsim::geometry::CoordinateTransform::CoordinateTransform ()

function CoordinateTransform [2/3]¶

Construct from base Rotation andTranslation .

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

Parameters:

rotation Base rotation component.
translation Base translation component.
time Optional time array.

function CoordinateTransform [3/3]¶

Construct from rotation and translation.

inline inertialsim::geometry::CoordinateTransform::CoordinateTransform (
    const  CoordinateRotation & rotation,
    const  CoordinateTranslation & translation,
    const std::optional< Timestamps > & time=std::nullopt
)

Parameters:

rotation Coordinate rotation component.
translation Coordinate translation component.
time Optional time array.

Public Static Functions Documentation¶

function FromHomogeneousMatrix¶

Construct from homogeneous transform matrices.

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

The input has block structure [[C, t], [0, 1]] where C is the coordinate rotation matrix and t is -C * translation.

Parameters:

matrices Vector of 4x4 homogeneous transform matrices.
time Optional time array.
orthonormalize If true, enforce orthonormality of rotation.

Returns:

CoordinateTransform instance.

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