Class inertialsim::geometry::CoordinateTranslation¶

ClassList > inertialsim > geometry > CoordinateTranslation

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

#include <coordinate_translation.h>

Inherits the following classes: inertialsim::geometry::VectorBase

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

Type	Name
typedef MatrixLieGroup< Derived, 4, 3 >	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
int	num_translations () const Number of translations stored.

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

See inertialsim::geometry::VectorBase

Type	Name
Array3D	AsSpherical () const Return spherical coordinates (radius, polar, azimuth).
Vector3D	AsXyz () const Return Cartesian coordinates.
Vector3D	Error (const Derived & reference) const Calculate error compared to a reference vector.
Vector3D	Error (const Vector3D & reference) const Calculate error compared to a reference array.
int	num_vectors () const Number of vectors stored.
Derived	operator* (double scalar) const Multiply by a scalar.
Derived	operator+ (const Derived & rhs) const Add two vectors.
Derived	operator- (const Derived & rhs) const Subtract two vectors.
Derived	operator/ (double scalar) const Divide by a scalar.

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 inherited from inertialsim::geometry::VectorBase¶

See inertialsim::geometry::VectorBase

Type	Name
Derived	FromSpherical (const Array3D & rpa, const std::optional< Timestamps > & time=std::nullopt) Construct from spherical coordinates (radius, polar, azimuth).
Derived	FromXyz (const Vector3D & xyz, const std::optional< Timestamps > & time=std::nullopt) Construct from Cartesian coordinates.

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 & rhs) const Apply coordinate translation to input vectors.
GroupArray	AsGroupImpl () const Return as group elements (for CRTP interface).

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

See inertialsim::geometry::VectorBase

Type	Name
Vector3D	ApplyImpl (const Vector3D & rhs) const Apply (add) vector to input vectors.
AlgebraArray	AsAlgebraImpl () const Return as algebra elements.
GroupArray	AsGroupImpl () const Return as group elements (for CRTP interface).
Derived	InverseImpl () const Return the inverse (negative) of the vector.
	VectorBase () Default constructor.
	VectorBase (const Vector3D & xyz, const std::optional< Timestamps > & time=std::nullopt) Construct from Cartesian coordinates.
int	num_elements_impl () const Number of vectors 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: vector to homogeneous transform matrix.
CoordinateTranslation	FromGroupImpl (const GroupArray & elements, const std::optional< Timestamps > & time) Construct from group elements (for CRTP interface).
AlgebraElement	LogImpl (const GroupElement & element) Logarithm map: homogeneous transform to vector.

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

See inertialsim::geometry::VectorBase

Type	Name
GroupElement	ExpImpl (const AlgebraElement & vector) Exponential map: vector to homogeneous transform matrix.
Derived	FromAlgebraImpl (const AlgebraArray & elements, const std::optional< Timestamps > & time=std::nullopt) Construct from algebra elements.
Derived	FromGroupImpl (const GroupArray & elements, const std::optional< Timestamps > & time) Construct from group elements (for CRTP interface).
Derived	FromIdentityImpl (int num_elements) Construct identity (zero) vectors.
Derived	FromRandomImpl (int num_elements, std::optional< uint64_t > seed=std::nullopt) Construct random vectors.
JacobianMatrixArray	JacobianImpl (const AlgebraArray & vectors, const std::string &="left", bool=false) Left/Right Jacobian of the vector group.
AlgebraElement	LogImpl (const GroupElement & element) Logarithm map: homogeneous transform to vector.

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¶

CoordinateTranslation stores translations using the passive convention for use in coordinate frame transforms.

In the passive convention, the translation is negated compared to the active convention used by Translation.

Public Functions Documentation¶

function num_translations¶

Number of translations stored.

inline int inertialsim::geometry::CoordinateTranslation::num_translations () const

Protected Functions Documentation¶

function ApplyImpl¶

Apply coordinate translation to input vectors.

inline Vector3D inertialsim::geometry::CoordinateTranslation::ApplyImpl (
    const Vector3D & rhs
) const

Parameters:

rhs Input vectors (3xN matrix).

Returns:

Translated vectors.

function AsGroupImpl¶

Return as group elements (for CRTP interface).

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

Returns:

Array of 4x4 homogeneous transform matrices.

Note: Uses passive convention - translation is negated.

Protected Static Functions Documentation¶

function ExpImpl¶

Exponential map: vector to homogeneous transform matrix.

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

Parameters:

vector 3D vector (algebra element).

Returns:

4x4 homogeneous transform matrix (group element).

Note: Uses passive convention - vector is negated before exponential.

function FromGroupImpl¶

Construct from group elements (for CRTP interface).

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

Parameters:

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

Returns:

CoordinateTranslation instance.

Note: Uses passive convention - translation is negated.

function LogImpl¶

Logarithm map: homogeneous transform to vector.

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

Parameters:

element 4x4 homogeneous transform matrix (group element).

Returns:

3D vector (algebra element).

Note: Uses passive convention - result is negated.

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