Class inertialsim::geometry::VectorBase

template <typename Derived>

ClassList > inertialsim > geometry > VectorBase

CRTP base for 3-dimensional vector types. More...

• #include <vector_base.h>

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

Public Types

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
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

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 (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.
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

Template parameters:

• Derived The derived class (Vector, Translation, or CoordinateTranslation).

Public Types Documentation

typedef Base

using inertialsim::geometry::VectorBase< Derived >::Base =  MatrixLieGroup<Derived, 4, 3>;

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Public Functions Documentation

function AsSpherical

Return spherical coordinates (radius, polar, azimuth).

inline Array3D inertialsim::geometry::VectorBase::AsSpherical () const

Returns:

Spherical coordinates (3xN matrix).

---

function AsXyz

Return Cartesian coordinates.

inline Vector3D inertialsim::geometry::VectorBase::AsXyz () const

Returns:

Cartesian coordinates (3xN matrix).

---

function Error [½]

Calculate error compared to a reference vector.

inline Vector3D inertialsim::geometry::VectorBase::Error (
    const Derived & reference
) const

Parameters:

• reference Reference vector.

Returns:

Error values.

---

function Error [2/2]

Calculate error compared to a reference array.

inline Vector3D inertialsim::geometry::VectorBase::Error (
    const Vector3D & reference
) const

Parameters:

• reference Reference coordinates (3xN matrix).

Returns:

Error values.

---

function num_vectors

Number of vectors stored.

inline int inertialsim::geometry::VectorBase::num_vectors () const

---

function operator*

Multiply by a scalar.

inline Derived inertialsim::geometry::VectorBase::operator* (
    double scalar
) const

Parameters:

• scalar Scalar multiplier.

Returns:

New vector containing the product.

---

function operator+

Add two vectors.

inline Derived inertialsim::geometry::VectorBase::operator+ (
    const Derived & rhs
) const

Parameters:

• rhs Right-hand side vector.

Returns:

New vector containing the sum.

---

function operator-

Subtract two vectors.

inline Derived inertialsim::geometry::VectorBase::operator- (
    const Derived & rhs
) const

Parameters:

• rhs Right-hand side vector.

Returns:

New vector containing the difference.

---

function operator/

Divide by a scalar.

inline Derived inertialsim::geometry::VectorBase::operator/ (
    double scalar
) const

Parameters:

• scalar Scalar divisor.

Returns:

New vector containing the quotient.

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Public Static Functions Documentation

function FromSpherical

Construct from spherical coordinates (radius, polar, azimuth).

static inline Derived inertialsim::geometry::VectorBase::FromSpherical (
    const Array3D & rpa,
    const std::optional< Timestamps > & time=std::nullopt
) 

Parameters:

• rpa Spherical coordinates (3xN matrix).
• time Optional time array.

Returns:

Derived instance.

---

function FromXyz

Construct from Cartesian coordinates.

static inline Derived inertialsim::geometry::VectorBase::FromXyz (
    const Vector3D & xyz,
    const std::optional< Timestamps > & time=std::nullopt
) 

Parameters:

• xyz Cartesian coordinates (3xN matrix).
• time Optional time array.

Returns:

Derived instance.

---

Protected Functions Documentation

function ApplyImpl

Apply (add) vector to input vectors.

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

Parameters:

• rhs Input vectors (3xN matrix).

Returns:

Sum of vectors.

---

function AsAlgebraImpl

Return as algebra elements.

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

Returns:

Algebra elements (3xN matrix).

---

function AsGroupImpl

Return as group elements (for CRTP interface).

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

Returns:

Array of 4x4 homogeneous transform matrices.

---

function InverseImpl

Return the inverse (negative) of the vector.

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

Returns:

Vector with negated coordinates.

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function VectorBase [½]

Default constructor.

inline inertialsim::geometry::VectorBase::VectorBase () 

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function VectorBase [2/2]

Construct from Cartesian coordinates.

inline explicit inertialsim::geometry::VectorBase::VectorBase (
    const Vector3D & xyz,
    const std::optional< Timestamps > & time=std::nullopt
) 

Parameters:

• xyz Cartesian coordinates (3xN matrix).
• time Optional time array.

---

function num_elements_impl

Number of vectors stored.

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

---

Protected Static Functions Documentation

function ExpImpl

Exponential map: vector to homogeneous transform matrix.

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

Parameters:

• vector 3D vector (algebra element).

Returns:

4x4 homogeneous transform matrix (group element).

---

function FromAlgebraImpl

Construct from algebra elements.

static inline Derived inertialsim::geometry::VectorBase::FromAlgebraImpl (
    const AlgebraArray & elements,
    const std::optional< Timestamps > & time=std::nullopt
) 

Parameters:

• elements Algebra elements (3xN matrix of vectors).
• time Optional time array.

Returns:

Derived instance.

---

function FromGroupImpl

Construct from group elements (for CRTP interface).

static inline Derived inertialsim::geometry::VectorBase::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 (zero) vectors.

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

Parameters:

• num_elements Number of zero vectors.

Returns:

Derived instance.

---

function FromRandomImpl

Construct random vectors.

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

Parameters:

• num_elements Number of random vectors.
• seed Optional random seed.

Returns:

Derived instance with random coordinates.

---

function JacobianImpl

Left/Right Jacobian of the vector group.

static inline JacobianMatrixArray inertialsim::geometry::VectorBase::JacobianImpl (
    const AlgebraArray & vectors,
    const std::string &="left",
    bool=false
) 

For vectors, both left and right Jacobians are identity.

Parameters:

• vectors Vectors (3xN matrix).
• inverse If true, return inverse Jacobian (also identity).

Returns:

Vector of 3x3 identity matrices.

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function LogImpl

Logarithm map: homogeneous transform to vector.

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

Parameters:

• element 4x4 homogeneous transform matrix (group element).

Returns:

3D vector (algebra element).

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Friends Documentation

friend operator*

Scalar multiplication from the left (friend declaration).

inline Derived inertialsim::geometry::VectorBase::operator* (
    double scalar,
    const Derived & vec
) 

Parameters:

• scalar Scalar multiplier.
• vec Vector to multiply.

Returns:

New vector containing the product.

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