#include <Gal3.h>

Inheritance diagram for gtsam::Gal3:

Classes
struct	ChartAtOrigin
	Chart at origin, uses Expmap/Logmap for Retract/Local. More...

Public Member Functions
Component Access
const Rot3 &	rotation (OptionalJacobian< 3, 10 > H={}) const
	Access rotation component (Rot3) More...

const Point3 &	translation (OptionalJacobian< 3, 10 > H={}) const
	Access translation component (Point3) More...

const Velocity3 &	velocity (OptionalJacobian< 3, 10 > H={}) const
	Access velocity component (Vector3) More...

const double &	time (OptionalJacobian< 1, 10 > H={}) const
	Access time component (double) More...

const Rot3 &	attitude (OptionalJacobian< 3, 10 > H={}) const

const Point3 &	position (OptionalJacobian< 3, 10 > H={}) const

Derived quantities
Matrix3	R () const
	Return rotation matrix (Matrix3) More...

Vector3	r () const
	Return position as Vector3. More...

const Vector3 &	v () const
	Return velocity as Vector3. More...

const double &	t () const
	Return time scalar. More...

Matrix5	matrix () const
	Return 5x5 homogeneous matrix representation. More...

Group Action
Event	act (const Event &e, OptionalJacobian< 4, 10 > Hself={}, OptionalJacobian< 4, 4 > He={}) const

Public Member Functions inherited from gtsam::LieGroup< Gal3, 10 >
Gal3	between (const Gal3 &g) const

Gal3	between (const Gal3 &g, ChartJacobian H1, ChartJacobian H2={}) const

SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

GTSAM_EXPORT SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

Gal3	compose (const Gal3 &g) const

Gal3	compose (const Gal3 &g, ChartJacobian H1, ChartJacobian H2={}) const

SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

GTSAM_EXPORT SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

const Gal3 &	derived () const

Gal3	expmap (const TangentVector &v) const

Gal3	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

Gal3	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Gal3 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Gal3 &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Gal3 &g) const

TangentVector	logmap (const Gal3 &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

Gal3	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Gal3	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Static Public Attributes
static constexpr size_t	dimension = 10
	The dimension of the tangent space. More...

Static Public Attributes inherited from gtsam::LieGroup< Gal3, 10 >
constexpr static auto	dimension

Private Attributes
Rot3	R_
	Rotation world R body. More...

Point3	r_
	Position in world frame, n_r_b. More...

double	t_
	Time component. More...

Velocity3	v_
	Velocity in world frame, n_v_b. More...

Constructors
	Gal3 ()
	Default constructor: Identity element. More...

	Gal3 (const Rot3 &R, const Point3 &r, const Velocity3 &v, double t)
	Construct from attitude, position, velocity, time. More...

	Gal3 (const Matrix5 &M)
	Construct from a 5x5 matrix representation. More...

static Gal3	Create (const Rot3 &R, const Point3 &r, const Velocity3 &v, double t, OptionalJacobian< 10, 3 > H1={}, OptionalJacobian< 10, 3 > H2={}, OptionalJacobian< 10, 3 > H3={}, OptionalJacobian< 10, 1 > H4={})
	Named constructor from components with derivatives. More...

static Gal3	FromPoseVelocityTime (const Pose3 &pose, const Velocity3 &v, double t, OptionalJacobian< 10, 6 > H1={}, OptionalJacobian< 10, 3 > H2={}, OptionalJacobian< 10, 1 > H3={})
	Named constructor from Pose3, velocity, and time with derivatives. More...

Testable
void	print (const std::string &s="") const
	Print with optional string prefix. More...

bool	equals (const Gal3 &other, double tol=1e-9) const
	Check equality within tolerance. More...

GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Gal3 &state)
	Output stream operator. More...

Group
Gal3	inverse () const
	Return the inverse of this element. More...

Gal3	operator* (const Gal3 &other) const
	Group composition operator. More...

static Gal3	Identity ()
	Return the identity element. More...

Lie Group Static Functions
Matrix10	AdjointMap () const
	Calculate Adjoint map Ad_g. More...

Vector10	Adjoint (const Vector10 &xi_base, OptionalJacobian< 10, 10 > H_g={}, OptionalJacobian< 10, 10 > H_xi={}) const
	Apply this element's AdjointMap Ad_g to a tangent vector xi_base at identity. More...

static Gal3	Expmap (const Vector10 &xi, OptionalJacobian< 10, 10 > Hxi={})
	Exponential map at identity: tangent vector xi -> manifold element g. More...

static Vector10	Logmap (const Gal3 &g, OptionalJacobian< 10, 10 > Hg={})
	Logarithmic map at identity: manifold element g -> tangent vector xi. More...

static Vector10	adjoint (const Vector10 &xi, const Vector10 &y, OptionalJacobian< 10, 10 > Hxi={}, OptionalJacobian< 10, 10 > Hy={})
	The adjoint action `ad(xi, y)` = `adjointMap(xi) * y` More...

static Matrix10	adjointMap (const Vector10 &xi)
	Compute the adjoint map `ad(xi)` associated with tangent vector xi. More...

static Matrix10	ExpmapDerivative (const Vector10 &xi)
	Derivative of Expmap(xi) w.r.t. xi evaluated at xi. More...

static Matrix10	LogmapDerivative (const Gal3 &g)
	Derivative of Logmap(g) w.r.t. g. More...

static Matrix5	Hat (const Vector10 &xi)
	Hat operator: maps tangent vector xi to Lie algebra matrix. More...

static Vector10	Vee (const Matrix5 &X)
	Vee operator: maps Lie algebra matrix to tangent vector xi. More...

Additional Inherited Members
Public Types inherited from gtsam::LieGroup< Gal3, 10 >
typedef OptionalJacobian< N, N >	ChartJacobian

typedef Eigen::Matrix< double, N, N >	Jacobian

typedef Eigen::Matrix< double, N, 1 >	TangentVector

Static Public Member Functions inherited from gtsam::LieGroup< Gal3, 10 >
static TangentVector	LocalCoordinates (const Gal3 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Gal3 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Gal3	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Gal3	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

Represents an element of the 3D Galilean group SGal(3). Internal state: rotation, translation, velocity, time.

Definition at line 45 of file Gal3.h.

Constructor & Destructor Documentation

◆ Gal3() [1/3]

gtsam::Gal3::Gal3 ( )

inline

Default constructor: Identity element.

Definition at line 61 of file Gal3.h.

◆ Gal3() [2/3]

gtsam::Gal3::Gal3	(	const Rot3 &	R,
		const Point3 &	r,
		const Velocity3 &	v,
		double	t
	)

inline

Construct from attitude, position, velocity, time.

Definition at line 64 of file Gal3.h.

◆ Gal3() [3/3]

gtsam::Gal3::Gal3 ( const Matrix5 & M )

explicit

Construct from a 5x5 matrix representation.

Definition at line 114 of file Gal3.cpp.

Member Function Documentation

◆ act()

Event gtsam::Gal3::act	(	const Event &	e,
		OptionalJacobian< 4, 10 >	Hself = `{}`,
		OptionalJacobian< 4, 4 >	He = `{}`
	)		const

Apply Galilean transform to a spacetime Event

Parameters

e	Input event (location, time)
Hself	Optional Jacobian wrt this Gal3 element's tangent space
He	Optional Jacobian wrt the input event's tangent space

Returns: Transformed event

Definition at line 463 of file Gal3.cpp.

◆ adjoint()

Vector10 gtsam::Gal3::adjoint	(	const Vector10 &	xi,
		const Vector10 &	y,
		OptionalJacobian< 10, 10 >	Hxi = `{}`,
		OptionalJacobian< 10, 10 >	Hy = `{}`
	)

static

The adjoint action ad(xi, y) = adjointMap(xi) * y

Definition at line 382 of file Gal3.cpp.

◆ Adjoint()

Vector10 gtsam::Gal3::Adjoint	(	const Vector10 &	xi_base,
		OptionalJacobian< 10, 10 >	H_g = `{}`,
		OptionalJacobian< 10, 10 >	H_xi = `{}`
	)		const

Apply this element's AdjointMap Ad_g to a tangent vector xi_base at identity.

Definition at line 336 of file Gal3.cpp.

◆ AdjointMap()

Matrix10 gtsam::Gal3::AdjointMap ( ) const

Calculate Adjoint map Ad_g.

Definition at line 312 of file Gal3.cpp.

◆ adjointMap()

Matrix10 gtsam::Gal3::adjointMap ( const Vector10 & xi )

static

Compute the adjoint map ad(xi) associated with tangent vector xi.

Definition at line 358 of file Gal3.cpp.

◆ attitude()

const Rot3& gtsam::Gal3::attitude ( OptionalJacobian< 3, 10 > H = {} ) const

inline

Definition at line 100 of file Gal3.h.

◆ Create()

Gal3 gtsam::Gal3::Create	(	const Rot3 &	R,
		const Point3 &	r,
		const Velocity3 &	v,
		double	t,
		OptionalJacobian< 10, 3 >	H1 = `{}`,
		OptionalJacobian< 10, 3 >	H2 = `{}`,
		OptionalJacobian< 10, 3 >	H3 = `{}`,
		OptionalJacobian< 10, 1 >	H4 = `{}`
	)

static

Named constructor from components with derivatives.

Definition at line 63 of file Gal3.cpp.

◆ equals()

bool gtsam::Gal3::equals	(	const Gal3 &	other,
		double	tol = `1e-9`
	)		const

Check equality within tolerance.

Definition at line 200 of file Gal3.cpp.

◆ Expmap()

gtsam::Gal3 gtsam::Gal3::Expmap	(	const Vector10 &	xi,
		OptionalJacobian< 10, 10 >	Hxi = `{}`
	)

static

Exponential map at identity: tangent vector xi -> manifold element g.

Definition at line 238 of file Gal3.cpp.

◆ ExpmapDerivative()

Matrix10 gtsam::Gal3::ExpmapDerivative ( const Vector10 & xi )

static

Derivative of Expmap(xi) w.r.t. xi evaluated at xi.

Definition at line 392 of file Gal3.cpp.

◆ FromPoseVelocityTime()

Gal3 gtsam::Gal3::FromPoseVelocityTime	(	const Pose3 &	pose,
		const Velocity3 &	v,
		double	t,
		OptionalJacobian< 10, 6 >	H1 = `{}`,
		OptionalJacobian< 10, 3 >	H2 = `{}`,
		OptionalJacobian< 10, 1 >	H3 = `{}`
	)

static

Named constructor from Pose3, velocity, and time with derivatives.

Definition at line 88 of file Gal3.cpp.

◆ Hat()

Matrix5 gtsam::Gal3::Hat ( const Vector10 & xi )

static

Hat operator: maps tangent vector xi to Lie algebra matrix.

Definition at line 419 of file Gal3.cpp.

◆ Identity()

static Gal3 gtsam::Gal3::Identity ( )

inlinestatic

Return the identity element.

Definition at line 141 of file Gal3.h.

◆ inverse()

Gal3 gtsam::Gal3::inverse ( ) const

Return the inverse of this element.

Definition at line 210 of file Gal3.cpp.

◆ Logmap()

Vector10 gtsam::Gal3::Logmap	(	const Gal3 &	g,
		OptionalJacobian< 10, 10 >	Hg = `{}`
	)

static

Logarithmic map at identity: manifold element g -> tangent vector xi.

Definition at line 273 of file Gal3.cpp.

◆ LogmapDerivative()

Matrix10 gtsam::Gal3::LogmapDerivative ( const Gal3 & g )

static

Derivative of Logmap(g) w.r.t. g.

Definition at line 404 of file Gal3.cpp.

◆ matrix()

Matrix5 gtsam::Gal3::matrix ( ) const

Return 5x5 homogeneous matrix representation.

Definition at line 168 of file Gal3.cpp.

◆ operator*()

Gal3 gtsam::Gal3::operator* ( const Gal3 & other ) const

Group composition operator.

Definition at line 220 of file Gal3.cpp.

◆ position()

const Point3& gtsam::Gal3::position ( OptionalJacobian< 3, 10 > H = {} ) const

inline

Definition at line 101 of file Gal3.h.

◆ print()

void gtsam::Gal3::print ( const std::string & s = "" ) const

Print with optional string prefix.

Definition at line 194 of file Gal3.cpp.

◆ R()

Matrix3 gtsam::Gal3::R ( ) const

inline

Return rotation matrix (Matrix3)

Definition at line 108 of file Gal3.h.

◆ r()

Vector3 gtsam::Gal3::r ( ) const

inline

Return position as Vector3.

Definition at line 111 of file Gal3.h.

◆ rotation()

const Rot3 & gtsam::Gal3::rotation ( OptionalJacobian< 3, 10 > H = {} ) const

Access rotation component (Rot3)

Definition at line 129 of file Gal3.cpp.

◆ t()

const double& gtsam::Gal3::t ( ) const

inline

Return time scalar.

Definition at line 117 of file Gal3.h.

◆ time()

const double & gtsam::Gal3::time ( OptionalJacobian< 1, 10 > H = {} ) const

Access time component (double)

Definition at line 157 of file Gal3.cpp.

◆ translation()

const Point3 & gtsam::Gal3::translation ( OptionalJacobian< 3, 10 > H = {} ) const

Access translation component (Point3)

Definition at line 138 of file Gal3.cpp.

◆ v()

const Vector3& gtsam::Gal3::v ( ) const

inline

Return velocity as Vector3.

Definition at line 114 of file Gal3.h.

◆ Vee()

Vector10 gtsam::Gal3::Vee ( const Matrix5 & X )

static

Vee operator: maps Lie algebra matrix to tangent vector xi.

Definition at line 435 of file Gal3.cpp.

◆ velocity()

const Velocity3 & gtsam::Gal3::velocity ( OptionalJacobian< 3, 10 > H = {} ) const

Access velocity component (Vector3)

Definition at line 148 of file Gal3.cpp.

Friends And Related Function Documentation

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Gal3 &	state
	)

friend

Output stream operator.

Definition at line 183 of file Gal3.cpp.

Member Data Documentation

◆ dimension

constexpr size_t gtsam::Gal3::dimension = 10

inlinestaticconstexpr

The dimension of the tangent space.

Definition at line 55 of file Gal3.h.

◆ R_

Rot3 gtsam::Gal3::R_

private

Rotation world R body.

Definition at line 47 of file Gal3.h.

◆ r_

Point3 gtsam::Gal3::r_

private

Position in world frame, n_r_b.

Definition at line 48 of file Gal3.h.

◆ t_

double gtsam::Gal3::t_

private

Time component.

Definition at line 50 of file Gal3.h.

◆ v_

Velocity3 gtsam::Gal3::v_

private

Velocity in world frame, n_v_b.

Definition at line 49 of file Gal3.h.

The documentation for this class was generated from the following files:

Classes

Public Member Functions

Static Public Attributes

Private Attributes

Constructors

Testable

Group

Lie Group Static Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Gal3() [1/3]

◆ Gal3() [2/3]

◆ Gal3() [3/3]

Member Function Documentation

◆ act()

◆ adjoint()

◆ Adjoint()

◆ AdjointMap()

◆ adjointMap()

◆ attitude()

◆ Create()

◆ equals()

◆ Expmap()

◆ ExpmapDerivative()

◆ FromPoseVelocityTime()

◆ Hat()

◆ Identity()

◆ inverse()

◆ Logmap()

◆ LogmapDerivative()

◆ matrix()

◆ operator*()

◆ position()

◆ print()

◆ R()

◆ r()

◆ rotation()

◆ t()

◆ time()

◆ translation()

◆ v()

◆ Vee()

◆ velocity()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ dimension

◆ R_

◆ r_

◆ t_

◆ v_