gtsam::Gal3 Class Reference

Detailed Description

Represents an element of the 3D Galilean group SGal(3).

Internal state: rotation, translation, velocity, time.

Inheritance diagram for gtsam::Gal3:

Matrix Lie Group
using	LieAlgebra = Matrix5
using	Vector25 = Eigen::Matrix<double, 25, 1>
Matrix5	matrix () const
	Return 5x5 homogeneous matrix representation.
Vector25	vec (OptionalJacobian< 25, 10 > H={}) const
	Vectorize 5x5 matrix into a 25-dim vector.
static LieAlgebra	Hat (const TangentVector &xi)
	Hat operator: maps tangent vector xi to Lie algebra matrix.
static TangentVector	Vee (const LieAlgebra &X)
	Vee operator: maps Lie algebra matrix to tangent vector xi.

Constructors
	Gal3 ()
	Default constructor: Identity element.
	Gal3 (const Rot3 &R, const Point3 &r, const Velocity3 &v, double t)
	Construct from attitude, position, velocity, time.
	Gal3 (const Matrix5 &M)
	Construct from a 5x5 matrix representation.
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.
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.

Testable
void	print (const std::string &s="") const
	Print with optional string prefix.
bool	equals (const Gal3 &other, double tol=1e-9) const
	Check equality within tolerance.
GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Gal3 &state)
	Output stream operator.

Group
Gal3	inverse () const
	Return the inverse of this element.
Gal3	operator* (const Gal3 &other) const
	Group composition operator.
static Gal3	Identity ()
	Return the identity element.

Lie Group
Jacobian	AdjointMap () const
	Calculate Adjoint map Ad_g.
static Gal3	Expmap (const TangentVector &xi, OptionalJacobian< 10, 10 > Hxi={})
	Exponential map at identity: tangent vector xi -> manifold element g.
static TangentVector	Logmap (const Gal3 &g, OptionalJacobian< 10, 10 > Hg={})
	Logarithmic map at identity: manifold element g -> tangent vector xi.
static Jacobian	adjointMap (const TangentVector &xi)
	Compute the adjoint map ad(xi) associated with tangent vector xi.
static Jacobian	ExpmapDerivative (const TangentVector &xi)
	Derivative of Expmap(xi) w.r.t. xi evaluated at xi.
static Jacobian	LogmapDerivative (const Gal3 &g)
	Derivative of Logmap(g) w.r.t. g.
static Jacobian	LogmapDerivative (const TangentVector &xi)
	Derivative of Logmap(g), tangent version.

Public Member Functions
Component Access
const Rot3 &	rotation (OptionalJacobian< 3, 10 > H={}) const
	Access rotation component (Rot3).
const Point3 &	translation (OptionalJacobian< 3, 10 > H={}) const
	Access translation component (Point3).
const Velocity3 &	velocity (OptionalJacobian< 3, 10 > H={}) const
	Access velocity component (Vector3).
const double &	time (OptionalJacobian< 1, 10 > H={}) const
	Access time component (double).
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).
Vector3	r () const
	Return position as Vector3.
const Vector3 &	v () const
	Return velocity as Vector3.
const double &	t () const
	Return time scalar.
double	range (const Point3 &point, OptionalJacobian< 1, 10 > Hself={}, OptionalJacobian< 1, 3 > Hpoint={}) const
	Calculate range to a 3D landmark.
Unit3	bearing (const Point3 &point, OptionalJacobian< 2, 10 > Hself={}, OptionalJacobian< 2, 3 > Hpoint={}) const
	Calculate bearing to a 3D landmark.
Group Action
Event	act (const Event &e, OptionalJacobian< 4, 10 > Hself={}, OptionalJacobian< 4, 4 > He={}) const
	Apply Galilean transform to a spacetime Event.
Public Member Functions inherited from gtsam::MatrixLieGroup< Gal3, 10, 5 >
std::enable_if_t< M !=Eigen::Dynamic, int >	dim () const
	Provided fixed dimension in dim() if needed.
Eigen::Matrix< double, internal::product(N, N), 1 >	vec (OptionalJacobian< internal::product(N, N), D > H={}) const
	Vectorize the matrix representation of a Lie group element.
Jacobian	AdjointMap () const
	A generic implementation of AdjointMap for matrix Lie groups.
TangentVector	Adjoint (const TangentVector &xi, ChartJacobian H_this={}, ChartJacobian H_xi={}) const
	Adjoint action on a tangent vector.
TangentVector	AdjointTranspose (const TangentVector &x, ChartJacobian H_this={}, ChartJacobian H_x={}) const
	Dual Adjoint action on a tangent covector.
Public Member Functions inherited from gtsam::LieGroup< Gal3, D >
SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
GTSAM_EXPORT SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
GTSAM_EXPORT SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const
std::enable_if_t< M !=Eigen::Dynamic, int >	dim () const
	Provided fixed dimension in dim() if needed.
const Gal3 &	derived () const
Gal3	inverse (ChartJacobian H) const
Gal3	expmap (const TangentVector &v) const
	expmap as required by manifold concept Applies exponential map to v and composes with *this
TangentVector	logmap (const Gal3 &g) const
	logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g
Gal3	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this
TangentVector	localCoordinates (const Gal3 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g

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

Additional Inherited Members
Static Public Member Functions inherited from gtsam::MatrixLieGroup< Gal3, 10, 5 >
static constexpr int	Dim ()
	Static method to get the dimension (compile-time or dynamic).
static Jacobian	adjointMap (const TangentVector &xi)
	Lie algebra adjoint map ad_xi, with optional specialization in derived classes.
static TangentVector	adjoint (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={})
	Lie algebra action ad_xi(y), with optional Jacobians.
static TangentVector	adjointTranspose (const TangentVector &xi, const TangentVector &y, ChartJacobian Hxi={}, ChartJacobian H_y={})
	Dual Lie algebra action ad_xi^T(y), with optional Jacobians.
Static Public Member Functions inherited from gtsam::LieGroup< Gal3, D >
static constexpr int	Dim ()
	Static method to get the dimension (compile-time or dynamic).
static Gal3	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity.
static TangentVector	LocalCoordinates (const Gal3 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity.
Static Public Attributes inherited from gtsam::MatrixLieGroup< Gal3, 10, 5 >
static constexpr auto	dimension
Static Public Attributes inherited from gtsam::LieGroup< Gal3, D >
static constexpr auto	dimension
Public Types inherited from gtsam::MatrixLieGroup< Gal3, 10, 5 >
using	Base
using	ChartJacobian
using	Jacobian
using	TangentVector
using	Vectorized
using	VectorizedJacobian
Public Types inherited from gtsam::LieGroup< Gal3, D >
typedef OptionalJacobian< N, N >	ChartJacobian
typedef Eigen::Matrix< double, N, N >	Jacobian
typedef Eigen::Matrix< double, N, 1 >	TangentVector

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

bearing()

Unit3 gtsam::Gal3::bearing	(	const Point3 &	point,
		OptionalJacobian< 2, 10 >	Hself = {},
		OptionalJacobian< 2, 3 >	Hpoint = {} ) const

Calculate bearing to a 3D landmark.

Parameters

point

3D location of landmark

Returns

bearing (Unit3)

range()

double gtsam::Gal3::range	(	const Point3 &	point,
		OptionalJacobian< 1, 10 >	Hself = {},
		OptionalJacobian< 1, 3 >	Hpoint = {} ) const

Calculate range to a 3D landmark.

Parameters

point

3D location of landmark

Returns

range (double)

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

• /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/geometry/Gal3.h
• /tmp/gtsam-4.3.0-doxygen.rsXPUS/source/gtsam/geometry/Gal3.cpp