#include <Pose2.h>

Inheritance diagram for gtsam::Pose2:

Classes
struct	ChartAtOrigin

Public Types
typedef Rot2	Rotation

typedef Point2	Translation

Public Types inherited from gtsam::LieGroup< Pose2, 3 >
enum

typedef OptionalJacobian< N, N >	ChartJacobian

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

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

Private Attributes
Rot2	r_

Point2	t_

Standard Constructors
	Pose2 ()

	Pose2 (const Pose2 &pose)

	Pose2 (double x, double y, double theta)

	Pose2 (double theta, const Point2 &t)

	Pose2 (const Rot2 &r, const Point2 &t)

	Pose2 (const Matrix &T)

Advanced Constructors
	Pose2 (const Vector &v)

static std::optional< Pose2 >	Align (const Point2Pairs &abPointPairs)

static std::optional< Pose2 >	Align (const Matrix &a, const Matrix &b)

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

bool	equals (const Pose2 &pose, double tol=1e-9) const

Group
Pose2	inverse () const
	inverse More...

Pose2	operator* (const Pose2 &p2) const
	compose syntactic sugar More...

static Pose2	Identity ()
	identity for group operation More...

Lie Group
Matrix3	AdjointMap () const

Vector3	Adjoint (const Vector3 &xi) const
	Apply AdjointMap to twist xi. More...

static Pose2	Expmap (const Vector3 &xi, ChartJacobian H={})
	Exponential map at identity - create a rotation from canonical coordinates $[T_x,T_y,\theta]$ . More...

static Vector3	Logmap (const Pose2 &p, ChartJacobian H={})
	Log map at identity - return the canonical coordinates $[T_x,T_y,\theta]$ of this rotation. More...

static Matrix3	adjointMap (const Vector3 &v)

static Vector3	adjoint (const Vector3 &xi, const Vector3 &y)

static Vector3	adjointTranspose (const Vector3 &xi, const Vector3 &y)

static Matrix3	adjointMap_ (const Vector3 &xi)

static Vector3	adjoint_ (const Vector3 &xi, const Vector3 &y)

static Matrix3	wedge (double vx, double vy, double w)

static Matrix3	ExpmapDerivative (const Vector3 &v)
	Derivative of Expmap. More...

static Matrix3	LogmapDerivative (const Pose2 &v)
	Derivative of Logmap. More...

Group Action on Point2
Point2	transformTo (const Point2 &point, OptionalJacobian< 2, 3 > Dpose={}, OptionalJacobian< 2, 2 > Dpoint={}) const

Matrix	transformTo (const Matrix &points) const
	transform many points in world coordinates and transform to Pose. More...

Point2	transformFrom (const Point2 &point, OptionalJacobian< 2, 3 > Dpose={}, OptionalJacobian< 2, 2 > Dpoint={}) const

Matrix	transformFrom (const Matrix &points) const
	transform many points in Pose coordinates and transform to world. More...

Point2	operator* (const Point2 &point) const

Standard Interface
double	x () const
	get x More...

double	y () const
	get y More...

double	theta () const
	get theta More...

const Point2 &	t () const
	translation More...

const Rot2 &	r () const
	rotation More...

const Point2 &	translation (OptionalJacobian< 2, 3 > Hself={}) const
	translation More...

const Rot2 &	rotation (OptionalJacobian< 1, 3 > Hself={}) const
	rotation More...

Matrix3	matrix () const

Rot2	bearing (const Point2 &point, OptionalJacobian< 1, 3 > H1={}, OptionalJacobian< 1, 2 > H2={}) const

Rot2	bearing (const Pose2 &pose, OptionalJacobian< 1, 3 > H1={}, OptionalJacobian< 1, 3 > H2={}) const

double	range (const Point2 &point, OptionalJacobian< 1, 3 > H1={}, OptionalJacobian< 1, 2 > H2={}) const

double	range (const Pose2 &point, OptionalJacobian< 1, 3 > H1={}, OptionalJacobian< 1, 3 > H2={}) const

Advanced Interface
static std::pair< size_t, size_t >	translationInterval ()

static std::pair< size_t, size_t >	rotationInterval ()

GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Pose2 &p)
	Output stream operator. More...

Additional Inherited Members
Public Member Functions inherited from gtsam::LieGroup< Pose2, 3 >
Pose2	between (const Pose2 &g) const

Pose2	between (const Pose2 &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

Pose2	compose (const Pose2 &g) const

Pose2	compose (const Pose2 &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 Pose2 &	derived () const

Pose2	expmap (const TangentVector &v) const

Pose2	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

Pose2	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Pose2 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Pose2 &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Pose2 &g) const

TangentVector	logmap (const Pose2 &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

Pose2	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Pose2	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Static Public Member Functions inherited from gtsam::LieGroup< Pose2, 3 >
static TangentVector	LocalCoordinates (const Pose2 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Pose2 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Pose2	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Pose2	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

A 2D pose (Point2,Rot2)

Definition at line 39 of file Pose2.h.

Member Typedef Documentation

◆ Rotation

typedef Rot2 gtsam::Pose2::Rotation

Pose Concept requirements

Definition at line 44 of file Pose2.h.

◆ Translation

typedef Point2 gtsam::Pose2::Translation

Definition at line 45 of file Pose2.h.

Constructor & Destructor Documentation

◆ Pose2() [1/7]

gtsam::Pose2::Pose2 ( )

inline

default constructor = origin

Definition at line 58 of file Pose2.h.

◆ Pose2() [2/7]

gtsam::Pose2::Pose2 ( const Pose2 & pose )

inline

copy constructor

Definition at line 63 of file Pose2.h.

◆ Pose2() [3/7]

gtsam::Pose2::Pose2	(	double	x,
		double	y,
		double	theta
	)

inline

construct from (x,y,theta)

Parameters

x	x coordinate
y	y coordinate
theta	angle with positive X-axis

Definition at line 71 of file Pose2.h.

◆ Pose2() [4/7]

gtsam::Pose2::Pose2	(	double	theta,
		const Point2 &	t
	)

inline

construct from rotation and translation

Definition at line 76 of file Pose2.h.

◆ Pose2() [5/7]

gtsam::Pose2::Pose2	(	const Rot2 &	r,
		const Point2 &	t
	)

inline

construct from r,t

Definition at line 81 of file Pose2.h.

◆ Pose2() [6/7]

gtsam::Pose2::Pose2 ( const Matrix & T )

inline

Constructor from 3*3 matrix

Definition at line 84 of file Pose2.h.

◆ Pose2() [7/7]

gtsam::Pose2::Pose2 ( const Vector & v )

inline

Construct from canonical coordinates $[T_x,T_y,\theta]$ (Lie algebra)

Definition at line 94 of file Pose2.h.

Member Function Documentation

◆ Adjoint()

Vector3 gtsam::Pose2::Adjoint ( const Vector3 & xi ) const

inline

Apply AdjointMap to twist xi.

Definition at line 152 of file Pose2.h.

◆ adjoint()

static Vector3 gtsam::Pose2::adjoint	(	const Vector3 &	xi,
		const Vector3 &	y
	)

inlinestatic

Action of the adjointMap on a Lie-algebra vector y, with optional derivatives

Definition at line 164 of file Pose2.h.

◆ adjoint_()

static Vector3 gtsam::Pose2::adjoint_	(	const Vector3 &	xi,
		const Vector3 &	y
	)

inlinestatic

Definition at line 177 of file Pose2.h.

◆ AdjointMap()

Matrix3 gtsam::Pose2::AdjointMap ( ) const

Calculate Adjoint map Ad_pose is 3*3 matrix that when applied to twist xi $[T_x,T_y,\theta]$ , returns Ad_pose(xi)

Definition at line 126 of file Pose2.cpp.

◆ adjointMap()

Matrix3 gtsam::Pose2::adjointMap ( const Vector3 & v )

static

Compute the [ad(w,v)] operator for SE2 as in [Kobilarov09siggraph], pg 19

Definition at line 137 of file Pose2.cpp.

◆ adjointMap_()

static Matrix3 gtsam::Pose2::adjointMap_ ( const Vector3 & xi )

inlinestatic

Definition at line 176 of file Pose2.h.

◆ adjointTranspose()

static Vector3 gtsam::Pose2::adjointTranspose	(	const Vector3 &	xi,
		const Vector3 &	y
	)

inlinestatic

The dual version of adjoint action, acting on the dual space of the Lie-algebra vector space.

Definition at line 171 of file Pose2.h.

◆ Align() [1/2]

std::optional< Pose2 > gtsam::Pose2::Align	(	const Matrix &	a,
		const Matrix &	b
	)

static

Definition at line 362 of file Pose2.cpp.

◆ Align() [2/2]

std::optional< Pose2 > gtsam::Pose2::Align ( const Point2Pairs & abPointPairs )

static

Create Pose2 by aligning two point pairs A pose aTb is estimated between pairs (a_point, b_point) such that a_point = aTb * b_point Note this allows for noise on the points but in that case the mapping will not be exact.

Definition at line 330 of file Pose2.cpp.

◆ bearing() [1/2]

Rot2 gtsam::Pose2::bearing	(	const Point2 &	point,
		OptionalJacobian< 1, 3 >	H1 = `{}`,
		OptionalJacobian< 1, 2 >	H2 = `{}`
	)		const

Calculate bearing to a landmark

Parameters

point 2D location of landmark

Returns: 2D rotation $\in SO(2)$

Definition at line 245 of file Pose2.cpp.

◆ bearing() [2/2]

Rot2 gtsam::Pose2::bearing	(	const Pose2 &	pose,
		OptionalJacobian< 1, 3 >	H1 = `{}`,
		OptionalJacobian< 1, 3 >	H2 = `{}`
	)		const

Calculate bearing to another pose

Parameters

point SO(2) location of other pose

Returns: 2D rotation $\in SO(2)$

Definition at line 259 of file Pose2.cpp.

◆ equals()

bool gtsam::Pose2::equals	(	const Pose2 &	pose,
		double	tol = `1e-9`
	)		const

assert equality up to a tolerance

Definition at line 61 of file Pose2.cpp.

◆ Expmap()

Pose2 gtsam::Pose2::Expmap	(	const Vector3 &	xi,
		ChartJacobian	H = `{}`
	)

static

Exponential map at identity - create a rotation from canonical coordinates $[T_x,T_y,\theta]$ .

Definition at line 66 of file Pose2.cpp.

◆ ExpmapDerivative()

Matrix3 gtsam::Pose2::ExpmapDerivative ( const Vector3 & v )

static

Derivative of Expmap.

Definition at line 148 of file Pose2.cpp.

◆ Identity()

static Pose2 gtsam::Pose2::Identity ( )

inlinestatic

identity for group operation

Definition at line 125 of file Pose2.h.

◆ inverse()

Pose2 gtsam::Pose2::inverse ( ) const

inverse

Definition at line 201 of file Pose2.cpp.

◆ Logmap()

Vector3 gtsam::Pose2::Logmap	(	const Pose2 &	p,
		ChartJacobian	H = `{}`
	)

static

Log map at identity - return the canonical coordinates $[T_x,T_y,\theta]$ of this rotation.

Definition at line 82 of file Pose2.cpp.

◆ LogmapDerivative()

Matrix3 gtsam::Pose2::LogmapDerivative ( const Pose2 & v )

static

Derivative of Logmap.

Definition at line 179 of file Pose2.cpp.

◆ matrix()

Matrix3 gtsam::Pose2::matrix ( ) const

Definition at line 36 of file Pose2.cpp.

◆ operator*() [1/2]

Point2 gtsam::Pose2::operator* ( const Point2 & point ) const

inline

syntactic sugar for transformFrom

Definition at line 237 of file Pose2.h.

◆ operator*() [2/2]

Pose2 gtsam::Pose2::operator* ( const Pose2 & p2 ) const

inline

compose syntactic sugar

Definition at line 131 of file Pose2.h.

◆ print()

void gtsam::Pose2::print ( const std::string & s = "" ) const

print with optional string

Definition at line 50 of file Pose2.cpp.

◆ r()

const Rot2& gtsam::Pose2::r ( ) const

inline

rotation

Definition at line 258 of file Pose2.h.

◆ range() [1/2]

double gtsam::Pose2::range	(	const Point2 &	point,
		OptionalJacobian< 1, 3 >	H1 = `{}`,
		OptionalJacobian< 1, 2 >	H2 = `{}`
	)		const

Calculate range to a landmark

Parameters

point 2D location of landmark

Returns: range (double)

Definition at line 270 of file Pose2.cpp.

◆ range() [2/2]

double gtsam::Pose2::range	(	const Pose2 &	point,
		OptionalJacobian< 1, 3 >	H1 = `{}`,
		OptionalJacobian< 1, 3 >	H2 = `{}`
	)		const

Calculate range to another pose

Parameters

point 2D location of other pose

Returns: range (double)

Definition at line 287 of file Pose2.cpp.

◆ rotation()

const Rot2& gtsam::Pose2::rotation ( OptionalJacobian< 1, 3 > Hself = {} ) const

inline

rotation

Definition at line 270 of file Pose2.h.

◆ rotationInterval()

static std::pair<size_t, size_t> gtsam::Pose2::rotationInterval ( )

inlinestatic

Return the start and end indices (inclusive) of the rotation component of the exponential map parameterization

Returns: a pair of [start, end] indices into the tangent space vector

Definition at line 328 of file Pose2.h.

◆ t()

const Point2& gtsam::Pose2::t ( ) const

inline

translation

Definition at line 255 of file Pose2.h.

◆ theta()

double gtsam::Pose2::theta ( ) const

inline

get theta

Definition at line 252 of file Pose2.h.

◆ transformFrom() [1/2]

Matrix gtsam::Pose2::transformFrom ( const Matrix & points ) const

transform many points in Pose coordinates and transform to world.

Parameters

points 2*N matrix in Pose coordinates

Returns: points in world coordinates, as 2*N Matrix

Definition at line 236 of file Pose2.cpp.

◆ transformFrom() [2/2]

Point2 gtsam::Pose2::transformFrom	(	const Point2 &	point,
		OptionalJacobian< 2, 3 >	Dpose = `{}`,
		OptionalJacobian< 2, 2 >	Dpoint = `{}`
	)		const

Return point coordinates in global frame

Definition at line 226 of file Pose2.cpp.

◆ transformTo() [1/2]

Matrix gtsam::Pose2::transformTo ( const Matrix & points ) const

transform many points in world coordinates and transform to Pose.

Parameters

points 2*N matrix in world coordinates

Returns: points in Pose coordinates, as 2*N Matrix

Definition at line 216 of file Pose2.cpp.

◆ transformTo() [2/2]

Point2 gtsam::Pose2::transformTo	(	const Point2 &	point,
		OptionalJacobian< 2, 3 >	Dpose = `{}`,
		OptionalJacobian< 2, 2 >	Dpoint = `{}`
	)		const

Return point coordinates in pose coordinate frame

Definition at line 207 of file Pose2.cpp.

◆ translation()

const Point2& gtsam::Pose2::translation ( OptionalJacobian< 2, 3 > Hself = {} ) const

inline

translation

Definition at line 261 of file Pose2.h.

◆ translationInterval()

static std::pair<size_t, size_t> gtsam::Pose2::translationInterval ( )

inlinestatic

Return the start and end indices (inclusive) of the translation component of the exponential map parameterization

Returns: a pair of [start, end] indices into the tangent space vector

Definition at line 321 of file Pose2.h.

◆ wedge()

static Matrix3 gtsam::Pose2::wedge	(	double	vx,
		double	vy,
		double	w
	)

inlinestatic

wedge for SE(2):

Parameters

xi	3-dim twist (v,omega) where omega is angular velocity v (vx,vy) = 2D velocity

Returns: xihat, 3*3 element of Lie algebra that can be exponentiated

Definition at line 186 of file Pose2.h.

◆ x()

double gtsam::Pose2::x ( ) const

inline

get x

Definition at line 246 of file Pose2.h.

◆ y()

double gtsam::Pose2::y ( ) const

inline

get y

Definition at line 249 of file Pose2.h.

Friends And Related Function Documentation

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Pose2 &	p
	)

friend

Output stream operator.

Definition at line 55 of file Pose2.cpp.

Member Data Documentation

◆ r_

Rot2 gtsam::Pose2::r_

private

Definition at line 49 of file Pose2.h.

◆ t_

Point2 gtsam::Pose2::t_

private

Definition at line 50 of file Pose2.h.

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

Classes

Public Types

Private Attributes

Standard Constructors

Advanced Constructors

Testable

Group

Lie Group

Group Action on Point2

Standard Interface

Advanced Interface

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Rotation

◆ Translation

Constructor & Destructor Documentation

◆ Pose2() [1/7]

◆ Pose2() [2/7]

◆ Pose2() [3/7]

◆ Pose2() [4/7]

◆ Pose2() [5/7]

◆ Pose2() [6/7]

◆ Pose2() [7/7]

Member Function Documentation

◆ Adjoint()

◆ adjoint()

◆ adjoint_()

◆ AdjointMap()

◆ adjointMap()

◆ adjointMap_()

◆ adjointTranspose()

◆ Align() [1/2]

◆ Align() [2/2]

◆ bearing() [1/2]

◆ bearing() [2/2]

◆ equals()

◆ Expmap()

◆ ExpmapDerivative()

◆ Identity()

◆ inverse()

◆ Logmap()

◆ LogmapDerivative()

◆ matrix()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ print()

◆ r()

◆ range() [1/2]

◆ range() [2/2]

◆ rotation()

◆ rotationInterval()

◆ t()

◆ theta()

◆ transformFrom() [1/2]

◆ transformFrom() [2/2]

◆ transformTo() [1/2]

◆ transformTo() [2/2]

◆ translation()

◆ translationInterval()

◆ wedge()

◆ x()

◆ y()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ r_

◆ t_