#include <EssentialMatrix.h>

Public Member Functions
Testable
GTSAM_EXPORT void	print (const std::string &s="") const
	print with optional string More...

bool	equals (const EssentialMatrix &other, double tol=1e-8) const
	assert equality up to a tolerance More...

Static Public Member Functions
static Vector3	Homogeneous (const Point2 &p)
	Static function to convert Point2 to homogeneous coordinates. More...

Private Attributes
Matrix3	E_
	Essential matrix. More...

Rot3	R_
	Rotation. More...

Unit3	t_
	Translation. More...

Friends
Streaming operators
GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const EssentialMatrix &E)
	stream to stream More...

GTSAM_EXPORT friend std::istream &	operator>> (std::istream &is, EssentialMatrix &E)
	stream from stream More...

Constructors and named constructors
static GTSAM_EXPORT EssentialMatrix	FromRotationAndDirection (const Rot3 &aRb, const Unit3 &aTb, OptionalJacobian< 5, 3 > H1={}, OptionalJacobian< 5, 2 > H2={})
	Named constructor with derivatives. More...

static GTSAM_EXPORT EssentialMatrix	FromPose3 (const Pose3 &_1P2_, OptionalJacobian< 5, 6 > H={})
	Named constructor converting a Pose3 with scale to EssentialMatrix (no scale) More...

template<typename Engine >
static EssentialMatrix	Random (Engine &rng)
	Random, using Rot3::Random and Unit3::Random. More...

	EssentialMatrix ()
	Default constructor. More...

	EssentialMatrix (const Rot3 &aRb, const Unit3 &aTb)
	Construct from rotation and translation. More...

virtual	~EssentialMatrix ()

Manifold
typedef OptionalJacobian< dimension, dimension >	ChartJacobian

constexpr static auto	dimension = 5

static size_t	Dim ()

size_t	dim () const

EssentialMatrix	retract (const Vector5 &xi) const
	Retract delta to manifold. More...

Vector5	localCoordinates (const EssentialMatrix &other) const
	Compute the coordinates in the tangent space. More...

Essential matrix methods
const Rot3 &	rotation () const
	Rotation. More...

const Unit3 &	direction () const
	Direction. More...

const Matrix3 &	matrix () const
	Return 3*3 matrix representation. More...

const Unit3 &	epipole_a () const
	Return epipole in image_a , as Unit3 to allow for infinity. More...

Unit3	epipole_b () const
	Return epipole in image_b, as Unit3 to allow for infinity. More...

GTSAM_EXPORT Point3	transformTo (const Point3 &p, OptionalJacobian< 3, 5 > DE={}, OptionalJacobian< 3, 3 > Dpoint={}) const
	takes point in world coordinates and transforms it to pose with \|t\|==1 More...

GTSAM_EXPORT EssentialMatrix	rotate (const Rot3 &cRb, OptionalJacobian< 5, 5 > HE={}, OptionalJacobian< 5, 3 > HR={}) const

GTSAM_EXPORT double	error (const Vector3 &vA, const Vector3 &vB, OptionalJacobian< 1, 5 > H={}) const
	epipolar error, algebraic More...

EssentialMatrix	operator* (const Rot3 &cRb, const EssentialMatrix &E)

Detailed Description

An essential matrix is like a Pose3, except with translation up to scale It is named after the 3*3 matrix aEb = [aTb]x aRb from computer vision, but here we choose instead to parameterize it as a (Rot3,Unit3) pair. We can then non-linearly optimize immediately on this 5-dimensional manifold.

Definition at line 26 of file EssentialMatrix.h.

Member Typedef Documentation

◆ ChartJacobian

typedef OptionalJacobian<dimension, dimension> gtsam::EssentialMatrix::ChartJacobian

Definition at line 89 of file EssentialMatrix.h.

Constructor & Destructor Documentation

◆ EssentialMatrix() [1/2]

gtsam::EssentialMatrix::EssentialMatrix ( )

inline

Default constructor.

Definition at line 42 of file EssentialMatrix.h.

◆ EssentialMatrix() [2/2]

gtsam::EssentialMatrix::EssentialMatrix	(	const Rot3 &	aRb,
		const Unit3 &	aTb
	)

inline

Construct from rotation and translation.

Definition at line 46 of file EssentialMatrix.h.

◆ ~EssentialMatrix()

virtual gtsam::EssentialMatrix::~EssentialMatrix ( )

inlinevirtual

Definition at line 65 of file EssentialMatrix.h.

Member Function Documentation

◆ Dim()

static size_t gtsam::EssentialMatrix::Dim ( )

inlinestatic

Definition at line 86 of file EssentialMatrix.h.

◆ dim()

size_t gtsam::EssentialMatrix::dim ( ) const

inline

Definition at line 87 of file EssentialMatrix.h.

◆ direction()

const Unit3& gtsam::EssentialMatrix::direction ( ) const

inline

Direction.

Definition at line 115 of file EssentialMatrix.h.

◆ epipole_a()

const Unit3& gtsam::EssentialMatrix::epipole_a ( ) const

inline

Return epipole in image_a , as Unit3 to allow for infinity.

Definition at line 125 of file EssentialMatrix.h.

◆ epipole_b()

Unit3 gtsam::EssentialMatrix::epipole_b ( ) const

inline

Return epipole in image_b, as Unit3 to allow for infinity.

Definition at line 130 of file EssentialMatrix.h.

◆ equals()

bool gtsam::EssentialMatrix::equals	(	const EssentialMatrix &	other,
		double	tol = `1e-8`
	)		const

inline

assert equality up to a tolerance

Definition at line 76 of file EssentialMatrix.h.

◆ error()

double gtsam::EssentialMatrix::error	(	const Vector3 &	vA,
		const Vector3 &	vB,
		OptionalJacobian< 1, 5 >	H = `{}`
	)		const

epipolar error, algebraic

Definition at line 104 of file EssentialMatrix.cpp.

◆ FromPose3()

EssentialMatrix gtsam::EssentialMatrix::FromPose3	(	const Pose3 &	_1P2_,
		OptionalJacobian< 5, 6 >	H = `{}`
	)

static

Named constructor converting a Pose3 with scale to EssentialMatrix (no scale)

Definition at line 27 of file EssentialMatrix.cpp.

◆ FromRotationAndDirection()

EssentialMatrix gtsam::EssentialMatrix::FromRotationAndDirection	(	const Rot3 &	aRb,
		const Unit3 &	aTb,
		OptionalJacobian< 5, 3 >	H1 = `{}`,
		OptionalJacobian< 5, 2 >	H2 = `{}`
	)

static

Named constructor with derivatives.

Definition at line 16 of file EssentialMatrix.cpp.

◆ Homogeneous()

static Vector3 gtsam::EssentialMatrix::Homogeneous ( const Point2 & p )

inlinestatic

Static function to convert Point2 to homogeneous coordinates.

Definition at line 34 of file EssentialMatrix.h.

◆ localCoordinates()

Vector5 gtsam::EssentialMatrix::localCoordinates ( const EssentialMatrix & other ) const

inline

Compute the coordinates in the tangent space.

Definition at line 97 of file EssentialMatrix.h.

◆ matrix()

const Matrix3& gtsam::EssentialMatrix::matrix ( ) const

inline

Return 3*3 matrix representation.

Definition at line 120 of file EssentialMatrix.h.

◆ print()

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

print with optional string

Definition at line 48 of file EssentialMatrix.cpp.

◆ Random()

template<typename Engine >

static EssentialMatrix gtsam::EssentialMatrix::Random ( Engine & rng )

inlinestatic

Random, using Rot3::Random and Unit3::Random.

Definition at line 61 of file EssentialMatrix.h.

◆ retract()

EssentialMatrix gtsam::EssentialMatrix::retract ( const Vector5 & xi ) const

inline

Retract delta to manifold.

Definition at line 92 of file EssentialMatrix.h.

◆ rotate()

EssentialMatrix gtsam::EssentialMatrix::rotate	(	const Rot3 &	cRb,
		OptionalJacobian< 5, 5 >	HE = `{}`,
		OptionalJacobian< 5, 3 >	HR = `{}`
	)		const

Given essential matrix E in camera frame B, convert to body frame C

Parameters

cRb	rotation from body frame to camera frame
E	essential matrix E in camera frame C

Definition at line 73 of file EssentialMatrix.cpp.

◆ rotation()

const Rot3& gtsam::EssentialMatrix::rotation ( ) const

inline

Rotation.

Definition at line 110 of file EssentialMatrix.h.

◆ transformTo()

Point3 gtsam::EssentialMatrix::transformTo	(	const Point3 &	p,
		OptionalJacobian< 3, 5 >	DE = `{}`,
		OptionalJacobian< 3, 3 >	Dpoint = `{}`
	)		const

takes point in world coordinates and transforms it to pose with |t|==1

Parameters

p	point in world coordinates
DE	optional 3*5 Jacobian wrpt to E
Dpoint	optional 3*3 Jacobian wrpt point

Returns: point in pose coordinates

Definition at line 55 of file EssentialMatrix.cpp.

Friends And Related Function Documentation

◆ operator*

EssentialMatrix operator*	(	const Rot3 &	cRb,
		const EssentialMatrix &	E
	)

friend

Given essential matrix E in camera frame B, convert to body frame C

Parameters

cRb	rotation from body frame to camera frame
E	essential matrix E in camera frame C

Definition at line 158 of file EssentialMatrix.h.

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const EssentialMatrix &	E
	)

friend

stream to stream

◆ operator>>

GTSAM_EXPORT friend std::istream& operator>>	(	std::istream &	is,
		EssentialMatrix &	E
	)

friend

stream from stream

Member Data Documentation

◆ dimension

constexpr static auto gtsam::EssentialMatrix::dimension = 5

inlinestaticconstexpr

Definition at line 85 of file EssentialMatrix.h.

◆ E_

Matrix3 gtsam::EssentialMatrix::E_

private

Essential matrix.

Definition at line 30 of file EssentialMatrix.h.

◆ R_

Rot3 gtsam::EssentialMatrix::R_

private

Rotation.

Definition at line 28 of file EssentialMatrix.h.

◆ t_

Unit3 gtsam::EssentialMatrix::t_

private

Translation.

Definition at line 29 of file EssentialMatrix.h.

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

Public Member Functions

Static Public Member Functions

Private Attributes

Friends

Constructors and named constructors

Manifold

Essential matrix methods

Detailed Description

Member Typedef Documentation

◆ ChartJacobian

Constructor & Destructor Documentation

◆ EssentialMatrix() [1/2]

◆ EssentialMatrix() [2/2]

◆ ~EssentialMatrix()

Member Function Documentation

◆ Dim()

◆ dim()

◆ direction()

◆ epipole_a()

◆ epipole_b()

◆ equals()

◆ error()

◆ FromPose3()

◆ FromRotationAndDirection()

◆ Homogeneous()

◆ localCoordinates()

◆ matrix()

◆ print()

◆ Random()

◆ retract()

◆ rotate()

◆ rotation()

◆ transformTo()

Friends And Related Function Documentation

◆ operator*

◆ operator<<

◆ operator>>

Member Data Documentation

◆ dimension

◆ E_

◆ R_

◆ t_