#include <Similarity2.h>

Inheritance diagram for gtsam::Similarity2:

Classes
struct	ChartAtOrigin
	Chart at the origin. More...

Public Member Functions
Constructors
	Similarity2 ()
	Default constructor. More...

	Similarity2 (double s)
	Construct pure scaling. More...

	Similarity2 (const Rot2 &R, const Point2 &t, double s)
	Construct from GTSAM types. More...

	Similarity2 (const Matrix2 &R, const Vector2 &t, double s)
	Construct from Eigen types. More...

	Similarity2 (const Matrix3 &T)
	Construct from matrix [R t; 0 s^-1]. More...

Public Member Functions inherited from gtsam::LieGroup< Similarity2, 4 >
Similarity2	between (const Similarity2 &g) const

Similarity2	between (const Similarity2 &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

Similarity2	compose (const Similarity2 &g) const

Similarity2	compose (const Similarity2 &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 Similarity2 &	derived () const

Similarity2	expmap (const TangentVector &v) const

Similarity2	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

Similarity2	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Similarity2 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Similarity2 &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Similarity2 &g) const

TangentVector	logmap (const Similarity2 &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

Similarity2	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Similarity2	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Private Types
Pose Concept
typedef Rot2	Rotation

typedef Point2	Translation

Private Attributes
Rot2	R_

double	s_

Point2	t_

Testable
bool	equals (const Similarity2 &sim, double tol) const
	Compare with tolerance. More...

bool	operator== (const Similarity2 &other) const
	Exact equality. More...

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

GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Similarity2 &p)

Group
Similarity2	operator* (const Similarity2 &S) const
	Composition. More...

Similarity2	inverse () const
	Return the inverse. More...

static Similarity2	Identity ()
	Return an identity transform. More...

Group action on Point2
Point2	transformFrom (const Point2 &p) const
	Action on a point p is s(Rp+t) More...

Pose2	transformFrom (const Pose2 &T) const

Point2	operator* (const Point2 &p) const

static Similarity2	Align (const Point2Pairs &abPointPairs)

static Similarity2	Align (const Pose2Pairs &abPosePairs)

Lie Group
Matrix4	AdjointMap () const
	Project from one tangent space to another. More...

static Vector4	Logmap (const Similarity2 &S, OptionalJacobian< 4, 4 > Hm={})

static Similarity2	Expmap (const Vector4 &v, OptionalJacobian< 4, 4 > Hm={})
	Exponential map at the identity. More...

Standard interface
Matrix3	matrix () const
	Calculate 4*4 matrix group equivalent. More...

Rot2	rotation () const
	Return a GTSAM rotation. More...

Point2	translation () const
	Return a GTSAM translation. More...

double	scale () const
	Return the scale. More...

size_t	dim () const
	Dimensionality of tangent space = 4 DOF. More...

static size_t	Dim ()
	Dimensionality of tangent space = 4 DOF - used to autodetect sizes. More...

Additional Inherited Members
Public Types inherited from gtsam::LieGroup< Similarity2, 4 >
enum

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< Similarity2, 4 >
static TangentVector	LocalCoordinates (const Similarity2 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Similarity2 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Similarity2	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Similarity2	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

2D similarity transform

Definition at line 35 of file Similarity2.h.

Member Typedef Documentation

◆ Rotation

typedef Rot2 gtsam::Similarity2::Rotation

private

Definition at line 38 of file Similarity2.h.

◆ Translation

typedef Point2 gtsam::Similarity2::Translation

private

Definition at line 39 of file Similarity2.h.

Constructor & Destructor Documentation

◆ Similarity2() [1/5]

gtsam::Similarity2::Similarity2 ( )

Default constructor.

Definition at line 102 of file Similarity2.cpp.

◆ Similarity2() [2/5]

gtsam::Similarity2::Similarity2 ( double s )

Construct pure scaling.

Definition at line 104 of file Similarity2.cpp.

◆ Similarity2() [3/5]

gtsam::Similarity2::Similarity2	(	const Rot2 &	R,
		const Point2 &	t,
		double	s
	)

Construct from GTSAM types.

Definition at line 106 of file Similarity2.cpp.

◆ Similarity2() [4/5]

gtsam::Similarity2::Similarity2	(	const Matrix2 &	R,
		const Vector2 &	t,
		double	s
	)

Construct from Eigen types.

Definition at line 109 of file Similarity2.cpp.

◆ Similarity2() [5/5]

gtsam::Similarity2::Similarity2 ( const Matrix3 & T )

Construct from matrix [R t; 0 s^-1].

Definition at line 112 of file Similarity2.cpp.

Member Function Documentation

◆ AdjointMap()

Matrix4 gtsam::Similarity2::AdjointMap ( ) const

Project from one tangent space to another.

Definition at line 221 of file Similarity2.cpp.

◆ Align() [1/2]

Similarity2 gtsam::Similarity2::Align ( const Point2Pairs & abPointPairs )

static

Create Similarity2 by aligning at least two point pairs

Definition at line 162 of file Similarity2.cpp.

◆ Align() [2/2]

Similarity2 gtsam::Similarity2::Align ( const Pose2Pairs & abPosePairs )

static

Create the Similarity2 object that aligns at least two pose pairs. Each pair is of the form (aTi, bTi). Given a list of pairs in frame a, and a list of pairs in frame b, Align() will compute the best-fit Similarity2 aSb transformation to align them. First, the rotation aRb will be computed as the average (Karcher mean) of many estimates aRb (from each pair). Afterwards, the scale factor will be computed using the algorithm described here: http://www5.informatik.uni-erlangen.de/Forschung/Publikationen/2005/Zinsser05-PSR.pdf

Definition at line 175 of file Similarity2.cpp.

◆ Dim()

static size_t gtsam::Similarity2::Dim ( )

inlinestatic

Dimensionality of tangent space = 4 DOF - used to autodetect sizes.

Definition at line 187 of file Similarity2.h.

◆ dim()

size_t gtsam::Similarity2::dim ( ) const

inline

Dimensionality of tangent space = 4 DOF.

Definition at line 190 of file Similarity2.h.

◆ equals()

bool gtsam::Similarity2::equals	(	const Similarity2 &	sim,
		double	tol
	)		const

Compare with tolerance.

Definition at line 117 of file Similarity2.cpp.

◆ Expmap()

Similarity2 gtsam::Similarity2::Expmap	(	const Vector4 &	v,
		OptionalJacobian< 4, 4 >	Hm = `{}`
	)

static

Exponential map at the identity.

Definition at line 210 of file Similarity2.cpp.

◆ Identity()

Similarity2 gtsam::Similarity2::Identity ( )

static

Return an identity transform.

Definition at line 135 of file Similarity2.cpp.

◆ inverse()

Similarity2 gtsam::Similarity2::inverse ( ) const

Return the inverse.

Definition at line 141 of file Similarity2.cpp.

◆ Logmap()

Vector4 gtsam::Similarity2::Logmap	(	const Similarity2 &	S,
		OptionalJacobian< 4, 4 >	Hm = `{}`
	)

static

Log map at the identity $[t_x, t_y, \delta, \lambda]$

Definition at line 197 of file Similarity2.cpp.

◆ matrix()

Matrix3 gtsam::Similarity2::matrix ( ) const

Calculate 4*4 matrix group equivalent.

Definition at line 231 of file Similarity2.cpp.

◆ operator*() [1/2]

Point2 gtsam::Similarity2::operator* ( const Point2 & p ) const

Definition at line 158 of file Similarity2.cpp.

◆ operator*() [2/2]

Similarity2 gtsam::Similarity2::operator* ( const Similarity2 & S ) const

Composition.

Definition at line 137 of file Similarity2.cpp.

◆ operator==()

bool gtsam::Similarity2::operator== ( const Similarity2 & other ) const

Exact equality.

Definition at line 123 of file Similarity2.cpp.

◆ print()

void gtsam::Similarity2::print ( const std::string & s = "" ) const

Print with optional string.

Definition at line 127 of file Similarity2.cpp.

◆ rotation()

Rot2 gtsam::Similarity2::rotation ( ) const

inline

Return a GTSAM rotation.

Definition at line 178 of file Similarity2.h.

◆ scale()

double gtsam::Similarity2::scale ( ) const

inline

Return the scale.

Definition at line 184 of file Similarity2.h.

◆ transformFrom() [1/2]

Point2 gtsam::Similarity2::transformFrom ( const Point2 & p ) const

Action on a point p is s*(R*p+t)

Definition at line 147 of file Similarity2.cpp.

◆ transformFrom() [2/2]

Pose2 gtsam::Similarity2::transformFrom ( const Pose2 & T ) const

Action on a pose T. |Rs ts| |R t| |Rs*R Rs*t+ts| |0 1/s| * |0 1| = | 0 1/s |, the result is still a Sim2 object. To retrieve a Pose2, we normalized the scale value into 1. |Rs*R Rs*t+ts| |Rs*R s(Rs*t+ts)| | 0 1/s | = | 0 1 |

This group action satisfies the compatibility condition. For more details, refer to: https://en.wikipedia.org/wiki/Group_action

Definition at line 152 of file Similarity2.cpp.

◆ translation()

Point2 gtsam::Similarity2::translation ( ) const

inline

Return a GTSAM translation.

Definition at line 181 of file Similarity2.h.

Friends And Related Function Documentation

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Similarity2 &	p
	)

friend

Definition at line 225 of file Similarity2.cpp.

Member Data Documentation

◆ R_

Rot2 gtsam::Similarity2::R_

private

Definition at line 43 of file Similarity2.h.

◆ s_

double gtsam::Similarity2::s_

private

Definition at line 45 of file Similarity2.h.

◆ t_

Point2 gtsam::Similarity2::t_

private

Definition at line 44 of file Similarity2.h.

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

Classes

Public Member Functions

Private Types

Private Attributes

Testable

Group

Group action on Point2

Lie Group

Standard interface

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Rotation

◆ Translation

Constructor & Destructor Documentation

◆ Similarity2() [1/5]

◆ Similarity2() [2/5]

◆ Similarity2() [3/5]

◆ Similarity2() [4/5]

◆ Similarity2() [5/5]

Member Function Documentation

◆ AdjointMap()

◆ Align() [1/2]

◆ Align() [2/2]

◆ Dim()

◆ dim()

◆ equals()

◆ Expmap()

◆ Identity()

◆ inverse()

◆ Logmap()

◆ matrix()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator==()

◆ print()

◆ rotation()

◆ scale()

◆ transformFrom() [1/2]

◆ transformFrom() [2/2]

◆ translation()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ R_

◆ s_

◆ t_