#include <Similarity3.h>

Inheritance diagram for gtsam::Similarity3:

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

Public Member Functions
Constructors
	Similarity3 ()
	Default constructor. More...

	Similarity3 (double s)
	Construct pure scaling. More...

	Similarity3 (const Rot3 &R, const Point3 &t, double s)
	Construct from GTSAM types. More...

	Similarity3 (const Matrix3 &R, const Vector3 &t, double s)
	Construct from Eigen types. More...

	Similarity3 (const Matrix4 &T)
	Construct from matrix [R t; 0 s^-1]. More...

Public Member Functions inherited from gtsam::LieGroup< Similarity3, 7 >
Similarity3	between (const Similarity3 &g) const

Similarity3	between (const Similarity3 &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

Similarity3	compose (const Similarity3 &g) const

Similarity3	compose (const Similarity3 &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 Similarity3 &	derived () const

Similarity3	expmap (const TangentVector &v) const

Similarity3	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	expmap with optional derivatives More...

Similarity3	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Similarity3 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2={}) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Similarity3 &g) const

TangentVector	logmap (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2={}) const
	logmap with optional derivatives More...

Similarity3	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Similarity3	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2={}) const
	retract with optional derivatives More...

Private Types
Pose Concept
typedef Rot3	Rotation

typedef Point3	Translation

Static Private Member Functions
Helper functions
static Matrix3	GetV (Vector3 w, double lambda)
	Calculate expmap and logmap coefficients. More...

Private Attributes
Rot3	R_

double	s_

Point3	t_

Testable
bool	equals (const Similarity3 &sim, double tol) const
	Compare with tolerance. More...

bool	operator== (const Similarity3 &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 Similarity3 &p)

Group
Similarity3	operator* (const Similarity3 &S) const
	Composition. More...

Similarity3	inverse () const
	Return the inverse. More...

static Similarity3	Identity ()
	Return an identity transform. More...

Group action on Point3
Point3	transformFrom (const Point3 &p, OptionalJacobian< 3, 7 > H1={}, OptionalJacobian< 3, 3 > H2={}) const
	Action on a point p is s(Rp+t) More...

Pose3	transformFrom (const Pose3 &T) const

Point3	operator* (const Point3 &p) const

static Similarity3	Align (const Point3Pairs &abPointPairs)

static Similarity3	Align (const Pose3Pairs &abPosePairs)

Lie Group
Matrix7	AdjointMap () const
	Project from one tangent space to another. More...

static Vector7	Logmap (const Similarity3 &s, OptionalJacobian< 7, 7 > Hm={})

static Similarity3	Expmap (const Vector7 &v, OptionalJacobian< 7, 7 > Hm={})

static Matrix4	wedge (const Vector7 &xi)

Standard interface
Matrix4	matrix () const
	Calculate 4*4 matrix group equivalent. More...

Rot3	rotation () const
	Return a GTSAM rotation. More...

Point3	translation () const
	Return a GTSAM translation. More...

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

size_t	dim () const
	Dimensionality of tangent space = 7 DOF. More...

static size_t	Dim ()
	Dimensionality of tangent space = 7 DOF - used to autodetect sizes. More...

Additional Inherited Members
Public Types inherited from gtsam::LieGroup< Similarity3, 7 >
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< Similarity3, 7 >
static TangentVector	LocalCoordinates (const Similarity3 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Similarity3 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Similarity3	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Similarity3	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

3D similarity transform

Definition at line 36 of file Similarity3.h.

Member Typedef Documentation

◆ Rotation

typedef Rot3 gtsam::Similarity3::Rotation

private

Definition at line 39 of file Similarity3.h.

◆ Translation

typedef Point3 gtsam::Similarity3::Translation

private

Definition at line 40 of file Similarity3.h.

Constructor & Destructor Documentation

◆ Similarity3() [1/5]

gtsam::Similarity3::Similarity3 ( )

Default constructor.

Definition at line 88 of file Similarity3.cpp.

◆ Similarity3() [2/5]

gtsam::Similarity3::Similarity3 ( double s )

Construct pure scaling.

Definition at line 92 of file Similarity3.cpp.

◆ Similarity3() [3/5]

gtsam::Similarity3::Similarity3	(	const Rot3 &	R,
		const Point3 &	t,
		double	s
	)

Construct from GTSAM types.

Definition at line 96 of file Similarity3.cpp.

◆ Similarity3() [4/5]

gtsam::Similarity3::Similarity3	(	const Matrix3 &	R,
		const Vector3 &	t,
		double	s
	)

Construct from Eigen types.

Definition at line 100 of file Similarity3.cpp.

◆ Similarity3() [5/5]

gtsam::Similarity3::Similarity3 ( const Matrix4 & T )

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

Definition at line 104 of file Similarity3.cpp.

Member Function Documentation

◆ AdjointMap()

Matrix7 gtsam::Similarity3::AdjointMap ( ) const

Project from one tangent space to another.

Definition at line 206 of file Similarity3.cpp.

◆ Align() [1/2]

Similarity3 gtsam::Similarity3::Align ( const Point3Pairs & abPointPairs )

static

Create Similarity3 by aligning at least three point pairs

Definition at line 161 of file Similarity3.cpp.

◆ Align() [2/2]

Similarity3 gtsam::Similarity3::Align ( const Pose3Pairs & abPosePairs )

static

Create the Similarity3 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 Similarity3 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 174 of file Similarity3.cpp.

◆ Dim()

static size_t gtsam::Similarity3::Dim ( )

inlinestatic

Dimensionality of tangent space = 7 DOF - used to autodetect sizes.

Definition at line 195 of file Similarity3.h.

◆ dim()

size_t gtsam::Similarity3::dim ( ) const

inline

Dimensionality of tangent space = 7 DOF.

Definition at line 198 of file Similarity3.h.

◆ equals()

bool gtsam::Similarity3::equals	(	const Similarity3 &	sim,
		double	tol
	)		const

Compare with tolerance.

Definition at line 108 of file Similarity3.cpp.

◆ Expmap()

Similarity3 gtsam::Similarity3::Expmap	(	const Vector7 &	v,
		OptionalJacobian< 7, 7 >	Hm = `{}`
	)

static

Exponential map at the identity

Definition at line 267 of file Similarity3.cpp.

◆ GetV()

Matrix3 gtsam::Similarity3::GetV	(	Vector3	w,
		double	lambda
	)

staticprivate

Calculate expmap and logmap coefficients.

Definition at line 218 of file Similarity3.cpp.

◆ Identity()

Similarity3 gtsam::Similarity3::Identity ( )

static

Return an identity transform.

Definition at line 124 of file Similarity3.cpp.

◆ inverse()

Similarity3 gtsam::Similarity3::inverse ( ) const

Return the inverse.

Definition at line 131 of file Similarity3.cpp.

◆ Logmap()

Vector7 gtsam::Similarity3::Logmap	(	const Similarity3 &	s,
		OptionalJacobian< 7, 7 >	Hm = `{}`
	)

static

Log map at the identity $[R_x,R_y,R_z, t_x, t_y, t_z, \lambda]$

Definition at line 254 of file Similarity3.cpp.

◆ matrix()

Matrix4 gtsam::Similarity3::matrix ( ) const

Calculate 4*4 matrix group equivalent.

Definition at line 284 of file Similarity3.cpp.

◆ operator*() [1/2]

Point3 gtsam::Similarity3::operator* ( const Point3 & p ) const

syntactic sugar for transformFrom

Definition at line 157 of file Similarity3.cpp.

◆ operator*() [2/2]

Similarity3 gtsam::Similarity3::operator* ( const Similarity3 & S ) const

Composition.

Definition at line 127 of file Similarity3.cpp.

◆ operator==()

bool gtsam::Similarity3::operator== ( const Similarity3 & other ) const

Exact equality.

Definition at line 113 of file Similarity3.cpp.

◆ print()

void gtsam::Similarity3::print ( const std::string & s = "" ) const

Print with optional string.

Definition at line 117 of file Similarity3.cpp.

◆ rotation()

Rot3 gtsam::Similarity3::rotation ( ) const

inline

Return a GTSAM rotation.

Definition at line 186 of file Similarity3.h.

◆ scale()

double gtsam::Similarity3::scale ( ) const

inline

Return the scale.

Definition at line 192 of file Similarity3.h.

◆ transformFrom() [1/2]

Point3 gtsam::Similarity3::transformFrom	(	const Point3 &	p,
		OptionalJacobian< 3, 7 >	H1 = `{}`,
		OptionalJacobian< 3, 3 >	H2 = `{}`
	)		const

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

Definition at line 137 of file Similarity3.cpp.

◆ transformFrom() [2/2]

Pose3 gtsam::Similarity3::transformFrom ( const Pose3 & 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 Sim3 object. To retrieve a Pose3, 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 151 of file Similarity3.cpp.

◆ translation()

Point3 gtsam::Similarity3::translation ( ) const

inline

Return a GTSAM translation.

Definition at line 189 of file Similarity3.h.

◆ wedge()

Matrix4 gtsam::Similarity3::wedge ( const Vector7 & xi )

static

wedge for Similarity3:

Parameters

xi	7-dim twist (w,u,lambda) where

Returns: 4*4 element of Lie algebra that can be exponentiated TODO(frank): rename to Hat, make part of traits

Definition at line 196 of file Similarity3.cpp.

Friends And Related Function Documentation

◆ operator<<

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Similarity3 &	p
	)

friend

Definition at line 278 of file Similarity3.cpp.

Member Data Documentation

◆ R_

Rot3 gtsam::Similarity3::R_

private

Definition at line 44 of file Similarity3.h.

◆ s_

double gtsam::Similarity3::s_

private

Definition at line 46 of file Similarity3.h.

◆ t_

Point3 gtsam::Similarity3::t_

private

Definition at line 45 of file Similarity3.h.

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

Classes

Public Member Functions

Private Types

Static Private Member Functions

Private Attributes

Testable

Group

Group action on Point3

Lie Group

Standard interface

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Rotation

◆ Translation

Constructor & Destructor Documentation

◆ Similarity3() [1/5]

◆ Similarity3() [2/5]

◆ Similarity3() [3/5]

◆ Similarity3() [4/5]

◆ Similarity3() [5/5]

Member Function Documentation

◆ AdjointMap()

◆ Align() [1/2]

◆ Align() [2/2]

◆ Dim()

◆ dim()

◆ equals()

◆ Expmap()

◆ GetV()

◆ Identity()

◆ inverse()

◆ Logmap()

◆ matrix()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator==()

◆ print()

◆ rotation()

◆ scale()

◆ transformFrom() [1/2]

◆ transformFrom() [2/2]

◆ translation()

◆ wedge()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ R_

◆ s_

◆ t_