#include <Similarity3.h>

Inheritance diagram for gtsam::Similarity3:

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

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

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

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

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

GTSAM_EXPORT	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=boost::none) const

Similarity3	compose (const Similarity3 &g) const

Similarity3	compose (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const

const Similarity3 &	derived () const

Similarity3	expmap (const TangentVector &v) const

Similarity3	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2=boost::none) 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=boost::none) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Similarity3 &g) const

TangentVector	logmap (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) 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=boost::none) 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
GTSAM_EXPORT bool	equals (const Similarity3 &sim, double tol) const
	Compare with tolerance. More...

GTSAM_EXPORT bool	operator== (const Similarity3 &other) const
	Exact equality. More...

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

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

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

Group action on Point3
GTSAM_EXPORT Point3	transformFrom (const Point3 &p, OptionalJacobian< 3, 7 > H1=boost::none, OptionalJacobian< 3, 3 > H2=boost::none) const
	Action on a point p is s(Rp+t) More...

GTSAM_EXPORT Pose3	transformFrom (const Pose3 &T) const

GTSAM_EXPORT Point3	operator* (const Point3 &p) const

static GTSAM_EXPORT Similarity3	Align (const std::vector< Point3Pair > &abPointPairs)

static GTSAM_EXPORT Similarity3	Align (const std::vector< Pose3Pair > &abPosePairs)

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

static GTSAM_EXPORT Vector7	Logmap (const Similarity3 &s, OptionalJacobian< 7, 7 > Hm=boost::none)

static GTSAM_EXPORT Similarity3	Expmap (const Vector7 &v, OptionalJacobian< 7, 7 > Hm=boost::none)

static GTSAM_EXPORT Matrix4	wedge (const Vector7 &xi)

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

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

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

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

GTSAM_EXPORT	operator Pose3 () const

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 37 of file Similarity3.h.

Member Typedef Documentation

typedef Rot3 gtsam::Similarity3::Rotation

private

Definition at line 41 of file Similarity3.h.

typedef Point3 gtsam::Similarity3::Translation

private

Definition at line 42 of file Similarity3.h.

Constructor & Destructor Documentation

gtsam::Similarity3::Similarity3 ( )

Default constructor.

Definition at line 87 of file Similarity3.cpp.

gtsam::Similarity3::Similarity3 ( double s )

Construct pure scaling.

Definition at line 91 of file Similarity3.cpp.

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

Construct from GTSAM types.

Definition at line 95 of file Similarity3.cpp.

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

Construct from Eigen types.

Definition at line 99 of file Similarity3.cpp.

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

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

Definition at line 103 of file Similarity3.cpp.

Member Function Documentation

Matrix7 gtsam::Similarity3::AdjointMap ( ) const

Project from one tangent space to another.

Definition at line 206 of file Similarity3.cpp.

Similarity3 gtsam::Similarity3::Align ( const std::vector< Point3Pair > & abPointPairs )

static

Create Similarity3 by aligning at least three point pairs

Definition at line 160 of file Similarity3.cpp.

Similarity3 gtsam::Similarity3::Align ( const std::vector< Pose3Pair > & 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 173 of file Similarity3.cpp.

static size_t gtsam::Similarity3::Dim ( )

inlinestatic

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

Definition at line 205 of file Similarity3.h.

size_t gtsam::Similarity3::dim ( ) const

inline

Dimensionality of tangent space = 7 DOF.

Definition at line 210 of file Similarity3.h.

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

Compare with tolerance.

Definition at line 107 of file Similarity3.cpp.

Similarity3 gtsam::Similarity3::Expmap	(	const Vector7 &	v,
		OptionalJacobian< 7, 7 >	Hm = `boost::none`
	)

static

Exponential map at the identity

Definition at line 267 of file Similarity3.cpp.

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

staticprivate

Calculate expmap and logmap coefficients.

Definition at line 218 of file Similarity3.cpp.

Similarity3 gtsam::Similarity3::identity ( )

static

Return an identity transform.

Definition at line 123 of file Similarity3.cpp.

Similarity3 gtsam::Similarity3::inverse ( ) const

Return the inverse.

Definition at line 130 of file Similarity3.cpp.

Vector7 gtsam::Similarity3::Logmap	(	const Similarity3 &	s,
		OptionalJacobian< 7, 7 >	Hm = `boost::none`
	)

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.

const Matrix4 gtsam::Similarity3::matrix ( ) const

Calculate 4*4 matrix group equivalent.

Definition at line 284 of file Similarity3.cpp.

gtsam::Similarity3::operator Pose3 ( ) const

Convert to a rigid body pose (R, s*t) TODO(frank): why is this here? Red flag! Definitely don't have it as a cast.

Definition at line 291 of file Similarity3.cpp.

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

Composition.

Definition at line 126 of file Similarity3.cpp.

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

syntactic sugar for transformFrom

Definition at line 156 of file Similarity3.cpp.

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

Exact equality.

Definition at line 112 of file Similarity3.cpp.

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

Print with optional string.

Definition at line 116 of file Similarity3.cpp.

const Rot3& gtsam::Similarity3::rotation ( ) const

inline

Return a GTSAM rotation.

Definition at line 186 of file Similarity3.h.

double gtsam::Similarity3::scale ( ) const

inline

Return the scale.

Definition at line 196 of file Similarity3.h.

Point3 gtsam::Similarity3::transformFrom	(	const Point3 &	p,
		OptionalJacobian< 3, 7 >	H1 = `boost::none`,
		OptionalJacobian< 3, 3 >	H2 = `boost::none`
	)		const

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

Definition at line 136 of file Similarity3.cpp.

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 150 of file Similarity3.cpp.

const Point3& gtsam::Similarity3::translation ( ) const

inline

Return a GTSAM translation.

Definition at line 191 of file Similarity3.h.

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

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

friend

Definition at line 278 of file Similarity3.cpp.

Member Data Documentation

Rot3 gtsam::Similarity3::R_

private

Definition at line 46 of file Similarity3.h.

double gtsam::Similarity3::s_

private

Definition at line 48 of file Similarity3.h.

Point3 gtsam::Similarity3::t_

private

Definition at line 47 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

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation