#include <Similarity3.h>

Inheritance diagram for gtsam::Similarity3:

Collaboration diagram for gtsam::Similarity3:

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

Public Types
enum

typedef OptionalJacobian< N, N >	ChartJacobian

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

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

Public Member Functions
const Similarity3 &	derived () const

Similarity3	compose (const Similarity3 &g) const

Similarity3	compose (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2={}) const

GTSAM_EXPORT SOn	compose (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

Similarity3	between (const Similarity3 &g) const

Similarity3	between (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2={}) const

GTSAM_EXPORT SOn	between (const SOn &g, DynamicJacobian H1, DynamicJacobian H2) const

Similarity3	inverse (ChartJacobian H) const

Similarity3	expmap (const TangentVector &v) const

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

TangentVector	logmap (const Similarity3 &g) const

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

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

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

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

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

Constructors
	Similarity3 ()
	Default constructor.

	Similarity3 (double s)
	Construct pure scaling.

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

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

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

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

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

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

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

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

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

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

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

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

Similarity3	inverse () const
	Return the inverse.

static Similarity3	Identity ()
	Return an identity transform.

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)

Pose3	transformFrom (const Pose3 &T) const

Point3	operator* (const Point3 &p) const

static Similarity3	Align (const Point3Pairs &abPointPairs)

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

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

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.

Rot3	rotation () const
	Return a GTSAM rotation.

Point3	translation () const
	Return a GTSAM translation.

double	scale () const
	Return the scale.

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

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

Detailed Description

3D similarity transform

Member Function Documentation

◆ Align() [1/2]

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

static

Create Similarity3 by aligning at least three point pairs

◆ Align() [2/2]

static 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

◆ expmap()

Similarity3 gtsam::LieGroup< Similarity3 , N >::expmap ( const TangentVector & v ) const

inlineinherited

expmap as required by manifold concept Applies exponential map to v and composes with *this

◆ Expmap()

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

static

Exponential map at the identity

◆ logmap()

TangentVector gtsam::LieGroup< Similarity3 , N >::logmap ( const Similarity3 & g ) const

inlineinherited

logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g

◆ Logmap()

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

static

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

◆ operator*()

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

syntactic sugar for transformFrom

◆ transformFrom()

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

◆ wedge()

static 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

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

/home/docs/checkouts/readthedocs.org/user_builds/gtsam-jlblanco-docs/checkouts/latest/gtsam/geometry/Similarity3.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Testable

Group

Group action on Point3

Lie Group

Standard interface

Detailed Description

Member Function Documentation

◆ Align() [1/2]

◆ Align() [2/2]

◆ expmap()

◆ Expmap()

◆ logmap()

◆ Logmap()

◆ operator*()

◆ transformFrom()

◆ wedge()