Detailed Description

3D similarity transform

Inheritance diagram for gtsam::Similarity3:

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

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

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

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

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

GTSAM_EXPORT Similarity3	inverse () const
	Return the inverse.

static GTSAM_EXPORT Similarity3	identity ()
	Return an identity transform.

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)

GTSAM_EXPORT Pose3	transformFrom (const Pose3 &T) const
	Action on a pose T. More...

GTSAM_EXPORT Point3	operator* (const Point3 &p) const
	syntactic sugar for transformFrom

static GTSAM_EXPORT Similarity3	Align (const std::vector< Point3Pair > &abPointPairs)
	Create Similarity3 by aligning at least three point pairs.

static GTSAM_EXPORT Similarity3	Align (const std::vector< Pose3Pair > &abPosePairs)
	Create the Similarity3 object that aligns at least two pose pairs. More...

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

static GTSAM_EXPORT Vector7	Logmap (const Similarity3 &s, OptionalJacobian< 7, 7 > Hm=boost::none)
	Log map at the identity \( [R_x,R_y,R_z, t_x, t_y, t_z, \lambda] \).

static GTSAM_EXPORT Similarity3	Expmap (const Vector7 &v, OptionalJacobian< 7, 7 > Hm=boost::none)
	Exponential map at the identity.

static GTSAM_EXPORT Matrix4	wedge (const Vector7 &xi)
	wedge for Similarity3: More...

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

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

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

double	scale () const
	Return the scale.

GTSAM_EXPORT	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.

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

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

Public Member Functions
Constructors
GTSAM_EXPORT	Similarity3 ()
	Default constructor.

GTSAM_EXPORT	Similarity3 (double s)
	Construct pure scaling.

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

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

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

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

Similarity3	compose (const Similarity3 &g) const

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

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

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=boost::none) const

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

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

Similarity3	inverse (ChartJacobian H) const

Similarity3	expmap (const TangentVector &v) const
	expmap as required by manifold concept Applies exponential map to v and composes with *this

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

TangentVector	logmap (const Similarity3 &g) const
	logmap as required by manifold concept Applies logarithmic map to group element that takes *this to g

TangentVector	logmap (const Similarity3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) 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=boost::none) 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=boost::none) const
	localCoordinates with optional derivatives

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

Additional Inherited Members
Static Public Member Functions inherited from gtsam::LieGroup< Similarity3, 7 >
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.

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

Member Function Documentation

◆ Align()

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

◆ 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()

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 files:

/Users/dellaert/git/github/gtsam/geometry/Similarity3.h
/Users/dellaert/git/github/gtsam/geometry/Similarity3.cpp

Detailed Description

Testable

Group

Group action on Point3

Lie Group

Standard interface

Public Member Functions

Classes

Additional Inherited Members

Member Function Documentation

◆ Align()

◆ transformFrom()

◆ wedge()