#include <Pose3.h>

Inheritance diagram for gtsam::Pose3:

Classes
struct	ChartAtOrigin

Public Types
typedef Rot3	Rotation

typedef Point3	Translation

Public Types inherited from gtsam::LieGroup< Pose3, 6 >
enum

typedef OptionalJacobian< N, N >	ChartJacobian

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

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

Public Member Functions
Testable
void	print (const std::string &s="") const
	print with optional string More...

bool	equals (const Pose3 &pose, double tol=1e-9) const
	assert equality up to a tolerance More...

Group Action on Point3
Point3	transformFrom (const Point3 &point, OptionalJacobian< 3, 6 > Hself=boost::none, OptionalJacobian< 3, 3 > Hpoint=boost::none) const
	takes point in Pose coordinates and transforms it to world coordinates More...

Point3	operator* (const Point3 &point) const

Point3	transformTo (const Point3 &point, OptionalJacobian< 3, 6 > Hself=boost::none, OptionalJacobian< 3, 3 > Hpoint=boost::none) const
	takes point in world coordinates and transforms it to Pose coordinates More...

Standard Interface
const Rot3 &	rotation (OptionalJacobian< 3, 6 > Hself=boost::none) const
	get rotation More...

const Point3 &	translation (OptionalJacobian< 3, 6 > Hself=boost::none) const
	get translation More...

double	x () const
	get x More...

double	y () const
	get y More...

double	z () const
	get z More...

Matrix4	matrix () const

Pose3	transformPoseFrom (const Pose3 &aTb, OptionalJacobian< 6, 6 > Hself=boost::none, OptionalJacobian< 6, 6 > HaTb=boost::none) const

Pose3	transformPoseTo (const Pose3 &wTb, OptionalJacobian< 6, 6 > Hself=boost::none, OptionalJacobian< 6, 6 > HwTb=boost::none) const

double	range (const Point3 &point, OptionalJacobian< 1, 6 > Hself=boost::none, OptionalJacobian< 1, 3 > Hpoint=boost::none) const

double	range (const Pose3 &pose, OptionalJacobian< 1, 6 > Hself=boost::none, OptionalJacobian< 1, 6 > Hpose=boost::none) const

Unit3	bearing (const Point3 &point, OptionalJacobian< 2, 6 > Hself=boost::none, OptionalJacobian< 2, 3 > Hpoint=boost::none) const

Unit3	bearing (const Pose3 &pose, OptionalJacobian< 2, 6 > Hself=boost::none, OptionalJacobian< 2, 6 > Hpose=boost::none) const

Public Member Functions inherited from gtsam::LieGroup< Pose3, 6 >
Pose3	between (const Pose3 &g) const

Pose3	between (const Pose3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const

Pose3	compose (const Pose3 &g) const

Pose3	compose (const Pose3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const

const Pose3 &	derived () const

Pose3	expmap (const TangentVector &v) const

Pose3	expmap (const TangentVector &v, ChartJacobian H1, ChartJacobian H2=boost::none) const
	expmap with optional derivatives More...

Pose3	inverse (ChartJacobian H) const

TangentVector	localCoordinates (const Pose3 &g) const
	localCoordinates as required by manifold concept: finds tangent vector between *this and g More...

TangentVector	localCoordinates (const Pose3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const
	localCoordinates with optional derivatives More...

TangentVector	logmap (const Pose3 &g) const

TangentVector	logmap (const Pose3 &g, ChartJacobian H1, ChartJacobian H2=boost::none) const
	logmap with optional derivatives More...

Pose3	retract (const TangentVector &v) const
	retract as required by manifold concept: applies v at *this More...

Pose3	retract (const TangentVector &v, ChartJacobian H1, ChartJacobian H2=boost::none) const
	retract with optional derivatives More...

Private Attributes
Rot3	R_
	Rotation gRp, between global and pose frame. More...

Point3	t_
	Translation gPp, from global origin to pose frame origin. More...

Standard Constructors
	Pose3 ()

	Pose3 (const Pose3 &pose)

	Pose3 (const Rot3 &R, const Point3 &t)

	Pose3 (const Pose2 &pose2)

	Pose3 (const Matrix &T)

static Pose3	Create (const Rot3 &R, const Point3 &t, OptionalJacobian< 6, 3 > HR=boost::none, OptionalJacobian< 6, 3 > Ht=boost::none)
	Named constructor with derivatives. More...

static boost::optional< Pose3 >	Align (const std::vector< Point3Pair > &abPointPairs)

Group
Pose3	inverse () const
	inverse transformation with derivatives More...

Pose3	operator* (const Pose3 &T) const
	compose syntactic sugar More...

Pose3	interpolateRt (const Pose3 &T, double t) const

static Pose3	identity ()
	identity for group operation More...

Lie Group
Matrix6	AdjointMap () const

Vector6	Adjoint (const Vector6 &xi_b) const
	FIXME Not tested - marked as incorrect. More...

static Pose3	Expmap (const Vector6 &xi, OptionalJacobian< 6, 6 > Hxi=boost::none)
	Exponential map at identity - create a rotation from canonical coordinates . More...

static Vector6	Logmap (const Pose3 &pose, OptionalJacobian< 6, 6 > Hpose=boost::none)
	Log map at identity - return the canonical coordinates of this rotation. More...

static Matrix6	adjointMap (const Vector6 &xi)
	FIXME Not tested - marked as incorrect. More...

static Vector6	adjoint (const Vector6 &xi, const Vector6 &y, OptionalJacobian< 6, 6 > Hxi=boost::none)

static Matrix6	adjointMap_ (const Vector6 &xi)

static Vector6	adjoint_ (const Vector6 &xi, const Vector6 &y)

static Vector6	adjointTranspose (const Vector6 &xi, const Vector6 &y, OptionalJacobian< 6, 6 > Hxi=boost::none)

static Matrix6	ExpmapDerivative (const Vector6 &xi)
	Derivative of Expmap. More...

static Matrix6	LogmapDerivative (const Pose3 &xi)
	Derivative of Logmap. More...

static Matrix3	ComputeQforExpmapDerivative (const Vector6 &xi, double nearZeroThreshold=1e-5)

static Matrix	wedge (double wx, double wy, double wz, double vx, double vy, double vz)

Advanced Interface
class	boost::serialization::access

GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const Pose3 &p)
	Output stream operator. More...

static std::pair< size_t, size_t >	translationInterval ()

static std::pair< size_t, size_t >	rotationInterval ()

template<class Archive >
void	serialize (Archive &ar, const unsigned int)

Additional Inherited Members
Static Public Member Functions inherited from gtsam::LieGroup< Pose3, 6 >
static TangentVector	LocalCoordinates (const Pose3 &g)
	LocalCoordinates at origin: possible in Lie group because it has an identity. More...

static TangentVector	LocalCoordinates (const Pose3 &g, ChartJacobian H)
	LocalCoordinates at origin with optional derivative. More...

static Pose3	Retract (const TangentVector &v)
	Retract at origin: possible in Lie group because it has an identity. More...

static Pose3	Retract (const TangentVector &v, ChartJacobian H)
	Retract at origin with optional derivative. More...

Detailed Description

Definition at line 37 of file Pose3.h.

Member Typedef Documentation

typedef Rot3 gtsam::Pose3::Rotation

Pose Concept requirements

Definition at line 41 of file Pose3.h.

typedef Point3 gtsam::Pose3::Translation

Definition at line 42 of file Pose3.h.

Constructor & Destructor Documentation

gtsam::Pose3::Pose3 ( )

inline

Default constructor is origin

Definition at line 55 of file Pose3.h.

gtsam::Pose3::Pose3 ( const Pose3 & pose )

inline

Copy constructor

Definition at line 58 of file Pose3.h.

gtsam::Pose3::Pose3	(	const Rot3 &	R,
		const Point3 &	t
	)

inline

Construct from R,t

Definition at line 63 of file Pose3.h.

Pose3::Pose3 ( const Pose2 & pose2 )

explicit

Construct from Pose2

Definition at line 36 of file Pose3.cpp.

gtsam::Pose3::Pose3 ( const Matrix & T )

inline

Constructor from 4*4 matrix

Definition at line 71 of file Pose3.h.

Member Function Documentation

Vector6 gtsam::Pose3::Adjoint ( const Vector6 & xi_b ) const

inline

FIXME Not tested - marked as incorrect.

Apply this pose's AdjointMap Ad_g to a twist $\xi_b$ , i.e. a body-fixed velocity, transforming it to the spatial frame $\xi^s = g*\xi^b*g^{-1} = Ad_g * \xi^b$

Definition at line 154 of file Pose3.h.

Vector6 Pose3::adjoint	(	const Vector6 &	xi,
		const Vector6 &	y,
		OptionalJacobian< 6, 6 >	Hxi = `boost::none`
	)

static

Action of the adjointMap on a Lie-algebra vector y, with optional derivatives

Definition at line 77 of file Pose3.cpp.

static Vector6 gtsam::Pose3::adjoint_	(	const Vector6 &	xi,
		const Vector6 &	y
	)

inlinestatic

Definition at line 183 of file Pose3.h.

Matrix6 Pose3::AdjointMap ( ) const

Calculate Adjoint map, transforming a twist in the this pose's (i.e, body) frame to the world spatial frame Ad_pose is 6*6 matrix that when applied to twist xi $ [R_x,R_y,R_z,T_x,T_y,T_z] $ , returns Ad_pose(xi)

Definition at line 58 of file Pose3.cpp.

Matrix6 Pose3::adjointMap ( const Vector6 & xi )

static

FIXME Not tested - marked as incorrect.

Compute the [ad(w,v)] operator as defined in [Kobilarov09siggraph], pg 11 [ad(w,v)] = [w^, zero3; v^, w^] Note that this is the matrix representation of the adjoint operator for se3 Lie algebra, aka the Lie bracket, and also the derivative of Adjoint map for the Lie group SE3.

Let $\hat{\xi}_i$ be the se3 Lie algebra, and $\hat{\xi}_i^\vee = \xi_i = [\omega_i,v_i] \in \mathbb{R}^6$ be its vector representation. We have the following relationship: $[\hat{\xi}_1,\hat{\xi}_2]^\vee = ad_{\xi_1}(\xi_2) = [ad_{(\omega_1,v_1)}]*\xi_2$

We use this to compute the discrete version of the inverse right-trivialized tangent map, and its inverse transpose in the discrete Euler Poincare' (DEP) operator.

Definition at line 67 of file Pose3.cpp.

static Matrix6 gtsam::Pose3::adjointMap_ ( const Vector6 & xi )

inlinestatic

Definition at line 182 of file Pose3.h.

Vector6 Pose3::adjointTranspose	(	const Vector6 &	xi,
		const Vector6 &	y,
		OptionalJacobian< 6, 6 >	Hxi = `boost::none`
	)

static

The dual version of adjoint action, acting on the dual space of the Lie-algebra vector space.

Definition at line 93 of file Pose3.cpp.

boost::optional< Pose3 > Pose3::Align ( const std::vector< Point3Pair > & abPointPairs )

static

Create Pose3 by aligning two point pairs A pose aTb is estimated between pairs (a_point, b_point) such that a_point = aTb * b_point Note this allows for noise on the points but in that case the mapping will not be exact.

Definition at line 387 of file Pose3.cpp.

Unit3 Pose3::bearing	(	const Point3 &	point,
		OptionalJacobian< 2, 6 >	Hself = `boost::none`,
		OptionalJacobian< 2, 3 >	Hpoint = `boost::none`
	)		const

Calculate bearing to a landmark

Parameters

point 3D location of landmark

Returns: bearing (Unit3)

Definition at line 360 of file Pose3.cpp.

Unit3 Pose3::bearing	(	const Pose3 &	pose,
		OptionalJacobian< 2, 6 >	Hself = `boost::none`,
		OptionalJacobian< 2, 6 >	Hpose = `boost::none`
	)		const

Calculate bearing to another pose

Parameters

other 3D location and orientation of other body. The orientation information is ignored.

Returns: bearing (Unit3)

Definition at line 377 of file Pose3.cpp.

Matrix3 Pose3::ComputeQforExpmapDerivative	(	const Vector6 &	xi,
		double	nearZeroThreshold = `1e-5`
	)

static

Compute the 3x3 bottom-left block Q of SE3 Expmap right derivative matrix J_r(xi) = [J_(w) Z_3x3; Q_r J_(w)] where J_(w) is the SO3 Expmap right derivative. (see Chirikjian11book2, pg 44, eq 10.95. The closed-form formula is identical to formula 102 in Barfoot14tro where Q_l of the SE3 Expmap left derivative matrix is given.

Definition at line 194 of file Pose3.cpp.

Pose3 Pose3::Create	(	const Rot3 &	R,
		const Point3 &	t,
		OptionalJacobian< 6, 3 >	HR = `boost::none`,
		OptionalJacobian< 6, 3 >	Ht = `boost::none`
	)

static

Named constructor with derivatives.

Definition at line 42 of file Pose3.cpp.

bool Pose3::equals	(	const Pose3 &	pose,
		double	tol = `1e-9`
	)		const

assert equality up to a tolerance

Definition at line 114 of file Pose3.cpp.

Pose3 Pose3::Expmap	(	const Vector6 &	xi,
		OptionalJacobian< 6, 6 >	Hxi = `boost::none`
	)

static

Exponential map at identity - create a rotation from canonical coordinates $ [R_x,R_y,R_z,T_x,T_y,T_z] $ .

Modified from Murray94book version (which assumes w and v normalized?)

Definition at line 120 of file Pose3.cpp.

Matrix6 Pose3::ExpmapDerivative ( const Vector6 & xi )

static

Derivative of Expmap.

Definition at line 237 of file Pose3.cpp.

static Pose3 gtsam::Pose3::identity ( )

inlinestatic

identity for group operation

Definition at line 103 of file Pose3.h.

Pose3 gtsam::Pose3::interpolateRt	(	const Pose3 &	T,
		double	t
	)		const

inline

Interpolate between two poses via individual rotation and translation interpolation.

The default "interpolate" method defined in Lie.h minimizes the geodesic distance on the manifold, leading to a screw motion interpolation in Cartesian space, which might not be what is expected. In contrast, this method executes a straight line interpolation for the translation, while still using interpolate (aka "slerp") for the rotational component. This might be more intuitive in many applications.

Parameters

T	End point of interpolation.
t	A value in [0, 1].

Definition at line 129 of file Pose3.h.

Pose3 Pose3::inverse ( ) const

inverse transformation with derivatives

Definition at line 50 of file Pose3.cpp.

Vector6 Pose3::Logmap	(	const Pose3 &	pose,
		OptionalJacobian< 6, 6 >	Hpose = `boost::none`
	)

static

Log map at identity - return the canonical coordinates $ [R_x,R_y,R_z,T_x,T_y,T_z] $ of this rotation.

Definition at line 139 of file Pose3.cpp.

Matrix6 Pose3::LogmapDerivative ( const Pose3 & xi )

static

Derivative of Logmap.

Definition at line 247 of file Pose3.cpp.

Matrix4 Pose3::matrix ( ) const

convert to 4*4 matrix

Definition at line 274 of file Pose3.cpp.

Pose3 gtsam::Pose3::operator* ( const Pose3 & T ) const

inline

compose syntactic sugar

Definition at line 111 of file Pose3.h.

Point3 gtsam::Pose3::operator* ( const Point3 & point ) const

inline

syntactic sugar for transformFrom

Definition at line 244 of file Pose3.h.

void Pose3::print ( const std::string & s = "" ) const

print with optional string

Definition at line 109 of file Pose3.cpp.

double Pose3::range	(	const Point3 &	point,
		OptionalJacobian< 1, 6 >	Hself = `boost::none`,
		OptionalJacobian< 1, 3 >	Hpoint = `boost::none`
	)		const

Calculate range to a landmark

Parameters

point 3D location of landmark

Returns: range (double)

Definition at line 334 of file Pose3.cpp.

double Pose3::range	(	const Pose3 &	pose,
		OptionalJacobian< 1, 6 >	Hself = `boost::none`,
		OptionalJacobian< 1, 6 >	Hpose = `boost::none`
	)		const

Calculate range to another pose

Parameters

pose	Other SO(3) pose

Returns: range (double)

Definition at line 351 of file Pose3.cpp.

const Rot3 & Pose3::rotation ( OptionalJacobian< 3, 6 > Hself = boost::none ) const

get rotation

Definition at line 266 of file Pose3.cpp.

static std::pair<size_t, size_t> gtsam::Pose3::rotationInterval ( )

inlinestatic

Return the start and end indices (inclusive) of the rotation component of the exponential map parameterization

Returns: a pair of [start, end] indices into the tangent space vector

Definition at line 352 of file Pose3.h.

template<class Archive >

void gtsam::Pose3::serialize	(	Archive &	ar,
		const unsigned	int
	)

inlineprivate

Definition at line 364 of file Pose3.h.

Point3 Pose3::transformFrom	(	const Point3 &	point,
		OptionalJacobian< 3, 6 >	Hself = `boost::none`,
		OptionalJacobian< 3, 3 >	Hpoint = `boost::none`
	)		const

takes point in Pose coordinates and transforms it to world coordinates

Parameters

point	point in Pose coordinates
Hself	optional 3*6 Jacobian wrpt this pose
Hpoint	optional 3*3 Jacobian wrpt point

Returns: point in world coordinates

Definition at line 298 of file Pose3.cpp.

Pose3 Pose3::transformPoseFrom	(	const Pose3 &	aTb,
		OptionalJacobian< 6, 6 >	Hself = `boost::none`,
		OptionalJacobian< 6, 6 >	HaTb = `boost::none`
	)		const

Assuming self == wTa, takes a pose aTb in local coordinates and transforms it to world coordinates wTb = wTa * aTb. This is identical to compose.

Definition at line 282 of file Pose3.cpp.

Pose3 Pose3::transformPoseTo	(	const Pose3 &	wTb,
		OptionalJacobian< 6, 6 >	Hself = `boost::none`,
		OptionalJacobian< 6, 6 >	HwTb = `boost::none`
	)		const

Assuming self == wTa, takes a pose wTb in world coordinates and transforms it to local coordinates aTb = inv(wTa) * wTb

Definition at line 289 of file Pose3.cpp.

Point3 Pose3::transformTo	(	const Point3 &	point,
		OptionalJacobian< 3, 6 >	Hself = `boost::none`,
		OptionalJacobian< 3, 3 >	Hpoint = `boost::none`
	)		const

takes point in world coordinates and transforms it to Pose coordinates

Parameters

point	point in world coordinates
Hself	optional 3*6 Jacobian wrpt this pose
Hpoint	optional 3*3 Jacobian wrpt point

Returns: point in Pose coordinates

Definition at line 314 of file Pose3.cpp.

const Point3 & Pose3::translation ( OptionalJacobian< 3, 6 > Hself = boost::none ) const

get translation

Definition at line 259 of file Pose3.cpp.

static std::pair<size_t, size_t> gtsam::Pose3::translationInterval ( )

inlinestatic

Return the start and end indices (inclusive) of the translation component of the exponential map parameterization

Returns: a pair of [start, end] indices into the tangent space vector

Definition at line 343 of file Pose3.h.

static Matrix gtsam::Pose3::wedge	(	double	wx,
		double	wy,
		double	wz,
		double	vx,
		double	vy,
		double	vz
	)

inlinestatic

wedge for Pose3:

Parameters

xi	6-dim twist (omega,v) where omega = (wx,wy,wz) 3D angular velocity v (vx,vy,vz) = 3D velocity

Returns: xihat, 4*4 element of Lie algebra that can be exponentiated

Definition at line 224 of file Pose3.h.

double gtsam::Pose3::x ( ) const

inline

get x

Definition at line 269 of file Pose3.h.

double gtsam::Pose3::y ( ) const

inline

get y

Definition at line 274 of file Pose3.h.

double gtsam::Pose3::z ( ) const

inline

get z

Definition at line 279 of file Pose3.h.

Friends And Related Function Documentation

friend class boost::serialization::access

friend

Serialization function

Definition at line 362 of file Pose3.h.

GTSAM_EXPORT friend std::ostream& operator<<	(	std::ostream &	os,
		const Pose3 &	p
	)

friend

Output stream operator.

Definition at line 419 of file Pose3.cpp.

Member Data Documentation

Rot3 gtsam::Pose3::R_

private

Rotation gRp, between global and pose frame.

Definition at line 46 of file Pose3.h.

Point3 gtsam::Pose3::t_

private

Translation gPp, from global origin to pose frame origin.

Definition at line 47 of file Pose3.h.

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

Classes

Public Types

Public Member Functions

Private Attributes

Standard Constructors

Group

Lie Group

Advanced Interface

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation