SE3Quat

SE(3) rigid body transformation represented by a unit quaternion and translation vector. More...

Collaboration diagram for SE3Quat:

Public Member Functions
	SE3Quat ()
	Default constructor.
	SE3Quat (const Matrix3< g_type > &R, const Vector3< g_type > &t)
	Constructs from a rotation matrix and translation vector.
template<typename Derived>
	SE3Quat (const MatrixBase< Derived > &v)
	templaized constructor which allows v to be an arbitrary Eigen Vector type, e.g., Vector6d or Map<Vector6d>
	SE3Quat (const Quaternion< g_type > &q, const Vector3< g_type > &t)
	Constructs from a quaternion and translation vector.
Eigen::Matrix< g_type, 6, 6 >	adj () const
	Computes the 6x6 adjoint matrix of this SE3 transform.
void	fromMinimalVector (const Vector6d &v)
	Initializes from a minimal 6D vector [t, qx, qy, qz], recovering qw.
void	fromVector (const Vector7d &v)
	Initializes from a 7D vector [t, qw, qx, qy, qz].
SE3Quat	inverse () const
	Computes the inverse of this SE3 transform.
Vector6d	log () const
	Computes the logarithmic map (SE3 -> 6D tangent vector).
Vector3< g_type >	map (const Vector3< g_type > &xyz) const
	Transforms a 3D point: R*xyz + t.
void	normalizeRotation ()
	Normalizes the rotation quaternion, ensuring positive w.
SE3Quat	operator* (const SE3Quat &tr2) const
	Composes two SE3 transforms: result = (*this) * tr2.
Vector3< g_type >	operator* (const Vector3< g_type > &v) const
	Transforms a 3D point: t + R*v.
SE3Quat &	operator*= (const SE3Quat &tr2)
	In-place composition with another SE3Quat.
g_type	operator[] (int i) const
	Const element access: 0-2 = translation, 3-6 = quaternion coeffs.
const Quaternion< g_type > &	rotation () const
	Returns a const reference to the rotation quaternion.
void	setRotation (const Quaternion< g_type > &r_)
	Sets the rotation quaternion.
void	setTranslation (const Vector3< g_type > &t_)
	Sets the translation vector.
Eigen::Matrix< g_type, 4, 4 >	to_homogeneous_matrix () const
	Converts to a 4x4 homogeneous transformation matrix.
Vector6d	toMinimalVector () const
	Converts to a minimal 6D vector [t, qx, qy, qz].
Vector7d	toVector () const
	Converts to a 7D vector [t, qx, qy, qz, qw].
const Vector3< g_type > &	translation () const
	Returns a const reference to the translation vector.

Static Public Member Functions
static SE3Quat	exp (const Vector6d &update)
	Computes the exponential map from a 6D tangent vector to SE3.

Protected Attributes
Quaternion< g_type >	_r
	Rotation component as a unit quaternion.
Vector3< g_type >	m_t
	Translation component.

Detailed Description

SE(3) rigid body transformation represented by a unit quaternion and translation vector.

Definition at line 42 of file se3quat.h.

Constructor & Destructor Documentation

SE3Quat() [1/3]

SE3Quat::SE3Quat ( )

inline

Default constructor.

Identity rotation, zero translation.

Definition at line 55 of file se3quat.h.

References _r, and m_t.

Referenced by exp(), inverse(), operator*(), and operator*=().

SE3Quat() [2/3]

SE3Quat::SE3Quat ( const Matrix3< g_type > & R, const Vector3< g_type > & t )

inline

Constructs from a rotation matrix and translation vector.

Parameters

[in]	R	The 3x3 rotation matrix.
[in]	t	The translation vector.

Definition at line 63 of file se3quat.h.

References _r, m_t, and normalizeRotation().

SE3Quat() [3/3]

SE3Quat::SE3Quat ( const Quaternion< g_type > & q, const Vector3< g_type > & t )

inline

Constructs from a quaternion and translation vector.

Parameters

[in]	q	The rotation quaternion.
[in]	t	The translation vector.

Definition at line 73 of file se3quat.h.

References _r, m_t, and normalizeRotation().

Member Function Documentation

adj()

Eigen::Matrix< g_type, 6, 6 > SE3Quat::adj ( ) const

inline

Computes the 6x6 adjoint matrix of this SE3 transform.

Returns

The adjoint matrix.

Definition at line 309 of file se3quat.h.

References _r, m_t, and skew().

Referenced by EdgeSE3Expmap::linearizeOplus().

exp()

SE3Quat SE3Quat::exp ( const Vector6d & update )

inlinestatic

Computes the exponential map from a 6D tangent vector to SE3.

Parameters

[in]

update

The 6D tangent vector [omega, upsilon].

Returns

The SE3Quat transformation.

Definition at line 272 of file se3quat.h.

References SE3Quat(), cos(), sin(), and skew().

Referenced by VertexSE3Expmap::oplusImpl().

fromMinimalVector()

void SE3Quat::fromMinimalVector ( const Vector6d & v )

inline

Initializes from a minimal 6D vector [t, qx, qy, qz], recovering qw.

Parameters

[in]

v

The 6D vector.

Definition at line 195 of file se3quat.h.

References _r, m_t, and sqrt().

fromVector()

void SE3Quat::fromVector ( const Vector7d & v )

inline

Initializes from a 7D vector [t, qw, qx, qy, qz].

Parameters

[in]

v

The 7D vector.

Definition at line 176 of file se3quat.h.

References _r, and m_t.

log()

Vector6d SE3Quat::log ( ) const

inline

Computes the logarithmic map (SE3 -> 6D tangent vector).

Returns

A 6D vector [omega, upsilon].

Definition at line 209 of file se3quat.h.

References _r, deltaR(), m_t, PI(), skew(), sqrt(), and tan().

Referenced by EdgeSE3::computeError(), and EdgeSE3Expmap::computeError().

map()

Vector3< g_type > SE3Quat::map ( const Vector3< g_type > & xyz ) const

inline

Transforms a 3D point: R*xyz + t.

Parameters

[in]

xyz

The point to transform.

Definition at line 263 of file se3quat.h.

References _r, and m_t.

Referenced by EdgeStereoSE3ProjectXYZ::linearizeOplus().

operator*()

Vector3< g_type > SE3Quat::operator* ( const Vector3< g_type > & v ) const

inline

Transforms a 3D point: t + R*v.

Parameters

[in]

v

The point to transform.

Definition at line 140 of file se3quat.h.

References _r, and m_t.

setRotation()

void SE3Quat::setRotation ( const Quaternion< g_type > & r_ )

inline

Sets the rotation quaternion.

Parameters

[in]

r_

The new rotation quaternion.

Definition at line 119 of file se3quat.h.

References _r.

setTranslation()

void SE3Quat::setTranslation ( const Vector3< g_type > & t_ )

inline

Sets the translation vector.

Parameters

[in]

t_

The new translation.

Definition at line 114 of file se3quat.h.

References m_t.

to_homogeneous_matrix()

Eigen::Matrix< g_type, 4, 4 > SE3Quat::to_homogeneous_matrix ( ) const

inline

Converts to a 4x4 homogeneous transformation matrix.

Returns

The homogeneous matrix.

Definition at line 322 of file se3quat.h.

References _r, and translation().

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

• GraphOptimization/Headers/se3quat.h