BIAS::Quaternion< T > Class Template Reference

class for rotation with axis and angle More...

#include <Base/Geometry/DualQuaternionOperators.hh>

Inheritance diagram for BIAS::Quaternion< T >:

Collaboration diagram for BIAS::Quaternion< T >:

Public Types
typedef QUAT_TYPE	value_type

Public Member Functions
void	Add (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const
	Addition with a scalar, storing results in destionation vector. More...
void	Add (const Vector4< QUAT_TYPE > &argvec, Vector4< QUAT_TYPE > &destvec) const
	adding of two vectors, storing the result in destvec More...
void	AddIP (const QUAT_TYPE &scalar)
	Addition (in place) of an scalar. More...
void	AddIP (const Vector4< QUAT_TYPE > &argvec)
	in place adding More...
void	clear ()
void	Copy (const QUAT_TYPE *pv)
	copy the array of vectorsize beginning at *T to this->data_ More...
double	Dist (const Vector4< QUAT_TYPE > &vec) const
	Return the euclidean distance of 2 vectors. More...
void	Divide (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const
	Division with a scalar, storing results in destionation vector. More...
void	DivideIP (const QUAT_TYPE &scalar)
	Division (in place) of an scalar. More...
void	ElementwiseProduct (const Vector4< QUAT_TYPE > &argvec, Vector4< QUAT_TYPE > &destvec) const
	multiply two vectors elementwise, storing the result in destvec More...
void	EnforceRigidCouplingConstraint (Quaternion< QUAT_TYPE > &other, bool useOtherAngle=false)
	Enforce rigid coupling constraint for this and the other given unit quaternion (equal rotation angle/equal scalar part for both). More...
int	GetAxisAngle (Vector3< QUAT_TYPE > &axis, QUAT_TYPE &angle) const
	Returns rotation in axis and angle notation (angle in radians). More...
const QUAT_TYPE *	GetData () const
	get the data pointer the member function itself is const (before {..}) because it doesn't change the this object. More...
QUAT_TYPE *	GetData ()
void	GetEquatorialPoint3D (Vector3< QUAT_TYPE > &p3D) const
	Compute minimal parametrization of unit quaternion by projecting it from the 4d hypersphere onto the 3d equatorial space, as described in: [TCBS+12] Terzakis et al. More...
const unsigned int	GetNumElements () const
Matrix4x4< QUAT_TYPE >	GetQuaternionMultMatrixLeft () const
	Returns matrix which expresses (left) quaternion multiplication. More...
Matrix4x4< QUAT_TYPE >	GetQuaternionMultMatrixRight () const
	Returns matrix which expresses right quaternion multiplication. More...
QUAT_TYPE	GetRotationAngle () const
	Returns rotation angle notation in radians. More...
Vector3< QUAT_TYPE >	GetRotationAxis () const
	Returns rotation axis. More...
int	GetRotationMatrix (RMatrixBase &R) const
	Returns a corresponding (quaternion) rotation matrix. More...
Quaternion< QUAT_TYPE >	Interpolate (const Quaternion< QUAT_TYPE > &to, const QUAT_TYPE &t) const
	Spherical interpolation between this and given quaternion. More...
Quaternion< QUAT_TYPE >	InterpolateLinear (const Quaternion< QUAT_TYPE > &to, const QUAT_TYPE &t) const
	Linear interpolation between this and given quaternion. More...
Quaternion< QUAT_TYPE >	Inverse () const
	returns the Inverse rotation Quaternion More...
void	Invert ()
	inverts this, by changing the rotation axis by *=-1 More...
bool	Load (const std::string &filename)
	method to load directly from a given filename. More...
void	MakeUnique ()
	makes Quaternion-representation uniqe, ensuring vector lies in upper (by real part) hemisphere. More...
void	Mult (const Quaternion< QUAT_TYPE > &quat)
	quaternion multiplication: this= this * quat More...
void	Mult (const Quaternion< QUAT_TYPE > &arg, Quaternion< QUAT_TYPE > &res) const
	quaternion multiplication: res = this * arg More...
void	Multiply (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const
	Multiplication with a scalar, storing results in destionation vector. More...
void	MultiplyIP (const QUAT_TYPE &scalar)
	Multiplication (in place) of an scalar. More...
void	MultLeft (const Quaternion< QUAT_TYPE > &quat)
	quaternion multiplication: this = quat * this More...
int	MultVec (const Vector3< QUAT_TYPE > &vec, Vector3< QUAT_TYPE > &res) const
	rotates the given Vector qith the quaternion ( q v q* ) the resulting vector is given in res More...
Vector3< QUAT_TYPE >	MultVec (const Vector3< QUAT_TYPE > &vec) const
void	Normalize ()
	Scales quaternion to unit length, i.e. More...
QUAT_TYPE	NormL1 () const
	Return the L1 norm: |a| + |b| + |c|+ |d|. More...
double	NormL2 () const
	Return the L2 norm: sqrt(a^2 + b^2 + c^2 + d^2) More...
bool	operator!= (const Vector4< QUAT_TYPE > &arg) const
	Comparison operator 'not equal'. More...
Vector4< QUAT_TYPE > &	operator*= (const QUAT_TYPE &scalar)
	Multiplication operator with scalar argument. More...
Vector4< QUAT_TYPE > &	operator+= (const QUAT_TYPE &scalar)
	Addition operator with scalar argument. More...
Vector4< QUAT_TYPE > &	operator+= (const Vector4< QUAT_TYPE > &argvec)
	add operator for two Vectors More...
Vector4< QUAT_TYPE > &	operator-= (const QUAT_TYPE &scalar)
	Substraction operator with scalar argument. More...
Vector4< QUAT_TYPE > &	operator-= (const Vector4< QUAT_TYPE > &argvec)
	sub operator for two Vectors More...
Vector4< QUAT_TYPE > &	operator/= (const QUAT_TYPE &scalar)
	Division operator with scalar argument. More...
Quaternion< QUAT_TYPE > &	operator= (const Quaternion< QUAT_TYPE > &vec)
	assignment operator More...
bool	operator== (const Vector4< QUAT_TYPE > &arg) const
	Comparison operator 'equal'. More...
const QUAT_TYPE &	operator[] (const int i) const
	access an element of the vector with 0-based indizes. More...
QUAT_TYPE &	operator[] (const int i)
	access an element of the vector with 0-based indizes. More...
Matrix4x4< QUAT_TYPE >	OuterProduct (const Vector4< QUAT_TYPE > &v) const
	outer product, constructs a matrix. More...
Quaternion< QUAT_TYPE >	Power (const QUAT_TYPE &scale) const
	Computes this^(scale), which scales the angle from axis/angle- representation with 'scale'. More...
	Quaternion ()
	Quaternion (const Vector4< QUAT_TYPE > &q)
	Quaternion (const Quaternion< QUAT_TYPE > &q)
	copy constructor More...
	Quaternion (QUAT_TYPE i, QUAT_TYPE j, QUAT_TYPE k, QUAT_TYPE r)
bool	Save (const std::string &filename) const
	method to save directly to a given filename. More...
void	ScalarProduct (const Vector4< QUAT_TYPE > &argvec, QUAT_TYPE &result) const
	scalar product (=inner product) of two vectors, storing the result in result More...
QUAT_TYPE	ScalarProduct (const Vector4< QUAT_TYPE > &argvec) const
void	Set (const QUAT_TYPE &scalar)
	set all elements to a scalat value More...
void	Set (const QUAT_TYPE &x, const QUAT_TYPE &y, const QUAT_TYPE &z, const QUAT_TYPE &w)
	set elementwise with given scalr values More...
void	SetFromEquatorialPoint3D (const Vector3< QUAT_TYPE > &p3D)
	Set unit quaternion from 3d point in equatorial space by back- projecting it onto the 4d hypersphere, as described in [TCBS+12]. More...
void	SetIdentity ()
void	SetQuaternion (QUAT_TYPE real, QUAT_TYPE i, QUAT_TYPE j, QUAT_TYPE k)
	Sets all parts of quaternion in mathematical order, real part first, then 1.,2. More...
void	SetValueAsAxisRad (const Vector3< QUAT_TYPE > &axis, QUAT_TYPE angle)
	sets the quaternion with given rotation axis and angle (in rad) More...
void	SetValueAsAxisRad (QUAT_TYPE axisX, QUAT_TYPE axisY, QUAT_TYPE axisZ, QUAT_TYPE angle)
	sets the quaternion with given rotation axis and angle (in rad) More...
int	SetXYZ (QUAT_TYPE radX, QUAT_TYPE radY, QUAT_TYPE radZ)
	Sets quaternion as concatenated rotations around x,y,z-axis; this = q_x * q_y * q_z (BIAS-RMatrix conform) More...
void	SetZero ()
	set all values to 0 More...
int	SetZYX (QUAT_TYPE radX, QUAT_TYPE radY, QUAT_TYPE radZ)
	Sets quaternion as concatenated rotations around x,y,z-axis; this = q_z * q_y * q_x (BIAS-RMatrix conform) More...
const unsigned int	Size () const
const unsigned int	size () const
void	Sub (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const
	Substraction with a scalar, storing results in destionation vector. More...
void	Sub (const Vector4< QUAT_TYPE > &argvec, Vector4< QUAT_TYPE > &destvec) const
	subtracting of two Vectors, storing the result in destvec More...
void	SubIP (const QUAT_TYPE &scalar)
	Substraction (in place) of an scalar. More...
void	SubIP (const Vector4< QUAT_TYPE > &argvec)
	in place substraction More...
Matrix< QUAT_TYPE >	transposed () const
	return a new Matrix with 1 row and 4 columns representing a transposed vector More...
	~Quaternion ()
Iterator Functions
QUAT_TYPEconst *	begin () const
	Iterator to first component of vector. More...
QUAT_TYPE *	begin ()
QUAT_TYPEconst *	end () const
	Iterator pointing to one element after the last vector element. More...
QUAT_TYPE *	end ()

Static Public Member Functions
static void	EnforceRigidCouplingConstraint (std::vector< Quaternion< QUAT_TYPE > > &quats, bool useFirstAngle=false)
	Enforce rigid coupling constraint for all quaternions in given vector. More...

Protected Attributes
QUAT_TYPE	data_ [VECTOR4SIZE]

Related Functions
(Note that these are not member functions.)
template<class T >
Quaternion< T >	operator* (const Quaternion< T > &l, const Quaternion< T > &r)
template<class T >
Quaternion< T > &	operator*= (Quaternion< T > &l, const Quaternion< T > &r)
template<class T >
Quaternion< T >	operator/ (const Quaternion< T > &l, const Quaternion< T > &r)
template<class T >
Quaternion< T > &	operator/= (Quaternion< T > &l, const Quaternion< T > &r)

Detailed Description

template<class T>
class BIAS::Quaternion< T >

class for rotation with axis and angle

Test:

tested with TestRotationConversion.cpp

Quaternions can be used for rotation around an axis through the origin by spcecifing the normal direction vector of the axis and an angle.

The rotation for positive angles is clockwise, when looking in direction of the axis.

Contains qx=[0], qy=[1], qz=[2], qw=[3].

Not every quaternion describes a rotation. Only quaternions of the form:

qx = x * sin(phi/2) , which is the imaginary part i

qy = y * sin(phi/2) , which is the imaginary part j

qz = z * sin(phi/2) , which is the imaginary part k

qw = cos(phi/2), , which is the real part

where (x, y, z) is the normalized direction vector of the axis and phi is the angle of rtoation.

Some usefull quaternions: x y z w Description 0 0 0 1 Identity quaternion, no rotation 1 0 0 0 180' turn around X axis 0 1 0 0 180' turn around Y axis 0 0 1 0 180' turn around Z axis sqrt(0.5) 0 0 sqrt(0.5) 90' rotation around X axis 0 sqrt(0.5) 0 sqrt(0.5) 90' rotation around Y axis 0 0 sqrt(0.5) sqrt(0.5) 90' rotation around Z axis -sqrt(0.5) 0 0 sqrt(0.5) -90' rotation around X axis 0 -sqrt(0.5) 0 sqrt(0.5) -90' rotation around Y axis 0 0 -sqrt(0.5) sqrt(0.5) -90' rotation around Z axis

Author

grest 06/2003

Definition at line 32 of file DualQuaternionOperators.hh.

Member Typedef Documentation

typedef QUAT_TYPE BIAS::Vector4< QUAT_TYPE >::value_type

inherited

Definition at line 67 of file Vector4.hh.

Constructor & Destructor Documentation

template<class T>

BIAS::Quaternion< T >::~Quaternion

(

)

template<class T>

BIAS::Quaternion< T >::Quaternion

(

)

template<class T>

BIAS::Quaternion< T >::Quaternion

(

const Vector4< QUAT_TYPE > &

q

)

template<class QUAT_TYPE >

BIAS::Quaternion< QUAT_TYPE >::Quaternion ( const Quaternion< QUAT_TYPE > &  q )

inline

copy constructor

Author

Daniel Grest (06/2003)

Definition at line 28 of file Quaternion.hh.

template<class T>

BIAS::Quaternion< T >::Quaternion	(	QUAT_TYPE	i,
		QUAT_TYPE	j,
		QUAT_TYPE	k,
		QUAT_TYPE	r
	)

Member Function Documentation

void BIAS::Vector4< QUAT_TYPE >::Add ( const QUAT_TYPE &  scalar, Vector4< QUAT_TYPE > &  dest  ) const

inlineinherited

Addition with a scalar, storing results in destionation vector.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::Add ( const Vector4< QUAT_TYPE > &  argvec, Vector4< QUAT_TYPE > &  destvec  ) const

inlineinherited

adding of two vectors, storing the result in destvec

Author

Ingo Thomsen tested

void BIAS::Vector4< QUAT_TYPE >::AddIP ( const QUAT_TYPE &  scalar )

inlineinherited

Addition (in place) of an scalar.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::AddIP ( const Vector4< QUAT_TYPE > &  argvec )

inlineinherited

in place adding

Author

Ingo Thomsen tested

QUAT_TYPE const* BIAS::Vector4< QUAT_TYPE >::begin ( ) const

inlineinherited

Iterator to first component of vector.

Author

Stefan Reinhold

Definition at line 152 of file Vector4.hh.

QUAT_TYPE * BIAS::Vector4< QUAT_TYPE >::begin ( )

inlineinherited

Definition at line 155 of file Vector4.hh.

void BIAS::Vector4< QUAT_TYPE >::clear ( )

inlineinherited

void BIAS::Vector4< QUAT_TYPE >::Copy ( const QUAT_TYPE *  pv )

inlineinherited

copy the array of vectorsize beginning at *T to this->data_

Author

Jan Woetzel untested (02/28/2002)

double BIAS::Vector4< QUAT_TYPE >::Dist ( const Vector4< QUAT_TYPE > &  vec ) const

inlineinherited

Return the euclidean distance of 2 vectors.

Author

Birger Streckel

Date

08/2002

void BIAS::Vector4< QUAT_TYPE >::Divide ( const QUAT_TYPE &  scalar, Vector4< QUAT_TYPE > &  dest  ) const

inlineinherited

Division with a scalar, storing results in destionation vector.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::DivideIP ( const QUAT_TYPE &  scalar )

inlineinherited

Division (in place) of an scalar.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::ElementwiseProduct ( const Vector4< QUAT_TYPE > &  argvec, Vector4< QUAT_TYPE > &  destvec  ) const

inlineinherited

multiply two vectors elementwise, storing the result in destvec

Author

Jan Woetzel untested (03/06/2002)

QUAT_TYPE const* BIAS::Vector4< QUAT_TYPE >::end ( ) const

inlineinherited

Iterator pointing to one element after the last vector element.

Author

Stefan Reinhold

Definition at line 161 of file Vector4.hh.

QUAT_TYPE * BIAS::Vector4< QUAT_TYPE >::end ( )

inlineinherited

Definition at line 164 of file Vector4.hh.

template<class T>

void BIAS::Quaternion< T >::EnforceRigidCouplingConstraint	(	Quaternion< QUAT_TYPE > &	other,
		bool	useOtherAngle = false
	)

Enforce rigid coupling constraint for this and the other given unit quaternion (equal rotation angle/equal scalar part for both).

Computes direct simple interpolation of both unit quaternion where the scalar parts of the resulting unit quaternion are identical. This solution can be used as initial guess for numerical refinement.

Parameters

	in/out]	other Quaternion to enforce rigid coupling constraint with
[in]	useOtherAngle	Use rotation angle (= scalar part) of other quaternion instead of interpolating both

Author

esquivel 02/2012

template<class T>

static void BIAS::Quaternion< T >::EnforceRigidCouplingConstraint ( std::vector< Quaternion< QUAT_TYPE > > &  quats, bool  useFirstAngle = false  )

static

Enforce rigid coupling constraint for all quaternions in given vector.

Parameters

	in/out]	quats Quaternions to enforce rigid coupling constraint for
[in]	useFirstAngle	Use rotation angle (= scalar part) of first quaternion instead of interpolating all

Author

esquivel 02/2012

template<class T>

int BIAS::Quaternion< T >::GetAxisAngle	(	Vector3< QUAT_TYPE > &	axis,
		QUAT_TYPE &	angle
	)		const

Returns rotation in axis and angle notation (angle in radians).

Note that the returned angle resides in the interval [0,PI) and the axis points into the according direction!

Author

woelk 12 2002

Referenced by BIAS::RMatrixBase::GetRotationAxisAngle(), BIAS::PMDImageProc::MetaFromPoseAndK(), BIAS::operator<<(), and BIAS::CovQuaternion2AxisAngle::Transform_().

const QUAT_TYPE * BIAS::Vector4< QUAT_TYPE >::GetData ( ) const

inlineinherited

get the data pointer

the member function itself is const (before {..}) because it doesn't change the this object.

Returns

the const pointer to the data array for reading

Author

Jan Woetzel untested (02/28/2002)

Definition at line 177 of file Vector4.hh.

QUAT_TYPE * BIAS::Vector4< QUAT_TYPE >::GetData ( )

inlineinherited

Definition at line 181 of file Vector4.hh.

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::GetEquatorialPoint3D ( Vector3< QUAT_TYPE > &  p3D ) const

inline

Compute minimal parametrization of unit quaternion by projecting it from the 4d hypersphere onto the 3d equatorial space, as described in: [TCBS+12] Terzakis et al.

: A Recipe on the Parameterization of Rotation Matrices for Non-Linear Optimization using Quaternions, 2012.

Parameters

[out]

p3D

Returns 3d point representation of unit quaternion

Author

esquivel 07/2013

Definition at line 212 of file Quaternion.hh.

const unsigned int BIAS::Vector4< QUAT_TYPE >::GetNumElements ( ) const

inlineinherited

Definition at line 145 of file Vector4.hh.

template<class T>

Matrix4x4<QUAT_TYPE> BIAS::Quaternion< T >::GetQuaternionMultMatrixLeft

(

)

const

Returns matrix which expresses (left) quaternion multiplication.

A quaternions stored in an object can be understood as a 4-vector q =(ix iy iz r)^T. Left multiplying a quaternion q2 with a quaternion q1 can be expressed in terms of matrix multiplication as qRes = q1*q2 = M(q1)*q2. This method returns the matrix M(*this).

Referenced by BIAS::PoseParametrizationCovariance::Transform().

template<class T>

Matrix4x4<QUAT_TYPE> BIAS::Quaternion< T >::GetQuaternionMultMatrixRight

(

)

const

Returns matrix which expresses right quaternion multiplication.

Right multiplying a quaternion q1 with quaternion q2 can be expressed as qRes = q1*q2 = N(q2)*q1. This method returns the matrix N(*this).

template<class T>

QUAT_TYPE BIAS::Quaternion< T >::GetRotationAngle

(

)

const

Returns rotation angle notation in radians.

Note that the returned angle resides in the interval [0,PI)!

Referenced by BIAS::EMatrix::GetRotationTranslation().

template<class T>

Vector3<QUAT_TYPE> BIAS::Quaternion< T >::GetRotationAxis

(

)

const

Returns rotation axis.

See GetRotationAxisAngle().

Referenced by BIAS::EMatrix::GetRotationTranslation().

template<class T>

int BIAS::Quaternion< T >::GetRotationMatrix

(

RMatrixBase &

R

)

const

Returns a corresponding (quaternion) rotation matrix.

Deprecated:

Transpose problem! This function is going to be removed! Use RMatrixBase::SetFromQuaternion() instead!

Author

grest

template<class T>

Quaternion<QUAT_TYPE> BIAS::Quaternion< T >::Interpolate	(	const Quaternion< QUAT_TYPE > &	to,
		const QUAT_TYPE &	t
	)		const

Spherical interpolation between this and given quaternion.

Note

Quaternions are assumed to be unit quaternions!

Referenced by BIAS::DualQuaternion< QUAT_TYPE >::Interpolate().

template<class T>

Quaternion<QUAT_TYPE> BIAS::Quaternion< T >::InterpolateLinear	(	const Quaternion< QUAT_TYPE > &	to,
		const QUAT_TYPE &	t
	)		const

Linear interpolation between this and given quaternion.

Note

Quaternions are assumed to be unit quaternions!

Referenced by BIAS::DualQuaternion< QUAT_TYPE >::InterpolateLinear().

template<class QUAT_TYPE >

Quaternion< QUAT_TYPE > BIAS::Quaternion< QUAT_TYPE >::Inverse ( ) const

inline

returns the Inverse rotation Quaternion

Definition at line 42 of file Quaternion.hh.

Referenced by BIAS::Quaternion< T >::operator/(), and BIAS::Quaternion< T >::operator/=().

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::Invert ( )

inline

inverts this, by changing the rotation axis by *=-1

Definition at line 34 of file Quaternion.hh.

Referenced by BIAS::Quaternion< QUAT_TYPE >::Inverse(), and BIAS::EParametrization::Invert().

bool BIAS::Vector4< QUAT_TYPE >::Load ( const std::string &  filename )

inherited

method to load directly from a given filename.

internally using stream operator

Author

Jan Woetzel 09/2005

Returns

false in case of error, true in case of success

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::MakeUnique ( )

inline

makes Quaternion-representation uniqe, ensuring vector lies in upper (by real part) hemisphere.

(inplace)

Definition at line 50 of file Quaternion.hh.

Referenced by BIAS::Quaternion< QUAT_TYPE >::EnforceRigidCouplingConstraint().

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::Mult ( const Quaternion< QUAT_TYPE > &  quat )

inline

quaternion multiplication: this= this * quat

Definition at line 73 of file Quaternion.hh.

References BIAS::Quaternion.

Referenced by BIAS::DualQuaternion< QUAT_TYPE >::GetRigidMotion(), BIAS::Quaternion< QUAT_TYPE >::Mult(), BIAS::Quaternion< T >::operator*(), BIAS::Quaternion< T >::operator*=(), BIAS::Quaternion< T >::operator/(), BIAS::Quaternion< T >::operator/=(), BIAS::Quaternion< QUAT_TYPE >::SetXYZ(), and BIAS::Quaternion< QUAT_TYPE >::SetZYX().

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::Mult ( const Quaternion< QUAT_TYPE > &  arg, Quaternion< QUAT_TYPE > &  res  ) const

inline

quaternion multiplication: res = this * arg

Definition at line 98 of file Quaternion.hh.

void BIAS::Vector4< QUAT_TYPE >::Multiply ( const QUAT_TYPE &  scalar, Vector4< QUAT_TYPE > &  dest  ) const

inlineinherited

Multiplication with a scalar, storing results in destionation vector.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::MultiplyIP ( const QUAT_TYPE &  scalar )

inlineinherited

Multiplication (in place) of an scalar.

Author

Ingo Thomsen

Referenced by BIAS::RMatrixBase::GetQuaternion().

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::MultLeft ( const Quaternion< QUAT_TYPE > &  quat )

inline

quaternion multiplication: this = quat * this

Definition at line 106 of file Quaternion.hh.

template<class QUAT_TYPE >

int BIAS::Quaternion< QUAT_TYPE >::MultVec ( const Vector3< QUAT_TYPE > &  vec, Vector3< QUAT_TYPE > &  res  ) const

inline

rotates the given Vector qith the quaternion ( q v q* ) the resulting vector is given in res

rotates the given Vector with the quaternion ( q v q* ) the resulting vector is given in res

Returns

0 in case of no error

Author

Daniel Grest, June 2003

Definition at line 136 of file Quaternion.hh.

Referenced by BIAS::CoordinateTransform3D::ConcatenateLocalTransform(), BIAS::ProjectionParametersSphericalFast::GetPerspectiveCutOutParameters(), BIAS::ProjectionParametersSpherical::GetPerspectiveCutOutParameters(), BIAS::EParametrization::Invert(), BIAS::FlyControl::LeftMouseMoved(), BIAS::TrackballControl::RotateAroundPOI(), BIAS::FlyControl::RotateAroundViewingDirection(), BIAS::TrackballControl::RotateAroundViewingDirection(), BIAS::ProjectionParametersSpherical::TransfCoordRotateSphere2Image_(), BIAS::CovTransformPose::Transform_(), BIAS::Triangulation::Triangulate(), and BIAS::ProjectionParametersCylindric::ViewDifference().

template<class QUAT_TYPE >

Vector3< QUAT_TYPE > BIAS::Quaternion< QUAT_TYPE >::MultVec ( const Vector3< QUAT_TYPE > &  vec ) const

inline

Definition at line 161 of file Quaternion.hh.

template<class T>

void BIAS::Quaternion< T >::Normalize ( )

inline

Scales quaternion to unit length, i.e.

norm equals 1.

Definition at line 236 of file Quaternion.hh.

Referenced by BIAS::RotationAveraging::ChordalL2Mean(), BIAS::Quaternion< QUAT_TYPE >::Interpolate(), BIAS::Quaternion< QUAT_TYPE >::InterpolateLinear(), BIAS::RotationAveraging::QuaternionL2Mean(), and BIAS::RMatrixBase::SetFromQuaternion().

QUAT_TYPE BIAS::Vector4< QUAT_TYPE >::NormL1 ( ) const

inlineinherited

Return the L1 norm: |a| + |b| + |c|+ |d|.

Author

Ingo Thomsen

Date

04/11/2002 untested

double BIAS::Vector4< QUAT_TYPE >::NormL2 ( ) const

inlineinherited

Return the L2 norm: sqrt(a^2 + b^2 + c^2 + d^2)

Author

Ingo Thomsen

Date

04/11/2002 untested

Referenced by BIAS::RMatrixBase::GetQuaternion(), and BIAS::RMatrixBase::SetFromQuaternion().

bool BIAS::Vector4< QUAT_TYPE >::operator!= ( const Vector4< QUAT_TYPE > &  arg ) const

inlineinherited

Comparison operator 'not equal'.

Author

Ingo Thomsen

Vector4<QUAT_TYPE >& BIAS::Vector4< QUAT_TYPE >::operator*= ( const QUAT_TYPE &  scalar )

inlineinherited

Multiplication operator with scalar argument.

Author

Ingo Thomsen tested

Vector4<QUAT_TYPE >& BIAS::Vector4< QUAT_TYPE >::operator+= ( const QUAT_TYPE &  scalar )

inlineinherited

Addition operator with scalar argument.

Author

Ingo Thomsen tested

Vector4<QUAT_TYPE >& BIAS::Vector4< QUAT_TYPE >::operator+= ( const Vector4< QUAT_TYPE > &  argvec )

inlineinherited

add operator for two Vectors

Author

Ingo Thomsen tested

Vector4<QUAT_TYPE >& BIAS::Vector4< QUAT_TYPE >::operator-= ( const QUAT_TYPE &  scalar )

inlineinherited

Substraction operator with scalar argument.

Author

Ingo Thomsen tested

Vector4<QUAT_TYPE >& BIAS::Vector4< QUAT_TYPE >::operator-= ( const Vector4< QUAT_TYPE > &  argvec )

inlineinherited

sub operator for two Vectors

Author

Ingo Thomsen tested

Vector4<QUAT_TYPE >& BIAS::Vector4< QUAT_TYPE >::operator/= ( const QUAT_TYPE &  scalar )

inlineinherited

Division operator with scalar argument.

Author

Ingo Thomsen tested

template<class T>

Quaternion<QUAT_TYPE>& BIAS::Quaternion< T >::operator=

(

const Quaternion< QUAT_TYPE > &

vec

)

assignment operator

Author

grest 06 2003

bool BIAS::Vector4< QUAT_TYPE >::operator== ( const Vector4< QUAT_TYPE > &  arg ) const

inlineinherited

Comparison operator 'equal'.

Author

Ingo Thomsen tested

const QUAT_TYPE & BIAS::Vector4< QUAT_TYPE >::operator[] ( const int  i ) const

inlineinherited

access an element of the vector with 0-based indizes.

read only (no write) member funciton const because it doesn't change this object

Author

Jan Woetzel alpha (03/01/2002)

QUAT_TYPE & BIAS::Vector4< QUAT_TYPE >::operator[] ( const int  i )

inlineinherited

access an element of the vector with 0-based indizes.

write allowed

Author

Jan Woetzel alpha (03/01/2002)

Matrix4x4<QUAT_TYPE > BIAS::Vector4< QUAT_TYPE >::OuterProduct ( const Vector4< QUAT_TYPE > &  v ) const

inherited

outer product, constructs a matrix.

Often written as v * v^T for col vectors

Author

frick

template<class T>

Quaternion<QUAT_TYPE> BIAS::Quaternion< T >::Power

(

const QUAT_TYPE &

scale

)

const

Computes this^(scale), which scales the angle from axis/angle- representation with 'scale'.

This is the same like inter-/extra- polating between (0,0,0,1)-quaternion and this!

bool BIAS::Vector4< QUAT_TYPE >::Save ( const std::string &  filename ) const

inherited

method to save directly to a given filename.

internally using stream operator

Author

Jan Woetzel 09/2009

Returns

false in case of error, true in case of success

void BIAS::Vector4< QUAT_TYPE >::ScalarProduct ( const Vector4< QUAT_TYPE > &  argvec, QUAT_TYPE &  result  ) const

inlineinherited

scalar product (=inner product) of two vectors, storing

the result in result

Author

Jan Woetzel untested

Examples:

ExampleQuaternion.cpp.

QUAT_TYPE BIAS::Vector4< QUAT_TYPE >::ScalarProduct ( const Vector4< QUAT_TYPE > &  argvec ) const

inlineinherited

void BIAS::Vector4< QUAT_TYPE >::Set ( const QUAT_TYPE &  scalar )

inlineinherited

set all elements to a scalat value

Author

Jan Woetzel untested (02/28/2002)

void BIAS::Vector4< QUAT_TYPE >::Set ( const QUAT_TYPE &  x, const QUAT_TYPE &  y, const QUAT_TYPE &  z, const QUAT_TYPE &  w  )

inlineinherited

set elementwise with given scalr values

Author

Jan Woetzel, Ingo Thomsen tested (02/28/2002)

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::SetFromEquatorialPoint3D ( const Vector3< QUAT_TYPE > &  p3D )

inline

Set unit quaternion from 3d point in equatorial space by back- projecting it onto the 4d hypersphere, as described in [TCBS+12].

Parameters

[in]

p3D

Constaint 3d point representation of unit quaternion

See Also

GetEquatorialPoint3D

Author

esquivel 07/2013

Definition at line 223 of file Quaternion.hh.

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::SetIdentity ( )

inline

Definition at line 168 of file Quaternion.hh.

Referenced by BIAS::Quaternion< QUAT_TYPE >::Power().

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::SetQuaternion ( QUAT_TYPE  real, QUAT_TYPE  i, QUAT_TYPE  j, QUAT_TYPE  k  )

inline

Sets all parts of quaternion in mathematical order, real part first, then 1.,2.

and 3. imaginary part

Definition at line 175 of file Quaternion.hh.

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::SetValueAsAxisRad ( const Vector3< QUAT_TYPE > &  axis, QUAT_TYPE  angle  )

inline

sets the quaternion with given rotation axis and angle (in rad)

Returns

0 in case of no error

Author

Daniel Grest, June 2003

Definition at line 183 of file Quaternion.hh.

Referenced by BIAS::ProjectionParametersSphericalFast::GetPerspectiveCutOutParameters(), BIAS::ProjectionParametersSpherical::GetPerspectiveCutOutParameters(), BIAS::FlyControl::LeftMouseMoved(), BIAS::TrackballControl::RotateAroundPOI(), BIAS::FlyControl::RotateAroundViewingDirection(), BIAS::TrackballControl::RotateAroundViewingDirection(), BIAS::ProjectionParametersCylindric::SetCylinderRotation(), BIAS::Quaternion< QUAT_TYPE >::SetXYZ(), BIAS::Quaternion< QUAT_TYPE >::SetZYX(), and BIAS::ProjectionParametersSpherical::TransfCoordRotateSphere2Image_().

template<class QUAT_TYPE >

void BIAS::Quaternion< QUAT_TYPE >::SetValueAsAxisRad ( QUAT_TYPE  axisX, QUAT_TYPE  axisY, QUAT_TYPE  axisZ, QUAT_TYPE  angle  )

inline

sets the quaternion with given rotation axis and angle (in rad)

Returns

0 in case of no error

Author

Daniel Grest, June 2003

Definition at line 190 of file Quaternion.hh.

template<class T>

int BIAS::Quaternion< T >::SetXYZ	(	QUAT_TYPE	radX,
		QUAT_TYPE	radY,
		QUAT_TYPE	radZ
	)

Sets quaternion as concatenated rotations around x,y,z-axis; this = q_x * q_y * q_z (BIAS-RMatrix conform)

Author

herzog 2005-07-19

void BIAS::Vector4< QUAT_TYPE >::SetZero ( )

inlineinherited

set all values to 0

Author

Jan Woetzel

template<class T>

int BIAS::Quaternion< T >::SetZYX	(	QUAT_TYPE	radX,
		QUAT_TYPE	radY,
		QUAT_TYPE	radZ
	)

Sets quaternion as concatenated rotations around x,y,z-axis; this = q_z * q_y * q_x (BIAS-RMatrix conform)

Author

herzog 2005-07-19

Referenced by BIAS::CovTransformPose::Transform_().

const unsigned int BIAS::Vector4< QUAT_TYPE >::Size ( ) const

inlineinherited

@return the size of this vector

Author

Jan Woetzel (02/28/2002)

const unsigned int BIAS::Vector4< QUAT_TYPE >::size ( ) const

inlineinherited

void BIAS::Vector4< QUAT_TYPE >::Sub ( const QUAT_TYPE &  scalar, Vector4< QUAT_TYPE > &  dest  ) const

inlineinherited

Substraction with a scalar, storing results in destionation vector.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::Sub ( const Vector4< QUAT_TYPE > &  argvec, Vector4< QUAT_TYPE > &  destvec  ) const

inlineinherited

subtracting of two Vectors, storing the result in destvec

Author

Ingo Thomsen tested

void BIAS::Vector4< QUAT_TYPE >::SubIP ( const QUAT_TYPE &  scalar )

inlineinherited

Substraction (in place) of an scalar.

Author

Ingo Thomsen

void BIAS::Vector4< QUAT_TYPE >::SubIP ( const Vector4< QUAT_TYPE > &  argvec )

inlineinherited

in place substraction

Author

Ingo Thomsen tested

Matrix<QUAT_TYPE > BIAS::Vector4< QUAT_TYPE >::transposed ( ) const

inlineinherited

return a new Matrix with 1 row and 4 columns representing a

transposed vector

Friends And Related Function Documentation

template<class T >

Quaternion< T > operator* ( const Quaternion< T > &  l, const Quaternion< T > &  r  )

related

what it stands for (wraps Mult())

Author

herzog 2005-07-15

Definition at line 42 of file QuaternionOperators.hh.

References BIAS::Quaternion< T >::Mult().

template<class T >

Quaternion< T > & operator*= ( Quaternion< T > &  l, const Quaternion< T > &  r  )

related

what it stands for (wraps Mult())

Author

herzog 2005-07-15

Definition at line 54 of file QuaternionOperators.hh.

References BIAS::Quaternion< T >::Mult().

template<class T >

Quaternion< T > operator/ ( const Quaternion< T > &  l, const Quaternion< T > &  r  )

related

what it stands for (wraps Mult() and Inverse())

Author

herzog 2005-07-15

Definition at line 65 of file QuaternionOperators.hh.

References BIAS::Quaternion< T >::Inverse(), and BIAS::Quaternion< T >::Mult().

template<class T >

Quaternion< T > & operator/= ( Quaternion< T > &  l, const Quaternion< T > &  r  )

related

what it stands for (wraps Mult() and Inverse())

Author

herzog 2005-07-15

Definition at line 77 of file QuaternionOperators.hh.

References BIAS::Quaternion< T >::Inverse(), and BIAS::Quaternion< T >::Mult().

Member Data Documentation

QUAT_TYPE BIAS::Vector4< QUAT_TYPE >::data_[VECTOR4SIZE]

protectedinherited

Definition at line 375 of file Vector4.hh.

---

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

• Base/Geometry/DualQuaternionOperators.hh
• Base/Geometry/Quaternion.hh
• Base/Geometry/QuaternionInl.hh
• Base/Geometry/QuaternionOperators.hh