Map< Quaternion< _Scalar >, _Options > Class Template Reference

Expression of a quaternion from a memory buffer. More...

#include <Quaternion.h>

Inheritance diagram for Map< Quaternion< _Scalar >, _Options >:

Public Types
typedef AngleAxis< Scalar >	AngleAxisType

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, 3, 1 >	Vector3

Public Member Functions
Vector3	_transformVector (Vector3 v) const

Vector3	_transformVector (Vector3 v) const

internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

internal::cast_return_type< Map< Quaternion< _Scalar >, _Options >, Quaternion< NewScalarType > >::type	cast () const

internal::cast_return_type< Map< Quaternion< _Scalar >, _Options >, Quaternion< NewScalarType > >::type	cast () const

Quaternion< Scalar >	conjugate () const

Quaternion< Scalar >	conjugate () const

Scalar	dot (const QuaternionBase< OtherDerived > &other) const

Scalar	dot (const QuaternionBase< OtherDerived > &other) const

Quaternion< Scalar >	inverse () const

Quaternion< Scalar >	inverse () const

bool	isApprox (const QuaternionBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const

bool	isApprox (const QuaternionBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const

	Map (PointerArgType data, const StrideType &stride=StrideType())

	Map (PointerArgType data, Index rows, Index cols, const StrideType &stride=StrideType())

	Map (PointerArgType data, Index size, const StrideType &stride=StrideType())

	Map (Scalar *coeffs)

RotationMatrixType	matrix () const

Scalar	norm () const

Scalar	norm () const

void	normalize ()

void	normalize ()

Quaternion< Scalar >	normalized () const

Quaternion< Scalar >	normalized () const

internal::rotation_base_generic_product_selector< Map< Quaternion< _Scalar >, _Options >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar >	operator* (const QuaternionBase< OtherDerived > &other) const

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar >	operator* (const QuaternionBase< OtherDerived > &other) const

Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const

Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const

RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const

Map< Quaternion< _Scalar >, _Options > &	operator*= (const QuaternionBase< OtherDerived > &q)

Map< Quaternion< _Scalar >, _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

Map< Quaternion< _Scalar >, _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

QuaternionBase &	setIdentity ()

QuaternionBase &	setIdentity ()

Quaternion< Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const

Quaternion< Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const

Scalar	squaredNorm () const

Scalar	squaredNorm () const

Matrix3	toRotationMatrix () const

Matrix3	toRotationMatrix () const

VectorBlock< Coefficients, 3 >	vec ()

VectorBlock< Coefficients, 3 >	vec ()

const VectorBlock< const Coefficients, 3 >	vec () const

const VectorBlock< const Coefficients, 3 >	vec () const

Scalar &	w ()

Scalar &	w ()

Scalar	w () const

Scalar	w () const

Scalar &	x ()

Scalar &	x ()

Scalar	x () const

Scalar	x () const

Scalar &	y ()

Scalar &	y ()

Scalar	y () const

Scalar	y () const

Scalar &	z ()

Scalar &	z ()

Scalar	z () const

Scalar	z () const

Static Public Member Functions
static Quaternion< Scalar >	Identity ()

static Quaternion< Scalar >	Identity ()

Detailed Description

template<typename _Scalar, int _Options>
class Eigen::Map< Quaternion< _Scalar >, _Options >

Expression of a quaternion from a memory buffer.

Template Parameters

_Scalar	the type of the Quaternion coefficients
_Options	see class Map

This is a specialization of class Map for Quaternion. This class allows to view a 4 scalar memory buffer as an Eigen's Quaternion object.

See also: class Map, class Quaternion, class QuaternionBase

Member Typedef Documentation

◆ AngleAxisType

typedef AngleAxis<Scalar> AngleAxisType

inherited

the equivalent angle-axis type

◆ Matrix3

typedef Matrix<Scalar,3,3> Matrix3

inherited

the equivalent rotation matrix type

◆ RotationMatrixType

template<typename Derived, int _Dim>

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

◆ Vector3

typedef Matrix<Scalar,3,1> Vector3

inherited

the type of a 3D vector

Constructor & Destructor Documentation

◆ Map() [1/4]

template<typename _Scalar, int _Options>

Map ( Scalar * coeffs )

inline

Constructs a Mapped Quaternion object from the pointer coeffs

The pointer coeffs must reference the four coeffecients of Quaternion in the following order:

*coeffs == {x, y, z, w}

Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::w

Scalar w() const

Definition Quaternion.h:66

Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::z

Scalar z() const

Definition Quaternion.h:64

Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::x

Scalar x() const

Definition Quaternion.h:60

Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::y

Scalar y() const

Definition Quaternion.h:62

If the template parameter _Options is set to Aligned, then the pointer coeffs must be aligned.

◆ Map() [2/4]

Map	(	PointerArgType	data,
		const StrideType &	stride = StrideType() )

inline

Constructor in the fixed-size case.

Parameters

data	pointer to the array to map
stride	optional Stride object, passing the strides.

◆ Map() [3/4]

Map	(	PointerArgType	data,
		Index	size,
		const StrideType &	stride = StrideType() )

inline

Constructor in the dynamic-size vector case.

Parameters

data	pointer to the array to map
size	the size of the vector expression
stride	optional Stride object, passing the strides.

◆ Map() [4/4]

Map	(	PointerArgType	data,
		Index	rows,
		Index	cols,
		const StrideType &	stride = StrideType() )

inline

Constructor in the dynamic-size matrix case.

Parameters

data	pointer to the array to map
rows	the number of rows of the matrix expression
cols	the number of columns of the matrix expression
stride	optional Stride object, passing the strides.

Member Function Documentation

◆ _transformVector() [1/2]

Vector3 _transformVector ( Vector3 v ) const

inlineinherited

return the result vector of v through the rotation

Rotation of a vector by a quaternion.

Remarks

If the quaternion is used to rotate several points (>1) then it is much more efficient to first convert it to a 3x3 Matrix. Comparison of the operation cost for n transformations:

Quaternion2: 30n
Via a Matrix3: 24 + 15n

◆ _transformVector() [2/2]

QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::Vector3 _transformVector ( Vector3 v ) const

inlineinherited

return the result vector of v through the rotation

Rotation of a vector by a quaternion.

Remarks

If the quaternion is used to rotate several points (>1) then it is much more efficient to first convert it to a 3x3 Matrix. Comparison of the operation cost for n transformations:

Quaternion2: 30n
Via a Matrix3: 24 + 15n

◆ angularDistance() [1/2]

internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar angularDistance ( const QuaternionBase< OtherDerived > & other ) const

inlineinherited

Returns: the angle (in radian) between two rotations

See also: dot()

◆ angularDistance() [2/2]

internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar angularDistance ( const QuaternionBase< OtherDerived > & other ) const

inlineinherited

Returns: the angle (in radian) between two rotations

See also: dot()

◆ cast() [1/2]

internal::cast_return_type< Map< Quaternion< _Scalar >, _Options >, Quaternion< NewScalarType > >::type cast ( ) const

inlineinherited

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

◆ cast() [2/2]

internal::cast_return_type< Map< Quaternion< _Scalar >, _Options >, Quaternion< NewScalarType > >::type cast ( ) const

inlineinherited

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

◆ conjugate() [1/2]

Quaternion< Scalar > conjugate ( ) const

inherited

Returns: the conjugated quaternion; the conjugate of the *this which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.

See also: Quaternion2::inverse()

◆ conjugate() [2/2]

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar > conjugate ( ) const

inlineinherited

Returns: the conjugated quaternion; the conjugate of the *this which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.

See also: Quaternion2::inverse()

◆ dot() [1/2]

Scalar dot ( const QuaternionBase< OtherDerived > & other ) const

inlineinherited

Returns: the dot product of *this and other Geometrically speaking, the dot product of two unit quaternions corresponds to the cosine of half the angle between the two rotations.

See also: angularDistance()

◆ dot() [2/2]

Scalar dot ( const QuaternionBase< OtherDerived > & other ) const

inlineinherited

Returns: the dot product of *this and other Geometrically speaking, the dot product of two unit quaternions corresponds to the cosine of half the angle between the two rotations.

See also: angularDistance()

◆ Identity() [1/2]

static Quaternion< Scalar > Identity ( )

inlinestaticinherited

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

◆ Identity() [2/2]

static Quaternion< Scalar > Identity ( )

inlinestaticinherited

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

◆ inverse() [1/2]

Quaternion< Scalar > inverse ( ) const

inherited

Returns: the quaternion describing the inverse rotation; the multiplicative inverse of *this Note that in most cases, i.e., if you simply want the opposite rotation, and/or the quaternion is normalized, then it is enough to use the conjugate.

See also: QuaternionBase::conjugate()

◆ inverse() [2/2]

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar > inverse ( ) const

inlineinherited

Returns: the quaternion describing the inverse rotation; the multiplicative inverse of *this Note that in most cases, i.e., if you simply want the opposite rotation, and/or the quaternion is normalized, then it is enough to use the conjugate.

See also: QuaternionBase::conjugate()

◆ isApprox() [1/2]

bool isApprox	(	const QuaternionBase< OtherDerived > &	other,
		RealScalar	prec = NumTraits<Scalar>::dummy_precision() ) const

inlineinherited

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

◆ isApprox() [2/2]

bool isApprox	(	const QuaternionBase< OtherDerived > &	other,
		RealScalar	prec = NumTraits<Scalar>::dummy_precision() ) const

inlineinherited

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

◆ matrix()

template<typename Derived, int _Dim>

RotationMatrixType matrix ( ) const

inlineinherited

Returns: an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

◆ norm() [1/2]

Scalar norm ( ) const

inlineinherited

Returns: the norm of the quaternion's coefficients

See also: QuaternionBase::squaredNorm(), MatrixBase::norm()

◆ norm() [2/2]

Scalar norm ( ) const

inlineinherited

Returns: the norm of the quaternion's coefficients

See also: QuaternionBase::squaredNorm(), MatrixBase::norm()

◆ normalize() [1/2]

void normalize ( )

inlineinherited

Normalizes the quaternion *this

See also: normalized(), MatrixBase::normalize()

◆ normalize() [2/2]

void normalize ( )

inlineinherited

Normalizes the quaternion *this

See also: normalized(), MatrixBase::normalize()

◆ normalized() [1/2]

Quaternion< Scalar > normalized ( ) const

inlineinherited

Returns: a normalized copy of *this

See also: normalize(), MatrixBase::normalized()

◆ normalized() [2/2]

Quaternion< Scalar > normalized ( ) const

inlineinherited

Returns: a normalized copy of *this

See also: normalize(), MatrixBase::normalized()

◆ operator*() [1/10]

( const EigenBase< OtherDerived > & e ) const

inherited

Returns

the concatenation of the rotation *this with a generic expression e e can be:

a DimxDim linear transformation matrix
a DimxDim diagonal matrix (axis aligned scaling)
a vector of size Dim

◆ operator*() [2/10]

internal::rotation_base_generic_product_selector< Map< Quaternion< _Scalar >, _Options >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType operator* ( const EigenBase< OtherDerived > & e ) const

inlineinherited

Returns

the concatenation of the rotation *this with a generic expression e e can be:

a DimxDim linear transformation matrix
a DimxDim diagonal matrix (axis aligned scaling)
a vector of size Dim

◆ operator*() [3/10]

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar > operator* ( const QuaternionBase< OtherDerived > & other ) const

inlineinherited

Returns: the concatenation of two rotations as a quaternion-quaternion product

◆ operator*() [4/10]

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar > operator* ( const QuaternionBase< OtherDerived > & other ) const

inlineinherited

Returns: the concatenation of two rotations as a quaternion-quaternion product

◆ operator*() [5/10]

( const Transform< Scalar, Dim, Mode, Options > & t ) const

inherited

Returns: the concatenation of the rotation *this with a transformation t

◆ operator*() [6/10]

Transform< Scalar, Dim, Mode > operator* ( const Transform< Scalar, Dim, Mode, Options > & t ) const

inlineinherited

Returns: the concatenation of the rotation *this with a transformation t

◆ operator*() [7/10]

( const Translation< Scalar, Dim > & t ) const

inherited

Returns: the concatenation of the rotation *this with a translation t

◆ operator*() [8/10]

Transform< Scalar, Dim, Isometry > operator* ( const Translation< Scalar, Dim > & t ) const

inlineinherited

Returns: the concatenation of the rotation *this with a translation t

◆ operator*() [9/10]

( const UniformScaling< Scalar > & s ) const

inherited

Returns: the concatenation of the rotation *this with a uniform scaling s

◆ operator*() [10/10]

RotationMatrixType operator* ( const UniformScaling< Scalar > & s ) const

inlineinherited

Returns: the concatenation of the rotation *this with a uniform scaling s

◆ operator*=()

template<typename _Scalar, int _Options>

Map< Quaternion< _Scalar >, _Options > & operator*= ( const QuaternionBase< OtherDerived > & q )

inline

See also: operator*(Quaternion)

◆ setFromTwoVectors() [1/2]

Map< Quaternion< _Scalar >, _Options > & setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b )

inherited

Returns: the quaternion which transform a into b through a rotation

Sets *this to be a quaternion representing a rotation between the two arbitrary vectors a and b. In other words, the built rotation represent a rotation sending the line of direction a to the line of direction b, both lines passing through the origin.

Returns: a reference to *this.

Note that the two input vectors do not have to be normalized, and do not need to have the same norm.

◆ setFromTwoVectors() [2/2]

Map< Quaternion< _Scalar >, _Options > & setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b )

inlineinherited

Returns: the quaternion which transform a into b through a rotation

Returns: a reference to *this.

Note that the two input vectors do not have to be normalized, and do not need to have the same norm.

◆ setIdentity() [1/2]

QuaternionBase & setIdentity ( )

inlineinherited

See also: QuaternionBase::Identity(), MatrixBase::setIdentity()

◆ setIdentity() [2/2]

QuaternionBase & setIdentity ( )

inlineinherited

See also: QuaternionBase::Identity(), MatrixBase::setIdentity()

◆ slerp() [1/4]

Quaternion< Scalar > slerp	(	Scalar	t,
		const QuaternionBase< OtherDerived > &	other ) const

inherited

Returns: an interpolation for a constant motion between other and *this t in [0;1] see http://en.wikipedia.org/wiki/Slerp

◆ slerp() [2/4]

Quaternion< Scalar > slerp	(	Scalar	t,
		const QuaternionBase< OtherDerived > &	other ) const

inherited

Returns: an interpolation for a constant motion between other and *this t in [0;1] see http://en.wikipedia.org/wiki/Slerp

◆ slerp() [3/4]

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar > slerp	(	Scalar	t,
		const QuaternionBase< OtherDerived > &	other ) const

inherited

Returns: the spherical linear interpolation between the two quaternions *this and other at the parameter t

◆ slerp() [4/4]

Quaternion< typename internal::traits< Map< Quaternion< _Scalar >, _Options > >::Scalar > slerp	(	Scalar	t,
		const QuaternionBase< OtherDerived > &	other ) const

inherited

Returns: the spherical linear interpolation between the two quaternions *this and other at the parameter t

◆ squaredNorm() [1/2]

Scalar squaredNorm ( ) const

inlineinherited

Returns: the squared norm of the quaternion's coefficients

See also: QuaternionBase::norm(), MatrixBase::squaredNorm()

◆ squaredNorm() [2/2]

Scalar squaredNorm ( ) const

inlineinherited

Returns: the squared norm of the quaternion's coefficients

See also: QuaternionBase::norm(), MatrixBase::squaredNorm()

◆ toRotationMatrix() [1/2]

Matrix3 toRotationMatrix ( void ) const

inherited

Returns: an equivalent 3x3 rotation matrix

Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to be normalized, otherwise the result is undefined.

◆ toRotationMatrix() [2/2]

QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::Matrix3 toRotationMatrix ( void ) const

inlineinherited

Returns: an equivalent 3x3 rotation matrix

Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to be normalized, otherwise the result is undefined.

◆ vec() [1/4]

VectorBlock< Coefficients, 3 > vec ( )

inlineinherited

Returns: a vector expression of the imaginary part (x,y,z)

◆ vec() [2/4]

VectorBlock< Coefficients, 3 > vec ( )

inlineinherited

Returns: a vector expression of the imaginary part (x,y,z)

◆ vec() [3/4]

const VectorBlock< const Coefficients, 3 > vec ( ) const

inlineinherited

Returns: a read-only vector expression of the imaginary part (x,y,z)

◆ vec() [4/4]

const VectorBlock< const Coefficients, 3 > vec ( ) const

inlineinherited

Returns: a read-only vector expression of the imaginary part (x,y,z)

◆ w() [1/4]

Scalar & w ( )

inlineinherited

Returns: a reference to the w coefficient

◆ w() [2/4]

Scalar & w ( )

inlineinherited

Returns: a reference to the w coefficient

◆ w() [3/4]

Scalar w ( ) const

inlineinherited

Returns: the w coefficient

◆ w() [4/4]

Scalar w ( ) const

inlineinherited

Returns: the w coefficient

◆ x() [1/4]

Scalar & x ( )

inlineinherited

Returns: a reference to the x coefficient

◆ x() [2/4]

Scalar & x ( )

inlineinherited

Returns: a reference to the x coefficient

◆ x() [3/4]

Scalar x ( ) const

inlineinherited

Returns: the x coefficient

◆ x() [4/4]

Scalar x ( ) const

inlineinherited

Returns: the x coefficient

◆ y() [1/4]

Scalar & y ( )

inlineinherited

Returns: a reference to the y coefficient

◆ y() [2/4]

Scalar & y ( )

inlineinherited

Returns: a reference to the y coefficient

◆ y() [3/4]

Scalar y ( ) const

inlineinherited

Returns: the y coefficient

◆ y() [4/4]

Scalar y ( ) const

inlineinherited

Returns: the y coefficient

◆ z() [1/4]

Scalar & z ( )

inlineinherited

Returns: a reference to the z coefficient

◆ z() [2/4]

Scalar & z ( )

inlineinherited

Returns: a reference to the z coefficient

◆ z() [3/4]

Scalar z ( ) const

inlineinherited

Returns: the z coefficient

◆ z() [4/4]

Scalar z ( ) const

inlineinherited

Returns: the z coefficient

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

Quaternion.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ AngleAxisType

◆ Matrix3

◆ RotationMatrixType

◆ Vector3

Constructor & Destructor Documentation

◆ Map() [1/4]

◆ Map() [2/4]

◆ Map() [3/4]

◆ Map() [4/4]

Member Function Documentation

◆ _transformVector() [1/2]

◆ _transformVector() [2/2]

◆ angularDistance() [1/2]

◆ angularDistance() [2/2]

◆ cast() [1/2]

◆ cast() [2/2]

◆ conjugate() [1/2]

◆ conjugate() [2/2]

◆ dot() [1/2]

◆ dot() [2/2]

◆ Identity() [1/2]

◆ Identity() [2/2]

◆ inverse() [1/2]

◆ inverse() [2/2]

◆ isApprox() [1/2]

◆ isApprox() [2/2]

◆ matrix()

◆ norm() [1/2]

◆ norm() [2/2]

◆ normalize() [1/2]

◆ normalize() [2/2]

◆ normalized() [1/2]

◆ normalized() [2/2]

◆ operator*() [1/10]

◆ operator*() [2/10]

◆ operator*() [3/10]

◆ operator*() [4/10]

◆ operator*() [5/10]

◆ operator*() [6/10]

◆ operator*() [7/10]

◆ operator*() [8/10]

◆ operator*() [9/10]

◆ operator*() [10/10]

◆ operator*=()

◆ setFromTwoVectors() [1/2]

◆ setFromTwoVectors() [2/2]

◆ setIdentity() [1/2]

◆ setIdentity() [2/2]

◆ slerp() [1/4]

◆ slerp() [2/4]

◆ slerp() [3/4]

◆ slerp() [4/4]

◆ squaredNorm() [1/2]

◆ squaredNorm() [2/2]

◆ toRotationMatrix() [1/2]

◆ toRotationMatrix() [2/2]

◆ vec() [1/4]

◆ vec() [2/4]

◆ vec() [3/4]

◆ vec() [4/4]

◆ w() [1/4]

◆ w() [2/4]

◆ w() [3/4]

◆ w() [4/4]

◆ x() [1/4]

◆ x() [2/4]

◆ x() [3/4]

◆ x() [4/4]

◆ y() [1/4]

◆ y() [2/4]

◆ y() [3/4]

◆ y() [4/4]

◆ z() [1/4]

◆ z() [2/4]

◆ z() [3/4]