Quaternion< _Scalar, _Options > Class Template Reference

The quaternion class used to represent 3D orientations and rotations. More...

#include <Quaternion.h>

Inheritance diagram for Quaternion< _Scalar, _Options >:

Public Types
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< Quaternion< _Scalar, _Options > >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const

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

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

internal::cast_return_type< 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

template<typename Derived1, typename Derived2>
Quaternion< Scalar, Options >	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)

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

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

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

Quaternion< typename internal::traits< 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

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

	Quaternion ()

	Quaternion (const AngleAxisType &aa)

template<typename Derived>
	Quaternion (const MatrixBase< Derived > &other)

template<typename OtherScalar, int OtherOptions>
	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)

template<class Derived>
	Quaternion (const QuaternionBase< Derived > &other)

	Quaternion (const Scalar *data)

	Quaternion (Scalar w, Scalar x, Scalar y, Scalar z)

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

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

Quaternion< typename internal::traits< 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::Quaternion< _Scalar, _Options >

The quaternion class used to represent 3D orientations and rotations.

This is defined in the Geometry module.

#include <Eigen/Geometry>

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Options	controls the memory alignement of the coeffecients. Can be # AutoAlign or # DontAlign. Default is AutoAlign.

This class represents a quaternion $ w+xi+yj+zk $ that is a convenient representation of orientations and rotations of objects in three dimensions. Compared to other representations like Euler angles or 3x3 matrices, quatertions offer the following advantages:

compact storage (4 scalars)
efficient to compose (28 flops),
stable spherical interpolation

The following two typedefs are provided for convenience:

Quaternionf for float
Quaterniond for double

See also: class AngleAxis, class Transform

Member Typedef Documentation

◆ 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

◆ Quaternion() [1/7]

template<typename _Scalar, int _Options>

Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

◆ Quaternion() [2/7]

template<typename _Scalar, int _Options>

Quaternion	(	Scalar	w,
		Scalar	x,
		Scalar	y,
		Scalar	z )

inline

Constructs and initializes the quaternion $ w+xi+yj+zk $ from its four coefficients w, x, y and z.

Warning: Note the order of the arguments: the real w coefficient first, while internally the coefficients are stored in the following order: [x, y, z, w]

◆ Quaternion() [3/7]

template<typename _Scalar, int _Options>

Quaternion ( const Scalar * data )

inline

Constructs and initialize a quaternion from the array data

◆ Quaternion() [4/7]

template<typename _Scalar, int _Options>

template<class Derived>

Quaternion ( const QuaternionBase< Derived > & other )

inline

Copy constructor

◆ Quaternion() [5/7]

template<typename _Scalar, int _Options>

Quaternion ( const AngleAxisType & aa )

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

◆ Quaternion() [6/7]

template<typename _Scalar, int _Options>

template<typename Derived>

Quaternion ( const MatrixBase< Derived > & other )

inlineexplicit

Constructs and initializes a quaternion from either:

a rotation matrix expression,
a 4D vector expression representing quaternion coefficients.

◆ Quaternion() [7/7]

template<typename _Scalar, int _Options>

template<typename OtherScalar, int OtherOptions>

Quaternion ( const Quaternion< OtherScalar, OtherOptions > & other )

inlineexplicit

Explicit copy constructor with scalar conversion

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

inlineinherited

Returns: the angle (in radian) between two rotations

See also: dot()

References dot().

◆ angularDistance() [2/2]

internal::traits< 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< 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< 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< 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()

References QuaternionBase< Derived >::coeffs().

Referenced by angularDistance(), and slerp().

◆ 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()

◆ FromTwoVectors()

template<typename _Scalar, int _Options>

template<typename Derived1, typename Derived2>

Quaternion< Scalar, Options > FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b )

Returns 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: resulting quaternion

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

◆ 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< 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()

References QuaternionBase< Derived >::coeffs().

◆ 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()

References QuaternionBase< Derived >::coeffs().

◆ 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()

References QuaternionBase< Derived >::coeffs().

◆ 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()

References QuaternionBase< Derived >::coeffs(), and QuaternionBase< Derived >::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< 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< 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< 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>

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

inline

See also: operator*(Quaternion)

◆ setFromTwoVectors() [1/2]

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]

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()

References QuaternionBase< Derived >::coeffs().

◆ 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< 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

References QuaternionBase< Derived >::coeffs(), coeffs(), and dot().

◆ slerp() [4/4]

Quaternion< typename internal::traits< 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()

References QuaternionBase< Derived >::coeffs().

◆ 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< 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)

References QuaternionBase< Derived >::coeffs().

◆ 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)

References QuaternionBase< Derived >::coeffs().

◆ 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 files:

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Matrix3

◆ RotationMatrixType

◆ Vector3

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

◆ Quaternion() [2/7]

◆ Quaternion() [3/7]

◆ Quaternion() [4/7]

◆ Quaternion() [5/7]

◆ Quaternion() [6/7]

◆ Quaternion() [7/7]

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]

◆ FromTwoVectors()

◆ 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]