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

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

Quaternion< Scalar >	conjugate () const

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

Quaternion< Scalar >	inverse () const

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

	Map (Scalar *coeffs)

RotationMatrixType	matrix () const

Scalar	norm () const

void	normalize ()

Quaternion< Scalar >	normalized () const

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

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

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

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

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

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

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

QuaternionBase &	setIdentity ()

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

Scalar	squaredNorm () const

Matrix3	toRotationMatrix () const

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

VectorBlock< Coefficients, 3 >	vec ()

Scalar	w () const

Scalar &	w ()

Scalar	x () const

Scalar &	x ()

Scalar	y () const

Scalar &	y ()

Scalar	z () const

Scalar &	z ()

Static Public Member Functions
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.

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

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()

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}

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

Member Function Documentation

◆ _transformVector()

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()

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()

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()

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()

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()

static Quaternion<Scalar> Identity ( )

inlinestaticinherited

Returns: a quaternion representing an identity rotation

See also: MatrixBase::Identity()

◆ inverse()

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()

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()

RotationMatrixType matrix ( ) const

inlineinherited

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

◆ norm()

Scalar norm ( ) const

inlineinherited

Returns: the norm of the quaternion's coefficients

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

◆ normalize()

void normalize ( void )

inlineinherited

Normalizes the quaternion *this

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

◆ normalized()

Quaternion<Scalar> normalized ( ) const

inlineinherited

Returns: a normalized copy of *this

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

◆ operator *() [1/5]

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

inlineinherited

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

◆ operator *() [2/5]

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

inlineinherited

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

◆ operator *() [3/5]

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 *() [4/5]

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 *() [5/5]

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 *=()

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

inlineinherited

See also: operator*(Quaternion)

◆ setFromTwoVectors()

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

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.

◆ setIdentity()

QuaternionBase& setIdentity ( )

inlineinherited

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

◆ slerp() [1/2]

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() [2/2]

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()

Scalar squaredNorm ( ) const

inlineinherited

Returns: the squared norm of the quaternion's coefficients

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

◆ toRotationMatrix()

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() [1/2]

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

inlineinherited

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

◆ vec() [2/2]

VectorBlock<Coefficients,3> vec ( )

inlineinherited

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

◆ w() [1/2]

Scalar w ( ) const

inlineinherited

Returns: the w coefficient

◆ w() [2/2]

Scalar& w ( )

inlineinherited

Returns: a reference to the w coefficient

◆ x() [1/2]

Scalar x ( ) const

inlineinherited

Returns: the x coefficient

◆ x() [2/2]

Scalar& x ( )

inlineinherited

Returns: a reference to the x coefficient

◆ y() [1/2]

Scalar y ( ) const

inlineinherited

Returns: the y coefficient

◆ y() [2/2]

Scalar& y ( )

inlineinherited

Returns: a reference to the y coefficient

◆ z() [1/2]

Scalar z ( ) const

inlineinherited

Returns: the z coefficient

◆ z() [2/2]

Scalar& z ( )

inlineinherited

Returns: a reference to 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

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

Member Typedef Documentation

◆ AngleAxisType

◆ Matrix3

◆ RotationMatrixType

◆ Vector3

Constructor & Destructor Documentation

◆ Map()

Member Function Documentation

◆ _transformVector()

◆ angularDistance()

◆ cast()

◆ conjugate()

◆ dot()

◆ Identity()

◆ inverse()

◆ isApprox()

◆ matrix()

◆ norm()

◆ normalize()

◆ normalized()

◆ operator *() [1/5]

◆ operator *() [2/5]

◆ operator *() [3/5]

◆ operator *() [4/5]

◆ operator *() [5/5]

◆ operator *=()

◆ setFromTwoVectors()

◆ setIdentity()

◆ slerp() [1/2]

◆ slerp() [2/2]

◆ squaredNorm()

◆ toRotationMatrix()

◆ vec() [1/2]

◆ vec() [2/2]

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]

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