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

Quaternion expression mapping a constant memory buffer. More...

#include <Quaternion.h>

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

List of all members.

Public Types
typedef AngleAxis< Scalar >	AngleAxisType
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef _Scalar	Scalar
typedef Matrix< Scalar, 3, 1 >	Vector3
Public Member Functions
Vector3	_transformVector (Vector3 v) const
internal::cast_return_type < Map< const Quaternion < _Scalar >, _Options > , Quaternion< NewScalarType > >::type	cast () const
internal::traits< Map< const Quaternion< _Scalar > , _Options > >::Coefficients &	coeffs ()
const Coefficients &	coeffs () 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 (const 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< const 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
Map< const Quaternion< _Scalar > , _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
QuaternionBase &	setIdentity ()
Quaternion< 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 ()
Friends
RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const Map< const Quaternion< _Scalar >, _Options > &r)
Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const Map< const Quaternion< _Scalar >, _Options > &r)

---

Detailed Description

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

Quaternion expression mapping a constant 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

typedef AngleAxis<Scalar> AngleAxisType [inherited]

the equivalent angle-axis type

typedef Matrix<Scalar,3,3> Matrix3 [inherited]

the equivalent rotation matrix type

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType [inherited]

corresponding linear transformation matrix type

typedef _Scalar Scalar

the scalar type of the coefficients

Reimplemented from QuaternionBase< Map< const Quaternion< _Scalar >, _Options > >.

typedef Matrix<Scalar,3,1> Vector3 [inherited]

the type of a 3D vector

---

Constructor & Destructor Documentation

Map

(

const 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

Vector3 _transformVector

(

Vector3

v

)

const [inline, inherited]

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

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

(

)

const [inline, inherited]

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.

internal::traits<Map< const Quaternion< _Scalar >, _Options > >::Coefficients& coeffs

(

)

[inline, inherited]

Returns:

a vector expression of the coefficients (x,y,z,w)

const Coefficients& coeffs

(

)

const [inline]

Returns:

a read-only vector expression of the coefficients (x,y,z,w)

Reimplemented from QuaternionBase< Map< const Quaternion< _Scalar >, _Options > >.

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()

Scalar dot

(

const QuaternionBase< OtherDerived > &

other

)

const [inline, inherited]

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()

static Quaternion<Scalar> Identity

(

)

[inline, static, inherited]

Returns:

a quaternion representing an identity rotation

See also:

MatrixBase::Identity()

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()

Reimplemented from RotationBase< Map< const Quaternion< _Scalar >, _Options >, 3 >.

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

Returns:

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

See also:

MatrixBase::isApprox()

RotationMatrixType matrix

(

)

const [inline, inherited]

Returns:

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

Scalar norm

(

)

const [inline, inherited]

Returns:

the norm of the quaternion's coefficients

See also:

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

void normalize

(

void

)

[inline, inherited]

Normalizes the quaternion *this

See also:

normalized(), MatrixBase::normalize()

Quaternion<Scalar> normalized

(

)

const [inline, inherited]

Returns:

a normalized copy of *this

See also:

normalize(), MatrixBase::normalized()

Transform<Scalar,Dim,Isometry> operator*

(

const Translation< Scalar, Dim > &

t

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a translation t

RotationMatrixType operator*

(

const UniformScaling< Scalar > &

s

)

const [inline, inherited]

Returns:

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

internal::rotation_base_generic_product_selector<Map< const Quaternion< _Scalar >, _Options > ,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType operator*

(

const EigenBase< OtherDerived > &

e

)

const [inline, 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

Transform<Scalar,Dim,Mode> operator*

(

const Transform< Scalar, Dim, Mode, Options > &

t

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a transformation t

Map< const 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.

QuaternionBase& setIdentity

(

)

[inline, inherited]

See also:

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

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

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

Scalar squaredNorm

(

)

const [inline, inherited]

Returns:

the squared norm of the quaternion's coefficients

See also:

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

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.

Reimplemented from RotationBase< Map< const Quaternion< _Scalar >, _Options >, 3 >.

const VectorBlock<const Coefficients,3> vec

(

)

const [inline, inherited]

Returns:

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

VectorBlock<Coefficients,3> vec

(

)

[inline, inherited]

Returns:

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

Scalar w

(

)

const [inline, inherited]

Returns:

the w coefficient

Scalar& w

(

)

[inline, inherited]

Returns:

a reference to the w coefficient

Scalar x

(

)

const [inline, inherited]

Returns:

the x coefficient

Scalar& x

(

)

[inline, inherited]

Returns:

a reference to the x coefficient

Scalar y

(

)

const [inline, inherited]

Returns:

the y coefficient

Scalar& y

(

)

[inline, inherited]

Returns:

a reference to the y coefficient

Scalar z

(

)

const [inline, inherited]

Returns:

the z coefficient

Scalar& z

(

)

[inline, inherited]

Returns:

a reference to the z coefficient

---

Friends And Related Function Documentation

RotationMatrixType operator*	(	const EigenBase< OtherDerived > &	l,
		const Map< const Quaternion< _Scalar >, _Options > &	r
	)		[friend, inherited]

Returns:

the concatenation of a linear transformation l with the rotation r

Transform<Scalar,Dim,Affine> operator*	(	const DiagonalMatrix< Scalar, Dim > &	l,
		const Map< const Quaternion< _Scalar >, _Options > &	r
	)		[friend, inherited]

Returns:

the concatenation of a scaling l with the rotation r

---

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

• Quaternion.h