Quaternion Class Template Reference
[Geometry module]

Inherits RotationBase< Eigen::Quaternion< _Scalar >, 3 >.

Inherited by ei_unaligned_type< Quaternion< _Scalar > >.

List of all members.

---

Detailed Description

template<typename _Scalar>
class Eigen::Quaternion< _Scalar >

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

This is defined in the Geometry module.

 #include <Eigen/Geometry> 

Parameters:

_Scalar

the scalar type, i.e., the type of the coefficients

This class represents a quaternion 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

Public Types
typedef AngleAxis< Scalar >	AngleAxisType
typedef Matrix< Scalar, 4, 1 >	Coefficients
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef _Scalar	Scalar
typedef Matrix< Scalar, 3, 1 >	Vector3
Public Member Functions
Scalar	angularDistance (const Quaternion &other) const
template<typename NewScalarType>
ei_cast_return_type < Quaternion, Quaternion < NewScalarType > >::type	cast () const
Coefficients &	coeffs ()
const Coefficients &	coeffs () const
Quaternion	conjugate (void) const
Scalar	dot (const Quaternion &other) const
Quaternion	inverse (void) const
bool	isApprox (const Quaternion &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
Scalar	norm () const
void	normalize ()
Quaternion	normalized () const
template<typename Derived>
Vector3	operator* (const MatrixBase< Derived > &vec) const
Quaternion	operator* (const Quaternion &q) const
Quaternion &	operator*= (const Quaternion &q)
template<typename Derived>
Quaternion &	operator= (const MatrixBase< Derived > &m)
Quaternion &	operator= (const AngleAxisType &aa)
Quaternion &	operator= (const Quaternion &other)
template<typename OtherScalarType>
	Quaternion (const Quaternion< OtherScalarType > &other)
template<typename Derived>
	Quaternion (const MatrixBase< Derived > &other)
	Quaternion (const AngleAxisType &aa)
	Quaternion (const Quaternion &other)
	Quaternion (Scalar w, Scalar x, Scalar y, Scalar z)
	Quaternion (ei_constructor_without_unaligned_array_assert)
	Quaternion ()
template<typename Derived1, typename Derived2>
Quaternion &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Quaternion &	setIdentity ()
Quaternion	slerp (Scalar t, const Quaternion &other) const
Scalar	squaredNorm () const
Matrix3	toRotationMatrix (void) const
Block< Coefficients, 3, 1 >	vec ()
const Block< Coefficients, 3, 1 >	vec () const
Scalar &	w ()
Scalar	w () const
Scalar &	x ()
Scalar	x () const
Scalar &	y ()
Scalar	y () const
Scalar &	z ()
Scalar	z () const
Static Public Member Functions
static Quaternion	Identity ()
Protected Attributes
Coefficients	m_coeffs

---

Member Typedef Documentation

typedef AngleAxis<Scalar> AngleAxisType

the equivalent angle-axis type

typedef Matrix<Scalar, 4, 1> Coefficients

the type of the Coefficients 4-vector

typedef Matrix<Scalar,3,3> Matrix3

the equivalent rotation matrix type

typedef _Scalar Scalar

the scalar type of the coefficients

Reimplemented from RotationBase.

typedef Matrix<Scalar,3,1> Vector3

the type of a 3D vector

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Constructor & Destructor Documentation

Quaternion

(

)

[inline]

Default constructor leaving the quaternion uninitialized.

Quaternion	(	Scalar	w,
		Scalar	x,
		Scalar	y,
		Scalar	z
	)			[inline]

Constructs and initializes the quaternion 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

(

const Quaternion< _Scalar > &

other

)

[inline]

Copy constructor

Quaternion

(

const AngleAxisType &

aa

)

[inline, explicit]

Constructs and initializes a quaternion from the angle-axis aa

Quaternion

(

const MatrixBase< Derived > &

other

)

[inline, explicit]

Constructs and initializes a quaternion from either:

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

  See also:

  operator=(MatrixBase<Derived>)

Quaternion

(

const Quaternion< OtherScalarType > &

other

)

[inline, explicit]

Copy constructor with scalar type conversion

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Member Function Documentation

Scalar angularDistance

(

const Quaternion< _Scalar > &

other

)

const [inline]

Returns:

the angle (in radian) between two rotations

See also:

dot()

ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast

(

)

const [inline]

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.

Coefficients& coeffs

(

)

[inline]

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)

Quaternion< Scalar > conjugate

(

void

)

const [inline]

Returns:

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:

Quaternion::inverse()

Scalar dot

(

const Quaternion< _Scalar > &

other

)

const [inline]

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 Identity

(

)

[inline, static]

Returns:

a quaternion representing an identity rotation

See also:

MatrixBase::Identity()

Quaternion< Scalar > inverse

(

void

)

const [inline]

Returns:

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:

Quaternion::conjugate()

Reimplemented from RotationBase.

bool isApprox	(	const Quaternion< _Scalar > &	other,
		typename NumTraits< Scalar >::Real	prec = precision<Scalar>()
	)			const [inline]

Returns:

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

See also:

MatrixBase::isApprox()

Scalar norm

(

)

const [inline]

Returns:

the norm of the quaternion's coefficients

See also:

Quaternion::squaredNorm(), MatrixBase::norm()

void normalize

(

)

[inline]

Normalizes the quaternion *this

See also:

normalized(), MatrixBase::normalize()

Quaternion normalized

(

)

const [inline]

Returns:

a normalized version of *this

See also:

normalize(), MatrixBase::normalized()

Quaternion< Scalar >::Vector3 operator*

(

const MatrixBase< Derived > &

v

)

const [inline]

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:

• Quaternion: 30n
• Via a Matrix3: 24 + 15n

Quaternion< Scalar > operator*

(

const Quaternion< _Scalar > &

other

)

const [inline]

Returns:

the concatenation of two rotations as a quaternion-quaternion product

Quaternion< Scalar > & operator*=

(

const Quaternion< _Scalar > &

other

)

[inline]

See also:

operator*(Quaternion)

Quaternion< Scalar > & operator=

(

const MatrixBase< Derived > &

xpr

)

[inline]

Set *this from the expression xpr:

• if xpr is a 4x1 vector, then xpr is assumed to be a quaternion
• if xpr is a 3x3 matrix, then xpr is assumed to be rotation matrix and xpr is converted to a quaternion

Quaternion< Scalar > & operator=

(

const AngleAxisType &

aa

)

[inline]

Set *this from an angle-axis aa and returns a reference to *this

Quaternion< Scalar > & setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)			[inline]

Sets *this to be a quaternion representing a rotation sending the vector a to the vector b.

Returns:

a reference to *this.

Note that the two input vectors do not have to be normalized.

Quaternion& setIdentity

(

)

[inline]

See also:

Quaternion::Identity(), MatrixBase::setIdentity()

Quaternion< Scalar > slerp	(	Scalar	t,
		const Quaternion< _Scalar > &	other
	)			const [inline]

Returns:

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

Scalar squaredNorm

(

)

const [inline]

Returns:

the squared norm of the quaternion's coefficients

See also:

Quaternion::norm(), MatrixBase::squaredNorm()

Quaternion< Scalar >::Matrix3 toRotationMatrix

(

void

)

const [inline]

Convert the quaternion to a 3x3 rotation matrix

Reimplemented from RotationBase.

Block<Coefficients,3,1> vec

(

)

[inline]

Returns:

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

const Block<Coefficients,3,1> vec

(

)

const [inline]

Returns:

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

Scalar& w

(

)

[inline]

Returns:

a reference to the w coefficient

Scalar w

(

)

const [inline]

Returns:

the w coefficient

Scalar& x

(

)

[inline]

Returns:

a reference to the x coefficient

Scalar x

(

)

const [inline]

Returns:

the x coefficient

Scalar& y

(

)

[inline]

Returns:

a reference to the y coefficient

Scalar y

(

)

const [inline]

Returns:

the y coefficient

Scalar& z

(

)

[inline]

Returns:

a reference to the z coefficient

Scalar z

(

)

const [inline]

Returns:

the z coefficient

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

• Geometry