Eigen::Map< const Quaternion< _Scalar >, _Options > Class Reference

---

Detailed Description

Quaternion expression mapping a constant 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

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

List of all members.

Public Types
typedef _Scalar	Scalar
typedef internal::traits< Map > ::Coefficients	Coefficients
enum
typedef NumTraits< Scalar >::Real	RealScalar
typedef Matrix< Scalar, 3, 1 >	Vector3
	the type of a 3D vector
typedef Matrix< Scalar, 3, 3 >	Matrix3
	the equivalent rotation matrix type
typedef AngleAxis< Scalar >	AngleAxisType
	the equivalent angle-axis type
Public Member Functions
EIGEN_STRONG_INLINE	Map (const Scalar *coeffs)
	Constructs a Mapped Quaternion object from the pointer coeffs.
const Coefficients &	coeffs () const
Scalar	x () const
Scalar &	x ()
Scalar	y () const
Scalar &	y ()
Scalar	z () const
Scalar &	z ()
Scalar	w () const
Scalar &	w ()
const VectorBlock< const Coefficients, 3 >	vec () const
VectorBlock< Coefficients, 3 >	vec ()
internal::traits< Derived > ::Coefficients &	coeffs ()
QuaternionBase &	setIdentity ()
Scalar	squaredNorm () const
Scalar	norm () const
void	normalize ()
	Normalizes the quaternion *this.
Quaternion< Scalar >	normalized () const
Scalar	dot (const QuaternionBase< OtherDerived > &other) const
Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
Matrix3	toRotationMatrix () const
Derived &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
EIGEN_STRONG_INLINE Quaternion < Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const
EIGEN_STRONG_INLINE Derived &	operator*= (const QuaternionBase< OtherDerived > &q)
Quaternion< Scalar >	inverse () const
Quaternion< Scalar >	conjugate () const
Quaternion< Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const
bool	isApprox (const QuaternionBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_STRONG_INLINE Vector3	_transformVector (Vector3 v) const
	return the result vector of v through the rotation
internal::cast_return_type < Derived, Quaternion < NewScalarType > >::type	cast () const
Static Public Member Functions
static Quaternion< Scalar >	Identity ()
Protected Attributes
const Coefficients	m_coeffs
Private Types
typedef QuaternionBase< Map < const Quaternion< _Scalar > , _Options > >	Base

---

Member Typedef Documentation

typedef AngleAxis<Scalar> Eigen::QuaternionBase::AngleAxisType [inherited]

the equivalent angle-axis type

Definition at line 63 of file Geometry.

typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Eigen::Map< const Quaternion< _Scalar >, _Options >::Base [private]

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

Definition at line 348 of file Geometry.

typedef internal::traits<Map>::Coefficients Eigen::Map< const Quaternion< _Scalar >, _Options >::Coefficients

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

Definition at line 352 of file Geometry.

typedef Matrix<Scalar,3,3> Eigen::QuaternionBase::Matrix3 [inherited]

the equivalent rotation matrix type

Definition at line 61 of file Geometry.

typedef NumTraits<Scalar>::Real Eigen::QuaternionBase::RealScalar [inherited]

Definition at line 51 of file Geometry.

typedef _Scalar Eigen::Map< const Quaternion< _Scalar >, _Options >::Scalar

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

Definition at line 351 of file Geometry.

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

the type of a 3D vector

Definition at line 59 of file Geometry.

---

Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 53 of file Geometry.

---

Constructor & Destructor Documentation

EIGEN_STRONG_INLINE Eigen::Map< const Quaternion< _Scalar >, _Options >::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.

Definition at line 362 of file Geometry.

---

Member Function Documentation

EIGEN_STRONG_INLINE Vector3 Eigen::QuaternionBase::_transformVector

(

Vector3

v

)

const [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

Scalar Eigen::QuaternionBase::angularDistance

(

const QuaternionBase< OtherDerived > &

other

)

const [inherited]

Returns:

the angle (in radian) between two rotations

See also:

dot()

internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type Eigen::QuaternionBase::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.

Definition at line 184 of file Geometry.

internal::traits<Derived>::Coefficients& Eigen::QuaternionBase::coeffs

(

)

[inline, inherited]

Returns:

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

Definition at line 95 of file Geometry.

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

(

)

const [inline]

Returns:

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

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

Definition at line 364 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase::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 Eigen::QuaternionBase::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()

Definition at line 141 of file Geometry.

static Quaternion<Scalar> Eigen::QuaternionBase::Identity

(

)

[inline, static, inherited]

Returns:

a quaternion representing an identity rotation

See also:

MatrixBase::Identity()

Definition at line 113 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase::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()

bool Eigen::QuaternionBase::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()

Definition at line 172 of file Geometry.

Scalar Eigen::QuaternionBase::norm

(

)

const [inline, inherited]

Returns:

the norm of the quaternion's coefficients

See also:

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

Definition at line 127 of file Geometry.

void Eigen::QuaternionBase::normalize

(

void

)

[inline, inherited]

Normalizes the quaternion *this.

See also:

normalized(), MatrixBase::normalize()

Definition at line 131 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase::normalized

(

)

const [inline, inherited]

Returns:

a normalized copy of *this

See also:

normalize(), MatrixBase::normalized()

Definition at line 134 of file Geometry.

EIGEN_STRONG_INLINE Quaternion<Scalar> Eigen::QuaternionBase::operator*

(

const QuaternionBase< OtherDerived > &

q

)

const [inherited]

Returns:

the concatenation of two rotations as a quaternion-quaternion product

EIGEN_STRONG_INLINE Derived& Eigen::QuaternionBase::operator*=

(

const QuaternionBase< OtherDerived > &

q

)

[inherited]

See also:

operator*(Quaternion)

Derived& Eigen::QuaternionBase::setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)		[inherited]

Sets *this to be a quaternion representing a rotation between the two arbitrary vectors a and b.

Returns:

the quaternion which transform a into b through a rotation

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& Eigen::QuaternionBase::setIdentity

(

)

[inline, inherited]

See also:

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

Definition at line 117 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase::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 Eigen::QuaternionBase::squaredNorm

(

)

const [inline, inherited]

Returns:

the squared norm of the quaternion's coefficients

See also:

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

Definition at line 122 of file Geometry.

Matrix3 Eigen::QuaternionBase::toRotationMatrix

(

)

const [inherited]

Convert the quaternion to a 3x3 rotation matrix.

Returns:

an equivalent 3x3 rotation matrix

The quaternion is required to be normalized, otherwise the result is undefined.

const VectorBlock<const Coefficients,3> Eigen::QuaternionBase::vec

(

)

const [inline, inherited]

Returns:

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

Definition at line 86 of file Geometry.

VectorBlock<Coefficients,3> Eigen::QuaternionBase::vec

(

)

[inline, inherited]

Returns:

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

Definition at line 89 of file Geometry.

Scalar Eigen::QuaternionBase::w

(

)

const [inline, inherited]

Returns:

the w coefficient

Definition at line 74 of file Geometry.

Scalar& Eigen::QuaternionBase::w

(

)

[inline, inherited]

Returns:

a reference to the w coefficient

Definition at line 83 of file Geometry.

Scalar Eigen::QuaternionBase::x

(

)

const [inline, inherited]

Returns:

the x coefficient

Definition at line 68 of file Geometry.

Scalar& Eigen::QuaternionBase::x

(

)

[inline, inherited]

Returns:

a reference to the x coefficient

Definition at line 77 of file Geometry.

Scalar Eigen::QuaternionBase::y

(

)

const [inline, inherited]

Returns:

the y coefficient

Definition at line 70 of file Geometry.

Scalar& Eigen::QuaternionBase::y

(

)

[inline, inherited]

Returns:

a reference to the y coefficient

Definition at line 79 of file Geometry.

Scalar Eigen::QuaternionBase::z

(

)

const [inline, inherited]

Returns:

the z coefficient

Definition at line 72 of file Geometry.

Scalar& Eigen::QuaternionBase::z

(

)

[inline, inherited]

Returns:

a reference to the z coefficient

Definition at line 81 of file Geometry.

---

Member Data Documentation

const Coefficients Eigen::Map< const Quaternion< _Scalar >, _Options >::m_coeffs [protected]

Definition at line 367 of file Geometry.