Quaternion< _Scalar > Class Template Reference [Geometry_Module]

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Detailed Description

template<typename _Scalar>
class Quaternion< _Scalar >

The quaternion class used to represent 3D orientations and rotations

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

Definition at line 231 of file Quaternion.h.

#include <src/Geometry/Quaternion.h>

Inheritance diagram for Quaternion< _Scalar >:

List of all members.

Public Types
typedef _Scalar	Scalar
	the scalar type of the coefficients
typedef internal::traits < Quaternion< Scalar > >::Coefficients	Coefficients
typedef Base::AngleAxisType	AngleAxisType
	the equivalent angle-axis type
Public Member Functions
	Quaternion ()
	Default constructor leaving the quaternion uninitialized.
	Quaternion (Scalar w, Scalar x, Scalar y, Scalar z)
	Constructs and initializes the quaternion from its four coefficients w, x, y and z.
	Quaternion (const Scalar *data)
	Constructs and initialize a quaternion from the array data.
template<class Derived >
EIGEN_STRONG_INLINE	Quaternion (const QuaternionBase< Derived > &other)
	Copy constructor.
	Quaternion (const AngleAxisType &aa)
	Constructs and initializes a quaternion from the angle-axis aa.
template<typename Derived >
	Quaternion (const MatrixBase< Derived > &other)
	Constructs and initializes a quaternion from either: a rotation matrix expression, a 4D vector expression representing quaternion coefficients.
Coefficients &	coeffs ()
const Coefficients &	coeffs () const
Protected Attributes
Coefficients	m_coeffs
Private Types
typedef QuaternionBase < Quaternion< _Scalar > >	Base

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Member Typedef Documentation

template<typename _Scalar>

typedef Base::AngleAxisType Quaternion< _Scalar >::AngleAxisType

the equivalent angle-axis type

Reimplemented from QuaternionBase< Quaternion< _Scalar > >.

Definition at line 240 of file Quaternion.h.

template<typename _Scalar>

typedef QuaternionBase<Quaternion<_Scalar> > Quaternion< _Scalar >::Base [private]

Reimplemented from QuaternionBase< Quaternion< _Scalar > >.

Definition at line 232 of file Quaternion.h.

template<typename _Scalar>

typedef internal::traits<Quaternion<Scalar> >::Coefficients Quaternion< _Scalar >::Coefficients

Reimplemented from QuaternionBase< Quaternion< _Scalar > >.

Definition at line 239 of file Quaternion.h.

template<typename _Scalar>

typedef _Scalar Quaternion< _Scalar >::Scalar

the scalar type of the coefficients

Reimplemented from QuaternionBase< Quaternion< _Scalar > >.

Definition at line 234 of file Quaternion.h.

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Constructor & Destructor Documentation

template<typename _Scalar>

Quaternion< _Scalar >::Quaternion

(

)

[inline]

Default constructor leaving the quaternion uninitialized.

Definition at line 243 of file Quaternion.h.

template<typename _Scalar>

Quaternion< _Scalar >::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]

Definition at line 252 of file Quaternion.h.

template<typename _Scalar>

Quaternion< _Scalar >::Quaternion

(

const Scalar *

data )

[inline]

Constructs and initialize a quaternion from the array data.

Definition at line 255 of file Quaternion.h.

template<typename _Scalar>

template<class Derived >

EIGEN_STRONG_INLINE Quaternion< _Scalar >::Quaternion

(

const QuaternionBase< Derived > &

other )

[inline]

Copy constructor.

Definition at line 258 of file Quaternion.h.

References QuaternionBase< Quaternion< _Scalar > >::operator=().

template<typename _Scalar>

Quaternion< _Scalar >::Quaternion

(

const AngleAxisType &

aa )

[inline, explicit]

Constructs and initializes a quaternion from the angle-axis aa.

Definition at line 261 of file Quaternion.h.

template<typename _Scalar>

template<typename Derived >

Quaternion< _Scalar >::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.

Definition at line 268 of file Quaternion.h.

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Member Function Documentation

template<typename _Scalar>

Coefficients& Quaternion< _Scalar >::coeffs

(

)

[inline]

Returns:

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

Reimplemented from QuaternionBase< Quaternion< _Scalar > >.

Definition at line 270 of file Quaternion.h.

References Quaternion< _Scalar >::m_coeffs.

template<typename _Scalar>

const Coefficients& Quaternion< _Scalar >::coeffs

(

)

const [inline]

Returns:

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

Reimplemented from QuaternionBase< Quaternion< _Scalar > >.

Definition at line 271 of file Quaternion.h.

References Quaternion< _Scalar >::m_coeffs.

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Member Data Documentation

template<typename _Scalar>

Coefficients Quaternion< _Scalar >::m_coeffs [protected]

Definition at line 274 of file Quaternion.h.

Referenced by Quaternion< _Scalar >::coeffs().