Eigen::Quaternion< _Scalar, _Options > Class Template Reference

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

#include <Quaternion.h>

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

Collaboration diagram for Eigen::Quaternion< _Scalar, _Options >:

List of all members.

Public Types
enum
typedef QuaternionBase < Quaternion< _Scalar, _Options > >	Base
typedef _Scalar	Scalar
typedef internal::traits < Quaternion >::Coefficients	Coefficients
typedef Base::AngleAxisType	AngleAxisType
Public Member Functions
	Quaternion ()
	Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
	Quaternion (const Scalar *data)
template<class Derived >
EIGEN_STRONG_INLINE	Quaternion (const QuaternionBase< Derived > &other)
	Quaternion (const AngleAxisType &aa)
template<typename Derived >
	Quaternion (const MatrixBase< Derived > &other)
template<typename OtherScalar , int OtherOptions>
	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)
Coefficients &	coeffs ()
const Coefficients &	coeffs () const
Static Public Member Functions
template<typename Derived1 , typename Derived2 >
static Quaternion	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Static Protected Member Functions
static EIGEN_STRONG_INLINE void	_check_template_params ()
Protected Attributes
Coefficients	m_coeffs

---

Detailed Description

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

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

Template Parameters:

_Scalar	the scalar type, i.e., the type of the coefficients
_Options	controls the memory alignment of the coefficients. Can be # AutoAlign or # DontAlign. Default is AutoAlign.

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, quaternions 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

Warning:

Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.

See also:

class AngleAxis, class Transform

Definition at line 227 of file Quaternion.h.

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Member Typedef Documentation

template<typename _Scalar, int _Options>

typedef Base::AngleAxisType Eigen::Quaternion< _Scalar, _Options >::AngleAxisType

the equivalent angle-axis type

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

Definition at line 239 of file Quaternion.h.

template<typename _Scalar, int _Options>

typedef QuaternionBase<Quaternion<_Scalar,_Options> > Eigen::Quaternion< _Scalar, _Options >::Base

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

Definition at line 230 of file Quaternion.h.

template<typename _Scalar, int _Options>

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

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

Definition at line 238 of file Quaternion.h.

template<typename _Scalar, int _Options>

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

the scalar type of the coefficients

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

Definition at line 233 of file Quaternion.h.

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Member Enumeration Documentation

template<typename _Scalar, int _Options>

anonymous enum

Definition at line 231 of file Quaternion.h.

{ NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };

---

Constructor & Destructor Documentation

template<typename _Scalar, int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

)

[inline]

Default constructor leaving the quaternion uninitialized.

Definition at line 242 of file Quaternion.h.

{}

template<typename _Scalar, int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion	(	const Scalar &	w,
		const Scalar &	x,
		const Scalar &	y,
		const 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 251 of file Quaternion.h.

: m_coeffs(x, y, z, w){}

template<typename _Scalar, int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const Scalar *

data

)

[inline, explicit]

Constructs and initialize a quaternion from the array data

Definition at line 254 of file Quaternion.h.

: m_coeffs(data) {}

template<typename _Scalar, int _Options>

template<class Derived >

EIGEN_STRONG_INLINE Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const QuaternionBase< Derived > &

other

)

[inline]

Copy constructor

Definition at line 257 of file Quaternion.h.

{ this->Base::operator=(other); }

template<typename _Scalar, int _Options>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const AngleAxisType &

aa

)

[inline, explicit]

Constructs and initializes a quaternion from the angle-axis aa

Definition at line 260 of file Quaternion.h.

{ *this = aa; }

template<typename _Scalar, int _Options>

template<typename Derived >

Eigen::Quaternion< _Scalar, _Options >::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 267 of file Quaternion.h.

{ *this = other; }

template<typename _Scalar, int _Options>

template<typename OtherScalar , int OtherOptions>

Eigen::Quaternion< _Scalar, _Options >::Quaternion

(

const Quaternion< OtherScalar, OtherOptions > &

other

)

[inline, explicit]

Explicit copy constructor with scalar conversion

Definition at line 271 of file Quaternion.h.

  { m_coeffs = other.coeffs().template cast<Scalar>(); }

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Member Function Documentation

template<typename _Scalar, int _Options>

static EIGEN_STRONG_INLINE void Eigen::Quaternion< _Scalar, _Options >::_check_template_params

(

)

[inline, static, protected]

Definition at line 290 of file Quaternion.h.

    {
      EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
        INVALID_MATRIX_TEMPLATE_PARAMETERS)
    }

template<typename _Scalar, int _Options>

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

(

)

[inline]

Returns:

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

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

Definition at line 277 of file Quaternion.h.

{ return m_coeffs;}

template<typename _Scalar, int _Options>

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

(

)

const [inline]

Returns:

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

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

Definition at line 278 of file Quaternion.h.

{ return m_coeffs;}

template<typename Scalar , int Options>

template<typename Derived1 , typename Derived2 >

Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)		[static]

Returns 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:

resulting quaternion

Note that the two input vectors do not have to be normalized, and do not need to have the same norm.

Definition at line 625 of file Quaternion.h.

{
    Quaternion quat;
    quat.setFromTwoVectors(a, b);
    return quat;
}

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Member Data Documentation

template<typename _Scalar, int _Options>

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

Definition at line 287 of file Quaternion.h.

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

• Quaternion.h