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_ >:

Public Types
enum
typedef QuaternionBase< Quaternion< Scalar_, Options_ > >	Base
typedef Scalar_	Scalar
typedef internal::traits< Quaternion >::Coefficients	Coefficients
typedef Base::AngleAxisType	AngleAxisType
Public Types inherited from Eigen::QuaternionBase< Quaternion< Scalar_, Options_ > >
enum
typedef RotationBase< Quaternion< Scalar_, Options_ >, 3 >	Base
typedef internal::traits< Quaternion< Scalar_, Options_ > >::Scalar	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients	Coefficients
typedef Coefficients::CoeffReturnType	CoeffReturnType
typedef std::conditional_t< bool(internal::traits< Quaternion< Scalar_, Options_ > >::Flags &LvalueBit), Scalar &, CoeffReturnType >	NonConstCoeffReturnType
typedef Matrix< Scalar, 3, 1 >	Vector3
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef AngleAxis< Scalar >	AngleAxisType
Public Types inherited from Eigen::RotationBase< Derived, Dim_ >
enum	{ Dim = Dim_ }
typedef internal::traits< Derived >::Scalar	Scalar
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
EIGEN_DEVICE_FUNC	Quaternion ()
EIGEN_DEVICE_FUNC	Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
template<typename Derived >
EIGEN_DEVICE_FUNC	Quaternion (const Scalar &w, const Eigen::MatrixBase< Derived > &vec)
EIGEN_DEVICE_FUNC	Quaternion (const Scalar *data)
template<class Derived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE	Quaternion (const QuaternionBase< Derived > &other)
EIGEN_DEVICE_FUNC	Quaternion (const AngleAxisType &aa)
template<typename Derived >
EIGEN_DEVICE_FUNC	Quaternion (const MatrixBase< Derived > &other)
template<typename OtherScalar , int OtherOptions>
EIGEN_DEVICE_FUNC	Quaternion (const Quaternion< OtherScalar, OtherOptions > &other)
EIGEN_DEVICE_FUNC	Quaternion (Quaternion &&other) EIGEN_NOEXCEPT_IF(std
EIGEN_DEVICE_FUNC Quaternion &	operator= (Quaternion &&other) EIGEN_NOEXCEPT_IF(std
EIGEN_DEVICE_FUNC Coefficients &	coeffs ()
EIGEN_DEVICE_FUNC const Coefficients &	coeffs () const
template<typename Derived1 , typename Derived2 >
EIGEN_DEVICE_FUNC Quaternion< Scalar, Options >	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< Scalar_, Options_ > >
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR CoeffReturnType	x () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR NonConstCoeffReturnType	x ()
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR CoeffReturnType	y () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR NonConstCoeffReturnType	y ()
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR CoeffReturnType	z () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR NonConstCoeffReturnType	z ()
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR CoeffReturnType	w () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR NonConstCoeffReturnType	w ()
EIGEN_DEVICE_FUNC const VectorBlock< const Coefficients, 3 >	vec () const
EIGEN_DEVICE_FUNC VectorBlock< Coefficients, 3 >	vec ()
EIGEN_DEVICE_FUNC const internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients &	coeffs () const
EIGEN_DEVICE_FUNC internal::traits< Quaternion< Scalar_, Options_ > >::Coefficients &	coeffs ()
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase< Quaternion< Scalar_, Options_ > > &	operator= (const QuaternionBase< Quaternion< Scalar_, Options_ > > &other)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< Scalar_, Options_ > &	operator= (const QuaternionBase< OtherDerived > &other)
EIGEN_DEVICE_FUNC Quaternion< Scalar_, Options_ > &	operator= (const AngleAxisType &aa)
EIGEN_DEVICE_FUNC Quaternion< Scalar_, Options_ > &	operator= (const MatrixBase< OtherDerived > &m)
EIGEN_DEVICE_FUNC Quaternion< Scalar_, Options_ > &	operator= (const MatrixBase< MatrixDerived > &xpr)
EIGEN_DEVICE_FUNC QuaternionBase &	setIdentity ()
EIGEN_DEVICE_FUNC Scalar	squaredNorm () const
EIGEN_DEVICE_FUNC Scalar	norm () const
EIGEN_DEVICE_FUNC void	normalize ()
EIGEN_DEVICE_FUNC Quaternion< Scalar >	normalized () const
EIGEN_DEVICE_FUNC Scalar	dot (const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC internal::traits< Quaternion< Scalar_, Options_ > >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC Matrix3	toRotationMatrix () const
EIGEN_DEVICE_FUNC Quaternion< Scalar_, Options_ > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< typename internal::traits< Quaternion< Scalar_, Options_ > >::Scalar >	operator* (const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion< Scalar_, Options_ > &	operator*= (const QuaternionBase< OtherDerived > &q)
EIGEN_DEVICE_FUNC Quaternion< Scalar >	inverse () const
EIGEN_DEVICE_FUNC Quaternion< Scalar >	conjugate () const
EIGEN_DEVICE_FUNC Quaternion< Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC Quaternion< typename internal::traits< Quaternion< Scalar_, Options_ > >::Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC bool	operator== (const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC bool	operator!= (const QuaternionBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC bool	isApprox (const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3	_transformVector (const Vector3 &v) const
EIGEN_DEVICE_FUNC std::enable_if_t< internal::is_same< Scalar, NewScalarType >::value, const Quaternion< Scalar_, Options_ > & >	cast () const
EIGEN_DEVICE_FUNC std::enable_if_t<!internal::is_same< Scalar, NewScalarType >::value, Quaternion< NewScalarType > >	cast () const
Public Member Functions inherited from Eigen::RotationBase< Derived, Dim_ >
EIGEN_DEVICE_FUNC const Derived &	derived () const
EIGEN_DEVICE_FUNC Derived &	derived ()
EIGEN_DEVICE_FUNC RotationMatrixType	toRotationMatrix () const
EIGEN_DEVICE_FUNC RotationMatrixType	matrix () const
EIGEN_DEVICE_FUNC Derived	inverse () const
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
EIGEN_DEVICE_FUNC RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const
template<int Mode, int Options>
EIGEN_DEVICE_FUNC Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
template<typename OtherVectorType >
EIGEN_DEVICE_FUNC VectorType	_transformVector (const OtherVectorType &v) const

Static Public Member Functions
static EIGEN_DEVICE_FUNC Quaternion	UnitRandom ()
template<typename Derived1 , typename Derived2 >
static EIGEN_DEVICE_FUNC Quaternion	FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Static Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< Scalar_, Options_ > >
static EIGEN_DEVICE_FUNC Quaternion< Scalar >	Identity ()

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.

\geometry_module

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 \( w+xi+yj+zk \) 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

Member Typedef Documentation

AngleAxisType

template<typename Scalar_ , int Options_>

typedef Base::AngleAxisType Eigen::Quaternion< Scalar_, Options_ >::AngleAxisType

Base

template<typename Scalar_ , int Options_>

typedef QuaternionBase<Quaternion<Scalar_, Options_> > Eigen::Quaternion< Scalar_, Options_ >::Base

Coefficients

template<typename Scalar_ , int Options_>

typedef internal::traits<Quaternion>::Coefficients Eigen::Quaternion< Scalar_, Options_ >::Coefficients

Scalar

template<typename Scalar_ , int Options_>

typedef Scalar_ Eigen::Quaternion< Scalar_, Options_ >::Scalar

Member Enumeration Documentation

anonymous enum

template<typename Scalar_ , int Options_>

anonymous enum

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

Constructor & Destructor Documentation

Quaternion() [1/9]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( )

inline

Default constructor leaving the quaternion uninitialized.

{}

Quaternion() [2/9]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const Scalar &  w, const Scalar &  x, const Scalar &  y, const Scalar &  z  )

inline

Constructs and initializes the quaternion \( w+xi+yj+zk \) 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]

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

Quaternion() [3/9]

template<typename Scalar_ , int Options_>

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const Scalar &  w, const Eigen::MatrixBase< Derived > &  vec  )

inline

Constructs and initializes a quaternion from its real part as a scalar, and its imaginary part as a 3-vector [x, y, z]

      : m_coeffs(vec.x(), vec.y(), vec.z(), w) {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 3);
  }

References EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE.

Quaternion() [4/9]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const Scalar *  data )

inlineexplicit

Constructs and initialize a quaternion from the array data

: m_coeffs(data) {}

Quaternion() [5/9]

template<typename Scalar_ , int Options_>

template<class Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const QuaternionBase< Derived > &  other )

inline

Copy constructor

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

References Eigen::QuaternionBase< Quaternion< Scalar_, Options_ > >::operator=().

Quaternion() [6/9]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const AngleAxisType &  aa )

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

{ *this = aa; }

Quaternion() [7/9]

template<typename Scalar_ , int Options_>

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const MatrixBase< Derived > &  other )

inlineexplicit

Constructs and initializes a quaternion from either:

• a rotation matrix expression,
• a 4D vector expression representing quaternion coefficients in the order [x, y, z, w].

                                                                                 {
    *this = other;
  }

Quaternion() [8/9]

template<typename Scalar_ , int Options_>

template<typename OtherScalar , int OtherOptions>

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( const Quaternion< OtherScalar, OtherOptions > &  other )

inlineexplicit

Explicit copy constructor with scalar conversion

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

References Eigen::Quaternion< Scalar_, Options_ >::coeffs(), and Eigen::Quaternion< Scalar_, Options_ >::m_coeffs.

Quaternion() [9/9]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Eigen::Quaternion< Scalar_, Options_ >::Quaternion ( Quaternion< Scalar_, Options_ > &&  other )

inline

Default move constructor

      : m_coeffs(std::move(other.coeffs())) {}

Member Function Documentation

coeffs() [1/2]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Coefficients& Eigen::Quaternion< Scalar_, Options_ >::coeffs ( )

inline

{ return m_coeffs; }

References Eigen::Quaternion< Scalar_, Options_ >::m_coeffs.

Referenced by Eigen::Quaternion< Scalar_, Options_ >::Quaternion().

coeffs() [2/2]

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC const Coefficients& Eigen::Quaternion< Scalar_, Options_ >::coeffs ( ) const

inline

{ return m_coeffs; }

References Eigen::Quaternion< Scalar_, Options_ >::m_coeffs.

FromTwoVectors() [1/2]

template<typename Scalar_ , int Options_>

template<typename Derived1 , typename Derived2 >

static EIGEN_DEVICE_FUNC Quaternion Eigen::Quaternion< Scalar_, Options_ >::FromTwoVectors ( const MatrixBase< Derived1 > &  a, const MatrixBase< Derived2 > &  b  )

static

FromTwoVectors() [2/2]

template<typename Scalar_ , int Options_>

template<typename Derived1 , typename Derived2 >

EIGEN_DEVICE_FUNC Quaternion<Scalar, Options> Eigen::Quaternion< Scalar_, Options_ >::FromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)

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.

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

References a, b, and Eigen::QuaternionBase< Derived >::setFromTwoVectors().

operator=()

template<typename Scalar_ , int Options_>

EIGEN_DEVICE_FUNC Quaternion& Eigen::Quaternion< Scalar_, Options_ >::operator= ( Quaternion< Scalar_, Options_ > &&  other )

inline

Default move assignment operator

                                                                    {
    m_coeffs = std::move(other.coeffs());
    return *this;
  }

References Eigen::Quaternion< Scalar_, Options_ >::m_coeffs.

UnitRandom()

template<typename Scalar , int Options>

EIGEN_DEVICE_FUNC Quaternion< Scalar, Options > Quaternion::UnitRandom

static

Returns

a random unit quaternion following a uniform distribution law on SO(3)

Note

The implementation is based on http://planning.cs.uiuc.edu/node198.html

                                                                                      {
  EIGEN_USING_STD(sqrt)
  EIGEN_USING_STD(sin)
  EIGEN_USING_STD(cos)
  const Scalar u1 = internal::random<Scalar>(0, 1), u2 = internal::random<Scalar>(0, 2 * EIGEN_PI),
               u3 = internal::random<Scalar>(0, 2 * EIGEN_PI);
  const Scalar a = sqrt(Scalar(1) - u1), b = sqrt(u1);
  return Quaternion(a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
}

References a, b, cos(), EIGEN_PI, EIGEN_USING_STD, sin(), and sqrt().

Member Data Documentation

m_coeffs

template<typename Scalar_ , int Options_>

Coefficients Eigen::Quaternion< Scalar_, Options_ >::m_coeffs

protected

Referenced by Eigen::Quaternion< Scalar_, Options_ >::coeffs(), Eigen::Quaternion< Scalar_, Options_ >::operator=(), and Eigen::Quaternion< Scalar_, Options_ >::Quaternion().

---

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

• ForwardDeclarations.h
• Eigen/Eigen/src/Geometry/Quaternion.h