Eigen::Quaternion< Scalar_, Options_ > Class Template Reference

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

Inheritance diagram for Eigen::Quaternion< Scalar_, Options_ >:

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

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

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

Definition/implementation of Quaternion<Scalar> This is defined in the Geometry module.

#include <Eigen/Geometry> 

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

Definition at line 275 of file Quaternion.h.

Member Typedef Documentation

AngleAxisType

template<typename Scalar_ , int Options_>

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

Definition at line 287 of file Quaternion.h.

Base

template<typename Scalar_ , int Options_>

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

Definition at line 278 of file Quaternion.h.

Coefficients

template<typename Scalar_ , int Options_>

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

Definition at line 286 of file Quaternion.h.

Scalar

template<typename Scalar_ , int Options_>

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

Definition at line 281 of file Quaternion.h.

Member Enumeration Documentation

anonymous enum

template<typename Scalar_ , int Options_>

anonymous enum

Definition at line 279 of file Quaternion.h.

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

Constructor & Destructor Documentation

Quaternion() [1/9]

template<typename Scalar_ , int Options_>

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

inline

Default constructor leaving the quaternion uninitialized.

Definition at line 290 of file Quaternion.h.

{}

Quaternion() [2/9]

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 \( w+xi+yj+zk \) 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]

Definition at line 299 of file Quaternion.h.

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

Quaternion() [3/9]

template<typename Scalar_ , int Options_>

template<typename Derived >

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]

Definition at line 305 of file Quaternion.h.

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

Quaternion() [4/9]

template<typename Scalar_ , int Options_>

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

inlineexplicit

Constructs and initialize a quaternion from the array data

Definition at line 311 of file Quaternion.h.

: m_coeffs(data) {}

Quaternion() [5/9]

template<typename Scalar_ , int Options_>

template<class Derived >

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

inline

Copy constructor

Definition at line 314 of file Quaternion.h.

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

Quaternion() [6/9]

template<typename Scalar_ , int Options_>

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

inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

Definition at line 317 of file Quaternion.h.

{ *this = aa; }

Quaternion() [7/9]

template<typename Scalar_ , int Options_>

template<typename Derived >

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].

Definition at line 324 of file Quaternion.h.

{ *this = other; }

Quaternion() [8/9]

template<typename Scalar_ , int Options_>

template<typename OtherScalar , int OtherOptions>

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

inlineexplicit

Explicit copy constructor with scalar conversion

Definition at line 328 of file Quaternion.h.

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

Quaternion() [9/9]

template<typename Scalar_ , int Options_>

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

inline

Default move constructor

Definition at line 333 of file Quaternion.h.

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

Member Function Documentation

coeffs() [1/2]

template<typename Scalar_ , int Options_>

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

inline

Definition at line 349 of file Quaternion.h.

{ return m_coeffs;}

coeffs() [2/2]

template<typename Scalar_ , int Options_>

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

inline

Definition at line 350 of file Quaternion.h.

{ return m_coeffs;}

FromTwoVectors() [1/2]

template<typename Scalar_ , int Options_>

template<typename Derived1 , typename Derived2 >

static 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 >

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.

Definition at line 711 of file Quaternion.h.

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

operator=()

template<typename Scalar_ , int Options_>

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

inline

Default move assignment operator

Definition at line 338 of file Quaternion.h.

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

UnitRandom()

template<typename Scalar , int Options>

Quaternion< Scalar, Options > Eigen::Quaternion< Scalar, Options >::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

Definition at line 685 of file Quaternion.h.

{
  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));
}

Member Data Documentation

m_coeffs

template<typename Scalar_ , int Options_>

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

protected

Definition at line 359 of file Quaternion.h.

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

• ForwardDeclarations.h
• Quaternion.h