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Eigen::Quaternion< Scalar, Options > Class Template Reference

Detailed Description

template<typename Scalar, int Options = AutoAlign>
class Eigen::Quaternion< Scalar, Options >

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

This is defined in the Geometry module.

#include <Eigen/Geometry>
Template Parameters
_Scalarthe scalar type, i.e., the type of the coefficients
_Optionscontrols 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
+ Inheritance diagram for Eigen::Quaternion< Scalar, Options >:

Public Member Functions

template<typename Derived1 , typename Derived2 >
Quaternion< Scalar, Options > FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
 
 Quaternion ()
 
 Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
 
 Quaternion (const Scalar *data)
 
template<class Derived >
 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)
 
- Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
Vector3 _transformVector (const Vector3 &v) const
 
internal::cast_return_type
< Quaternion< _Scalar,
_Options >, Quaternion
< NewScalarType > >::type 
cast () const
 
const internal::traits
< Quaternion< _Scalar,
_Options > >::Coefficients & 
coeffs () const
 
internal::traits< Quaternion
< _Scalar, _Options >
>::Coefficients & 
coeffs ()
 
Quaternion< Scalarconjugate () const
 
Scalar dot (const QuaternionBase< OtherDerived > &other) const
 
Quaternion< Scalarinverse () const
 
bool isApprox (const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
Scalar norm () const
 
void normalize ()
 
Quaternion< Scalarnormalized () const
 
Quaternion< _Scalar, _Options > & setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
 
QuaternionBasesetIdentity ()
 
Scalar squaredNorm () const
 
Matrix3 toRotationMatrix () const
 
const VectorBlock< const
Coefficients, 3 > 
vec () const
 
VectorBlock< Coefficients, 3 > vec ()
 
Scalar w () const
 
Scalarw ()
 
Scalar x () const
 
Scalarx ()
 
Scalar y () const
 
Scalary ()
 
Scalar z () const
 
Scalarz ()
 
- Public Member Functions inherited from Eigen::RotationBase< Quaternion< _Scalar, _Options >, 3 >
Quaternion< _Scalar, _Options > inverse () const
 
RotationMatrixType matrix () const
 
Transform< Scalar, Dim, Isometry > operator* (const Translation< Scalar, Dim > &t) const
 
RotationMatrixType operator* (const UniformScaling< Scalar > &s) const
 
internal::rotation_base_generic_product_selector
< Quaternion< _Scalar,
_Options >, OtherDerived,
OtherDerived::IsVectorAtCompileTime >
::ReturnType 
operator* (const EigenBase< OtherDerived > &e) const
 
Transform< Scalar, Dim, Mode > operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
 
RotationMatrixType toRotationMatrix () const
 

Static Public Member Functions

static Quaternion UnitRandom ()
 
- Static Public Member Functions inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
static Quaternion< ScalarIdentity ()
 

Additional Inherited Members

- Public Types inherited from Eigen::QuaternionBase< Quaternion< _Scalar, _Options > >
typedef AngleAxis< ScalarAngleAxisType
 
typedef Matrix< Scalar, 3, 3 > Matrix3
 
typedef Matrix< Scalar, 3, 1 > Vector3
 
- Public Types inherited from Eigen::RotationBase< Quaternion< _Scalar, _Options >, 3 >
typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
 
typedef internal::traits
< Quaternion< _Scalar,
_Options > >::Scalar 
Scalar
 

Constructor & Destructor Documentation

template<typename Scalar , int Options = AutoAlign>
Eigen::Quaternion< Scalar, Options >::Quaternion ( )
inline

Default constructor leaving the quaternion uninitialized.

template<typename Scalar , int Options = AutoAlign>
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]
template<typename Scalar , int Options = AutoAlign>
Eigen::Quaternion< Scalar, Options >::Quaternion ( const Scalar *  data)
inlineexplicit

Constructs and initialize a quaternion from the array data

template<typename Scalar , int Options = AutoAlign>
template<class Derived >
Eigen::Quaternion< Scalar, Options >::Quaternion ( const QuaternionBase< Derived > &  other)
inline

Copy constructor

template<typename Scalar , int Options = AutoAlign>
Eigen::Quaternion< Scalar, Options >::Quaternion ( const AngleAxisType aa)
inlineexplicit

Constructs and initializes a quaternion from the angle-axis aa

template<typename Scalar , int Options = AutoAlign>
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.
template<typename Scalar , int Options = AutoAlign>
template<typename OtherScalar , int OtherOptions>
Eigen::Quaternion< Scalar, Options >::Quaternion ( const Quaternion< OtherScalar, OtherOptions > &  other)
inlineexplicit

Explicit copy constructor with scalar conversion

Member Function Documentation

template<typename Scalar , int Options = AutoAlign>
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.

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

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