AngleAxis< _Scalar > Class Template Reference

Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...

Inheritance diagram for AngleAxis< _Scalar >:

Public Types
typedef _Scalar	Scalar

Public Member Functions
	AngleAxis ()
template<typename Derived >
	AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
template<typename QuatDerived >
	AngleAxis (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)
template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)
template<typename NewScalarType >
internal::cast_return_type < AngleAxis, AngleAxis < NewScalarType > >::type	cast () const
template<typename Derived >
AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)
	Sets *this from a 3x3 rotation matrix.
AngleAxis	inverse () const
bool	isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
QuaternionType	operator* (const AngleAxis &other) const
QuaternionType	operator* (const QuaternionType &other) const
template<class QuatDerived >
AngleAxis &	operator= (const QuaternionBase< QuatDerived > &q)
template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)
Matrix3	toRotationMatrix (void) const

Friends
QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)

Detailed Description

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >

Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.

This is defined in the Geometry module.

#include <Eigen/Geometry> 

Parameters

_Scalar

the scalar type, i.e., the type of the coefficients.

Warning

When setting up an AngleAxis object, the axis vector must be normalized.

The following two typedefs are provided for convenience:

• AngleAxisf for float
• AngleAxisd for double

Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily mimic Euler-angles. Here is an example:

Matrix3f m;
m = AngleAxisf(0.25*M_PI, Vector3f::UnitX())
  * AngleAxisf(0.5*M_PI,  Vector3f::UnitY())
  * AngleAxisf(0.33*M_PI, Vector3f::UnitZ());
cout << m << endl << "is unitary: " << m.isUnitary() << endl;

Output:

1.19e-07        0        1
   0.969   -0.249        0
   0.249    0.969 1.19e-07
is unitary: 1

Note

This class is not aimed to be used to store a rotation transformation, but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) and transformation objects.

See Also

class Quaternion, class Transform, MatrixBase::UnitX()

Member Typedef Documentation

typedef _Scalar Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

AngleAxis ( )

inline

Default constructor without initialization.

AngleAxis ( Scalar  angle, const MatrixBase< Derived > &  axis  )

inline

Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.

Warning

If the axis vector is not normalized, then the angle-axis object represents an invalid rotation.

AngleAxis ( const QuaternionBase< QuatDerived > &  q )

inlineexplicit

Constructs and initialize the angle-axis rotation from a quaternion q.

AngleAxis ( const MatrixBase< Derived > &  m )

inlineexplicit

Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.

AngleAxis ( const AngleAxis< OtherScalarType > &  other )

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast ( ) const

inline

Returns

*this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

AngleAxis inverse ( ) const

inline

Returns

the inverse rotation, i.e., an angle-axis with opposite rotation angle

Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.

bool isApprox ( const AngleAxis< _Scalar > &  other, typename NumTraits< Scalar >::Real  prec = NumTraits<Scalar>::dummy_precision()  ) const

inline

Returns

true if *this is approximately equal to other, within the precision determined by prec.

See Also

MatrixBase::isApprox()

QuaternionType operator* ( const AngleAxis< _Scalar > &  other ) const

inline

Concatenates two rotations

QuaternionType operator* ( const QuaternionType &  other ) const

inline

Concatenates two rotations

AngleAxis< Scalar > & operator=

(

const QuaternionBase< QuatDerived > &

q

)

Set *this from a unit quaternion. The axis is normalized.

Warning

As any other method dealing with quaternion, if the input quaternion is not normalized then the result is undefined.

AngleAxis< Scalar > & operator=

(

const MatrixBase< Derived > &

mat

)

Set *this from a 3x3 rotation matrix mat.

AngleAxis< Scalar >::Matrix3 toRotationMatrix

(

void

)

const

Constructs and

Returns

an equivalent 3x3 rotation matrix.

Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.

Friends And Related Function Documentation

QuaternionType operator* ( const QuaternionType &  a, const AngleAxis< _Scalar > &  b  )

friend

Concatenates two rotations

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