Eigen::AngleAxis< _Scalar > Class Template Reference

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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()

Inheritance diagram for Eigen::AngleAxis< _Scalar >:

List of all members.

Public Types
typedef _Scalar	Scalar
Public Member Functions
Scalar	angle () const
Scalar &	angle ()
	AngleAxis ()
template<typename Derived >
	AngleAxis (const 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)
const Vector3 &	axis () const
Vector3 &	axis ()
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, const 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)

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Member Typedef Documentation

template<typename _Scalar>

typedef _Scalar Eigen::AngleAxis< _Scalar >::Scalar

the scalar type of the coefficients

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

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Constructor & Destructor Documentation

template<typename _Scalar>

Eigen::AngleAxis< _Scalar >::AngleAxis

(

)

[inline]

Default constructor without initialization.

template<typename _Scalar>

template<typename Derived >

Eigen::AngleAxis< _Scalar >::AngleAxis	(	const 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.

template<typename _Scalar>

template<typename QuatDerived >

Eigen::AngleAxis< _Scalar >::AngleAxis

(

const QuaternionBase< QuatDerived > &

q

)

[inline, explicit]

Constructs and initialize the angle-axis rotation from a quaternion q. This function implicitly normalizes the quaternion q.

template<typename _Scalar>

template<typename Derived >

Eigen::AngleAxis< _Scalar >::AngleAxis

(

const MatrixBase< Derived > &

m

)

[inline, explicit]

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

template<typename _Scalar>

template<typename OtherScalarType >

Eigen::AngleAxis< _Scalar >::AngleAxis

(

const AngleAxis< OtherScalarType > &

other

)

[inline, explicit]

Copy constructor with scalar type conversion

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Member Function Documentation

template<typename _Scalar>

Scalar Eigen::AngleAxis< _Scalar >::angle

(

)

const [inline]

Returns:

the value of the rotation angle in radian

template<typename _Scalar>

Scalar& Eigen::AngleAxis< _Scalar >::angle

(

)

[inline]

Returns:

a read-write reference to the stored angle in radian

template<typename _Scalar>

const Vector3& Eigen::AngleAxis< _Scalar >::axis

(

)

const [inline]

Returns:

the rotation axis

template<typename _Scalar>

Vector3& Eigen::AngleAxis< _Scalar >::axis

(

)

[inline]

Returns:

a read-write reference to the stored rotation axis.

Warning:

The rotation axis must remain a unit vector.

template<typename _Scalar>

template<typename NewScalarType >

internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::AngleAxis< _Scalar >::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.

template<typename _Scalar>

AngleAxis Eigen::AngleAxis< _Scalar >::inverse

(

)

const [inline]

Returns:

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

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

template<typename _Scalar>

bool Eigen::AngleAxis< _Scalar >::isApprox	(	const AngleAxis< _Scalar > &	other,
		const 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()

template<typename _Scalar>

QuaternionType Eigen::AngleAxis< _Scalar >::operator*

(

const AngleAxis< _Scalar > &

other

)

const [inline]

Concatenates two rotations

template<typename _Scalar>

QuaternionType Eigen::AngleAxis< _Scalar >::operator*

(

const QuaternionType &

other

)

const [inline]

Concatenates two rotations

template<typename Scalar >

template<typename QuatDerived >

AngleAxis< Scalar > & Eigen::AngleAxis< Scalar >::operator=

(

const QuaternionBase< QuatDerived > &

q

)

Set *this from a unit quaternion.

The resulting axis is normalized, and the computed angle is in the [0,pi] range.

This function implicitly normalizes the quaternion q.

template<typename Scalar >

template<typename Derived >

AngleAxis< Scalar > & Eigen::AngleAxis< Scalar >::operator=

(

const MatrixBase< Derived > &

mat

)

Set *this from a 3x3 rotation matrix mat.

template<typename Scalar >

AngleAxis< Scalar >::Matrix3 Eigen::AngleAxis< Scalar >::toRotationMatrix

(

void

)

const

Constructs and

Returns:

an equivalent 3x3 rotation matrix.

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

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Friends And Related Function Documentation

template<typename _Scalar>

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:

• AngleAxis.h