AngleAxis< _Scalar > Class Template Reference [Geometry module]

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

List of all members.

Public Types
enum	{ Dim }
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Quaternion< Scalar >	QuaternionType
typedef _Scalar	Scalar
typedef Matrix< Scalar, 3, 1 >	Vector3
Public Member Functions
Scalar	angle () const
Scalar &	angle ()
	AngleAxis ()
template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)
template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)
template<typename Derived >
	AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
	AngleAxis (const QuaternionType &q)
Vector3 &	axis ()
const Vector3 &	axis () const
template<typename NewScalarType >
ei_cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type	cast () const
template<typename Derived >
AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)
AngleAxis	inverse () const
bool	isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
QuaternionType	operator* (const AngleAxis &other) const
Vector3	operator* (const Vector3 &other) const
Matrix3	operator* (const Matrix3 &other) const
QuaternionType	operator* (const QuaternionType &other) const
AngleAxis &	operator= (const QuaternionType &q)
template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)
Matrix3	toRotationMatrix (void) const
Protected Attributes
Scalar	m_angle
Vector3	m_axis
Friends
QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)
Matrix3	operator* (const Matrix3 &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.

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

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

---

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.

AngleAxis

(

const QuaternionType &

q

)

[inline]

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

AngleAxis

(

const MatrixBase< Derived > &

m

)

[inline, explicit]

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

AngleAxis

(

const AngleAxis< OtherScalarType > &

other

)

[inline, explicit]

Copy constructor with scalar type conversion

---

Member Function Documentation

ei_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

(

void

)

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 = precision<Scalar>()
	)			const [inline]

Returns:

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

See also:

MatrixBase::isApprox()

Matrix3 operator*

(

const Matrix3 &

other

)

const [inline]

Concatenates two rotations

Vector3 operator*

(

const Vector3 &

other

)

const [inline]

Applies rotation to vector

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 QuaternionType &

q

)

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

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

Matrix3 operator*	(	const Matrix3 &	a,
		const AngleAxis< _Scalar > &	b
	)			[friend]

Concatenates two rotations

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