AngleAxis< _Scalar > Class Template Reference
[Geometry_Module]

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

#include <AngleAxis.h>

Inheritance diagram for AngleAxis< _Scalar >:

[legend]

List of all members.

Public Types
enum	{ Dim = 3 }
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Quaternion< Scalar >	QuaternionType
typedef _Scalar	Scalar
typedef Matrix< Scalar, 3, 1 >	Vector3
Public Member Functions
Scalar &	angle ()
Scalar	angle () const
template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)
template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)
	AngleAxis (const QuaternionType &q)
template<typename Derived >
	AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
	AngleAxis ()
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
Vector3	operator* (const Vector3 &other) const
Matrix3	operator* (const Matrix3 &other) const
QuaternionType	operator* (const QuaternionType &other) const
QuaternionType	operator* (const AngleAxis &other) const
template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)
AngleAxis &	operator= (const QuaternionType &q)
Matrix3	toRotationMatrix (void) const
Protected Attributes
Scalar	m_angle
Vector3	m_axis
Private Types
typedef RotationBase < AngleAxis< _Scalar >, 3 >	Base
Friends
Matrix3	operator* (const Matrix3 &a, const AngleAxis &b)
QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)

---

Detailed Description

template<typename _Scalar>
class AngleAxis< _Scalar >

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

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

AngleAxisForEuler How to define a rotation from Euler-angles

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

Output:

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()

Definition at line 60 of file AngleAxis.h.

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Member Typedef Documentation

template<typename _Scalar>

typedef RotationBase<AngleAxis<_Scalar>,3> AngleAxis< _Scalar >::Base [private]

Definition at line 62 of file AngleAxis.h.

template<typename _Scalar>

typedef Matrix<Scalar,3,3> AngleAxis< _Scalar >::Matrix3

Definition at line 71 of file AngleAxis.h.

template<typename _Scalar>

typedef Quaternion<Scalar> AngleAxis< _Scalar >::QuaternionType

Definition at line 73 of file AngleAxis.h.

template<typename _Scalar>

typedef _Scalar AngleAxis< _Scalar >::Scalar

the scalar type of the coefficients

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

Definition at line 70 of file AngleAxis.h.

template<typename _Scalar>

typedef Matrix<Scalar,3,1> AngleAxis< _Scalar >::Vector3

Definition at line 72 of file AngleAxis.h.

---

Member Enumeration Documentation

template<typename _Scalar>

anonymous enum

Enumerator:

Dim

Definition at line 68 of file AngleAxis.h.

---

Constructor & Destructor Documentation

template<typename _Scalar>

AngleAxis< _Scalar >::AngleAxis

(

)

[inline]

Default constructor without initialization.

Definition at line 83 of file AngleAxis.h.

template<typename _Scalar>

template<typename Derived >

AngleAxis< _Scalar >::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.

Definition at line 87 of file AngleAxis.h.

template<typename _Scalar>

AngleAxis< _Scalar >::AngleAxis

(

const QuaternionType &

q

)

[inline]

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

Definition at line 89 of file AngleAxis.h.

template<typename _Scalar>

template<typename Derived >

AngleAxis< _Scalar >::AngleAxis

(

const MatrixBase< Derived > &

m

)

[inline, explicit]

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

Definition at line 92 of file AngleAxis.h.

template<typename _Scalar>

template<typename OtherScalarType >

AngleAxis< _Scalar >::AngleAxis

(

const AngleAxis< OtherScalarType > &

other

)

[inline, explicit]

Copy constructor with scalar type conversion

Definition at line 147 of file AngleAxis.h.

---

Member Function Documentation

template<typename _Scalar>

Scalar& AngleAxis< _Scalar >::angle

(

)

[inline]

Definition at line 95 of file AngleAxis.h.

template<typename _Scalar>

Scalar AngleAxis< _Scalar >::angle

(

)

const [inline]

Definition at line 94 of file AngleAxis.h.

template<typename _Scalar>

Vector3& AngleAxis< _Scalar >::axis

(

)

[inline]

Definition at line 98 of file AngleAxis.h.

template<typename _Scalar>

const Vector3& AngleAxis< _Scalar >::axis

(

)

const [inline]

Definition at line 97 of file AngleAxis.h.

template<typename _Scalar>

template<typename NewScalarType >

ei_cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type 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.

Definition at line 142 of file AngleAxis.h.

template<typename _Scalar>

template<typename Derived >

AngleAxis& AngleAxis< _Scalar >::fromRotationMatrix

(

const MatrixBase< Derived > &

m

)

[inline]

template<typename _Scalar>

AngleAxis AngleAxis< _Scalar >::inverse

(

)

const [inline]

Returns:

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

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

Definition at line 125 of file AngleAxis.h.

template<typename _Scalar>

bool AngleAxis< _Scalar >::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()

Definition at line 157 of file AngleAxis.h.

template<typename _Scalar>

Vector3 AngleAxis< _Scalar >::operator*

(

const Vector3 &

other

)

const [inline]

Applies rotation to vector

Definition at line 121 of file AngleAxis.h.

template<typename _Scalar>

Matrix3 AngleAxis< _Scalar >::operator*

(

const Matrix3 &

other

)

const [inline]

Concatenates two rotations

Definition at line 113 of file AngleAxis.h.

template<typename _Scalar>

QuaternionType AngleAxis< _Scalar >::operator*

(

const QuaternionType &

other

)

const [inline]

Concatenates two rotations

Definition at line 105 of file AngleAxis.h.

template<typename _Scalar>

QuaternionType AngleAxis< _Scalar >::operator*

(

const AngleAxis< _Scalar > &

other

)

const [inline]

Concatenates two rotations

Definition at line 101 of file AngleAxis.h.

template<typename Scalar >

template<typename Derived >

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

(

const MatrixBase< Derived > &

mat

)

[inline]

Set *this from a 3x3 rotation matrix mat.

Definition at line 192 of file AngleAxis.h.

template<typename Scalar >

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

(

const QuaternionType &

q

)

[inline]

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

Definition at line 172 of file AngleAxis.h.

template<typename Scalar >

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

(

void

)

const [inline]

Constructs and

Returns:

an equivalent 3x3 rotation matrix.

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

Definition at line 203 of file AngleAxis.h.

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Friends And Related Function Documentation

template<typename _Scalar>

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

Concatenates two rotations

Definition at line 117 of file AngleAxis.h.

template<typename _Scalar>

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

Concatenates two rotations

Definition at line 109 of file AngleAxis.h.

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Member Data Documentation

template<typename _Scalar>

Scalar AngleAxis< _Scalar >::m_angle [protected]

Definition at line 78 of file AngleAxis.h.

template<typename _Scalar>

Vector3 AngleAxis< _Scalar >::m_axis [protected]

Definition at line 77 of file AngleAxis.h.

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

• AngleAxis.h