AngleAxis< _Scalar > Class Template Reference

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

#include <AngleAxis.h>

Inheritance diagram for AngleAxis< _Scalar >:

Public Types
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef _Scalar	Scalar

Public Member Functions
	AngleAxis ()
template<typename OtherScalarType>
	AngleAxis (const AngleAxis< OtherScalarType > &other)
template<typename Derived>
	AngleAxis (const MatrixBase< Derived > &m)
template<typename QuatDerived>
	AngleAxis (const QuaternionBase< QuatDerived > &q)
template<typename Derived>
	AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)
template<typename NewScalarType>
internal::cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type	cast () const
template<typename Derived>
AngleAxis< Scalar > &	fromRotationMatrix (const MatrixBase< Derived > &mat)
	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
RotationMatrixType	matrix () const
RotationMatrixType	matrix () const
QuaternionType	operator* (const AngleAxis &other) const
internal::rotation_base_generic_product_selector< AngleAxis< _Scalar >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const
QuaternionType	operator* (const QuaternionType &other) const
Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
template<typename Derived>
AngleAxis< Scalar > &	operator= (const MatrixBase< Derived > &mat)
template<typename QuatDerived>
AngleAxis< Scalar > &	operator= (const QuaternionBase< QuatDerived > &q)
Matrix3	toRotationMatrix (void) const

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

RotationMatrixType [1/2]

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

RotationMatrixType [2/2]

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

Scalar

template<typename _Scalar>

typedef _Scalar Scalar

the scalar type of the coefficients

Constructor & Destructor Documentation

AngleAxis() [1/5]

template<typename _Scalar>

AngleAxis ( )

inline

Default constructor without initialization.

Referenced by AngleAxis< float >::inverse().

AngleAxis() [2/5]

template<typename _Scalar>

template<typename Derived>

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() [3/5]

template<typename _Scalar>

template<typename QuatDerived>

AngleAxis ( const QuaternionBase< QuatDerived > & q )

inlineexplicit

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

AngleAxis() [4/5]

template<typename _Scalar>

template<typename Derived>

AngleAxis ( const MatrixBase< Derived > & m )

inlineexplicit

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

AngleAxis() [5/5]

template<typename _Scalar>

template<typename OtherScalarType>

AngleAxis ( const AngleAxis< OtherScalarType > & other )

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

cast()

template<typename _Scalar>

template<typename NewScalarType>

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.

Referenced by AngleAxis< float >::AngleAxis().

inverse()

template<typename _Scalar>

AngleAxis inverse ( ) const

inline

Returns

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

isApprox()

template<typename _Scalar>

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()

matrix() [1/2]

RotationMatrixType matrix ( ) const

inlineinherited

Returns

an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

matrix() [2/2]

RotationMatrixType matrix ( ) const

inlineinherited

Returns

an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

operator*() [1/6]

template<typename _Scalar>

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

inline

Concatenates two rotations

operator*() [2/6]

template<typename _Scalar>

internal::rotation_base_generic_product_selector< AngleAxis< _Scalar >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType operator* ( const EigenBase< OtherDerived > & e ) const

inline

Returns

the concatenation of the rotation *this with a generic expression e e can be:

• a DimxDim linear transformation matrix
• a DimxDim diagonal matrix (axis aligned scaling)
• a vector of size Dim

operator*() [3/6]

template<typename _Scalar>

QuaternionType operator* ( const QuaternionType & other ) const

inline

Concatenates two rotations

operator*() [4/6]

template<typename _Scalar>

Transform< Scalar, Dim, Mode > operator* ( const Transform< Scalar, Dim, Mode, Options > & t ) const

inline

Returns

the concatenation of the rotation *this with a transformation t

operator*() [5/6]

template<typename _Scalar>

Transform< Scalar, Dim, Isometry > operator* ( const Translation< Scalar, Dim > & t ) const

inline

Returns

the concatenation of the rotation *this with a translation t

operator*() [6/6]

template<typename _Scalar>

RotationMatrixType operator* ( const UniformScaling< Scalar > & s ) const

inline

Returns

the concatenation of the rotation *this with a uniform scaling s

operator=() [1/2]

template<typename _Scalar>

template<typename Derived>

AngleAxis< Scalar > & operator=

(

const MatrixBase< Derived > &

mat

)

Set *this from a 3x3 rotation matrix mat.

operator=() [2/2]

template<typename _Scalar>

template<typename QuatDerived>

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.

toRotationMatrix()

template<typename Scalar>

AngleAxis< Scalar >::Matrix3 toRotationMatrix

(

void

)

const

Constructs and

Returns

an equivalent 3x3 rotation matrix.

References MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::diagonal().

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

• ForwardDeclarations.h
• AngleAxis.h