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Eigen  3.2.5
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AngleAxis< _Scalar > Class Template Reference
[Geometry module]

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

Inheritance diagram for AngleAxis< _Scalar >:

List of all members.

Public Types

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

Public Member Functions

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

Friends

Transform< Scalar, Dim, Affine > operator* (const DiagonalMatrix< Scalar, Dim > &l, const AngleAxis< _Scalar > &r)
RotationMatrixType operator* (const EigenBase< OtherDerived > &l, const AngleAxis< _Scalar > &r)
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:

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 Matrix<Scalar,Dim,Dim> RotationMatrixType [inherited]

corresponding linear transformation matrix type

typedef _Scalar Scalar

the scalar type of the coefficients

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


Constructor & Destructor Documentation

AngleAxis (  )  [inline]

Default constructor without initialization.

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

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.
AngleAxis ( const QuaternionBase< QuatDerived > &  q  )  [inline, explicit]

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

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 >.

References AngleAxis< _Scalar >::AngleAxis().

bool 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()
RotationMatrixType matrix (  )  const [inline, inherited]
Returns:
an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.
Transform<Scalar,Dim,Mode> operator* ( const Transform< Scalar, Dim, Mode, Options > &  t  )  const [inline, inherited]
Returns:
the concatenation of the rotation *this with a transformation t
internal::rotation_base_generic_product_selector<AngleAxis< _Scalar > ,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType operator* ( const EigenBase< OtherDerived > &  e  )  const [inline, inherited]
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
RotationMatrixType operator* ( const UniformScaling< Scalar > &  s  )  const [inline, inherited]
Returns:
the concatenation of the rotation *this with a uniform scaling s
Transform<Scalar,Dim,Isometry> operator* ( const Translation< Scalar, Dim > &  t  )  const [inline, inherited]
Returns:
the concatenation of the rotation *this with a translation t
QuaternionType operator* ( const QuaternionType other  )  const [inline]

Concatenates two rotations

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

Concatenates two rotations

AngleAxis< Scalar > & operator= ( const MatrixBase< Derived > &  mat  )  [inline]

Set *this from a 3x3 rotation matrix mat.

AngleAxis< Scalar > & operator= ( const QuaternionBase< QuatDerived > &  q  )  [inline]

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.

References QuaternionBase< Derived >::vec(), and QuaternionBase< Derived >::w().

AngleAxis< Scalar >::Matrix3 toRotationMatrix ( void   )  const [inline]

Constructs and

Returns:
an equivalent 3x3 rotation matrix.

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

References MatrixBase< Derived >::diagonal().


Friends And Related Function Documentation

Transform<Scalar,Dim,Affine> operator* ( const DiagonalMatrix< Scalar, Dim > &  l,
const AngleAxis< _Scalar > &  r 
) [friend, inherited]
Returns:
the concatenation of a scaling l with the rotation r
RotationMatrixType operator* ( const EigenBase< OtherDerived > &  l,
const AngleAxis< _Scalar > &  r 
) [friend, inherited]
Returns:
the concatenation of a linear transformation l with the rotation r
QuaternionType operator* ( const QuaternionType a,
const AngleAxis< _Scalar > &  b 
) [friend]

Concatenates two rotations


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