Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...
#include <AngleAxis.h>
Public Types | |
enum | { Dim } |
enum | |
typedef Matrix< Scalar, 3, 3 > | Matrix3 |
typedef Quaternion< Scalar > | QuaternionType |
typedef Matrix< Scalar, Dim, Dim > | RotationMatrixType |
typedef _Scalar | Scalar |
typedef Matrix< Scalar, 3, 1 > | Vector3 |
typedef Matrix< Scalar, Dim, 1 > | VectorType |
Public Member Functions | |
VectorType | _transformVector (const OtherVectorType &v) const |
Scalar | angle () const |
Scalar & | angle () |
AngleAxis () | |
template<typename Derived > | |
AngleAxis (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 |
const AngleAxis< _Scalar > & | derived () const |
AngleAxis< _Scalar > & | derived () |
template<typename Derived > | |
AngleAxis & | fromRotationMatrix (const MatrixBase< Derived > &m) |
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 |
Transform< Scalar, Dim, Isometry > | operator* (const Translation< Scalar, Dim > &t) const |
RotationMatrixType | operator* (const UniformScaling< Scalar > &s) const |
internal::rotation_base_generic_product_selector < AngleAxis< _Scalar > , OtherDerived, OtherDerived::IsVectorAtCompileTime > ::ReturnType | operator* (const EigenBase< OtherDerived > &e) const |
Transform< Scalar, Dim, Mode > | operator* (const Transform< Scalar, Dim, Mode, Options > &t) 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 |
Static Public Member Functions | |
static const AngleAxis | Identity () |
Protected Attributes | |
Scalar | m_angle |
Vector3 | m_axis |
Friends | |
RotationMatrixType | operator* (const EigenBase< OtherDerived > &l, const AngleAxis< _Scalar > &r) |
Transform< Scalar, Dim, Affine > | operator* (const DiagonalMatrix< Scalar, Dim > &l, const AngleAxis< _Scalar > &r) |
QuaternionType | operator* (const QuaternionType &a, const AngleAxis &b) |
Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.
This is defined in the Geometry module.
#include <Eigen/Geometry>
_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:
8.67e-08 0 1 0.969 -0.249 -5.36e-09 0.249 0.969 1.13e-07 is unitary: 1
typedef Quaternion<Scalar> QuaternionType |
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 >.
typedef Matrix<Scalar,Dim,1> VectorType [inherited] |
anonymous enum [inherited] |
AngleAxis | ( | ) | [inline] |
Default constructor without initialization.
Referenced by AngleAxis< _Scalar >::Identity(), and AngleAxis< _Scalar >::inverse().
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 QuaternionBase< QuatDerived > & | q | ) | [inline, explicit] |
Constructs and initialize the angle-axis rotation from a quaternion q.
References q.
AngleAxis | ( | const MatrixBase< Derived > & | m | ) | [inline, explicit] |
Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.
Copy constructor with scalar type conversion
References AngleAxis< _Scalar >::angle(), AngleAxis< _Scalar >::axis(), AngleAxis< _Scalar >::m_angle, and AngleAxis< _Scalar >::m_axis.
VectorType _transformVector | ( | const OtherVectorType & | v | ) | const [inline, inherited] |
References AngleAxis< _Scalar >::m_angle.
Referenced by AngleAxis< _Scalar >::AngleAxis(), and QuaternionBase< Derived >::operator=().
References AngleAxis< _Scalar >::m_angle.
References AngleAxis< _Scalar >::m_axis.
Referenced by AngleAxis< _Scalar >::AngleAxis(), and QuaternionBase< Derived >::operator=().
References AngleAxis< _Scalar >::m_axis.
*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< Scalar > & fromRotationMatrix | ( | const MatrixBase< Derived > & | m | ) |
Sets *this
from a 3x3 rotation matrix.
References AngleAxis< _Scalar >::AngleAxis().
Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.
References AngleAxis< _Scalar >::AngleAxis(), AngleAxis< _Scalar >::m_angle, and AngleAxis< _Scalar >::m_axis.
bool isApprox | ( | const AngleAxis< _Scalar > & | other, |
typename NumTraits< Scalar >::Real | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inline] |
true
if *this
is approximately equal to other, within the precision determined by prec.References AngleAxis< _Scalar >::m_angle, and AngleAxis< _Scalar >::m_axis.
RotationMatrixType matrix | ( | ) | const [inline, inherited] |
Transform<Scalar,Dim,Isometry> operator* | ( | const Translation< Scalar, Dim > & | t | ) | const [inline, inherited] |
*this
with a translation t RotationMatrixType operator* | ( | const UniformScaling< Scalar > & | s | ) | const [inline, inherited] |
*this
with a uniform scaling s internal::rotation_base_generic_product_selector<AngleAxis< _Scalar > ,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType operator* | ( | const EigenBase< OtherDerived > & | e | ) | const [inline, inherited] |
*this
with a generic expression e e can be:Transform<Scalar,Dim,Mode> operator* | ( | const Transform< Scalar, Dim, Mode, Options > & | t | ) | const [inline, inherited] |
*this
with a transformation t 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 QuaternionBase< QuatDerived > & | q | ) |
Set *this
from a unit quaternion. The axis is normalized.
References acos(), sqrt(), QuaternionBase< Derived >::vec(), and QuaternionBase< Derived >::w().
AngleAxis< Scalar > & operator= | ( | const MatrixBase< Derived > & | mat | ) |
Set *this
from a 3x3 rotation matrix mat.
AngleAxis< Scalar >::Matrix3 toRotationMatrix | ( | void | ) | const |
Constructs and
Reimplemented from RotationBase< AngleAxis< _Scalar >, 3 >.
References PlainObjectBase< Derived >::coeffRef(), cos(), MatrixBase< Derived >::diagonal(), and sin().
RotationMatrixType operator* | ( | const EigenBase< OtherDerived > & | l, |
const AngleAxis< _Scalar > & | r | ||
) | [friend, inherited] |
Transform<Scalar,Dim,Affine> operator* | ( | const DiagonalMatrix< Scalar, Dim > & | l, |
const AngleAxis< _Scalar > & | r | ||
) | [friend, inherited] |
QuaternionType operator* | ( | const QuaternionType & | a, |
const AngleAxis< _Scalar > & | b | ||
) | [friend] |
Concatenates two rotations