template<typename _Scalar, int _Options>
class Eigen::Quaternion< _Scalar, _Options >
The quaternion class used to represent 3D orientations and rotations.
This is defined in the Geometry module.
#include <Eigen/Geometry>
- Template Parameters
-
_Scalar | the scalar type, i.e., the type of the coefficients |
_Options | controls the memory alignment of the coefficients. Can be # AutoAlign or # DontAlign. Default is AutoAlign. |
This class represents a quaternion \( w+xi+yj+zk \) that is a convenient representation of orientations and rotations of objects in three dimensions. Compared to other representations like Euler angles or 3x3 matrices, quaternions offer the following advantages:
- compact storage (4 scalars)
- efficient to compose (28 flops),
- stable spherical interpolation
The following two typedefs are provided for convenience:
- Warning
- Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
- See also
- class AngleAxis, class Transform
|
template<typename Derived1, typename Derived2> |
Quaternion< Scalar, Options > | FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b) |
Quaternion< _Scalar, _Options > & | operator*= (const QuaternionBase< OtherDerived > &q) |
| Quaternion () |
| Quaternion (const AngleAxisType &aa) |
template<typename Derived> |
| Quaternion (const MatrixBase< Derived > &other) |
template<typename OtherScalar, int OtherOptions> |
| Quaternion (const Quaternion< OtherScalar, OtherOptions > &other) |
template<class Derived> |
| Quaternion (const QuaternionBase< Derived > &other) |
| Quaternion (const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z) |
| Quaternion (const Scalar *data) |
Vector3 | _transformVector (const Vector3 &v) const |
internal::traits< Quaternion< _Scalar, _Options > >::Scalar | angularDistance (const QuaternionBase< OtherDerived > &other) const |
internal::cast_return_type< Quaternion< _Scalar, _Options >, Quaternion< NewScalarType > >::type | cast () const |
internal::traits< Quaternion< _Scalar, _Options > >::Coefficients & | coeffs () |
const internal::traits< Quaternion< _Scalar, _Options > >::Coefficients & | coeffs () const |
Quaternion< Scalar > | conjugate () const |
Scalar | dot (const QuaternionBase< OtherDerived > &other) const |
Quaternion< Scalar > | inverse () const |
bool | isApprox (const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
Scalar | norm () const |
void | normalize () |
Quaternion< Scalar > | normalized () const |
bool | operator!= (const QuaternionBase< OtherDerived > &other) const |
Quaternion< typename internal::traits< Quaternion< _Scalar, _Options > >::Scalar > | operator* (const QuaternionBase< OtherDerived > &other) const |
Quaternion< _Scalar, _Options > & | operator= (const MatrixBase< MatrixDerived > &xpr) |
bool | operator== (const QuaternionBase< OtherDerived > &other) const |
Quaternion< _Scalar, _Options > & | setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b) |
QuaternionBase & | setIdentity () |
Quaternion< typename internal::traits< Quaternion< _Scalar, _Options > >::Scalar > | slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const |
Scalar | squaredNorm () const |
Matrix3 | toRotationMatrix () const |
VectorBlock< Coefficients, 3 > | vec () |
const VectorBlock< const Coefficients, 3 > | vec () const |
NonConstCoeffReturnType | w () |
CoeffReturnType | w () const |
NonConstCoeffReturnType | x () |
CoeffReturnType | x () const |
NonConstCoeffReturnType | y () |
CoeffReturnType | y () const |
NonConstCoeffReturnType | z () |
CoeffReturnType | z () const |
Derived | inverse () const |
RotationMatrixType | matrix () const |
template<typename OtherDerived> |
internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType | operator* (const EigenBase< OtherDerived > &e) const |
template<int Mode, int Options> |
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 |
RotationMatrixType | toRotationMatrix () const |
template<typename _Scalar, int _Options>
template<typename Derived1, typename Derived2>
Returns a quaternion representing a rotation between the two arbitrary vectors a and b. In other words, the built rotation represent a rotation sending the line of direction a to the line of direction b, both lines passing through the origin.
- Returns
- resulting quaternion
Note that the two input vectors do not have to be normalized, and do not need to have the same norm.