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:
Quaternionf
for float
Quaterniond
for double
- 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 & | operator= (Quaternion &&other) EIGEN_NOEXCEPT_IF(std |
|
| 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) |
|
| Quaternion (Quaternion &&other) EIGEN_NOEXCEPT_IF(std |
|
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 QuaternionBase< OtherDerived > &q) |
|
Quaternion< Scalar_, Options_ > & | operator= (const AngleAxisType &aa) |
|
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.