The quaternion class used to represent 3D orientations and rotations. More...
#include <Quaternion.h>
Public Types | |
typedef Base::AngleAxisType | AngleAxisType |
typedef Matrix< Scalar, 3, 3 > | Matrix3 |
typedef Matrix< Scalar, Dim, Dim > | RotationMatrixType |
typedef _Scalar | Scalar |
typedef Matrix< Scalar, 3, 1 > | Vector3 |
Public Member Functions | |
Vector3 | _transformVector (Vector3 v) const |
internal::cast_return_type < Quaternion< _Scalar, _Options >, Quaternion < NewScalarType > >::type | cast () const |
Coefficients & | coeffs () |
const Coefficients & | coeffs () const |
Quaternion< Scalar > | conjugate () const |
Scalar | dot (const QuaternionBase< OtherDerived > &other) const |
Quaternion< Scalar > | inverse () const |
bool | isApprox (const QuaternionBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
RotationMatrixType | matrix () const |
Scalar | norm () const |
void | normalize () |
Quaternion< Scalar > | normalized () 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 < Quaternion< _Scalar, _Options >, OtherDerived, OtherDerived::IsVectorAtCompileTime > ::ReturnType | operator* (const EigenBase< OtherDerived > &e) const |
Transform< Scalar, Dim, Mode > | operator* (const Transform< Scalar, Dim, Mode, Options > &t) const |
Quaternion () | |
Quaternion (Scalar w, Scalar x, Scalar y, Scalar z) | |
Quaternion (const Scalar *data) | |
template<class Derived > | |
Quaternion (const QuaternionBase< Derived > &other) | |
Quaternion (const AngleAxisType &aa) | |
template<typename Derived > | |
Quaternion (const MatrixBase< Derived > &other) | |
template<typename OtherScalar , int OtherOptions> | |
Quaternion (const Quaternion< OtherScalar, OtherOptions > &other) | |
Quaternion< _Scalar, _Options > & | setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b) |
QuaternionBase & | setIdentity () |
Quaternion< Scalar > | slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const |
Scalar | squaredNorm () const |
Matrix3 | toRotationMatrix () const |
const VectorBlock< const Coefficients, 3 > | vec () const |
VectorBlock< Coefficients, 3 > | vec () |
Scalar | w () const |
Scalar & | w () |
Scalar | x () const |
Scalar & | x () |
Scalar | y () const |
Scalar & | y () |
Scalar | z () const |
Scalar & | z () |
Static Public Member Functions | |
template<typename Derived1 , typename Derived2 > | |
static Quaternion | FromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b) |
static Quaternion< Scalar > | Identity () |
Friends | |
RotationMatrixType | operator* (const EigenBase< OtherDerived > &l, const Quaternion< _Scalar, _Options > &r) |
Transform< Scalar, Dim, Affine > | operator* (const DiagonalMatrix< Scalar, Dim > &l, const Quaternion< _Scalar, _Options > &r) |
The quaternion class used to represent 3D orientations and rotations.
This is defined in the Geometry module.
#include <Eigen/Geometry>
_Scalar | the scalar type, i.e., the type of the coefficients |
This class represents a quaternion that is a convenient representation of orientations and rotations of objects in three dimensions. Compared to other representations like Euler angles or 3x3 matrices, quatertions offer the following advantages:
The following two typedefs are provided for convenience:
Quaternionf
for float
Quaterniond
for double
typedef Base::AngleAxisType AngleAxisType |
the equivalent angle-axis type
Reimplemented from QuaternionBase< Quaternion< _Scalar, _Options > >.
typedef Matrix<Scalar,Dim,Dim> RotationMatrixType [inherited] |
corresponding linear transformation matrix type
typedef _Scalar Scalar |
the scalar type of the coefficients
Reimplemented from QuaternionBase< Quaternion< _Scalar, _Options > >.
Quaternion | ( | ) | [inline] |
Default constructor leaving the quaternion uninitialized.
Quaternion | ( | Scalar | w, |
Scalar | x, | ||
Scalar | y, | ||
Scalar | z | ||
) | [inline] |
Constructs and initializes the quaternion from its four coefficients w, x, y and z.
x
, y
, z
, w
] Quaternion | ( | const Scalar * | data | ) | [inline] |
Constructs and initialize a quaternion from the array data
Quaternion | ( | const QuaternionBase< Derived > & | other | ) | [inline] |
Copy constructor
Quaternion | ( | const AngleAxisType & | aa | ) | [inline, explicit] |
Constructs and initializes a quaternion from the angle-axis aa
Quaternion | ( | const MatrixBase< Derived > & | other | ) | [inline, explicit] |
Constructs and initializes a quaternion from either:
Quaternion | ( | const Quaternion< OtherScalar, OtherOptions > & | other | ) | [inline, explicit] |
Explicit copy constructor with scalar conversion
References Quaternion< _Scalar, _Options >::coeffs().
Vector3 _transformVector | ( | Vector3 | v | ) | const [inline, inherited] |
return the result vector of v through the rotation
Rotation of a vector by a quaternion.
internal::cast_return_type<Quaternion< _Scalar, _Options > ,Quaternion<NewScalarType> >::type cast | ( | ) | const [inline, inherited] |
*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
.
Coefficients& coeffs | ( | ) | [inline] |
Reimplemented from QuaternionBase< Quaternion< _Scalar, _Options > >.
Referenced by Quaternion< _Scalar, _Options >::Quaternion().
const Coefficients& coeffs | ( | ) | const [inline] |
Reimplemented from QuaternionBase< Quaternion< _Scalar, _Options > >.
Quaternion<Scalar> conjugate | ( | ) | const [inherited] |
*this
which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.Scalar dot | ( | const QuaternionBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other Geometrically speaking, the dot product of two unit quaternions corresponds to the cosine of half the angle between the two rotations. References QuaternionBase< Derived >::coeffs().
Quaternion< Scalar, Options > FromTwoVectors | ( | const MatrixBase< Derived1 > & | a, |
const MatrixBase< Derived2 > & | b | ||
) | [static] |
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.
Note that the two input vectors do not have to be normalized, and do not need to have the same norm.
References QuaternionBase< Derived >::setFromTwoVectors().
static Quaternion<Scalar> Identity | ( | ) | [inline, static, inherited] |
Quaternion<Scalar> inverse | ( | ) | const [inherited] |
*this
Note that in most cases, i.e., if you simply want the opposite rotation, and/or the quaternion is normalized, then it is enough to use the conjugate.Reimplemented from RotationBase< Quaternion< _Scalar, _Options >, 3 >.
bool isApprox | ( | const QuaternionBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inline, inherited] |
true
if *this
is approximately equal to other, within the precision determined by prec.References QuaternionBase< Derived >::coeffs().
RotationMatrixType matrix | ( | ) | const [inline, inherited] |
References QuaternionBase< Derived >::coeffs().
void normalize | ( | void | ) | [inline, inherited] |
Normalizes the quaternion *this
References QuaternionBase< Derived >::coeffs().
Quaternion<Scalar> normalized | ( | ) | const [inline, inherited] |
*this
References QuaternionBase< Derived >::coeffs().
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<Quaternion< _Scalar, _Options > ,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 Quaternion< _Scalar, _Options > & setFromTwoVectors | ( | const MatrixBase< Derived1 > & | a, |
const MatrixBase< Derived2 > & | b | ||
) | [inherited] |
Sets *this
to be 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.
*this
.Note that the two input vectors do not have to be normalized, and do not need to have the same norm.
QuaternionBase& setIdentity | ( | ) | [inline, inherited] |
References QuaternionBase< Derived >::coeffs().
Quaternion<Scalar> slerp | ( | Scalar | t, |
const QuaternionBase< OtherDerived > & | other | ||
) | const [inherited] |
*this
t in [0;1] see http://en.wikipedia.org/wiki/Slerp*this
and other at the parameter t Scalar squaredNorm | ( | ) | const [inline, inherited] |
References QuaternionBase< Derived >::coeffs().
Matrix3 toRotationMatrix | ( | void | ) | const [inherited] |
Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to be normalized, otherwise the result is undefined.
Reimplemented from RotationBase< Quaternion< _Scalar, _Options >, 3 >.
const VectorBlock<const Coefficients,3> vec | ( | ) | const [inline, inherited] |
References QuaternionBase< Derived >::coeffs().
VectorBlock<Coefficients,3> vec | ( | ) | [inline, inherited] |
References QuaternionBase< Derived >::coeffs().
RotationMatrixType operator* | ( | const EigenBase< OtherDerived > & | l, |
const Quaternion< _Scalar, _Options > & | r | ||
) | [friend, inherited] |
Transform<Scalar,Dim,Affine> operator* | ( | const DiagonalMatrix< Scalar, Dim > & | l, |
const Quaternion< _Scalar, _Options > & | r | ||
) | [friend, inherited] |