The quaternion class used to represent 3D orientations and rotations. More...
#include <Quaternion.h>
Public Types | |
enum | |
enum | |
typedef Base::AngleAxisType | AngleAxisType |
typedef internal::traits < Quaternion >::Coefficients | Coefficients |
typedef Matrix< Scalar, 3, 3 > | Matrix3 |
typedef NumTraits< Scalar >::Real | RealScalar |
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 |
Vector3 | _transformVector (Vector3 v) const |
Scalar | angularDistance (const QuaternionBase< OtherDerived > &other) const |
internal::cast_return_type < Quaternion< _Scalar, _Options >, Quaternion < NewScalarType > >::type | cast () const |
Coefficients & | coeffs () |
const Coefficients & | coeffs () const |
Quaternion< Scalar > | conjugate () const |
const Quaternion< _Scalar, _Options > & | derived () const |
Quaternion< _Scalar, _Options > & | derived () |
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< Scalar > | operator* (const QuaternionBase< OtherDerived > &q) const |
Quaternion< _Scalar, _Options > & | operator*= (const QuaternionBase< OtherDerived > &q) |
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 () |
Protected Attributes | |
Coefficients | m_coeffs |
The quaternion class used to represent 3D orientations and rotations.
This is defined in the Geometry module.
_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 |
typedef internal::traits<Quaternion>::Coefficients Coefficients |
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inherited |
corresponding linear transformation matrix type
typedef _Scalar Scalar |
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inherited |
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inherited |
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inline |
Default constructor leaving the quaternion uninitialized.
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inline |
Constructs and initializes the quaternion from its four coefficients w, x, y and z.
x
, y
, z
, w
]
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Constructs and initialize a quaternion from the array data
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inline |
Copy constructor
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inlineexplicit |
Constructs and initializes a quaternion from the angle-axis aa
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inlineexplicit |
Constructs and initializes a quaternion from either:
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inlineexplicit |
Explicit copy constructor with scalar conversion
References Quaternion< _Scalar, _Options >::coeffs().
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inlineinherited |
return the result vector of v through the rotation
Rotation of a vector by a quaternion.
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inherited |
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inlineinherited |
*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
.
References RotationBase< Derived, 3 >::derived().
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Reimplemented from QuaternionBase< Quaternion< _Scalar, _Options > >.
Referenced by Quaternion< _Scalar, _Options >::Quaternion().
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Reimplemented from QuaternionBase< Quaternion< _Scalar, _Options > >.
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inherited |
*this
which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.
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inlineinherited |
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inlineinherited |
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inlineinherited |
*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().
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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().
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inlinestaticinherited |
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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 >.
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inlineinherited |
true
if *this
is approximately equal to other, within the precision determined by prec.References QuaternionBase< Derived >::coeffs().
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inlineinherited |
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inlineinherited |
References QuaternionBase< Derived >::coeffs().
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inlineinherited |
Normalizes the quaternion *this
References QuaternionBase< Derived >::coeffs().
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inlineinherited |
*this
References QuaternionBase< Derived >::coeffs().
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inlineinherited |
*this
with a translation t
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inlineinherited |
*this
with a uniform scaling s
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inlineinherited |
*this
with a generic expression e e can be:
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inlineinherited |
*this
with a transformation t
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inlineinherited |
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inlineinherited |
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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.
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inlineinherited |
References QuaternionBase< Derived >::coeffs().
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inherited |
*this
t in [0;1] see http://en.wikipedia.org/wiki/Slerp*this
and other at the parameter t
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inlineinherited |
References QuaternionBase< Derived >::coeffs().
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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 >.
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inlineinherited |
References QuaternionBase< Derived >::coeffs().
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inlineinherited |
References QuaternionBase< Derived >::coeffs().
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inlineinherited |
w
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
w
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
x
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
x
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
y
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
y
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
z
coefficient References RotationBase< Derived, 3 >::derived().
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inlineinherited |
z
coefficient References RotationBase< Derived, 3 >::derived().
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protected |