The quaternion class used to represent 3D orientations and rotations. More...
Public Types | |
typedef AngleAxis< Scalar > | AngleAxisType |
typedef Matrix< Scalar, 4, 1 > | Coefficients |
typedef Matrix< Scalar, 3, 3 > | Matrix3 |
typedef _Scalar | Scalar |
typedef Matrix< Scalar, 3, 1 > | Vector3 |
![]() | |
enum | |
typedef Matrix< Scalar, Dim, Dim > | RotationMatrixType |
typedef ei_traits< Quaternion < _Scalar > >::Scalar | Scalar |
Public Member Functions | |
Scalar | angularDistance (const Quaternion &other) const |
template<typename NewScalarType > | |
ei_cast_return_type < Quaternion, Quaternion < NewScalarType > >::type | cast () const |
const Coefficients & | coeffs () const |
Coefficients & | coeffs () |
Quaternion | conjugate (void) const |
Scalar | dot (const Quaternion &other) const |
Quaternion | inverse (void) const |
bool | isApprox (const Quaternion &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const |
Scalar | norm () const |
void | normalize () |
Quaternion | normalized () const |
Quaternion | operator* (const Quaternion &q) const |
template<typename Derived > | |
Vector3 | operator* (const MatrixBase< Derived > &vec) const |
Quaternion & | operator*= (const Quaternion &q) |
Quaternion & | operator= (const Quaternion &other) |
Quaternion & | operator= (const AngleAxisType &aa) |
template<typename Derived > | |
Quaternion & | operator= (const MatrixBase< Derived > &m) |
Quaternion () | |
Quaternion (Scalar w, Scalar x, Scalar y, Scalar z) | |
Quaternion (const Quaternion &other) | |
Quaternion (const AngleAxisType &aa) | |
template<typename Derived > | |
Quaternion (const MatrixBase< Derived > &other) | |
template<typename OtherScalarType > | |
Quaternion (const Quaternion< OtherScalarType > &other) | |
template<typename Derived1 , typename Derived2 > | |
Quaternion & | setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b) |
Quaternion & | setIdentity () |
Quaternion | slerp (Scalar t, const Quaternion &other) const |
Scalar | squaredNorm () const |
Matrix3 | toRotationMatrix (void) const |
const Block< Coefficients, 3, 1 > | vec () const |
Block< Coefficients, 3, 1 > | vec () |
Scalar | w () const |
Scalar & | w () |
Scalar | x () const |
Scalar & | x () |
Scalar | y () const |
Scalar & | y () |
Scalar | z () const |
Scalar & | z () |
![]() | |
const Quaternion< _Scalar > & | derived () const |
Quaternion< _Scalar > & | derived () |
Transform< Scalar, Dim > | operator* (const Translation< Scalar, Dim > &t) const |
RotationMatrixType | operator* (const Scaling< Scalar, Dim > &s) const |
Transform< Scalar, Dim > | operator* (const Transform< Scalar, Dim > &t) const |
Static Public Member Functions | |
static Quaternion | 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 AngleAxis<Scalar> AngleAxisType |
the equivalent angle-axis type
typedef Matrix<Scalar, 4, 1> Coefficients |
the type of the Coefficients 4-vector
typedef _Scalar Scalar |
the scalar type of the coefficients
|
inline |
Default constructor leaving the quaternion uninitialized.
|
inline |
Constructs and initializes the quaternion from its four coefficients w, x, y and z.
x
, y
, z
, w
]
|
inline |
Copy constructor
|
inlineexplicit |
Constructs and initializes a quaternion from the angle-axis aa
|
inlineexplicit |
Constructs and initializes a quaternion from either:
|
inlineexplicit |
Copy constructor with scalar type conversion
|
inline |
|
inline |
*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
.
|
inline |
|
inline |
|
inline |
*this
which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.
|
inline |
*this
and other Geometrically speaking, the dot product of two unit quaternions corresponds to the cosine of half the angle between the two rotations.
|
inlinestatic |
|
inline |
*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 >, 3 >.
|
inline |
true
if *this
is approximately equal to other, within the precision determined by prec.
|
inline |
|
inline |
Normalizes the quaternion *this
|
inline |
*this
|
inline |
|
inline |
Rotation of a vector by a quaternion.
|
inline |
|
inline |
Set *this
from an angle-axis aa and returns a reference to *this
|
inline |
Set *this
from the expression xpr:
|
inline |
Sets *this to be a quaternion representing a rotation sending the vector a to the vector b.
Note that the two input vectors do not have to be normalized.
|
inline |
Quaternion< Scalar > slerp | ( | Scalar | t, |
const Quaternion< _Scalar > & | other | ||
) | const |
*this
and other at the parameter t
|
inline |
|
inline |
Convert the quaternion to a 3x3 rotation matrix
Reimplemented from RotationBase< Quaternion< _Scalar >, 3 >.
|
inline |
|
inline |
|
inline |
w
coefficient
|
inline |
w
coefficient
|
inline |
x
coefficient
|
inline |
x
coefficient
|
inline |
y
coefficient
|
inline |
y
coefficient
|
inline |
z
coefficient
|
inline |
z
coefficient