Basic Image AlgorithmS Library
2.8.0
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class for rotation with axis and angle More...
#include <Base/Geometry/DualQuaternionOperators.hh>
Public Types | |
typedef QUAT_TYPE | value_type |
Public Member Functions | |
void | Add (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const |
Addition with a scalar, storing results in destionation vector. More... | |
void | Add (const Vector4< QUAT_TYPE > &argvec, Vector4< QUAT_TYPE > &destvec) const |
adding of two vectors, storing the result in destvec More... | |
void | AddIP (const QUAT_TYPE &scalar) |
Addition (in place) of an scalar. More... | |
void | AddIP (const Vector4< QUAT_TYPE > &argvec) |
in place adding More... | |
void | clear () |
void | Copy (const QUAT_TYPE *pv) |
copy the array of vectorsize beginning at *T to this->data_ More... | |
double | Dist (const Vector4< QUAT_TYPE > &vec) const |
Return the euclidean distance of 2 vectors. More... | |
void | Divide (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const |
Division with a scalar, storing results in destionation vector. More... | |
void | DivideIP (const QUAT_TYPE &scalar) |
Division (in place) of an scalar. More... | |
void | ElementwiseProduct (const Vector4< QUAT_TYPE > &argvec, Vector4< QUAT_TYPE > &destvec) const |
multiply two vectors elementwise, storing the result in destvec More... | |
void | EnforceRigidCouplingConstraint (Quaternion< QUAT_TYPE > &other, bool useOtherAngle=false) |
Enforce rigid coupling constraint for this and the other given unit quaternion (equal rotation angle/equal scalar part for both). More... | |
int | GetAxisAngle (Vector3< QUAT_TYPE > &axis, QUAT_TYPE &angle) const |
Returns rotation in axis and angle notation (angle in radians). More... | |
const QUAT_TYPE * | GetData () const |
get the data pointer the member function itself is const (before {..}) because it doesn't change the this object. More... | |
QUAT_TYPE * | GetData () |
void | GetEquatorialPoint3D (Vector3< QUAT_TYPE > &p3D) const |
Compute minimal parametrization of unit quaternion by projecting it from the 4d hypersphere onto the 3d equatorial space, as described in: [TCBS+12] Terzakis et al. More... | |
const unsigned int | GetNumElements () const |
Matrix4x4< QUAT_TYPE > | GetQuaternionMultMatrixLeft () const |
Returns matrix which expresses (left) quaternion multiplication. More... | |
Matrix4x4< QUAT_TYPE > | GetQuaternionMultMatrixRight () const |
Returns matrix which expresses right quaternion multiplication. More... | |
QUAT_TYPE | GetRotationAngle () const |
Returns rotation angle notation in radians. More... | |
Vector3< QUAT_TYPE > | GetRotationAxis () const |
Returns rotation axis. More... | |
int | GetRotationMatrix (RMatrixBase &R) const |
Returns a corresponding (quaternion) rotation matrix. More... | |
Quaternion< QUAT_TYPE > | Interpolate (const Quaternion< QUAT_TYPE > &to, const QUAT_TYPE &t) const |
Spherical interpolation between this and given quaternion. More... | |
Quaternion< QUAT_TYPE > | InterpolateLinear (const Quaternion< QUAT_TYPE > &to, const QUAT_TYPE &t) const |
Linear interpolation between this and given quaternion. More... | |
Quaternion< QUAT_TYPE > | Inverse () const |
returns the Inverse rotation Quaternion More... | |
void | Invert () |
inverts this, by changing the rotation axis by *=-1 More... | |
bool | Load (const std::string &filename) |
method to load directly from a given filename. More... | |
void | MakeUnique () |
makes Quaternion-representation uniqe, ensuring vector lies in upper (by real part) hemisphere. More... | |
void | Mult (const Quaternion< QUAT_TYPE > &quat) |
quaternion multiplication: this= this * quat More... | |
void | Mult (const Quaternion< QUAT_TYPE > &arg, Quaternion< QUAT_TYPE > &res) const |
quaternion multiplication: res = this * arg More... | |
void | Multiply (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const |
Multiplication with a scalar, storing results in destionation vector. More... | |
void | MultiplyIP (const QUAT_TYPE &scalar) |
Multiplication (in place) of an scalar. More... | |
void | MultLeft (const Quaternion< QUAT_TYPE > &quat) |
quaternion multiplication: this = quat * this More... | |
int | MultVec (const Vector3< QUAT_TYPE > &vec, Vector3< QUAT_TYPE > &res) const |
rotates the given Vector qith the quaternion ( q v q* ) the resulting vector is given in res More... | |
Vector3< QUAT_TYPE > | MultVec (const Vector3< QUAT_TYPE > &vec) const |
void | Normalize () |
Scales quaternion to unit length, i.e. More... | |
QUAT_TYPE | NormL1 () const |
Return the L1 norm: |a| + |b| + |c|+ |d|. More... | |
double | NormL2 () const |
Return the L2 norm: sqrt(a^2 + b^2 + c^2 + d^2) More... | |
bool | operator!= (const Vector4< QUAT_TYPE > &arg) const |
Comparison operator 'not equal'. More... | |
Vector4< QUAT_TYPE > & | operator*= (const QUAT_TYPE &scalar) |
Multiplication operator with scalar argument. More... | |
Vector4< QUAT_TYPE > & | operator+= (const QUAT_TYPE &scalar) |
Addition operator with scalar argument. More... | |
Vector4< QUAT_TYPE > & | operator+= (const Vector4< QUAT_TYPE > &argvec) |
add operator for two Vectors More... | |
Vector4< QUAT_TYPE > & | operator-= (const QUAT_TYPE &scalar) |
Substraction operator with scalar argument. More... | |
Vector4< QUAT_TYPE > & | operator-= (const Vector4< QUAT_TYPE > &argvec) |
sub operator for two Vectors More... | |
Vector4< QUAT_TYPE > & | operator/= (const QUAT_TYPE &scalar) |
Division operator with scalar argument. More... | |
Quaternion< QUAT_TYPE > & | operator= (const Quaternion< QUAT_TYPE > &vec) |
assignment operator More... | |
bool | operator== (const Vector4< QUAT_TYPE > &arg) const |
Comparison operator 'equal'. More... | |
const QUAT_TYPE & | operator[] (const int i) const |
access an element of the vector with 0-based indizes. More... | |
QUAT_TYPE & | operator[] (const int i) |
access an element of the vector with 0-based indizes. More... | |
Matrix4x4< QUAT_TYPE > | OuterProduct (const Vector4< QUAT_TYPE > &v) const |
outer product, constructs a matrix. More... | |
Quaternion< QUAT_TYPE > | Power (const QUAT_TYPE &scale) const |
Computes this^(scale), which scales the angle from axis/angle- representation with 'scale'. More... | |
Quaternion () | |
Quaternion (const Vector4< QUAT_TYPE > &q) | |
Quaternion (const Quaternion< QUAT_TYPE > &q) | |
copy constructor More... | |
Quaternion (QUAT_TYPE i, QUAT_TYPE j, QUAT_TYPE k, QUAT_TYPE r) | |
bool | Save (const std::string &filename) const |
method to save directly to a given filename. More... | |
void | ScalarProduct (const Vector4< QUAT_TYPE > &argvec, QUAT_TYPE &result) const |
scalar product (=inner product) of two vectors, storing the result in result More... | |
QUAT_TYPE | ScalarProduct (const Vector4< QUAT_TYPE > &argvec) const |
void | Set (const QUAT_TYPE &scalar) |
set all elements to a scalat value More... | |
void | Set (const QUAT_TYPE &x, const QUAT_TYPE &y, const QUAT_TYPE &z, const QUAT_TYPE &w) |
set elementwise with given scalr values More... | |
void | SetFromEquatorialPoint3D (const Vector3< QUAT_TYPE > &p3D) |
Set unit quaternion from 3d point in equatorial space by back- projecting it onto the 4d hypersphere, as described in [TCBS+12]. More... | |
void | SetIdentity () |
void | SetQuaternion (QUAT_TYPE real, QUAT_TYPE i, QUAT_TYPE j, QUAT_TYPE k) |
Sets all parts of quaternion in mathematical order, real part first, then 1.,2. More... | |
void | SetValueAsAxisRad (const Vector3< QUAT_TYPE > &axis, QUAT_TYPE angle) |
sets the quaternion with given rotation axis and angle (in rad) More... | |
void | SetValueAsAxisRad (QUAT_TYPE axisX, QUAT_TYPE axisY, QUAT_TYPE axisZ, QUAT_TYPE angle) |
sets the quaternion with given rotation axis and angle (in rad) More... | |
int | SetXYZ (QUAT_TYPE radX, QUAT_TYPE radY, QUAT_TYPE radZ) |
Sets quaternion as concatenated rotations around x,y,z-axis; this = q_x * q_y * q_z (BIAS-RMatrix conform) More... | |
void | SetZero () |
set all values to 0 More... | |
int | SetZYX (QUAT_TYPE radX, QUAT_TYPE radY, QUAT_TYPE radZ) |
Sets quaternion as concatenated rotations around x,y,z-axis; this = q_z * q_y * q_x (BIAS-RMatrix conform) More... | |
const unsigned int | Size () const |
const unsigned int | size () const |
void | Sub (const QUAT_TYPE &scalar, Vector4< QUAT_TYPE > &dest) const |
Substraction with a scalar, storing results in destionation vector. More... | |
void | Sub (const Vector4< QUAT_TYPE > &argvec, Vector4< QUAT_TYPE > &destvec) const |
subtracting of two Vectors, storing the result in destvec More... | |
void | SubIP (const QUAT_TYPE &scalar) |
Substraction (in place) of an scalar. More... | |
void | SubIP (const Vector4< QUAT_TYPE > &argvec) |
in place substraction More... | |
Matrix< QUAT_TYPE > | transposed () const |
return a new Matrix with 1 row and 4 columns representing a transposed vector More... | |
~Quaternion () | |
Iterator Functions | |
QUAT_TYPEconst * | begin () const |
Iterator to first component of vector. More... | |
QUAT_TYPE * | begin () |
QUAT_TYPEconst * | end () const |
Iterator pointing to one element after the last vector element. More... | |
QUAT_TYPE * | end () |
Static Public Member Functions | |
static void | EnforceRigidCouplingConstraint (std::vector< Quaternion< QUAT_TYPE > > &quats, bool useFirstAngle=false) |
Enforce rigid coupling constraint for all quaternions in given vector. More... | |
Protected Attributes | |
QUAT_TYPE | data_ [VECTOR4SIZE] |
Related Functions | |
(Note that these are not member functions.) | |
template<class T > | |
Quaternion< T > | operator* (const Quaternion< T > &l, const Quaternion< T > &r) |
template<class T > | |
Quaternion< T > & | operator*= (Quaternion< T > &l, const Quaternion< T > &r) |
template<class T > | |
Quaternion< T > | operator/ (const Quaternion< T > &l, const Quaternion< T > &r) |
template<class T > | |
Quaternion< T > & | operator/= (Quaternion< T > &l, const Quaternion< T > &r) |
class for rotation with axis and angle
Quaternions can be used for rotation around an axis through the origin by spcecifing the normal direction vector of the axis and an angle.
The rotation for positive angles is clockwise, when looking in direction of the axis.
Contains qx=[0], qy=[1], qz=[2], qw=[3].
Not every quaternion describes a rotation. Only quaternions of the form:
qx = x * sin(phi/2) , which is the imaginary part i
qy = y * sin(phi/2) , which is the imaginary part j
qz = z * sin(phi/2) , which is the imaginary part k
qw = cos(phi/2), , which is the real part
where (x, y, z) is the normalized direction vector of the axis and phi is the angle of rtoation.
Some usefull quaternions: x y z w Description 0 0 0 1 Identity quaternion, no rotation 1 0 0 0 180' turn around X axis 0 1 0 0 180' turn around Y axis 0 0 1 0 180' turn around Z axis sqrt(0.5) 0 0 sqrt(0.5) 90' rotation around X axis 0 sqrt(0.5) 0 sqrt(0.5) 90' rotation around Y axis 0 0 sqrt(0.5) sqrt(0.5) 90' rotation around Z axis -sqrt(0.5) 0 0 sqrt(0.5) -90' rotation around X axis 0 -sqrt(0.5) 0 sqrt(0.5) -90' rotation around Y axis 0 0 -sqrt(0.5) sqrt(0.5) -90' rotation around Z axis
Definition at line 32 of file DualQuaternionOperators.hh.
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Definition at line 67 of file Vector4.hh.
BIAS::Quaternion< T >::~Quaternion | ( | ) |
BIAS::Quaternion< T >::Quaternion | ( | ) |
BIAS::Quaternion< T >::Quaternion | ( | const Vector4< QUAT_TYPE > & | q | ) |
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copy constructor
Definition at line 28 of file Quaternion.hh.
BIAS::Quaternion< T >::Quaternion | ( | QUAT_TYPE | i, |
QUAT_TYPE | j, | ||
QUAT_TYPE | k, | ||
QUAT_TYPE | r | ||
) |
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Addition with a scalar, storing results in destionation vector.
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adding of two vectors, storing the result in destvec
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Addition (in place) of an scalar.
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in place adding
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Iterator to first component of vector.
Definition at line 152 of file Vector4.hh.
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Definition at line 155 of file Vector4.hh.
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copy the array of vectorsize beginning at *T to this->data_
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Return the euclidean distance of 2 vectors.
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Division with a scalar, storing results in destionation vector.
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Division (in place) of an scalar.
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multiply two vectors elementwise, storing the result in destvec
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Iterator pointing to one element after the last vector element.
Definition at line 161 of file Vector4.hh.
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Definition at line 164 of file Vector4.hh.
void BIAS::Quaternion< T >::EnforceRigidCouplingConstraint | ( | Quaternion< QUAT_TYPE > & | other, |
bool | useOtherAngle = false |
||
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Enforce rigid coupling constraint for this and the other given unit quaternion (equal rotation angle/equal scalar part for both).
Computes direct simple interpolation of both unit quaternion where the scalar parts of the resulting unit quaternion are identical. This solution can be used as initial guess for numerical refinement.
in/out] | other Quaternion to enforce rigid coupling constraint with | |
[in] | useOtherAngle | Use rotation angle (= scalar part) of other quaternion instead of interpolating both |
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Enforce rigid coupling constraint for all quaternions in given vector.
in/out] | quats Quaternions to enforce rigid coupling constraint for | |
[in] | useFirstAngle | Use rotation angle (= scalar part) of first quaternion instead of interpolating all |
int BIAS::Quaternion< T >::GetAxisAngle | ( | Vector3< QUAT_TYPE > & | axis, |
QUAT_TYPE & | angle | ||
) | const |
Returns rotation in axis and angle notation (angle in radians).
Note that the returned angle resides in the interval [0,PI) and the axis points into the according direction!
Referenced by BIAS::RMatrixBase::GetRotationAxisAngle(), BIAS::PMDImageProc::MetaFromPoseAndK(), BIAS::operator<<(), and BIAS::CovQuaternion2AxisAngle::Transform_().
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get the data pointer
the member function itself is const (before {..}) because it doesn't change the this object.
Definition at line 177 of file Vector4.hh.
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Definition at line 181 of file Vector4.hh.
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Compute minimal parametrization of unit quaternion by projecting it from the 4d hypersphere onto the 3d equatorial space, as described in: [TCBS+12] Terzakis et al.
: A Recipe on the Parameterization of Rotation Matrices for Non-Linear Optimization using Quaternions, 2012.
[out] | p3D | Returns 3d point representation of unit quaternion |
Definition at line 212 of file Quaternion.hh.
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Definition at line 145 of file Vector4.hh.
Matrix4x4<QUAT_TYPE> BIAS::Quaternion< T >::GetQuaternionMultMatrixLeft | ( | ) | const |
Returns matrix which expresses (left) quaternion multiplication.
A quaternions stored in an object can be understood as a 4-vector q =(ix iy iz r)^T. Left multiplying a quaternion q2 with a quaternion q1 can be expressed in terms of matrix multiplication as qRes = q1*q2 = M(q1)*q2. This method returns the matrix M(*this).
Referenced by BIAS::PoseParametrizationCovariance::Transform().
Matrix4x4<QUAT_TYPE> BIAS::Quaternion< T >::GetQuaternionMultMatrixRight | ( | ) | const |
Returns matrix which expresses right quaternion multiplication.
Right multiplying a quaternion q1 with quaternion q2 can be expressed as qRes = q1*q2 = N(q2)*q1. This method returns the matrix N(*this).
QUAT_TYPE BIAS::Quaternion< T >::GetRotationAngle | ( | ) | const |
Returns rotation angle notation in radians.
Note that the returned angle resides in the interval [0,PI)!
Referenced by BIAS::EMatrix::GetRotationTranslation().
Vector3<QUAT_TYPE> BIAS::Quaternion< T >::GetRotationAxis | ( | ) | const |
Returns rotation axis.
See GetRotationAxisAngle().
Referenced by BIAS::EMatrix::GetRotationTranslation().
int BIAS::Quaternion< T >::GetRotationMatrix | ( | RMatrixBase & | R | ) | const |
Returns a corresponding (quaternion) rotation matrix.
Quaternion<QUAT_TYPE> BIAS::Quaternion< T >::Interpolate | ( | const Quaternion< QUAT_TYPE > & | to, |
const QUAT_TYPE & | t | ||
) | const |
Spherical interpolation between this and given quaternion.
Referenced by BIAS::DualQuaternion< QUAT_TYPE >::Interpolate().
Quaternion<QUAT_TYPE> BIAS::Quaternion< T >::InterpolateLinear | ( | const Quaternion< QUAT_TYPE > & | to, |
const QUAT_TYPE & | t | ||
) | const |
Linear interpolation between this and given quaternion.
Referenced by BIAS::DualQuaternion< QUAT_TYPE >::InterpolateLinear().
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returns the Inverse rotation Quaternion
Definition at line 42 of file Quaternion.hh.
Referenced by BIAS::Quaternion< T >::operator/(), and BIAS::Quaternion< T >::operator/=().
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inverts this, by changing the rotation axis by *=-1
Definition at line 34 of file Quaternion.hh.
Referenced by BIAS::Quaternion< QUAT_TYPE >::Inverse(), and BIAS::EParametrization::Invert().
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method to load directly from a given filename.
internally using stream operator
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makes Quaternion-representation uniqe, ensuring vector lies in upper (by real part) hemisphere.
(inplace)
Definition at line 50 of file Quaternion.hh.
Referenced by BIAS::Quaternion< QUAT_TYPE >::EnforceRigidCouplingConstraint().
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quaternion multiplication: this= this * quat
Definition at line 73 of file Quaternion.hh.
References BIAS::Quaternion.
Referenced by BIAS::DualQuaternion< QUAT_TYPE >::GetRigidMotion(), BIAS::Quaternion< QUAT_TYPE >::Mult(), BIAS::Quaternion< T >::operator*(), BIAS::Quaternion< T >::operator*=(), BIAS::Quaternion< T >::operator/(), BIAS::Quaternion< T >::operator/=(), BIAS::Quaternion< QUAT_TYPE >::SetXYZ(), and BIAS::Quaternion< QUAT_TYPE >::SetZYX().
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quaternion multiplication: res = this * arg
Definition at line 98 of file Quaternion.hh.
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Multiplication with a scalar, storing results in destionation vector.
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Multiplication (in place) of an scalar.
Referenced by BIAS::RMatrixBase::GetQuaternion().
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quaternion multiplication: this = quat * this
Definition at line 106 of file Quaternion.hh.
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rotates the given Vector qith the quaternion ( q v q* ) the resulting vector is given in res
rotates the given Vector with the quaternion ( q v q* ) the resulting vector is given in res
Definition at line 136 of file Quaternion.hh.
Referenced by BIAS::CoordinateTransform3D::ConcatenateLocalTransform(), BIAS::ProjectionParametersSphericalFast::GetPerspectiveCutOutParameters(), BIAS::ProjectionParametersSpherical::GetPerspectiveCutOutParameters(), BIAS::EParametrization::Invert(), BIAS::FlyControl::LeftMouseMoved(), BIAS::TrackballControl::RotateAroundPOI(), BIAS::FlyControl::RotateAroundViewingDirection(), BIAS::TrackballControl::RotateAroundViewingDirection(), BIAS::ProjectionParametersSpherical::TransfCoordRotateSphere2Image_(), BIAS::CovTransformPose::Transform_(), BIAS::Triangulation::Triangulate(), and BIAS::ProjectionParametersCylindric::ViewDifference().
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Definition at line 161 of file Quaternion.hh.
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Scales quaternion to unit length, i.e.
norm equals 1.
Definition at line 236 of file Quaternion.hh.
Referenced by BIAS::RotationAveraging::ChordalL2Mean(), BIAS::Quaternion< QUAT_TYPE >::Interpolate(), BIAS::Quaternion< QUAT_TYPE >::InterpolateLinear(), BIAS::RotationAveraging::QuaternionL2Mean(), and BIAS::RMatrixBase::SetFromQuaternion().
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Return the L1 norm: |a| + |b| + |c|+ |d|.
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Return the L2 norm: sqrt(a^2 + b^2 + c^2 + d^2)
Referenced by BIAS::RMatrixBase::GetQuaternion(), and BIAS::RMatrixBase::SetFromQuaternion().
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Comparison operator 'not equal'.
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Multiplication operator with scalar argument.
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Addition operator with scalar argument.
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add operator for two Vectors
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Substraction operator with scalar argument.
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sub operator for two Vectors
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Division operator with scalar argument.
Quaternion<QUAT_TYPE>& BIAS::Quaternion< T >::operator= | ( | const Quaternion< QUAT_TYPE > & | vec | ) |
assignment operator
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Comparison operator 'equal'.
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access an element of the vector with 0-based indizes.
read only (no write) member funciton const because it doesn't change this object
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access an element of the vector with 0-based indizes.
write allowed
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outer product, constructs a matrix.
Often written as v * v^T for col vectors
Quaternion<QUAT_TYPE> BIAS::Quaternion< T >::Power | ( | const QUAT_TYPE & | scale | ) | const |
Computes this^(scale), which scales the angle from axis/angle- representation with 'scale'.
This is the same like inter-/extra- polating between (0,0,0,1)-quaternion and this!
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method to save directly to a given filename.
internally using stream operator
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scalar product (=inner product) of two vectors, storing
the result in result
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set all elements to a scalat value
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set elementwise with given scalr values
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Set unit quaternion from 3d point in equatorial space by back- projecting it onto the 4d hypersphere, as described in [TCBS+12].
[in] | p3D | Constaint 3d point representation of unit quaternion |
Definition at line 223 of file Quaternion.hh.
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Definition at line 168 of file Quaternion.hh.
Referenced by BIAS::Quaternion< QUAT_TYPE >::Power().
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Sets all parts of quaternion in mathematical order, real part first, then 1.,2.
and 3. imaginary part
Definition at line 175 of file Quaternion.hh.
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sets the quaternion with given rotation axis and angle (in rad)
Definition at line 183 of file Quaternion.hh.
Referenced by BIAS::ProjectionParametersSphericalFast::GetPerspectiveCutOutParameters(), BIAS::ProjectionParametersSpherical::GetPerspectiveCutOutParameters(), BIAS::FlyControl::LeftMouseMoved(), BIAS::TrackballControl::RotateAroundPOI(), BIAS::FlyControl::RotateAroundViewingDirection(), BIAS::TrackballControl::RotateAroundViewingDirection(), BIAS::ProjectionParametersCylindric::SetCylinderRotation(), BIAS::Quaternion< QUAT_TYPE >::SetXYZ(), BIAS::Quaternion< QUAT_TYPE >::SetZYX(), and BIAS::ProjectionParametersSpherical::TransfCoordRotateSphere2Image_().
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sets the quaternion with given rotation axis and angle (in rad)
Definition at line 190 of file Quaternion.hh.
int BIAS::Quaternion< T >::SetXYZ | ( | QUAT_TYPE | radX, |
QUAT_TYPE | radY, | ||
QUAT_TYPE | radZ | ||
) |
Sets quaternion as concatenated rotations around x,y,z-axis; this = q_x * q_y * q_z (BIAS-RMatrix conform)
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set all values to 0
int BIAS::Quaternion< T >::SetZYX | ( | QUAT_TYPE | radX, |
QUAT_TYPE | radY, | ||
QUAT_TYPE | radZ | ||
) |
Sets quaternion as concatenated rotations around x,y,z-axis; this = q_z * q_y * q_x (BIAS-RMatrix conform)
Referenced by BIAS::CovTransformPose::Transform_().
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@return the size of this vector
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Substraction with a scalar, storing results in destionation vector.
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subtracting of two Vectors, storing the result in destvec
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Substraction (in place) of an scalar.
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in place substraction
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return a new Matrix with 1 row and 4 columns representing a
transposed vector
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what it stands for (wraps Mult())
Definition at line 42 of file QuaternionOperators.hh.
References BIAS::Quaternion< T >::Mult().
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what it stands for (wraps Mult())
Definition at line 54 of file QuaternionOperators.hh.
References BIAS::Quaternion< T >::Mult().
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what it stands for (wraps Mult() and Inverse())
Definition at line 65 of file QuaternionOperators.hh.
References BIAS::Quaternion< T >::Inverse(), and BIAS::Quaternion< T >::Mult().
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what it stands for (wraps Mult() and Inverse())
Definition at line 77 of file QuaternionOperators.hh.
References BIAS::Quaternion< T >::Inverse(), and BIAS::Quaternion< T >::Mult().
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Definition at line 375 of file Vector4.hh.