User Documentation |
RAVL, Recognition And Vision Library |
PUBLIC |
Quatern3dC::Quatern3dC(void)
Quatern3dC::Quatern3dC(RealT,RealT,RealT,RealT)
Quatern3dC::Quatern3dC(const Vector3dC &)
Quatern3dC::Quatern3dC(const Vector3dC &,RealT)
Quatern3dC::Quatern3dC(const Matrix3dC &,bool)
Quatern3dC::Set(const Vector3dC &)
Quatern3dC::Set(const Vector3dC &,RealT)
Quatern3dC::Set(const Matrix3dC &,bool)
Quatern3dC::operator [](UIntT)
Quatern3dC::operator [](UIntT) const
Quatern3dC::MakePositive(void)
Quatern3dC::Norm(void)
Quatern3dC::Normalize(void)
Quatern3dC::Inverse(void) const
Quatern3dC::Conjugate(void) const
Quatern3dC::I(void) const
Quatern3dC::Rotate(Vector3dC) const
Quatern3dC::ExportAxTheta(void) const
Quatern3dC::ExportRotationAngle(void) const
Quatern3dC::ExportRotationAxis(void) const
Quatern3dC::ExportQuatMat(void) const
Quatern3dC::ExportQuatMat2(void) const
Quatern3dC::ExportRotationMatrix(bool) const
Quatern3dC::ExportVector(void) const
Quatern3dC::ExportEuler(void) const
Quatern3dC::ExportEuler(const JointT &,const bool &) const
Quatern3dC::DQuatDRotVec(void) const
Quatern3dC::DRotVecDQuat(void) const
Quatern3dC::func_alpha(const RealT &,const RealT &) const
Quatern3dC::func_gRavl(const RealT &,const RealT &) const
Quatern3dC::func_kappa(const RealT &,const RealT &) const
Quatern3dC::func_lambda(const RealT &,const RealT &) const
Quatern3dC::func_tau(const RealT &) const
Quatern3dC::func_ups(const RealT &) const
Quatern3dC::Dq0q1Dq(const Quatern3dC &,const int &) const
Quatern3dC::Dq0q1q2Dq(const Quatern3dC &,const Quatern3dC &,const int &) const
Quatern3dC::Print(void) const
Quatern3dC::LongPrint(void) const
Quatern3dC::operator *(const Quatern3dC) const
Quatern3dC::operator *(const RealT &) const
Quatern3dC::operator +(const Quatern3dC &) const
Quatern3dC::operator -(const Quatern3dC &) const
Quatern3dC::operator <<(ostream &,const Quatern3dC &)
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Quatern3dC
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Quaternion
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include | "Ravl/Quatern3d.hh" |
Created: | 13/11/95 |
User Level: | Normal |
Library: | RavlMath |
In Scope: | RavlN |
Comments:
Two quarternions may represent the same rotation q and -q,
both are valid, but it can be convenient to keep q[0]>0.
This code usually tries to keep q[0] positive. All the non trivial
constructors build a quarternion with q[0]>=0.
The multiply operation can exit with q[0]<0, this is necessary if
the Rotate member function is to work.
There are many tricky conversions, and stability issues
with rotations and the conversions.
Be careful of angles in particular angles near 0 or PI. This affects
some conversions as indicated
A "valid" quarternion has norm 1, however when a quarternion
contains a vector it does not have norm 1.
Be careful when using operations that may cause the quarternion
not to be valid.
When a quarternion is read in it should always be normalised
so that it obeys normalisation to full machine precision
which is the normal state of affairs
In addition it is possible that small errors may creep in during
repeated multiplication. The user should consider using the
Normalize() function to correct this. It is NOT done automatically
during multiplication.
Variables:
Methods:
Constructors
- Quatern3dC()
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Null Constructor, zero rotation, (1,0,0,0)
- Quatern3dC(RealT q0,RealT q1,RealT q2,RealT q3)
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Constructor - quarternion is not tested for validity.
- Quatern3dC(const Vector3dC & axtheta)
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Constructor from axis * angle in radians
- Quatern3dC(const Vector3dC & axis,RealT theta)
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Constructor
If theta != zero then axis must be non zero
the axis vector is normalized inside this routine!
- Quatern3dC(const Matrix3dC & rotate,bool check = true)
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Constructor
matrix is checked for orthogonality if check!=0
This routine is reliable for small angles!!
NOT ACCURATE FOR ANGLES NEAR PI
General operations
- void Set(const Vector3dC & axtheta)
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Set as specifed
- void Set(const Vector3dC & axis,RealT theta)
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Set as specifed
- void Set(const Matrix3dC & rotate,bool check = true)
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Set as specifed
- RealT & operator [](UIntT i)
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Access to ith element of the quarternion
- RealT operator [](UIntT i) const
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Access to ith element of the quarternion
- void MakePositive(void)
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replace quarternion by one with q[0] positive
which performs the same rotation
- RealT Norm()
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the norm of the quaternion (quareroot of the sum of the squares of the elements)
- void Normalize(void)
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impose the condition that norm=1
- Quatern3dC Inverse() const
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returns inverse of q, does not change q (Doesn't normalize q; is in fact
the conjugate of q)
- Quatern3dC Conjugate() const
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Conjugate
- Quatern3dC I() const
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returns inverse of q, does not change q
- Vector3dC Rotate(Vector3dC r) const
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applies rotation q to r and returns the result
- Vector3dC ExportAxTheta() const
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return the rotation as a unit vector axis times angle in radians
Note warnings for ExportRotAxis();
- RealT ExportRotationAngle() const
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return the angle of rotation, which should always be 0-PI
I believe this routine is accurate for theta near 0 and near PI
- Vector3dC ExportRotationAxis() const
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return the rotation as a unit vector axis around which rotated
If Null Rotation return axis as (1,1,1) vector
********** NB ************
For angles very close to PI this routines is not reliable
but it is OK for angles near zero.
If angle==PI the axis is garbage!
- Matrix4dC ExportQuatMat() const
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return quaternion as a 4x4 matrix - see Schmitts ECCV 98 paper
- MatrixC ExportQuatMat2() const
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return quaternion as a MatrixC (4x4) - see Schmitts ECCV 98 paper
- Matrix3dC ExportRotationMatrix(bool normalize = false) const
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return rotation as 3x3 rotation matrix
as far as I know always OK
- Vector3dC ExportVector() const
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returns the 3 vector components as they are, used for rotating vectors
- Vector3dC ExportEuler() const
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The angles returned correspond to rotations
around static axes XYZ in radians.
- Vector3dC ExportEuler(const JointT & jtype,const bool & premult) const
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The angles returned correspond to rotations
- MatrixC DQuatDRotVec() const
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derivative of the quaternion to the rotation vector
- MatrixC DRotVecDQuat() const
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derivative of the rotation vector to the quaternion
- RealT func_alpha(const RealT & x,const RealT & thres) const
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- RealT func_gRavl(const RealT & x,const RealT & thres) const
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- RealT func_kappa(const RealT & x,const RealT & thres) const
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- RealT func_lambda(const RealT & x,const RealT & thres) const
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- RealT func_tau(const RealT & thres) const
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- RealT func_ups(const RealT & thres) const
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functions used in DQuatDRotVec & DRotVecDQuat
- MatrixC Dq0q1Dq(const Quatern3dC & q,const int & nr) const
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derivative of the product ('this' * 'q') with respect to 'this' (nr=0)
or 'q' (nr=1)
- MatrixC Dq0q1q2Dq(const Quatern3dC & q1,const Quatern3dC & q2,const int & nr) const
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derivative of the product ('this' * 'q1' * 'q2') with respect to
'this' (nr=0), 'q1' (nr=1) or 'q2' (nr=2)
- void Print() const
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short print out
- void LongPrint() const
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detailed print out
- Quatern3dC operator *(const Quatern3dC p) const
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returns q x p, quarternion multiplication
can return q[0] < 0
- Quatern3dC operator *(const RealT & val) const
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returns q[i] = q1[i]*val, for i=0..3
- Quatern3dC operator +(const Quatern3dC & p) const
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returns q[i] = q1[i] + q2[i], for i=0..3
- Quatern3dC operator -(const Quatern3dC & p) const
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returns q[i] = q1[i] - q2[i], for i=0..3
- ostream & operator <<(ostream & outS,const Quatern3dC & quartern)
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ouput stream operator
Maintainer:Andrew Stoddart, Created: 13/11/95, Documentation by CxxDoc: Tue Aug 13 09:59:02 2002
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