QuarternC -

User Documentation

Centre for Vision, Speech & Signal Processing

Comments:
This list may be extended in time. Therefore please always use default in a switch to test for unprocessed option, and not for any other task.

Variables:

const double axthetaconv = 1e-8;: used in the conversion between axtheta and quartern when below this bound use shortcut for better accuracy
const double nearlyzero = 1e-13;: used in the orthogonality error check for the constructor from matrix
const double underflow = 1e-50;: angles smaller than this value are assumed zero, used when constructing from angle and axis. If the length of the axis is less than this, an error is recorded Export Angle and Export Axis are also affected.
const double axthetaconv;: used in the conversion between axtheta and quartern when below this bound use shortcut for better accuracy
const double nearlyzero;: used in the orthogonality error check for the constructor from matrix
const double underflow;: angles smaller than this value are assumed zero, used when constructing from angle and axis. If the length of the axis is less than this, an error is recorded Export Angle and Export Axis are also affected.

Methods:

QuarternC(): Null Constructor, zero rotation, (1,0,0,0)
QuarternC(const QuarternC & qu): Copy constructor
QuarternC & operator=(const QuarternC & qu): Assignment
QuarternC(double q0,double q1,double q2,double q3): Constructor - quarternion is not tested for validity.
QuarternC(Vector3dC axtheta): Constructor from axis * angle in radians
QuarternC(Vector3dC axis,double theta): Constructor If theta != zero then axis must be non zero the axis vector is normalized inside this routine!
QuarternC(Matrix3d3C rotate,int check = 1): 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(Vector3dC axtheta): Set as specifed
void Set(Vector3dC axis,double theta): Set as specifed
void Set(Matrix3d3C rotate,int check = 1): Set as specifed
double & operator[](const int i): Access to ith element of the quarternion
const double & operator[](const int i) const: Access to ith element of the quarternion
void MakePositive(void): replace quarternion by one with q[0] positive which performs the same rotation
RealT Norm(): the norm of the quaternion (quareroot of the sum of the squares of the elements)
void Normalize(void): impose the condition that norm=1
QuarternC Inverse() const: returns inverse of q, does not change q (Doesn't normalize q; is in fact the conjugate of q)
QuarternC Conjugate() const
QuarternC I() const: returns inverse of q, does not change q
Vector3dC Rotate(Vector3dC r) const: applies rotation q to r and returns the result
Vector3dC ExportAxTheta() const: return the rotation as a unit vector axis times angle in radians Note warnings for ExportRotAxis();
double ExportRotAngle() const: 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 ExportRotAxis() const: 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!
Matrix4d4C ExportQuatMat() const: return quaternion as a 4x4 matrix - see Schmitts ECCV 98 paper
MatrixC ExportQuatMat2() const: return quaternion as a MatrixC (4x4) - see Schmitts ECCV 98 paper
Matrix3d3C ExportRotMat(BooleanT normalize = FALSE) const: return rotation as 3x3 rotation matrix as far as I know always OK
Vector3dC ExportVector() const: returns the 3 vector components as they are, used for rotating vectors
Vector3dC ExportEuler() const: The angles returned correspond to rotations around static axes XYZ in radians.
Vector3dC ExportEuler(const JointT & jtype,const BooleanT & premult) const: The angles returned correspond to rotations
MatrixC DQuatDRotVec() const: derivative of the quaternion to the rotation vector
MatrixC DRotVecDQuat() const: derivative of the rotation vector to the quaternion
RealT func_alpha(const RealT & x,const RealT & thres) const
RealT func_gamma(const RealT & x,const RealT & thres) const
RealT func_kappa(const RealT & x,const RealT & thres) const
RealT func_lambda(const RealT & x,const RealT & thres) const
RealT func_tau(const RealT & thres) const
RealT func_ups(const RealT & thres) const: functions used in DQuatDRotVec & DRotVecDQuat
MatrixC Dq0q1Dq(const QuarternC & q,const int & nr) const: derivative of the product ('this' * 'q') with respect to 'this' (nr=0)
or 'q' (nr=1)
MatrixC Dq0q1q2Dq(const QuarternC & q1,const QuarternC & q2,const int & nr) const: derivative of the product ('this' * 'q1' * 'q2') with respect to
'this' (nr=0), 'q1' (nr=1) or 'q2' (nr=2)
void KwikPrint(ostream & outS,int w = 10,int p = 7) const: One line printout to specified precision
void Print() const: short print out
void LongPrint() const: detailed print out
QuarternC operator*(const QuarternC q,const QuarternC p): returns q x p, quarternion multiplication can return q[0] < 0
QuarternC operator*(const QuarternC & q1,const RealT & val): returns q[i] = q1[i]*val, for i=0..3
QuarternC operator+(const QuarternC & q1,const QuarternC & q2): returns q[i] = q1[i] + q2[i], for i=0..3
QuarternC operator-(const QuarternC & q1,const QuarternC & q2): returns q[i] = q1[i] - q2[i], for i=0..3
ostream & operator<<(ostream & outS,const QuarternC & quartern): ouput stream operator

Programmer:Andrew Stoddart, Documentation by CxxDoc: Tue Mar 20 10:48:08 2001

QuarternC

include	"amma/Quartern.hh"
User Level:	Default
Library:	RigidT
Example:	aff_transf.cc
Section:	3D Surface.Rigid Body Transforms
In Scope:	std