Open CASCADE Technology  6.5.4
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines
Public Member Functions
gp_Quaternion Class Reference

Represents operation of rotation in 3d space as queternion
and implements operations with rotations basing on
quaternion mathematics.

In addition, provides methods for conversion to and from other
representatons of rotation (3*3 matrix, vector and
angle, Euler angles)

#include <gp_Quaternion.hxx>

Public Member Functions

DEFINE_STANDARD_ALLOC gp_Quaternion ()
 Creates an identity quaternion

 gp_Quaternion (const Standard_Real x, const Standard_Real y, const Standard_Real z, const Standard_Real w)
 Creates quaternion directly from component values

 gp_Quaternion (const gp_Quaternion &theToCopy)
 Creates copy of another quaternion

 gp_Quaternion (const gp_Vec &theVecFrom, const gp_Vec &theVecTo)
 Creates quaternion representing shortest-arc rotation
operator producing vector theVecTo from vector theVecFrom.

 gp_Quaternion (const gp_Vec &theVecFrom, const gp_Vec &theVecTo, const gp_Vec &theHelpCrossVec)
 Creates quaternion representing shortest-arc rotation
operator producing vector theVecTo from vector theVecFrom.
Additional vector theHelpCrossVec defines preferred direction for
rotation and is used when theVecTo and theVecFrom are directed
oppositely.

 gp_Quaternion (const gp_Vec &theAxis, const Standard_Real theAngle)
 Creates quaternion representing rotation on angle
theAngle around vector theAxis

 gp_Quaternion (const gp_Mat &theMat)
 Creates quaternion from rotation matrix 3*3
(which should be orthonormal skew-symmetric matrix)

Standard_Boolean IsEqual (const gp_Quaternion &theOther) const
 Simple equal test without precision

void SetRotation (const gp_Vec &theVecFrom, const gp_Vec &theVecTo)
 Sets quaternion to shortest-arc rotation producing
vector theVecTo from vector theVecFrom.
If vectors theVecFrom and theVecTo are opposite then rotation
axis is computed as theVecFrom ^ (1,0,0) or theVecFrom ^ (0,0,1).

void SetRotation (const gp_Vec &theVecFrom, const gp_Vec &theVecTo, const gp_Vec &theHelpCrossVec)
 Sets quaternion to shortest-arc rotation producing
vector theVecTo from vector theVecFrom.
If vectors theVecFrom and theVecTo are opposite then rotation
axis is computed as theVecFrom ^ theHelpCrossVec.

void SetVectorAndAngle (const gp_Vec &theAxis, const Standard_Real theAngle)
 Create a unit quaternion from Axis+Angle representation

void GetVectorAndAngle (gp_Vec &theAxis, Standard_Real &theAngle) const
 Convert a quaternion to Axis+Angle representation,
preserve the axis direction and angle from -PI to +PI

void SetMatrix (const gp_Mat &theMat)
 Create a unit quaternion by rotation matrix
matrix must contain only rotation (not scale or shear)

For numerical stability we find first the greatest component of quaternion
and than search others from this one

gp_Mat GetMatrix () const
 Returns rotation operation as 3*3 matrix

void SetEulerAngles (const gp_EulerSequence theOrder, const Standard_Real theAlpha, const Standard_Real theBeta, const Standard_Real theGamma)
 Create a unit quaternion representing rotation defined
by generalized Euler angles

void GetEulerAngles (const gp_EulerSequence theOrder, Standard_Real &theAlpha, Standard_Real &theBeta, Standard_Real &theGamma) const
 Returns Euler angles describing current rotation

void Set (const Standard_Real x, const Standard_Real y, const Standard_Real z, const Standard_Real w)
void Set (const gp_Quaternion &theQuaternion)
Standard_Real X () const
Standard_Real Y () const
Standard_Real Z () const
Standard_Real W () const
void SetIdent ()
 Make identity quaternion (zero-rotation)

void Reverse ()
 Reverse direction of rotation (conjugate quaternion)

gp_Quaternion Reversed () const
 Return rotation with reversed direction (conjugated quaternion)

void Invert ()
 Inverts quaternion (both rotation direction and norm)

gp_Quaternion Inverted () const
 Return inversed quaternion q^-1

Standard_Real SquareNorm () const
 Returns square norm of quaternion

Standard_Real Norm () const
 Returns norm of quaternion

void Scale (const Standard_Real theScale)
 Scale all components by quaternion by theScale; note that
rotation is not changed by this operation (except 0-scaling)

void operator*= (const Standard_Real theScale)
gp_Quaternion Scaled (const Standard_Real theScale) const
 Returns scaled quaternion

gp_Quaternion operator* (const Standard_Real theScale) const
void StabilizeLength ()
 Stabilize quaternion length within 1 - 1/4.
This operation is a lot faster than normalization
and preserve length goes to 0 or infinity

void Normalize ()
 Scale quaternion that its norm goes to 1.
The appearing of 0 magnitude or near is a error,
so we can be sure that can divide by magnitude

gp_Quaternion Normalized () const
 Returns quaternion scaled so that its norm goes to 1.

gp_Quaternion Negated () const
 Returns quaternion with all components negated.
Note that this operation does not affect neither
rotation operator defined by quaternion nor its norm.

gp_Quaternion operator- () const
gp_Quaternion Added (const gp_Quaternion &theOther) const
 Makes sum of quaternion components; result is "rotations mix"

gp_Quaternion operator+ (const gp_Quaternion &theOther) const
gp_Quaternion Subtracted (const gp_Quaternion &theOther) const
 Makes difference of quaternion components; result is "rotations mix"

gp_Quaternion operator- (const gp_Quaternion &theOther) const
gp_Quaternion Multiplied (const gp_Quaternion &theOther) const
 Multiply function - work the same as Matrices multiplying.
qq' = (cross(v,v') + wv' + w'v, ww' - dot(v,v'))
Result is rotation combination: q' than q (here q=this, q'=theQ).
Notices than:
qq' != q'q;
qq^-1 = q;

gp_Quaternion operator* (const gp_Quaternion &theOther) const
void Add (const gp_Quaternion &theOther)
 Adds componnets of other quaternion; result is "rotations mix"

void operator+= (const gp_Quaternion &theOther)
void Subtract (const gp_Quaternion &theOther)
 Subtracts componnets of other quaternion; result is "rotations mix"

void operator-= (const gp_Quaternion &theOther)
void Multiply (const gp_Quaternion &theOther)
 Adds rotation by multiplication

void operator*= (const gp_Quaternion &theOther)
Standard_Real Dot (const gp_Quaternion &theOther) const
 Computes inner product / scalar product / Dot

Standard_Real GetRotationAngle () const
 Return rotation angle from -PI to PI

gp_Vec Multiply (const gp_Vec &theVec) const
 Rotates vector by quaternion as rotation operator

gp_Vec operator* (const gp_Vec &theVec) const

Constructor & Destructor Documentation

gp_Quaternion::gp_Quaternion ( const gp_Vec theVecFrom,
const gp_Vec theVecTo 
)
gp_Quaternion::gp_Quaternion ( const gp_Vec theVecFrom,
const gp_Vec theVecTo,
const gp_Vec theHelpCrossVec 
)

Member Function Documentation

void gp_Quaternion::GetEulerAngles ( const gp_EulerSequence  theOrder,
Standard_Real theAlpha,
Standard_Real theBeta,
Standard_Real theGamma 
) const
void gp_Quaternion::GetVectorAndAngle ( gp_Vec theAxis,
Standard_Real theAngle 
) const
gp_Quaternion gp_Quaternion::operator* ( const Standard_Real  theScale) const [inline]
gp_Quaternion gp_Quaternion::operator* ( const gp_Quaternion theOther) const [inline]
gp_Vec gp_Quaternion::operator* ( const gp_Vec theVec) const [inline]
void gp_Quaternion::operator*= ( const Standard_Real  theScale) [inline]
void gp_Quaternion::operator*= ( const gp_Quaternion theOther) [inline]
gp_Quaternion gp_Quaternion::operator+ ( const gp_Quaternion theOther) const [inline]
void gp_Quaternion::operator+= ( const gp_Quaternion theOther) [inline]
gp_Quaternion gp_Quaternion::operator- ( ) const [inline]
gp_Quaternion gp_Quaternion::operator- ( const gp_Quaternion theOther) const [inline]
void gp_Quaternion::operator-= ( const gp_Quaternion theOther) [inline]
void gp_Quaternion::SetRotation ( const gp_Vec theVecFrom,
const gp_Vec theVecTo 
)
void gp_Quaternion::SetRotation ( const gp_Vec theVecFrom,
const gp_Vec theVecTo,
const gp_Vec theHelpCrossVec 
)

The documentation for this class was generated from the following file: