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)
More...

#include <gp_Quaternion.hxx>

Public Member Functions
	gp_Quaternion ()
	Creates an identity quaternion More...
	gp_Quaternion (const Standard_Real x, const Standard_Real y, const Standard_Real z, const Standard_Real w)
	Creates quaternion directly from component values More...
	gp_Quaternion (const gp_Quaternion &theToCopy)
	Creates copy of another quaternion More...
	gp_Quaternion (const gp_Vec &theVecFrom, const gp_Vec &theVecTo)
	Creates quaternion representing shortest-arc rotation operator producing vector theVecTo from vector theVecFrom. More...
	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. More...
	gp_Quaternion (const gp_Vec &theAxis, const Standard_Real theAngle)
	Creates quaternion representing rotation on angle theAngle around vector theAxis More...
	gp_Quaternion (const gp_Mat &theMat)
	Creates quaternion from rotation matrix 3*3 (which should be orthonormal skew-symmetric matrix) More...
Standard_Boolean	IsEqual (const gp_Quaternion &theOther) const
	Simple equal test without precision More...
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). More...
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. More...
void	SetVectorAndAngle (const gp_Vec &theAxis, const Standard_Real theAngle)
	Create a unit quaternion from Axis+Angle representation More...
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 More...
void	SetMatrix (const gp_Mat &theMat)
	Create a unit quaternion by rotation matrix <br> matrix must contain only rotation (not scale or shear) <br> For numerical stability we find first the greatest component of quaternion and than search others from this one More...
gp_Mat	GetMatrix () const
	Returns rotation operation as 3*3 matrix More...
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 More...
void	GetEulerAngles (const gp_EulerSequence theOrder, Standard_Real &theAlpha, Standard_Real &theBeta, Standard_Real &theGamma) const
	Returns Euler angles describing current rotation More...
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) More...
void	Reverse ()
	Reverse direction of rotation (conjugate quaternion) More...
gp_Quaternion	Reversed () const
	Return rotation with reversed direction (conjugated quaternion) More...
void	Invert ()
	Inverts quaternion (both rotation direction and norm) More...
gp_Quaternion	Inverted () const
	Return inversed quaternion q^-1 More...
Standard_Real	SquareNorm () const
	Returns square norm of quaternion More...
Standard_Real	Norm () const
	Returns norm of quaternion More...
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) More...
void	operator*= (const Standard_Real theScale)
gp_Quaternion	Scaled (const Standard_Real theScale) const
	Returns scaled quaternion More...
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 More...
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 More...
gp_Quaternion	Normalized () const
	Returns quaternion scaled so that its norm goes to 1. More...
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. More...
gp_Quaternion	operator- () const
gp_Quaternion	Added (const gp_Quaternion &theOther) const
	Makes sum of quaternion components; result is "rotations mix" More...
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" More...
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; More...
gp_Quaternion	operator* (const gp_Quaternion &theOther) const
void	Add (const gp_Quaternion &theOther)
	Adds componnets of other quaternion; result is "rotations mix" More...
void	operator+= (const gp_Quaternion &theOther)
void	Subtract (const gp_Quaternion &theOther)
	Subtracts componnets of other quaternion; result is "rotations mix" More...
void	operator-= (const gp_Quaternion &theOther)
void	Multiply (const gp_Quaternion &theOther)
	Adds rotation by multiplication More...
void	operator*= (const gp_Quaternion &theOther)
Standard_Real	Dot (const gp_Quaternion &theOther) const
	Computes inner product / scalar product / Dot More...
Standard_Real	GetRotationAngle () const
	Return rotation angle from -PI to PI More...
gp_Vec	Multiply (const gp_Vec &theVec) const
	Rotates vector by quaternion as rotation operator More...
gp_Vec	operator* (const gp_Vec &theVec) const

Detailed Description

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)

Constructor & Destructor Documentation

gp_Quaternion::gp_Quaternion

(

)

Creates an identity quaternion

gp_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::gp_Quaternion

(

const gp_Quaternion &

theToCopy

)

Creates copy of another quaternion

gp_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::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::gp_Quaternion	(	const gp_Vec &	theAxis,
		const Standard_Real	theAngle
	)

Creates quaternion representing rotation on angle
theAngle around vector theAxis

gp_Quaternion::gp_Quaternion

(

const gp_Mat &

theMat

)

Creates quaternion from rotation matrix 3*3
(which should be orthonormal skew-symmetric matrix)

Member Function Documentation

void gp_Quaternion::Add

(

const gp_Quaternion &

theOther

)

Adds componnets of other quaternion; result is "rotations mix"

gp_Quaternion gp_Quaternion::Added

(

const gp_Quaternion &

theOther

)

const

Makes sum of quaternion components; result is "rotations mix"

Standard_Real gp_Quaternion::Dot

(

const gp_Quaternion &

theOther

)

const

Computes inner product / scalar product / Dot

void gp_Quaternion::GetEulerAngles	(	const gp_EulerSequence	theOrder,
		Standard_Real &	theAlpha,
		Standard_Real &	theBeta,
		Standard_Real &	theGamma
	)		const

Returns Euler angles describing current rotation

gp_Mat gp_Quaternion::GetMatrix

(

)

const

Returns rotation operation as 3*3 matrix

Standard_Real gp_Quaternion::GetRotationAngle

(

)

const

Return rotation angle from -PI to PI

void gp_Quaternion::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 gp_Quaternion::Invert

(

)

Inverts quaternion (both rotation direction and norm)

gp_Quaternion gp_Quaternion::Inverted

(

)

const

Return inversed quaternion q^-1

Standard_Boolean gp_Quaternion::IsEqual

(

const gp_Quaternion &

theOther

)

const

Simple equal test without precision

gp_Quaternion 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;

void gp_Quaternion::Multiply

(

const gp_Quaternion &

theOther

)

Adds rotation by multiplication

gp_Vec gp_Quaternion::Multiply

(

const gp_Vec &

theVec

)

const

Rotates vector by quaternion as rotation operator

gp_Quaternion 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.

Standard_Real gp_Quaternion::Norm

(

)

const

Returns norm of quaternion

void gp_Quaternion::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 gp_Quaternion::Normalized

(

)

const

Returns quaternion scaled so that its norm goes to 1.

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::Reverse

(

)

Reverse direction of rotation (conjugate quaternion)

gp_Quaternion gp_Quaternion::Reversed

(

)

const

Return rotation with reversed direction (conjugated quaternion)

void gp_Quaternion::Scale

(

const Standard_Real

theScale

)

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

gp_Quaternion gp_Quaternion::Scaled

(

const Standard_Real

theScale

)

const

Returns scaled quaternion

void gp_Quaternion::Set	(	const Standard_Real	x,
		const Standard_Real	y,
		const Standard_Real	z,
		const Standard_Real	w
	)

void gp_Quaternion::Set

(

const gp_Quaternion &

theQuaternion

)

void gp_Quaternion::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 gp_Quaternion::SetIdent

(

)

Make identity quaternion (zero-rotation)

void gp_Quaternion::SetMatrix

(

const gp_Mat &

theMat

)

 Create a unit quaternion by rotation matrix <br>
     matrix must contain only rotation (not scale or shear) <br>

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

void gp_Quaternion::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 gp_Quaternion::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 gp_Quaternion::SetVectorAndAngle	(	const gp_Vec &	theAxis,
		const Standard_Real	theAngle
	)

Create a unit quaternion from Axis+Angle representation

Standard_Real gp_Quaternion::SquareNorm

(

)

const

Returns square norm of quaternion

void gp_Quaternion::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 gp_Quaternion::Subtract

(

const gp_Quaternion &

theOther

)

Subtracts componnets of other quaternion; result is "rotations mix"

gp_Quaternion gp_Quaternion::Subtracted

(

const gp_Quaternion &

theOther

)

const

Makes difference of quaternion components; result is "rotations mix"

Standard_Real gp_Quaternion::W

(

)

const

Standard_Real gp_Quaternion::X

(

)

const

Standard_Real gp_Quaternion::Y

(

)

const

Standard_Real gp_Quaternion::Z

(

)

const

---

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

• gp_Quaternion.hxx