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

#include <gp_Quaternion.hxx>

Public Member Functions
	gp_Quaternion ()
	Creates an identity quaternion. More...

	gp_Quaternion (const Standard_Real theX, const Standard_Real theY, const Standard_Real theZ, const Standard_Real theW)
	Creates quaternion directly from component values. 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 matrix must contain only rotation (not scale or shear) 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 theX, const Standard_Real theY, const Standard_Real theZ, const Standard_Real theW)

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. More...

gp_Quaternion	operator* (const gp_Quaternion &theOther) const

void	Add (const gp_Quaternion &theOther)
	Adds components of other quaternion; result is "rotations mix". More...

void	operator+= (const gp_Quaternion &theOther)

void	Subtract (const gp_Quaternion &theOther)
	Subtracts components 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 quaternion and implements operations with rotations basing on quaternion mathematics.

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

Constructor & Destructor Documentation

◆ gp_Quaternion() [1/6]

gp_Quaternion::gp_Quaternion ( )

inline

Creates an identity quaternion.

◆ gp_Quaternion() [2/6]

gp_Quaternion::gp_Quaternion	(	const Standard_Real	theX,
		const Standard_Real	theY,
		const Standard_Real	theZ,
		const Standard_Real	theW
	)

inline

Creates quaternion directly from component values.

◆ gp_Quaternion() [3/6]

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

inline

Creates quaternion representing shortest-arc rotation operator producing vector theVecTo from vector theVecFrom.

◆ gp_Quaternion() [4/6]

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

inline

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() [5/6]

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

inline

Creates quaternion representing rotation on angle theAngle around vector theAxis.

◆ gp_Quaternion() [6/6]

gp_Quaternion::gp_Quaternion ( const gp_Mat & theMat )

inline

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

Member Function Documentation

◆ Add()

void gp_Quaternion::Add ( const gp_Quaternion & theOther )

inline

Adds components of other quaternion; result is "rotations mix".

◆ Added()

gp_Quaternion gp_Quaternion::Added ( const gp_Quaternion & theOther ) const

inline

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

◆ Dot()

Standard_Real gp_Quaternion::Dot ( const gp_Quaternion & theOther ) const

inline

Computes inner product / scalar product / Dot.

◆ GetEulerAngles()

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

Returns Euler angles describing current rotation.

◆ GetMatrix()

gp_Mat gp_Quaternion::GetMatrix ( ) const

Returns rotation operation as 3*3 matrix.

◆ GetRotationAngle()

Standard_Real gp_Quaternion::GetRotationAngle ( ) const

Return rotation angle from -PI to PI.

◆ GetVectorAndAngle()

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.

◆ Invert()

void gp_Quaternion::Invert ( )

inline

Inverts quaternion (both rotation direction and norm)

◆ Inverted()

gp_Quaternion gp_Quaternion::Inverted ( ) const

inline

Return inversed quaternion q^-1.

◆ IsEqual()

Standard_Boolean gp_Quaternion::IsEqual ( const gp_Quaternion & theOther ) const

Simple equal test without precision.

◆ Multiplied()

gp_Quaternion gp_Quaternion::Multiplied ( const gp_Quaternion & theOther ) const

inline

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 that:

qq' != q'q;

qq^-1 = q;

◆ Multiply() [1/2]

void gp_Quaternion::Multiply ( const gp_Quaternion & theOther )

inline

Adds rotation by multiplication.

◆ Multiply() [2/2]

gp_Vec gp_Quaternion::Multiply ( const gp_Vec & theVec ) const

Rotates vector by quaternion as rotation operator.

◆ Negated()

gp_Quaternion gp_Quaternion::Negated ( ) const

inline

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

◆ Norm()

Standard_Real gp_Quaternion::Norm ( ) const

inline

Returns norm of quaternion.

◆ Normalize()

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.

◆ Normalized()

gp_Quaternion gp_Quaternion::Normalized ( ) const

inline

Returns quaternion scaled so that its norm goes to 1.

◆ operator*() [1/3]

gp_Quaternion gp_Quaternion::operator* ( const Standard_Real theScale ) const

inline

◆ operator*() [2/3]

gp_Quaternion gp_Quaternion::operator* ( const gp_Quaternion & theOther ) const

inline

◆ operator*() [3/3]

gp_Vec gp_Quaternion::operator* ( const gp_Vec & theVec ) const

inline

◆ operator*=() [1/2]

void gp_Quaternion::operator*= ( const Standard_Real theScale )

inline

◆ operator*=() [2/2]

void gp_Quaternion::operator*= ( const gp_Quaternion & theOther )

inline

◆ operator+()

gp_Quaternion gp_Quaternion::operator+ ( const gp_Quaternion & theOther ) const

inline

◆ operator+=()

void gp_Quaternion::operator+= ( const gp_Quaternion & theOther )

inline

◆ operator-() [1/2]

gp_Quaternion gp_Quaternion::operator- ( ) const

inline

◆ operator-() [2/2]

gp_Quaternion gp_Quaternion::operator- ( const gp_Quaternion & theOther ) const

inline

◆ operator-=()

void gp_Quaternion::operator-= ( const gp_Quaternion & theOther )

inline

◆ Reverse()

void gp_Quaternion::Reverse ( )

inline

Reverse direction of rotation (conjugate quaternion)

◆ Reversed()

gp_Quaternion gp_Quaternion::Reversed ( ) const

inline

Return rotation with reversed direction (conjugated quaternion)

◆ Scale()

void gp_Quaternion::Scale ( const Standard_Real theScale )

inline

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

◆ Scaled()

gp_Quaternion gp_Quaternion::Scaled ( const Standard_Real theScale ) const

inline

Returns scaled quaternion.

◆ Set() [1/2]

void gp_Quaternion::Set	(	const Standard_Real	theX,
		const Standard_Real	theY,
		const Standard_Real	theZ,
		const Standard_Real	theW
	)

inline

◆ Set() [2/2]

void gp_Quaternion::Set ( const gp_Quaternion & theQuaternion )

inline

◆ SetEulerAngles()

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.

◆ SetIdent()

void gp_Quaternion::SetIdent ( )

inline

Make identity quaternion (zero-rotation)

◆ SetMatrix()

void gp_Quaternion::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

◆ SetRotation() [1/2]

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).

◆ SetRotation() [2/2]

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.

◆ SetVectorAndAngle()

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

Create a unit quaternion from Axis+Angle representation.

◆ SquareNorm()

Standard_Real gp_Quaternion::SquareNorm ( ) const

inline

Returns square norm of quaternion.

◆ StabilizeLength()

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.

◆ Subtract()

void gp_Quaternion::Subtract ( const gp_Quaternion & theOther )

inline

Subtracts components of other quaternion; result is "rotations mix".

◆ Subtracted()

gp_Quaternion gp_Quaternion::Subtracted ( const gp_Quaternion & theOther ) const

inline

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

◆ W()

Standard_Real gp_Quaternion::W ( ) const

inline

◆ X()

Standard_Real gp_Quaternion::X ( ) const

inline

◆ Y()

Standard_Real gp_Quaternion::Y ( ) const

inline

◆ Z()

Standard_Real gp_Quaternion::Z ( ) const

inline

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

gp_Quaternion.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ gp_Quaternion() [1/6]

◆ gp_Quaternion() [2/6]

◆ gp_Quaternion() [3/6]

◆ gp_Quaternion() [4/6]

◆ gp_Quaternion() [5/6]

◆ gp_Quaternion() [6/6]

Member Function Documentation

◆ Add()

◆ Added()

◆ Dot()

◆ GetEulerAngles()

◆ GetMatrix()

◆ GetRotationAngle()

◆ GetVectorAndAngle()

◆ Invert()

◆ Inverted()

◆ IsEqual()

◆ Multiplied()

◆ Multiply() [1/2]

◆ Multiply() [2/2]

◆ Negated()

◆ Norm()

◆ Normalize()

◆ Normalized()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ Reverse()

◆ Reversed()

◆ Scale()

◆ Scaled()

◆ Set() [1/2]

◆ Set() [2/2]

◆ SetEulerAngles()

◆ SetIdent()

◆ SetMatrix()

◆ SetRotation() [1/2]

◆ SetRotation() [2/2]

◆ SetVectorAndAngle()

◆ SquareNorm()

◆ StabilizeLength()

◆ Subtract()

◆ Subtracted()

◆ W()

◆ X()

◆ Y()

◆ Z()