gp_Quaternion Class Reference

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
constexpr	gp_Quaternion () noexcept
	Creates an identity quaternion.
constexpr	gp_Quaternion (const double theX, const double theY, const double theZ, const double theW) noexcept
	Creates quaternion directly from component values.
	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 double 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)
bool	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 double theAngle)
	Create a unit quaternion from Axis+Angle representation.
void	GetVectorAndAngle (gp_Vec &theAxis, double &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)
gp_Mat	GetMatrix () const
	Returns rotation operation as 3*3 matrix.
void	SetEulerAngles (const gp_EulerSequence theOrder, const double theAlpha, const double theBeta, const double theGamma)
	Create a unit quaternion representing rotation defined by generalized Euler angles.
void	GetEulerAngles (const gp_EulerSequence theOrder, double &theAlpha, double &theBeta, double &theGamma) const
	Returns Euler angles describing current rotation.
constexpr void	Set (const double theX, const double theY, const double theZ, const double theW) noexcept
constexpr void	Set (const gp_Quaternion &theQuaternion) noexcept
constexpr double	X () const noexcept
constexpr double	Y () const noexcept
constexpr double	Z () const noexcept
constexpr double	W () const noexcept
constexpr void	SetIdent () noexcept
	Make identity quaternion (zero-rotation)
constexpr void	Reverse () noexcept
	Reverse direction of rotation (conjugate quaternion)
constexpr gp_Quaternion	Reversed () const noexcept
	Return rotation with reversed direction (conjugated quaternion)
constexpr void	Invert ()
	Inverts quaternion (both rotation direction and norm)
constexpr gp_Quaternion	Inverted () const
	Return inversed quaternion q^-1.
constexpr double	SquareNorm () const noexcept
	Returns square norm of quaternion.
double	Norm () const
	Returns norm of quaternion.
constexpr void	Scale (const double theScale) noexcept
	Scale all components by quaternion by theScale; note that rotation is not changed by this operation (except 0-scaling)
void	operator*= (const double theScale)
constexpr gp_Quaternion	Scaled (const double theScale) const noexcept
	Returns scaled quaternion.
constexpr gp_Quaternion	operator* (const double theScale) const noexcept
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.
constexpr gp_Quaternion	Negated () const noexcept
	Returns quaternion with all components negated. Note that this operation does not affect neither rotation operator defined by quaternion nor its norm.
constexpr gp_Quaternion	operator- () const noexcept
constexpr gp_Quaternion	Added (const gp_Quaternion &theOther) const noexcept
	Makes sum of quaternion components; result is "rotations mix".
constexpr gp_Quaternion	operator+ (const gp_Quaternion &theOther) const noexcept
constexpr gp_Quaternion	Subtracted (const gp_Quaternion &theOther) const noexcept
	Makes difference of quaternion components; result is "rotations mix".
constexpr gp_Quaternion	operator- (const gp_Quaternion &theOther) const noexcept
constexpr gp_Quaternion	Multiplied (const gp_Quaternion &theOther) const noexcept
	Multiply function - work the same as Matrices multiplying.
constexpr gp_Quaternion	operator* (const gp_Quaternion &theOther) const noexcept
constexpr void	Add (const gp_Quaternion &theOther) noexcept
	Adds components of other quaternion; result is "rotations mix".
void	operator+= (const gp_Quaternion &theOther)
constexpr void	Subtract (const gp_Quaternion &theOther) noexcept
	Subtracts components 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)
constexpr double	Dot (const gp_Quaternion &theOther) const noexcept
	Computes inner product / scalar product / Dot.
double	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

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]

constexpr gp_Quaternion::gp_Quaternion ( )

inlineconstexprnoexcept

Creates an identity quaternion.

gp_Quaternion() [2/6]

constexpr gp_Quaternion::gp_Quaternion ( const double theX, const double theY, const double theZ, const double theW )

inlineconstexprnoexcept

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 double 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()

constexpr void gp_Quaternion::Add ( const gp_Quaternion & theOther )

inlineconstexprnoexcept

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

Added()

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

inlineconstexprnoexcept

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

Dot()

constexpr double gp_Quaternion::Dot ( const gp_Quaternion & theOther ) const

inlineconstexprnoexcept

Computes inner product / scalar product / Dot.

GetEulerAngles()

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

Returns Euler angles describing current rotation.

GetMatrix()

gp_Mat gp_Quaternion::GetMatrix

(

)

const

Returns rotation operation as 3*3 matrix.

GetRotationAngle()

double gp_Quaternion::GetRotationAngle

(

)

const

Return rotation angle from -PI to PI.

GetVectorAndAngle()

void gp_Quaternion::GetVectorAndAngle	(	gp_Vec &	theAxis,
		double &	theAngle ) const

Convert a quaternion to Axis+Angle representation, preserve the axis direction and angle from -PI to +PI.

Invert()

constexpr void gp_Quaternion::Invert ( )

inlineconstexpr

Inverts quaternion (both rotation direction and norm)

Inverted()

constexpr gp_Quaternion gp_Quaternion::Inverted ( ) const

inlineconstexpr

Return inversed quaternion q^-1.

IsEqual()

bool gp_Quaternion::IsEqual

(

const gp_Quaternion &

theOther

)

const

Simple equal test without precision.

Multiplied()

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

inlineconstexprnoexcept

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()

constexpr gp_Quaternion gp_Quaternion::Negated ( ) const

inlineconstexprnoexcept

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

Norm()

double 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]

constexpr gp_Quaternion gp_Quaternion::operator* ( const double theScale ) const

inlineconstexprnoexcept

operator*() [2/3]

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

inlineconstexprnoexcept

operator*() [3/3]

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

inline

operator*=() [1/2]

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

inline

operator*=() [2/2]

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

inline

operator+()

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

inlineconstexprnoexcept

operator+=()

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

inline

operator-() [1/2]

constexpr gp_Quaternion gp_Quaternion::operator- ( ) const

inlineconstexprnoexcept

operator-() [2/2]

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

inlineconstexprnoexcept

operator-=()

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

inline

Reverse()

constexpr void gp_Quaternion::Reverse ( )

inlineconstexprnoexcept

Reverse direction of rotation (conjugate quaternion)

Reversed()

constexpr gp_Quaternion gp_Quaternion::Reversed ( ) const

inlineconstexprnoexcept

Return rotation with reversed direction (conjugated quaternion)

Scale()

constexpr void gp_Quaternion::Scale ( const double theScale )

inlineconstexprnoexcept

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

Scaled()

constexpr gp_Quaternion gp_Quaternion::Scaled ( const double theScale ) const

inlineconstexprnoexcept

Returns scaled quaternion.

Set() [1/2]

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

inlineconstexprnoexcept

Set() [2/2]

constexpr void gp_Quaternion::Set ( const gp_Quaternion & theQuaternion )

inlineconstexprnoexcept

SetEulerAngles()

void gp_Quaternion::SetEulerAngles	(	const gp_EulerSequence	theOrder,
		const double	theAlpha,
		const double	theBeta,
		const double	theGamma )

Create a unit quaternion representing rotation defined by generalized Euler angles.

SetIdent()

constexpr void gp_Quaternion::SetIdent ( )

inlineconstexprnoexcept

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 double	theAngle )

Create a unit quaternion from Axis+Angle representation.

SquareNorm()

constexpr double gp_Quaternion::SquareNorm ( ) const

inlineconstexprnoexcept

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()

constexpr void gp_Quaternion::Subtract ( const gp_Quaternion & theOther )

inlineconstexprnoexcept

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

Subtracted()

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

inlineconstexprnoexcept

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

W()

constexpr double gp_Quaternion::W ( ) const

inlineconstexprnoexcept

X()

constexpr double gp_Quaternion::X ( ) const

inlineconstexprnoexcept

Y()

constexpr double gp_Quaternion::Y ( ) const

inlineconstexprnoexcept

Z()

constexpr double gp_Quaternion::Z ( ) const

inlineconstexprnoexcept

---

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

• gp_Quaternion.hxx