Quaternion class used to perform rotations in 3D space. More...

#include <quaternion.H>

Collaboration diagram for quaternion:

[legend]

Public Types
enum	eulerOrder : unsigned char { XZX , XYX , YXY , YZY , ZYZ , ZXZ , XZY , XYZ , YXZ , YZX , ZYX , ZXY , ROLL_PITCH_YAW = XYZ , YAW_PITCH_ROLL = ZYX }
	Euler-angle rotation order. More...
typedef scalar	cmptType
	Component type.
typedef scalar	magType
	Magnitude type.

Public Member Functions
	quaternion ()=default
	Default construct.
	quaternion (const quaternion &)=default
	Copy construct.
quaternion &	operator= (const quaternion &)=default
	Copy assignment.
	quaternion (const Foam::zero)
	Construct initialized to zero.
	quaternion (const scalar w, const vector &v)
	Construct given scalar and vector parts.
	quaternion (const vector &d, const scalar theta)
	Construct rotation quaternion given direction d and angle theta.
	quaternion (const vector &d, const scalar cosTheta, const bool isNormalised)
	Construct a rotation quaternion given direction d and cosine angle cosTheta and flag if d is normalised.
	quaternion (const scalar w)
	Construct a real quaternion from the given scalar part, the vector part = zero.
	quaternion (const vector &v)
	Construct a pure imaginary quaternion given the vector part, the scalar part = 0.
	quaternion (const eulerOrder order, const vector &angles)
	Construct from three Euler rotation angles.
	quaternion (const tensor &rotationTensor)
	Construct from a rotation tensor.
	quaternion (Istream &is)
	Construct from Istream.
scalar	w () const noexcept
	Scalar part of the quaternion ( = cos(theta/2) for rotation).
const vector &	v () const noexcept
	Vector part of the quaternion ( = axis of rotation).
tensor	R () const
	The rotation tensor corresponding to the quaternion.
vector	eulerAngles (const eulerOrder order) const
	Return the Euler rotation angles corresponding to the specified rotation order.
scalar &	w () noexcept
	Scalar part of the quaternion ( = cos(theta/2) for rotation).
vector &	v () noexcept
	Vector part of the quaternion ( = axis of rotation).
quaternion &	normalise (const scalar tol=ROOTVSMALL)
	Inplace normalise the quaternion by its magnitude.
vector	transform (const vector &v) const
	Rotate the given vector.
vector	invTransform (const vector &v) const
	Rotate the given vector anti-clockwise.
quaternion	transform (const quaternion &q) const
	Rotate the given quaternion (and normalise).
quaternion	invTransform (const quaternion &q) const
	Rotate the given quaternion anti-clockwise (and normalise).
void	operator+= (const quaternion &q)
void	operator-= (const quaternion &q)
void	operator*= (const quaternion &q)
void	operator/= (const quaternion &q)
void	operator= (const scalar s)
	Change scalar portion only.
void	operator= (const vector &v)
	Change vector portion only.
void	operator= (const Foam::zero)
	Assign scalar and vector to zero.
void	operator*= (const scalar s)
void	operator/= (const scalar s)
void	normalize ()
	Inplace normalise the quaternion by its magnitude.
quaternion	normalized () const
	Return the quaternion normalised by its magnitude.

Static Public Member Functions
static quaternion	unit (const vector &v)
	Return the unit quaternion (versor) from the given vector (w = sqrt(1 - \|sqr(v)\|)).

Static Public Attributes
static const Enum< eulerOrder >	eulerOrderNames
	The names for Euler-angle and Tait-Bryan angles, including "rollPitchYaw" and "yawPitchRoll" aliases.
static constexpr direction	rank = 1
	Rank of quaternion is 1.
static constexpr const char *const	typeName = "quaternion"
static const quaternion	zero
static const quaternion	I

Detailed Description

Quaternion class used to perform rotations in 3D space.

Source files

Definition at line 53 of file quaternion.H.

Member Typedef Documentation

◆ cmptType

typedef scalar cmptType

Component type.

Definition at line 105 of file quaternion.H.

◆ magType

typedef scalar magType

Magnitude type.

Definition at line 110 of file quaternion.H.

Member Enumeration Documentation

◆ eulerOrder

enum eulerOrder : unsigned char

Euler-angle rotation order.

Enumerator
XZX
XYX
YXY
YZY
ZYZ
ZXZ
XZY
XYZ
YXZ
YZX
ZYX
ZXY
ROLL_PITCH_YAW
YAW_PITCH_ROLL

Definition at line 115 of file quaternion.H.

Constructor & Destructor Documentation

◆ quaternion() [1/11]

quaternion ( )

default

Default construct.

Referenced by invTransform(), normalized(), operator*=(), operator+=(), operator-=(), operator/=(), operator=(), quaternion(), quaternion(), transform(), and unit().

Here is the caller graph for this function:

◆ quaternion() [2/11]

quaternion ( const quaternion & )

default

Copy construct.

References quaternion().

Here is the call graph for this function:

◆ quaternion() [3/11]

quaternion ( const Foam::zero )

inline

Construct initialized to zero.

Definition at line 24 of file quaternionI.H.

References Foam::Zero.

◆ quaternion() [4/11]

quaternion	(	const scalar	w,
		const vector &	v )

inline

Construct given scalar and vector parts.

Definition at line 31 of file quaternionI.H.

References v(), and w().

Here is the call graph for this function:

◆ quaternion() [5/11]

quaternion	(	const vector &	d,
		const scalar	theta )

inline

Construct rotation quaternion given direction d and angle theta.

Definition at line 38 of file quaternionI.H.

References Foam::cos(), Foam::normalised(), and Foam::sin().

Here is the call graph for this function:

◆ quaternion() [6/11]

quaternion	(	const vector &	d,
		const scalar	cosTheta,
		const bool	isNormalised )

inline

Construct a rotation quaternion given direction d and cosine angle cosTheta and flag if d is normalised.

Definition at line 45 of file quaternionI.H.

References Foam::normalised(), and Foam::sqrt().

Here is the call graph for this function:

◆ quaternion() [7/11]

quaternion ( const scalar w )

inlineexplicit

Construct a real quaternion from the given scalar part, the vector part = zero.

Definition at line 66 of file quaternionI.H.

References w(), and Foam::Zero.

Here is the call graph for this function:

◆ quaternion() [8/11]

quaternion ( const vector & v )

inlineexplicit

Construct a pure imaginary quaternion given the vector part, the scalar part = 0.

Definition at line 73 of file quaternionI.H.

References v().

Here is the call graph for this function:

◆ quaternion() [9/11]

quaternion	(	const eulerOrder	order,
		const vector &	angles )

inline

Construct from three Euler rotation angles.

Definition at line 86 of file quaternionI.H.

References Foam::abort(), Foam::FatalError, FatalErrorInFunction, operator*=(), operator=(), quaternion(), Vector< Cmpt >::x(), XYX, XYZ, XZX, XZY, Vector< Cmpt >::y(), YXY, YXZ, YZX, YZY, Vector< Cmpt >::z(), ZXY, ZXZ, ZYX, and ZYZ.

Here is the call graph for this function:

◆ quaternion() [10/11]

quaternion ( const tensor & rotationTensor )

inlineexplicit

Construct from a rotation tensor.

Definition at line 199 of file quaternionI.H.

References Foam::rotationTensor(), s(), and Foam::sqrt().

Here is the call graph for this function:

◆ quaternion() [11/11]

quaternion ( Istream & is )

explicit

Construct from Istream.

Definition at line 58 of file quaternion.C.

Member Function Documentation

◆ operator=() [1/4]

quaternion & operator= ( const quaternion & )

default

Copy assignment.

References eulerAngles(), Foam::FOAM_DEPRECATED_FOR(), invTransform(), Foam::noexcept, normalise(), quaternion(), R(), Foam::rotationTensor(), s(), transform(), v(), w(), and zero.

Referenced by quaternion().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ unit()

Foam::quaternion unit ( const vector & v )

inlinestatic

Return the unit quaternion (versor) from the given vector (w = sqrt(1 - |sqr(v)|)).

Definition at line 80 of file quaternionI.H.

References Foam::magSqr(), quaternion(), Foam::sqrt(), and v().

Referenced by joint::unitQuaternion().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ w() [1/2]

Foam::scalar w ( ) const

inlinenoexcept

Scalar part of the quaternion ( = cos(theta/2) for rotation).

Definition at line 278 of file quaternionI.H.

References Foam::noexcept.

Referenced by Foam::conjugate(), eulerAngles(), Foam::exp(), Foam::inv(), Foam::magSqr(), Foam::name(), Foam::operator&(), Foam::operator*(), Foam::operator*(), operator*=(), Foam::operator-(), Foam::operator/(), Foam::operator<<(), operator=(), Foam::operator==(), Foam::operator>>(), Foam::pow(), Foam::pow(), quaternion(), quaternion(), and R().

Here is the caller graph for this function:

◆ v() [1/2]

const Foam::vector & v ( ) const

inlinenoexcept

Vector part of the quaternion ( = axis of rotation).

Definition at line 284 of file quaternionI.H.

References Foam::noexcept.

Referenced by Foam::conjugate(), eulerAngles(), Foam::exp(), Foam::inv(), Foam::magSqr(), Foam::name(), Foam::operator&(), Foam::operator*(), Foam::operator*(), operator*=(), Foam::operator-(), Foam::operator/(), Foam::operator<<(), operator=(), operator=(), Foam::operator==(), Foam::operator>>(), Foam::pow(), Foam::pow(), quaternion(), quaternion(), R(), unit(), and joint::unitQuaternion().

Here is the caller graph for this function:

◆ R()

Foam::tensor R ( ) const

inline

The rotation tensor corresponding to the quaternion.

Definition at line 352 of file quaternionI.H.

References Foam::sqr(), v(), w(), w2, x, and y.

Referenced by operator=(), axisAngle::rotation(), Foam::transform(), and triad::triad().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ eulerAngles()

Foam::vector eulerAngles ( const eulerOrder order ) const

inline

Return the Euler rotation angles corresponding to the specified rotation order.

Definition at line 401 of file quaternionI.H.

References Foam::abort(), Foam::FatalError, FatalErrorInFunction, Foam::sqr(), v(), w(), w2, x, XYX, XYZ, XZX, XZY, y, YXY, YXZ, YZX, YZY, Foam::Zero, ZXY, ZXZ, ZYX, and ZYZ.

Referenced by operator=(), and sixDoFRigidBodyState::write().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ w() [2/2]

Foam::scalar & w ( )

inlinenoexcept

Scalar part of the quaternion ( = cos(theta/2) for rotation).

Definition at line 290 of file quaternionI.H.

References Foam::noexcept.

◆ v() [2/2]

Foam::vector & v ( )

inlinenoexcept

Vector part of the quaternion ( = axis of rotation).

Definition at line 296 of file quaternionI.H.

References Foam::noexcept.

◆ normalise()

Foam::quaternion & normalise ( const scalar tol = ROOTVSMALL )

inline

Inplace normalise the quaternion by its magnitude.

For small magnitudes (less than ROOTVSMALL) set to zero.

Definition at line 302 of file quaternionI.H.

References Foam::mag(), and s().

Referenced by Foam::average(), rigidBodySolver::correctQuaternionJoints(), normalize(), normalized(), and operator=().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ transform() [1/2]

Foam::vector transform ( const vector & v ) const

inline

Rotate the given vector.

Definition at line 325 of file quaternionI.H.

References Foam::conjugate().

Referenced by searchableExtrudedCircle::findParametricNearest(), polyline::operator()(), and operator=().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ invTransform() [1/2]

Foam::vector invTransform ( const vector & v ) const

inline

Rotate the given vector anti-clockwise.

Definition at line 331 of file quaternionI.H.

References Foam::conjugate().

Referenced by operator=().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ transform() [2/2]

Foam::quaternion transform ( const quaternion & q ) const

inline

Rotate the given quaternion (and normalise).

Definition at line 337 of file quaternionI.H.

References Foam::normalised(), and quaternion().

Here is the call graph for this function:

◆ invTransform() [2/2]

Foam::quaternion invTransform ( const quaternion & q ) const

inline

Rotate the given quaternion anti-clockwise (and normalise).

Definition at line 343 of file quaternionI.H.

References Foam::conjugate(), Foam::normalised(), and quaternion().

Here is the call graph for this function:

◆ operator+=()

void operator+= ( const quaternion & q )

inline

Definition at line 582 of file quaternionI.H.

References quaternion().

Here is the call graph for this function:

◆ operator-=()

void operator-= ( const quaternion & q )

inline

Definition at line 588 of file quaternionI.H.

References quaternion().

Here is the call graph for this function:

◆ operator*=() [1/2]

void operator*= ( const quaternion & q )

inline

Definition at line 594 of file quaternionI.H.

References quaternion(), v(), w(), and w0.

Referenced by operator/=(), and quaternion().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ operator/=() [1/2]

void operator/= ( const quaternion & q )

inline

Definition at line 601 of file quaternionI.H.

References Foam::inv(), operator*=(), and quaternion().

Here is the call graph for this function:

◆ operator=() [2/4]

void operator= ( const scalar s )

inline

Change scalar portion only.

Definition at line 607 of file quaternionI.H.

References s().

Here is the call graph for this function:

◆ operator=() [3/4]

void operator= ( const vector & v )

inline

Change vector portion only.

Definition at line 613 of file quaternionI.H.

References v().

Here is the call graph for this function:

◆ operator=() [4/4]

void operator= ( const Foam::zero )

inline

Assign scalar and vector to zero.

Definition at line 619 of file quaternionI.H.

References Foam::Zero.

◆ operator*=() [2/2]

void operator*= ( const scalar s )

inline

Definition at line 626 of file quaternionI.H.

References s().

Here is the call graph for this function:

◆ operator/=() [2/2]

void operator/= ( const scalar s )

inline

Definition at line 632 of file quaternionI.H.

References s().

Here is the call graph for this function:

◆ normalize()

void normalize ( )

inline

Inplace normalise the quaternion by its magnitude.

Definition at line 332 of file quaternion.H.

References normalise(), and normalize().

Referenced by normalize().

Here is the call graph for this function:

Here is the caller graph for this function:

◆ normalized()

quaternion normalized ( ) const

inline

Return the quaternion normalised by its magnitude.

Definition at line 338 of file quaternion.H.

References normalise(), normalized(), and quaternion().

Referenced by normalized().

Here is the call graph for this function:

Here is the caller graph for this function:

Member Data Documentation

◆ eulerOrderNames

const Foam::Enum< Foam::quaternion::eulerOrder > eulerOrderNames

static

The names for Euler-angle and Tait-Bryan angles, including "rollPitchYaw" and "yawPitchRoll" aliases.

Definition at line 132 of file quaternion.H.

Referenced by Foam::lumpedPointTools::lumpedPointStates(), lumpedPointState::writeDict(), and euler::writeEntry().

◆ rank

direction rank = 1

staticconstexpr

Rank of quaternion is 1.

Definition at line 140 of file quaternion.H.

◆ typeName

const char* const typeName = "quaternion"

staticconstexpr

Definition at line 145 of file quaternion.H.

◆ zero

const Foam::quaternion zero

static

Definition at line 147 of file quaternion.H.

Referenced by operator=().

◆ I

const Foam::quaternion I

static

Definition at line 148 of file quaternion.H.

Referenced by septernion::operator=().

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

src/OpenFOAM/primitives/quaternion/quaternion.H
src/OpenFOAM/primitives/quaternion/quaternion.C
src/OpenFOAM/primitives/quaternion/quaternionI.H

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ cmptType

◆ magType

Member Enumeration Documentation

◆ eulerOrder

Constructor & Destructor Documentation

◆ quaternion() [1/11]

◆ quaternion() [2/11]

◆ quaternion() [3/11]

◆ quaternion() [4/11]

◆ quaternion() [5/11]

◆ quaternion() [6/11]

◆ quaternion() [7/11]

◆ quaternion() [8/11]

◆ quaternion() [9/11]

◆ quaternion() [10/11]

◆ quaternion() [11/11]

Member Function Documentation

◆ operator=() [1/4]

◆ unit()

◆ w() [1/2]

◆ v() [1/2]

◆ R()

◆ eulerAngles()

◆ w() [2/2]

◆ v() [2/2]

◆ normalise()

◆ transform() [1/2]

◆ invTransform() [1/2]

◆ transform() [2/2]

◆ invTransform() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator*=() [1/2]

◆ operator/=() [1/2]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator*=() [2/2]

◆ operator/=() [2/2]

◆ normalize()

◆ normalized()

Member Data Documentation

◆ eulerOrderNames

◆ rank

◆ typeName

◆ zero

◆ I