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

Collaboration diagram for quaternion:

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. More...

typedef scalar	magType
	Magnitude type. More...

Public Member Functions
	quaternion ()=default
	Default construct. More...

	quaternion (const quaternion &)=default
	Copy construct. More...

quaternion &	operator= (const quaternion &)=default
	Copy assignment. More...

	quaternion (const Foam::zero)
	Construct initialized to zero. More...

	quaternion (const scalar w, const vector &v)
	Construct given scalar and vector parts. More...

	quaternion (const vector &d, const scalar theta)
	Construct rotation quaternion given direction d and angle theta. More...

	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. More...

	quaternion (const scalar w)
	Construct a real quaternion from the given scalar part, the vector part = zero. More...

	quaternion (const vector &v)
	Construct a pure imaginary quaternion given the vector part, the scalar part = 0. More...

	quaternion (const eulerOrder order, const vector &angles)
	Construct from three Euler rotation angles. More...

	quaternion (const tensor &rotationTensor)
	Construct from a rotation tensor. More...

	quaternion (Istream &is)
	Construct from Istream. More...

scalar	w () const noexcept
	Scalar part of the quaternion ( = cos(theta/2) for rotation) More...

const vector &	v () const noexcept
	Vector part of the quaternion ( = axis of rotation) More...

tensor	R () const
	The rotation tensor corresponding to the quaternion. More...

vector	eulerAngles (const eulerOrder order) const
	Return the Euler rotation angles corresponding to the specified rotation order. More...

scalar &	w () noexcept
	Scalar part of the quaternion ( = cos(theta/2) for rotation) More...

vector &	v () noexcept
	Vector part of the quaternion ( = axis of rotation) More...

quaternion &	normalise ()
	Inplace normalise the quaternion by its magnitude. More...

vector	transform (const vector &v) const
	Rotate the given vector. More...

vector	invTransform (const vector &v) const
	Rotate the given vector anti-clockwise. More...

quaternion	transform (const quaternion &q) const
	Rotate the given quaternion (and normalise) More...

quaternion	invTransform (const quaternion &q) const
	Rotate the given quaternion anti-clockwise (and normalise) More...

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. More...

void	operator= (const vector &v)
	Change vector portion only. More...

void	operator= (const Foam::zero)
	Assign scalar and vector to zero. More...

void	operator*= (const scalar s)

void	operator/= (const scalar s)

void	normalize ()
	Inplace normalise the quaternion by its magnitude. More...

quaternion	normalized () const
	Return the quaternion normalised by its magnitude. More...

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

Static Public Attributes
static const Enum< eulerOrder >	eulerOrderNames
	The names for Euler-angle and Tait-Bryan angles, including "rollPitchYaw" and "yawPitchRoll" aliases. More...

static constexpr direction	rank = 1
	Rank of quaternion is 1. More...

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.

◆ quaternion() [2/11]

quaternion ( const quaternion & )

default

Copy construct.

◆ quaternion() [3/11]

quaternion ( const Foam::zero )

inline

Construct initialized to zero.

Definition at line 24 of file quaternionI.H.

◆ 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.

◆ 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.

◆ 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 46 of file quaternionI.H.

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

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◆ 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.

◆ 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.

◆ quaternion() [9/11]

quaternion	(	const eulerOrder	order,
		const vector &	angles
	)

inline

Construct from three Euler rotation angles.

Definition at line 87 of file quaternionI.H.

References Foam::abort(), Foam::FatalError, and FatalErrorInFunction.

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◆ quaternion() [10/11]

quaternion ( const tensor & rotationTensor )

inlineexplicit

Construct from a rotation tensor.

Definition at line 200 of file quaternionI.H.

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

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◆ 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.

◆ 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(), and Foam::sqrt().

Referenced by joint::unitQuaternion().

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◆ 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.

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

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◆ 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.

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

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◆ R()

Foam::tensor R ( ) const

inline

The rotation tensor corresponding to the quaternion.

Definition at line 351 of file quaternionI.H.

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

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

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◆ 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(), w2, x, y, and Foam::Zero.

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◆ 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.

◆ v() [2/2]

Foam::vector & v ( )

inlinenoexcept

Vector part of the quaternion ( = axis of rotation)

Definition at line 296 of file quaternionI.H.

◆ normalise()

Foam::quaternion & normalise ( )

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(), s, and Foam::Zero.

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

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◆ transform() [1/2]

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

inline

Rotate the given vector.

Definition at line 324 of file quaternionI.H.

References Foam::conjugate().

Referenced by searchableExtrudedCircle::findParametricNearest(), polyline::operator()(), Foam::operator*(), Foam::operator/(), and septernion::operator/=().

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◆ invTransform() [1/2]

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

inline

Rotate the given vector anti-clockwise.

Definition at line 330 of file quaternionI.H.

References Foam::conjugate().

Referenced by Foam::operator*(), and septernion::operator*=().

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◆ transform() [2/2]

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

inline

Rotate the given quaternion (and normalise)

Definition at line 336 of file quaternionI.H.

References Foam::normalised().

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◆ 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(), and Foam::normalised().

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◆ operator+=()

void operator+= ( const quaternion & q )

inline

Definition at line 581 of file quaternionI.H.

◆ operator-=()

void operator-= ( const quaternion & q )

inline

Definition at line 587 of file quaternionI.H.

◆ operator*=() [1/2]

void operator*= ( const quaternion & q )

inline

Definition at line 593 of file quaternionI.H.

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

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◆ operator/=() [1/2]

void operator/= ( const quaternion & q )

inline

Definition at line 600 of file quaternionI.H.

References Foam::inv().

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◆ operator=() [2/4]

void operator= ( const scalar s )

inline

Change scalar portion only.

Definition at line 606 of file quaternionI.H.

References s.

◆ operator=() [3/4]

void operator= ( const vector & v )

inline

Change vector portion only.

Definition at line 612 of file quaternionI.H.

◆ operator=() [4/4]

void operator= ( const Foam::zero )

inline

Assign scalar and vector to zero.

Definition at line 618 of file quaternionI.H.

References Foam::Zero.

◆ operator*=() [2/2]

void operator*= ( const scalar s )

inline

Definition at line 625 of file quaternionI.H.

References s.

◆ operator/=() [2/2]

void operator/= ( const scalar s )

inline

Definition at line 631 of file quaternionI.H.

References s.

◆ normalize()

void normalize ( )

inline

Inplace normalise the quaternion by its magnitude.

Definition at line 332 of file quaternion.H.

References quaternion::normalise().

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◆ normalized()

quaternion normalized ( ) const

inline

Return the quaternion normalised by its magnitude.

Definition at line 338 of file quaternion.H.

References quaternion::normalise().

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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 lumpedPointMovement::readDict(), lumpedPointState::writeDict(), and euler::writeEntry().

◆ rank

constexpr direction rank = 1

static

Rank of quaternion is 1.

Definition at line 140 of file quaternion.H.

◆ typeName

constexpr const char* const typeName = "quaternion"

static

Definition at line 145 of file quaternion.H.

◆ zero

const Foam::quaternion zero

static

Definition at line 147 of file quaternion.H.

◆ 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