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

Collaboration diagram for quaternion:

Public Types
enum	rotationSequence { ZYX, ZYZ, ZXY, ZXZ, YXZ, YXY, YZX, YZY, XYZ, XYX, XZY, XZX }
	Euler-angle rotation sequence. More...

typedef scalar	cmptType
	Component type. More...

Public Member Functions
	quaternion ()
	Construct null. More...

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

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

	quaternion (const vector &d, const scalar cosTheta, const bool normalized)
	Construct a rotation quaternion given the direction d. More...

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

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

	quaternion (const rotationSequence rs, const vector &angles)
	Construct a quaternion given the three Euler angles. More...

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

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

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

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

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

vector	eulerAngles (const rotationSequence rs) const
	Return a vector of euler angles corresponding to the. More...

quaternion	normalized () const

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

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

void	normalize ()

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 normalize) More...

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

void	operator+= (const quaternion &)

void	operator-= (const quaternion &)

void	operator*= (const quaternion &)

void	operator/= (const quaternion &)

void	operator= (const scalar)

void	operator= (const vector &)

void	operator*= (const scalar)

void	operator/= (const scalar)

Static Public Member Functions
static quaternion	unit (const vector &v)
	Return the unit quaternion (versor) from the given vector. More...

Static Public Attributes
static const direction	rank = 1
	Rank of quaternion is 1. More...

static const char *const	typeName = "quaternion"

static const quaternion	zero

static const quaternion	I

Friends
Istream &	operator>> (Istream &is, quaternion &)

Ostream &	operator<< (Ostream &os, const quaternion &C)

Detailed Description

Quaternion class used to perform rotations in 3D space.

Source files

Definition at line 60 of file quaternion.H.

Member Typedef Documentation

◆ cmptType

typedef scalar cmptType

Component type.

Definition at line 98 of file quaternion.H.

Member Enumeration Documentation

◆ rotationSequence

enum rotationSequence

Euler-angle rotation sequence.

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

Definition at line 101 of file quaternion.H.

Constructor & Destructor Documentation

◆ quaternion() [1/9]

quaternion ( )

inline

Construct null.

Definition at line 28 of file quaternionI.H.

Referenced by Foam::conjugate(), Foam::exp(), Foam::inv(), quaternion::normalize(), Foam::operator*(), Foam::operator+(), Foam::operator-(), Foam::operator/(), quaternion::quaternion(), and quaternion::unit().

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◆ quaternion() [2/9]

quaternion	(	const scalar	w,
		const vector &	v
	)

inline

Construct given scalar and vector parts.

Definition at line 32 of file quaternionI.H.

◆ quaternion() [3/9]

quaternion	(	const vector &	d,
		const scalar	theta
	)

inline

Construct a rotation quaternion given the direction d.

and angle theta

Definition at line 39 of file quaternionI.H.

References quaternion::quaternion().

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◆ quaternion() [4/9]

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

inline

Construct a rotation quaternion given the direction d.

and cosine angle cosTheta and a if d is normalized

Definition at line 47 of file quaternionI.H.

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

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◆ quaternion() [5/9]

quaternion ( const scalar w )

inlineexplicit

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

Definition at line 67 of file quaternionI.H.

◆ quaternion() [6/9]

quaternion ( const vector & v )

inlineexplicit

Construct a pure imaginary quaternion given the vector part,.

the scalar part = 0

Definition at line 74 of file quaternionI.H.

◆ quaternion() [7/9]

quaternion	(	const rotationSequence	rs,
		const vector &	angles
	)

inline

Construct a quaternion given the three Euler angles.

Definition at line 88 of file quaternionI.H.

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

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◆ quaternion() [8/9]

quaternion ( const tensor & rotationTensor )

inlineexplicit

Construct a quaternion from a rotation tensor.

Definition at line 176 of file quaternionI.H.

References s(), Foam::sqrt(), Tensor< Cmpt >::xx(), Tensor< Cmpt >::xy(), Tensor< Cmpt >::xz(), Tensor< Cmpt >::yx(), Tensor< Cmpt >::yy(), Tensor< Cmpt >::yz(), Tensor< Cmpt >::zx(), Tensor< Cmpt >::zy(), and Tensor< Cmpt >::zz().

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◆ quaternion() [9/9]

quaternion ( Istream & is )

Construct from Istream.

Definition at line 38 of file quaternion.C.

Member Function Documentation

◆ 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 81 of file quaternionI.H.

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

Referenced by joint::unitQuaternion().

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◆ w() [1/2]

Foam::scalar w ( ) const

inline

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

Definition at line 254 of file quaternionI.H.

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

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◆ v() [1/2]

const Foam::vector & v ( ) const

inline

Vector part of the quaternion ( = axis of rotation)

Definition at line 260 of file quaternionI.H.

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

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◆ R()

Foam::tensor R ( ) const

inline

The rotation tensor corresponding the quaternion.

Definition at line 323 of file quaternionI.H.

References Foam::acos(), Foam::asin(), Foam::atan2(), Foam::constant::physicoChemical::c2, quaternion::eulerAngles(), Foam::sqr(), quaternion::v(), quaternion::w(), w2, x, Vector< Cmpt >::x(), y, Vector< Cmpt >::y(), and Vector< Cmpt >::z().

Referenced by Foam::transform(), Foam::transformPoints(), and triad::triad().

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◆ eulerAngles()

Foam::vector eulerAngles ( const rotationSequence rs ) const

inline

Return a vector of euler angles corresponding to the.

specified rotation sequence

Definition at line 373 of file quaternionI.H.

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

Referenced by quaternion::R().

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◆ normalized()

Foam::quaternion normalized ( ) const

inline

Definition at line 278 of file quaternionI.H.

References Foam::mag().

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◆ w() [2/2]

Foam::scalar & w ( )

inline

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

Definition at line 266 of file quaternionI.H.

◆ v() [2/2]

Foam::vector & v ( )

inline

Vector part of the quaternion ( = axis of rotation)

Definition at line 272 of file quaternionI.H.

◆ normalize()

void normalize ( )

inline

Definition at line 284 of file quaternionI.H.

References Foam::mag(), quaternion::operator/=(), quaternion::quaternion(), quaternion::v(), and quaternion::w().

Referenced by Foam::average().

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◆ transform() [1/2]

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

inline

Rotate the given vector.

Definition at line 296 of file quaternionI.H.

References Foam::conjugate().

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

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◆ invTransform() [1/2]

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

inline

Rotate the given vector anti-clockwise.

Definition at line 302 of file quaternionI.H.

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

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

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◆ transform() [2/2]

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

inline

Rotate the given quaternion (and normalize)

Definition at line 308 of file quaternionI.H.

References quaternion::invTransform(), and Foam::normalize().

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◆ invTransform() [2/2]

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

inline

Rotate the given quaternion anti-clockwise (and normalize)

Definition at line 315 of file quaternionI.H.

References Foam::conjugate(), and Foam::normalize().

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◆ operator+=()

void operator+= ( const quaternion & q )

inline

Definition at line 526 of file quaternionI.H.

◆ operator-=()

void operator-= ( const quaternion & q )

inline

Definition at line 532 of file quaternionI.H.

◆ operator*=() [1/2]

void operator*= ( const quaternion & q )

inline

Definition at line 538 of file quaternionI.H.

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

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

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◆ operator/=() [1/2]

void operator/= ( const quaternion & q )

inline

Definition at line 545 of file quaternionI.H.

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

Referenced by quaternion::normalize().

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◆ operator=() [1/2]

void operator= ( const scalar s )

inline

Definition at line 551 of file quaternionI.H.

References s().

Referenced by quaternion::quaternion().

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◆ operator=() [2/2]

void operator= ( const vector & v )

inline

Definition at line 557 of file quaternionI.H.

References quaternion::v().

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◆ operator*=() [2/2]

void operator*= ( const scalar s )

inline

Definition at line 563 of file quaternionI.H.

References s().

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◆ operator/=() [2/2]

void operator/= ( const scalar s )

inline

Definition at line 569 of file quaternionI.H.

References s().

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Friends And Related Function Documentation

◆ operator>>

Istream& operator>>	(	Istream &	is,
		quaternion &
	)

friend

◆ operator<<

Ostream& operator<<	(	Ostream &	os,
		const quaternion &	C
	)

friend

Member Data Documentation

◆ rank

const direction rank = 1

static

Rank of quaternion is 1.

Definition at line 110 of file quaternion.H.

◆ typeName

const char *const typeName = "quaternion"

static

Definition at line 115 of file quaternion.H.

◆ zero

const Foam::quaternion zero

static

Definition at line 117 of file quaternion.H.

◆ I

const Foam::quaternion I

static

Definition at line 118 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

Friends

Detailed Description

Member Typedef Documentation

◆ cmptType

Member Enumeration Documentation

◆ rotationSequence

Constructor & Destructor Documentation

◆ quaternion() [1/9]

◆ quaternion() [2/9]

◆ quaternion() [3/9]

◆ quaternion() [4/9]

◆ quaternion() [5/9]

◆ quaternion() [6/9]

◆ quaternion() [7/9]

◆ quaternion() [8/9]

◆ quaternion() [9/9]

Member Function Documentation

◆ unit()

◆ w() [1/2]

◆ v() [1/2]

◆ R()

◆ eulerAngles()

◆ normalized()

◆ w() [2/2]

◆ v() [2/2]

◆ normalize()

◆ transform() [1/2]

◆ invTransform() [1/2]

◆ transform() [2/2]

◆ invTransform() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator*=() [1/2]

◆ operator/=() [1/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator*=() [2/2]

◆ operator/=() [2/2]

Friends And Related Function Documentation

◆ operator>>

◆ operator<<

Member Data Documentation

◆ rank

◆ typeName

◆ zero

◆ I