quaternion Class Reference

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 normalised)
 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 vectorv () 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 normalised () const
 
scalar & w ()
 Scalar part of the quaternion ( = cos(theta/2) for rotation) More...
 
vectorv ()
 Vector part of the quaternion ( = axis of rotation) More...
 
void normalise ()
 
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 &)
 
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

Istreamoperator>> (Istream &is, quaternion &)
 
Ostreamoperator<< (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

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.

◆ 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.

◆ quaternion() [4/9]

quaternion ( const vector d,
const scalar  cosTheta,
const bool  normalised 
)
inline

Construct a rotation quaternion given the direction d.

and cosine angle cosTheta and a if d is normalised

Definition at line 46 of file quaternionI.H.

References Foam::mag(), Foam::normalised(), 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 87 of file quaternionI.H.

References Foam::abort(), Foam::FatalError, FatalErrorInFunction, Vector< Cmpt >::x(), Vector< Cmpt >::y(), and Vector< Cmpt >::z().

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◆ quaternion() [8/9]

quaternion ( const tensor rotationTensor)
inlineexplicit

Construct a quaternion from a rotation tensor.

Definition at line 175 of file quaternionI.H.

References Foam::rotationTensor(), 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(), 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(), Foam::exp(), Foam::inv(), Foam::magSqr(), Foam::name(), Foam::operator&(), Foam::operator*(), quaternion::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
inline

◆ R()

Foam::tensor R ( ) const
inline

The rotation tensor corresponding the quaternion.

Definition at line 323 of file quaternionI.H.

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

Referenced by cyclicTransform::cyclicTransform(), function::jcalc(), functionDot::jcalc(), rotating::jcalc(), Foam::transform(), 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 372 of file quaternionI.H.

References Foam::abort(), Foam::FatalError, FatalErrorInFunction, Foam::sqr(), w2, x, y, and Foam::Zero.

Referenced by rigidBodyState::write(), and sixDoFRigidBodyState::write().

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◆ normalised()

Foam::quaternion normalised ( ) 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.

◆ normalise()

void normalise ( )
inline

Definition at line 284 of file quaternionI.H.

References Foam::mag().

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(), 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 302 of file quaternionI.H.

References Foam::conjugate().

Referenced by 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 308 of file quaternionI.H.

References Foam::normalise().

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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 314 of file quaternionI.H.

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

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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.

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◆ operator/=() [1/2]

void operator/= ( const quaternion q)
inline

Definition at line 545 of file quaternionI.H.

References Foam::inv().

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◆ operator=() [1/2]

void operator= ( const scalar  s)
inline

Definition at line 551 of file quaternionI.H.

References s().

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◆ operator=() [2/2]

void operator= ( const vector v)
inline

Definition at line 557 of file quaternionI.H.

◆ 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: