OGRE  1.9.0
Ogre::Quaternion Class Reference

Implementation of a Quaternion, i.e. More...

#include <OgreQuaternion.h>

Public Member Functions

 Quaternion ()
 Default constructor, initializes to identity rotation (aka 0°)
 
 Quaternion (const Matrix3 &rot)
 Construct a quaternion from a rotation matrix.
 
 Quaternion (const Radian &rfAngle, const Vector3 &rkAxis)
 Construct a quaternion from an angle/axis.
 
 Quaternion (const Vector3 &xaxis, const Vector3 &yaxis, const Vector3 &zaxis)
 Construct a quaternion from 3 orthonormal local axes.
 
 Quaternion (const Vector3 *akAxis)
 Construct a quaternion from 3 orthonormal local axes.
 
 Quaternion (Real *valptr)
 Construct a quaternion from 4 manual w/x/y/z values.
 
 Quaternion (Real fW, Real fX, Real fY, Real fZ)
 Construct from an explicit list of values.
 
Real Dot (const Quaternion &rkQ) const
 Returns the dot product of the quaternion.
 
bool equals (const Quaternion &rhs, const Radian &tolerance) const
 Equality with tolerance (tolerance is max angle difference)
 
Quaternion Exp () const
 Apply to unit-length quaternion.
 
void FromAngleAxis (const Radian &rfAngle, const Vector3 &rkAxis)
 Setups the quaternion using the supplied vector, and "roll" around that vector by the specified radians.
 
void FromAxes (const Vector3 &xAxis, const Vector3 &yAxis, const Vector3 &zAxis)
 
void FromAxes (const Vector3 *akAxis)
 Constructs the quaternion using 3 axes, the axes are assumed to be orthonormal.
 
void FromRotationMatrix (const Matrix3 &kRot)
 
Radian getPitch (bool reprojectAxis=true) const
 Calculate the local pitch element of this quaternion.
 
Radian getRoll (bool reprojectAxis=true) const
 Calculate the local roll element of this quaternion.
 
Radian getYaw (bool reprojectAxis=true) const
 Calculate the local yaw element of this quaternion.
 
Quaternion Inverse () const
 
bool isNaN () const
 Check whether this quaternion contains valid values.
 
Quaternion Log () const
 
Real Norm () const
 
Real normalise (void)
 Normalises this quaternion, and returns the previous length.
 
bool operator!= (const Quaternion &rhs) const
 
Quaternion operator* (const Quaternion &rkQ) const
 
Vector3 operator* (const Vector3 &rkVector) const
 Rotation of a vector by a quaternion.
 
Quaternion operator* (Real fScalar) const
 
Quaternion operator+ (const Quaternion &rkQ) const
 
Quaternion operator- () const
 
Quaternion operator- (const Quaternion &rkQ) const
 
Quaternionoperator= (const Quaternion &rkQ)
 
bool operator== (const Quaternion &rhs) const
 
Realoperator[] (const size_t i)
 Array accessor operator.
 
Real operator[] (const size_t i) const
 Array accessor operator.
 
bool orientationEquals (const Quaternion &other, Real tolerance=1e-3) const
 Compare two quaternions which are assumed to be used as orientations.
 
Realptr ()
 Pointer accessor for direct copying.
 
const Realptr () const
 Pointer accessor for direct copying.
 
void swap (Quaternion &other)
 Exchange the contents of this quaternion with another.
 
void ToAngleAxis (Degree &dAngle, Vector3 &rkAxis) const
 
void ToAngleAxis (Radian &rfAngle, Vector3 &rkAxis) const
 
void ToAxes (Vector3 &xAxis, Vector3 &yAxis, Vector3 &zAxis) const
 
void ToAxes (Vector3 *akAxis) const
 Gets the 3 orthonormal axes defining the quaternion.
 
void ToRotationMatrix (Matrix3 &kRot) const
 
Quaternion UnitInverse () const
 Apply to non-zero quaternion.
 
Vector3 xAxis (void) const
 Returns the X orthonormal axis defining the quaternion.
 
Vector3 yAxis (void) const
 Returns the Y orthonormal axis defining the quaternion.
 
Vector3 zAxis (void) const
 Returns the Z orthonormal axis defining the quaternion.
 

Static Public Member Functions

static void Intermediate (const Quaternion &rkQ0, const Quaternion &rkQ1, const Quaternion &rkQ2, Quaternion &rka, Quaternion &rkB)
 Setup for spherical quadratic interpolation.
 
static Quaternion nlerp (Real fT, const Quaternion &rkP, const Quaternion &rkQ, bool shortestPath=false)
 Performs Normalised linear interpolation between two quaternions, and returns the result.
 
static Quaternion Slerp (Real fT, const Quaternion &rkP, const Quaternion &rkQ, bool shortestPath=false)
 Performs Spherical linear interpolation between two quaternions, and returns the result.
 
static Quaternion SlerpExtraSpins (Real fT, const Quaternion &rkP, const Quaternion &rkQ, int iExtraSpins)
 
static Quaternion Squad (Real fT, const Quaternion &rkP, const Quaternion &rkA, const Quaternion &rkB, const Quaternion &rkQ, bool shortestPath=false)
 Spherical quadratic interpolation.
 

Public Attributes

Real w
 
Real x
 
Real y
 
Real z
 

Static Public Attributes

static const Quaternion IDENTITY
 
static const Real msEpsilon
 Cutoff for sine near zero.
 
static const Quaternion ZERO
 

Friends

_OgreExport friend Quaternion operator* (Real fScalar, const Quaternion &rkQ)
 
_OgreExport friend std::ostream & operator<< (std::ostream &o, const Quaternion &q)
 Function for writing to a stream.
 

Detailed Description

Implementation of a Quaternion, i.e.

a rotation around an axis. For more information about Quaternions and the theory behind it, we recommend reading: http://www.ogre3d.org/tikiwiki/Quaternion+and+Rotation+Primer and http://www.cprogramming.com/tutorial/3d/quaternions.html and http://www.gamedev.net/page/resources/_/reference/programming/math-and-physics/quaternions/quaternion-powers-r1095

Definition at line 56 of file OgreQuaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

Ogre::Quaternion::Quaternion ( )

Default constructor, initializes to identity rotation (aka 0°)

Definition at line 60 of file OgreQuaternion.h.

◆ Quaternion() [2/7]

Ogre::Quaternion::Quaternion ( Real fW,
Real fX,
Real fY,
Real fZ )

Construct from an explicit list of values.

Definition at line 65 of file OgreQuaternion.h.

◆ Quaternion() [3/7]

Ogre::Quaternion::Quaternion ( const Matrix3 & rot)

Construct a quaternion from a rotation matrix.

Definition at line 72 of file OgreQuaternion.h.

◆ Quaternion() [4/7]

Ogre::Quaternion::Quaternion ( const Radian & rfAngle,
const Vector3 & rkAxis )

Construct a quaternion from an angle/axis.

Definition at line 77 of file OgreQuaternion.h.

◆ Quaternion() [5/7]

Ogre::Quaternion::Quaternion ( const Vector3 & xaxis,
const Vector3 & yaxis,
const Vector3 & zaxis )

Construct a quaternion from 3 orthonormal local axes.

Definition at line 82 of file OgreQuaternion.h.

◆ Quaternion() [6/7]

Ogre::Quaternion::Quaternion ( const Vector3 * akAxis)

Construct a quaternion from 3 orthonormal local axes.

Definition at line 87 of file OgreQuaternion.h.

◆ Quaternion() [7/7]

Ogre::Quaternion::Quaternion ( Real * valptr)

Construct a quaternion from 4 manual w/x/y/z values.

Definition at line 92 of file OgreQuaternion.h.

Member Function Documentation

◆ Dot()

Real Ogre::Quaternion::Dot ( const Quaternion & rkQ) const

Returns the dot product of the quaternion.

◆ equals()

bool Ogre::Quaternion::equals ( const Quaternion & rhs,
const Radian & tolerance ) const

Equality with tolerance (tolerance is max angle difference)

Remarks
Both equals() and orientationEquals() measure the exact same thing. One measures the difference by angle, the other by a different, non-linear metric.

◆ Exp()

Quaternion Ogre::Quaternion::Exp ( ) const

Apply to unit-length quaternion.

◆ FromAngleAxis()

void Ogre::Quaternion::FromAngleAxis ( const Radian & rfAngle,
const Vector3 & rkAxis )

Setups the quaternion using the supplied vector, and "roll" around that vector by the specified radians.

Referenced by Ogre::Vector3::getRotationTo(), and Ogre::Vector3::randomDeviant().

◆ FromAxes() [1/2]

void Ogre::Quaternion::FromAxes ( const Vector3 & xAxis,
const Vector3 & yAxis,
const Vector3 & zAxis )

◆ FromAxes() [2/2]

void Ogre::Quaternion::FromAxes ( const Vector3 * akAxis)

Constructs the quaternion using 3 axes, the axes are assumed to be orthonormal.

See also
FromAxes

◆ FromRotationMatrix()

void Ogre::Quaternion::FromRotationMatrix ( const Matrix3 & kRot)

◆ getPitch()

Radian Ogre::Quaternion::getPitch ( bool reprojectAxis = true) const

Calculate the local pitch element of this quaternion.

Parameters
reprojectAxisBy default the method returns the 'intuitive' result that is, if you projected the local Z of the quaternion onto the X and Y axes, the angle between them is returned. If set to true though, the result is the actual yaw that will be used to implement the quaternion, which is the shortest possible path to get to the same orientation and may involve less axial rotation. The co-domain of the returned value is from -180 to 180 degrees.

◆ getRoll()

Radian Ogre::Quaternion::getRoll ( bool reprojectAxis = true) const

Calculate the local roll element of this quaternion.

Parameters
reprojectAxisBy default the method returns the 'intuitive' result that is, if you projected the local Y of the quaternion onto the X and Y axes, the angle between them is returned. If set to false though, the result is the actual yaw that will be used to implement the quaternion, which is the shortest possible path to get to the same orientation and may involve less axial rotation. The co-domain of the returned value is from -180 to 180 degrees.

◆ getYaw()

Radian Ogre::Quaternion::getYaw ( bool reprojectAxis = true) const

Calculate the local yaw element of this quaternion.

Parameters
reprojectAxisBy default the method returns the 'intuitive' result that is, if you projected the local Y of the quaternion onto the X and Z axes, the angle between them is returned. If set to true though, the result is the actual yaw that will be used to implement the quaternion, which is the shortest possible path to get to the same orientation and may involve less axial rotation. The co-domain of the returned value is from -180 to 180 degrees.

◆ Intermediate()

static void Ogre::Quaternion::Intermediate ( const Quaternion & rkQ0,
const Quaternion & rkQ1,
const Quaternion & rkQ2,
Quaternion & rka,
Quaternion & rkB )
static

Setup for spherical quadratic interpolation.

◆ Inverse()

Quaternion Ogre::Quaternion::Inverse ( ) const

◆ isNaN()

bool Ogre::Quaternion::isNaN ( ) const

Check whether this quaternion contains valid values.

Definition at line 320 of file OgreQuaternion.h.

◆ Log()

Quaternion Ogre::Quaternion::Log ( ) const

◆ nlerp()

static Quaternion Ogre::Quaternion::nlerp ( Real fT,
const Quaternion & rkP,
const Quaternion & rkQ,
bool shortestPath = false )
static

Performs Normalised linear interpolation between two quaternions, and returns the result.

nlerp ( 0.0f, A, B ) = A nlerp ( 1.0f, A, B ) = B

Remarks
Nlerp is faster than Slerp. Nlerp has the proprieties of being commutative (
See also
Slerp; commutativity is desired in certain places, like IK animation), and being torque-minimal (unless shortestPath=false). However, it's performing the interpolation at non-constant velocity; sometimes this is desired, sometimes it is not. Having a non-constant velocity can produce a more natural rotation feeling without the need of tweaking the weights; however if your scene relies on the timing of the rotation or assumes it will point at a specific angle at a specific weight value, Slerp is a better choice.

◆ Norm()

Real Ogre::Quaternion::Norm ( ) const

◆ normalise()

Real Ogre::Quaternion::normalise ( void )

Normalises this quaternion, and returns the previous length.

Referenced by Ogre::Vector3::getRotationTo().

◆ operator!=()

bool Ogre::Quaternion::operator!= ( const Quaternion & rhs) const

Definition at line 191 of file OgreQuaternion.h.

References Ogre::operator==().

◆ operator*() [1/3]

Quaternion Ogre::Quaternion::operator* ( const Quaternion & rkQ) const

◆ operator*() [2/3]

Vector3 Ogre::Quaternion::operator* ( const Vector3 & rkVector) const

Rotation of a vector by a quaternion.

◆ operator*() [3/3]

Quaternion Ogre::Quaternion::operator* ( Real fScalar) const

◆ operator+()

Quaternion Ogre::Quaternion::operator+ ( const Quaternion & rkQ) const

◆ operator-() [1/2]

Quaternion Ogre::Quaternion::operator- ( ) const

◆ operator-() [2/2]

Quaternion Ogre::Quaternion::operator- ( const Quaternion & rkQ) const

◆ operator=()

Quaternion & Ogre::Quaternion::operator= ( const Quaternion & rkQ)

Definition at line 171 of file OgreQuaternion.h.

References w, x, y, and z.

◆ operator==()

bool Ogre::Quaternion::operator== ( const Quaternion & rhs) const

Definition at line 186 of file OgreQuaternion.h.

References w, x, y, and z.

◆ operator[]() [1/2]

Real & Ogre::Quaternion::operator[] ( const size_t i)

Array accessor operator.

Definition at line 116 of file OgreQuaternion.h.

◆ operator[]() [2/2]

Real Ogre::Quaternion::operator[] ( const size_t i) const

Array accessor operator.

Definition at line 108 of file OgreQuaternion.h.

◆ orientationEquals()

bool Ogre::Quaternion::orientationEquals ( const Quaternion & other,
Real tolerance = 1e-3 ) const

Compare two quaternions which are assumed to be used as orientations.

Remarks
Both equals() and orientationEquals() measure the exact same thing. One measures the difference by angle, the other by a different, non-linear metric.
Returns
true if the two orientations are the same or very close, relative to the given tolerance.

Definition at line 254 of file OgreQuaternion.h.

◆ ptr() [1/2]

Real * Ogre::Quaternion::ptr ( )

Pointer accessor for direct copying.

Definition at line 124 of file OgreQuaternion.h.

Referenced by Ogre::AnimableValue::setAsBaseValue().

◆ ptr() [2/2]

const Real * Ogre::Quaternion::ptr ( ) const

Pointer accessor for direct copying.

Definition at line 130 of file OgreQuaternion.h.

◆ Slerp()

static Quaternion Ogre::Quaternion::Slerp ( Real fT,
const Quaternion & rkP,
const Quaternion & rkQ,
bool shortestPath = false )
static

Performs Spherical linear interpolation between two quaternions, and returns the result.

Slerp ( 0.0f, A, B ) = A Slerp ( 1.0f, A, B ) = B

Returns
Interpolated quaternion
Remarks
Slerp has the proprieties of performing the interpolation at constant velocity, and being torque-minimal (unless shortestPath=false). However, it's NOT commutative, which means Slerp ( 0.75f, A, B ) != Slerp ( 0.25f, B, A ); therefore be careful if your code relies in the order of the operands. This is specially important in IK animation.

◆ SlerpExtraSpins()

static Quaternion Ogre::Quaternion::SlerpExtraSpins ( Real fT,
const Quaternion & rkP,
const Quaternion & rkQ,
int iExtraSpins )
static
See also
Slerp. It adds extra "spins" (i.e. rotates several times) specified by parameter 'iExtraSpins' while interpolating before arriving to the final values

◆ Squad()

static Quaternion Ogre::Quaternion::Squad ( Real fT,
const Quaternion & rkP,
const Quaternion & rkA,
const Quaternion & rkB,
const Quaternion & rkQ,
bool shortestPath = false )
static

Spherical quadratic interpolation.

◆ swap()

void Ogre::Quaternion::swap ( Quaternion & other)

Exchange the contents of this quaternion with another.

Definition at line 99 of file OgreQuaternion.h.

References std::swap(), w, x, y, and z.

◆ ToAngleAxis() [1/2]

void Ogre::Quaternion::ToAngleAxis ( Degree & dAngle,
Vector3 & rkAxis ) const

Definition at line 142 of file OgreQuaternion.h.

◆ ToAngleAxis() [2/2]

void Ogre::Quaternion::ToAngleAxis ( Radian & rfAngle,
Vector3 & rkAxis ) const

◆ ToAxes() [1/2]

void Ogre::Quaternion::ToAxes ( Vector3 & xAxis,
Vector3 & yAxis,
Vector3 & zAxis ) const

◆ ToAxes() [2/2]

void Ogre::Quaternion::ToAxes ( Vector3 * akAxis) const

Gets the 3 orthonormal axes defining the quaternion.

See also
FromAxes

◆ ToRotationMatrix()

void Ogre::Quaternion::ToRotationMatrix ( Matrix3 & kRot) const

Referenced by Ogre::Matrix4::Matrix4().

◆ UnitInverse()

Quaternion Ogre::Quaternion::UnitInverse ( ) const

Apply to non-zero quaternion.

◆ xAxis()

Vector3 Ogre::Quaternion::xAxis ( void ) const

Returns the X orthonormal axis defining the quaternion.

Same as doing xAxis = Vector3::UNIT_X * this. Also called the local X-axis

◆ yAxis()

Vector3 Ogre::Quaternion::yAxis ( void ) const

Returns the Y orthonormal axis defining the quaternion.

Same as doing yAxis = Vector3::UNIT_Y * this. Also called the local Y-axis

◆ zAxis()

Vector3 Ogre::Quaternion::zAxis ( void ) const

Returns the Z orthonormal axis defining the quaternion.

Same as doing zAxis = Vector3::UNIT_Z * this. Also called the local Z-axis

Friends And Related Symbol Documentation

◆ operator*

_OgreExport friend Quaternion operator* ( Real fScalar,
const Quaternion & rkQ )
friend

◆ operator<<

_OgreExport friend std::ostream & operator<< ( std::ostream & o,
const Quaternion & q )
friend

Function for writing to a stream.

Outputs "Quaternion(w, x, y, z)" with w,x,y,z being the member values of the quaternion.

Definition at line 328 of file OgreQuaternion.h.

Member Data Documentation

◆ IDENTITY

const Quaternion Ogre::Quaternion::IDENTITY
static

Definition at line 315 of file OgreQuaternion.h.

◆ msEpsilon

const Real Ogre::Quaternion::msEpsilon
static

Cutoff for sine near zero.

Definition at line 311 of file OgreQuaternion.h.

◆ w

Real Ogre::Quaternion::w

Definition at line 317 of file OgreQuaternion.h.

Referenced by Ogre::Vector3::getRotationTo(), operator=(), operator==(), and swap().

◆ x

Real Ogre::Quaternion::x

Definition at line 317 of file OgreQuaternion.h.

Referenced by Ogre::Vector3::getRotationTo(), operator=(), operator==(), and swap().

◆ y

Real Ogre::Quaternion::y

Definition at line 317 of file OgreQuaternion.h.

Referenced by Ogre::Vector3::getRotationTo(), operator=(), operator==(), and swap().

◆ z

Real Ogre::Quaternion::z

Definition at line 317 of file OgreQuaternion.h.

Referenced by Ogre::Vector3::getRotationTo(), operator=(), operator==(), and swap().

◆ ZERO

const Quaternion Ogre::Quaternion::ZERO
static

Definition at line 314 of file OgreQuaternion.h.


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