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Ogre::Quaternion Class Reference

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

#include <OgreQuaternion.h>

+ Collaboration diagram for Ogre::Quaternion:

Public Member Functions

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

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. More...
 
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. More...
 
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. More...
 
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. More...
 

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. More...
 
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. More...
 

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 http://www.cprogramming.com/tutorial/3d/quaternions.html http://www.gamedev.net/page/resources/_/reference/programming/math-and-physics/ quaternions/quaternion-powers-r1095

Definition at line 57 of file OgreQuaternion.h.

Constructor & Destructor Documentation

Ogre::Quaternion::Quaternion ( )
inline

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

Definition at line 61 of file OgreQuaternion.h.

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

Construct from an explicit list of values.

Definition at line 66 of file OgreQuaternion.h.

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

Construct a quaternion from a rotation matrix.

Definition at line 73 of file OgreQuaternion.h.

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

Construct a quaternion from an angle/axis.

Definition at line 78 of file OgreQuaternion.h.

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

Construct a quaternion from 3 orthonormal local axes.

Definition at line 83 of file OgreQuaternion.h.

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

Construct a quaternion from 3 orthonormal local axes.

Definition at line 88 of file OgreQuaternion.h.

Ogre::Quaternion::Quaternion ( Real valptr)
inline

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

Definition at line 93 of file OgreQuaternion.h.

Member Function Documentation

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

Returns the dot product of the quaternion.

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

Equality with tolerance (tolerance is max angle difference)

Quaternion Ogre::Quaternion::Exp ( ) const

Apply to unit-length quaternion.

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().

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

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

See also
FromAxes
void Ogre::Quaternion::FromAxes ( const Vector3 xAxis,
const Vector3 yAxis,
const Vector3 zAxis 
)
void Ogre::Quaternion::FromRotationMatrix ( const Matrix3 kRot)
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.
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.
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.
static void Ogre::Quaternion::Intermediate ( const Quaternion rkQ0,
const Quaternion rkQ1,
const Quaternion rkQ2,
Quaternion rka,
Quaternion rkB 
)
static

Setup for spherical quadratic interpolation.

Quaternion Ogre::Quaternion::Inverse ( ) const
bool Ogre::Quaternion::isNaN ( void  ) const
inline

Check whether this quaternion contains valid values.

Definition at line 306 of file OgreQuaternion.h.

References Ogre::Math::isNaN().

Quaternion Ogre::Quaternion::Log ( ) const
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.
Real Ogre::Quaternion::Norm ( ) const
Real Ogre::Quaternion::normalise ( void  )

Normalises this quaternion, and returns the previous length.

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

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

Definition at line 192 of file OgreQuaternion.h.

References Ogre::operator==().

Quaternion Ogre::Quaternion::operator* ( const Quaternion rkQ) const
Quaternion Ogre::Quaternion::operator* ( Real  fScalar) const
Vector3 Ogre::Quaternion::operator* ( const Vector3 rkVector) const

Rotation of a vector by a quaternion.

Quaternion Ogre::Quaternion::operator+ ( const Quaternion rkQ) const
Quaternion Ogre::Quaternion::operator- ( const Quaternion rkQ) const
Quaternion Ogre::Quaternion::operator- ( ) const
Quaternion& Ogre::Quaternion::operator= ( const Quaternion rkQ)
inline

Definition at line 172 of file OgreQuaternion.h.

References w, x, y, and z.

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

Definition at line 187 of file OgreQuaternion.h.

References w, x, y, and z.

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

Array accessor operator.

Definition at line 109 of file OgreQuaternion.h.

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

Array accessor operator.

Definition at line 117 of file OgreQuaternion.h.

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

Pointer accessor for direct copying.

Definition at line 125 of file OgreQuaternion.h.

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

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

Pointer accessor for direct copying.

Definition at line 131 of file OgreQuaternion.h.

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.
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
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.

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

Exchange the contents of this quaternion with another.

Definition at line 100 of file OgreQuaternion.h.

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

void Ogre::Quaternion::ToAngleAxis ( Radian rfAngle,
Vector3 rkAxis 
) const
void Ogre::Quaternion::ToAngleAxis ( Degree dAngle,
Vector3 rkAxis 
) const
inline

Definition at line 143 of file OgreQuaternion.h.

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

Gets the 3 orthonormal axes defining the quaternion.

See also
FromAxes
void Ogre::Quaternion::ToAxes ( Vector3 xAxis,
Vector3 yAxis,
Vector3 zAxis 
) const
void Ogre::Quaternion::ToRotationMatrix ( Matrix3 kRot) const

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

Quaternion Ogre::Quaternion::UnitInverse ( ) const

Apply to non-zero quaternion.

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

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

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 Function Documentation

_OgreExport friend Quaternion operator* ( Real  fScalar,
const Quaternion rkQ 
)
friend
_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 315 of file OgreQuaternion.h.

Member Data Documentation

const Quaternion Ogre::Quaternion::IDENTITY
static

Definition at line 301 of file OgreQuaternion.h.

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

const Real Ogre::Quaternion::msEpsilon
static

Cutoff for sine near zero.

Definition at line 297 of file OgreQuaternion.h.

const Quaternion Ogre::Quaternion::ZERO
static

Definition at line 300 of file OgreQuaternion.h.


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