Ogre::Quaternion Class Reference
[Math]

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

#include <OgreQuaternion.h>

Public Member Functions
	Quaternion ()
	Default constructor, initializes to identity rotation (aka 0°).
	Quaternion (Real fW, Real fX, Real fY, Real fZ)
	Construct from an explicit list of values.
	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.
void	swap (Quaternion &other)
	Exchange the contents of this quaternion with another.
Real	operator[] (const size_t i) const
	Array accessor operator.
Real &	operator[] (const size_t i)
	Array accessor operator.
Real *	ptr ()
	Pointer accessor for direct copying.
const Real *	ptr () const
	Pointer accessor for direct copying.
void	FromRotationMatrix (const Matrix3 &kRot)
void	ToRotationMatrix (Matrix3 &kRot) const
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	ToAngleAxis (Radian &rfAngle, Vector3 &rkAxis) const
void	ToAngleAxis (Degree &dAngle, Vector3 &rkAxis) const
void	FromAxes (const Vector3 *akAxis)
	Constructs the quaternion using 3 axes, the axes are assumed to be orthonormal.
void	FromAxes (const Vector3 &xAxis, const Vector3 &yAxis, const Vector3 &zAxis)
void	ToAxes (Vector3 *akAxis) const
	Gets the 3 orthonormal axes defining the quaternion.
void	ToAxes (Vector3 &xAxis, Vector3 &yAxis, Vector3 &zAxis) const
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.
Quaternion &	operator= (const Quaternion &rkQ)
Quaternion	operator+ (const Quaternion &rkQ) const
Quaternion	operator- (const Quaternion &rkQ) const
Quaternion	operator* (const Quaternion &rkQ) const
Quaternion	operator* (Real fScalar) const
Quaternion	operator- () const
bool	operator== (const Quaternion &rhs) const
bool	operator!= (const Quaternion &rhs) const
Real	Dot (const Quaternion &rkQ) const
	Returns the dot product of the quaternion.
Real	Norm () const
Real	normalise (void)
	Normalises this quaternion, and returns the previous length.
Quaternion	Inverse () const
Quaternion	UnitInverse () const
Quaternion	Exp () const
Quaternion	Log () const
Vector3	operator* (const Vector3 &rkVector) const
	Rotation of a vector by a quaternion.
Radian	getRoll (bool reprojectAxis=true) const
	Calculate the local roll element of this quaternion.
Radian	getPitch (bool reprojectAxis=true) const
	Calculate the local pitch element of this quaternion.
Radian	getYaw (bool reprojectAxis=true) const
	Calculate the local yaw element of this quaternion.
bool	equals (const Quaternion &rhs, const Radian &tolerance) const
	Equality with tolerance (tolerance is max angle difference).
bool	isNaN () const
	Check whether this quaternion contains valid values.
Static Public Member Functions
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 void	Intermediate (const Quaternion &rkQ0, const Quaternion &rkQ1, const Quaternion &rkQ2, Quaternion &rka, Quaternion &rkB)
static Quaternion	Squad (Real fT, const Quaternion &rkP, const Quaternion &rkA, const Quaternion &rkB, const Quaternion &rkQ, bool shortestPath=false)
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.
Public Attributes
Real	w
Real	x
Real	y
Real	z
Static Public Attributes
static const Real	msEpsilon
	Cutoff for sine near zero.
static const Quaternion	ZERO
static const Quaternion	IDENTITY
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 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 ( )

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
	)

Construct from an explicit list of values.

Definition at line 66 of file OgreQuaternion.h.

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

Construct a quaternion from a rotation matrix.

Definition at line 73 of file OgreQuaternion.h.

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

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
	)

Construct a quaternion from 3 orthonormal local axes.

Definition at line 83 of file OgreQuaternion.h.

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

Construct a quaternion from 3 orthonormal local axes.

Definition at line 88 of file OgreQuaternion.h.

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

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

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 &	xAxis,
		const Vector3 &	yAxis,
		const Vector3 &	zAxis
	)

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::FromRotationMatrix ( const Matrix3 & kRot )

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

Calculate the local pitch element of this quaternion.

Parameters:

reprojectAxis

By 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:

reprojectAxis

By 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:

reprojectAxis

By 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]`

Quaternion Ogre::Quaternion::Inverse ( ) const

bool Ogre::Quaternion::isNaN ( ) const

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

Definition at line 192 of file OgreQuaternion.h.

References Ogre::operator==().

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

Rotation of a vector by a quaternion.

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

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 ) const

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

Definition at line 172 of file OgreQuaternion.h.

References w, x, y, and z.

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

Definition at line 187 of file OgreQuaternion.h.

References w, x, y, and z.

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

Array accessor operator.

Definition at line 117 of file OgreQuaternion.h.

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

Array accessor operator.

Definition at line 109 of file OgreQuaternion.h.

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

Pointer accessor for direct copying.

Definition at line 131 of file OgreQuaternion.h.

Real* Ogre::Quaternion::ptr ( )

Pointer accessor for direct copying.

Definition at line 125 of file OgreQuaternion.h.

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

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]`