The QQuaternion class represents a quaternion consisting of a vector and scalar. More...

Public Methods
	QQuaternion ()

	QQuaternion (const QVector4D &vector)

	QQuaternion (qreal scalar, const QVector3D &vector)

	QQuaternion (qreal scalar, qreal xpos, qreal ypos, qreal zpos)

QQuaternion	conjugate () const

bool	isIdentity () const

bool	isNull () const

qreal	length () const

qreal	lengthSquared () const

void	normalize ()

QQuaternion	normalized () const

	operator QVariant () const

QQuaternion &	operator*= (const QQuaternion &quaternion)

QQuaternion &	operator*= (qreal factor)

QQuaternion &	operator+= (const QQuaternion &quaternion)

QQuaternion &	operator-= (const QQuaternion &quaternion)

QQuaternion &	operator/= (qreal divisor)

QVector3D	rotatedVector (const QVector3D &vector) const

qreal	scalar () const

void	setScalar (qreal scalar)

void	setVector (const QVector3D &vector)

void	setVector (qreal x, qreal y, qreal z)

void	setX (qreal x)

void	setY (qreal y)

void	setZ (qreal z)

QVector4D	toVector4D () const

QVector3D	vector () const

qreal	x () const

qreal	y () const

qreal	z () const

Static Public Methods
static QQuaternion	fromAxisAndAngle (const QVector3D &axis, qreal angle)

static QQuaternion	fromAxisAndAngle (qreal x, qreal y, qreal z, qreal angle)

static QQuaternion	nlerp (const QQuaternion &q1, const QQuaternion &q2, qreal t)

static QQuaternion	slerp (const QQuaternion &q1, const QQuaternion &q2, qreal t)

Friends
bool	operator!= (const QQuaternion &q1, const QQuaternion &q2)

const QQuaternion	operator* (const QQuaternion &q1, const QQuaternion &q2)

const QQuaternion	operator* (const QQuaternion &quaternion, qreal factor)

const QQuaternion	operator* (qreal factor, const QQuaternion &quaternion)

const QQuaternion	operator+ (const QQuaternion &q1, const QQuaternion &q2)

const QQuaternion	operator- (const QQuaternion &q1, const QQuaternion &q2)

const QQuaternion	operator- (const QQuaternion &quaternion)

const QQuaternion	operator/ (const QQuaternion &quaternion, qreal divisor)

bool	operator== (const QQuaternion &q1, const QQuaternion &q2)

bool	qFuzzyCompare (const QQuaternion &q1, const QQuaternion &q2)

Related Functions
These are not member functions
QDataStream &	operator<< (QDataStream &stream, const QQuaternion &quaternion)

QDataStream &	operator>> (QDataStream &stream, QEasingCurve &easing)

QDataStream &	operator>> (QDataStream &stream, QQuaternion &quaternion)

Detailed Description

The QQuaternion class represents a quaternion consisting of a vector and scalar.

Quaternions are used to represent rotations in 3D space, and consist of a 3D rotation axis specified by the x, y, and z coordinates, and a scalar representing the rotation angle.

See also: vector(), scalar()

Constructor & Destructor Documentation

QQuaternion::QQuaternion ( )

inline

Constructs an identity quaternion, i.e. with coordinates (1, 0, 0, 0).

QQuaternion::QQuaternion	(	qreal	scalar,
		qreal	xpos,
		qreal	ypos,
		qreal	zpos
	)

inline

Constructs a quaternion with the vector (xpos, ypos, zpos) and scalar.

QQuaternion::QQuaternion	(	qreal	scalar,
		const QVector3D &	vector
	)

inline

Constructs a quaternion vector from the specified vector and scalar.

See also: vector(), scalar()

QQuaternion::QQuaternion ( const QVector4D & vector )

inlineexplicit

Constructs a quaternion from the components of vector.

Method Documentation

QQuaternion QQuaternion::conjugate ( ) const

inline

Returns the conjugate of this quaternion, which is (-x, -y, -z, scalar).

QQuaternion QQuaternion::fromAxisAndAngle	(	const QVector3D &	axis,
		qreal	angle
	)

static

Creates a normalized quaternion that corresponds to rotating through angle degrees about the specified 3D axis.

QQuaternion QQuaternion::fromAxisAndAngle	(	qreal	x,
		qreal	y,
		qreal	z,
		qreal	angle
	)

static

Creates a normalized quaternion that corresponds to rotating through angle degrees about the 3D axis (x, y, z).

bool QQuaternion::isIdentity ( ) const

inline

Returns true if the x, y, and z components of this quaternion are set to 0.0, and the scalar component is set to 1.0, otherwise returns false.

bool QQuaternion::isNull ( ) const

inline

Returns true if the x, y, z, and scalar components of this quaternion are set to 0.0, otherwise returns false.

qreal QQuaternion::length ( ) const

Returns the length of the quaternion. This is also called the "norm".

See also: lengthSquared(), normalized()

qreal QQuaternion::lengthSquared ( ) const

Returns the squared length of the quaternion.

See also: length()

QQuaternion QQuaternion::nlerp	(	const QQuaternion &	q1,
		const QQuaternion &	q2,
		qreal	t
	)

static

Interpolates along the shortest linear path between the rotational positions q1 and q2. The value t should be between 0 and 1, indicating the distance to travel between q1 and q2. The result will be normalized().

If t is less than or equal to 0, then q1 will be returned. If t is greater than or equal to 1, then q2 will be returned.

The nlerp() function is typically faster than slerp() and will give approximate results to spherical interpolation that are good enough for some applications.

See also: slerp()

void QQuaternion::normalize ( )

Normalizes the current quaternion in place. Nothing happens if this is a null quaternion or the length of the quaternion is very close to 1.

See also: length(), normalized()

QQuaternion QQuaternion::normalized ( ) const

Returns the normalized unit form of this quaternion.

If this quaternion is null, then a null quaternion is returned. If the length of the quaternion is very close to 1, then the quaternion will be returned as-is. Otherwise the normalized form of the quaternion of length 1 will be returned.

See also: length(), normalize()

QQuaternion::operator QVariant ( ) const

Returns the quaternion as a QVariant.

QQuaternion & QQuaternion::operator*= ( const QQuaternion & quaternion )

inline

Multiplies this quaternion by quaternion and returns a reference to this quaternion.

QQuaternion & QQuaternion::operator*= ( qreal factor )

inline

Multiplies this quaternion's components by the given factor, and returns a reference to this quaternion.

See also: operator/=()

QQuaternion & QQuaternion::operator+= ( const QQuaternion & quaternion )

inline

Adds the given quaternion to this quaternion and returns a reference to this quaternion.

See also: operator-=()

QQuaternion & QQuaternion::operator-= ( const QQuaternion & quaternion )

inline

Subtracts the given quaternion from this quaternion and returns a reference to this quaternion.

See also: operator+=()

QQuaternion & QQuaternion::operator/= ( qreal divisor )

inline

Divides this quaternion's components by the given divisor, and returns a reference to this quaternion.

See also: operator*=()

QVector3D QQuaternion::rotatedVector ( const QVector3D & vector ) const

Rotates vector with this quaternion to produce a new vector in 3D space. The following code:

QVector3D result = q.rotatedVector(vector);

is equivalent to the following:

QVector3D result = (q * QQuaternion(0, vector) * q.conjugate()).vector();

qreal QQuaternion::scalar ( ) const

inline

Returns the scalar component of this quaternion.

See also: setScalar(), x(), y(), z()

void QQuaternion::setScalar ( qreal scalar )

inline

Sets the scalar component of this quaternion to scalar.

See also: scalar(), setX(), setY(), setZ()

void QQuaternion::setVector ( const QVector3D & vector )

inline

Sets the vector component of this quaternion to vector.

See also: vector(), setScalar()

void QQuaternion::setVector	(	qreal	x,
		qreal	y,
		qreal	z
	)

inline

Sets the vector component of this quaternion to (x, y, z).

See also: vector(), setScalar()

void QQuaternion::setX ( qreal x )

inline

Sets the x coordinate of this quaternion's vector to the given x coordinate.

See also: x(), setY(), setZ(), setScalar()

void QQuaternion::setY ( qreal y )

inline

Sets the y coordinate of this quaternion's vector to the given y coordinate.

See also: y(), setX(), setZ(), setScalar()

void QQuaternion::setZ ( qreal z )

inline

Sets the z coordinate of this quaternion's vector to the given z coordinate.

See also: z(), setX(), setY(), setScalar()

QQuaternion QQuaternion::slerp	(	const QQuaternion &	q1,
		const QQuaternion &	q2,
		qreal	t
	)

static

Interpolates along the shortest spherical path between the rotational positions q1 and q2. The value t should be between 0 and 1, indicating the spherical distance to travel between q1 and q2.

If t is less than or equal to 0, then q1 will be returned. If t is greater than or equal to 1, then q2 will be returned.

See also: nlerp()

QVector4D QQuaternion::toVector4D ( ) const

inline

Returns this quaternion as a 4D vector.

QVector3D QQuaternion::vector ( ) const

inline

Returns the vector component of this quaternion.

See also: setVector(), scalar()

qreal QQuaternion::x ( ) const

inline

Returns the x coordinate of this quaternion's vector.

See also: setX(), y(), z(), scalar()

qreal QQuaternion::y ( ) const

inline

Returns the y coordinate of this quaternion's vector.

See also: setY(), x(), z(), scalar()

qreal QQuaternion::z ( ) const

inline

Returns the z coordinate of this quaternion's vector.

See also: setZ(), x(), y(), scalar()

Friends And Related Function Documentation

bool operator!=	(	const QQuaternion &	q1,
		const QQuaternion &	q2
	)

friend

Returns true if q1 is not equal to q2, otherwise returns false. This operator uses an exact floating-point comparison.

const QQuaternion operator*	(	const QQuaternion &	q1,
		const QQuaternion &	q2
	)

friend

Multiplies q1 and q2 using quaternion multiplication. The result corresponds to applying both of the rotations specified by q1 and q2.

See also: QQuaternion::operator*=()

const QQuaternion operator*	(	const QQuaternion &	quaternion,
		qreal	factor
	)

friend

Returns a copy of the given quaternion, multiplied by the given factor.

See also: QQuaternion::operator*=()

const QQuaternion operator*	(	qreal	factor,
		const QQuaternion &	quaternion
	)

friend

Returns a copy of the given quaternion, multiplied by the given factor.

See also: QQuaternion::operator*=()

const QQuaternion operator+	(	const QQuaternion &	q1,
		const QQuaternion &	q2
	)

friend

Returns a QQuaternion object that is the sum of the given quaternions, q1 and q2; each component is added separately.

See also: QQuaternion::operator+=()

const QQuaternion operator-	(	const QQuaternion &	q1,
		const QQuaternion &	q2
	)

friend

Returns a QQuaternion object that is formed by subtracting q2 from q1; each component is subtracted separately.

See also: QQuaternion::operator-=()

const QQuaternion operator- ( const QQuaternion & quaternion )

friend

Returns a QQuaternion object that is formed by changing the sign of all three components of the given quaternion.

Equivalent to QQuaternion(0,0,0,0) - quaternion.

const QQuaternion operator/	(	const QQuaternion &	quaternion,
		qreal	divisor
	)

friend

Returns the QQuaternion object formed by dividing all components of the given quaternion by the given divisor.

See also: QQuaternion::operator/=()

QDataStream & operator<<	(	QDataStream &	stream,
		const QQuaternion &	quaternion
	)

Refer to Serializing Data Types for additional information.

bool operator==	(	const QQuaternion &	q1,
		const QQuaternion &	q2
	)

friend

Returns true if q1 is equal to q2, otherwise returns false. This operator uses an exact floating-point comparison.

QDataStream & operator>>	(	QDataStream &	stream,
		QEasingCurve &	easing
	)

Refer to Serializing Data Types for additional information.

QDataStream & operator>>	(	QDataStream &	stream,
		QQuaternion &	quaternion
	)

Refer to Serializing Data Types for additional information.

bool qFuzzyCompare	(	const QQuaternion &	q1,
		const QQuaternion &	q2
	)

friend

Returns true if q1 and q2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.

Public Methods

Static Public Methods

Friends

Related Functions

Detailed Description

Constructor & Destructor Documentation

Method Documentation

Friends And Related Function Documentation