QVQuaternion Class Reference
[Math functionality]

Implementation of quaternions. More...

#include <QVQuaternion>

Inherits QVVector.

List of all members.

Public Member Functions
	QVQuaternion ()
	Identity constructor.
	QVQuaternion (const QVVector direction, const double phi)
	Axis rotation constructor.
	QVQuaternion (const QVVector &source)
	Construct from a vector.
	QVQuaternion (const QVVector direction, float phi)
	Axis rotation constructor.
	QVQuaternion (const double i, const double j, const double k, const double r)
	Direct coordinates constructor.
	QVQuaternion (const double xAngle, const double yAngle, const double zAngle)
	Constructor from 3 euler angles.
	QVQuaternion (const QVMatrix &matrix)
	Rotation matrix constructor.
QVQuaternion	operator* (const QVQuaternion &quaternion) const
	Quaternion product.
	QVQuaternion (const QVQuaternion &quaternion)
	Copy constructor.
QVQuaternion	quaternionProduct (const QVQuaternion &quaternion) const
	Combination operation for quaternions.
void	toEulerAngles (double &xAngle, double &yAngle, double &zAngle) const
	Gets the Euler angles corresponding to the Quaternion.
QVMatrix	toRotationMatrix () const
	Gets the rotation matrix corresponding to the Quaternion.
QVQuaternion	conjugate () const
	Gets the conjugate of the quaternion.
QVQuaternion	inverse () const
	Gets the inverse of the quaternion.
double	norm2 () const
	Gets the norm2 of the quaternion.
QV3DPointF	rotate (const QV3DPointF &v) const
	Direct vector rotation.
double &	real ()
	Returns the coordinate for the real component of the cuaternion.
double &	i ()
	Returns the coordinate i of the cuaternion.
double &	j ()
	Returns the coordinate j of the cuaternion.
double &	k ()
	Returns the coordinate k of the cuaternion.
double	real () const
	Sets the coordinate for the real component of the cuaternion.
double	i () const
	Sets the coordinate i of the cuaternion.
double	j () const
	Sets the coordinate j of the cuaternion.
double	k () const
	Sets the coordinate k of the cuaternion.
QVQuaternion	normalizeQuaternion () const
	Retuns a normalized quaternion.
Static Public Member Functions
static QVQuaternion	trackball (float p1x, float p1y, float p2x, float p2y)
	Gets the quaternion corresponding to a trackball rotation.

---

Detailed Description

Implementation of quaternions.

Quaternions are an extension of the imaginary numbers. They are mostly used to represent rotations in the euclidean 3D space.

Definition at line 44 of file qvquaternion.h.

---

Constructor & Destructor Documentation

QVQuaternion::QVQuaternion

(

)

Identity constructor.

Creates quaternion to identity rotation.

Definition at line 32 of file qvquaternion.cpp.

Referenced by QVQuaternion(), and trackball().

QVQuaternion::QVQuaternion	(	const QVVector	direction,
		const double	phi
	)

Axis rotation constructor.

Creates a quaternion object which rotates around a direction a given angle.

Parameters:

	direction	quaternion will rotate around this direction.
	phi	quaternion will rotate this angle, given in radians.

Definition at line 39 of file qvquaternion.cpp.

QVQuaternion::QVQuaternion

(

const QVVector &

source

)

[inline]

Construct from a vector.

Creates a quaternion from a vector of size 4.

Parameters:

source

The vector of size 4.

Definition at line 68 of file qvquaternion.h.

QVQuaternion::QVQuaternion	(	const QVVector	direction,
		float	phi
	)

Axis rotation constructor.

Creates a quaternion object which rotates around a direction a given angle.

Parameters:

	direction	quaternion will rotate around this direction.
	phi	quaternion will rotate this angle, given in radians.

QVQuaternion::QVQuaternion	(	const double	i,
		const double	j,
		const double	k,
		const double	r
	)

Direct coordinates constructor.

Creates a quaternion from its coordinate coefficients.

Parameters:

	i	Coefficient for the i coordinate
	j	Coefficient for the j coordinate
	k	Coefficient for the k coordinate
	r	Coefficient for the real coordinate

Definition at line 147 of file qvquaternion.cpp.

QVQuaternion::QVQuaternion	(	const double	xAngle,
		const double	yAngle,
		const double	zAngle
	)

Constructor from 3 euler angles.

Creates a quaternion given the three euler angles of the rotation it represents.

Parameters:

	xAngle	Euler angle for the x axis.
	yAngle	Euler angle for the y axis.
	zAngle	Euler angle for the z axis.

Definition at line 158 of file qvquaternion.cpp.

QVQuaternion::QVQuaternion

(

const QVMatrix &

matrix

)

Rotation matrix constructor.

Creates a quaternion from a rotation matrix.

Parameters:

matrix

rotation matrix to create the quaternion from

Definition at line 52 of file qvquaternion.cpp.

QVQuaternion::QVQuaternion

(

const QVQuaternion &

quaternion

)

[inline]

Copy constructor.

Creates a quaternion copying its coordinates from a given one.

Parameters:

quaternion

quaternion to copy coordinates

Definition at line 114 of file qvquaternion.h.

---

Member Function Documentation

QVQuaternion QVQuaternion::operator*

(

const QVQuaternion &

quaternion

)

const [inline]

Quaternion product.

Parameters:

quaternion

operand for the product

See also:

quaternionProduct

Definition at line 107 of file qvquaternion.h.

QVQuaternion QVQuaternion::trackball	(	float	p1x,
		float	p1y,
		float	p2x,
		float	p2y
	)			[static]

Gets the quaternion corresponding to a trackball rotation.

Creates a quaternion which rotates given two points at a plane, mapped to a sphere.

Parameters:

	p1x	first coordinate for first point.
	p1y	second coordinate for first point.
	p2x	first coordinate for second point.
	p2y	second coordinate for second point.

Returns:

quaternion corresponding to rotate in a sphere from point (p1x, p1y) to (p2x, p2y). corresponding to this quaternion, and at element (4,4), the unity.

Definition at line 186 of file qvquaternion.cpp.

QVQuaternion QVQuaternion::quaternionProduct

(

const QVQuaternion &

quaternion

)

const

Combination operation for quaternions.

Creates a quaternion corresponding to combination of rotations corresponding to actual quaternion and the one received by parameter

Parameters:

quaternion

operand in the combining operation.

Returns:

resulting quaternion.

Definition at line 218 of file qvquaternion.cpp.

Referenced by operator*().

void QVQuaternion::toEulerAngles	(	double &	xAngle,
		double &	yAngle,
		double &	zAngle
	)			const

Gets the Euler angles corresponding to the Quaternion.

Parameters:

	xAxis	Return variable that will contain the rotation in the x angle for the quaternion.
	yAxis	Return variable that will contain the rotation in the y angle for the quaternion.
	zAxis	Return variable that will contain the rotation in the z angle for the quaternion.

Definition at line 234 of file qvquaternion.cpp.

QVMatrix QVQuaternion::toRotationMatrix

(

)

const

Gets the rotation matrix corresponding to the Quaternion.

Returns:

rotation matrix

Definition at line 253 of file qvquaternion.cpp.

Referenced by QVMatrix::QVMatrix(), QVCameraPose::toProjectionMatrix(), and QVEuclideanMapping3::toRotationTranslationMatrix().

QVQuaternion QVQuaternion::conjugate

(

)

const

Gets the conjugate of the quaternion.

Returns:

The conjugate quaternion.

Definition at line 280 of file qvquaternion.cpp.

Referenced by inverse(), and rotate().

QVQuaternion QVQuaternion::inverse

(

)

const

Gets the inverse of the quaternion.

Returns:

The inverse quaternion.

Definition at line 290 of file qvquaternion.cpp.

Referenced by QVCameraPose::compose(), QVEuclideanMapping3::inverse(), and QVCameraPose::inverse().

double QVQuaternion::norm2

(

)

const

Gets the norm2 of the quaternion.

Returns:

The value of the norm 2

Reimplemented from QVVector.

Definition at line 302 of file qvquaternion.cpp.

Referenced by QVCameraPose::compose(), conjugate(), inverse(), QVCameraPose::inverse(), QVCameraPose::operator QVEuclideanMapping3(), QVCameraPose::operator QVVector(), QVCameraPose::operator!=(), QVCameraPose::operator==(), QVCameraPose::project(), quaternionProduct(), QVCameraPose::QVCameraPose(), QVQuaternion(), rotate(), QVCameraPose::toCameraReferenceCoordinates(), toEulerAngles(), QVCameraPose::toProjectionMatrix(), toRotationMatrix(), and trackball().

QV3DPointF QVQuaternion::rotate

(

const QV3DPointF &

v

)

const

Direct vector rotation.

Rotates a 3D Applies the quaternion rotation to a 3D point.

Returns:

resulting 3D point.

Definition at line 307 of file qvquaternion.cpp.

Referenced by QVEuclideanMapping3::apply(), QVEuclideanMapping3::compose(), QVCameraPose::compose(), QVEuclideanMapping3::inverse(), QVCameraPose::inverse(), QVCameraPose::operator QVEuclideanMapping3(), QVCameraPose::project(), QVCameraPose::toCameraReferenceCoordinates(), and QVCameraPose::toProjectionMatrix().

double& QVQuaternion::real

(

)

[inline]

Returns the coordinate for the real component of the cuaternion.

Definition at line 172 of file qvquaternion.h.

Referenced by QVQuaternion().

double& QVQuaternion::i

(

)

[inline]

Returns the coordinate i of the cuaternion.

Definition at line 175 of file qvquaternion.h.

Referenced by normalizeQuaternion(), and QVQuaternion().

double& QVQuaternion::j

(

)

[inline]

Returns the coordinate j of the cuaternion.

Definition at line 178 of file qvquaternion.h.

Referenced by QVQuaternion().

double& QVQuaternion::k

(

)

[inline]

Returns the coordinate k of the cuaternion.

Definition at line 181 of file qvquaternion.h.

Referenced by QVQuaternion().

double QVQuaternion::real

(

)

const [inline]

Sets the coordinate for the real component of the cuaternion.

Definition at line 184 of file qvquaternion.h.

double QVQuaternion::i

(

)

const [inline]

Sets the coordinate i of the cuaternion.

Definition at line 187 of file qvquaternion.h.

double QVQuaternion::j

(

)

const [inline]

Sets the coordinate j of the cuaternion.

Definition at line 190 of file qvquaternion.h.

double QVQuaternion::k

(

)

const [inline]

Sets the coordinate k of the cuaternion.

Definition at line 193 of file qvquaternion.h.

QVQuaternion QVQuaternion::normalizeQuaternion

(

)

const

Retuns a normalized quaternion.

Definition at line 207 of file qvquaternion.cpp.

---

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

• src/qvmath/qvquaternion.h
• src/qvmath/qvquaternion.cpp