QQuaternion Class

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

Header:	#include <QQuaternion>
qmake:	QT += gui
Since:	Qt 4.6

This class was introduced in Qt 4.6.

• List of all members, including inherited members
• Obsolete members

Public Functions

	QQuaternion(const QVector4D &vector)
	QQuaternion(float scalar, const QVector3D &vector)
	QQuaternion(float scalar, float xpos, float ypos, float zpos)
	QQuaternion()
QQuaternion	conjugated() const
void	getAxes(QVector3D *xAxis, QVector3D *yAxis, QVector3D *zAxis) const
void	getAxisAndAngle(float *x, float *y, float *z, float *angle) const
void	getAxisAndAngle(QVector3D *axis, float *angle) const
void	getEulerAngles(float *pitch, float *yaw, float *roll) const
QQuaternion	inverted() const
bool	isIdentity() const
bool	isNull() const
float	length() const
float	lengthSquared() const
void	normalize()
QQuaternion	normalized() const
QVector3D	rotatedVector(const QVector3D &vector) const
float	scalar() const
void	setScalar(float scalar)
void	setVector(const QVector3D &vector)
void	setVector(float x, float y, float z)
void	setX(float x)
void	setY(float y)
void	setZ(float z)
QVector3D	toEulerAngles() const
QMatrix3x3	toRotationMatrix() const
QVector4D	toVector4D() const
QVector3D	vector() const
float	x() const
float	y() const
float	z() const
QVariant	operator QVariant() const
QQuaternion &	operator*=(float factor)
QQuaternion &	operator*=(const QQuaternion &quaternion)
QQuaternion &	operator+=(const QQuaternion &quaternion)
QQuaternion &	operator-=(const QQuaternion &quaternion)
QQuaternion &	operator/=(float divisor)

Static Public Members

float	dotProduct(const QQuaternion &q1, const QQuaternion &q2)
QQuaternion	fromAxes(const QVector3D &xAxis, const QVector3D &yAxis, const QVector3D &zAxis)
QQuaternion	fromAxisAndAngle(const QVector3D &axis, float angle)
QQuaternion	fromAxisAndAngle(float x, float y, float z, float angle)
QQuaternion	fromDirection(const QVector3D &direction, const QVector3D &up)
QQuaternion	fromEulerAngles(float pitch, float yaw, float roll)
QQuaternion	fromEulerAngles(const QVector3D &eulerAngles)
QQuaternion	fromRotationMatrix(const QMatrix3x3 &rot3x3)
QQuaternion	nlerp(const QQuaternion &q1, const QQuaternion &q2, float t)
QQuaternion	rotationTo(const QVector3D &from, const QVector3D &to)
QQuaternion	slerp(const QQuaternion &q1, const QQuaternion &q2, float t)

Related Non-Members

bool	qFuzzyCompare(const QQuaternion &q1, const QQuaternion &q2)
bool	operator!=(const QQuaternion &q1, const QQuaternion &q2)
const QQuaternion	operator*(float factor, const QQuaternion &quaternion)
const QQuaternion	operator*(const QQuaternion &quaternion, float factor)
const QQuaternion	operator*(const QQuaternion &q1, const QQuaternion &q2)
QVector3D	operator*(const QQuaternion &quaternion, const QVector3D &vec)
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, float divisor)
QDataStream &	operator<<(QDataStream &stream, const QQuaternion &quaternion)
bool	operator==(const QQuaternion &q1, const QQuaternion &q2)
QDataStream &	operator>>(QDataStream &stream, QQuaternion &quaternion)

Detailed Description

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.

Member Function Documentation

QQuaternion::QQuaternion(const QVector4D &vector)

Constructs a quaternion from the components of vector.

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

Constructs a quaternion vector from the specified vector and scalar.

See also vector() and scalar().

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

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

QQuaternion::QQuaternion()

Constructs an identity quaternion (1, 0, 0, 0), i.e. with the vector (0, 0, 0) and scalar 1.

QQuaternion QQuaternion::conjugated() const

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

This function was introduced in Qt 5.5.

[static] float QQuaternion::dotProduct(const QQuaternion &q1, const QQuaternion &q2)

Returns the dot product of q1 and q2.

This function was introduced in Qt 5.5.

See also length().

[static] QQuaternion QQuaternion::fromAxes(const QVector3D &xAxis, const QVector3D &yAxis, const QVector3D &zAxis)

Constructs the quaternion using 3 axes (xAxis, yAxis, zAxis).

Note: The axes are assumed to be orthonormal.

This function was introduced in Qt 5.5.

See also getAxes() and fromRotationMatrix().

[static] QQuaternion QQuaternion::fromAxisAndAngle(const QVector3D &axis, float angle)

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

See also getAxisAndAngle().

[static] QQuaternion QQuaternion::fromAxisAndAngle(float x, float y, float z, float angle)

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

See also getAxisAndAngle().

[static] QQuaternion QQuaternion::fromDirection(const QVector3D &direction, const QVector3D &up)

Constructs the quaternion using specified forward direction direction and upward direction up. If the upward direction was not specified or the forward and upward vectors are collinear, a new orthonormal upward direction will be generated.

This function was introduced in Qt 5.5.

See also fromAxes() and rotationTo().

[static] QQuaternion QQuaternion::fromEulerAngles(float pitch, float yaw, float roll)

Creates a quaternion that corresponds to a rotation of roll degrees around the z axis, pitch degrees around the x axis, and yaw degrees around the y axis (in that order).

This function was introduced in Qt 5.5.

See also getEulerAngles().

[static] QQuaternion QQuaternion::fromEulerAngles(const QVector3D &eulerAngles)

This is an overloaded function.

Creates a quaternion that corresponds to a rotation of eulerAngles: eulerAngles.z() degrees around the z axis, eulerAngles.x() degrees around the x axis, and eulerAngles.y() degrees around the y axis (in that order).

This function was introduced in Qt 5.5.

See also toEulerAngles().

[static] QQuaternion QQuaternion::fromRotationMatrix(const QMatrix3x3 &rot3x3)

Creates a quaternion that corresponds to a rotation matrix rot3x3.

Note: If a given rotation matrix is not normalized, the resulting quaternion will contain scaling information.

This function was introduced in Qt 5.5.

See also toRotationMatrix() and fromAxes().

void QQuaternion::getAxes(QVector3D *xAxis, QVector3D *yAxis, QVector3D *zAxis) const

Returns the 3 orthonormal axes (xAxis, yAxis, zAxis) defining the quaternion.

This function was introduced in Qt 5.5.

See also fromAxes() and toRotationMatrix().

void QQuaternion::getAxisAndAngle(float *x, float *y, float *z, float *angle) const

Extracts a 3D axis (x, y, z) and a rotating angle angle (in degrees) that corresponds to this quaternion.

This function was introduced in Qt 5.5.

See also fromAxisAndAngle().

void QQuaternion::getAxisAndAngle(QVector3D *axis, float *angle) const

This is an overloaded function.

Extracts a 3D axis axis and a rotating angle angle (in degrees) that corresponds to this quaternion.

This function was introduced in Qt 5.5.

See also fromAxisAndAngle().

void QQuaternion::getEulerAngles(float *pitch, float *yaw, float *roll) const

Calculates roll, pitch, and yaw Euler angles (in degrees) that corresponds to this quaternion.

This function was introduced in Qt 5.5.

See also fromEulerAngles().

QQuaternion QQuaternion::inverted() const

Returns the inverse of this quaternion. If this quaternion is null, then a null quaternion is returned.

This function was introduced in Qt 5.5.

See also isNull() and length().

bool QQuaternion::isIdentity() const

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

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

float QQuaternion::length() const

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

See also lengthSquared(), normalized(), and dotProduct().

float QQuaternion::lengthSquared() const

Returns the squared length of the quaternion.

See also length() and dotProduct().

[static] QQuaternion QQuaternion::nlerp(const QQuaternion &q1, const QQuaternion &q2, float t)

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() and 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 normalize(), length(), and dotProduct().

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.conjugated()).vector();

[static] QQuaternion QQuaternion::rotationTo(const QVector3D &from, const QVector3D &to)

Returns the shortest arc quaternion to rotate from the direction described by the vector from to the direction described by the vector to.

This function was introduced in Qt 5.5.

See also fromDirection().

float QQuaternion::scalar() const

Returns the scalar component of this quaternion.

See also setScalar(), x(), y(), and z().

void QQuaternion::setScalar(float scalar)

Sets the scalar component of this quaternion to scalar.

See also scalar(), setX(), setY(), and setZ().

void QQuaternion::setVector(const QVector3D &vector)

Sets the vector component of this quaternion to vector.

See also vector() and setScalar().

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

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

See also vector() and setScalar().

void QQuaternion::setX(float x)

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

See also x(), setY(), setZ(), and setScalar().

void QQuaternion::setY(float y)

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

See also y(), setX(), setZ(), and setScalar().

void QQuaternion::setZ(float z)

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

See also z(), setX(), setY(), and setScalar().

[static] QQuaternion QQuaternion::slerp(const QQuaternion &q1, const QQuaternion &q2, float t)

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().

QVector3D QQuaternion::toEulerAngles() const

This is an overloaded function.

Calculates roll, pitch, and yaw Euler angles (in degrees) that corresponds to this quaternion.

This function was introduced in Qt 5.5.

See also fromEulerAngles().

QMatrix3x3 QQuaternion::toRotationMatrix() const

Creates a rotation matrix that corresponds to this quaternion.

Note: If this quaternion is not normalized, the resulting rotation matrix will contain scaling information.

This function was introduced in Qt 5.5.

See also fromRotationMatrix() and getAxes().

QVector4D QQuaternion::toVector4D() const

Returns this quaternion as a 4D vector.

QVector3D QQuaternion::vector() const

Returns the vector component of this quaternion.

See also setVector() and scalar().

float QQuaternion::x() const

Returns the x coordinate of this quaternion's vector.

See also setX(), y(), z(), and scalar().

float QQuaternion::y() const

Returns the y coordinate of this quaternion's vector.

See also setY(), x(), z(), and scalar().

float QQuaternion::z() const

Returns the z coordinate of this quaternion's vector.

See also setZ(), x(), y(), and scalar().

QVariant QQuaternion::operator QVariant() const

Returns the quaternion as a QVariant.

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

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)

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

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

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

See also operator-=().

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

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

See also operator+=().

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

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

See also operator*=().