The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space. More...

Public Methods
	QMatrix4x4 ()

template<int N, int M>
	QMatrix4x4 (const QGenericMatrix< N, M, qreal > &matrix)

	QMatrix4x4 (const QMatrix &matrix)

	QMatrix4x4 (const qreal *values)

	QMatrix4x4 (const QTransform &transform)

	QMatrix4x4 (qreal m11, qreal m12, qreal m13, qreal m14, qreal m21, qreal m22, qreal m23, qreal m24, qreal m31, qreal m32, qreal m33, qreal m34, qreal m41, qreal m42, qreal m43, qreal m44)

QVector4D	column (int index) const

const qreal *	constData () const

void	copyDataTo (qreal *values) const

qreal *	data ()

const qreal *	data () const

qreal	determinant () const

void	fill (qreal value)

void	flipCoordinates ()

void	frustum (qreal left, qreal right, qreal bottom, qreal top, qreal nearPlane, qreal farPlane)

QMatrix4x4	inverted (bool *invertible=nullptr) const

bool	isAffine () const

bool	isIdentity () const

void	lookAt (const QVector3D &eye, const QVector3D &center, const QVector3D &up)

QPoint	map (const QPoint &point) const

QPointF	map (const QPointF &point) const

QVector3D	map (const QVector3D &point) const

QVector4D	map (const QVector4D &point) const

QRect	mapRect (const QRect &rect) const

QRectF	mapRect (const QRectF &rect) const

QVector3D	mapVector (const QVector3D &vector) const

QMatrix3x3	normalMatrix () const

qreal &	operator () (int row, int column)

const qreal &	operator () (int row, int column) const

	operator QVariant () const

bool	operator!= (const QMatrix4x4 &other) const

QMatrix4x4 &	operator*= (QMatrix4x4 other)

QMatrix4x4 &	operator*= (qreal factor)

QMatrix4x4 &	operator+= (const QMatrix4x4 &other)

QMatrix4x4 &	operator-= (const QMatrix4x4 &other)

QMatrix4x4 &	operator/= (qreal divisor)

bool	operator== (const QMatrix4x4 &other) const

void	optimize ()

void	ortho (const QRect &rect)

void	ortho (const QRectF &rect)

void	ortho (qreal left, qreal right, qreal bottom, qreal top, qreal nearPlane, qreal farPlane)

void	perspective (qreal angle, qreal aspect, qreal nearPlane, qreal farPlane)

void	rotate (const QQuaternion &quaternion)

void	rotate (qreal angle, const QVector3D &vector)

void	rotate (qreal angle, qreal x, qreal y, qreal z=0.0f)

QVector4D	row (int index) const

void	scale (const QVector3D &vector)

void	scale (qreal factor)

void	scale (qreal x, qreal y)

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

void	setColumn (int index, const QVector4D &value)

void	setRow (int index, const QVector4D &value)

void	setToIdentity ()

QMatrix	toAffine () const

template<int N, int M>
QGenericMatrix< N, M, qreal >	toGenericMatrix () const

QTransform	toTransform () const

QTransform	toTransform (qreal distanceToPlane) const

void	translate (const QVector3D &vector)

void	translate (qreal x, qreal y)

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

QMatrix4x4	transposed () const

void	viewport (const QRectF &rect)

void	viewport (qreal left, qreal bottom, qreal width, qreal height, qreal nearPlane=0.0, qreal farPlane=1.0)

Friends
class	QGraphicsRotation

Detailed Description

The QMatrix4x4 class represents a 4x4 transformation matrix in 3D space.

See also: QVector3D, QGenericMatrix

Constructor & Destructor Documentation

QMatrix4x4::QMatrix4x4 ( )

inline

Constructs an identity matrix.

QMatrix4x4::QMatrix4x4 ( const qreal * values )

explicit

Constructs a matrix from the given 16 floating-point values. The contents of the array values is assumed to be in row-major order. If the matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

See also: copyDataTo(), optimize()

QMatrix4x4::QMatrix4x4	(	qreal	m11,
		qreal	m12,
		qreal	m13,
		qreal	m14,
		qreal	m21,
		qreal	m22,
		qreal	m23,
		qreal	m24,
		qreal	m31,
		qreal	m32,
		qreal	m33,
		qreal	m34,
		qreal	m41,
		qreal	m42,
		qreal	m43,
		qreal	m44
	)

inline

Constructs a matrix from the 16 elements m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, and m44. The elements are specified in row-major order.

If the matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

See also: optimize()

template<int N, int M>

QMatrix4x4::QMatrix4x4 ( const QGenericMatrix< N, M, qreal > & matrix )

inlineexplicit

Constructs a 4x4 matrix from the left-most 4 columns and top-most 4 rows of matrix. If matrix has less than 4 columns or rows, the remaining elements are filled with elements from the identity matrix.

See also: toGenericMatrix()

QMatrix4x4::QMatrix4x4 ( const QTransform & transform )

Constructs a 4x4 matrix from the conventional 2D transformation matrix transform.

If transform has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

See also: toTransform(), optimize()

QMatrix4x4::QMatrix4x4 ( const QMatrix & matrix )

Constructs a 4x4 matrix from a conventional 2D affine transformation matrix.

If matrix has a special type (identity, translate, scale, etc), the programmer should follow this constructor with a call to optimize() if they wish QMatrix4x4 to optimize further calls to translate(), scale(), etc.

See also: toAffine(), optimize()

Method Documentation

QVector4D QMatrix4x4::column ( int index ) const

inline

Returns the elements of column index as a 4D vector.

See also: setColumn(), row()

const qreal * QMatrix4x4::constData ( ) const

inline

Returns a constant pointer to the raw data of this matrix.

See also: data()

void QMatrix4x4::copyDataTo ( qreal * values ) const

Retrieves the 16 items in this matrix and copies them to values in row-major order.

qreal * QMatrix4x4::data ( )

inline

Returns a pointer to the raw data of this matrix.

See also: constData(), optimize()

const qreal * QMatrix4x4::data ( ) const

inline

Returns a constant pointer to the raw data of this matrix.

See also: constData()

qreal QMatrix4x4::determinant ( ) const

Returns the determinant of this matrix.

void QMatrix4x4::fill ( qreal value )

inline

Fills all elements of this matrix with value.

void QMatrix4x4::flipCoordinates ( )

Flips between right-handed and left-handed coordinate systems by multiplying the y and z coordinates by -1. This is normally used to create a left-handed orthographic view without scaling the viewport as ortho() does.

See also: ortho()

void QMatrix4x4::frustum	(	qreal	left,
		qreal	right,
		qreal	bottom,
		qreal	top,
		qreal	nearPlane,
		qreal	farPlane
	)

Multiplies this matrix by another that applies a perspective frustum projection for a window with lower-left corner (left, bottom), upper-right corner (right, top), and the specified nearPlane and farPlane clipping planes.

See also: ortho(), perspective()

QMatrix4x4 QMatrix4x4::inverted ( bool * invertible = nullptr ) const

Returns the inverse of this matrix. Returns the identity if this matrix can not be inverted; i.e. determinant() is zero. If invertible is not null, then true will be written to that location if the matrix can be inverted; false otherwise.

If the matrix is recognized as the identity or an orthonormal matrix, then this function will quickly invert the matrix using optimized routines.

See also: determinant(), normalMatrix()

bool QMatrix4x4::isAffine ( ) const

inline

Returns true if this matrix is an affine matrix, return false otherwise. An affine matrix is a 4x4 matrix with row 3 equal to (0, 0, 0, 1), e.g. no projective coefficients.

See also: isIdentity()

bool QMatrix4x4::isIdentity ( ) const

inline

Returns true if this matrix is the identity; false otherwise.

See also: setToIdentity()

void QMatrix4x4::lookAt	(	const QVector3D &	eye,
		const QVector3D &	center,
		const QVector3D &	up
	)

Multiplies this matrix by another that applies an eye position transformation. The center value indicates the center of the view that the eye is looking at. The up value indicates which direction should be considered up with respect to the eye.

QPoint QMatrix4x4::map ( const QPoint & point ) const

inline

Maps point by multiplying this matrix by point.

See also: mapRect()

QPointF QMatrix4x4::map ( const QPointF & point ) const

inline

Maps point by multiplying this matrix by point.

See also: mapRect()

QVector3D QMatrix4x4::map ( const QVector3D & point ) const

inline

Maps point by multiplying this matrix by point.

See also: mapRect(), mapVector()

QVector4D QMatrix4x4::map ( const QVector4D & point ) const

inline

Maps point by multiplying this matrix by point.

See also: mapRect()

QRect QMatrix4x4::mapRect ( const QRect & rect ) const

Maps rect by multiplying this matrix by the corners of rect and then forming a new rectangle from the results. The returned rectangle will be an ordinary 2D rectangle with sides parallel to the horizontal and vertical axes.

See also: map()

QRectF QMatrix4x4::mapRect ( const QRectF & rect ) const

Maps rect by multiplying this matrix by the corners of rect and then forming a new rectangle from the results. The returned rectangle will be an ordinary 2D rectangle with sides parallel to the horizontal and vertical axes.

See also: map()

QVector3D QMatrix4x4::mapVector ( const QVector3D & vector ) const

inline

Maps vector by multiplying the top 3x3 portion of this matrix by vector. The translation and projection components of this matrix are ignored.

See also: map()

QMatrix3x3 QMatrix4x4::normalMatrix ( ) const

Returns the normal matrix corresponding to this 4x4 transformation. The normal matrix is the transpose of the inverse of the top-left 3x3 part of this 4x4 matrix. If the 3x3 sub-matrix is not invertible, this method returns the identity.

See also: inverted()

qreal & QMatrix4x4::operator ()	(	int	row,
		int	column
	)

inline

Returns a reference to the element at position (row, column) in this matrix so that the element can be assigned to.

See also: optimize(), setColumn(), setRow()

const qreal & QMatrix4x4::operator ()	(	int	row,
		int	column
	)		const

inline

Returns a constant reference to the element at position (row, column) in this matrix.

See also: column(), row()

QMatrix4x4::operator QVariant ( ) const

Returns the matrix as a QVariant.

bool QMatrix4x4::operator!= ( const QMatrix4x4 & other ) const

inline

Returns true if this matrix is not identical to other, otherwise returns false. This operator uses an exact floating point comparison.

QMatrix4x4 & QMatrix4x4::operator*= ( QMatrix4x4 other )

inline

Multiplies the contents of other by this matrix.

QMatrix4x4 & QMatrix4x4::operator*= ( qreal factor )

inline

Multiplies all elements of this matrix by factor.

QMatrix4x4 & QMatrix4x4::operator+= ( const QMatrix4x4 & other )

inline

Adds the contents of other to this matrix.

QMatrix4x4 & QMatrix4x4::operator-= ( const QMatrix4x4 & other )

inline

Subtracts the contents of other from this matrix.

QMatrix4x4 & QMatrix4x4::operator/= ( qreal divisor )

Divides all elements of this matrix by divisor.

bool QMatrix4x4::operator== ( const QMatrix4x4 & other ) const

inline

Returns true if this matrix is identical to other; false otherwise. This operator uses an exact floating-point comparison.

void QMatrix4x4::optimize ( )

Optimize the usage of this matrix from its current elements. Some operations such as translate(), scale(), and rotate() can be performed more efficiently if the matrix being modified is already known to be the identity, a previous translate(), a previous scale(), etc.

Normally the QMatrix4x4 class keeps track of this special type internally as operations are performed. However, if the matrix is modified directly with operator() or data(), then QMatrix4x4 will lose track of the special type and will revert to the safest but least efficient operations thereafter.

By calling this method after directly modifying the matrix you can force QMatrix4x4 to recover the special type if the elements appear to conform to one of the known optimized types.

See also: operator()(), data(), translate()

void QMatrix4x4::ortho ( const QRect & rect )

Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by rect. The near and far clipping planes will be -1 and 1 respectively.

See also: frustum(), perspective()

void QMatrix4x4::ortho ( const QRectF & rect )

Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by rect. The near and far clipping planes will be -1 and 1 respectively.

See also: frustum(), perspective()

void QMatrix4x4::ortho	(	qreal	left,
		qreal	right,
		qreal	bottom,
		qreal	top,
		qreal	nearPlane,
		qreal	farPlane
	)

Multiplies this matrix by another that applies an orthographic projection for a window with lower-left corner (left, bottom), upper-right corner (right, top), and the specified nearPlane and farPlane clipping planes.

See also: frustum(), perspective()

void QMatrix4x4::perspective	(	qreal	angle,
		qreal	aspect,
		qreal	nearPlane,
		qreal	farPlane
	)

Multiplies this matrix by another that applies a perspective projection. The field of view will be angle degrees within a window with a given aspect ratio. The projection will have the specified nearPlane and farPlane clipping planes.

See also: ortho(), frustum()

void QMatrix4x4::rotate ( const QQuaternion & quaternion )

Multiples this matrix by another that rotates coordinates according to a specified quaternion. The quaternion is assumed to have been normalized.

See also: scale(), translate(), QQuaternion

void QMatrix4x4::rotate	(	qreal	angle,
		const QVector3D &	vector
	)

Multiples this matrix by another that rotates coordinates through angle degrees about vector.

See also: scale(), translate()

void QMatrix4x4::rotate	(	qreal	angle,
		qreal	x,
		qreal	y,
		qreal	z = `0.0f`
	)

Multiplies this matrix by another that rotates coordinates through angle degrees about the vector (x, y, z).

See also: scale(), translate()

QVector4D QMatrix4x4::row ( int index ) const

inline

Returns the elements of row index as a 4D vector.

See also: setRow(), column()

void QMatrix4x4::scale ( const QVector3D & vector )

Multiplies this matrix by another that scales coordinates by the components of vector.

See also: translate(), rotate()

void QMatrix4x4::scale ( qreal factor )

Multiplies this matrix by another that scales coordinates by the given factor.

See also: translate(), rotate()

void QMatrix4x4::scale	(	qreal	x,
		qreal	y
	)

Multiplies this matrix by another that scales coordinates by the components x, and y.

See also: translate(), rotate()

void QMatrix4x4::scale	(	qreal	x,
		qreal	y,
		qreal	z
	)

Multiplies this matrix by another that scales coordinates by the components x, y, and z.

See also: translate(), rotate()

void QMatrix4x4::setColumn	(	int	index,
		const QVector4D &	value
	)

inline

Sets the elements of column index to the components of value.

See also: column(), setRow()

void QMatrix4x4::setRow	(	int	index,
		const QVector4D &	value
	)

inline

Sets the elements of row index to the components of value.

See also: row(), setColumn()

void QMatrix4x4::setToIdentity ( )

inline

Sets this matrix to the identity.

See also: isIdentity()

QMatrix QMatrix4x4::toAffine ( ) const

Returns the conventional 2D affine transformation matrix that corresponds to this matrix. It is assumed that this matrix only contains 2D affine transformation elements.

See also: toTransform()

template<int N, int M>

QGenericMatrix< N, M, qreal > QMatrix4x4::toGenericMatrix ( ) const

Constructs a NxM generic matrix from the left-most N columns and top-most M rows of this 4x4 matrix. If N or M is greater than 4, then the remaining elements are filled with elements from the identity matrix.

QTransform QMatrix4x4::toTransform ( ) const

Returns the conventional 2D transformation matrix that corresponds to this matrix.

The returned QTransform is formed by simply dropping the third row and third column of the QMatrix4x4. This is suitable for implementing orthographic projections where the z coordinate should be dropped rather than projected.

See also: toAffine()

QTransform QMatrix4x4::toTransform ( qreal distanceToPlane ) const

Returns the conventional 2D transformation matrix that corresponds to this matrix.

If distanceToPlane is non-zero, it indicates a projection factor to use to adjust for the z coordinate. The value of 1024 corresponds to the projection factor used by QTransform::rotate() for the x and y axes.

If distanceToPlane is zero, then the returned QTransform is formed by simply dropping the third row and third column of the QMatrix4x4. This is suitable for implementing orthographic projections where the z coordinate should be dropped rather than projected.

See also: toAffine()

void QMatrix4x4::translate ( const QVector3D & vector )

Multiplies this matrix by another that translates coordinates by the components of vector.

See also: scale(), rotate()

void QMatrix4x4::translate	(	qreal	x,
		qreal	y
	)

Multiplies this matrix by another that translates coordinates by the components x, and y.

See also: scale(), rotate()

void QMatrix4x4::translate	(	qreal	x,
		qreal	y,
		qreal	z
	)

Multiplies this matrix by another that translates coordinates by the components x, y, and z.

See also: scale(), rotate()

QMatrix4x4 QMatrix4x4::transposed ( ) const

Returns this matrix, transposed about its diagonal.

void QMatrix4x4::viewport ( const QRectF & rect )

inline

Sets up viewport transform for viewport bounded by rect and with near and far set to 0 and 1 respectively.

void QMatrix4x4::viewport	(	qreal	left,
		qreal	bottom,
		qreal	width,
		qreal	height,
		qreal	nearPlane = `0.0`,
		qreal	farPlane = `1.0`
	)

Multiplies this matrix by a viewport matrix. The result can be used to transform from normalized device coordinates (NDC) to viewport (window) coordinates.

Points are mapped from the cube ranging over [-1, 1] in each dimension to the viewport with the near-lower-left corner at (left, bottom, nearPlane) and with size (width, height, (farPlane - nearPlane)).

Public Methods

Friends

Detailed Description

Constructor & Destructor Documentation

Method Documentation