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

#include <qmatrix4x4.h>

Inheritance diagram for QMatrix4x4:

Collaboration diagram for QMatrix4x4:

Public Types
enum	Flag { Identity = 0x0000 , Translation = 0x0001 , Scale = 0x0002 , Rotation2D = 0x0004 , Rotation = 0x0008 , Perspective = 0x0010 , General = 0x001f }

Public Member Functions
	QMatrix4x4 ()
	Constructs an identity matrix.
	QMatrix4x4 (Qt::Initialization)
	QMatrix4x4 (const float *values)
	Constructs a matrix from the given 16 floating-point values.
	QMatrix4x4 (float m11, float m12, float m13, float m14, float m21, float m22, float m23, float m24, float m31, float m32, float m33, float m34, float m41, float m42, float m43, float m44)
	Constructs a matrix from the 16 elements m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, and m44.
template<int N, int M>
	QMatrix4x4 (const QGenericMatrix< N, M, float > &matrix)
	Constructs a 4x4 matrix from the left-most 4 columns and top-most 4 rows of matrix.
	QMatrix4x4 (const float *values, int cols, int rows)
	QMatrix4x4 (const QTransform &transform)
	Constructs a 4x4 matrix from the conventional Qt 2D transformation matrix transform.
const float &	operator() (int row, int column) const
	Returns a constant reference to the element at position (row, column) in this matrix.
float &	operator() (int row, int column)
	Returns a reference to the element at position (row, column) in this matrix so that the element can be assigned to.
QVector4D	column (int index) const
	Returns the elements of column index as a 4D vector.
void	setColumn (int index, const QVector4D &value)
	Sets the elements of column index to the components of value.
QVector4D	row (int index) const
	Returns the elements of row index as a 4D vector.
void	setRow (int index, const QVector4D &value)
	Sets the elements of row index to the components of value.
bool	isAffine () const
bool	isIdentity () const
	Returns `true` if this matrix is the identity; false otherwise.
void	setToIdentity ()
	Sets this matrix to the identity.
void	fill (float value)
	Fills all elements of this matrx with value.
double	determinant () const
	Returns the determinant of this matrix.
QMatrix4x4	inverted (bool *invertible=nullptr) const
	Returns the inverse of this matrix.
QMatrix4x4	transposed () const
	Returns this matrix, transposed about its diagonal.
QMatrix3x3	normalMatrix () const
	Returns the normal matrix corresponding to this 4x4 transformation.
QMatrix4x4 &	operator+= (const QMatrix4x4 &other)
	Adds the contents of other to this matrix.
QMatrix4x4 &	operator-= (const QMatrix4x4 &other)
	Subtracts the contents of other from this matrix.
QMatrix4x4 &	operator*= (const QMatrix4x4 &other)
	Multiplies the contents of other by this matrix.
QMatrix4x4 &	operator*= (float factor)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies all elements of this matrix by factor.
QMatrix4x4 &	operator/= (float divisor)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Divides all elements of this matrix by divisor.
bool	operator== (const QMatrix4x4 &other) const
	Returns `true` if this matrix is identical to other; false otherwise.
bool	operator!= (const QMatrix4x4 &other) const
	Returns `true` if this matrix is not identical to other; false otherwise.
void	scale (const QVector3D &vector)
	Multiplies this matrix by another that scales coordinates by the components of vector.
void	translate (const QVector3D &vector)
	Multiplies this matrix by another that translates coordinates by the components of vector.
void	rotate (float angle, const QVector3D &vector)
	Multiples this matrix by another that rotates coordinates through angle degrees about vector.
void	scale (float x, float y)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that scales coordinates by the components x, and y.
void	scale (float x, float y, float z)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that scales coordinates by the components x, y, and z.
void	scale (float factor)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that scales coordinates by the given factor.
void	translate (float x, float y)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that translates coordinates by the components x, and y.
void	translate (float x, float y, float z)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that translates coordinates by the components x, y, and z.
void	rotate (float angle, float x, float y, float z=0.0f)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that rotates coordinates through angle degrees about the vector (x, y, z).
void	rotate (const QQuaternion &quaternion)
	Multiples this matrix by another that rotates coordinates according to a specified quaternion.
void	ortho (const QRect &rect)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by rect.
void	ortho (const QRectF &rect)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that applies an orthographic projection for a window with boundaries specified by rect.
void	ortho (float left, float right, float bottom, float top, float nearPlane, float 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.
void	frustum (float left, float right, float bottom, float top, float nearPlane, float 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.
void	perspective (float verticalAngle, float aspectRatio, float nearPlane, float farPlane)
	Multiplies this matrix by another that applies a perspective projection.
void	lookAt (const QVector3D &eye, const QVector3D &center, const QVector3D &up)
	Multiplies this matrix by a viewing matrix derived from an eye point.
void	viewport (const QRectF &rect)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Sets up viewport transform for viewport bounded by rect and with near and far set to 0 and 1 respectively.
void	viewport (float left, float bottom, float width, float height, float nearPlane=0.0f, float farPlane=1.0f)
	Multiplies this matrix by another that performs the scale and bias transformation used by OpenGL to transform from normalized device coordinates (NDC) to viewport (window) coordinates.
void	flipCoordinates ()
void	copyDataTo (float *values) const
	Retrieves the 16 items in this matrix and copies them to values in row-major order.
QTransform	toTransform () const
	Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.
QTransform	toTransform (float distanceToPlane) const
	Returns the conventional Qt 2D transformation matrix that corresponds to this matrix.
QPoint	map (const QPoint &point) const
	Maps point by multiplying this matrix by point.
QPointF	map (const QPointF &point) const
	Maps point by post-multiplying this matrix by point.
QVector3D	map (const QVector3D &point) const
	Maps point by multiplying this matrix by point extended to a 4D vector by assuming 1.0 for the w coordinate.
QVector3D	mapVector (const QVector3D &vector) const
	Maps vector by multiplying the top 3x3 portion of this matrix by vector.
QVector4D	map (const QVector4D &point) const
	Maps point by multiplying this matrix by point.
QRect	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.
QRectF	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.
template<int N, int M>
QGenericMatrix< N, M, float >	toGenericMatrix () const
	Constructs a NxM generic matrix from the left-most N columns and top-most M rows of this 4x4 matrix.
float *	data ()
	Returns a pointer to the raw data of this matrix.
const float *	data () const
	Returns a constant pointer to the raw data of this matrix.
const float *	constData () const
	Returns a constant pointer to the raw data of this matrix.
void	optimize ()
	Optimize the usage of this matrix from its current elements.
	operator QVariant () const
	Returns the matrix as a QVariant.
void	projectedRotate (float angle, float x, float y, float z, float distanceToPlane=1024.0)
Flags	flags () const
template<int N, int M>
Q_INLINE_TEMPLATE	QMatrix4x4 (const QGenericMatrix< N, M, float > &matrix)

Friends
class	::tst_QMatrixNxN
QMatrix4x4	operator+ (const QMatrix4x4 &m1, const QMatrix4x4 &m2)
	Returns the sum of m1 and m2.
QMatrix4x4	operator- (const QMatrix4x4 &m1, const QMatrix4x4 &m2)
	Returns the difference of m1 and m2.
QMatrix4x4	operator* (const QMatrix4x4 &m1, const QMatrix4x4 &m2)
	Returns the product of m1 and m2.
QVector4D	operator* (const QVector4D &vector, const QMatrix4x4 &matrix)
	Returns the result of transforming vector according to matrix, with the matrix applied post-vector.
QVector4D	operator* (const QMatrix4x4 &matrix, const QVector4D &vector)
	Returns the result of transforming vector according to matrix, with the matrix applied pre-vector.
QPoint	operator* (const QPoint &point, const QMatrix4x4 &matrix)
	Returns the result of transforming point according to matrix, with the matrix applied post-point.
QPointF	operator* (const QPointF &point, const QMatrix4x4 &matrix)
	Returns the result of transforming point according to matrix, with the matrix applied post-point.
QMatrix4x4	operator- (const QMatrix4x4 &matrix)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
QMatrix4x4	operator* (float factor, const QMatrix4x4 &matrix)
	Returns the result of multiplying all elements of matrix by factor.
QMatrix4x4	operator* (const QMatrix4x4 &matrix, float factor)
	Returns the result of multiplying all elements of matrix by factor.
Q_GUI_EXPORT QMatrix4x4	operator/ (const QMatrix4x4 &matrix, float divisor)
	Returns the result of dividing all elements of matrix by divisor.
Q_GUI_EXPORT bool	qFuzzyCompare (const QMatrix4x4 &m1, const QMatrix4x4 &m2)
	Returns `true` if m1 and m2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.
Q_GUI_EXPORT QDebug	operator<< (QDebug dbg, const QMatrix4x4 &m)

Related Symbols
(Note that these are not member symbols.)
QDataStream &	operator<< (QDataStream &stream, const QMatrix4x4 &matrix)
	Writes the given matrix to the given stream and returns a reference to the stream.
QDataStream &	operator>> (QDataStream &stream, QMatrix4x4 &matrix)
	Reads a 4x4 matrix from the given stream into the given matrix and returns a reference to the stream.

Detailed Description

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

Since: 4.6

\inmodule QtGui

The QMatrix4x4 class in general is treated as a row-major matrix, in that the constructors and operator() functions take data in row-major format, as is familiar in C-style usage.

Internally the data is stored as column-major format, so as to be optimal for passing to OpenGL functions, which expect column-major data.

When using these functions be aware that they return data in {column-major} format: \list

data()
constData() \endlist

See also: QVector3D, QGenericMatrix

Definition at line 26 of file qmatrix4x4.h.

Member Enumeration Documentation

◆ Flag

enum QMatrix4x4::Flag

\omitvalue Identity \omitvalue Translation \omitvalue Scale \omitvalue Rotation2D \omitvalue Rotation \omitvalue Perspective \omitvalue General

Enumerator
Identity
Translation
Scale
Rotation2D
Rotation
Perspective
General

Definition at line 169 of file qmatrix4x4.h.

Constructor & Destructor Documentation

◆ QMatrix4x4() [1/8]

QMatrix4x4::QMatrix4x4 ( )

inline

Constructs an identity matrix.

Definition at line 29 of file qmatrix4x4.h.

◆ QMatrix4x4() [2/8]

QMatrix4x4::QMatrix4x4 ( Qt::Initialization )

inlineexplicit

Since: 5.5

Constructs a matrix without initializing the contents.

Definition at line 30 of file qmatrix4x4.h.

◆ QMatrix4x4() [3/8]

QMatrix4x4::QMatrix4x4 ( const float * 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()

Definition at line 69 of file qmatrix4x4.cpp.

◆ QMatrix4x4() [4/8]

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

Definition at line 198 of file qmatrix4x4.h.

◆ QMatrix4x4() [5/8]

template<int N, int M>

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

explicit

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() [6/8]

QMatrix4x4::QMatrix4x4	(	const float *	values,
		int	cols,
		int	rows )

Definition at line 116 of file qmatrix4x4.cpp.

◆ QMatrix4x4() [7/8]

QMatrix4x4::QMatrix4x4 ( const QTransform & transform )

Constructs a 4x4 matrix from the conventional Qt 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()

Definition at line 142 of file qmatrix4x4.cpp.

◆ QMatrix4x4() [8/8]

template<int N, int M>

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

Definition at line 212 of file qmatrix4x4.h.

Member Function Documentation

◆ column()

QVector4D QMatrix4x4::column ( int index ) const

inline

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

See also: setColumn(), row()

Definition at line 261 of file qmatrix4x4.h.

◆ constData()

const float * QMatrix4x4::constData ( ) const

inline

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

This raw data is stored in column-major format.

See also: data()

Definition at line 149 of file qmatrix4x4.h.

◆ copyDataTo()

void QMatrix4x4::copyDataTo ( float * values ) const

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

Definition at line 1634 of file qmatrix4x4.cpp.

◆ data() [1/2]

float * QMatrix4x4::data ( )

inline

Returns a pointer to the raw data of this matrix.

See also: constData(), optimize()

Definition at line 1052 of file qmatrix4x4.h.

◆ data() [2/2]

const float * QMatrix4x4::data ( ) const

inline

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

This raw data is stored in column-major format.

See also: constData()

Definition at line 148 of file qmatrix4x4.h.

◆ determinant()

double QMatrix4x4::determinant ( ) const

Returns the determinant of this matrix.

Definition at line 292 of file qmatrix4x4.cpp.

◆ fill()

void QMatrix4x4::fill ( float value )

inline

Fills all elements of this matrx with value.

Definition at line 339 of file qmatrix4x4.h.

◆ flags()

Flags QMatrix4x4::flags ( ) const

inline

Definition at line 180 of file qmatrix4x4.h.

◆ flipCoordinates()

void QMatrix4x4::flipCoordinates ( )

Deprecated

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()

Deprecated

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()

Definition at line 1608 of file qmatrix4x4.cpp.

◆ frustum()

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

Definition at line 1427 of file qmatrix4x4.cpp.

◆ inverted()

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

Returns the inverse of this matrix.

Returns the identity if this matrix cannot 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()

Definition at line 318 of file qmatrix4x4.cpp.

◆ isAffine()

bool QMatrix4x4::isAffine ( ) const

inline

Since: 5.5

Returns true if this matrix is affine matrix; 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()

Definition at line 296 of file qmatrix4x4.h.

◆ isIdentity()

bool QMatrix4x4::isIdentity ( ) const

inline

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

See also: setToIdentity()

Definition at line 301 of file qmatrix4x4.h.

◆ lookAt()

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

Multiplies this matrix by a viewing matrix derived from an eye point.

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.

Note: The up vector must not be parallel to the line of sight from eye to center.

Definition at line 1517 of file qmatrix4x4.cpp.

◆ map() [1/4]

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

inline

Maps point by multiplying this matrix by point.

The matrix is applied pre-point.

See also: mapRect()

Definition at line 910 of file qmatrix4x4.h.

◆ map() [2/4]

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

inline

Maps point by post-multiplying this matrix by point.

The matrix is applied pre-point.

See also: mapRect()

Definition at line 942 of file qmatrix4x4.h.

◆ map() [3/4]

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

inline

Maps point by multiplying this matrix by point extended to a 4D vector by assuming 1.0 for the w coordinate.

The matrix is applied pre-point.

Note: This function is not the same as mapVector(). For points, always use map(). mapVector() is suitable for vectors (directions) only.

See also: mapRect(), mapVector()

Definition at line 979 of file qmatrix4x4.h.

◆ map() [4/4]

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

inline

Maps point by multiplying this matrix by point.

The matrix is applied pre-point.

See also: mapRect()

Definition at line 1045 of file qmatrix4x4.h.

◆ mapRect() [1/2]

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()

Definition at line 1765 of file qmatrix4x4.cpp.

◆ mapRect() [2/2]

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()

Definition at line 1811 of file qmatrix4x4.cpp.

◆ mapVector()

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. The matrix is applied pre-vector.

See also: map()

Definition at line 1018 of file qmatrix4x4.h.

◆ normalMatrix()

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 function returns the identity.

See also: inverted()

Definition at line 438 of file qmatrix4x4.cpp.

◆ operator QVariant()

QMatrix4x4::operator QVariant ( ) const

Returns the matrix as a QVariant.

Definition at line 1977 of file qmatrix4x4.cpp.

◆ operator!=()

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

inline

Returns true if this matrix is not identical to other; false otherwise.

This operator uses an exact floating-point comparison.

Definition at line 545 of file qmatrix4x4.h.

◆ operator()() [1/2]

float & 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()

Definition at line 253 of file qmatrix4x4.h.

◆ operator()() [2/2]

const float & 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()

Definition at line 247 of file qmatrix4x4.h.

◆ operator*=() [1/2]

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

inline

Multiplies the contents of other by this matrix.

Definition at line 404 of file qmatrix4x4.h.

◆ operator*=() [2/2]

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

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies all elements of this matrix by factor.

Definition at line 503 of file qmatrix4x4.h.

◆ operator+=()

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

inline

Adds the contents of other to this matrix.

Definition at line 360 of file qmatrix4x4.h.

◆ operator-=()

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

inline

Subtracts the contents of other from this matrix.

Definition at line 382 of file qmatrix4x4.h.

◆ operator/=()

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

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Divides all elements of this matrix by divisor.

Definition at line 537 of file qmatrix4x4.cpp.

◆ operator==()

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.

Definition at line 525 of file qmatrix4x4.h.

◆ optimize()

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()(int, int) or data(), then QMatrix4x4 will lose track of the special type and will revert to the safest but least efficient operations thereafter.

By calling optimize() after directly modifying the matrix, the programmer can force QMatrix4x4 to recover the special type if the elements appear to conform to one of the known optimized types.

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

Definition at line 1922 of file qmatrix4x4.cpp.

◆ ortho() [1/3]

void QMatrix4x4::ortho ( const QRect & rect )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.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()

Definition at line 1355 of file qmatrix4x4.cpp.

◆ ortho() [2/3]

void QMatrix4x4::ortho ( const QRectF & rect )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.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()

Definition at line 1373 of file qmatrix4x4.cpp.

◆ ortho() [3/3]

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

Definition at line 1386 of file qmatrix4x4.cpp.

◆ perspective()

void QMatrix4x4::perspective	(	float	verticalAngle,
		float	aspectRatio,
		float	nearPlane,
		float	farPlane )

Multiplies this matrix by another that applies a perspective projection.

The vertical field of view will be verticalAngle degrees within a window with a given aspectRatio that determines the horizontal field of view. The projection will have the specified nearPlane and farPlane clipping planes which are the distances from the viewer to the corresponding planes.

See also: ortho(), frustum()

Definition at line 1470 of file qmatrix4x4.cpp.

◆ projectedRotate()

void QMatrix4x4::projectedRotate	(	float	angle,
		float	x,
		float	y,
		float	z,
		float	distanceToPlane = 1024.0 )

Definition at line 1168 of file qmatrix4x4.cpp.

◆ rotate() [1/3]

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

Definition at line 1304 of file qmatrix4x4.cpp.

◆ rotate() [2/3]

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

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

See also: scale(), translate()

Definition at line 1046 of file qmatrix4x4.cpp.

◆ rotate() [3/3]

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

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that rotates coordinates through angle degrees about the vector (x, y, z).

See also: scale(), translate()

Definition at line 1061 of file qmatrix4x4.cpp.

◆ row()

QVector4D QMatrix4x4::row ( int index ) const

inline

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

See also: setRow(), column()

Definition at line 277 of file qmatrix4x4.h.

◆ scale() [1/4]

void QMatrix4x4::scale ( const QVector3D & vector )

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

See also: translate(), rotate()

Definition at line 768 of file qmatrix4x4.cpp.

◆ scale() [2/4]

void QMatrix4x4::scale ( float factor )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that scales coordinates by the given factor.

See also: translate(), rotate()

Definition at line 889 of file qmatrix4x4.cpp.

◆ scale() [3/4]

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

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that scales coordinates by the components x, and y.

See also: translate(), rotate()

Definition at line 814 of file qmatrix4x4.cpp.

◆ scale() [4/4]

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

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that scales coordinates by the components x, y, and z.

See also: translate(), rotate()

Definition at line 848 of file qmatrix4x4.cpp.

◆ setColumn()

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

inline

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

See also: column(), setRow()

Definition at line 267 of file qmatrix4x4.h.

◆ 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()

Definition at line 283 of file qmatrix4x4.h.

◆ setToIdentity()

void QMatrix4x4::setToIdentity ( )

inline

Sets this matrix to the identity.

See also: isIdentity()

Definition at line 318 of file qmatrix4x4.h.

◆ toGenericMatrix()

template<int N, int M>

QGenericMatrix< N, M, float > 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.

Definition at line 230 of file qmatrix4x4.h.

◆ toTransform() [1/2]

QTransform QMatrix4x4::toTransform ( ) const

Returns the conventional Qt 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.

Definition at line 1650 of file qmatrix4x4.cpp.

◆ toTransform() [2/2]

QTransform QMatrix4x4::toTransform ( float distanceToPlane ) const

Returns the conventional Qt 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.

Definition at line 1672 of file qmatrix4x4.cpp.

◆ translate() [1/3]

void QMatrix4x4::translate ( const QVector3D & vector )

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

See also: scale(), rotate()

Definition at line 930 of file qmatrix4x4.cpp.

◆ translate() [2/3]

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

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that translates coordinates by the components x, and y.

See also: scale(), rotate()

Definition at line 973 of file qmatrix4x4.cpp.

◆ translate() [3/3]

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

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Multiplies this matrix by another that translates coordinates by the components x, y, and z.

See also: scale(), rotate()

Definition at line 1007 of file qmatrix4x4.cpp.

◆ transposed()

QMatrix4x4 QMatrix4x4::transposed ( ) const

Returns this matrix, transposed about its diagonal.

Definition at line 494 of file qmatrix4x4.cpp.

◆ viewport() [1/2]

void QMatrix4x4::viewport ( const QRectF & rect )

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Sets up viewport transform for viewport bounded by rect and with near and far set to 0 and 1 respectively.

Definition at line 1060 of file qmatrix4x4.h.

◆ viewport() [2/2]

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

Multiplies this matrix by another that performs the scale and bias transformation used by OpenGL to transform from normalized device coordinates (NDC) to viewport (window) coordinates.

That is it maps points from the cube ranging over [-1, 1] in each dimension to the viewport with it's near-lower-left corner at (left, bottom, nearPlane) and with size (width, height, farPlane - nearPlane).

This matches the transform used by the fixed function OpenGL viewport transform controlled by the functions glViewport() and glDepthRange().

Definition at line 1571 of file qmatrix4x4.cpp.

◆ ::tst_QMatrixNxN

friend class ::tst_QMatrixNxN

friend

Definition at line 188 of file qmatrix4x4.h.

◆ operator* [1/7]

QMatrix4x4 operator*	(	const QMatrix4x4 &	m1,
		const QMatrix4x4 &	m2 )

friend

Returns the product of m1 and m2.

Definition at line 609 of file qmatrix4x4.h.

◆ operator* [2/7]

QVector4D operator*	(	const QMatrix4x4 &	matrix,
		const QVector4D &	vector )

friend

Returns the result of transforming vector according to matrix, with the matrix applied pre-vector.

Definition at line 761 of file qmatrix4x4.h.

◆ operator* [3/7]

QMatrix4x4 operator*	(	const QMatrix4x4 &	matrix,
		float	factor )

friend

Returns the result of multiplying all elements of matrix by factor.

Definition at line 888 of file qmatrix4x4.h.

◆ operator* [4/7]

QPoint operator*	(	const QPoint &	point,
		const QMatrix4x4 &	matrix )

friend

Returns the result of transforming point according to matrix, with the matrix applied post-point.

Definition at line 785 of file qmatrix4x4.h.

◆ operator* [5/7]

QPointF operator*	(	const QPointF &	point,
		const QMatrix4x4 &	matrix )

friend

Returns the result of transforming point according to matrix, with the matrix applied post-point.

Definition at line 806 of file qmatrix4x4.h.

◆ operator* [6/7]

QVector4D operator*	(	const QVector4D &	vector,
		const QMatrix4x4 &	matrix )

friend

Returns the result of transforming vector according to matrix, with the matrix applied post-vector.

Definition at line 739 of file qmatrix4x4.h.

◆ operator* [7/7]

QMatrix4x4 operator*	(	float	factor,
		const QMatrix4x4 &	matrix )

friend

Returns the result of multiplying all elements of matrix by factor.

Definition at line 866 of file qmatrix4x4.h.

◆ operator+

QMatrix4x4 operator+	(	const QMatrix4x4 &	m1,
		const QMatrix4x4 &	m2 )

friend

Returns the sum of m1 and m2.

Definition at line 565 of file qmatrix4x4.h.

◆ operator- [1/2]

QMatrix4x4 operator-	(	const QMatrix4x4 &	m1,
		const QMatrix4x4 &	m2 )

friend

Returns the difference of m1 and m2.

Definition at line 587 of file qmatrix4x4.h.

◆ operator- [2/2]

QMatrix4x4 operator- ( const QMatrix4x4 & matrix )

friend

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Returns the negation of matrix.

Definition at line 844 of file qmatrix4x4.h.

◆ operator/

QMatrix4x4 operator/	(	const QMatrix4x4 &	matrix,
		float	divisor )

friend

Returns the result of dividing all elements of matrix by divisor.

Definition at line 710 of file qmatrix4x4.cpp.

◆ operator<<() [1/2]

QDataStream & operator<<	(	QDataStream &	stream,
		const QMatrix4x4 &	matrix )

Writes the given matrix to the given stream and returns a reference to the stream.

See also: {Serializing Qt Data Types}

◆ operator<< [2/2]

Q_GUI_EXPORT QDebug operator<<	(	QDebug	dbg,
		const QMatrix4x4 &	m )

friend

Definition at line 1984 of file qmatrix4x4.cpp.

◆ operator>>()

QDataStream & operator>>	(	QDataStream &	stream,
		QMatrix4x4 &	matrix )

Reads a 4x4 matrix from the given stream into the given matrix and returns a reference to the stream.

See also: {Serializing Qt Data Types}

◆ qFuzzyCompare

Q_GUI_EXPORT bool qFuzzyCompare	(	const QMatrix4x4 &	m1,
		const QMatrix4x4 &	m2 )

friend

Returns true if m1 and m2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.

Definition at line 739 of file qmatrix4x4.cpp.

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

qtbase/src/gui/math3d/qmatrix4x4.h (b27e79ec0c4f07838bab6a8bcee31795883decb4)
qtbase/src/gui/math3d/qmatrix4x4.cpp (f03b51a19589136ba66e8068a9bff50397c52cb1)

Public Types

Public Member Functions

Friends

Related Symbols

Detailed Description

Member Enumeration Documentation

◆ Flag

Constructor & Destructor Documentation

◆ QMatrix4x4() [1/8]

◆ QMatrix4x4() [2/8]

◆ QMatrix4x4() [3/8]

◆ QMatrix4x4() [4/8]

◆ QMatrix4x4() [5/8]

◆ QMatrix4x4() [6/8]

◆ QMatrix4x4() [7/8]

◆ QMatrix4x4() [8/8]

Member Function Documentation

◆ column()

◆ constData()

◆ copyDataTo()

◆ data() [1/2]

◆ data() [2/2]

◆ determinant()

◆ fill()

◆ flags()

◆ flipCoordinates()

◆ frustum()

◆ inverted()

◆ isAffine()

◆ isIdentity()

◆ lookAt()

◆ map() [1/4]

◆ map() [2/4]

◆ map() [3/4]

◆ map() [4/4]

◆ mapRect() [1/2]

◆ mapRect() [2/2]

◆ mapVector()

◆ normalMatrix()

◆ operator QVariant()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator==()

◆ optimize()

◆ ortho() [1/3]

◆ ortho() [2/3]

◆ ortho() [3/3]

◆ perspective()

◆ projectedRotate()

◆ rotate() [1/3]

◆ rotate() [2/3]

◆ rotate() [3/3]

◆ row()

◆ scale() [1/4]

◆ scale() [2/4]

◆ scale() [3/4]

◆ scale() [4/4]

◆ setColumn()

◆ setRow()

◆ setToIdentity()

◆ toGenericMatrix()

◆ toTransform() [1/2]

◆ toTransform() [2/2]

◆ translate() [1/3]

◆ translate() [2/3]

◆ translate() [3/3]

◆ transposed()

◆ viewport() [1/2]

◆ viewport() [2/2]

Friends And Related Symbol Documentation

◆ ::tst_QMatrixNxN

◆ operator* [1/7]

◆ operator* [2/7]

◆ operator* [3/7]