QMatrix Class Reference

The QMatrix class specifies 2D transformations of a coordinate system. More...

#include <qmatrix.h>

Public Functions
QT_DEPRECATED qreal	det () const
	Returns the matrix's determinant. More...
qreal	determinant () const
	Returns the matrix's determinant. More...
qreal	dx () const
	Returns the horizontal translation factor. More...
qreal	dy () const
	Returns the vertical translation factor. More...
QMatrix	inverted (bool *invertible=0) const
	Returns an inverted copy of this matrix. More...
bool	isIdentity () const
	Returns true if the matrix is the identity matrix, otherwise returns false. More...
bool	isInvertible () const
	Returns true if the matrix is invertible, otherwise returns false. More...
qreal	m11 () const
	Returns the horizontal scaling factor. More...
qreal	m12 () const
	Returns the vertical shearing factor. More...
qreal	m21 () const
	Returns the horizontal shearing factor. More...
qreal	m22 () const
	Returns the vertical scaling factor. More...
void	map (int x, int y, int *tx, int *ty) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Maps the given coordinates x and y into the coordinate system defined by this matrix. More...
void	map (qreal x, qreal y, qreal *tx, qreal *ty) const
	Maps the given coordinates x and y into the coordinate system defined by this matrix. More...
QPoint	map (const QPoint &p) const
	Creates and returns a QPoint object that is a copy of the given point, mapped into the coordinate system defined by this matrix. More...
QPointF	map (const QPointF &p) const
	Creates and returns a QPointF object that is a copy of the given point, mapped into the coordinate system defined by this matrix. More...
QLine	map (const QLine &l) const
	Creates and returns a QLine object that is a copy of the given line, mapped into the coordinate system defined by this matrix. More...
QLineF	map (const QLineF &l) const
	Creates and returns a QLineF object that is a copy of the given line, mapped into the coordinate system defined by this matrix. More...
QPolygonF	map (const QPolygonF &a) const
	Creates and returns a QPolygonF object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix. More...
QPolygon	map (const QPolygon &a) const
	Creates and returns a QPolygon object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix. More...
QRegion	map (const QRegion &r) const
	Creates and returns a QRegion object that is a copy of the given region, mapped into the coordinate system defined by this matrix. More...
QPainterPath	map (const QPainterPath &p) const
	Creates and returns a QPainterPath object that is a copy of the given path, mapped into the coordinate system defined by this matrix. More...
QRect	mapRect (const QRect &) const
	Creates and returns a QRect object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix. More...
QRectF	mapRect (const QRectF &) const
	Creates and returns a QRectF object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix. More...
QPolygon	mapToPolygon (const QRect &r) const
	Creates and returns a QPolygon representation of the given rectangle, mapped into the coordinate system defined by this matrix. More...
	operator QVariant () const
	Returns the matrix as a QVariant. More...
bool	operator!= (const QMatrix &) const
	Returns true if this matrix is not equal to the given matrix, otherwise returns false. More...
QMatrix	operator* (const QMatrix &o) const
	Returns the result of multiplying this matrix by the given matrix. More...
QMatrix &	operator*= (const QMatrix &)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Returns the result of multiplying this matrix by the given matrix. More...
QMatrix &	operator= (const QMatrix &)
	Assigns the given matrix's values to this matrix. More...
bool	operator== (const QMatrix &) const
	Returns true if this matrix is equal to the given matrix, otherwise returns false. More...
	QMatrix (Qt::Initialization)
	QMatrix ()
	Constructs an identity matrix. More...
	QMatrix (qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
	Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy. More...
	QMatrix (const QMatrix &matrix)
	Constructs a matrix that is a copy of the given matrix. More...
void	reset ()
	Resets the matrix to an identity matrix, i.e. More...
QMatrix &	rotate (qreal a)
	Rotates the coordinate system the given degrees counterclockwise. More...
QMatrix &	scale (qreal sx, qreal sy)
	Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix. More...
void	setMatrix (qreal m11, qreal m12, qreal m21, qreal m22, qreal dx, qreal dy)
	Sets the matrix elements to the specified values, m11, m12, m21, m22, dx and dy. More...
QMatrix &	shear (qreal sh, qreal sv)
	Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix. More...
QMatrix &	translate (qreal dx, qreal dy)
	Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix. More...

Private Functions
	QMatrix (bool)
	QMatrix (qreal am11, qreal am12, qreal am21, qreal am22, qreal adx, qreal ady, bool)

Properties
qreal	_dx
qreal	_dy
qreal	_m11
qreal	_m12
qreal	_m21
qreal	_m22

Friends
class	QTransform

Related Functions
(Note that these are not member functions.)
QPoint	operator* (const QPoint &point, const QMatrix &matrix)
QPointF	operator* (const QPointF &point, const QMatrix &matrix)
QLineF	operator* (const QLineF &line, const QMatrix &matrix)
QLine	operator* (const QLine &line, const QMatrix &matrix)
QPolygonF	operator* (const QPolygonF &polygon, const QMatrix &matrix)
QPolygon	operator* (const QPolygon &polygon, const QMatrix &matrix)
QRegion	operator* (const QRegion &region, const QMatrix &matrix)
QPainterPath	operator* (const QPainterPath &path, const QMatrix &matrix)
QDataStream &	operator<< (QDataStream &stream, const QMatrix &matrix)
	Writes the given matrix to the given stream and returns a reference to the stream. More...
QDataStream &	operator>> (QDataStream &stream, QMatrix &matrix)
	Reads the given matrix from the given stream and returns a reference to the stream. More...
bool	qFuzzyCompare (const QMatrix &m1, const QMatrix &m2)
	The qFuzzyCompare function is for comparing two matrices using a fuzziness factor. More...

Detailed Description

The QMatrix class specifies 2D transformations of a coordinate system.

A matrix specifies how to translate, scale, shear or rotate the coordinate system, and is typically used when rendering graphics. QMatrix, in contrast to QTransform, does not allow perspective transformations. QTransform is the recommended transformation class in Qt.

A QMatrix object can be built using the setMatrix(), scale(), rotate(), translate() and shear() functions. Alternatively, it can be built by applying basic matrix operations. The matrix can also be defined when constructed, and it can be reset to the identity matrix (the default) using the reset() function.

The QMatrix class supports mapping of graphic primitives: A given point, line, polygon, region, or painter path can be mapped to the coordinate system defined by this matrix using the map() function. In case of a rectangle, its coordinates can be transformed using the mapRect() function. A rectangle can also be transformed into a polygon (mapped to the coordinate system defined by this matrix), using the mapToPolygon() function.

QMatrix provides the isIdentity() function which returns true if the matrix is the identity matrix, and the isInvertible() function which returns true if the matrix is non-singular (i.e. AB = BA = I). The inverted() function returns an inverted copy of this matrix if it is invertible (otherwise it returns the identity matrix). In addition, QMatrix provides the determinant() function returning the matrix's determinant.

Finally, the QMatrix class supports matrix multiplication, and objects of the class can be streamed as well as compared.

Rendering Graphics

When rendering graphics, the matrix defines the transformations but the actual transformation is performed by the drawing routines in QPainter.

By default, QPainter operates on the associated device's own coordinate system. The standard coordinate system of a QPaintDevice has its origin located at the top-left position. The x values increase to the right; y values increase downward. For a complete description, see the Coordinate System documentation.

QPainter has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix. For example:

void SimpleTransformation::paintEvent(QPaintEvent *) { QPainter painter(this); painter.setPen(QPen(Qt::blue, 1, Qt::DashLine)); painter.drawRect(0, 0, 100, 100); painter.rotate(45); painter.setFont(QFont("Helvetica", 24)); painter.setPen(QPen(Qt::black, 1)); painter.drawText(20, 10, "QMatrix"); }

Although these functions are very convenient, it can be more efficient to build a QMatrix and call QPainter::setMatrix() if you want to perform more than a single transform operation. For example:

void CombinedTransformation::paintEvent(QPaintEvent *) { QPainter painter(this); painter.setPen(QPen(Qt::blue, 1, Qt::DashLine)); painter.drawRect(0, 0, 100, 100); QMatrix matrix; matrix.translate(50, 50); matrix.rotate(45); matrix.scale(0.5, 1.0); painter.setMatrix(matrix); painter.setFont(QFont("Helvetica", 24)); painter.setPen(QPen(Qt::black, 1)); painter.drawText(20, 10, "QMatrix"); }

Basic Matrix Operations

A QMatrix object contains a 3 x 3 matrix. The dx and dy elements specify horizontal and vertical translation. The m11 and m22 elements specify horizontal and vertical scaling. And finally, the m21 and m12 elements specify horizontal and vertical shearing.

QMatrix transforms a point in the plane to another point using the following formulas:

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy

The point (x, y) is the original point, and (x', y') is the transformed point. (x', y') can be transformed back to (x, y) by performing the same operation on the inverted() matrix.

The various matrix elements can be set when constructing the matrix, or by using the setMatrix() function later on. They can also be manipulated using the translate(), rotate(), scale() and shear() convenience functions, The currently set values can be retrieved using the m11(), m12(), m21(), m22(), dx() and dy() functions.

Translation is the simplest transformation. Setting dx and dy will move the coordinate system dx units along the X axis and dy units along the Y axis. Scaling can be done by setting m11 and m22. For example, setting m11 to 2 and m22 to 1.5 will double the height and increase the width by 50%. The identity matrix has m11 and m22 set to 1 (all others are set to 0) mapping a point to itself. Shearing is controlled by m12 and m21. Setting these elements to values different from zero will twist the coordinate system. Rotation is achieved by carefully setting both the shearing factors and the scaling factors.

Here's the combined transformations example using basic matrix operations:

void BasicOperations::paintEvent(QPaintEvent *) { double pi = 3.14; double a = pi/180 * 45.0; double sina = sin(a); double cosa = cos(a); QMatrix translationMatrix(1, 0, 0, 1, 50.0, 50.0); QMatrix rotationMatrix(cosa, sina, -sina, cosa, 0, 0); QMatrix scalingMatrix(0.5, 0, 0, 1.0, 0, 0); QMatrix matrix; matrix = scalingMatrix * rotationMatrix * translationMatrix; QPainter painter(this); painter.setPen(QPen(Qt::blue, 1, Qt::DashLine)); painter.drawRect(0, 0, 100, 100); painter.setMatrix(matrix); painter.setFont(QFont("Helvetica", 24)); painter.setPen(QPen(Qt::black, 1)); painter.drawText(20, 10, "QMatrix"); }

See also

QPainter, QTransform, {Coordinate System}, {demos/affine}{Affine Transformations Demo}, {Transformations Example}

Definition at line 61 of file qmatrix.h.

Constructors and Destructors

QMatrix() [1/6]

QMatrix::QMatrix ( Qt::Initialization  )

inlineexplicit

Warning

This function is not part of the public interface.

Definition at line 64 of file qmatrix.h.

{}

QMatrix() [2/6]

QMatrix::QMatrix

(

)

Constructs an identity matrix.

All elements are set to zero except m11 and m22 (specifying the scale), which are set to 1.

See also

reset()

Definition at line 216 of file qmatrix.cpp.

Referenced by inverted(), and operator*().

    : _m11(1.)
    , _m12(0.)
    , _m21(0.)
    , _m22(1.)
    , _dx(0.)
    , _dy(0.)
{
}

QMatrix() [3/6]

QMatrix::QMatrix	(	qreal	m11,
		qreal	m12,
		qreal	m21,
		qreal	m22,
		qreal	dx,
		qreal	dy
	)

Constructs a matrix with the elements, m11, m12, m21, m22, dx and dy.

See also

setMatrix()

Definition at line 233 of file qmatrix.cpp.

    : _m11(m11)
    , _m12(m12)
    , _m21(m21)
    , _m22(m22)
    , _dx(dx)
    , _dy(dy)
{
}

QMatrix() [4/6]

QMatrix::QMatrix

(

const QMatrix &

matrix

)

Constructs a matrix that is a copy of the given matrix.

Definition at line 247 of file qmatrix.cpp.

    : _m11(matrix._m11)
    , _m12(matrix._m12)
    , _m21(matrix._m21)
    , _m22(matrix._m22)
    , _dx(matrix._dx)
    , _dy(matrix._dy)
{
}

QMatrix() [5/6]

QMatrix::QMatrix ( bool  )

inlineprivate

Definition at line 128 of file qmatrix.h.

            : _m11(1.)
            , _m12(0.)
            , _m21(0.)
            , _m22(1.)
            , _dx(0.)
            , _dy(0.) {}

QMatrix() [6/6]

QMatrix::QMatrix ( qreal  am11, qreal  am12, qreal  am21, qreal  am22, qreal  adx, qreal  ady, bool    )

inlineprivate

Definition at line 135 of file qmatrix.h.

            : _m11(am11)
            , _m12(am12)
            , _m21(am21)
            , _m22(am22)
            , _dx(adx)
            , _dy(ady) {}

Functions

det()

qreal QMatrix::det ( ) const

inline

Returns the matrix's determinant.

See also

determinant()

Definition at line 106 of file qmatrix.h.

{ return _m11*_m22 - _m12*_m21; }

determinant()

qreal QMatrix::determinant ( ) const

inline

Returns the matrix's determinant.

Since

4.6

Definition at line 104 of file qmatrix.h.

Referenced by inverted().

{ return _m11*_m22 - _m12*_m21; }

dx()

qreal QMatrix::dx ( ) const

inline

Returns the horizontal translation factor.

See also

translate(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 77 of file qmatrix.h.

Referenced by QWindowsXPStylePrivate::drawBackgroundDirectly(), QWin32PrintEngine::drawPixmap(), map(), operator<<(), operator>>(), qFuzzyCompare(), QMatrix4x4::QMatrix4x4(), setMatrix(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{ return _dx; }

dy()

qreal QMatrix::dy ( ) const

inline

Returns the vertical translation factor.

See also

translate(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 78 of file qmatrix.h.

Referenced by QWindowsXPStylePrivate::drawBackgroundDirectly(), map(), operator<<(), operator>>(), qFuzzyCompare(), QMatrix4x4::QMatrix4x4(), setMatrix(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{ return _dy; }

inverted()

QMatrix QMatrix::inverted

(

bool *

invertible = 0

)

const

Returns an inverted copy of this matrix.

If the matrix is singular (not invertible), the returned matrix is the identity matrix. If invertible is valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.

See also

isInvertible()

Definition at line 1066 of file qmatrix.cpp.

Referenced by QTransform::inverted(), QGraphicsViewPrivate::mapToScene(), QPainter::setViewTransformEnabled(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{
    qreal dtr = determinant();
    if (dtr == 0.0) {
        if (invertible)
            *invertible = false;                // singular matrix
        return QMatrix(true);
    }
    else {                                        // invertible matrix
        if (invertible)
            *invertible = true;
        qreal dinv = 1.0/dtr;
        return QMatrix((_m22*dinv),        (-_m12*dinv),
                       (-_m21*dinv), (_m11*dinv),
                       ((_m21*_dy - _m22*_dx)*dinv),
                       ((_m12*_dx - _m11*_dy)*dinv),
                       true);
    }
}

isIdentity()

bool QMatrix::isIdentity ( ) const

inline

Returns true if the matrix is the identity matrix, otherwise returns false.

See also

reset()

Definition at line 166 of file qmatrix.h.

Referenced by QSvgGradientStyle::brush(), map(), parseBaseGradient(), parseTransform(), and qt_plastique_draw_gradient().

{
    return qFuzzyIsNull(_m11 - 1) && qFuzzyIsNull(_m22 - 1) && qFuzzyIsNull(_m12)
           && qFuzzyIsNull(_m21) && qFuzzyIsNull(_dx) && qFuzzyIsNull(_dy);
}

isInvertible()

bool QMatrix::isInvertible ( ) const

inline

Returns true if the matrix is invertible, otherwise returns false.

See also

inverted()

Definition at line 103 of file qmatrix.h.

{ return !qFuzzyIsNull(_m11*_m22 - _m12*_m21); }

m11()

qreal QMatrix::m11 ( ) const

inline

Returns the horizontal scaling factor.

See also

scale(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 73 of file qmatrix.h.

Referenced by map(), operator<<(), operator>>(), qFuzzyCompare(), QMatrix4x4::QMatrix4x4(), setMatrix(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{ return _m11; }

m12()

qreal QMatrix::m12 ( ) const

inline

Returns the vertical shearing factor.

See also

shear(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 74 of file qmatrix.h.

Referenced by map(), operator<<(), operator>>(), qFuzzyCompare(), QMatrix4x4::QMatrix4x4(), setMatrix(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{ return _m12; }

m21()

qreal QMatrix::m21 ( ) const

inline

Returns the horizontal shearing factor.

See also

shear(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 75 of file qmatrix.h.

Referenced by map(), operator<<(), operator>>(), qFuzzyCompare(), QMatrix4x4::QMatrix4x4(), setMatrix(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{ return _m21; }

m22()

qreal QMatrix::m22 ( ) const

inline

Returns the vertical scaling factor.

See also

scale(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 76 of file qmatrix.h.

Referenced by map(), operator<<(), operator>>(), qFuzzyCompare(), QMatrix4x4::QMatrix4x4(), setMatrix(), and QPdfEnginePrivate::~QPdfEnginePrivate().

{ return _m22; }

map() [1/10]

void QMatrix::map	(	int	x,
		int	y,
		int *	tx,
		int *	ty
	)		const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Maps the given coordinates x and y into the coordinate system defined by this matrix.

The resulting values are put in *tx and *ty, respectively. Note that the transformed coordinates are rounded to the nearest integer.

Definition at line 384 of file qmatrix.cpp.

Referenced by map(), QGraphicsViewPrivate::mapToScene(), operator*(), and QTextControl::processEvent().

{
    MAPINT(x, y, *tx, *ty);
}

map() [2/10]

void QMatrix::map	(	qreal	x,
		qreal	y,
		qreal *	tx,
		qreal *	ty
	)		const

Maps the given coordinates x and y into the coordinate system defined by this matrix.

The resulting values are put in *tx and *ty, respectively.

The coordinates are transformed using the following formulas:

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy

The point (x, y) is the original point, and (x', y') is the transformed point.

See also

{QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 368 of file qmatrix.cpp.

{
    MAPDOUBLE(x, y, *tx, *ty);
}

map() [3/10]

QPoint QMatrix::map

(

const QPoint &

point

)

const

Creates and returns a QPoint object that is a copy of the given point, mapped into the coordinate system defined by this matrix.

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

Note that the transformed coordinates are rounded to the nearest integer.

Definition at line 525 of file qmatrix.cpp.

{
    qreal fx = p.x();
    qreal fy = p.y();
    return QPoint(qRound(_m11*fx + _m21*fy + _dx),
                   qRound(_m12*fx + _m22*fy + _dy));
}

map() [4/10]

QPointF QMatrix::map

(

const QPointF &

point

)

const

Creates and returns a QPointF object that is a copy of the given point, mapped into the coordinate system defined by this matrix.

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

Definition at line 552 of file qmatrix.cpp.

{
    qreal fx = point.x();
    qreal fy = point.y();
    return QPointF(_m11*fx + _m21*fy + _dx, _m12*fx + _m22*fy + _dy);
}

map() [5/10]

QLine QMatrix::map

(

const QLine &

line

)

const

Creates and returns a QLine object that is a copy of the given line, mapped into the coordinate system defined by this matrix.

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

Note that the transformed coordinates are rounded to the nearest integer.

Definition at line 615 of file qmatrix.cpp.

{
    return QLine(map(line.p1()), map(line.p2()));
}

map() [6/10]

QLineF QMatrix::map

(

const QLineF &

line

)

const

Creates and returns a QLineF object that is a copy of the given line, mapped into the coordinate system defined by this matrix.

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

Definition at line 599 of file qmatrix.cpp.

{
    return QLineF(map(line.p1()), map(line.p2()));
}

map() [7/10]

QPolygonF QMatrix::map

(

const QPolygonF &

polygon

)

const

Creates and returns a QPolygonF object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix.

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

Definition at line 662 of file qmatrix.cpp.

{
    int size = a.size();
    int i;
    QPolygonF p(size);
    const QPointF *da = a.constData();
    QPointF *dp = p.data();
    for(i = 0; i < size; i++) {
        MAPDOUBLE(da[i].xp, da[i].yp, dp[i].xp, dp[i].yp);
    }
    return p;
}

map() [8/10]

QPolygon QMatrix::map

(

const QPolygon &

polygon

)

const

Creates and returns a QPolygon object that is a copy of the given polygon, mapped into the coordinate system defined by this matrix.

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

Note that the transformed coordinates are rounded to the nearest integer.

Definition at line 638 of file qmatrix.cpp.

{
    int size = a.size();
    int i;
    QPolygon p(size);
    const QPoint *da = a.constData();
    QPoint *dp = p.data();
    for(i = 0; i < size; i++) {
        MAPINT(da[i].x(), da[i].y(), dp[i].rx(), dp[i].ry());
    }
    return p;
}

map() [9/10]

QRegion QMatrix::map

(

const QRegion &

region

)

const

Creates and returns a QRegion object that is a copy of the given region, mapped into the coordinate system defined by this matrix.

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

Calling this method can be rather expensive if rotations or shearing are used.

Definition at line 712 of file qmatrix.cpp.

{
    if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) { // translate or identity
        if (_dx == 0.0 && _dy == 0.0) // Identity
            return r;
        QRegion copy(r);
        copy.translate(qRound(_dx), qRound(_dy));
        return copy;
    }

    QPainterPath p = map(qt_regionToPath(r));
    return p.toFillPolygon().toPolygon();
}

map() [10/10]

QPainterPath QMatrix::map

(

const QPainterPath &

path

)

const

Creates and returns a QPainterPath object that is a copy of the given path, mapped into the coordinate system defined by this matrix.

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

Definition at line 745 of file qmatrix.cpp.

{
    if (path.isEmpty())
        return QPainterPath();

    QPainterPath copy = path;

    // Translate or identity
    if (_m11 == 1.0 && _m22 == 1.0 && _m12 == 0.0 && _m21 == 0.0) {

        // Translate
        if (_dx != 0.0 || _dy != 0.0) {
            copy.detach();
            for (int i=0; i<path.elementCount(); ++i) {
                QPainterPath::Element &e = copy.d_ptr->elements[i];
                e.x += _dx;
                e.y += _dy;
            }
        }

    // Full xform
    } else {
        copy.detach();
        for (int i=0; i<path.elementCount(); ++i) {
            QPainterPath::Element &e = copy.d_ptr->elements[i];
            qreal fx = e.x, fy = e.y;
            e.x = _m11*fx + _m21*fy + _dx;
            e.y =  _m12*fx + _m22*fy + _dy;
        }
    }

    return copy;
}

mapRect() [1/2]

QRect QMatrix::mapRect

(

const QRect &

rectangle

)

const

Creates and returns a QRect object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix.

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

Note that the transformed coordinates are rounded to the nearest integer.

Definition at line 389 of file qmatrix.cpp.

Referenced by QCommonStyle::drawControl(), QWindowsStyle::drawControl(), and QPainter::setViewTransformEnabled().

{
    QRect result;
    if (_m12 == 0.0F && _m21 == 0.0F) {
        int x = qRound(_m11*rect.x() + _dx);
        int y = qRound(_m22*rect.y() + _dy);
        int w = qRound(_m11*rect.width());
        int h = qRound(_m22*rect.height());
        if (w < 0) {
            w = -w;
            x -= w;
        }
        if (h < 0) {
            h = -h;
            y -= h;
        }
        result = QRect(x, y, w, h);
    } else {
        // see mapToPolygon for explanations of the algorithm.
        qreal x0, y0;
        qreal x, y;
        MAPDOUBLE(rect.left(), rect.top(), x0, y0);
        qreal xmin = x0;
        qreal ymin = y0;
        qreal xmax = x0;
        qreal ymax = y0;
        MAPDOUBLE(rect.right() + 1, rect.top(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.right() + 1, rect.bottom() + 1, x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.left(), rect.bottom() + 1, x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        result = QRect(qRound(xmin), qRound(ymin), qRound(xmax)-qRound(xmin), qRound(ymax)-qRound(ymin));
    }
    return result;
}

mapRect() [2/2]

QRectF QMatrix::mapRect

(

const QRectF &

rectangle

)

const

Creates and returns a QRectF object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix.

The rectangle's coordinates are transformed using the following formulas:

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy

If rotation or shearing has been specified, this function returns the bounding rectangle. To retrieve the exact region the given rectangle maps to, use the mapToPolygon() function instead.

See also

mapToPolygon(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 457 of file qmatrix.cpp.

{
    QRectF result;
    if (_m12 == 0.0F && _m21 == 0.0F) {
        qreal x = _m11*rect.x() + _dx;
        qreal y = _m22*rect.y() + _dy;
        qreal w = _m11*rect.width();
        qreal h = _m22*rect.height();
        if (w < 0) {
            w = -w;
            x -= w;
        }
        if (h < 0) {
            h = -h;
            y -= h;
        }
        result = QRectF(x, y, w, h);
    } else {
        qreal x0, y0;
        qreal x, y;
        MAPDOUBLE(rect.x(), rect.y(), x0, y0);
        qreal xmin = x0;
        qreal ymin = y0;
        qreal xmax = x0;
        qreal ymax = y0;
        MAPDOUBLE(rect.x() + rect.width(), rect.y(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.x() + rect.width(), rect.y() + rect.height(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        MAPDOUBLE(rect.x(), rect.y() + rect.height(), x, y);
        xmin = qMin(xmin, x);
        ymin = qMin(ymin, y);
        xmax = qMax(xmax, x);
        ymax = qMax(ymax, y);
        result = QRectF(xmin, ymin, xmax-xmin, ymax - ymin);
    }
    return result;
}

mapToPolygon()

QPolygon QMatrix::mapToPolygon

(

const QRect &

rectangle

)

const

Creates and returns a QPolygon representation of the given rectangle, mapped into the coordinate system defined by this matrix.

The rectangle's coordinates are transformed using the following formulas:

x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy

Polygons and rectangles behave slightly differently when transformed (due to integer rounding), so matrix.map(QPolygon(rectangle)) is not always the same as matrix.mapToPolygon(rectangle).

See also

mapRect(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 841 of file qmatrix.cpp.

Referenced by map().

{
    QPolygon a(4);
    qreal x[4], y[4];
    if (_m12 == 0.0F && _m21 == 0.0F) {
        x[0] = _m11*rect.x() + _dx;
        y[0] = _m22*rect.y() + _dy;
        qreal w = _m11*rect.width();
        qreal h = _m22*rect.height();
        if (w < 0) {
            w = -w;
            x[0] -= w;
        }
        if (h < 0) {
            h = -h;
            y[0] -= h;
        }
        x[1] = x[0]+w;
        x[2] = x[1];
        x[3] = x[0];
        y[1] = y[0];
        y[2] = y[0]+h;
        y[3] = y[2];
    } else {
        qreal right = rect.x() + rect.width();
        qreal bottom = rect.y() + rect.height();
        MAPDOUBLE(rect.x(), rect.y(), x[0], y[0]);
        MAPDOUBLE(right, rect.y(), x[1], y[1]);
        MAPDOUBLE(right, bottom, x[2], y[2]);
        MAPDOUBLE(rect.x(), bottom, x[3], y[3]);
    }
#if 0
    int i;
    for(i = 0; i< 4; i++)
        qDebug("coords(%d) = (%f/%f) (%d/%d)", i, x[i], y[i], qRound(x[i]), qRound(y[i]));
    qDebug("width=%f, height=%f", qSqrt((x[1]-x[0])*(x[1]-x[0]) + (y[1]-y[0])*(y[1]-y[0])),
            qSqrt((x[0]-x[3])*(x[0]-x[3]) + (y[0]-y[3])*(y[0]-y[3])));
#endif
    // all coordinates are correctly, tranform to a pointarray
    // (rounding to the next integer)
    a.setPoints(4, qRound(x[0]), qRound(y[0]),
                 qRound(x[1]), qRound(y[1]),
                 qRound(x[2]), qRound(y[2]),
                 qRound(x[3]), qRound(y[3]));
    return a;
}

operator QVariant()

QMatrix::operator QVariant

(

)

const

Returns the matrix as a QVariant.

Since

4.2

Definition at line 1195 of file qmatrix.cpp.

{
    return QVariant(QVariant::Matrix, this);
}

operator!=()

bool QMatrix::operator!=

(

const QMatrix &

matrix

)

const

Returns true if this matrix is not equal to the given matrix, otherwise returns false.

Definition at line 1117 of file qmatrix.cpp.

{
    return _m11 != m._m11 ||
           _m12 != m._m12 ||
           _m21 != m._m21 ||
           _m22 != m._m22 ||
           _dx != m._dx ||
           _dy != m._dy;
}

operator*()

QMatrix QMatrix::operator*

(

const QMatrix &

matrix

)

const

Returns the result of multiplying this matrix by the given matrix.

Note that matrix multiplication is not commutative, i.e. a*b != b*a.

Definition at line 1161 of file qmatrix.cpp.

{
    qreal tm11 = _m11*m._m11 + _m12*m._m21;
    qreal tm12 = _m11*m._m12 + _m12*m._m22;
    qreal tm21 = _m21*m._m11 + _m22*m._m21;
    qreal tm22 = _m21*m._m12 + _m22*m._m22;

    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;
    return QMatrix(tm11, tm12, tm21, tm22, tdx, tdy, true);
}

operator*=()

QMatrix & QMatrix::operator*=

(

const QMatrix &

matrix

)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.Returns the result of multiplying this matrix by the given matrix.

Definition at line 1135 of file qmatrix.cpp.

{
    qreal tm11 = _m11*m._m11 + _m12*m._m21;
    qreal tm12 = _m11*m._m12 + _m12*m._m22;
    qreal tm21 = _m21*m._m11 + _m22*m._m21;
    qreal tm22 = _m21*m._m12 + _m22*m._m22;

    qreal tdx  = _dx*m._m11  + _dy*m._m21 + m._dx;
    qreal tdy =  _dx*m._m12  + _dy*m._m22 + m._dy;

    _m11 = tm11; _m12 = tm12;
    _m21 = tm21; _m22 = tm22;
    _dx = tdx; _dy = tdy;
    return *this;
}

operator=()

QMatrix & QMatrix::operator=

(

const QMatrix &

matrix

)

Assigns the given matrix's values to this matrix.

Definition at line 1176 of file qmatrix.cpp.

{
    _m11 = matrix._m11;
    _m12 = matrix._m12;
    _m21 = matrix._m21;
    _m22 = matrix._m22;
    _dx  = matrix._dx;
    _dy  = matrix._dy;
    return *this;
}

operator==()

bool QMatrix::operator==

(

const QMatrix &

matrix

)

const

Returns true if this matrix is equal to the given matrix, otherwise returns false.

Definition at line 1097 of file qmatrix.cpp.

{
    return _m11 == m._m11 &&
           _m12 == m._m12 &&
           _m21 == m._m21 &&
           _m22 == m._m22 &&
           _dx == m._dx &&
           _dy == m._dy;
}

reset()

void QMatrix::reset

(

)

Resets the matrix to an identity matrix, i.e.

all elements are set to zero, except m11 and m22 (specifying the scale) which are set to 1.

See also

QMatrix(), isIdentity(), {QMatrix::Basic Matrix Operations}{Basic Matrix Operations}

Definition at line 897 of file qmatrix.cpp.

Referenced by QPainterState::init().

{
    _m11 = _m22 = 1.0;
    _m12 = _m21 = _dx = _dy = 0.0;
}

rotate()

QMatrix & QMatrix::rotate

(

qreal

degrees

)

Rotates the coordinate system the given degrees counterclockwise.

Note that if you apply a QMatrix to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.

Returns a reference to the matrix.

See also

setMatrix()

Definition at line 990 of file qmatrix.cpp.

Referenced by QWindowsXPStylePrivate::drawBackgroundThruNativeBuffer(), QCommonStyle::drawControl(), QWindowsStyle::drawControl(), QMacStyle::drawPrimitive(), QGraphicsItemAnimation::matrixAt(), parseTransformationMatrix(), QTiffHandler::read(), and rotateTabPainter().

{
    qreal sina = 0;
    qreal cosa = 0;
    if (a == 90. || a == -270.)
        sina = 1.;
    else if (a == 270. || a == -90.)
        sina = -1.;
    else if (a == 180.)
        cosa = -1.;
    else{
        qreal b = deg2rad*a;                        // convert to radians
        sina = qSin(b);               // fast and convenient
        cosa = qCos(b);
    }
    qreal tm11 = cosa*_m11 + sina*_m21;
    qreal tm12 = cosa*_m12 + sina*_m22;
    qreal tm21 = -sina*_m11 + cosa*_m21;
    qreal tm22 = -sina*_m12 + cosa*_m22;
    _m11 = tm11; _m12 = tm12;
    _m21 = tm21; _m22 = tm22;
    return *this;
}

scale()

QMatrix & QMatrix::scale	(	qreal	sx,
		qreal	sy
	)

Scales the coordinate system by sx horizontally and sy vertically, and returns a reference to the matrix.

See also

setMatrix()

Definition at line 941 of file qmatrix.cpp.

Referenced by QGraphicsItemAnimation::matrixAt(), and parseTransformationMatrix().

{
    _m11 *= sx;
    _m12 *= sx;
    _m21 *= sy;
    _m22 *= sy;
    return *this;
}

setMatrix()

void QMatrix::setMatrix	(	qreal	m11,
		qreal	m12,
		qreal	m21,
		qreal	m22,
		qreal	dx,
		qreal	dy
	)

Sets the matrix elements to the specified values, m11, m12, m21, m22, dx and dy.

Note that this function replaces the previous values. QMatrix provide the translate(), rotate(), scale() and shear() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.

See also

QMatrix()

Definition at line 269 of file qmatrix.cpp.

Referenced by operator>>().

{
    _m11 = m11;
    _m12 = m12;
    _m21 = m21;
    _m22 = m22;
    _dx  = dx;
    _dy  = dy;
}

shear()

QMatrix & QMatrix::shear	(	qreal	sh,
		qreal	sv
	)

Shears the coordinate system by sh horizontally and sv vertically, and returns a reference to the matrix.

See also

setMatrix()

Definition at line 957 of file qmatrix.cpp.

Referenced by QGraphicsItemAnimation::matrixAt(), and parseTransformationMatrix().

{
    qreal tm11 = sv*_m21;
    qreal tm12 = sv*_m22;
    qreal tm21 = sh*_m11;
    qreal tm22 = sh*_m12;
    _m11 += tm11;
    _m12 += tm12;
    _m21 += tm21;
    _m22 += tm22;
    return *this;
}

translate()

QMatrix & QMatrix::translate	(	qreal	dx,
		qreal	dy
	)

Moves the coordinate system dx along the x axis and dy along the y axis, and returns a reference to the matrix.

See also

setMatrix()

Definition at line 922 of file qmatrix.cpp.

Referenced by QCommonStyle::drawControl(), QWindowsStyle::drawControl(), QMacStyle::drawPrimitive(), QGraphicsItemAnimation::matrixAt(), parseTransformationMatrix(), QTextControl::processEvent(), and rotateTabPainter().

{
    _dx += dx*_m11 + dy*_m21;
    _dy += dy*_m22 + dx*_m12;
    return *this;
}

Friends and Related Functions

operator*() [1/8]

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

related

This is the same as {matrix}.map({point}).

See also

QMatrix::map()

Definition at line 150 of file qmatrix.h.

{ return m.map(p); }

operator*() [2/8]

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

related

Same as {matrix}.map({point}).

See also

QMatrix::map()

Definition at line 152 of file qmatrix.h.

{ return m.map(p); }

operator*() [3/8]

QLineF operator* ( const QLineF &  line, const QMatrix &  matrix  )

related

This is the same as {matrix}.map({line}).

See also

QMatrix::map()

Definition at line 154 of file qmatrix.h.

{ return m.map(l); }

operator*() [4/8]

QLine operator* ( const QLine &  line, const QMatrix &  matrix  )

related

This is the same as {matrix}.map({line}).

See also

QMatrix::map()

Definition at line 156 of file qmatrix.h.

{ return m.map(l); }

operator*() [5/8]

QPolygonF operator* ( const QPolygonF &  polygon, const QMatrix &  matrix  )

related

This is the same as {matrix}.map({polygon}).

See also

QMatrix::map()

Definition at line 160 of file qmatrix.h.

{ return m.map(a); }

operator*() [6/8]

QPolygon operator* ( const QPolygon &  polygon, const QMatrix &  matrix  )

related

This is the same as {matrix}.map({polygon}).

See also

QMatrix::map()

Definition at line 158 of file qmatrix.h.

{ return m.map(a); }

operator*() [7/8]

QRegion operator* ( const QRegion &  region, const QMatrix &  matrix  )

related

This is the same as {matrix}.map({region}).

See also

QMatrix::map()

Definition at line 162 of file qmatrix.h.

{ return m.map(r); }

operator*() [8/8]

QPainterPath operator* ( const QPainterPath &  path, const QMatrix &  matrix  )

related

This is the same as {matrix}.map({path}).

See also

QMatrix::map()

Definition at line 1200 of file qmatrix.cpp.

{
    return m.map(p);
}

operator<<()

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

related

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

See also

{Serializing Qt Data Types}

Definition at line 1223 of file qmatrix.cpp.

{
    if (s.version() == 1) {
        s << (float)m.m11() << (float)m.m12() << (float)m.m21()
          << (float)m.m22() << (float)m.dx()  << (float)m.dy();
    } else {
        s << double(m.m11())
          << double(m.m12())
          << double(m.m21())
          << double(m.m22())
          << double(m.dx())
          << double(m.dy());
    }
    return s;
}

operator>>()

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

related

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

See also

{Serializing Qt Data Types}

Definition at line 1252 of file qmatrix.cpp.

{
    if (s.version() == 1) {
        float m11, m12, m21, m22, dx, dy;
        s >> m11;  s >> m12;  s >> m21;  s >> m22;
        s >> dx;   s >> dy;
        m.setMatrix(m11, m12, m21, m22, dx, dy);
    }
    else {
        double m11, m12, m21, m22, dx, dy;
        s >> m11;
        s >> m12;
        s >> m21;
        s >> m22;
        s >> dx;
        s >> dy;
        m.setMatrix(m11, m12, m21, m22, dx, dy);
    }
    return s;
}

qFuzzyCompare()

bool qFuzzyCompare ( const QMatrix &  m1, const QMatrix &  m2  )

related

The qFuzzyCompare function is for comparing two matrices using a fuzziness factor.

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

Since

4.6

Definition at line 172 of file qmatrix.h.

Referenced by qt_polygon_isect_line().

{
    return qFuzzyCompare(m1.m11(), m2.m11())
        && qFuzzyCompare(m1.m12(), m2.m12())
        && qFuzzyCompare(m1.m21(), m2.m21())
        && qFuzzyCompare(m1.m22(), m2.m22())
        && qFuzzyCompare(m1.dx(), m2.dx())
        && qFuzzyCompare(m1.dy(), m2.dy());
}

QTransform

friend class QTransform

friend

Definition at line 142 of file qmatrix.h.

Properties

_dx

qreal QMatrix::_dx

private

Definition at line 145 of file qmatrix.h.

Referenced by QTransform::adjoint(), inverted(), QTransform::inverted(), map(), QTransform::map(), mapRect(), QTransform::mapRect(), mapToPolygon(), QTransform::mapToPolygon(), operator!=(), operator*(), QTransform::operator*(), operator*=(), QTransform::operator*=(), operator=(), QTransform::operator=(), operator==(), QTransform::operator==(), reset(), QTransform::reset(), setMatrix(), QTransform::setMatrix(), translate(), QTransform::translate(), QTransform::transposed(), and QTransform::type().

_dy

qreal QMatrix::_dy

private

Definition at line 145 of file qmatrix.h.

Referenced by QTransform::adjoint(), inverted(), QTransform::inverted(), map(), QTransform::map(), mapRect(), QTransform::mapRect(), mapToPolygon(), QTransform::mapToPolygon(), operator!=(), operator*(), QTransform::operator*(), operator*=(), QTransform::operator*=(), operator=(), QTransform::operator=(), operator==(), QTransform::operator==(), reset(), QTransform::reset(), setMatrix(), QTransform::setMatrix(), translate(), QTransform::translate(), QTransform::transposed(), and QTransform::type().

_m11

qreal QMatrix::_m11

private

Definition at line 143 of file qmatrix.h.

Referenced by QTransform::adjoint(), inverted(), QTransform::inverted(), map(), QTransform::map(), mapRect(), QTransform::mapRect(), mapToPolygon(), QTransform::mapToPolygon(), operator!=(), operator*(), QTransform::operator*(), operator*=(), QTransform::operator*=(), operator=(), QTransform::operator=(), operator==(), QTransform::operator==(), reset(), QTransform::reset(), rotate(), QTransform::rotate(), QTransform::rotateRadians(), scale(), QTransform::scale(), setMatrix(), QTransform::setMatrix(), shear(), QTransform::shear(), translate(), QTransform::translate(), QTransform::transposed(), and QTransform::type().

_m12

qreal QMatrix::_m12

private

Definition at line 143 of file qmatrix.h.

Referenced by QTransform::adjoint(), inverted(), map(), QTransform::map(), mapRect(), mapToPolygon(), operator!=(), operator*(), QTransform::operator*(), operator*=(), QTransform::operator*=(), operator=(), QTransform::operator=(), operator==(), QTransform::operator==(), reset(), QTransform::reset(), rotate(), QTransform::rotate(), QTransform::rotateRadians(), scale(), QTransform::scale(), setMatrix(), QTransform::setMatrix(), shear(), QTransform::shear(), translate(), QTransform::translate(), QTransform::transposed(), and QTransform::type().

_m21

qreal QMatrix::_m21

private

Definition at line 144 of file qmatrix.h.

Referenced by QTransform::adjoint(), inverted(), map(), QTransform::map(), mapRect(), mapToPolygon(), operator!=(), operator*(), QTransform::operator*(), operator*=(), QTransform::operator*=(), operator=(), QTransform::operator=(), operator==(), QTransform::operator==(), reset(), QTransform::reset(), rotate(), QTransform::rotate(), QTransform::rotateRadians(), scale(), QTransform::scale(), setMatrix(), QTransform::setMatrix(), shear(), QTransform::shear(), translate(), QTransform::translate(), QTransform::transposed(), and QTransform::type().

_m22

qreal QMatrix::_m22

private

Definition at line 144 of file qmatrix.h.

Referenced by QTransform::adjoint(), inverted(), QTransform::inverted(), map(), QTransform::map(), mapRect(), QTransform::mapRect(), mapToPolygon(), QTransform::mapToPolygon(), operator!=(), operator*(), QTransform::operator*(), operator*=(), QTransform::operator*=(), operator=(), QTransform::operator=(), operator==(), QTransform::operator==(), reset(), QTransform::reset(), rotate(), QTransform::rotate(), QTransform::rotateRadians(), scale(), QTransform::scale(), setMatrix(), QTransform::setMatrix(), shear(), QTransform::shear(), translate(), QTransform::translate(), QTransform::transposed(), and QTransform::type().

---

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

• /src/gui/painting/qmatrix.h
• /src/gui/painting/qmatrix.cpp