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<td width="1"> </td><td class="postheader" valign="center"><a href="index.html"><font color="#004faf">Home</font></a> · <a href="classes.html"><font color="#004faf">All Classes</font></a> · <a href="mainclasses.html"><font color="#004faf">Main Classes</font></a> · <a href="groups.html"><font color="#004faf">Grouped Classes</font></a> · <a href="modules.html"><font color="#004faf">Modules</font></a> · <a href="functions.html"><font color="#004faf">Functions</font></a></td>
<td align="right" valign="top" width="230"><a href="http://www.trolltech.com"><img src="images/trolltech-logo.png" align="right" width="203" height="32" border="0" /></a></td></tr></table><h1 align="center">QMatrix Class Reference<br /><sup><sup>[<a href="qtgui.html">QtGui</a> module]</sup></sup></h1>
<p>The QMatrix class specifies 2D transformations of a coordinate system. <a href="#details">More...</a></p>
<pre> #include <QMatrix></pre><ul>
<li><a href="qmatrix-members.html">List of all members, including inherited members</a></li>
<li><a href="qmatrix-qt3.html">Qt 3 support members</a></li>
</ul>
<a name="public-functions"></a>
<h3>Public Functions</h3>
<ul>
<li><div class="fn"/><b><a href="qmatrix.html#QMatrix">QMatrix</a></b> ()</li>
<li><div class="fn"/><b><a href="qmatrix.html#QMatrix-2">QMatrix</a></b> ( qreal <i>m11</i>, qreal <i>m12</i>, qreal <i>m21</i>, qreal <i>m22</i>, qreal <i>dx</i>, qreal <i>dy</i> )</li>
<li><div class="fn"/><b><a href="qmatrix.html#QMatrix-3">QMatrix</a></b> ( const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#m11">m11</a></b> () const</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#m12">m12</a></b> () const</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#m21">m21</a></b> () const</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#m22">m22</a></b> () const</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#det">det</a></b> () const</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#dx">dx</a></b> () const</li>
<li><div class="fn"/>qreal <b><a href="qmatrix.html#dy">dy</a></b> () const</li>
<li><div class="fn"/>QMatrix <b><a href="qmatrix.html#inverted">inverted</a></b> ( bool * <i>invertible</i> = 0 ) const</li>
<li><div class="fn"/>bool <b><a href="qmatrix.html#isIdentity">isIdentity</a></b> () const</li>
<li><div class="fn"/>bool <b><a href="qmatrix.html#isInvertible">isInvertible</a></b> () const</li>
<li><div class="fn"/>void <b><a href="qmatrix.html#map">map</a></b> ( qreal <i>x</i>, qreal <i>y</i>, qreal * <i>tx</i>, qreal * <i>ty</i> ) const</li>
<li><div class="fn"/>void <b><a href="qmatrix.html#map-3">map</a></b> ( int <i>x</i>, int <i>y</i>, int * <i>tx</i>, int * <i>ty</i> ) const</li>
<li><div class="fn"/>QPointF <b><a href="qmatrix.html#map-4">map</a></b> ( const QPointF & <i>point</i> ) const</li>
<li><div class="fn"/>QPoint <b><a href="qmatrix.html#map-5">map</a></b> ( const QPoint & <i>point</i> ) const</li>
<li><div class="fn"/>QLineF <b><a href="qmatrix.html#map-6">map</a></b> ( const QLineF & <i>line</i> ) const</li>
<li><div class="fn"/>QLine <b><a href="qmatrix.html#map-7">map</a></b> ( const QLine & <i>line</i> ) const</li>
<li><div class="fn"/>QPolygonF <b><a href="qmatrix.html#map-8">map</a></b> ( const QPolygonF & <i>polygon</i> ) const</li>
<li><div class="fn"/>QPolygon <b><a href="qmatrix.html#map-9">map</a></b> ( const QPolygon & <i>polygon</i> ) const</li>
<li><div class="fn"/>QRegion <b><a href="qmatrix.html#map-10">map</a></b> ( const QRegion & <i>region</i> ) const</li>
<li><div class="fn"/>QPainterPath <b><a href="qmatrix.html#map-11">map</a></b> ( const QPainterPath & <i>path</i> ) const</li>
<li><div class="fn"/>QRectF <b><a href="qmatrix.html#mapRect">mapRect</a></b> ( const QRectF & <i>rectangle</i> ) const</li>
<li><div class="fn"/>QRect <b><a href="qmatrix.html#mapRect-2">mapRect</a></b> ( const QRect & <i>rectangle</i> ) const</li>
<li><div class="fn"/>QPolygon <b><a href="qmatrix.html#mapToPolygon">mapToPolygon</a></b> ( const QRect & <i>rectangle</i> ) const</li>
<li><div class="fn"/>void <b><a href="qmatrix.html#reset">reset</a></b> ()</li>
<li><div class="fn"/>QMatrix & <b><a href="qmatrix.html#rotate">rotate</a></b> ( qreal <i>degrees</i> )</li>
<li><div class="fn"/>QMatrix & <b><a href="qmatrix.html#scale">scale</a></b> ( qreal <i>sx</i>, qreal <i>sy</i> )</li>
<li><div class="fn"/>void <b><a href="qmatrix.html#setMatrix">setMatrix</a></b> ( qreal <i>m11</i>, qreal <i>m12</i>, qreal <i>m21</i>, qreal <i>m22</i>, qreal <i>dx</i>, qreal <i>dy</i> )</li>
<li><div class="fn"/>QMatrix & <b><a href="qmatrix.html#shear">shear</a></b> ( qreal <i>sh</i>, qreal <i>sv</i> )</li>
<li><div class="fn"/>QMatrix & <b><a href="qmatrix.html#translate">translate</a></b> ( qreal <i>dx</i>, qreal <i>dy</i> )</li>
<li><div class="fn"/><b><a href="qmatrix.html#operator-QVariant">operator QVariant</a></b> () const</li>
<li><div class="fn"/>bool <b><a href="qmatrix.html#operator-not-eq">operator!=</a></b> ( const QMatrix & <i>matrix</i> ) const</li>
<li><div class="fn"/>QMatrix <b><a href="qmatrix.html#operator-2a">operator*</a></b> ( const QMatrix & <i>matrix</i> ) const</li>
<li><div class="fn"/>QMatrix & <b><a href="qmatrix.html#operator-2a-eq">operator*=</a></b> ( const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QMatrix & <b><a href="qmatrix.html#operator-eq">operator=</a></b> ( const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>bool <b><a href="qmatrix.html#operator-eq-eq">operator==</a></b> ( const QMatrix & <i>matrix</i> ) const</li>
</ul>
<a name="related-non-members"></a>
<h3>Related Non-Members</h3>
<ul>
<li><div class="fn"/>QPoint <b><a href="qmatrix.html#operator-2a-5">operator*</a></b> ( const QPoint & <i>point</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QPointF <b><a href="qmatrix.html#operator-2a-6">operator*</a></b> ( const QPointF & <i>point</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QLineF <b><a href="qmatrix.html#operator-2a-7">operator*</a></b> ( const QLineF & <i>line</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QLine <b><a href="qmatrix.html#operator-2a-8">operator*</a></b> ( const QLine & <i>line</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QPolygon <b><a href="qmatrix.html#operator-2a-9">operator*</a></b> ( const QPolygon & <i>polygon</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QPolygonF <b><a href="qmatrix.html#operator-2a-10">operator*</a></b> ( const QPolygonF & <i>polygon</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QRegion <b><a href="qmatrix.html#operator-2a-11">operator*</a></b> ( const QRegion & <i>region</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QPainterPath <b><a href="qmatrix.html#operator-2a-12">operator*</a></b> ( const QPainterPath & <i>path</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QDataStream & <b><a href="qmatrix.html#operator-lt-lt-87">operator<<</a></b> ( QDataStream & <i>stream</i>, const QMatrix & <i>matrix</i> )</li>
<li><div class="fn"/>QDataStream & <b><a href="qmatrix.html#operator-gt-gt-52">operator>></a></b> ( QDataStream & <i>stream</i>, QMatrix & <i>matrix</i> )</li>
</ul>
<a name="details"></a>
<hr />
<h2>Detailed Description</h2>
<p>The QMatrix class specifies 2D transformations of a coordinate system.</p>
<p>A matrix specifies how to translate, scale, shear or rotate the coordinate system, and is typically used when rendering graphics.</p>
<p>A QMatrix object can be built using the <a href="qmatrix.html#setMatrix">setMatrix</a>(), <a href="qmatrix.html#scale">scale</a>(), <a href="qmatrix.html#rotate">rotate</a>(), <a href="qmatrix.html#translate">translate</a>() and <a href="qmatrix.html#shear">shear</a>() functions. Alternatively, it can be built by applying <a href="#basic-matrix-operations">basic matrix operations</a>. The matrix can also be defined when constructed, and it can be reset to the identity matrix (the default) using the <a href="qmatrix.html#reset">reset</a>() function.</p>
<p>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 <i>this</i> matrix using the <a href="qmatrix.html#map">map</a>() function. In case of a rectangle, its coordinates can be transformed using the <a href="qmatrix.html#mapRect">mapRect</a>() function. A rectangle can also be transformed into a <i>polygon</i> (mapped to the coordinate system defined by <i>this</i> matrix), using the <a href="qmatrix.html#mapToPolygon">mapToPolygon</a>() function.</p>
<p>QMatrix provides the <a href="qmatrix.html#isIdentity">isIdentity</a>() function which returns true if the matrix is the identity matrix, and the <a href="qmatrix.html#isInvertible">isInvertible</a>() function which returns true if the matrix is non-singular (i.e. AB = BA = I). The <a href="qmatrix.html#inverted">inverted</a>() function returns an inverted copy of <i>this</i> matrix if it is invertible (otherwise it returns the identity matrix). In addition, QMatrix provides the <a href="qmatrix.html#det">det</a>() function returning the matrix's determinant.</p>
<p>Finally, the QMatrix class supports matrix multiplication, and objects of the class can be streamed as well as compared.</p>
<ul><li><a href="#rendering-graphics">Rendering Graphics</a></li>
<li><a href="#basic-matrix-operations">Basic Matrix Operations</a></li>
</ul>
<a name="rendering-graphics"></a>
<h3>Rendering Graphics</h3>
<p>When rendering graphics, the matrix defines the transformations but the actual transformation is performed by the drawing routines in <a href="qpainter.html">QPainter</a>.</p>
<p>By default, <a href="qpainter.html">QPainter</a> operates on the associated device's own coordinate system. The standard coordinate system of a <a href="qpaintdevice.html">QPaintDevice</a> has its origin located at the top-left position. The <i>x</i> values increase to the right; <i>y</i> values increase downward. For a complete description, see the <a href="coordsys.html">coordinate system</a> documentation.</p>
<p><a href="qpainter.html">QPainter</a> has functions to translate, scale, shear and rotate the coordinate system without using a QMatrix. For example:</p>
<p><table width="100%" align="center" cellpadding="2" cellspacing="1" border="0">
<tr valign="top" class="odd"><td><img src="images/qmatrix-simpletransformation.png" /></td><td><pre> 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");
}</pre>
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</table></p>
<p>Although these functions are very convenient, it can be more efficient to build a QMatrix and call <a href="qpainter-obsolete.html#setMatrix">QPainter::setMatrix</a>() if you want to perform more than a single transform operation. For example:</p>
<p><table width="100%" align="center" cellpadding="2" cellspacing="1" border="0">
<tr valign="top" class="odd"><td><img src="images/qmatrix-combinedtransformation.png" /></td><td><pre> 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");
}</pre>
</td></tr>
</table></p>
<a name="basic-matrix-operations"></a>
<h3>Basic Matrix Operations</h3>
<p align="center"><img src="images/qmatrix-representation.png" /></p><p>A QMatrix object contains a 3 x 3 matrix. The <tt>dx</tt> and <tt>dy</tt> elements specify horizontal and vertical translation. The <tt>m11</tt> and <tt>m22</tt> elements specify horizontal and vertical scaling. And finally, the <tt>m21</tt> and <tt>m12</tt> elements specify horizontal and vertical <i>shearing</i>.</p>
<p>QMatrix transforms a point in the plane to another point using the following formulas:</p>
<pre> x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy</pre>
<p>The point <i>(x, y)</i> is the original point, and <i>(x', y')</i> is the transformed point. <i>(x', y')</i> can be transformed back to <i>(x, y)</i> by performing the same operation on the <a href="qmatrix.html#inverted">inverted</a>() matrix.</p>
<p>The various matrix elements can be set when constructing the matrix, or by using the <a href="qmatrix.html#setMatrix">setMatrix</a>() function later on. They also be manipulated using the <a href="qmatrix.html#translate">translate</a>(), <a href="qmatrix.html#rotate">rotate</a>(), <a href="qmatrix.html#scale">scale</a>() and <a href="qmatrix.html#shear">shear</a>() convenience functions, The currently set values can be retrieved using the <a href="qmatrix.html#m11">m11</a>(), <a href="qmatrix.html#m12">m12</a>(), <a href="qmatrix.html#m21">m21</a>(), <a href="qmatrix.html#m22">m22</a>(), <a href="qmatrix.html#dx">dx</a>() and <a href="qmatrix.html#dy">dy</a>() functions.</p>
<p>Translation is the simplest transformation. Setting <tt>dx</tt> and <tt>dy</tt> will move the coordinate system <tt>dx</tt> units along the X axis and <tt>dy</tt> units along the Y axis. Scaling can be done by setting <tt>m11</tt> and <tt>m22</tt>. For example, setting <tt>m11</tt> to 2 and <tt>m22</tt> to 1.5 will double the height and increase the width by 50%. The identity matrix has <tt>m11</tt> and <tt>m22</tt> set to 1 (all others are set to 0) mapping a point to itself. Shearing is controlled by <tt>m12</tt> and <tt>m21</tt>. 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.</p>
<p>Here's the combined transformations example using basic matrix operations:</p>
<p><table width="100%" align="center" cellpadding="2" cellspacing="1" border="0">
<tr valign="top" class="odd"><td><img src="images/qmatrix-combinedtransformation.png" /></td><td><pre> 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");
}</pre>
</td></tr>
</table></p>
<p>See also <a href="qpainter.html">QPainter</a>, <a href="coordsys.html">The Coordinate System</a>, <a href="demos-affine.html">Affine Transformations Demo</a>, and <a href="painting-transformations.html">Transformations Example</a>.</p>
<hr />
<h2>Member Function Documentation</h2>
<h3 class="fn"><a name="QMatrix"></a>QMatrix::QMatrix ()</h3>
<p>Constructs an identity matrix.</p>
<p>All elements are set to zero except <tt>m11</tt> and <tt>m22</tt> (specifying the scale), which are set to 1.</p>
<p>See also <a href="qmatrix.html#reset">reset</a>().</p>
<h3 class="fn"><a name="QMatrix-2"></a>QMatrix::QMatrix ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m11</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m12</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m21</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m22</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>dx</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>dy</i> )</h3>
<p>Constructs a matrix with the elements, <i>m11</i>, <i>m12</i>, <i>m21</i>, <i>m22</i>, <i>dx</i> and <i>dy</i>.</p>
<p>See also <a href="qmatrix.html#setMatrix">setMatrix</a>().</p>
<h3 class="fn"><a name="QMatrix-3"></a>QMatrix::QMatrix ( const QMatrix & <i>matrix</i> )</h3>
<p>Constructs a matrix that is a copy of the given <i>matrix</i>.</p>
<h3 class="fn"><a name="m11"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::m11 () const</h3>
<p>Returns the horizontal scaling factor.</p>
<p>See also <a href="qmatrix.html#scale">scale</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="m12"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::m12 () const</h3>
<p>Returns the vertical shearing factor.</p>
<p>See also <a href="qmatrix.html#shear">shear</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="m21"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::m21 () const</h3>
<p>Returns the horizontal shearing factor.</p>
<p>See also <a href="qmatrix.html#shear">shear</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="m22"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::m22 () const</h3>
<p>Returns the vertical scaling factor.</p>
<p>See also <a href="qmatrix.html#scale">scale</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="det"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::det () const</h3>
<p>Returns the matrix's determinant.</p>
<h3 class="fn"><a name="dx"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::dx () const</h3>
<p>Returns the horizontal translation factor.</p>
<p>See also <a href="qmatrix.html#translate">translate</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="dy"></a><a href="qtglobal.html#qreal-typedef">qreal</a> QMatrix::dy () const</h3>
<p>Returns the vertical translation factor.</p>
<p>See also <a href="qmatrix.html#translate">translate</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="inverted"></a>QMatrix QMatrix::inverted ( bool * <i>invertible</i> = 0 ) const</h3>
<p>Returns an inverted copy of this matrix.</p>
<p>If the matrix is singular (not invertible), the returned matrix is the identity matrix. If <i>invertible</i> is valid (i.e. not 0), its value is set to true if the matrix is invertible, otherwise it is set to false.</p>
<p>See also <a href="qmatrix.html#isInvertible">isInvertible</a>().</p>
<h3 class="fn"><a name="isIdentity"></a>bool QMatrix::isIdentity () const</h3>
<p>Returns true if the matrix is the identity matrix, otherwise returns false.</p>
<p>See also <a href="qmatrix.html#reset">reset</a>().</p>
<h3 class="fn"><a name="isInvertible"></a>bool QMatrix::isInvertible () const</h3>
<p>Returns true if the matrix is invertible, otherwise returns false.</p>
<p>See also <a href="qmatrix.html#inverted">inverted</a>().</p>
<h3 class="fn"><a name="map"></a>void QMatrix::map ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>x</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>y</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> * <i>tx</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> * <i>ty</i> ) const</h3>
<p>Maps the given coordinates <i>x</i> and <i>y</i> into the coordinate system defined by this matrix. The resulting values are put in *<i>tx</i> and *<i>ty</i>, respectively.</p>
<p>The coordinates are transformed using the following formulas:</p>
<pre> x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy</pre>
<p>The point (x, y) is the original point, and (x', y') is the transformed point.</p>
<p>See also <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="map-3"></a>void QMatrix::map ( int <i>x</i>, int <i>y</i>, int * <i>tx</i>, int * <i>ty</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Maps the given coordinates <i>x</i> and <i>y</i> into the coordinate system defined by this matrix. The resulting values are put in *<i>tx</i> and *<i>ty</i>, respectively. Note that the transformed coordinates are rounded to the nearest integer.</p>
<h3 class="fn"><a name="map-4"></a><a href="qpointf.html">QPointF</a> QMatrix::map ( const <a href="qpointf.html">QPointF</a> & <i>point</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qpointf.html">QPointF</a> object that is a copy of the given <i>point</i>, mapped into the coordinate system defined by this matrix.</p>
<h3 class="fn"><a name="map-5"></a><a href="qpoint.html">QPoint</a> QMatrix::map ( const <a href="qpoint.html">QPoint</a> & <i>point</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qpoint.html">QPoint</a> object that is a copy of the given <i>point</i>, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.</p>
<h3 class="fn"><a name="map-6"></a><a href="qlinef.html">QLineF</a> QMatrix::map ( const <a href="qlinef.html">QLineF</a> & <i>line</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qlinef.html">QLineF</a> object that is a copy of the given <i>line</i>, mapped into the coordinate system defined by this matrix.</p>
<h3 class="fn"><a name="map-7"></a><a href="qline.html">QLine</a> QMatrix::map ( const <a href="qline.html">QLine</a> & <i>line</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qline.html">QLine</a> object that is a copy of the given <i>line</i>, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.</p>
<h3 class="fn"><a name="map-8"></a><a href="qpolygonf.html">QPolygonF</a> QMatrix::map ( const <a href="qpolygonf.html">QPolygonF</a> & <i>polygon</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qpolygonf.html">QPolygonF</a> object that is a copy of the given <i>polygon</i>, mapped into the coordinate system defined by this matrix.</p>
<h3 class="fn"><a name="map-9"></a><a href="qpolygon.html">QPolygon</a> QMatrix::map ( const <a href="qpolygon.html">QPolygon</a> & <i>polygon</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qpolygon.html">QPolygon</a> object that is a copy of the given <i>polygon</i>, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.</p>
<h3 class="fn"><a name="map-10"></a><a href="qregion.html">QRegion</a> QMatrix::map ( const <a href="qregion.html">QRegion</a> & <i>region</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qregion.html">QRegion</a> object that is a copy of the given <i>region</i>, mapped into the coordinate system defined by this matrix.</p>
<p>Calling this method can be rather expensive if rotations or shearing are used.</p>
<h3 class="fn"><a name="map-11"></a><a href="qpainterpath.html">QPainterPath</a> QMatrix::map ( const <a href="qpainterpath.html">QPainterPath</a> & <i>path</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qpainterpath.html">QPainterPath</a> object that is a copy of the given <i>path</i>, mapped into the coordinate system defined by this matrix.</p>
<h3 class="fn"><a name="mapRect"></a><a href="qrectf.html">QRectF</a> QMatrix::mapRect ( const <a href="qrectf.html">QRectF</a> & <i>rectangle</i> ) const</h3>
<p>Creates and returns a <a href="qrectf.html">QRectF</a> object that is a copy of the given <i>rectangle</i>, mapped into the coordinate system defined by this matrix.</p>
<p>The rectangle's coordinates are transformed using the following formulas:</p>
<pre> x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy</pre>
<p>If rotation or shearing has been specified, this function returns the <i>bounding</i> rectangle. To retrieve the exact region the given <i>rectangle</i> maps to, use the <a href="qmatrix.html#mapToPolygon">mapToPolygon</a>() function instead.</p>
<p>See also <a href="qmatrix.html#mapToPolygon">mapToPolygon</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="mapRect-2"></a><a href="qrect.html">QRect</a> QMatrix::mapRect ( const <a href="qrect.html">QRect</a> & <i>rectangle</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qrect.html">QRect</a> object that is a copy of the given <i>rectangle</i>, mapped into the coordinate system defined by this matrix. Note that the transformed coordinates are rounded to the nearest integer.</p>
<h3 class="fn"><a name="mapToPolygon"></a><a href="qpolygon.html">QPolygon</a> QMatrix::mapToPolygon ( const <a href="qrect.html">QRect</a> & <i>rectangle</i> ) const</h3>
<p>Creates and returns a <a href="qpolygon.html">QPolygon</a> representation of the given <i>rectangle</i>, mapped into the coordinate system defined by this matrix.</p>
<p>The rectangle's coordinates are transformed using the following formulas:</p>
<pre> x' = m11*x + m21*y + dx
y' = m22*y + m12*x + dy</pre>
<p>Polygons and rectangles behave slightly differently when transformed (due to integer rounding), so <tt>matrix.map(QPolygon(rectangle))</tt> is not always the same as <tt>matrix.mapToPolygon(rectangle)</tt>.</p>
<p>See also <a href="qmatrix.html#mapRect">mapRect</a>() and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="reset"></a>void QMatrix::reset ()</h3>
<p>Resets the matrix to an identity matrix, i.e. all elements are set to zero, except <tt>m11</tt> and <tt>m22</tt> (specifying the scale) which are set to 1.</p>
<p>See also <a href="qmatrix.html#QMatrix">QMatrix</a>(), <a href="qmatrix.html#isIdentity">isIdentity</a>(), and <a href="qmatrix.html#basic-matrix-operations">Basic Matrix Operations</a>.</p>
<h3 class="fn"><a name="rotate"></a>QMatrix & QMatrix::rotate ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>degrees</i> )</h3>
<p>Rotates the coordinate system the given <i>degrees</i> counterclockwise.</p>
<p>Note that if you apply a <a href="qmatrix.html">QMatrix</a> to a point defined in widget coordinates, the direction of the rotation will be clockwise because the y-axis points downwards.</p>
<p>Returns a reference to the matrix.</p>
<p>See also <a href="qmatrix.html#setMatrix">setMatrix</a>().</p>
<h3 class="fn"><a name="scale"></a>QMatrix & QMatrix::scale ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>sx</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>sy</i> )</h3>
<p>Scales the coordinate system by <i>sx</i> horizontally and <i>sy</i> vertically, and returns a reference to the matrix.</p>
<p>See also <a href="qmatrix.html#setMatrix">setMatrix</a>().</p>
<h3 class="fn"><a name="setMatrix"></a>void QMatrix::setMatrix ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m11</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m12</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m21</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>m22</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>dx</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>dy</i> )</h3>
<p>Sets the matrix elements to the specified values, <i>m11</i>, <i>m12</i>, <i>m21</i>, <i>m22</i>, <i>dx</i> and <i>dy</i>.</p>
<p>Note that this function replaces the previous values. <a href="qmatrix.html">QMatrix</a> provide the <a href="qmatrix.html#translate">translate</a>(), <a href="qmatrix.html#rotate">rotate</a>(), <a href="qmatrix.html#scale">scale</a>() and <a href="qmatrix.html#shear">shear</a>() convenience functions to manipulate the various matrix elements based on the currently defined coordinate system.</p>
<p>See also <a href="qmatrix.html#QMatrix">QMatrix</a>().</p>
<h3 class="fn"><a name="shear"></a>QMatrix & QMatrix::shear ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>sh</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>sv</i> )</h3>
<p>Shears the coordinate system by <i>sh</i> horizontally and <i>sv</i> vertically, and returns a reference to the matrix.</p>
<p>See also <a href="qmatrix.html#setMatrix">setMatrix</a>().</p>
<h3 class="fn"><a name="translate"></a>QMatrix & QMatrix::translate ( <a href="qtglobal.html#qreal-typedef">qreal</a> <i>dx</i>, <a href="qtglobal.html#qreal-typedef">qreal</a> <i>dy</i> )</h3>
<p>Moves the coordinate system <i>dx</i> along the x axis and <i>dy</i> along the y axis, and returns a reference to the matrix.</p>
<p>See also <a href="qmatrix.html#setMatrix">setMatrix</a>().</p>
<h3 class="fn"><a name="operator-QVariant"></a>QMatrix::operator QVariant () const</h3>
<p>Returns the matrix as a <a href="qvariant.html">QVariant</a>.</p>
<p>This function was introduced in Qt 4.2.</p>
<h3 class="fn"><a name="operator-not-eq"></a>bool QMatrix::operator!= ( const QMatrix & <i>matrix</i> ) const</h3>
<p>Returns true if this matrix is not equal to the given <i>matrix</i>, otherwise returns false.</p>
<h3 class="fn"><a name="operator-2a"></a>QMatrix QMatrix::operator* ( const QMatrix & <i>matrix</i> ) const</h3>
<p>Returns the result of multiplying this matrix by the given <i>matrix</i>.</p>
<p>Note that matrix multiplication is not commutative, i.e. a*b != b*a.</p>
<h3 class="fn"><a name="operator-2a-eq"></a>QMatrix & QMatrix::operator*= ( const QMatrix & <i>matrix</i> )</h3>
<p>Returns the result of multiplying this matrix by the given <i>matrix</i>.</p>
<h3 class="fn"><a name="operator-eq"></a>QMatrix & QMatrix::operator= ( const QMatrix & <i>matrix</i> )</h3>
<p>Assigns the given <i>matrix</i>'s values to this matrix.</p>
<h3 class="fn"><a name="operator-eq-eq"></a>bool QMatrix::operator== ( const QMatrix & <i>matrix</i> ) const</h3>
<p>Returns true if this matrix is equal to the given <i>matrix</i>, otherwise returns false.</p>
<hr />
<h2>Related Non-Members</h2>
<h3 class="fn"><a name="operator-2a-5"></a><a href="qpoint.html">QPoint</a> operator* ( const <a href="qpoint.html">QPoint</a> & <i>point</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>point</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-6"></a><a href="qpointf.html">QPointF</a> operator* ( const <a href="qpointf.html">QPointF</a> & <i>point</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Same as <i>matrix</i>.map(<i>point</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-7"></a><a href="qlinef.html">QLineF</a> operator* ( const <a href="qlinef.html">QLineF</a> & <i>line</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>line</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-8"></a><a href="qline.html">QLine</a> operator* ( const <a href="qline.html">QLine</a> & <i>line</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>line</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-9"></a><a href="qpolygon.html">QPolygon</a> operator* ( const <a href="qpolygon.html">QPolygon</a> & <i>polygon</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>polygon</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-10"></a><a href="qpolygonf.html">QPolygonF</a> operator* ( const <a href="qpolygonf.html">QPolygonF</a> & <i>polygon</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>polygon</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-11"></a><a href="qregion.html">QRegion</a> operator* ( const <a href="qregion.html">QRegion</a> & <i>region</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>region</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-2a-12"></a><a href="qpainterpath.html">QPainterPath</a> operator* ( const <a href="qpainterpath.html">QPainterPath</a> & <i>path</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>This is the same as <i>matrix</i>.map(<i>path</i>).</p>
<p>See also <a href="qmatrix.html#map">QMatrix::map</a>().</p>
<h3 class="fn"><a name="operator-lt-lt-87"></a><a href="qdatastream.html">QDataStream</a> & operator<< ( <a href="qdatastream.html">QDataStream</a> & <i>stream</i>, const QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Writes the given <i>matrix</i> to the given <i>stream</i> and returns a reference to the stream.</p>
<p>See also <a href="datastreamformat.html">Format of the QDataStream Operators</a>.</p>
<h3 class="fn"><a name="operator-gt-gt-52"></a><a href="qdatastream.html">QDataStream</a> & operator>> ( <a href="qdatastream.html">QDataStream</a> & <i>stream</i>, QMatrix & <i>matrix</i> )</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Reads the given <i>matrix</i> from the given <i>stream</i> and returns a reference to the stream.</p>
<p>See also <a href="datastreamformat.html">Format of the QDataStream Operators</a>.</p>
<hr />
<h2>Member Function Documentation</h2>
<h3 class="fn"><a name="invert"></a>QMatrix QMatrix::invert ( bool * <i>invertible</i> = 0 ) const</h3>
<p>Returns an inverted copy of this matrix.</p>
<p>Use the <a href="qmatrix.html#inverted">inverted</a>() function instead.</p>
<h3 class="fn"><a name="map-2"></a><a href="qrect.html">QRect</a> QMatrix::map ( const <a href="qrect.html">QRect</a> & <i>rect</i> ) const</h3>
<p>This is an overloaded member function, provided for convenience.</p>
<p>Creates and returns a <a href="qrect.html">QRect</a> object that is a copy of the given rectangle, mapped into the coordinate system defined by this matrix.</p>
<p>Use the <a href="qmatrix.html#mapRect">mapRect</a>() function instead.</p>
<h3 class="fn"><a name="mapToRegion"></a><a href="qregion.html">QRegion</a> QMatrix::mapToRegion ( const <a href="qrect.html">QRect</a> & <i>rectangle</i> ) const</h3>
<p>Returns the transformed rectangle <i>rectangle</i> as a <a href="qregion.html">QRegion</a> object. A rectangle which has been rotated or sheared may result in a non-rectangular region being returned.</p>
<p>Use the <a href="qmatrix.html#mapToPolygon">mapToPolygon</a>() or <a href="qmatrix.html#map">map</a>() function instead.</p>
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